From 02c7ab1eddfb164dc950de48a7fe401f64ebb02f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?L=C3=B6fdahl=20Grelsson?= Date: Fri, 3 Oct 2025 10:25:09 +0200 Subject: [PATCH 1/8] first working draft --- content/QKE.ipynb | 1790 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1790 insertions(+) create mode 100644 content/QKE.ipynb diff --git a/content/QKE.ipynb b/content/QKE.ipynb new file mode 100644 index 0000000..b15ffae --- /dev/null +++ b/content/QKE.ipynb @@ -0,0 +1,1790 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e4b10801-19d8-4751-8e31-a9bfd2df03d1", + "metadata": {}, + "source": [ + "# Tutorial - Quantum support vector regression for disability insurance\n", + "\n", + "B. Djehiche and B. Löfdahl – KTH, Department of Mathematics / SEB – \n", + "Risks 2021, 9(12), 216; https://doi.org/10.3390/risks9120216\n", + "\n", + "Hands-on assistance: https://enccs.se/anastasiia-andriievska" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "b6f8b962-5fde-46f8-af33-dda094485734", + "metadata": {}, + "outputs": [], + "source": [ + "# install necessary packages via pip\n", + "# import the packages\n", + "#import networkx as nx\n", + "#import pylatexenc\n", + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.svm import SVR\n", + "from copy import copy\n", + "from qrisp import QuantumVariable, QuantumCircuit\n", + "from sympy import symbols" + ] + }, + { + "cell_type": "markdown", + "id": "d9224010-d6e9-4d8a-a391-cd5350418491", + "metadata": {}, + "source": [ + "First, we create some dummy data. The x-variable holds the available data. x[1] represents gender (0 or 1). x[2] represents age, normalized to the [0,1] interval. The y-variable is the value that we seek to model. It represents the logistic transition probability between two states. The w-variable represents the weight that we assign to each data point." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "168cfc3c-d7ba-4b88-b60a-7cbd67738d83", + "metadata": {}, + "outputs": [], + "source": [ + "nsamp = 100\n", + "x = np.array( [[0.0, x/nsamp] for x in range(nsamp)] + [[1.0, x/nsamp] for x in range(nsamp)] )\n", + "y = np.array([-4.5 + 0.2*a[0] + a[1]*(1+a[0]*0.2) + 0.1*np.random.normal() for a in x])\n", + "\n", + "p = 1/(1+np.exp(-y))\n", + "\n", + "n = [int(200 + 600*xj[1]/0.7) if xj[1] <= 0.7 else int(800 - 300*(xj[1]-0.7)/0.3) for xj in x]\n", + "\n", + "d = [nj*pj for nj,pj in zip(n,p)]" + ] + }, + { + "cell_type": "markdown", + "id": "6404a54d-b5d7-4395-96ab-d4bb9f75df61", + "metadata": {}, + "source": [ + "We can use the Pandas library to create a DataFrame and then save it as a CSV file, which support column headers. This will create a CSV file with each column labeled as ‘gender’, ‘age group (normalized)’, ‘population size’, and ‘number of transitions’ respectively. The index=False argument is used to prevent pandas from writing row indices into the file." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "98b3d891-41c2-4ead-90dd-a8419e79809e", + "metadata": {}, + "outputs": [], + "source": [ + "# Create a DataFrame\n", + "df = pd.DataFrame({\n", + " 'gender': [a[0] for a in x],\n", + " 'age group (normalized)': [a[1] for a in x],\n", + " 'population size': n,\n", + " 'number of transitions': d\n", + "})\n", + "\n", + "# Write the DataFrame to a CSV file\n", + "df.to_csv('fdata.csv', index=False) # index=False argument is used to prevent pandas from writing row indices into the CSV file" + ] + }, + { + "cell_type": "markdown", + "id": "79a2034c-1509-44c2-9fdb-ed63b301a727", + "metadata": {}, + "source": [ + "One can read the data back from the file like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0da27f10-d9b1-4c75-afcd-cf69122586a6", + "metadata": {}, + "outputs": [], + "source": [ + "data = pd.read_csv('fdata.csv')" + ] + }, + { + "cell_type": "markdown", + "id": "e0d5741f-c5fb-4fb8-84a2-da56f6fa2ae9", + "metadata": {}, + "source": [ + "### Transform and inspect data" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "84552a98-075b-48de-b7a9-68e018e95e83", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 0. ]\n", + " [0. 0.01]\n", + " [0. 0.02]\n", + " [0. 0.03]\n", + " [0. 0.04]\n", + " [0. 0.05]\n", + " [0. 0.06]\n", + " [0. 0.07]\n", + " [0. 0.08]\n", + " [0. 0.09]\n", + " [0. 0.1 ]\n", + " [0. 0.11]\n", + " [0. 0.12]\n", + " [0. 0.13]\n", + " [0. 0.14]\n", + " [0. 0.15]\n", + " [0. 0.16]\n", + " [0. 0.17]\n", + " [0. 0.18]\n", + " [0. 0.19]\n", + " [0. 0.2 ]\n", + " [0. 0.21]\n", + " [0. 0.22]\n", + " [0. 0.23]\n", + " [0. 0.24]\n", + " [0. 0.25]\n", + " [0. 0.26]\n", + " [0. 0.27]\n", + " [0. 0.28]\n", + " [0. 0.29]\n", + " [0. 0.3 ]\n", + " [0. 0.31]\n", + " [0. 0.32]\n", + " [0. 0.33]\n", + " 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0.89]\n", + " [0. 0.9 ]\n", + " [0. 0.91]\n", + " [0. 0.92]\n", + " [0. 0.93]\n", + " [0. 0.94]\n", + " [0. 0.95]\n", + " [0. 0.96]\n", + " [0. 0.97]\n", + " [0. 0.98]\n", + " [0. 0.99]\n", + " [1. 0. ]\n", + " [1. 0.01]\n", + " [1. 0.02]\n", + " [1. 0.03]\n", + " [1. 0.04]\n", + " [1. 0.05]\n", + " [1. 0.06]\n", + " [1. 0.07]\n", + " [1. 0.08]\n", + " [1. 0.09]\n", + " [1. 0.1 ]\n", + " [1. 0.11]\n", + " [1. 0.12]\n", + " [1. 0.13]\n", + " [1. 0.14]\n", + " [1. 0.15]\n", + " [1. 0.16]\n", + " [1. 0.17]\n", + " [1. 0.18]\n", + " [1. 0.19]\n", + " [1. 0.2 ]\n", + " [1. 0.21]\n", + " [1. 0.22]\n", + " [1. 0.23]\n", + " [1. 0.24]\n", + " [1. 0.25]\n", + " [1. 0.26]\n", + " [1. 0.27]\n", + " [1. 0.28]\n", + " [1. 0.29]\n", + " [1. 0.3 ]\n", + " [1. 0.31]\n", + " [1. 0.32]\n", + " [1. 0.33]\n", + " [1. 0.34]\n", + " [1. 0.35]\n", + " [1. 0.36]\n", + " [1. 0.37]\n", + " [1. 0.38]\n", + " [1. 0.39]\n", + " [1. 0.4 ]\n", + " [1. 0.41]\n", + " [1. 0.42]\n", + " [1. 0.43]\n", + " [1. 0.44]\n", + " [1. 0.45]\n", + " [1. 0.46]\n", + " [1. 0.47]\n", + " [1. 0.48]\n", + " [1. 0.49]\n", + " [1. 0.5 ]\n", + " [1. 0.51]\n", + " [1. 0.52]\n", + " [1. 0.53]\n", + " [1. 0.54]\n", + " [1. 0.55]\n", + " [1. 0.56]\n", + " [1. 0.57]\n", + " [1. 0.58]\n", + " [1. 0.59]\n", + " [1. 0.6 ]\n", + " [1. 0.61]\n", + " [1. 0.62]\n", + " [1. 0.63]\n", + " [1. 0.64]\n", + " [1. 0.65]\n", + " [1. 0.66]\n", + " [1. 0.67]\n", + " [1. 0.68]\n", + " [1. 0.69]\n", + " [1. 0.7 ]\n", + " [1. 0.71]\n", + " [1. 0.72]\n", + " [1. 0.73]\n", + " [1. 0.74]\n", + " [1. 0.75]\n", + " [1. 0.76]\n", + " [1. 0.77]\n", + " [1. 0.78]\n", + " [1. 0.79]\n", + " [1. 0.8 ]\n", + " [1. 0.81]\n", + " [1. 0.82]\n", + " [1. 0.83]\n", + " [1. 0.84]\n", + " [1. 0.85]\n", + " [1. 0.86]\n", + " [1. 0.87]\n", + " [1. 0.88]\n", + " [1. 0.89]\n", + " [1. 0.9 ]\n", + " [1. 0.91]\n", + " [1. 0.92]\n", + " [1. 0.93]\n", + " [1. 0.94]\n", + " [1. 0.95]\n", + " [1. 0.96]\n", + " [1. 0.97]\n", + " [1. 0.98]\n", + " [1. 0.99]]\n" + ] + } + ], + "source": [ + "x = np.array( [[a,b] for a,b in zip(data['gender'], data['age group (normalized)'])] )\n", + "print(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "e7447d0f-64e9-4d56-8a41-299cdd3b044e", + "metadata": {}, + "outputs": [], + "source": [ + "# raw transition frequency per group, used for plots\n", + "p_raw = [a/b for a,b in zip(d,n)]\n", + "\n", + "# logistic probability, used as input to SVR optimization\n", + "y = np.array([np.log( p / (1-p) ) for p in p_raw])\n", + "\n", + "# calculate weights for SVR based on population size\n", + "w = np.array([1./nj for nj in n])\n", + "\n", + "# normalize weights (equivalent to changing the hyperparameters of the SVR)\n", + "w = w/sum(w)*len(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "0fe05211-ed34-463f-81ea-37069c0fd93f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "axs.plot([xj[1] for xj,p in zip(x, p_raw) if xj[0] == 0], [p for xj,p in zip(x, p_raw) if xj[0] == 0], 'or')\n", + "axs.plot([xj[1] for xj,p in zip(x, p_raw) if xj[0] == 1], [p for xj,p in zip(x, p_raw) if xj[0] == 1], 'ob')\n", + "axs.set_title(\"raw transition frequencies\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cd869a15-a44e-406c-9ef7-22009f1f4bd0", + "metadata": {}, + "source": [ + "The first step of the modelling is to define the mapping from data space to our quantum feature space. This is done by setting up the qc circuit. The circuit below is a very simplified two-variable circuit. Feel free to experiment!" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "fc0a3769-6fa5-4cb0-a2ad-60295f32738d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "###TO BE REMOVED\n", + "\n", + "# set up 'kernel circuit'\n", + "#p = ParameterVector('x', length=2)\n", + "#qc = QuantumCircuit(2)\n", + "\n", + "#qc.ry(p[0]*np.pi, 0)\n", + "#qc.ry(p[1]*np.pi, 1)\n", + "\n", + "#qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "f6546726-7f76-4f7d-992c-95ee972abf17", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "QuantumCircuit:\n", + "---------------\n", + " ┌──────────┐\n", + "feature_map.0: ┤ Ry(π*x0) ├\n", + " ├──────────┤\n", + "feature_map.1: ┤ Ry(π*x1) ├\n", + " └──────────┘\n", + "Live QuantumVariables:\n", + "----------------------\n", + "QuantumVariable feature_map\n" + ] + } + ], + "source": [ + "# set up 'kernel feature map' with sympy parameters\n", + "\n", + "def build_feature_map(sym):\n", + " n = 2\n", + " feature_map = QuantumVariable(n)\n", + " params = symbols(sym+':'+str(n))\n", + " ry(np.pi * params[0], feature_map[0])\n", + " ry(np.pi * params[1], feature_map[1])\n", + "\n", + " return feature_map\n", + "\n", + "feature_map = build_feature_map('x')\n", + "print(feature_map.qs)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "id": "2c128f3c-da92-4dd2-b94d-27dd25970626", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " ┌────────────┐\n", + "feature_map.0: ┤ Ry(1.2185) ├\n", + " ├────────────┤\n", + "feature_map.1: ┤ Ry(2.8328) ├\n", + " └────────────┘\n" + ] + } + ], + "source": [ + "# example, assign random data as parameters and print cirquit\n", + "\n", + "subs_dic = {params[i] : np.random.rand() for i in range(2)}\n", + "bound_qc = feature_map.qs.bind_parameters(subs_dic)\n", + "print(bound_qc)" + ] + }, + { + "cell_type": "markdown", + "id": "b9fefbd4-5e78-4b09-8e7f-8e5a9f342e60", + "metadata": {}, + "source": [ + "## Exercise 1 TODO rewrite to qrisp calls\n", + "\n", + "Experimenting with quantum circuits involves changing the structure of the circuit or the parameters used. Here are a few ways you can experiment with the given circuit:\n", + "\n", + "1. **Change the gates**: Instead of using `ry` gates, you could use other gates like `rx`, `rz`, `h` (Hadamard), etc.\n", + "\n", + "```python\n", + "qc.rx(p[0]*np.pi, 0)\n", + "qc.rz(p[1]*np.pi, 1)\n", + "```\n", + "\n", + "2. **Add more gates**: You can add more gates to your circuit to make it more complex.\n", + "\n", + "```python\n", + "qc.ry(p[0]*np.pi, 0)\n", + "qc.ry(p[1]*np.pi, 1)\n", + "qc.h(0)\n", + "qc.cx(0, 1) # CNOT gate\n", + "```\n", + "\n", + "3. **Change the parameters**: Instead of multiplying the parameters by `pi`, you could multiply them by other constants or use more complex functions of the parameters.\n", + "\n", + "```python\n", + "qc.ry(p[0], 0)\n", + "qc.ry(np.sin(p[1]), 1)\n", + "```\n", + "\n", + "4. **Increase the number of qubits**: You can increase the number of qubits in your circuit and see how that affects your results.\n", + "\n", + "Remember, when experimenting with quantum circuits, it's important to understand what each gate does and how changing the circuit might affect your results. Happy experimenting! 😊\n", + "\n", + "A few general guidelines for experimenting with quantum circuits:\n", + "\n", + "1. **Understand the problem**: Before you start experimenting, make sure you understand the problem you're trying to solve and how a quantum circuit could help solve it.\n", + "\n", + "2. **Start simple**: Start with a simple circuit and gradually add complexity. This makes it easier to understand what each part of your circuit is doing.\n", + "\n", + "3. **Use a variety of gates**: Different gates can have different effects on your quantum state, so try using a variety of gates in your experiments.\n", + "\n", + "4. **Test on a simulator first**: Before running your circuit on a real quantum computer, test it on a simulator to make sure it's working as expected.\n", + "\n", + "5. **Analyze your results**: After running your circuit, analyze the results to see if they make sense and if they're helping you solve your problem.\n", + "\n", + "6. **Iterate**: Experimenting with quantum circuits often involves a lot of trial and error. Don't be afraid to iterate on your design and try new things.\n", + "\n", + "In the context of the Quantum Support Vector Regression (QSVR) for disability insurance that you're working on, you might want to experiment with different ways of encoding your data into the quantum state or different types of quantum kernels. Remember, the goal is to find a quantum circuit that can effectively model your data and help you make accurate predictions." + ] + }, + { + "cell_type": "markdown", + "id": "3dc158a8-1035-47fa-80bd-4d0b4743eabe", + "metadata": {}, + "source": [ + "#### Hints\n", + "1. x[0] is a binary variable representing gender. Hence, flipping the first qubit from |0> to |1> based on gender will maximize the distance (wrt only the first qubit) between two subpopulations belong to different genders.\n", + "\n", + "2. x[1] is a representing age. For two sub-populations of similar age, the rotations of the second qubit will be similar, causing a low distance (wrt only the second qubit).\n", + "\n", + "3. One possible extension is to add a third qubit that would capture a first order interaction effect between x[0] and x[1], e.g. a cy or cx gate. We could also incorporate this by adding more gates to qubits 1 or 2." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "339246ed-877a-4235-9009-69f77e6e057b", + "metadata": {}, + "outputs": [], + "source": [ + "# Test code here\n", + "# Then rerun the following cells \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 241, + "id": "17cc99d0-a6b8-4e61-8d51-d89f582c7e77", + "metadata": {}, + "outputs": [], + "source": [ + "def train_kernel_matrix(x, f_feature_map, shots=1000, backend=None):\n", + " kernel = f_feature_map('x')\n", + " x_params = copy(kernel.qs.abstract_params)\n", + " adjoint_qs = f_feature_map('y').qs.inverse()\n", + " y_params = adjoint_qs.abstract_params\n", + " kernel.qs.append(adjoint_qs.to_op(), kernel.qs.qubits)\n", + " kernel.qs = kernel.qs.transpile()\n", + " if backend is not None:#measurement only needed when running shots\n", + " kernel.qs.measure(kernel.qs.qubits)\n", + " n = len(x)\n", + " K = np.eye(n)\n", + " for i in range(n):\n", + " subs_dic = {p : x[i][int(p.name[1:])] for p in x_params}\n", + " for j in range(i+1,n):\n", + " for p in y_params:\n", + " subs_dic[p] = x[j][int(p.name[1:])]\n", + " bound_kernel = kernel.qs.bind_parameters(subs_dic)\n", + " if backend is not None:\n", + " res = bound_kernel.run(shots=shots, backend=backend)\n", + " K_ij = res['0'*len(kernel.qs.qubits)] / shots if '0'*len(kernel.qs.qubits) in res else 0.0\n", + " else:#if no backend use statevector simulation\n", + " res = bound_kernel.statevector_array()\n", + " K_ij = np.abs(res[0])**2\n", + " \n", + " K[i,j] = K[j,i] = K_ij\n", + " return K\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7f4860a3-be61-45b4-aa12-4741bcf59771", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "94ad5388-c776-492a-8247-053834f05260", + "metadata": {}, + "source": [ + "The QuantumKernel function prepares the kernel estimation by setting up inner product circuits, based on each combination of two data points." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "ae5d1df5-8f87-4626-a89e-baa40b219a00", + "metadata": {}, + "outputs": [], + "source": [ + "# TO BE REMOVED\n", + "\n", + "#zz_kernel = QuantumKernel(feature_map=qc, quantum_instance=Aer.get_backend('statevector_simulator'))" + ] + }, + { + "cell_type": "markdown", + "id": "9ccad195-ef4e-4826-bca1-8060e1d46eac", + "metadata": {}, + "source": [ + "Then we specify the quantum instance: " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "dbcc8420-4d8f-4278-b503-11afdbd12fcd", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# TO BE REMOVED\n", + "\n", + "#zz_circuit = zz_kernel.construct_circuit(ParameterVector('x_i', length=2),ParameterVector('x_j', length=2))\n", + "#zz_circuit.decompose().draw(output='mpl')" + ] + }, + { + "cell_type": "markdown", + "id": "6684d892-b617-4556-926e-e23e10353aec", + "metadata": {}, + "source": [ + "We evaluate the kernel matrix based on our x data and the build_feature_map helper function." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "908ec069-24b6-4d5b-bb47-e677339e3279", + "metadata": {}, + "outputs": [], + "source": [ + "matrix_train = train_kernel_matrix(x, build_feature_map)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "eb647d85-131e-43e7-b139-fddc282a177c", + "metadata": {}, + "outputs": [], + "source": [ + "#TO BE REMOVED\n", + "\n", + "#matrix_train = zz_kernel.evaluate(x_vec=x)" + ] + }, + { + "cell_type": "code", + "execution_count": 244, + "id": "cc7771e0-7f0c-4a32-b6bd-d6a7dd50da52", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the kernel matrix\n", + "\n", + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(matrix_train),\n", + " interpolation='nearest', origin='upper', cmap='Blues')\n", + "axs.set_title(\"training kernel matrix\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b5e309fb-7fb7-4fed-9e3f-05ff9aa6ea87", + "metadata": {}, + "source": [ + "Figure 1 displays the estimated kernel matrix. This matrix has an interesting structure: it is block-diagonal. This is due to the fact that the second quadrant of the matrix correspond to the inner products of the population groups with gender=0. These share the common characteristic gender=0, and each row is similar to its neighbours due to the encoding: similar ages are also similar in the quantum feature space. Analogously, the fourth quadrant of the matrix contains the gender=1 population groups. The first and third quadrants contain the inner products between gender=0 and gender=1 population groups and so are dissimilar in the quantum feature space." + ] + }, + { + "cell_type": "markdown", + "id": "5169b0dc-a666-4d0a-a19e-63de0ca8e6c2", + "metadata": {}, + "source": [ + "Next, we run a support vector regression (SVR) taking the kernel matrix, the weights, and the y-values as input." + ] + }, + { + "cell_type": "code", + "execution_count": 245, + "id": "ab02281d-bcb6-4cf3-af08-a786e0f22b79", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "score: 0.9142137205414308\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "f_matrix_train = matrix_train\n", + "\n", + "zzpc_svr = SVR(kernel='precomputed')\n", + "zzpc_svr.fit(f_matrix_train, y, w)\n", + "zzpc_score = zzpc_svr.score(f_matrix_train, y, w)\n", + "print(f'score: {zzpc_score}')\n", + "pred = zzpc_svr.predict(f_matrix_train)\n", + "\n", + "p_hat = 1/(1+np.exp(-pred))\n", + "p = 1/(1+np.exp(-y))\n", + "plt.figure()\n", + "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p) if a[0] == 0],'or')\n", + "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", + "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", + "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", + "plt.legend(['Group 0', 'Group 0 model', 'Group 1', 'Group 1 model'])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ad0da92a-1f89-4289-a2c2-e0cb5d4e1bc6", + "metadata": {}, + "source": [ + "The score you see is the R-squared score from the SVR model. This score represents the proportion of the variance in the dependent variable that is predictable from the independent variables1. In other words, it gives you a measure of how well your model is fitting the data. A score of 1.0 indicates a perfect fit." + ] + }, + { + "cell_type": "markdown", + "id": "f2bc9cc6-7642-4f93-a152-f78ac3ccc29a", + "metadata": {}, + "source": [ + "We check the results against a classical SVR." + ] + }, + { + "cell_type": "code", + "execution_count": 232, + "id": "df66e9a5-409b-4014-911e-c8880f081a7c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "score: 0.9327125659537808\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "classical = SVR(kernel='rbf')\n", + "classical.fit(x, y, w)\n", + "classical_score = classical.score(x, y, w)\n", + "print(f'score: {classical_score}')\n", + "pred = classical.predict(x)\n", + "\n", + "p_hat = 1/(1+np.exp(-pred))\n", + "p = 1/(1+np.exp(-y))\n", + "plt.figure()\n", + "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p) if a[0] == 0],'or')\n", + "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", + "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", + "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", + "plt.legend(['Group 0', 'Group 0 model', 'Group 1', 'Group 1 model'])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "22f6ed9d-0b80-43c2-9a59-21bfb1d7a695", + "metadata": {}, + "source": [ + "The above analysis is done in-sample. Below, we use the leave-one-out cross-validation functionality from the sklearn module." + ] + }, + { + "cell_type": "code", + "execution_count": 246, + "id": "aed94e25-bbcc-473e-92f2-53b5ef265fa4", + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.model_selection import LeaveOneOut\n", + "from sklearn.metrics import r2_score\n", + "\n", + "zzpc_svr = SVR(kernel='precomputed')\n", + "classical = SVR(kernel='rbf')\n", + "\n", + "cols = range(len(x))\n", + "\n", + "loo = LeaveOneOut()\n", + "pred_loo = []\n", + "pred_loo_classic = []\n", + "used_K = matrix_train\n", + "for train_index, test_index in loo.split(cols):\n", + " #print(x[train_index])\n", + " zzpc_svr.fit(used_K[np.ix_(train_index,train_index)], y[train_index], w[train_index])\n", + " pred = zzpc_svr.predict(used_K[np.ix_(test_index,train_index)])\n", + " for p in pred:\n", + " pred_loo.append(p)\n", + " classical.fit(x[train_index], y[train_index], w[train_index])\n", + " cpred = classical.predict(x[test_index])\n", + " for p in cpred:\n", + " pred_loo_classic.append(p)\n", + "pred_loo = np.array(pred_loo)\n", + "pred_loo_classic = np.array(pred_loo_classic)" + ] + }, + { + "cell_type": "code", + "execution_count": 247, + "id": "d0936803-5081-44b5-9a13-2e46e05a819b", + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.model_selection import LeaveOneOut\n", + "from sklearn.metrics import r2_score\n", + "\n", + "def predict_loo(K, y, w, zzpc_svr):\n", + " cols = range(len(y))\n", + " loo = LeaveOneOut()\n", + " pred_loo = []\n", + " for train_index, test_index in loo.split(cols):\n", + " #print(x[train_index])\n", + " zzpc_svr.fit(K[np.ix_(train_index,train_index)], y[train_index], w[train_index])\n", + " pred = zzpc_svr.predict(K[np.ix_(test_index,train_index)])\n", + " for p in pred:\n", + " pred_loo.append(p)\n", + " return np.array(pred_loo)\n", + "\n", + "statevector_loo = predict_loo(matrix_train, y, w, SVR(kernel='precomputed'))" + ] + }, + { + "cell_type": "code", + "execution_count": 248, + "id": "b8d8628e-d9fd-4aff-b06a-f1db1df1c531", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "score: 0.9105234598498793\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p_hat = 1/(1+np.exp(-statevector_loo))\n", + "p = 1/(1+np.exp(-y))\n", + "score = r2_score(p, p_hat, sample_weight=w)\n", + "print(f'score: {score}')\n", + "fig, ax = plt.subplots(1, 1)\n", + "plt.plot(np.array([a[1] for a in x if a[0] == 0])*100, [p for a,p in zip(x,p) if a[0] == 0],'or')\n", + "plt.plot(np.array([a[1] for a in x if a[0] == 1])*100, [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", + "plt.plot(np.array([a[1] for a in x if a[0] == 0])*100, [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", + "plt.plot(np.array([a[1] for a in x if a[0] == 1])*100, [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", + "plt.legend(['Group 0', 'Group 1', 'Group 0, statevector', 'Group 1, statevector'])\n", + "ax.axes.yaxis.set_ticklabels([])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8ecebea2-79c9-4903-8f1c-8ffbc5393330", + "metadata": {}, + "source": [ + "Quantum Support Vector Regression (QSVR) Score (0.9155345528008413): This score suggests that your QSVR model is doing a good job of capturing the relationship between your features and your target variable.\n", + "\n", + "Classical Support Vector Regression (SVR) Score (0.9295558682302361): This score is slightly higher than your QSVR score, suggesting that your classical SVR model might be fitting the data slightly better than your QSVR model.\n", + "\n", + "Leave-One-Out Cross-Validation Score (0.8977158412990511): This score is lower than both your QSVR and classical SVR scores. This isn’t surprising, as leave-one-out cross-validation can often result in lower scores because it’s a more rigorous form of validation. It’s a good way to get an unbiased estimate of how well your model will perform on unseen data.\n", + "\n", + "To compare these results, you can look at how much each score deviates from 1.0. The closer the score is to 1.0, the better the model is fitting your data. However, keep in mind that a high R-squared score doesn’t always mean your model will perform well on unseen data. It’s important to also look at other metrics and plots (like residuals) to assess your model’s performance." + ] + }, + { + "cell_type": "markdown", + "id": "dd9e815f-feef-465e-8f0b-3aefe268e477", + "metadata": {}, + "source": [ + "## Exercise 2: Residuals\n", + "In the context of regression analysis, residuals are the difference between the observed (actual) and predicted values for a data point. In other words, a residual is an error in prediction.\n", + "\n", + "Mathematically, if you have an observed value $$y_{\\text{obs}}$$ and a predicted value $$y_{\\text{pred}}$$ for a data point, the residual $$e$$ for that data point is calculated as:\n", + "\n", + "$$e = y_{\\text{obs}} - y_{\\text{pred}}$$\n", + "\n", + "Residuals are used to understand the accuracy of a regression model. If a model fits the data well, the residuals should be small and randomly distributed around zero. Patterns or trends in the residuals can indicate that the model is not adequately capturing some aspect of the data.\n", + "\n", + "In our case, we will plot a histogram of residuals from our QSVR model. This visualization can help us understand the distribution of errors made by the model.\n", + "If the model is performing well, we would expect to see most residuals close to zero, indicating that the predicted and actual values are close. Large residuals indicate that the model's predictions are far off from the actual values.\n", + "\n", + "#### Hints\n", + "1. use `residuals = y - pred`\n", + "2. in `plt.hist`use `bins=20` # bins parameter determines the number of bins (or bars) to divide your data into\n", + "3. use appropriate lables\n", + "4. *Advanced* – use `p_hat-p` for residuals" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "039e7e99-e44a-474d-bff8-08321ac03656", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "971cfa01-0662-4e8b-9b9b-6d7aa8a3ef52", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "45284812-ff18-4017-a649-9276f0c071ea", + "metadata": {}, + "source": [ + "You've done a great job implementing the Quantum Support Vector Regression (QSVR) and comparing it with a classical SVR. You've also used leave-one-out cross-validation to evaluate the performance of your models, which is a robust method for estimating the generalization error.\n", + "\n", + "In terms of the residuals, you've plotted two histograms:\n", + "1. The first histogram represents the residuals calculated as `y - pred`, where `y` is the observed value and `pred` is the predicted value from your QSVR model. This gives you an idea of how well your model is predicting the actual `y` values. If your model is accurate, most residuals should be close to zero, indicating that the predicted and actual values are close. Large residuals indicate that the model's predictions are far off from the actual values.\n", + "2. The second histogram represents the residuals calculated as `p_hat - p`, where `p_hat` is the predicted probability and `p` is the actual probability. This gives you an idea of how well your model is predicting the actual probabilities. Again, if your model is accurate, most residuals should be close to zero.\n", + "\n", + "To describe the results, you would typically look at the distribution of residuals in your histograms. If your model is performing well, you would expect to see a distribution centered around zero, indicating that most predictions are close to the actual values or probabilities. If you see a skewed distribution or a distribution with a long tail, it might indicate that your model is systematically overestimating or underestimating the values or probabilities.\n", + "\n", + "In terms of what you've done here, you've implemented a QSVR for modeling transition probabilities in disability insurance, compared it with a classical SVR, and evaluated their performance using leave-one-out cross-validation and residual analysis. This is a comprehensive approach to developing and evaluating predictive models. Great work! 😊" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ef5179d6-bb8c-46f7-a192-80d23beaf97e", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bf6ece14-57fb-4ea5-85f5-5e5f3919414f", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "8d6c503e-5292-4644-8155-b5e76134ebf1", + "metadata": {}, + "source": [ + "### We used the statevector simulator and now we'll run it on Helmi." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "95b0744c-60be-403a-ade5-0518b63c58df", + "metadata": {}, + "outputs": [], + "source": [ + "provider = IQMProvider(\"https://qc.vtt.fi/cocos\")\n", + "backend = provider.get_backend()" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "ceea2aee-3acf-4c85-998b-b08c6147d48c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Native operations: ['r', 'id', 'cz', 'measure']\n", + "Number of qubits: 5\n", + "Coupling map: [[0, 2], [2, 0], [1, 2], [2, 1], [2, 3], [3, 2], [2, 4], [4, 2]]\n" + ] + } + ], + "source": [ + "print(f'Native operations: {backend.operation_names}')\n", + "print(f'Number of qubits: {backend.num_qubits}')\n", + "print(f'Coupling map: {backend.coupling_map}')" + ] + }, + { + "cell_type": "markdown", + "id": "15595412-8121-43a4-a786-083a9ed0e27a", + "metadata": {}, + "source": [ + "The `feature_map` function is a way to encode classical data into a quantum state. In this case, it's creating a quantum circuit `qc` with 2 qubits. It then applies a rotation around the y-axis (`ry`) on each qubit. The rotation angle is determined by the input data `x` multiplied by `pi`. The `ParameterVector` is a way to create a list of parameters." + ] + }, + { + "cell_type": "markdown", + "id": "19f6461a-7bc1-47e9-bf5b-6bf606fbc586", + "metadata": {}, + "source": [ + "First, we create some dummy data, but smaller (fewer data points) than it was before." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "ed4cad78-d89f-4dff-981c-8113ca649e12", + "metadata": {}, + "outputs": [], + "source": [ + "nsamp = 10\n", + "x = np.array( [[0.0, x/nsamp] for x in range(nsamp)] + [[1.0, x/nsamp] for x in range(nsamp)] )\n", + "y = np.array([-4.5 + 0.2*a[0] + a[1]*(1+a[0]*0.2) + 0.1*np.random.normal() for a in x])\n", + "\n", + "p = 1/(1+np.exp(-y))\n", + "\n", + "n = [int(200 + 600*xj[1]/0.7) if xj[1] <= 0.7 else int(800 - 300*(xj[1]-0.7)/0.3) for xj in x]\n", + "\n", + "d = [nj*pj for nj,pj in zip(n,p)]" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "6b244442-219f-448c-bee8-21b566d906c4", + "metadata": {}, + "outputs": [], + "source": [ + "# Create a DataFrame\n", + "df1 = pd.DataFrame({\n", + " 'gender': [a[0] for a in x],\n", + " 'age group (normalized)': [a[1] for a in x],\n", + " 'population size': n,\n", + " 'number of transitions': d\n", + "})\n", + "\n", + "# Write the DataFrame to a CSV file\n", + "df1.to_csv('fdata1.csv', index=False) # index=False argument is used to prevent pandas from writing row indices into the CSV file" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "670765b0-5135-4965-a15f-57e5ea90c130", + "metadata": {}, + "outputs": [], + "source": [ + "data1 = df1\n", + "# data1 = pd.read_csv('fdata1.csv')" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "f04e1346-2773-4918-9789-b72c9354f381", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 0. ]\n", + " [0. 0.1]\n", + " [0. 0.2]\n", + " [0. 0.3]\n", + " [0. 0.4]\n", + " [0. 0.5]\n", + " [0. 0.6]\n", + " [0. 0.7]\n", + " [0. 0.8]\n", + " [0. 0.9]\n", + " [1. 0. ]\n", + " [1. 0.1]\n", + " [1. 0.2]\n", + " [1. 0.3]\n", + " [1. 0.4]\n", + " [1. 0.5]\n", + " [1. 0.6]\n", + " [1. 0.7]\n", + " [1. 0.8]\n", + " [1. 0.9]]\n" + ] + } + ], + "source": [ + "# Transform and inspect data\n", + "x1 = np.array( [[a,b] for a,b in zip(data1['gender'], data1['age group (normalized)'])] )\n", + "print(x1)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "3b74a992-8a26-481b-b40a-05cc775ce58f", + "metadata": {}, + "outputs": [], + "source": [ + "# raw transition frequency per group, used for plots\n", + "p_raw = [a/b for a,b in zip(d,n)]\n", + "\n", + "# logistic probability, used as input to SVR optimization\n", + "y = np.array([np.log( p / (1-p) ) for p in p_raw])\n", + "\n", + "# calculate weights for SVR based on population size\n", + "w = np.array([1./nj for nj in n])\n", + "\n", + "# normalize weights (equivalent to changing the hyperparameters of the SVR)\n", + "w = w/sum(w)*len(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "c4e5c7fd-1c28-4867-8e1a-4ba20b711f1f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "axs.plot([x1j[1] for x1j,p in zip(x1, p_raw) if x1j[0] == 0], [p for x1j,p in zip(x1, p_raw) if x1j[0] == 0], 'or')\n", + "axs.plot([x1j[1] for x1j,p in zip(x1, p_raw) if x1j[0] == 1], [p for x1j,p in zip(x1, p_raw) if x1j[0] == 1], 'ob')\n", + "axs.set_title(\"raw transition frequencies\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "08783390-fb9a-4d24-ae8b-02eb0923c632", + "metadata": {}, + "source": [ + "## Exercise 3: Implement and Visualize a Quantum Feature Map\n", + "\n", + "In this exercise, you will implement a quantum feature map using Qiskit and visualize the resulting quantum circuit. The feature map is a way of encoding classical data into quantum states. In this case, we will use a simple feature map that applies a rotation around the y-axis on each qubit.\n", + "\n", + "### Task 1: Implement the Feature Map\n", + "\n", + "First, let's implement the feature map. Here is the function you need to complete:\n", + "\n", + "```python\n", + "def feature_map(x1):\n", + " p = ParameterVector('x1', length=2)\n", + " qc = QuantumCircuit(2)\n", + "\n", + " # TODO: Apply a rotation around the y-axis on each qubit\n", + " # Hint: Use the ry gate and the input data x1\n", + "\n", + " return qc\n", + "```\n", + "\n", + "### Task 2: Visualize the Circuit\n", + "\n", + "After implementing the feature map, you visualize the resulting quantum circuit, as we did at the beginning of this lesson. \n", + "\n", + "Good luck with your exercise! If you have any questions or need further clarification, feel free to ask. 😊" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "24c26430-a283-4a99-8fb7-058c52bf4c7e", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dc63aa1a-0bf0-4e1f-9bf2-580c12aadbdb", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "52aa44c7-40bc-4ec2-b273-94d6b457a8dc", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "13cf3642-2745-4250-ac18-9006bb457793", + "metadata": {}, + "source": [ + "The following part of the code implements a list of all possible quantum circuits for the given data `x1`. For each pair of data points `(x1[i], x1[j])`, it creates two circuits using the `feature_map` function. The feature map is a way of encoding classical data into quantum states. It then appends the inverse of `qc_j` to `qc_i` using the `compose` function. This function combines two circuits, and with `.inverse()`, it applies the inverse of the second circuit. After composing the circuits, it adds a measurement on all qubits using `measure_all()`. The circuit is then transpiled for a specific backend using the `transpile` function." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "051f839e-9306-44eb-b198-eaeafa837238", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "190\n" + ] + } + ], + "source": [ + "# from qiskit import transpile\n", + "\n", + "# Initialize an empty list to store all circuits\n", + "all_circuits = []\n", + "\n", + "for i in range(len(x1)):\n", + " for j in range(i):\n", + " # Substitute parameters with values from your data\n", + " qc_i = feature_map(x1[i])\n", + " qc_j = feature_map(x1[j])\n", + " \n", + " # Append the inverse of qc_j to qc_i and measure\n", + " qc_ij = qc_i.compose(qc_j.inverse())\n", + " qc_ij.measure_all()\n", + " \n", + " # Transpile the circuit for the backend\n", + " qc_ij_transpiled = transpile(qc_ij, backend=backend)\n", + " \n", + " # Add the transpiled circuit to the list\n", + " all_circuits.append(qc_ij_transpiled)\n", + "\n", + "print(len(all_circuits))" + ] + }, + { + "cell_type": "markdown", + "id": "b50ea21e-efef-4102-82c5-9a36ecde6552", + "metadata": {}, + "source": [ + "This block of code defines a batch size and splits the transpiled circuits into batches. It then initializes a list to store job IDs. Each batch of circuits is executed on the backend with 1024 shots per circuit execution. Also, it can take some time to execute." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "23cde26c-9afe-42ca-80e1-657f120f26ac", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tracking execution of job1:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job2:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job3:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job4:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job5:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job6:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job7:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job8:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job9:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job10:\n", + "Job Status: job has successfully run\n" + ] + } + ], + "source": [ + "# Define the batch size\n", + "batch_size = 20\n", + "\n", + "# Split the transpiled circuits into batches\n", + "batches = [all_circuits[i:i + batch_size] for i in range(0, len(all_circuits), batch_size)]\n", + "\n", + "# Initialize a list to store job IDs\n", + "job_ids = []\n", + "\n", + "# Execute each batch of circuits\n", + "for batch in batches:\n", + " job = backend.run(batch, shots=1024)\n", + " job_ids.append(job.job_id())\n", + "\n", + "# This block of code executes each batch until it's successful or an exception occurs\n", + "# If an exception occurs, it waits for a random amount of time between 1 and 10 seconds before retrying\n", + "\n", + "import time\n", + "import random\n", + "\n", + "# Initialize a list to store results\n", + "results = []\n", + "n_shots = 1024\n", + "\n", + "# Initialize a counter for the job number\n", + "job_number = 1\n", + "\n", + "for batch in batches:\n", + " success = False\n", + " while not success:\n", + " try:\n", + " # Execute the batch of circuits\n", + " job = backend.run(batch, shots=n_shots)\n", + " \n", + " # Print job execution status\n", + " print(f\"Tracking execution of job{job_number}:\")\n", + " job_monitor(job)\n", + " \n", + " # Wait for the job to finish and get the result\n", + " result = job.result()\n", + " \n", + " # If successful, append the result and break the loop\n", + " results.append(result)\n", + " success = True\n", + " \n", + " except Exception as e:\n", + " print(f\"Execution failed with error: {e}\")\n", + " \n", + " # Sleep for a bit (random backoff) before retrying\n", + " time.sleep(random.randint(1, 10))\n", + " \n", + " # Increment the job number for the next iteration\n", + " job_number += 1" + ] + }, + { + "cell_type": "markdown", + "id": "fc8b2a3d-9729-4c20-acf5-f40d9851ef30", + "metadata": {}, + "source": [ + "**Job Retrieval and Frequency Calculation**: The script starts by iterating over a list of `job_ids`. For each `job_id`, it retrieves the job result from the backend. It then calculates the frequency of the '00' state in the results and appends this frequency to the `estimates` list." + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "6f002a91-d87c-4278-905c-dbfacf9a03f0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Job1: ea63caca-9859-4988-afcc-4617a4422261\n", + "Job2: 4ea8454c-0146-47e3-a4f3-22e7098bf8b5\n", + "Job3: 29c17939-328b-46bd-bcf6-e2df758b4efd\n", + "Job4: 80e39182-931b-4bc9-83d7-f100a877d81b\n", + "Job5: bae16e48-b12a-4cea-bdf4-287bce4e11ab\n", + "Job6: ed7f15be-36d1-41c4-b0e1-794746789a48\n", + "Job7: b07bd0df-a786-4389-8def-ea0926f2fd17\n", + "Job8: d346a014-4afc-43ee-8ee4-d16e229e7c1e\n", + "Job9: baf11441-c6d0-4b0b-8641-068a929c72c4\n", + "Job10: 1895b727-95b8-4925-bc95-e7e2347493f7\n" + ] + } + ], + "source": [ + "# Initialize a counter for the job number\n", + "job_number = 1\n", + "\n", + "for job_id in job_ids:\n", + " print(f\"Job{job_number}: {job_id}\")\n", + " job_number += 1" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "bacb231a-f8cc-4922-82fd-079a6b568dc9", + "metadata": {}, + "outputs": [], + "source": [ + "estimates = []\n", + "\n", + "for job_id in job_ids:\n", + " job_res = backend.retrieve_job(job_id).result()\n", + " for res in job_res.results:\n", + " if '00' in res.data.counts:\n", + " freq = res.data.counts['00']/n_shots\n", + " else:\n", + " freq = 0.0\n", + " estimates.append(freq)" + ] + }, + { + "cell_type": "markdown", + "id": "3ab74e22-d559-46b8-8777-396d0af98e79", + "metadata": {}, + "source": [ + "**Kernel Matrix Construction**: The script constructs a kernel matrix `K_helmi` using the estimates. The kernel matrix is a symmetric matrix where each element represents a measure of similarity between two data points." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "77466963-5ed7-4a93-adcd-4c9dd0867a18", + "metadata": {}, + "outputs": [], + "source": [ + "K_helmi = np.identity(len(x1))\n", + "\n", + "cnt = 0\n", + "for i in range(len(x1)):\n", + " for j in range(i):\n", + " #print(i, ' ', j)\n", + " K_helmi[i,j] = estimates[cnt]\n", + " K_helmi[j,i] = estimates[cnt]\n", + " cnt += 1" + ] + }, + { + "cell_type": "markdown", + "id": "9f7f0f1d-bf79-45fd-9763-2b448c10c884", + "metadata": {}, + "source": [ + " **Kernel Matrix Visualization**: The kernel matrix is then visualized using matplotlib's `imshow` function. The color map 'Blues' is used, and a color bar is added for reference." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "e09a4a10-61a5-4f02-92a3-2bdd33a5e7ba", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(K_helmi),\n", + " interpolation='nearest', origin='upper', cmap='Blues')\n", + "axs.set_title(\"kernel matrix from Helmi\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0cc501ab-40c7-4b26-aefb-f20ff7369b72", + "metadata": {}, + "source": [ + "**Support Vector Regression (SVR)**: The script uses the Support Vector Regression (SVR) model from scikit-learn with a precomputed kernel. It fits the model to the data (`f_matrix_train` and `y`) and calculates the score of the model using the `score` method.\n", + "\n", + "**Prediction and Plotting**: The fitted model is used to predict outcomes, which are then plotted against the actual outcomes for two groups (Group 0 and Group 1)." + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "77e7a3fc-3bd0-4d7f-acb7-17e5fbb2132e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "score: 0.9001754733534563\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "f_matrix_train = K_helmi\n", + "\n", + "zzpc_svr = SVR(kernel='precomputed')\n", + "zzpc_svr.fit(f_matrix_train, y, w)\n", + "zzpc_score = zzpc_svr.score(f_matrix_train, y, w)\n", + "print(f'score: {zzpc_score}')\n", + "pred = zzpc_svr.predict(f_matrix_train)\n", + "\n", + "p_hat = 1/(1+np.exp(-pred))\n", + "p = 1/(1+np.exp(-y))\n", + "plt.figure()\n", + "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p) if a[0] == 0],'or')\n", + "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", + "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", + "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", + "plt.legend(['Group 0', 'Group 0 model', 'Group 1', 'Group 1 model'])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5e211b3e-7c28-4de0-967d-14bb3c502bd8", + "metadata": {}, + "source": [ + "**Error Calculation and Visualization**: Finally, the script calculates the absolute errors between `K_helmi` and `matrix_train`, visualizes these errors using `imshow`, and displays this with a color bar for reference." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "8a3b538d-9deb-418a-9a3c-4e14590e6074", + "metadata": {}, + "outputs": [], + "source": [ + "# redo the steps for statevector kernel to compare with the Helmi results\n", + "\n", + "zz_kernel = QuantumKernel(feature_map=qc, quantum_instance=Aer.get_backend('statevector_simulator'))\n", + "zz_circuit = zz_kernel.construct_circuit(ParameterVector('x_i', length=2),ParameterVector('x_j', length=2))\n", + "zz_circuit.decompose().draw(output='mpl')\n", + "matrix_train = zz_kernel.evaluate(x_vec=x)" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "656b8465-c4a3-4794-b301-f50f68c61dc7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "errors = np.abs(K_helmi - matrix_train)\n", + "\n", + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(errors),\n", + " interpolation='nearest', origin='upper', cmap='Reds')\n", + "axs.set_title(\"erorrs\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "47fa3d94-0b0e-41f9-ba3b-4571be968882", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3ca65f4a-c3b7-43da-b27b-35bf2a7c73d1", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "30df1f84-8e4b-4e3b-a607-3ecf25e9d375", + "metadata": {}, + "outputs": [], + "source": [ + "# solution ex2\n", + "residuals = y - pred\n", + "plt.hist(residuals, bins=20)\n", + "plt.xlabel('Residuals')\n", + "plt.ylabel('Frequency')\n", + "plt.title('Histogram of Residuals')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "97aab143-92b2-4765-853c-1c8757bd79b0", + "metadata": {}, + "outputs": [], + "source": [ + "# solution1 ex2\n", + "residuals1 = p_hat-p\n", + "plt.hist(residuals1, bins=20)\n", + "plt.xlabel('Residuals')\n", + "plt.ylabel('Frequency')\n", + "plt.title('Histogram of Residuals')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c3a78eab-1e43-4f1b-a992-526d1c131b4a", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "a26ddc57-a2fc-48ac-b3ae-f3ece0a2b507", + "metadata": {}, + "outputs": [], + "source": [ + "# solution ex3\n", + "\n", + "def feature_map(x1):\n", + " p = ParameterVector('x1', length=2)\n", + " qc = QuantumCircuit(2)\n", + "\n", + " qc.ry(x1[0]*np.pi, 0)\n", + " qc.ry(x1[1]*np.pi, 1)\n", + "\n", + " return qc" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "681cbb1a-dcc1-4870-990f-7935e14b8d81", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# solution1 ex3\n", + "# Draw the circuit\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d1960e7f-a57d-4047-b7eb-6054e37ee913", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "eaae61c0-9258-4bf7-a929-065ab90d36aa", + "metadata": {}, + "source": [ + "#### TEST CODE" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3397e118-363f-4cb2-b0aa-3166d83ae03f", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6d2dad5d-6493-460a-a5d6-898448124f31", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 0f1e5efcecaf3eca7a8ea10d4785364ccb332269 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?L=C3=B6fdahl=20Grelsson?= Date: Fri, 10 Oct 2025 13:16:47 +0200 Subject: [PATCH 2/8] second draft --- content/QKE.ipynb | 489 +++++++++++++--------------------------------- 1 file changed, 137 insertions(+), 352 deletions(-) diff --git a/content/QKE.ipynb b/content/QKE.ipynb index b15ffae..b779326 100644 --- a/content/QKE.ipynb +++ b/content/QKE.ipynb @@ -5,7 +5,7 @@ "id": "e4b10801-19d8-4751-8e31-a9bfd2df03d1", "metadata": {}, "source": [ - "# Tutorial - Quantum support vector regression for disability insurance\n", + "# Tutorial - Quantum kernel estimation with application to disability insurance\n", "\n", "B. Djehiche and B. Löfdahl – KTH, Department of Mathematics / SEB – \n", "Risks 2021, 9(12), 216; https://doi.org/10.3390/risks9120216\n", @@ -21,9 +21,7 @@ "outputs": [], "source": [ "# install necessary packages via pip\n", - "# import the packages\n", - "#import networkx as nx\n", - "#import pylatexenc\n", + "\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", @@ -43,18 +41,18 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 40, "id": "168cfc3c-d7ba-4b88-b60a-7cbd67738d83", "metadata": {}, "outputs": [], "source": [ "nsamp = 100\n", "x = np.array( [[0.0, x/nsamp] for x in range(nsamp)] + [[1.0, x/nsamp] for x in range(nsamp)] )\n", - "y = np.array([-4.5 + 0.2*a[0] + a[1]*(1+a[0]*0.2) + 0.1*np.random.normal() for a in x])\n", + "y = np.array([-4.5 + 0.2*a[0]*(1-5*a[1]**2) + a[1]*(1+a[0]*0.2) + 0.1*np.random.normal() for a in x])\n", "\n", "p = 1/(1+np.exp(-y))\n", "\n", - "n = [int(200 + 600*xj[1]/0.7) if xj[1] <= 0.7 else int(800 - 300*(xj[1]-0.7)/0.3) for xj in x]\n", + "n = [int(2000 + 6000*xj[1]/0.7) if xj[1] <= 0.7 else int(8000 - 3000*(xj[1]-0.7)/0.3) for xj in x]\n", "\n", "d = [nj*pj for nj,pj in zip(n,p)]" ] @@ -69,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 41, "id": "98b3d891-41c2-4ead-90dd-a8419e79809e", "metadata": {}, "outputs": [], @@ -79,7 +77,7 @@ " 'gender': [a[0] for a in x],\n", " 'age group (normalized)': [a[1] for a in x],\n", " 'population size': n,\n", - " 'number of transitions': d\n", + " 'number of transitions': [int(round(a)) for a in d]\n", "})\n", "\n", "# Write the DataFrame to a CSV file\n", @@ -96,7 +94,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 42, "id": "0da27f10-d9b1-4c75-afcd-cf69122586a6", "metadata": {}, "outputs": [], @@ -114,7 +112,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 70, "id": "84552a98-075b-48de-b7a9-68e018e95e83", "metadata": {}, "outputs": [ @@ -131,208 +129,40 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" [1. 0.17]\n", - " [1. 0.18]\n", - " [1. 0.19]\n", - " [1. 0.2 ]\n", - " [1. 0.21]\n", - " [1. 0.22]\n", - " [1. 0.23]\n", - " [1. 0.24]\n", - " [1. 0.25]\n", - " [1. 0.26]\n", - " [1. 0.27]\n", - " [1. 0.28]\n", - " [1. 0.29]\n", - " [1. 0.3 ]\n", - " [1. 0.31]\n", - " [1. 0.32]\n", - " [1. 0.33]\n", - " [1. 0.34]\n", - " [1. 0.35]\n", - " [1. 0.36]\n", - " [1. 0.37]\n", - " [1. 0.38]\n", - " [1. 0.39]\n", - " [1. 0.4 ]\n", - " [1. 0.41]\n", - " [1. 0.42]\n", - " [1. 0.43]\n", - " [1. 0.44]\n", - " [1. 0.45]\n", - " [1. 0.46]\n", - " [1. 0.47]\n", - " [1. 0.48]\n", - " [1. 0.49]\n", - " [1. 0.5 ]\n", - " [1. 0.51]\n", - " [1. 0.52]\n", - " [1. 0.53]\n", - " [1. 0.54]\n", - " [1. 0.55]\n", - " [1. 0.56]\n", - " [1. 0.57]\n", - " [1. 0.58]\n", - " [1. 0.59]\n", - " [1. 0.6 ]\n", - " [1. 0.61]\n", - " [1. 0.62]\n", - " [1. 0.63]\n", - " [1. 0.64]\n", - " [1. 0.65]\n", - " [1. 0.66]\n", - " [1. 0.67]\n", - " [1. 0.68]\n", - " [1. 0.69]\n", - " [1. 0.7 ]\n", - " [1. 0.71]\n", - " [1. 0.72]\n", - " [1. 0.73]\n", - " [1. 0.74]\n", - " [1. 0.75]\n", - " [1. 0.76]\n", - " [1. 0.77]\n", - " [1. 0.78]\n", - " [1. 0.79]\n", - " [1. 0.8 ]\n", - " [1. 0.81]\n", - " [1. 0.82]\n", - " [1. 0.83]\n", - " [1. 0.84]\n", - " [1. 0.85]\n", - " [1. 0.86]\n", - " [1. 0.87]\n", - " [1. 0.88]\n", - " [1. 0.89]\n", - " [1. 0.9 ]\n", - " [1. 0.91]\n", - " [1. 0.92]\n", - " [1. 0.93]\n", - " [1. 0.94]\n", - " [1. 0.95]\n", - " [1. 0.96]\n", - " [1. 0.97]\n", - " [1. 0.98]\n", - " [1. 0.99]]\n" + " [0. 0.09]]\n" ] } ], "source": [ "x = np.array( [[a,b] for a,b in zip(data['gender'], data['age group (normalized)'])] )\n", - "print(x)" + "print(x[0:10])" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 71, + "id": "5bfef017-385e-47c0-8b46-89a280406102", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-4.5444026 , -4.60062263, -4.34262549, -4.54103397, -4.40819711,\n", + " -4.54385044, -4.38964424, -4.41688114, -4.52361368, -4.24510111])" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y[0:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 43, "id": "e7447d0f-64e9-4d56-8a41-299cdd3b044e", "metadata": {}, "outputs": [], @@ -352,13 +182,13 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 44, "id": "0fe05211-ed34-463f-81ea-37069c0fd93f", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -380,43 +210,12 @@ "id": "cd869a15-a44e-406c-9ef7-22009f1f4bd0", "metadata": {}, "source": [ - "The first step of the modelling is to define the mapping from data space to our quantum feature space. This is done by setting up the qc circuit. The circuit below is a very simplified two-variable circuit. Feel free to experiment!" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "fc0a3769-6fa5-4cb0-a2ad-60295f32738d", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "###TO BE REMOVED\n", - "\n", - "# set up 'kernel circuit'\n", - "#p = ParameterVector('x', length=2)\n", - "#qc = QuantumCircuit(2)\n", - "\n", - "#qc.ry(p[0]*np.pi, 0)\n", - "#qc.ry(p[1]*np.pi, 1)\n", - "\n", - "#qc.draw('mpl')" + "The first step of the modelling is to define the mapping from data space to our quantum feature space. This is done by setting up the build_feature_map function. The circuit below is a very simplified two-variable circuit. Feel free to experiment!" ] }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 67, "id": "f6546726-7f76-4f7d-992c-95ee972abf17", "metadata": {}, "outputs": [ @@ -426,28 +225,29 @@ "text": [ "QuantumCircuit:\n", "---------------\n", - " ┌──────────┐\n", - "feature_map.0: ┤ Ry(π*x0) ├\n", - " ├──────────┤\n", - "feature_map.1: ┤ Ry(π*x1) ├\n", - " └──────────┘\n", + " ┌──────────┐\n", + "q.0: ┤ Ry(π*x0) ├\n", + " ├──────────┤\n", + "q.1: ┤ Ry(π*x1) ├\n", + " └──────────┘\n", "Live QuantumVariables:\n", "----------------------\n", - "QuantumVariable feature_map\n" + "QuantumVariable q\n" ] } ], "source": [ "# set up 'kernel feature map' with sympy parameters\n", + "from qrisp import ry\n", "\n", "def build_feature_map(sym):\n", - " n = 2\n", - " feature_map = QuantumVariable(n)\n", + " n = 2#number of qubits\n", + " q = QuantumVariable(n)\n", " params = symbols(sym+':'+str(n))\n", - " ry(np.pi * params[0], feature_map[0])\n", - " ry(np.pi * params[1], feature_map[1])\n", + " ry(np.pi * params[0], q[0])\n", + " ry(np.pi * params[1], q[1])\n", "\n", - " return feature_map\n", + " return q\n", "\n", "feature_map = build_feature_map('x')\n", "print(feature_map.qs)\n", @@ -456,7 +256,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 68, "id": "2c128f3c-da92-4dd2-b94d-27dd25970626", "metadata": {}, "outputs": [ @@ -464,22 +264,64 @@ "name": "stdout", "output_type": "stream", "text": [ - " ┌────────────┐\n", - "feature_map.0: ┤ Ry(1.2185) ├\n", - " ├────────────┤\n", - "feature_map.1: ┤ Ry(2.8328) ├\n", - " └────────────┘\n" + " ┌────────────┐\n", + "q.0: ┤ Ry(1.7798) ├\n", + " ├────────────┤\n", + "q.1: ┤ Ry(1.5008) ├\n", + " └────────────┘\n" ] } ], "source": [ "# example, assign random data as parameters and print cirquit\n", "\n", - "subs_dic = {params[i] : np.random.rand() for i in range(2)}\n", + "subs_dic = {a : np.random.rand() for a in feature_map.qs.abstract_params}\n", "bound_qc = feature_map.qs.bind_parameters(subs_dic)\n", "print(bound_qc)" ] }, + { + "cell_type": "markdown", + "id": "45f26e2c-cf15-4e67-a9b7-d774cb11c2eb", + "metadata": {}, + "source": [ + "For a data pair $(x, y)$, we create the kernel circuit by calling the build_feature_map twice, once for $x$ and once for $y$, inverting the latter, and joining them together" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "id": "ce778494-1f6a-40f0-89e9-02123cd6600a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " ┌──────────┐┌─────────────┐┌─┐ \n", + " q.0: ┤ Ry(π*x0) ├┤ Ry((-π)*y0) ├┤M├───\n", + " ├──────────┤├─────────────┤└╥┘┌─┐\n", + " q.1: ┤ Ry(π*x1) ├┤ Ry((-π)*y1) ├─╫─┤M├\n", + " └──────────┘└─────────────┘ ║ └╥┘\n", + "cb_0: ════════════════════════════╩══╬═\n", + " ║ \n", + "cb_1: ═══════════════════════════════╩═\n", + " \n" + ] + } + ], + "source": [ + "\n", + "kernel = build_feature_map('x')\n", + "y_inverse = build_feature_map('y').qs.inverse()\n", + "\n", + "kernel.qs.append(y_inverse.to_op(), kernel.qs.qubits)\n", + "\n", + "kernel.qs.measure(kernel.qs.qubits)\n", + "\n", + "print(kernel.qs.transpile())" + ] + }, { "cell_type": "markdown", "id": "b9fefbd4-5e78-4b09-8e7f-8e5a9f342e60", @@ -558,19 +400,29 @@ "\n" ] }, + { + "cell_type": "markdown", + "id": "7ed23841-0821-40bd-8a6e-0e7fd12ed22b", + "metadata": {}, + "source": [ + "#### Estimating the kernel matrix\n", + "\n", + "The train_kernel_matrix function prepares the kernel estimation by setting up inner product circuits, based on each combination of two data points. The kernel circuits are then run on a either a specified backend, or using statevector simulation." + ] + }, { "cell_type": "code", - "execution_count": 241, + "execution_count": 48, "id": "17cc99d0-a6b8-4e61-8d51-d89f582c7e77", "metadata": {}, "outputs": [], "source": [ "def train_kernel_matrix(x, f_feature_map, shots=1000, backend=None):\n", - " kernel = f_feature_map('x')\n", + " kernel = f_feature_map('x') #call feature map function\n", " x_params = copy(kernel.qs.abstract_params)\n", - " adjoint_qs = f_feature_map('y').qs.inverse()\n", + " adjoint_qs = f_feature_map('y').qs.inverse() #call feature map funciton again and apply inverse\n", " y_params = adjoint_qs.abstract_params\n", - " kernel.qs.append(adjoint_qs.to_op(), kernel.qs.qubits)\n", + " kernel.qs.append(adjoint_qs.to_op(), kernel.qs.qubits) #create inner product circuit\n", " kernel.qs = kernel.qs.transpile()\n", " if backend is not None:#measurement only needed when running shots\n", " kernel.qs.measure(kernel.qs.qubits)\n", @@ -581,7 +433,7 @@ " for j in range(i+1,n):\n", " for p in y_params:\n", " subs_dic[p] = x[j][int(p.name[1:])]\n", - " bound_kernel = kernel.qs.bind_parameters(subs_dic)\n", + " bound_kernel = kernel.qs.bind_parameters(subs_dic) #bind parameters for data pair (x_i, x_j)\n", " if backend is not None:\n", " res = bound_kernel.run(shots=shots, backend=backend)\n", " K_ij = res['0'*len(kernel.qs.qubits)] / shots if '0'*len(kernel.qs.qubits) in res else 0.0\n", @@ -594,108 +446,41 @@ " " ] }, - { - "cell_type": "code", - "execution_count": null, - "id": "7f4860a3-be61-45b4-aa12-4741bcf59771", - "metadata": {}, - "outputs": [], - "source": [] - }, { "cell_type": "markdown", - "id": "94ad5388-c776-492a-8247-053834f05260", + "id": "6684d892-b617-4556-926e-e23e10353aec", "metadata": {}, "source": [ - "The QuantumKernel function prepares the kernel estimation by setting up inner product circuits, based on each combination of two data points." + "We evaluate the kernel matrix based on our $x$ data and the build_feature_map helper function." ] }, { "cell_type": "code", - "execution_count": 10, - "id": "ae5d1df5-8f87-4626-a89e-baa40b219a00", - "metadata": {}, - "outputs": [], - "source": [ - "# TO BE REMOVED\n", - "\n", - "#zz_kernel = QuantumKernel(feature_map=qc, quantum_instance=Aer.get_backend('statevector_simulator'))" - ] - }, - { - "cell_type": "markdown", - "id": "9ccad195-ef4e-4826-bca1-8060e1d46eac", + "execution_count": 49, + "id": "908ec069-24b6-4d5b-bb47-e677339e3279", "metadata": {}, - "source": [ - "Then we specify the quantum instance: " - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "dbcc8420-4d8f-4278-b503-11afdbd12fcd", - "metadata": { - "scrolled": true - }, "outputs": [ { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" + "name": "stdout", + "output_type": "stream", + "text": [ + " \u001b[2K" + ] } ], - "source": [ - "# TO BE REMOVED\n", - "\n", - "#zz_circuit = zz_kernel.construct_circuit(ParameterVector('x_i', length=2),ParameterVector('x_j', length=2))\n", - "#zz_circuit.decompose().draw(output='mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "6684d892-b617-4556-926e-e23e10353aec", - "metadata": {}, - "source": [ - "We evaluate the kernel matrix based on our x data and the build_feature_map helper function." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "908ec069-24b6-4d5b-bb47-e677339e3279", - "metadata": {}, - "outputs": [], "source": [ "matrix_train = train_kernel_matrix(x, build_feature_map)" ] }, { "cell_type": "code", - "execution_count": null, - "id": "eb647d85-131e-43e7-b139-fddc282a177c", - "metadata": {}, - "outputs": [], - "source": [ - "#TO BE REMOVED\n", - "\n", - "#matrix_train = zz_kernel.evaluate(x_vec=x)" - ] - }, - { - "cell_type": "code", - "execution_count": 244, + "execution_count": 50, "id": "cc7771e0-7f0c-4a32-b6bd-d6a7dd50da52", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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"text/plain": [ "
" ] @@ -710,7 +495,7 @@ "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", "pos = axs.imshow(np.asmatrix(matrix_train),\n", " interpolation='nearest', origin='upper', cmap='Blues')\n", - "axs.set_title(\"training kernel matrix\")\n", + "axs.set_title(\"trained kernel matrix\")\n", "fig.colorbar(pos, ax=axs)\n", "plt.show()" ] @@ -733,7 +518,7 @@ }, { "cell_type": "code", - "execution_count": 245, + "execution_count": 51, "id": "ab02281d-bcb6-4cf3-af08-a786e0f22b79", "metadata": {}, "outputs": [ @@ -741,12 +526,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "score: 0.9142137205414308\n" + "score: 0.8103104968457695\n" ] }, { "data": { - "image/png": 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", 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rXXfdJU1P7OLgIFNOswWxp127djLlG64nAAAArhI1M2fOlBkro0ePliXpL7vsMurUqVOBkvIq3MunV69eUoRwWXvOHuHFty8QZ5JwNgqXsP/xxx+lYLrhhhtkPx8VFjS///47ffvttzR//nz64Ycf6MEHH4z0ewMAAADAYxgOFGbLDKfHsghRC5zVrFlTpuM+9dRTBbbnFFquocJCRIVTdps2bUrvvfdeyKAgTivm3jpc8ZXrpnCaspo6+/XXX9NNN91Eu3btourVq4cdNwKFQSzBOQYAAA4LFOYKsFygzLcJIddE4efBmhDyet/tGbbsBNueP2Py5MnyC7AVSN0HuzZ8a4HwPvmzA91UAAAAALCQnBxOeyWaPl155OduLL534MAB2StH7a2jws+50JsWXIVVa3te7wtbcriL8smTJ2U5enYzqZVaedvKlSv7D7xwYVm0LXA/KtzzyLfvESs9AAAAAERBWhrRkCFEu3blr0tJIXrrLaIePSjWOCb7ieuccPl9jsHh6q5c5TZYnI4exo4dK6096sIuMgAAAABEIWhuu81f0DC7dyvr+XU3iRq2nHCvHG466EuoJoS8Xs/2nPnEfXQ43ubDDz+Ulhh+VPcRKHC4Vw9nRAX73BEjRkj/m7rs3LnTyFcFAAAAgAq7mNhCoxWGq64bOjTmrihDoiY5OVn2EvJtQsiBwvw8WBNCXu+7PcOupXBNC3m/qvuIt+Xmgr4NB7/77ju5DQcua1GkSBEZUOS7AAAAACACli4taKEJFDZsPODt3OR+4nTuDz74gD7++GOZlfTwww/L7KZ7771Xvt63b19pJVEZMmSIzFR6/fXXZdwN16RZvXo1DR48WL7O73366adlh+ft27dL4XLffffR7t276fbbb8/rsswuqf79+8uaONxhmd/PMTh6Mp+8Hj/FcUV8nNnSxZk1HLPETS65OSPHKDkVDgjnGjcsOBMSEvy6YgMAAHAQmZnmbueULt2cos31Y5599lk5mXJqNosWNRh4x44dMitJ5aqrrqJp06bJzs4sXi666CL6v//7P7r00kvl6+zOYrHDIokDkbnLM6eML126lBo1apS3n88++0wKGU7x5v3feuut9J///IfiPX5q69atUsBwdtjLL78sixuylYpr/rBoqFGjBt1yyy2a7z137hwlJSVRrGDBxWKVF18hDAAAwGFUq2budlYh4gSru3SnpgqRkMD2N/+F1/HCr1tBp06dREpKijhx4oTm67m5uXn/5+/PHbm7dOkiu2JzV+lwXbq1Ol4fPnxYs0v3/PnzRePGjWWn61atWokNGzbo+g7q+3m/XgVdugEAriY7W4iUFO2JTp3satZUtothl27HZD+5mVjFTx08eJAWLlxIgwYNkoHWWrBbxxd2/3Xv3l1actjNN3fuXOm6evzxx2WV5wEDBkhXYnp6uuHxDB8+XLoZuUhipUqVqEuXLtIaBAAAwOUkJipuByZgXsl7PmGCsl0MgahxcfzUX3/9JXsuNWjQoECWWsmSJeXy5JNP+r3Wu3dvKVrq1atHtWrVotdee43uueceGjhwoGxXwTFTPXr0kOuNwq0zOnbsKF1g7E7kLDcWTQAAADxAjx5Ec+YQ1ajhv57jLHg96tR4A6fFT3EwNdf84Zgk3wKEjG9VZoaDvTkmxxd+zuuN4pvRxoURWWxFsh8AAHA0Dq6oazksXLZtI2Jr/rRpymNGhiMETUSBwsA58VOc7cTupS1btvitZysMU6xYsQLvCeamCoYa9O3bIgwuJQBA3OLwirq2wC6mdu3IicBSYwJt2ijndKCbUYXXc0Fj3s5MOFOM3T3cXJRT4yOB0+U5Rd4Xfs4NRBmOjWEyfcxMbAXSgtPyVQ4fPkx//PGH3D8AAHgCF1TUjXdgqTExforPaRYwvgHDVsdPTZo0SbqL2K3EQcBNmjSR1hUO1uVUeS6WGC64l1tSXH755bJJ6Lx58ygtLU12SFetPVzledy4cbLDNFd25vR8LcaMGSOFFqf3jxw5Usb2dOvWLehnc0kAXjg2iOHg5VKlSslYH3ZfAQCAazJC+GLPGSFdu8Y8WDauEXGC1SndDKdtc8abb5YbZ7hZlc6tsmfPHjF48GBRt25dmZZdsmRJ0bJlS/Hqq6+KrKysvO34+8+dO7fA+0OldDN8bFq3bi2KFSsmmjZtKhYuXKiZ0j1v3jzRqFEjkZycLD9//fr1IcfNKeX8vsBlypQpwmsgpRsAl8PXO61U5sDl/HURxCalO4H/oTiAu3RzY0vuAxXYMuH06dOUkZEhLRFckTdaMc9ZTuyt4Rgadjl5XbQvWbJENiRllxMXAQQFMfMcAwDEAA4K7t07/HYcPNurlx0jihuOhZi/A4H7KX7ipwAAAHi9om6cg0BhAAAAwKkZIcAQEDUgargpJXsx4XoCAHgWl1TUjXcgagAAAACPVNSNdxBTAwAAAOiFhQunbXs1IyTH3dkuEDUAAACAEbyaEZLm/mrJcD8BAAAA8d5HKs0b1ZIhagAAAIBYwEKhTh2i9u2VGjj8yM/tFhA5YaolM1wt2QWNOyFqAAAAgHi2jCxdWnAcgcJm505lO4cDUQNAiFT1oXx3opOpU6cirR0A4D7LSGamudvFEIgaD8BNIYcMGUIXXnihLMHPDSW5yeW7775LJ0+eJKcyefJkKRy47HVCQgIdOXIk1kMCAADrcZplpJp3qiUj+8nlbN26VQoYthC8/PLL1LhxYypSpIjseM2ioUaNGnTLLbdovvfcuXOUlJREsYIF14033iiXESNGxGwcAABgK06zjLQ5Xy2ZXV9a1iMuLsivu6BaMiw1LmfgwIFUuHBhWr16NfXs2ZMaNmxI9erVo65du9KCBQuoS5cueduyNYStNyxySpQoQS+99JJcz+suuOACSk5OpgYNGtD//ve/vPds27ZNvm/dunV569iiwuu4kSXDj/ycP69JkybSWnTllVfSb7/9FnLs7Np56qmn5LZ6YcvOI488It9brlw5aZX64IMPKCsri+69914qVaqUtFh99dVXfu/7/vvvqWXLllLwVatWTX5udnZ23uv8/r59+1LJkiXl66+//nqBzz5z5gz9+9//lkKRj1+rVq3yjgEAALjWMpLonWrJEDVBYLGalRWbRW/f9IMHD9LChQtp0KBBcpLVgsWGL8899xx1795dWnLuu+8+mjt3rnRdPf7441KEDBgwQIqD9PR0w8ds+PDhUgz8/PPPVKlSJSmo2BpkNh9//DFVrFiRVq1aJQXOww8/TLfffjtdddVV9Msvv9ANN9xAffr0yXO97d69m2666SZq0aIFrV+/Xoq4Dz/8kF588UW/sbPw+fzzz+UxZbHC+/Jl8ODBtGLFCpoxYwb9+uuv8jPZyvTnn3+a/h0BAB7GiX2kenikWrKIE44ePcpSQT4GcurUKbFx40b5qHLiBEuL2Cz82XpYuXKl/E5paWl+6ytUqCBKlCghlyeeeCJvPW87dOhQv22vuuoq0b9/f791t99+u7jpppvk/zMyMuT71q5dm/f64cOH5br09HT5nB/5+YwZM/K2OXjwoChWrJiYOXNm2O+hvp/3G462bduKa665Ju95dna2/J59+vTJW5eZmSn3t2LFCvn86aefFg0aNBC5ubl520ycOFGULFlS5OTkiOPHj4vk5GQxa9asAuMfMmSIfL59+3aRmJgodu/e7Tee66+/XowYMUL+f8qUKaJMmTKa49Y6xwAAcUxqqhAJCcriOwGo6/j1WJCdzRdlIaZNUx75uYPn70AQU+NB2IKRm5tLd911l3SZ+NK8eXO/55s2baIHH3zQbx3H6LylmiIN0Lp167z/ly9fXrqyeP9mwy4ulcTERKpQoYKMJVJhlxSzf/9++chj4LH5Wq34O544cYJ27dpFhw8fprNnz0p3UuD4VdiylZOTQ/Xr1/cbCx9f/nwAAIjIMqJVwZddPbGyjCS6u1oyRE0QihcnOnEidp+tB44d4Yl6y5Ytfus5poYpVqxYgfcEc1MFo1AhxUOpGHoUrHApGSEwuJmPge86VbywsDMLFkAsoNasWSMffeE4HAAAMIzX+0jFAIiaIPC8aHD+tx22EHTs2JHeeecdGVtiVLAwHFi8bNky6tevX946fn7JJZfI/3NsDJOZmUmXX365/L9v0LAvK1eupFq1asn/s/Xjjz/+kPuPNTyG1NRUKcxUwcPfkYOKU1JSpFWGRdFPP/1UYPxt27aVz/m7s6WGrT9tXJABAABwSWPISCwjLm86aSUQNS5n0qRJ0pXCbiUOAmbXDFtXOFh38+bN1KxZs5Dv5wBZzpriSbtDhw40b948SktLo0WLFuVZezg7ady4cVS3bl05qY8aNUpzX2PGjJFCi90/I0eOlMG83bp1C1lfh5e//vorz8XDQoOFBQsNMzPEJkyYIIUfB/uyZWv06NH02GOPyWPFlpb7779fHgsef+XKleX4VSsVw24ndudxhhQHQ/Px+ueff2jx4sXymHfu3Nm08QIAXI6VjSE90HTSUkScYDRQ2E3s2bNHDB48WNStW1ckJSXJANiWLVuKV199VWRlZeVtx99/7ty5Bd4/adIkUa9ePfne+vXri08++cTvdT42rVu3loGzTZs2FQsXLtQMFJ43b55o1KiRDLrlz1+/fn3IcY8ePVq+L3DhgNtQgcJq8K5K7dq1xZtvvum3LvC7LlmyRLRo0UKOrWrVquLJJ58U586dy3udg4XvvvtuUbx4cVGlShUxfvz4Ap919uxZ8eyzz4o6derIY1WtWjXRvXt38euvv8rXESgMAMgLAA7MADEjANjKfTsYI4HCCfwPxQHHjh2jMmXK0NGjR2UFW19Onz5NGRkZ0hLBNVaAMTj9uX379tJlgzYB2uAcAyAOYLcQN6QMVi1YLWKXkWHcXWTlvs3AQpdYqPk7ENSpAQAAAJze/sBprRWc2G0cogYAAABwQfsDp7VWcGK3cYgaYAbcuoC9mHA9AQDiGivbHzittYITu41D1AAAAAAuaH/gxNYKS53nEoOoAQAAAJzeGNKJTScznecSg6jxIU4SwUAMwLkFQJxgZWNIpzWdrOY8lxiK7/mU3eeuzlqtBQCIFu4txQS2WAAAeBCz2x8Epkv//TfR8uWxryjc5rxLjIOCtW7c1DRzG11iEDXnJxoOclUbIBYvXtyv+SEA0cA9qLj6MJ9XhQvjJwdAXGBWY8hQFYR79aKYknjeJcZZTjxn+gqbGLnEUHzvPHwYuGT/kSNHYjI+4G245QIX3ktOTo71UAAAbkFNlw6cplXBEAuXk17hxUHLJnUbN1J8D6ImAG5aGOsu1MB7sJjx7SUFAACuriDs0IrCsIVruKIQ9wAAACCmGEmXNsPN5RR3W5Tg1hEAAABwGg5Ml3YDEDUAAACA03BgurQbgPsJAAAAcBpWpEvnWBf34hRgqQEAAACchtkVhNOc00nbSiBqAAAAAF9rxpIlRNOnK482NmO0rIJwmrM6aVsJUroBAACAcIXuYlkPJhq3UY7LUsM1QEo3AAAAYEahO9WaEctCd9GkSy91WWp4lMD9BAAAIL5hawZbaLQcF+q6oUNj64qKlMz4Sg2HqAEAABDfGLFmuI1q8ZUaDlEDAAAgvvGyNaPN+dTwYE2aeT33abKxk7aVQNQAAACIb7xszUg0OTXc4UDUAAAAiG+8bs3oYVJquAtA9hMAAID4RrVmcJYTCxjfgGGvWDN69CDq2tXzFYUhagAAALifaFsAqNYMrTo1LGi8YM1IdEYnbSuBqAEAAOBuzCqaFyfWDC+DisIAAADca4UJVjRPdRt5LGYkHjlmYP5GoDAAAADnEqoRo5eL5oGIgKgBAADgTMI1YnzpJe8WzQMRAVEDAADAeeixwqj1V7xYNA9EBEQNAAAAd7YuOHTIu0XzQERA1AAAAHAeeq0r5ct7t2geMAxEDQAAAOeh17rCLqo4aQEAwoM6NQAAAJzbuoCDgrXiali08OsjRxJdeqm3i+bp4dQpov37iY4c4Rzo/OX4caKzZ4nOnVMeeeHjWaiQIvbUx+LFlaVECeWRU6crVFAWtoYlJZEbgKgBAADg7tYFXiqap1WT5/Rpor/+Itq2jWjHDqLt25VHFnEsZHhh8WIlZcoo4+H+UerCrr0LLyS64AKiWrWIChd2Z/G9iRMn0quvvkp79+6lyy67jN5++21q2bJl0O1nz55NzzzzDG3bto0uuugieuWVV+imm26Sr507d45GjRpFX375JW3dulUW2OnQoQONGzeOqlevnrePOnXq0Hb+Q/owduxYeuqpp3SNGcX3AADAI9WCeTL1ohXm00+JHnuM6J9/8texMNNbZyc5mahcOUWA8DzHS8mSREWKKK/xwhYXts7wPnNzlYWtOGzpycoiOnlSeTx6lOjgQcXyo0cmsKCpXZuoY0eid98lMzEyfxuWVTNnzqTHHnuM3nvvPWrVqhVNmDCBOnXqRFu2bKHKlSsX2H758uXUq1cvKUBuvvlmmjZtGnXr1o1++eUXuvTSS+nkyZPy/yx6WCAdPnyYhgwZQrfccgutXr3ab19jxoyh/v375z0vVaqU0eEDAABwE16ywvjCooHnuJ9+Ivr5Z54sFYtLIKqgYXFy8cWKRYTFAz+yuKtShYjnXn4sXTp40HSk8OcfPkx04ADRnj2KO5AXFplsaPj7b6KtW4nOnFH+z65AN1lqWMi0aNGC3nnnHfk8NzeXatasSY888oim1eSOO+6grKwsmj9/ft66K6+8kpo2bSqFkRY///yztPywZaYW/+HOW2qGDh0ql0iApQYAAEDMYNfRDz8oCwuYzZv1WUBUWMBkZDhTzOXmKoKHRU3RoiwU3NEm4ezZs7RmzRrpHsrbQaFC8vmKFSs038Prfbdn2LITbHuGB56QkEBly5b1W88uqQoVKtDll18u3V/Z2dlGhg8AAEDrTnzJEqLp05VHtBQwB57kP/6YqE8fxbJSty5Rv35EH35ItGmTImi43cMddxA9/HD4/RmtjJxj49+V3VkcmN22remCxiiG3E8HDhygnJwcqsJmLh/4+WZWnRpw3I3W9rxei9OnT9OTTz4pXVa+iuzRRx+lK664gsqXLy9dWiNGjKDMzEx64403NPdz5swZufgqPQAAABZ0twaK++X774m++YZo4UKi334rGHPSvDnRtdcSXXONMvmrIRssPPTEoeit3ZMWv3/X2Icq+8BBwz179iT2iL0b8AfmOB6VJk2aUHJyMg0YMEDG6hThIKgAeP3zzz9vy7gBAMB1BOturfZVQnfr8HBF4y+/JPriC6Kvv/bPQOLYFhYxN9ygNOG88kolXTqamjx6tkuL77+rIVFTsWJFSkxMpH379vmt5+dVq1bVfA+v17O9Kmg4jua7774L6zfj2B52P3FGVYMGDQq8zpYcXyHElhqO/QEAgLgnXF8lnpA5fpEDdJ0YwxFLOJiXhcPs2Yplxtetw/MaZ/Z26kR0/fVKjRcza/KEq4ycg7+roZgato40a9aMFi9enLeOA4X5eevWrTXfw+t9t2e+/fZbv+1VQfPnn3/SokWLZNxMONatWyfjebQyrhi23rAw8l0AAADo7KuE7tb5cGozJ7Zcd51iLeEYmO++U0REkyZEo0YpWUwsSjhmpmdP/YLGtyZPtJWRl+Lvatj9xNaPfv36UfPmzWWGEqd0c3bTvffeK1/v27cv1ahRQ7p/GE7Pbtu2Lb3++uvUuXNnmjFjhkzVnjx5cp6gue2222RaN2dIccyOGm/D8TMspDio+KeffqL27dvLNG5+PmzYMLr77rupHOfkAwAA0I/e2Ix47m7NBe84a/d//yP66iullosKu5Vuv11x59SrZ87nsUuIXUPRVEbOxN+V41cM8/bbb4tatWqJ5ORk0bJlS7Fy5cq819q2bSv69evnt/2sWbNE/fr15faNGjUSCxYsyHstIyOD7WSaS3p6utxmzZo1olWrVqJMmTKiaNGiomHDhuLll18Wp0+f1j3mo0ePyn3yIwAAxDV8bVXu20Mv56/BcUNurhA//STEgw8KUaaM/7G4/HIhxo8XYutWa8eQna0c92nTlEd+Hud/16MG5u+IKgq7EdSpAQCA87DbhNOJw8VwOLUuihXuJa7my66jDRvy13Mc5l13Ed19N1GjRuR4crz5d7W0ojAAAIA46qvkVfg7cxzMpElEs2YpKdkMZ9PycbnvPqJ27ZQaLG4hEX9XF/21AAAAmIYaw8GNCX3hO3kvp/1yb6P//peoWTPOZFFiZljQNG1KxJXyOd6ErTYcFOwmQRPvf9fzwP0EAADxjFZXaC/eyXPw7cSJRO+/r/QyYrik/513Eg0cSNSiBXmKHO/8XeF+AgAAoA+e6NjN4lW4WeSbbyp1ZdTWOpyxxELmnnuMpV67iUSP/12DAFEDAADAW7ADgiv8vvKKUiBPhXsTDRtGdPPNrrVagNBA1AAAAPAGbImZOZNo/HiiX39V1iUlEfXqpVTSvfzy2I7PQy4hpwJRAwAAwN2cPUs0dSrRuHFKujJTsiTRgAGKmOEg2VgTx00m7QSiBgAAgHur/nJtGXYzcfl/plIlRTxwzIxTKs7HeZNJO0H2EwAAAPeJmQ8+IOJ2PGrJf3bnPPkkUf/+RMWLk+MK4gXryeTSgnh2guwnAAAA3nQzTZlC9OKL+SKBq/4+9ZRSLI9TtJ0WC2OkyWQcZiuZDUQNAAAAe4hUHPD7uCDe88/nx8xwcTnujs1iJjnZubEwaDJpKy4slwgAAMB1sDhgN0z79kS9eyuP/JzXh7JifP45UZMmSk0ZFjRVqiiC4q+/iB56yHpBwzEvgZYWNRYm1NhVWLzpQe92ICSIqQEAABCbQFm1H5FWoCxbdNittHy58rx8eeX5oEH2xMyYFQvj0SaTTp2/YakBAABgHTyps/tGa0JX13HaNW/HbN5M1LUr0bXXKoKmWDGip58m+vtvouHD7QsCNhILo6fJpK+Ii7Mmk3YCUQMAAF6FhcKSJUTTpyuPqnCwE73i4IsvFCvMpZcq/+dJnuvMsJvppZeIypa1c9TmxsLEeZNJO0GgMAAAeBGnFHvTKw7uuovo1Cnl/2yp4dozDRpQzDA7FoaPOX8vVBS2FIgaAADwGk4q9qZ30mdB06wZ0WuvOSO1mQUHi8BwsTC8nV7itMmkncD9BAAA8RzDYpc4CIwnCZzsP/6YaNUq50z6iIVxJRA1AADgJcwKcLVCHATjk0+I+vYlKuSwKQmxMK7DYWcQAACAqHBisTeOJXnwwYKihV1TqalK3RqnwsJl2zai9HSiadOUR06/hqBxJIipAQAALxFtgGs0LQG0+OknosGDiVavVp7Xq6cEBV93XX48CmdmGfk8s8cYDsTCuAaIGgAA8BLRBLiamTF16JBSLI8bTzJcNO2FF5Tu2YULR/55TsnqAo4E7icAAPASkQa4mtESgGEhNXWqko6tChpucfDHH0SPPuovaIx+nlljBJ4FbRIAAMCNhHPBaFk0uKM1C5pAi4ZZLQF+/13px/Tjj8pzLqT37rtE11wT/eeZNUbgOtAmAQAA4r05pJEA12gzprjGzIgRRJddpgiaokWV4nm//FJQ0ET6eU7L6gKOBDE1AADg1cJ6egNco8mYWryY6O67ifbuzV93+jTR228TXXihtoiK5POcmNUFHAcsNQAAEO+F9SLJmDpwgKhfP6IOHfwFjZ44l0g+z+y2BcCTQNQAAIBbsMoFo6fqb6VKilBhN9ZnnxE1bKgUzQs1lmAiK9zn8XqO//HN0IrkPSDugKgBAAC3YJULJlTGlMo//yhuJq4vw49sqalbN/R+g4msSDK00LYA6ACiBgAA3IKVLphgLQFCcfPNkYusSFoQoG2BueTkKIUPp09XHu3qB2YhSOkGAAC3oKY1hyusF01as5oqzp8xbJhiodGCP6tixeCv+8Iuq2ABy5FUB7a7orAXSXNPEUMj8zdEDQAAuDH7ifG9fKsuGLMsFt99R3T99eG341gbdkVZJbKAfRl0CSafQyaBOjUAAOBVF4AdLpi//iIaNEjfttzHiUGcS3xn0DkEiBoAAHByET07O0fn5ir1ZZo0Idq8WX8HbsS5uIel3i5iiOJ7AADg9CJ6dnSOZlF0332KtYhhgbVpE9G+feEbY/JYWNzEc5yLW+J8Mr1dxBCWGgAAiGcXAH/ee+8RNW6sCJrixYkmTiRatEh51OtaUkVWr17KoxMndKdZ3GJBNW8XMYSoAQCAeHUBsFXoX/8ievhhoqwsomuvJdqwgWjgQKJChaKP3/FgyrDrO4e38XYRQ4gaAACINxcAiyYWGtxF+5tvlAaUb76pxObUq2dO/I5brBfRCC8nWdz0kujtIoYQNQAAEE8ugIMHie68UxEaR44QNW9OtHatMvmydUYLo64lt1gvohVeTrG4GaWHd4sYQtQAAEC8uAC+/lqJnZk1i6hwYaLnnydavpzo4ovN+wy3WC/MEF6xtrhFQw+LMuhiDEQNAMA04iGEwpUugJMniQYPVuJneILlZpQrVxI9+yxRUhKZihusF2YJL7cH3SZ6L7gbogYAYApuCaFwhQtg5kyi8uXNUYerVxNdcUV+JtOjjxKtWUPUrBlZghusF2YJL48H3boR1KkBAMS85ErcwgclsL4LtxzgnkvR9uRhITRuHNFzzxFlZxNVr040ZQrRDTeQpbjBemGW8FItbnySs4DRalvh4qBbNwJLDQAgppb8uHdZ+boADh0i6tkz+gBbjpXgfY4apQgafi+nalstaNxivTBTeHk46NaNoKElACAqWIiwqymSRs0uahRsXwfuYG4Rvc0hP/tMqTNz7BhRyZJE77xD1LdvcJHh5qabTup27paKwi4EDS0BAI635Lsl69c1cR5HjyrNJe++WxE0rVsTrV9P1K+fvYLGDdYLKwK1PRh060YgagAAtlvy3ZL165o4D07LbtpUSc3lyZRTtX/4oWAhPTtxesqw04UXiAgECgMATAmhCGfJ9w2hMGKUMLNno+fUIcfLvPQS0ZgxSoftunUV9xNbaZyA2U03jRLOJaQVqA23kauBqAEAREUkCSBuyPp1vDrcvl1xNy1bpjzv00eJn0HMoLGArVgLL2AqcD8BAGy35Lsh69dJcR45lEhLRFuafuscWrI0kXJmzCa67DJF0JQqRfTpp0SffAJBo4KArbgF2U8AANPQmwBiRfKJ1WOOlYUhjbrTkMR3aFdO9bxNUmgnvUVDqMeVmUq8CrudgLlZZMCV8zdEDQAgJjgh6zeqlHIr1dD5fad9nki3TbiGBAk/w3oC5cp/58zMoR49EUVgWo0B4EiQ0g0AcDyxTj4J7aEQlDbmt+AVAbV6QtSurQTsmlFFMDGRctq0oyH/a1ZA0DBCPhc0dODZ+MoQ0wMCtuIaWGoA8LIrwwXE4piF9VBQLqXQLsqgupTIVhFf802wnhCBRFlFcMniHGrfIfyBSF+UQ+2ux0mWByw1ngOWGgBiABo6RkYsapaFTSmnQrSTatFSauMfYDp7dvACO4FEGZSa+fFCfdst2RLR/j2LG9o0AMuAqAHABJBs4VEPBZ1Pv1JFzKBBodWQGVUEedvnn6dq/xuva/NqBDeK5dWCgWuAqAEgSlAd133oTin3FQz8x/znH2MfFK61QSCsgq+/XnbWbkM/yCwnJSi4ILy+Ju2gNu3cMznb1rw01gFbIGZA1AAQ45Y9wIEeClUw0FL7TEMLFii1Z77/XjaiTPx4Cr1VYUzeeALHx0yo8CIltnOHG8V296zT2zQAS4CoASBKkGzhMQ+FKhhoqBIkHEilSsYbRIYyDZ09S/T440Q330x08CDR5ZcT/fKL7KzdY/K/aA7dTjVot99bOIiZ1/eYfKMhN4ptlhKnuGfRZDLugKgBIEpQHdedBPVQSMFwG/WgudoBppMm5T8PR7igVLYcXHMN0RtvKM8ffZRoxQqiiy7KG2SP1LtoW41rKJ3a0TTqJR8zUq6V641YHWIVyA73LLATpHQDECVOqo4Lokwp//MHajP6OkpMyA1dEVCral8g4aoI8voHHiA6epSoXDmiKVOU5ooW5L0Hy0K3o9AhMqyBnfM3SlECEIOGjsA5+PczvJbo0lnaZYb5j6jO/IHdnf/8k+iDD0K/R+X0aaLHHiN6913lOXfUnjGDqFYtvYM01VLC5yhbSvjrWHGOwj0L7ASWGgBMQuvmnT0PWvMacDiRWEb0vOePP4h69iRav155/tRTShXipCTLvkqsLSWx/nzgfmCpASAGBN68o6Kwi4nEMhLuPZyBM2AA0YkTSrAxd9W+8UaymlhbStRMs3DuWTXsCFW5ge2BwhMnTqQ6depQ0aJFqVWrVrRq1aqQ28+ePZsuvvhiuX3jxo3pyy+/zHvt3Llz9OSTT8r1JUqUoOrVq1Pfvn1pz549fvs4dOgQ3XXXXVKllS1blu6//346wRcHABwEki2AHzxDf/010XXXEd11lyJo+MRYt84WQeOEQHYjtfBQlRtEjTDIjBkzRHJysvjoo4/E77//Lvr37y/Kli0r9u3bp7n9smXLRGJiohg/frzYuHGjGDVqlEhKShIbNmyQrx85ckR06NBBzJw5U2zevFmsWLFCtGzZUjRr1sxvPzfeeKO47LLLxMqVK8XSpUvFhRdeKHr16qV73EePHuV7BPkIAHA/2dlCpKcLMW2a8sjPHUVqqhBVqrBxIn8pVUqIWbNsHQYfl5QUIRIS/IeiLry+Zk3rjx8fDh6H72fz5/J69XWtMfI6XtTtQPxx1MD8bVjUsOAYNGhQ3vOcnBxRvXp1MXbsWM3te/bsKTp37uy3rlWrVmLAgAFBP2PVqlXyC2zfvl0+ZzHEz3/++ee8bb766iuRkJAgdu/erWvcEDUAeAetCZKfO2bi44FoKQh1GTrUViWmCoZA0WC3YAgmRFXhFexwmSa8HK+EQbTztyH309mzZ2nNmjXUoUOHvHWFChWSz1dwbQUNeL3v9kynTp2Cbs9wMFBCQoJ0M6n74P83b948bxveJ3/2Tz/9ZOQrAOBaIimcFqtia3HdZ+v4caI+fUJvw/4WG30rTukaEMw9a0tVbp2+LS/+ZuIJQ6LmwIEDlJOTQ1WqVPFbz8/37t2r+R5eb2T706dPyxibXr165UU587aVK1f2265w4cJUvnz5oPs5c+aMjJj2XQBwK5HEGngxPsHxhdw2biRq0oTo5El929uoxEzvGmDi7G95MLNOJezF30y84aiKwhw03LNnT3aJ0btqDYcIGTt2rEwBU5eanFsLQJxYJhxvzfBiny3OZmrRQlEOerFZiZkWyG7y7G9pMLNOJZw2J8eTv5l4w5CoqVixIiUmJtK+ffv81vPzqlWrar6H1+vZXhU027dvp2+//dYvF5233b9/v9/22dnZMiMq2OeOGDFCurHUZSdf6QCIA8uE460ZLk5P1oStMvfdR9Svn/L/Zs2Mvd9tHU8tUMwy7bvCydAdySucDNptQq8SzqFCtITa0nS6Uz7ycz7+OTt305CB5zz5m4k3DIma5ORkatasGS1evDhvXW5urnzemqtiasDrfbdnWLT4bq8Kmj///JMWLVpEFSpUKLCPI0eOyHgele+++05+NqeUa1GkSBEpjHwXAOLBMuFoa4bL05M13U0tWyotDgoVUgrpLV+e1wJccxK1UYmZHh9ikWJOpBx6i4aE7kguG4xG8AXOH9c06k51aBu1pyXUm6bLR37O65dSG9r1T1FP/mbiDhFBSneRIkXE1KlTZVbSgw8+KFO69+7dK1/v06ePeOqpp/xSugsXLixee+01sWnTJjF69Gi/lO6zZ8+KW265RaSkpIh169aJzMzMvOXMmTN+Kd2XX365+Omnn8SPP/4oLrroIqR0A8/DSRqhkmjUhbeL5j2WYXK2iSnpyWaN6eOPhSheXPngqlWVfamkpopU6iFSaId/hhbtEKnUXXvwvu93aoYYj1HPyWX0u5zfLx+bwGNWk7bnH7NIjlF6unx/AuUIkovP+UI5chlKrzvnNwPsTelm3n77bVGrVi1Zr4ZTvLl2jErbtm1Fv379/LafNWuWqF+/vty+UaNGYsGCBXmvZWRkyMFqLek+J/DBgweliClZsqQoXbq0uPfee8Xx48d1jxmiBriRSOYQq+Ydp+RdR5WebMaYsrKEuO++/Pd36CDE+Zs6vzFSbtBJ1E/YWFAoxrKaL1YpZp/9ZlMhkU5txTS6Uz7y82hURfaZbJGSuLvA38L3b1Kp0H5n/GZAbESNG4GoAW4kEsuEI4qtWVxJLVwhN8vG9PvvQjRqpLyvUCEhXnihwIEMW3OFcqT1QU7WFhSKsbTmi8WWGitUhd5dV6oU+wKFQBuIGg0gaoBbicQyEdNiazZVUjPkRTJjTJ98EtzdFMn8TG11KDHjWGqps0oxW6jE9RqXuB6iEwoUAhuL7wEA7CeSwmkxLbZmU6SyofTkaMbEGU3330/Ut6/yfy4myr2bgjSv1J2hNWpSVIViggUBW5ohZqSRk837DXY89AaNczNaJxQoBNGBLt3AcrzSdTeW3yOSDuAx6xruxLzrSMfE2U09exL9/ruS3TR6NNHIkSEPou4Mresv4bSfiOCsaU5C8tVpPPmyLrA8Q0xVzFoDYOHhM/sb+s0Y2K+R48G/Ab1dwnlsMfnNAPMQcQLcT7HB8T164ux72IJjIpWjHFNgdtN33+n6KKtjmsKFBnG/TFtiqsL4/yL+zRjMTtMTKuWU3ld2ku2hNleIqdEAosZ+oonLdNIPEt2DDeKISOUoxsTZTffeGzK7KRxWTaJ6Q4Nmzzb3843+Hu36zRgJlYoouNylpHrsJgyiRgOIGnuJJi7TST9I27oHew0n3hrrGVNgdtPzz0f8x7ViEjVicDLr843+Hu38zRg1wDnpZskqUj14EwZRowFEjTs8EE77QTrRkxIrDE8ITrw1DjWmqVMjcjeFwuxJ1GiZmGg/P5Lfo52/GUcVmnQA2R69CTMyfyNQGDgmLjNcBXYO6OMK7BzIZ1fgnhNjXmNBqEDMoPGbZkYqmxWlrTWmK64gevRRoo8/Vrbh7KZPPyWqUoWiRc3QMgujQcDRfH6kv0c7fzOOa5sR4wSEpQaS/Mw8L50ERA2whEguNk78QXrhomlW/8LAyU3tXxgy3dWMWT0tjXIeHUZLd9elTKpG1SiT2tTIoMT/vBlZnq3vmDir6coriTZtUrKbnnuO6OmnHZvuIhs/hsrkISEbQ7bJ+ZkoJ7q0nUh/j3b+ZsIeD5/MJs/cLIQgEzdhxhpaAmD0YhNYckKF19es6X+xceIPMpLv4SVi3vE7LY3Sbv2M6uz+0b8R4e4f5fpIOkLnDf6jj4hatFAETfnyRCNGOP4PGbKci2z8KGjCwT6U2KE9UZ06kR+fKH6Pdv5mrCqb49Jm54SbMKR0AwfFijo1fsWJMa92xXDE9G+SnS1SKzwQshFhaoX+xr8k94zr0yd/Z0WKuC5NRDM0yLfxowknaDR/e7t/M04M34pF7Et2mCQ/tR3Ep5+6K1AagcIaQNTEBiMXGydmAkfyPWKFFVljsQzEzF6Ufr5jc07oHkqLDCiq9euFaNAgP7sp2InmNLUaTMAuyhbTyg8q2PjRhB9NtL9HK38zWuLdTZlNVt4spAYRlFqLC/S7BKJGA4ia2GHkYuNkq4iTL5r5WSq5AcctN6rjFktLTfqoRfo+e9Si8DvLzRXivffyrTI1aii3rGbfKtuNxX+gUL9HfuSM91C/Byt+M04q+eDUm4VUjWPkYv1uaP5O4H8oDjh27BiVKVOGjh49SqVLl471cIDB4Dn2wYeplB63cDwLh0/s2sU/5QTt4NGaCbLNkNHYAnXf4QIxI9l3OKY/s5F6v3hJ2O2mjdpIvV4Isd2xY0QPPkg0c6by/F//IhowgKhbt/CDSE83HOh87hzR8eNEJ04oj7xkZRGdOqUs3D6KH8+e9V/4fXy8s7OVx1wOkdGgcGHlWPNj4c2/UdLcmVSEzlAynZWPvBSnk3IpRqfkY4mXR1Gpnv+iUsVzqNSvy6jowd2UUF1fqo3W77FCBeXx4EFzAlyjDVpX42fc0qOJe1O1b2/J6Vcgq4p/u8OGEf3zD2kS+Bt2YlsbI/M3RA1wJE78YcXrBVKdSBjfq4XVE8mSxTnUvkP4P3r6ohxqd32Q7dasIbrjDqK//1ZUwNixRI89pgic3r1D7jeXEujQe7Npf5tbaf9+ZVLgR57IfZcjR5Tl6FHlkQWL0ylM56gsHaGyhU9Q2dplqWzdcjJWmsWK71K5spLZzv/fskU5Bn/+qSSJ2S0s8sW79utWCmyzsfNmYYmB68OhQ+ZmY8Vi/kZKN3AkZtf38DKZu3N1JTLq3c7EPoNR0aZdokxP3n2wKAmNcXO2T0qF09SmXfGCb+aZ4u23if79b8UEUquWImQ4fZuIjpZKoV10Ce2ilLxlN9WQKePqso+qUM5DkV8iixQhKlWKqGRJohIliIoXJypWTHksWlR5nZfkZGXxtcDwI2eYB2b0sPXG15qTfS6Xzn08jc5kZdNZSpZ2mtNUlE5RMWmr4ceswmUoq2QVOn4kh7KopNxPNiXRAapEB7IrEf1NyqIDFjcs3rQmYnUdnydW1JJyYsmHaLO2+GaB/8ZaNwtmZW1l6sxi+/xzZUwRlW5wEBA1ALicav/8SkRNTdvOKR2/5YV/cnG67VYhBYyvsFHSlxNowuTiBcdw6BAd7zOQMr7cSFvpJtp6aVfKaN2Ltr9clLZvJ7kcPcr5xL/rGgdbMNhiwUvFisqiWjX4kZeyZfMXvpFkMZOURDZQiOj64qFNadNmKtapI7sohwpRFpWgY1Sa7TTnl3J0uPwFdPiZN+jg4UJ04IBigeJH1TrFjyyifN1NwWDhwVaIiy8mql1b+X/dukQXXEBUrx5RpUrB071D4cSSD9Fg181CNZ3p2599FlqsPvSQYoWsUcPZlnO4n4DtwLVk7jHK+WwG1bn7amlpCGrRoF2U8elySrzrTnIbSkyHoF278mfCmimCxo5LoIYNif74Q3GJ8PLX2mP018az9E9uxbD7LVEkm6qc2U716Q+qSTupOu2RSzXaq9hqJj9Ple+5ySZxYmEgGquuKP2TbCFiQTNlCtGTT0Y3VLZcsbi56CL/pUGD0ILHjjgUL14Pc3S4ulioB4u50cJulxRiajSAqPFmBU0vYvgYLVlCae3/Q7fRHPm0oEWDaA7dRj3SH3XE1d7oRZwvths2EH3xhVInjyfXfftCuyKYimXPUd2LkuQEypYCthrwe/77X+X9KimJe+itnMHUg+a6Oyo92IGdPj1s/JBk2jSiXr1CbqJXWLz5JlG5copVbNs2oq1blYWPf6gZh9/DFh51adSI6JJLlL8dvy9WQetuJy1MXBxfb/iU14vdgdmG5m8RJyClO/Y4rVmlZ47R+YIiqdTjfF2XwIJsPfzSk2OZmh4qHffYMSFWrBDi/feFGDxYiHbthKhYMXRKKmdlX93ijLin2lfiJRohZtFt4pcbR4iju44ZOLa5IoFyRerQH5yXq++wtO9oa9ecPi3E5s1CLFggxIQJQgwcKETHjkLUrh26rkqJEkI0b66cE25OTY4lqSHqBuk9RWJV9QAp3RrAUhNbvJS5YNXx4bvgnj2VDATDx+j8rViOKERL6Zr8Hkn0IyUm5ObdUsXSUhYsHVcPbGnhu3Z2N/HCrgpeKqz+hqhvXyXwgyNwH3mEqEkTourV/UxAcX3+mZxqY1U2HMdrsAtx82ZlYavcxo3K/znlPRQcw3T//UT9+xPVr68EWwP9xrxwp0is3X2w1GgAS01scWoLBBWnWS8iOkZhSrjGwlLGNe8yMoSYOVOIUqXCf7dq1YS44QYhHn9ciKlThVi9WogTJzR2fOaMEP/+d/4b+Va/ShVtE5BN55+TizOaXdXSzgrb584p1h3eNxf7u/VWIerXD27ZKVZMiCuvVKxAH34oxLp1Qpw9a/64vEaqgUrEVlcTDwQVhTWAqImeaC7asSy37+QKpcGERsTHKMgfyapeM4Hs2yfEF18I8cwzQtx4Y3j3UUSi4q+/hGjRIv9NnToF/1LnJ+xYVHB1XJVbk5VIrEVcVpYQP/0kxOTJioC56irFTaX1dy1aVIjWrYV49FEh/vc/RSTl5Ng7XjeQavAGK9obAb1A1GgAURMd0V60nWqpiUmcz/nZIPvT6SKl0qkCrQ2sOEZWHH+Oj1i+XIg33hDijjuEqFNHe59JScFfMywqPvss3+RTrpwQc+boUmvcI8mqY+uqWDELlUisRQ7DQoUFC4+BrX3t2wtRurT235pPH9bDo0cL8eWXQhw8aP94nUj2+b8jN73kmDUn9OKDqNEAoiZyzLho29Ws0siF1S7rRTB1yE0IjYiZaMZjhqUiM1PREDxZ8F1vcrL2GC+5RIh+/YR45x3lTvrUKRNEFXfWvuee/A2vuUaI7dt171g2x4zi/At2XsXkHHIgTrZUqUKHLTRsqeFzly03Wn+vhg2FuO8+If77XyE2blTcp/FMqkN68UHUaABRExlmXrSt/oEYvbDabj0KUIfT6E5DgibwGBkRcEa/K1/MN20S4oMPFIFywQXa2/Od3C23CPHSS0IsWiTEkSMWiFoOrLnoovzO2s8+qwRaGFRrkZ5/oc4rp1og7cRVlqrzcIwNn1YsvPv0yT+9ApcKFZTze/x4xSrJoVzxRqqN8VPBgKjRAKImMsy+aFv1A4nkwmprnI+GOjRiqQk8Rspx9Hdb8fNgxzFPVAR1deXKONs331QCMbUaWPNxbNxYiIceEuKTT5TQFiN3svmiQmcncb7Ffu01xX+lKonvv4/qBDV6/oU7r4YOtfEcciBeslTt36/Eg40YIUTbtkrAceD3YQsPu7TYZbV4sRLXEw9kx9i1CFGjAURNZFgx8Zv9A4n0wmrrXbbGh2VTIVlXJoFygn52+fKKBcR37HKileLE/328H1lvJdgEPXzF+W0CP4/3lat5AeeL+8iRQnz1lRCHD0d/GHgMKYm7/UVF4i65voCvyzcAuEcP7aCHCExAes8/PeeVlviz7BxyIF62VLFVZuVKRVd366Yd9M56++qrld/It9/Gj8ixG4gaDSBqvHvRinSMdsX5hFKHqdRdU2gEszDJMVfIKiBofIVNzQpZBcacey5b/FblOnE/fSCKUpbme0slHBM3dsoVL78sxI8/KoHApnLe7MFijq1U7H7jx2xK9P+y8+fnqwVWVu+9F9okZJFfU+955ZRgyljg5KxGs+FTkONs+HTs3VuIGjW0RQ6He7Elh42Kpv+G4pSjEDUFgaiJDFsn/hhcWG0LhAsxQ7KwKVAJOIhLRHcWz6JssW2bUqejVy8hqpQ7U2CbYpQlWtFyMY6Gi1XUXJxjcWGVOtVj9uDXuZSwuq5JEyF++y1mfk295xW7oMw+h2Jt7vfSTY8V8N/ju+8Ud+3w4ULcfbf26c0uLK6Y/MorQqxZgzTySIGo0QCixv0R8FZdWG0JhAujDtlakV7pdjHt05yQk9i0Ub/r+q5Vyp3WFDEd6Rsxlp4UP1ELRcTYdUttsA579iNDRfo3Z4xN6iYrASPnlZnnUKSZRLEQQm646TGbYH8fzgzkODOum3PnnUJUrqwdeHz77UorEC5KCfQBUaMBRI37I+CtvLBGMiEYfo8J6jB91CLd2iAxUSlIxoXwlrz5izhNybG7pdZr9ihdWqSOXOOI9GCj55UZoiLSTCInFJB06k2PmYT6+/AjVzxW//6coMeGRu5x1aWLdkXtCy9UCgf+3//xHBXrb+dcIGo0gKiJHiebxM2+sIb7rhFPIlGqw62fLRdl6WCIgn25oiQdE3PH/Op/kYz1LbVOs4cMZnZQerCdE3akAe9OSKl28k2PXX+fwCXwesBp5MuWKcKH4274psN3+8KFhbj2WiFj2uCq8geiRgOIGu9j1oU1nGCJehIxoA450JCzKh57TCkMFvpCqgQcp1bor73PWN5ShxNV7HKqUatAmrqduivYn4gnITsm7EjcqE5KqXbyTY8ZGO1kHe5nxVMRW2gGDVIsNoHvZ/cV19Dh43nggIhrjkLUFASiJj6I9sIaTrDMmmX9JLJjh+Jz56Jfgb1suPZc6wYHxB00XVSivf4TLW0XqdQj9Gwby1tq/owQBy79+e8NT+pWDTPwEHGmi69rwYoJO5KA93gN1I0Fev8+kV4P/v5biEmTlN99yZIav/vWQrzwgmLFibdKx0cNzN9o0A48RWIiUbt2kb03J4doyBDlMhIIr0tIIBo0iOiff4Lvg7fbuZNo6VL948jOJlq5kmjBAmXZsMH/9apViW68kehf/yLq2JGoXLkKRGnJlPNoS1q6uy5lUjWqRpnUJmUbJb71BlGPHsE/jF/r2lUZYGYmUbVqRG3aKAcukgNmZD8pKcp2vL0vNWsSTZhAmWeu1fWxgW83k7Q0ottuK3gO7NlD9NxzRHPmRH5+hTuMGzfq254PodFjYeUxixd8j7tejFwP6tUjevhhZTl7lmjZMqKvvlKW334jWrFCWZ55RhkLXw86d1auCaVKRfy1vIeIE2CpAWabl/XeTWtx6JCyDde74AJ7gXdlHOD74otC/PJLCN96LO39RoKKOGKSzRxqEAGbPbiiWcC4Y211iIUrx0hXZK3Pt+KYed2NZKEHNeLrgV7rbdeuBa23XBuH08bfekvJvvIicD9pAFEDrDAvG5lEtmxR5nKu0hsYJMgdg1ngcBNqx/vPjQQV/fmnEFdemb9Nz55B2yG7JJbZNFEV7DAG++5BizGaeMyc3JjSCQQLS7NTVHKc3cKFQgwZot2TrWFDIZ54QoilS70jSCFqNICoAXZXkOWFLyxcnKtBg4Lb8mTBhfGWLMnvz+h49Joz+Atx6dXixZX1pUsrbZLDBAPEMpbZzuq4RjNp9PSnivaYOSGLyg1Ea10zU1Tyz4k7kL/+utKTqnDhgnVx+vZVaugcOyZcC0SNBhA18YvRXj/hBMvs2cEnEX5kEcOdrfmCEmgm5iK5Zcu6+E5Yr/Jr1Uo+ypYIlw0R097ar9uVEWksc7RuE92WmjfX2lbYb9Qofd8l2vhvJ2VR2U20NarYs2q3qAw25sOHhZgxQ7H6svXXdz/JyULceKMQ774rxK5dwlVA1GgAUROfGL3z0XvXq7VfblOkNpRWF76wcAn1mTMVQ4Xr74QN+OhSC/cUKWWORSTgjE40ZrhNwopa7qtF26VQi1aJOq1RbKzjmWKFWe42O0Wl3jGfO6dYgbkchFbKeIsWStzehg3Oz6aCqIkjUYOgPnuqswZeoDhUhPu5XHppwc+oV0/pB8R/Dy645ak7Yb1F9KoOFAkJubYIODPdJkFFrVoDiLqb8kWcJiLiqTGlVe42O0SlahUyOubc8804x45VQtwC98GxOY8/rjSydeI1CKImTkQNgvqCE62ICLxA8V3P6tWKO6BRo4L7a95cqSER7K7HaZOYpUX0SpUVKTVybBFwVohFTVErawB1N+2LxDoo2rPnp06h4bSbDL2iMjBTMtIxZ2YqPao6dxaiSJGCRf/69xdiwQLndBmHqIkDUYOgPusv0nxxYPMtZxnUquX/Pg7I69BBiHfeEWLnzji7Ew6TtmNnET2zY1P8JsM314ppdKdIp7aKy8nkL+KknklOE1lW3/Q5TcSZWU4i3eCYjx9X4gTvukuIMmX898X9qrg5J7vPYxloDFHjcVHjtLsMJxKpiOA7ky+/FOKBB5QsJ99tOZGnRw8lNobrzBjBaRfRqPGtO6MuXH8mNdVWAWc0Dd+QJdOCLxJoOeDJxCk9k5wksqy+6WP3sF3nqFmiMpSVxqwxnz2rtGXhJpvVq/vvly06N98sxEcf2V92AqLG46LGcxNkjI/RiRPKRZAzBjjzODDQlzOZuEfLyZMRDOT8LJb96XSRUumUZpxJrIWooViArCwhHnkkf+BVqggxcmTMiuiZ3Y8nop3r/CLBLAfcesMpcXFeaEyp56Yv8IbFCdfQcKKS7yPsHHNOjhArVig1bwIDjfl+5vrrhZg4UYg9e4TlQNR4XNR4ypURw+qffOfTvbsQxYr5r69WTblTWbQoP9DXjBmCYzKUgNNcx9wJG4rL4ihC36vbgw9q2qTtdGVEUuVV9+eb+EXc5C52YvKBkTGZXW/KKaIyli7C3Fwhfv1VEVaXXVbwc6++WqmVk5EhLAGixuOiBpYa86t/1qmjpD4uWxaiLUEkHx7wQdxwMoV2aF607Eb3RMvWGbbXqxuzm+nrrx3jyrC0yqsJXwTuYnsTIvTe9KmntNPcbaEEXKjTkR+ft7jpqgq3Yxg/3r9YuLrccIP5nwdR43FRo9cKwZaGeL9Qsv83sNidurDPmGvI/PyzyXUawsxi2ZQo0ivdLqZ9mhOzO2HdE+133/vXYr/vPqXCl44rcurzG0RKSq4tAs5IlVfDlswofTK4CYmcSCxcRo63G91tWmPmQp+BxT5TbMqE5UJ+b78tRLt2St+6e+4x/zMgajwuaozcncZjivfu3UpWkvoj8z0eVasWjJsx/Ri5YBbTPURqm3+QvvrK8NU2u0YtmQ1lx92jqqc408n0wx+FTwbu4siI1MJl1E3jRHdbJBWNjQg/q8aUlqY01jT7OELUxIGo0Xt3GmtTql1wWvWECUJcc03BHzjXkOGiU3w3YcuP3wWzmO4h0p1C3H+/EEeOuCZoxK7YA72ToQs0riOJ5rh5KZPLia7NbB1ZfGbeLELUxImoUU8udjOZVZTJb8cOv33ZulWIhx8W4qKLCn5n9vVyR2w1cM3WH78LZjHdQ3zlJ+HGoBGrJzUjcR5erAFjB9HeG7jRteSGS02qTlevmQISoiaORI0lJ7aDSxWzSHn1VW0hww3b7r1XuxierT9+F8xi4fsc5YqaNXJCDjFP9476PXyBuhiIOKsmtUiMUvFiOXBiAU2H35vpItj3sNsonBq67qZllzqImjgTNaae2A5yI6j8/bcQ48YpbqRI7wxs9wi5YBZThpgr08wDBU24IWrqXtpRsJWAJQdXP2ZPatEYpeLBcmBFKwMH3xvYcj46pTJydphz38rPh6iJM1Fj2ontIDcCN4zkOJgrrvAfAgf+BvYq0TPEmHiEjMxidt9ScrrXRx+J1BJ9DKeYB9W9gU0fLT24sSHa88grlgOzCGcUdsG9gW4iMYCHu8fkwo12Cb/0KFo5RHs/A1ETZ6LGtDuaGMeCbNkixEsvCdG0acHqldxn6b33lOj6SIYYs7s+PbOY3e4+VoxcDvT8Z2Vf3lykT/5D10QbVvdSjmz+6OeKcuMttXtjwF2DXqOwFyxckRjA9d5jcpCuHcJvmsGWJGZOGRA1cSZqTLujicEVe/Nmpbt1kyYFhUzHjkon2f37zRmiI+/67HT3cXnkl18WomhR5TP4kStocQtyq1LB3XhL7e4YcFdg1CjsZgtXpAZwp9XbSY/AUoOYGgvxuqhhoj6xbbpib9okxJgxQjRuXFDIcDXKDz4Q4p9/Cr6PfxhvvhndEHUfIzuuona6+7iJy6WX5u+bTV9ssbEyFdyKK2uM8WKcRyyIJ3EY6Xc1egNn9SUr22BLEmQ/uVTUOO0OIqrxWHjF3rhRKRLlO6/yUriwEDfeKMSHH4bu/GokjTDcEMMeI7vcQXZc2bn6LzeyUv+mFSsqbcbDlVAOcpB0D3nUImf8ICzAkRY/lxFPbrxIv6sThV+qgZYkZt7PQNTYJGocnPkc8ys2z5kbNggxerQQl1ziv6ukJCFuuklpYXDwoP4hUUAjyMDnpkwqdrqDrLyy8x9g+nSlhLK6H65frmUCM3Biw1LhnTiPWOLECdtp39Wpv7XUIOe+ld3mIWpsEDUOzHyO+RWb59H165Uy9RdfXFDIdO4sxNSpQhw6FImHJtf6OwML3EEhrUJWXdnZrcQBSer7GzQQ4rvvTDuxYalwppXWTTh1wnbad7X6t5Yd4Tls97kPUWOxqHFQ5rN16DxrWcj88osQTz9dsCAeF8Pr0kWITz4J3QMxFHrnfY61ifp4mywywlryzL6ynzypmMbUnHd+ZJ/fN9/ou/oYOLFhqQDREk/iOJrvamURyRSXeBogaiwWNfFkOg0mZLiz9ZNP+jdwVufRrl2VsI1w7YL0wJ2s9Rxr3s5J7iDdljyzruwLFghRr17++9lSw109jVy1DJ7Ylt6twQwSF8STOI7mu5r9c0h1macBosZiURNPQW4qOTlKAs3jjwtRu7b/9+TM4B49lBCOY8fM/dz0N9fqm2ffXCucolYNW/Kiudpt2yZEt27576tRQ3Fuz5lj/KrllBPbTbeQHiDW+jHWn2/nGJ3wXbNd6GmwXNS88847onbt2qJIkSKiZcuW4qefQje9mzVrlmjQoIHc/tJLLxUL+K7Sh9TUVNGxY0dRvnx5OfC1awtOUG3btpWv+S4DBgxwtKXGFJdIDOGx//CDEI8+WvBHUKKEED17KvPniRMWjuHT6bLibWAp/wLF3j6dbsKHmeMOikgbGb3anTqlFPgpViw/H/7f/1ZUpdWFMThoyqorsttuIV0O9GP8HaN0F3oaLBU1M2bMEMnJyeKjjz4Sv//+u+jfv78oW7as2Ldvn+b2y5YtE4mJiWL8+PFi48aNYtSoUSIpKUls4NSY83zyySfi+eefFx988EFIUcOflZmZmbcYEShWxNToSWtz28nP9dm+/VaIhx4SokoV/+9SqpQQvXsr3ycry6YBpafLsvtqCf6gZfnN+gWa4A6y3OAxb56/q+naa5VUM6vTLaw+ud14C+lioB/j8xhNc4hB1jGihi0zgwYNynuek5MjqlevLsZyox4NevbsKTpz2osPrVq10rSyZGRkhBQ1Q4YMEU7Lfgp3/XfDyX/6tBDz5ysdrsuX9x9/2bJC9OunzKNsHLCd8xNdKvUo2KOItsv1pk90UTr6LbsT+uMPJYVM3UH16sqVJ7DmjBVll+04ud14C+lSoB/j9xilu/BnZpmoOXPmjLS6zJ0712993759xS233KL5npo1a4o32Q/jw7PPPiuacF18g6KmYsWKokKFCqJRo0biqaeeElkGzAV21akx8+S30v/KLiMOu+jVS7HA+I6X67M98IAQX3/Nf3MRe85PtNmUKMvvc7VafuTnlinGKA6+6emqfM4OH67kxfMO+PGJJ4IHMEV71eJ6NDVqBRzrQtZf2d14C+lS3Dix2Y1Xj1G2C9PpLRM1u3fvljtevny53/rhw4dLC44W7GqaFnARmjhxoqhcubIhUfP++++Lr7/+Wvz666/i008/FTVq1BDdu3cPOtbTp0/LA6AuO3futKyicLSl++3y43J9GE6v5rhStf2P700/G+C4nImBVkD24bI0CVOSmjg6mysU+voBufwyN8yy8KqlHGr/ukBsJQvafdusK7tXZxEHAv0Y38co1WXp9J4UNYEsXrxYbvvXX39pvj569OgCgcVW9X4y++Q304+7Z48Q776rZPhySwLf/dWtq8SW8p+T50/H44TUAbt02NKlQjRvnv9GLgLEPsJw7Q2ivGoFPfd845esurK78RbSpUA/hsfrxyjVRfeJnnQ/BXLixAm5LVtvYmmpMfvkN8OPyzrv1VeFaN264PzAvZeefVaIdev0z48gcuGVfSbbmA7bulWI22/P/4Oxb5A7aUfiBzR41Qp77qmZZlquKAcFaoPwQD+GJx6OUbZL7hMtDxQePHiwX6Awu4JCBQrffPPNfutat25tOFA4kB9//FFuu57r8se4S7eZJ38kAonFyZo1SqZtYMNIXtiIxn+ecF4LECXR+Az5vBwxIr8acKFCQvTvL8TevbZdtXSfe9TW2iu7m24hXQz0Y3hwjOIkpZvrzUydOlWmaD/44IMypXvv+Ytvnz59ZBCvb0p34cKFxWuvvSY2bdok3UKBKd0HDx6UQobr1/DA+TP4OadtM+xiGjNmjFi9erUUPp9//rmoV6+euJZTWXVipagx8+TX68ri2JjFi4V45BEhatXyf41Lllx3nVJQdudOYStuUf6mE6nPkHPoJ00SolKl/Pdcf73SRMtmdLtR6U7rr+xxeyLZC/RjeHCM4qD43ttvvy1q1aol69Ww5WblypV+WUr9OAc4oPhe/fr15facuRRYfG/KlCma8S8sgJgdO3ZIAcPF+VhQXXjhhTKOJ1Z1aqw8+fXeLRcvXvA5V/VlsaOn87UVeK1IlW4i8Rmyee3zz5Vmk+p29esr62LkFzRsqTHryg4BE1Nw+K05Rjiu5oE2CTESNWacyEbqn7GHgi0yPA9yL8NY4sUiVbox6jPkm4C2bf1z6NmsxlabGBLejZoralY6pVRvNusqbbUSxswCYkDc3uBZBERNDEVNtPBN+uuv65sjVdEQ6x+KV4tUme63ee01IW69Nf8559VzHI0ZnT/dGENgtRLGzAJiQFzf4Dlg/k7gfygOOHbsGJUpU4aOHj1KpUuXJidx+jTRkiVE8+Ypy86d+t+bkECUkkKUkUGUmEgxgcfevn347dLTidq1I/eSk0O0dClRZiZRtWpEbdooB13vAShUiCg3V/mj3XMP0fPPE9WsSU4jLY1oyBCiXbvy1/EwJ0wg6tHDxGNZp47/h5h5YvOXuO02ZT4J3C8zZ46JXwYAe07reOWYgfm7sG2jAn7s3Uv05ZdE8+cTLVxIlJWV/1qxYkQdOxLdfLMyf44eHXw/fM1mEcRzbVDBEGwyNgnerZnbORKtmZ6vTm+9RdS1q/L/3bsLTqK+sKDhP+rYsUSXXhr68yz+m4WC53r+SpZ+PO882JVf94kd4tjx30rrb8HreGYZOlT5kphZgEtOa6APiBqb4Pnsl1+IFixQhMzq1f6vV6+uzHdduhBdf70ibJjp06MUDKEmY5PuVHnSM3M7xxHsrp9FDK/nu34+nvx/njC1JtP69Yk++IDo2mv1fZ7Ff7Nw8Fxv6UXXSiWMmQXEiLi4wXM4EDUWcvQo0bffKhaZr75SrDO+NG+eL2QuvzzfMm6aYNAzGUc5SfJNMS/lyxMdOhTa5Mp3+5ZjtoVD710/25M/+4zo4YeVP7xKUhLR448Tvfyy9h84Bn8zR2ClEsbMAmKE52/w3ICIE+wIFOYg319/FeKVV4Ro165gW4KSJZW06w8/FOJ8CR7rCvvZEL2rp6GnrcFxVgSG6s1sevRRpYGW+pzbgIwcaSyjKZ4irq0s1+r1+vbAscRDFeJYgOwnG0UNN0pOS1O6WmvNR1yGZNgwIRYt4tYNNmakWHxhDxbhH7jYVqTKqpQDvZlNvl948uTI0rPjbTKONtUqWLo2ZhYQQ1CF2HwgamwUNVOm+J+4nKX7r38J8Z//KD2YYlbYz8IWs+EMCryUL68IOVvmDSstHHqFRoUK3Kk1cuVq5G/GbUrMrLkSy1oukVasDGeVw8wCYgiqEJsLRI2NoobdSFwIlr0PX30VeRE8PfOKobnHwrt+xxkUrByQnmqIZcsKcfy4fd9DaxJ3cy0Xo6JKr1UOMwuIIaj7aB4QNS4rvmfJvGKhCd5CI1BkWD2gcPs3s/qt3nLSZlgd3FglzKhVDjMLAHE1fxeKdaByvKMmuwRmoKrJLvx6RHDGD6cAM4FZN+pzrqZ2PjOIk3y4hhynkPMjP3dNhL9VAzp2jOiVV5TsJy04pYsL6J05E/6gRfs304KncYazr4x+drisrkj3azVG0rV9c9N79VIeUZcGAE+DisJerz6ZlkY5jw6jpbvrUiZVo2qUSVfV2EHLH5xKmRddK+f5AweIhg3TXxZFHXewWnORjDuqTGyzB7RvH9F//kM0cWJ+enbdukRPPEFUrx7RwYNEf/6p1J2xopaMVp0as8s1u7UMNKvu3r3DbzdtmiJkAADxNX+LOMGJ7ic7YlMU11au3/4SE3Oj9mwYisMM4wIwxf1mRmDo1q1CDByoRHur77/4YqX1+blz9rpt1GPGQcFWuNYc50N0a0AXAMBqEFPjElFj9byiN+1ab3iC1v7DxmGGUSym6oNIA0N//lmIO+5Q2p6r72vZUsnVz8mJbS0ZqyZxt4oDpGsDEHcchahxh6ixI2knUkGj9/Ozz2SL9DfXimmDl8lHfp5HGMWSPSvVfH2gNzCUxcr8+UqVRN8PbdxYiDfe8LfMxFIMWDWJu1kcIF0bgLjiKESNO0SNE4qqRmUpCmWF0aGq0kt1sd9YkJUlxPvvC9GwYf4HJCYKUby49vdwgtvGqknczeIA6doAxA1Hkf3kDgwmKBnCzLY2IftKBUvbeumlsIGumcdL2PNdOJB49myibt2ULzNgANGmTUSlShHdcovy+smT+tLPYpH6xYHH3POpRg3/9RyYHE0vKKv2awc8tm3blEBmDgrmRw4Ed/KYAQCWg+wnB6CV7FKzpiJoIr1G601uCUXQpCE9aVvlygXvcKmOkdpSe1piXQIOn9pjxxK9+CLRqVP56/nL9O1L9NprRJddZiz9zIrUr1g167R6vwAAYPP8DVETA7TmEMbs5tKh5t5wqJYizRt2MxQTj5EKUR3aRrupBgkqaDRMoFxKqXCaMvYVN3YsWMDMmKGIma1bg3/B554jGj2aDKsq1UrF+B7ckAcNAACA1fM33E82w/Mhiw3WBFxugx/5+eefm1sjLHQdt0CVk1tgXUgPhF5/UPnyIYvIJVIuvUVD8gSML+rzCTSUEklnATiuHfPvfyuDv+++4IJGRT1A4Qj8vm522wAAgIeBqPFC9eAgBJt7A0VCTdpFs6gnpT//g77wBL3xImol3hDCpgfNpTl0G9Wg3X7rU2iXXN/j4Af51WG1OHdOOXA33EBUvz7R668rbq8qVUKPjS0sYdxjIb8vYjoAAMBxwP1kBzk5lLNkKdXp2YJ2HSou7RC2h2IsyaHMnkOo2qHf6CpaRsvp6rwKw21oKSUmCP0DMBJXwiYoHdVx2RW1lNr4j0m13mhVh2UrzH//SzRlCtHevfmf+69/ET38sFIJ+O679VmTDh+2Pz4GAACALlBR2Ekp3edTT9Oprf3py1bWVzGSDszp3YsWCVG+fGQ55eqYTp0SYsYMIa6/3v/1SpWEeOoppSKw0e/7/PPuTWsGAIA44ChSup3nb2ILhN2p2BHtWO92wXxb/JwDcH2bPLKV4/rrlV5JbP3Q06zR11JSvDjR4MFE1asT3Xkn0eLFymvscuJUbbYCcZYT92dS4Uhrfm+wz+L1nGI2ciTiYwAAwCMUjvUAPEtAF2R2qcS0s7UV9VV4wu/aNT9tS23y6JtR5NvkURVCeps18rFjQdSqlf/++vUjeuABxQUWLlKaRSULGK0sJbUIUOD3QFozAAC4EsTUWIVP2jPHi3BNlp40mw5ROc34bMvDN6yur6JapQL3rZXmHJjTrtUm3JciRYi6dye6917F4mNkfFYUAQIAAODI+RuWGqs478ZJo+40hN6iXVTT50We+BNMqx6sCyOWC6P12AKsUn7wOt7/0KGKNYR3wota94WzlxYtImrbVhEgvkXyWrcm6tNHcTlxMb9IgBUGAADiBogaq6hWTQqa22hOgaowgbCBxBbDQTD3T8AAtIwbvl6kArBgCOVOYmGzc6eyHYsZFkHLlikF8mbNIjp4MH9bjothIcOZSxddZMrX9hNRAAAAPAvcTxaRczaH6hTfR7tyqgYpB5RL5ROO0KxvylC76xLtNRyEMMMY8SLlMX26UkkwHM88o6RP807UNGymcmWinj2VtG22zugNJEZ5fwAA8DzH4H6KPUuXJ9KunOohtihEh0R5SkyKwTwcxHJh1ItkOLj4hRfy/1+2rNJgUi2rXNjgqWjYnAQAAMDrQNS4JIPaDsuEUS9SgfTpcI2mypRRAn5vv52oQwei5OTIBhrMnKSWZg6Xig0LDwAAeBLUqXFLBnWwplEm9laIWIjt20fUuXNoQcP1YPbvVyoA33RT5IImnDmJYXMSbxej4wgAACA2QNRYhN7ab2qHbic0jdItxCrnEK1YocTINGumFK57/33tjfkgpKYqHbONCBkWJZwWz/E6ahE/o+akWDffAgAAYCsIFLYQdQ5ltDKo/bwkwVwian2ZYBO5iQVuwpayIUEpRf6hjMIXUWLWMf8xcIG8Ll0Uiw03iuRA4EhdO6HiZbhSsZ6g5MB+UTYeRwAAAOaBQGGHoDODOvQkzg0XIwp0ibaUjeAGSHmvJZxvLjnhzEOUeOa8oClWTKnsy66lcF2xzYqX4RYMkZidIg4YAgAA4BbgfrIYFi7bthGlpyvGA35kY4CfoAnlEuEu13pgF4+vm8YoJ08Sffcd9Vj7DM25aATVEP7jSaFdNIduox40N3/l6dNE77yj1JwxAz3xMtyGIRK/niWR2wAAAJwE3E+xRI9LpGJFon/+0b9PvWnNR48qcTHff0/0ww9EP/+sVPdVh0aFaGn1OymzfluqtmY+tTm+gBLPW2ssc9v4tJYIyfPP51tswvr1DO6bVScsNQAA4BjgfnILelwiLGgqVVL6I+nRn1ppzfy+rVuJli9XrCr8+NtvIfeXWLUytXv7VsX91X6ePW4bvVYSrjSsy69nIO1cFWe6IrcBAAA4EYiaWKJ3Er/rLsX6EtizSQv19QEDiNavVywwq1b5tyJQqVePqHZtxTpBGmnaLI5YONjltjGSB88CykhPJ4O9rwAAALgPuJ9iiRGXCGcUBVomjMDp1FdcQXT11URXXaUsbAEyy/1lhtvG6k7iDLp2AwCAZ+dviJpYYmQS56BcdhnNnUv0zTdE69aF3/811yg9lTjd+rLLiIoUiUxUhXJ/mZ0KbSgPPkJQURgAAFwDYmrcQiiXCMPPudkjx5CwaDAK91oKZT2J1v1lhdtGdx58FKBrNwAAeBJYauyGM4w4sHb7dkWo/P23YjEJyD4KajG59FKiSy5R8sO547UWeq0n0bq/rHTbwJoCAACAYKmJHSdOKJV0eeHJmN1KLALUZccOZV2uRmq0ryDhQnZNmhBdfDFRgwaKiGnUSBE1KtddF9pNo8d6YiQjiPdlJDA3WmBNAQAAYBCImmhZtIjooYcUIZOVpe89HNvCsTSceXTBBUQXXpj/yBlJXKnXDjeN0YwgCA0AAAAOBqImWgoXVlxIKiVKEFWtqiwsMLjZo/pYq5YiZjhOppAJxZxZuERrPbEjhgUAAACwAcTURL9jog0bFBHDbqOSJcmVIIYFAACAA0FMjZ3wAebaL24HriUAAAAuBw0tAQAAAOAJIGoAAAAA4AkgagAAAADgCSBqAAAAAOAJIGoAAAAA4AmQ/eQ1kJoNAAAgToGo8RLc4VqriB5XDUYRPQAAAB4H7qdYWVO4meT06cojPzdD0HC7A19Bw3BfJ17PrwMAAAAeBhWF7Xb3GLGm6N03b8ftFwIFjdGu3QAAAICL529YaqKBBQqLifbtiXr3Vh75eTCriBFripF9s/AJJmgY1q07dyrbAQAAAB4FosYudw9bU9hCo2UYU9cNHapsZ3TfbMnRg97tAAAAABcCURMJRgSKUWsKx9gY3Te7pvSgdzsAAADAhUDUREIk7h69VhIWNUb3zbE2HDPDsTNa8PqaNZXtAAAAAI8CURMJkbh7zLaS+O6bg3850JgJFDbq8wkTECQMAADA00DUREIk7h691pR27SIbA2dOzZlDVKOG/3r+TF6POjUAAAA8DlK6I0FNoebAXa3DFyyFWg0AZnzfpwodFh9du0a2b9+xoaIwAAAAj2B5SvfEiROpTp06VLRoUWrVqhWtWrUq5PazZ8+miy++WG7fuHFj+vLLL/1eT0tLoxtuuIEqVKhACQkJtG7dugL7OH36NA0aNEhuU7JkSbr11ltp3759FBNCuXsYFiO33qqIC9+AXj3WlGhdSbyerT29eimPEDQAAADiBMOiZubMmfTYY4/R6NGj6ZdffqHLLruMOnXqRPv379fcfvny5dSrVy+6//77ae3atdStWze5/Pbbb3nbZGVl0TXXXEOvvPJK0M8dNmwYzZs3Twqk77//nvbs2UM9YulSCSZQVBHBwkOrtgy/b9s2ovR0omnTlEe2uvh+F7iSAAAAAOvdT2yZadGiBb3zzjvyeW5uLtWsWZMeeeQReuqppwpsf8cdd0jRMn/+/Lx1V155JTVt2pTee+89v223bdtGdevWleKHX1dhk1OlSpVo2rRpdNt5983mzZupYcOGtGLFCrm/mFcU/vxzRcgE4utaMipG4EoCAAAQ5xyzyv109uxZWrNmDXXo0CF/B4UKyecsLrTg9b7bM2zZCba9FvyZ586d89sPu7Nq1aplaD+WwCKDxQaLFi2C1ZbRu2+4kgAAAABdGBI1Bw4coJycHKpSpYrfen6+d+9ezffweiPbB9tHcnIylS1bVvd+zpw5I9Wd72IZaFMAAAAAxBzPpnSPHTtWmqvUhV1kloE2BQAAAIC7RE3FihUpMTGxQNYRP69atarme3i9ke2D7YNdX0eOHNG9nxEjRkj/m7rsZEuJVaBNAQAAAOAuUcMuoGbNmtHixYvz1nGgMD9v3bq15nt4ve/2zLfffht0ey34M5OSkvz2s2XLFtqxY0fQ/RQpUkQGFPkuloE2BQAAAEDMKWz0DZzO3a9fP2revDm1bNmSJkyYILOb7r33Xvl63759qUaNGtL9wwwZMoTatm1Lr7/+OnXu3JlmzJhBq1evpsmTJ+ft89ChQ1KgcJq2KlgYtsLwwu4jTgnnzy5fvrwUKJxtxYJGT+aT5ai1ZTgziwWMVmE9tCkAAAAArEVEwNtvvy1q1aolkpOTRcuWLcXKlSvzXmvbtq3o16+f3/azZs0S9evXl9s3atRILFiwwO/1KVOmsAoosIwePTpvm1OnTomBAweKcuXKieLFi4vu3buLzMxM3WM+evSo3Cc/WkZqqhApKSxp8peaNZX1AAAAADCMkfkbbRLMBrVlAAAAgJjM34bdT0BnbRkAAAAA2IpnU7oBAAAAEF9A1AAAAADAE0DUAAAAAMATQNQAAAAAwBNA1AAAAADAE0DUAAAAAMATQNQAAAAAwBNA1AAAAADAE0DUAAAAAMATxE1FYbUbBJdbBgAAAIA7UOdtPV2d4kbUHD9+XD7WrFkz1kMBAAAAQATzOPeACkXcNLTMzc2lPXv2UKlSpSghIcF0FcliaefOndY2ywQ41jaCY20fONb2gWPtvmPNMoUFTfXq1alQodBRM3FjqeEDkZKSYuln8B8NPxJ7wLG2Dxxr+8Cxtg8ca3cd63AWGhUECgMAAADAE0DUAAAAAMATQNSYQJEiRWj06NHyEVgLjrV94FjbB461feBYe/tYx02gMAAAAAC8DSw1AAAAAPAEEDUAAAAA8AQQNQAAAADwBBA1AAAAAPAEEDU6mThxItWpU4eKFi1KrVq1olWrVoXcfvbs2XTxxRfL7Rs3bkxffvmlbWONp2P9wQcfUJs2bahcuXJy6dChQ9i/DYj8vFaZMWOGrMzdrVs3y8cYr8f6yJEjNGjQIKpWrZrMHqlfvz6uIxYd6wkTJlCDBg2oWLFisgLusGHD6PTp07aN16388MMP1KVLF1npl68H//d//xf2PUuWLKErrrhCntMXXnghTZ061dxBcfYTCM2MGTNEcnKy+Oijj8Tvv/8u+vfvL8qWLSv27dunuf2yZctEYmKiGD9+vNi4caMYNWqUSEpKEhs2bLB97F4/1r179xYTJ04Ua9euFZs2bRL33HOPKFOmjNi1a5ftY/f6sVbJyMgQNWrUEG3atBFdu3a1bbzxdKzPnDkjmjdvLm666Sbx448/ymO+ZMkSsW7dOtvH7vVj/dlnn4kiRYrIRz7O33zzjahWrZoYNmyY7WN3G19++aUYOXKkSEtL4yxqMXfu3JDbb926VRQvXlw89thjcm58++235Vz59ddfmzYmiBodtGzZUgwaNCjveU5OjqhevboYO3as5vY9e/YUnTt39lvXqlUrMWDAAMvHGm/HOpDs7GxRqlQp8fHHH1s4yvg91nx8r7rqKvHf//5X9OvXD6LGomP97rvvinr16omzZ8/aOMr4PNa87XXXXee3jifdq6++2vKxegnSIWqeeOIJ0ahRI791d9xxh+jUqZNp44D7KQxnz56lNWvWSLeGbx8pfr5ixQrN9/B63+2ZTp06Bd0eRH6sAzl58iSdO3eOypcvb+FI4/dYjxkzhipXrkz333+/TSONz2P9xRdfUOvWraX7qUqVKnTppZfSyy+/TDk5OTaOPD6O9VVXXSXfo7qotm7dKt18N910k23jjhdW2DA3xk1Dy0g5cOCAvJDwhcUXfr5582bN9+zdu1dze14PzD3WgTz55JPSvxv4wwHRH+sff/yRPvzwQ1q3bp1No4zfY80T63fffUd33XWXnGD/+usvGjhwoBTsXKEVmHese/fuLd93zTXXyG7Q2dnZ9NBDD9HTTz9t06jjh71B5kbu5n3q1CkZ0xQtsNQAzzBu3DgZwDp37lwZIAjM4/jx49SnTx8ZmF2xYsVYD8fz5ObmSovY5MmTqVmzZnTHHXfQyJEj6b333ov10DwHB66yFWzSpEn0yy+/UFpaGi1YsIBeeOGFWA8NRAAsNWHgC3hiYiLt27fPbz0/r1q1quZ7eL2R7UHkx1rltddek6Jm0aJF1KRJE4tHGn/H+u+//6Zt27bJTAffiZcpXLgwbdmyhS644AIbRh4f5zVnPCUlJcn3qTRs2FDe6bKLJTk52fJxx8uxfuaZZ6Rgf+CBB+RzzlbNysqiBx98UApJdl8Bcwg2N5YuXdoUKw2Dv1YY+OLBd0qLFy/2u5jzc/Z5a8Hrfbdnvv3226Dbg8iPNTN+/Hh5V/X1119T8+bNbRptfB1rLk+wYcMG6XpSl1tuuYXat28v/89psMC88/rqq6+WLidVODJ//PGHFDsQNOYea47DCxQuqphEa0RzsWVuNC3k2OMpgpzyN3XqVJmG9uCDD8oUwb1798rX+/TpI5566im/lO7ChQuL1157TaYZjx49GindFh3rcePGyfTNOXPmiMzMzLzl+PHjMfwW3jzWgSD7ybpjvWPHDpnFN3jwYLFlyxYxf/58UblyZfHiiy/G8Ft481jz9ZmP9fTp02XK8cKFC8UFF1wgs1hBaPg6y+U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" ] @@ -793,7 +578,7 @@ }, { "cell_type": "code", - "execution_count": 232, + "execution_count": 52, "id": "df66e9a5-409b-4014-911e-c8880f081a7c", "metadata": {}, "outputs": [ @@ -801,12 +586,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "score: 0.9327125659537808\n" + "score: 0.8251845288722951\n" ] }, { "data": { - "image/png": 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", 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", 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" ] @@ -843,7 +628,7 @@ }, { "cell_type": "code", - "execution_count": 246, + "execution_count": 53, "id": "aed94e25-bbcc-473e-92f2-53b5ef265fa4", "metadata": {}, "outputs": [], @@ -876,7 +661,7 @@ }, { "cell_type": "code", - "execution_count": 247, + "execution_count": 54, "id": "d0936803-5081-44b5-9a13-2e46e05a819b", "metadata": {}, "outputs": [], @@ -901,7 +686,7 @@ }, { "cell_type": "code", - "execution_count": 248, + "execution_count": 55, "id": "b8d8628e-d9fd-4aff-b06a-f1db1df1c531", "metadata": {}, "outputs": [ @@ -909,12 +694,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "score: 0.9105234598498793\n" + "score: 0.7968219718898861\n" ] }, { "data": { - "image/png": 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", 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z5gm=5FFYj<6-*}MK-Sxt;g5B8o#SSFIZnX7OKo?XJ5lh0ofR4sV`4_lO$^G327mnb jA2_!E|M!2`1Hjs}=1wl|PL@_=A`o#hE-po_+hqR>Aq#$0 literal 0 HcmV?d00001 From 26178cc43ecbd8d497ef8efaffcf4664a8b86e8a Mon Sep 17 00:00:00 2001 From: Anastasiia Andriievska <79667606+fomalhautn@users.noreply.github.com> Date: Fri, 24 Oct 2025 14:40:44 +0200 Subject: [PATCH 4/8] current updated tutorial without execution on Quantum --- content/QKE_AA.ipynb | 2835 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 2835 insertions(+) create mode 100644 content/QKE_AA.ipynb diff --git a/content/QKE_AA.ipynb b/content/QKE_AA.ipynb new file mode 100644 index 0000000..06ef0d2 --- /dev/null +++ b/content/QKE_AA.ipynb @@ -0,0 +1,2835 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e4b10801-19d8-4751-8e31-a9bfd2df03d1", + "metadata": { + "id": "e4b10801-19d8-4751-8e31-a9bfd2df03d1" + }, + "source": [ + "# Tutorial - Quantum kernel estimation with application to disability insurance\n", + "\n", + "B. Djehiche and B. Löfdahl – KTH, Department of Mathematics / SEB –\n", + "Risks 2021, 9(12), 216; https://doi.org/10.3390/risks9120216\n", + "\n", + "Hands-on assistance: [Anastasiia Andriievska](https://www.linkedin.com/in/aandriievska/)" + ] + }, + { + "cell_type": "code", + "source": [ + "!pip install qrisp==0.7.9 pandas numpy matplotlib scikit-learn sympy" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "YWc5tpIJbric", + "outputId": "efec0699-82c6-47d6-9d37-58ae5e24b10d" + }, + "id": "YWc5tpIJbric", + "execution_count": 1, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Collecting qrisp==0.7.9\n", + " Downloading qrisp-0.7.9-py3-none-any.whl.metadata (7.0 kB)\n", + "Requirement already satisfied: pandas in /usr/local/lib/python3.12/dist-packages (2.2.2)\n", + "Requirement already satisfied: numpy in /usr/local/lib/python3.12/dist-packages (2.0.2)\n", + "Requirement already satisfied: matplotlib in 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jax\n", + " Found existing installation: jax 0.7.2\n", + " Uninstalling jax-0.7.2:\n", + " Successfully uninstalled jax-0.7.2\n", + "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n", + "torch 2.8.0+cu126 requires sympy>=1.13.3, but you have sympy 1.13.0 which is incompatible.\u001b[0m\u001b[31m\n", + "\u001b[0mSuccessfully installed jax-0.6.0 jaxlib-0.6.0 qiskit-2.2.2 qrisp-0.7.9 rustworkx-0.17.1 stevedore-5.5.0 sympy-1.13.0 tdqm-0.0.1 waitress-3.0.2\n" + ] + } + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "b6f8b962-5fde-46f8-af33-dda094485734", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "b6f8b962-5fde-46f8-af33-dda094485734", + "outputId": "e4bc7ea9-0e86-4c20-ba97-38a87027d057" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "/usr/local/lib/python3.12/dist-packages/jaxlib/plugin_support.py:71: RuntimeWarning: JAX plugin jax_cuda12_plugin version 0.7.2 is installed, but it is not compatible with the installed jaxlib version 0.6.0, so it will not be used.\n", + " warnings.warn(\n" + ] + } + ], + "source": [ + "# install necessary packages via pip\n", + "\n", + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.svm import SVR\n", + "from copy import copy\n", + "from qrisp import QuantumVariable, QuantumCircuit\n", + "from sympy import symbols" + ] + }, + { + "cell_type": "markdown", + "id": "d9224010-d6e9-4d8a-a391-cd5350418491", + "metadata": { + "id": "d9224010-d6e9-4d8a-a391-cd5350418491" + }, + "source": [ + "First, we create some synthetic data. The x-variable holds the available data. x[i][0] represents gender (0 or 1). x[i][1] represents age, normalized to the [0,1] interval. The y-variable is the value that we seek to model. It represents the logistic transition probability between two states. The w-variable represents the weight that we assign to each data point." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "168cfc3c-d7ba-4b88-b60a-7cbd67738d83", + "metadata": { + "id": "168cfc3c-d7ba-4b88-b60a-7cbd67738d83" + }, + "outputs": [], + "source": [ + "# Set random seed for reproducibility\n", + "np.random.seed(42)\n", + "\n", + "# Number of samples per gender\n", + "nsamp = 100\n", + "\n", + "# Create feature matrix: gender (0 or 1), normalized age [0, 1]\n", + "x = np.array([[0.0, i/nsamp] for i in range(nsamp)] + [[1.0, i/nsamp] for i in range(nsamp)])\n", + "\n", + "# Generate target values with noise\n", + "y = np.array([\n", + " -4.5 + 0.2*a[0]*(1 - 5*a[1]**2) + a[1]*(1 + a[0]*0.2) + 0.1*np.random.normal()\n", + " for a in x\n", + "])\n", + "\n", + "# Logistic transformation\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# Population size based on age\n", + "n = [\n", + " int(2000 + 6000*xj[1]/0.7) if xj[1] <= 0.7 else int(8000 - 3000*(xj[1] - 0.7)/0.3)\n", + " for xj in x\n", + "]\n", + "\n", + "# Weighted transitions\n", + "d = [nj * pj for nj, pj in zip(n, p)]" + ] + }, + { + "cell_type": "markdown", + "id": "6404a54d-b5d7-4395-96ab-d4bb9f75df61", + "metadata": { + "id": "6404a54d-b5d7-4395-96ab-d4bb9f75df61" + }, + "source": [ + "We can use the Pandas library to create a DataFrame and then save it as a CSV file, which support column headers. This will create a CSV file with each column labeled as ‘gender’, ‘age group (normalized)’, ‘population size’, and ‘number of transitions’ respectively. The index=False argument is used to prevent pandas from writing row indices into the file." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "98b3d891-41c2-4ead-90dd-a8419e79809e", + "metadata": { + "id": "98b3d891-41c2-4ead-90dd-a8419e79809e" + }, + "outputs": [], + "source": [ + "# Create a DataFrame\n", + "df = pd.DataFrame({\n", + " 'gender': [a[0] for a in x],\n", + " 'age group (normalized)': [a[1] for a in x],\n", + " 'population size': n,\n", + " 'number of transitions': [int(round(a)) for a in d]\n", + "})\n", + "\n", + "# Write the DataFrame to a CSV file\n", + "df.to_csv('fdata.csv', index=False) # index=False argument is used to prevent pandas from writing row indices into the CSV file" + ] + }, + { + "cell_type": "markdown", + "id": "79a2034c-1509-44c2-9fdb-ed63b301a727", + "metadata": { + "id": "79a2034c-1509-44c2-9fdb-ed63b301a727" + }, + "source": [ + "One can read the data back from the file like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "0da27f10-d9b1-4c75-afcd-cf69122586a6", + "metadata": { + "id": "0da27f10-d9b1-4c75-afcd-cf69122586a6" + }, + "outputs": [], + "source": [ + "data = pd.read_csv('fdata.csv')" + ] + }, + { + "cell_type": "markdown", + "id": "e0d5741f-c5fb-4fb8-84a2-da56f6fa2ae9", + "metadata": { + "id": "e0d5741f-c5fb-4fb8-84a2-da56f6fa2ae9" + }, + "source": [ + "### Transform and inspect data" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "84552a98-075b-48de-b7a9-68e018e95e83", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "84552a98-075b-48de-b7a9-68e018e95e83", + "outputId": "859c109d-3ab3-4a3c-b673-355c8b43a60b" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "[[0. 0. ]\n", + " [0. 0.01]\n", + " [0. 0.02]\n", + " [0. 0.03]\n", + " [0. 0.04]\n", + " [0. 0.05]\n", + " [0. 0.06]\n", + " [0. 0.07]\n", + " [0. 0.08]\n", + " [0. 0.09]]\n" + ] + } + ], + "source": [ + "x = np.array( [[a,b] for a,b in zip(data['gender'], data['age group (normalized)'])] )\n", + "print(x[0:10])" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "5bfef017-385e-47c0-8b46-89a280406102", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "5bfef017-385e-47c0-8b46-89a280406102", + "outputId": "846425a9-d74d-4427-a528-d2d8d9191bf4" + }, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-4.45032858, -4.50382643, -4.41523115, -4.31769701, -4.48341534,\n", + " -4.4734137 , -4.28207872, -4.35325653, -4.46694744, -4.355744 ])" + ] + }, + "metadata": {}, + "execution_count": 7 + } + ], + "source": [ + "y[0:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "e7447d0f-64e9-4d56-8a41-299cdd3b044e", + "metadata": { + "id": "e7447d0f-64e9-4d56-8a41-299cdd3b044e" + }, + "outputs": [], + "source": [ + "# raw transition frequency per group, used for plots\n", + "p_raw = [a/b for a,b in zip(d,n)]\n", + "\n", + "# logistic probability, used as input to SVR optimization\n", + "y = np.array([np.log( p / (1-p) ) for p in p_raw])\n", + "\n", + "# calculate weights for SVR based on population size\n", + "w = np.array([1./nj for nj in n])\n", + "\n", + "# normalize weights (equivalent to changing the hyperparameters of the SVR)\n", + "w = w/sum(w)*len(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "0fe05211-ed34-463f-81ea-37069c0fd93f", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 468 + }, + "id": "0fe05211-ed34-463f-81ea-37069c0fd93f", + "outputId": "6b8f90cb-61bc-4b51-e8da-375034d03537" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "

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\n" + }, + "metadata": {} + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "axs.plot([xj[1] for xj,p in zip(x, p_raw) if xj[0] == 0], [p for xj,p in zip(x, p_raw) if xj[0] == 0], 'or')\n", + "axs.plot([xj[1] for xj,p in zip(x, p_raw) if xj[0] == 1], [p for xj,p in zip(x, p_raw) if xj[0] == 1], 'ob')\n", + "axs.set_title(\"raw transition frequencies\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cd869a15-a44e-406c-9ef7-22009f1f4bd0", + "metadata": { + "id": "cd869a15-a44e-406c-9ef7-22009f1f4bd0" + }, + "source": [ + "The first step of the modelling is to define the mapping from data space to our quantum feature space. This is done by setting up the build_feature_map function. The circuit below is a very simplified two-variable circuit. Feel free to experiment!" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "f6546726-7f76-4f7d-992c-95ee972abf17", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "f6546726-7f76-4f7d-992c-95ee972abf17", + "outputId": "dff222f3-4d86-435c-b11e-defffd550a33" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "QuantumCircuit:\n", + "---------------\n", + " ┌──────────┐\n", + "q.0: ┤ Ry(π*x0) ├\n", + " ├──────────┤\n", + "q.1: ┤ Ry(π*x1) ├\n", + " └──────────┘\n", + "Live QuantumVariables:\n", + "----------------------\n", + "QuantumVariable q\n" + ] + } + ], + "source": [ + "from qrisp import ry\n", + "\n", + "# Define a simple feature map using Ry rotations\n", + "def build_feature_map(sym):\n", + " n = 2 # Number of qubits\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n)) # Create symbolic parameters: x:0, x:1\n", + " ry(np.pi * params[0], q[0]) # Apply Ry rotation to qubit 0\n", + " ry(np.pi * params[1], q[1]) # Apply Ry rotation to qubit 1\n", + " return q\n", + "\n", + "# Build the feature map\n", + "feature_map = build_feature_map('x')\n", + "\n", + "# Inspect the quantum state\n", + "print(feature_map.qs)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "2c128f3c-da92-4dd2-b94d-27dd25970626", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "2c128f3c-da92-4dd2-b94d-27dd25970626", + "outputId": "ae3bcf0e-c252-4faa-bc39-b81fa3c542ad" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + " ┌────────────┐\n", + "q.0: ┤ Ry(2.3272) ├\n", + " ├────────────┤\n", + "q.1: ┤ Ry(2.7563) ├\n", + " └────────────┘\n" + ] + } + ], + "source": [ + "# example, assign random data as parameters and print cirquit\n", + "\n", + "subs_dic = {a : np.random.rand() for a in feature_map.qs.abstract_params}\n", + "bound_qc = feature_map.qs.bind_parameters(subs_dic)\n", + "print(bound_qc)" + ] + }, + { + "cell_type": "markdown", + "id": "45f26e2c-cf15-4e67-a9b7-d774cb11c2eb", + "metadata": { + "id": "45f26e2c-cf15-4e67-a9b7-d774cb11c2eb" + }, + "source": [ + "For a data pair $(x, y)$, we create the kernel circuit by calling the build_feature_map twice, once for $x$ and once for $y$, inverting the latter, and joining them together" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "ce778494-1f6a-40f0-89e9-02123cd6600a", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "ce778494-1f6a-40f0-89e9-02123cd6600a", + "outputId": "1ab5c81e-ed04-4d95-a115-89b324a1c45e" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + " ┌──────────┐┌─────────────┐┌─┐ \n", + " q.0: ┤ Ry(π*x0) ├┤ Ry((-π)*y0) ├┤M├───\n", + " ├──────────┤├─────────────┤└╥┘┌─┐\n", + " q.1: ┤ Ry(π*x1) ├┤ Ry((-π)*y1) ├─╫─┤M├\n", + " └──────────┘└─────────────┘ ║ └╥┘\n", + "cb_0: ════════════════════════════╩══╬═\n", + " ║ \n", + "cb_1: ═══════════════════════════════╩═\n", + " \n" + ] + } + ], + "source": [ + "kernel = build_feature_map('x')\n", + "y_inverse = build_feature_map('y').qs.inverse()\n", + "\n", + "kernel.qs.append(y_inverse.to_op(), kernel.qs.qubits)\n", + "\n", + "kernel.qs.measure(kernel.qs.qubits)\n", + "\n", + "print(kernel.qs.transpile())" + ] + }, + { + "cell_type": "markdown", + "id": "b9fefbd4-5e78-4b09-8e7f-8e5a9f342e60", + "metadata": { + "id": "b9fefbd4-5e78-4b09-8e7f-8e5a9f342e60" + }, + "source": [ + "## Experimenting\n", + "\n", + "Remember, when experimenting with quantum circuits, it's important to understand what each gate does and how changing the circuit might affect your results. Happy experimenting! 😊\n", + "\n", + "A few general guidelines for experimenting with quantum circuits:\n", + "\n", + "1. **Understand the problem**: Before you start experimenting, make sure you understand the problem you're trying to solve and how a quantum circuit could help solve it.\n", + "\n", + "2. **Start simple**: Start with a simple circuit and gradually add complexity. This makes it easier to understand what each part of your circuit is doing.\n", + "\n", + "3. **Use a variety of gates**: Different gates can have different effects on your quantum state, so try using a variety of gates in your experiments.\n", + "\n", + "4. **Test on a simulator first**: Before running your circuit on a real quantum computer, test it on a simulator to make sure it's working as expected.\n", + "\n", + "5. **Analyze your results**: After running your circuit, analyze the results to see if they make sense and if they're helping you solve your problem.\n", + "\n", + "6. **Iterate**: Experimenting with quantum circuits often involves a lot of trial and error. Don't be afraid to iterate on your design and try new things.\n", + "\n", + "In the context of the Quantum Support Vector Regression (QSVR) for disability insurance that you're working on, you might want to experiment with different ways of encoding your data into the quantum state or different types of quantum kernels. Remember, the goal is to find a quantum circuit that can effectively model your data and help you make accurate predictions." + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Exercise 1 – Experimenting with Quantum Feature Maps\n", + "\n", + "🧪 Goal:\n", + "Explore how different quantum circuit designs affect the feature mapping in quantum kernel estimation." + ], + "metadata": { + "id": "cStNolKC62xl" + }, + "id": "cStNolKC62xl" + }, + { + "cell_type": "markdown", + "source": [ + "#####1.1 Change the rotation gates\n", + "Try replacing ry with other single-qubit gates like rx, rz, or combinations:" + ], + "metadata": { + "id": "XUGk2fHP7CHo" + }, + "id": "XUGk2fHP7CHo" + }, + { + "cell_type": "code", + "source": [ + "from qrisp import rx, rz\n", + "rx(np.pi * params[0], q[0])\n", + "rz(np.pi * params[1], q[1])" + ], + "metadata": { + "id": "haddGeZA6gXM" + }, + "id": "haddGeZA6gXM", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "What to observe:\n", + "\n", + "How does the circuit look after transpiling?\n", + "Does the kernel matrix change significantly?\n", + "Does SVR performance improve or degrade?" + ], + "metadata": { + "id": "33oWLNjK8MPY" + }, + "id": "33oWLNjK8MPY" + }, + { + "cell_type": "markdown", + "source": [ + "1.2 Add entanglement\n", + "Introduce gates like cx or cz to create entanglement between qubits:" + ], + "metadata": { + "id": "-lBC_HZS7mJY" + }, + "id": "-lBC_HZS7mJY" + }, + { + "cell_type": "code", + "source": [ + "from qrisp import cx, h\n", + "h(q[0])\n", + "cx(q[0], q[1])" + ], + "metadata": { + "id": "yQnWPe_q7mZM" + }, + "id": "yQnWPe_q7mZM", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "What to observe:\n", + "\n", + "Does entanglement improve the expressiveness of the kernel?\n", + "Is the circuit still efficient to simulate?" + ], + "metadata": { + "id": "OVna9A--8Oiy" + }, + "id": "OVna9A--8Oiy" + }, + { + "cell_type": "markdown", + "source": [ + "1.3 Use nonlinear parameter functions\n", + "Instead of linear scaling, try nonlinear transformations:" + ], + "metadata": { + "id": "TKLmbiZ57m3K" + }, + "id": "TKLmbiZ57m3K" + }, + { + "cell_type": "code", + "source": [ + "ry(np.sin(params[0] * np.pi), q[0])\n", + "ry(np.log1p(params[1]) * np.pi, q[1])" + ], + "metadata": { + "id": "tSmjrs4-7nI2" + }, + "id": "tSmjrs4-7nI2", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "What to observe:\n", + "\n", + "Does the kernel matrix capture more subtle patterns?\n", + "Are the results more stable or more sensitive?" + ], + "metadata": { + "id": "jyhJD1TC8Qd3" + }, + "id": "jyhJD1TC8Qd3" + }, + { + "cell_type": "markdown", + "source": [ + "1.4 Increase the number of qubits\n", + "Modify n = 2 to n = 3 or more, and expand your feature map accordingly." + ], + "metadata": { + "id": "KTOBmogV7nSn" + }, + "id": "KTOBmogV7nSn" + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "ATwqZ79m7naC" + }, + "id": "ATwqZ79m7naC", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "What to observe:\n", + "\n", + "How does the circuit scale?\n", + "Does the SVR model benefit from higher-dimensional quantum features?" + ], + "metadata": { + "id": "Ys1Mm-iz8Slg" + }, + "id": "Ys1Mm-iz8Slg" + }, + { + "cell_type": "markdown", + "id": "3dc158a8-1035-47fa-80bd-4d0b4743eabe", + "metadata": { + "id": "3dc158a8-1035-47fa-80bd-4d0b4743eabe" + }, + "source": [ + "#### Hints\n", + "1. Use .transpile() to inspect how your circuit changes.\n", + "2. Try binding real data instead of random values to see how the circuit behaves.\n", + "3. Consider how each change might affect the kernel similarity between data points." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "339246ed-877a-4235-9009-69f77e6e057b", + "metadata": { + "id": "339246ed-877a-4235-9009-69f77e6e057b" + }, + "outputs": [], + "source": [ + "# Test code here\n", + "# Then rerun the following cells\n", + "\n" + ] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "RcEnL1fJ_Z26" + }, + "id": "RcEnL1fJ_Z26", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "id": "7ed23841-0821-40bd-8a6e-0e7fd12ed22b", + "metadata": { + "id": "7ed23841-0821-40bd-8a6e-0e7fd12ed22b" + }, + "source": [ + "#### Estimating the kernel matrix\n", + "\n", + "The train_kernel_matrix function prepares the kernel estimation by setting up inner product circuits, based on each combination of two data points. The kernel circuits are then run on a either a specified backend, or using statevector simulation." + ] + }, + { + "cell_type": "code", + "source": [ + "def train_kernel_matrix(x, f_feature_map, shots=1000, backend=None):\n", + " # Build base kernel circuit\n", + " kernel = f_feature_map('x')\n", + " x_params = copy(kernel.qs.abstract_params)\n", + "\n", + " # Build inverse feature map for y\n", + " adjoint_qs = f_feature_map('y').qs.inverse()\n", + " y_params = adjoint_qs.abstract_params\n", + " # Combine circuits\n", + " kernel.qs.append(adjoint_qs.to_op(), kernel.qs.qubits)\n", + " kernel.qs = kernel.qs.transpile()\n", + "\n", + " # Add measurement if using backend\n", + " if backend is not None:\n", + " kernel.qs.measure(kernel.qs.qubits)\n", + "\n", + " # Initialize kernel matrix\n", + " n = len(x)\n", + " K = np.eye(n)\n", + "\n", + " # Loop over all pairs (i, j)\n", + " for i in range(n):\n", + " subs_dic = {p: x[i][int(p.name[1:])] for p in x_params}\n", + " for j in range(i + 1, n):\n", + " for p in y_params:\n", + " subs_dic[p] = x[j][int(p.name[1:])]\n", + "\n", + " # Bind parameters\n", + " bound_kernel = kernel.qs.bind_parameters(subs_dic)\n", + "\n", + " # Run circuit\n", + " if backend is not None:\n", + " res = bound_kernel.run(shots=shots, backend=backend)\n", + " K_ij = res.get('0' * len(kernel.qs.qubits), 0) / shots\n", + " else:\n", + " res = bound_kernel.statevector_array()\n", + " K_ij = np.abs(res[0]) ** 2\n", + "\n", + " # Fill symmetric matrix\n", + " K[i, j] = K[j, i] = K_ij\n", + "\n", + " return K" + ], + "metadata": { + "id": "N6x2RwdvLInI" + }, + "id": "N6x2RwdvLInI", + "execution_count": 13, + "outputs": [] + }, + { + "cell_type": "markdown", + "id": "6684d892-b617-4556-926e-e23e10353aec", + "metadata": { + "id": "6684d892-b617-4556-926e-e23e10353aec" + }, + "source": [ + "We evaluate the kernel matrix based on our $x$ data and the build_feature_map helper function." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "908ec069-24b6-4d5b-bb47-e677339e3279", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "908ec069-24b6-4d5b-bb47-e677339e3279", + "outputId": "0a444975-2c62-430b-a17c-2398e6c52a74" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [] + } + ], + "source": [ + "matrix_train = train_kernel_matrix(x, build_feature_map)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "cc7771e0-7f0c-4a32-b6bd-d6a7dd50da52", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 468 + }, + "id": "cc7771e0-7f0c-4a32-b6bd-d6a7dd50da52", + "outputId": "171aeae9-7343-4c0f-df53-2f13a86b75f3" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "# Plot the kernel matrix\n", + "\n", + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(matrix_train),\n", + " interpolation='nearest', origin='upper', cmap='Blues')\n", + "axs.set_title(\"trained kernel matrix\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b5e309fb-7fb7-4fed-9e3f-05ff9aa6ea87", + "metadata": { + "id": "b5e309fb-7fb7-4fed-9e3f-05ff9aa6ea87" + }, + "source": [ + "Figure 1 displays the estimated kernel matrix. This matrix has an interesting structure: it is block-diagonal. This is due to the fact that the second quadrant of the matrix correspond to the inner products of the population groups with gender=0. These share the common characteristic gender=0, and each row is similar to its neighbours due to the encoding: similar ages are also similar in the quantum feature space. Analogously, the fourth quadrant of the matrix contains the gender=1 population groups. The first and third quadrants contain the inner products between gender=0 and gender=1 population groups and so are dissimilar in the quantum feature space." + ] + }, + { + "cell_type": "markdown", + "id": "5169b0dc-a666-4d0a-a19e-63de0ca8e6c2", + "metadata": { + "id": "5169b0dc-a666-4d0a-a19e-63de0ca8e6c2" + }, + "source": [ + "Next, we run a support vector regression (SVR) taking the kernel matrix, the weights, and the y-values as input." + ] + }, + { + "cell_type": "code", + "source": [ + "# Train SVR model using precomputed kernel\n", + "f_matrix_train = matrix_train\n", + "zzpc_svr = SVR(kernel='precomputed')\n", + "zzpc_svr.fit(f_matrix_train, y, w)\n", + "\n", + "# Evaluate model\n", + "zzpc_score = zzpc_svr.score(f_matrix_train, y, w)\n", + "print(f\"SVR model R² score on training data: {zzpc_score:.4f}\")\n", + "\n", + "# Predict and transform back to probabilities\n", + "pred = zzpc_svr.predict(f_matrix_train)\n", + "p_hat = 1 / (1 + np.exp(-pred))\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# Sort data by age for smoother plots\n", + "group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", + "group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", + "group_0.sort()\n", + "group_1.sort()\n", + "\n", + "# Plot actual vs predicted transition probabilities\n", + "plt.figure(figsize=(10, 5))\n", + "plt.plot([a for a, _, _ in group_0], [p for _, p, _ in group_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_0], [p_hat for _, _, p_hat in group_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_1], [p for _, p, _ in group_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_1], [p_hat for _, _, p_hat in group_1], 'b', label='Group 1 model')\n", + "\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.title(\"SVR Prediction vs Actual by Gender\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + }, + "id": "HYtBGKbnQm0-", + "outputId": "385138d4-452f-446a-da42-5c11d1b551ac" + }, + "id": "HYtBGKbnQm0-", + "execution_count": 16, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "SVR model R² score on training data: 0.8609\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "id": "ad0da92a-1f89-4289-a2c2-e0cb5d4e1bc6", + "metadata": { + "id": "ad0da92a-1f89-4289-a2c2-e0cb5d4e1bc6" + }, + "source": [ + "The score you see is the R-squared score from the SVR model. This score represents the proportion of the variance in the dependent variable that is predictable from the independent variables. In other words, it gives you a measure of how well your model is fitting the data. A score of 1.0 indicates a perfect fit." + ] + }, + { + "cell_type": "markdown", + "id": "f2bc9cc6-7642-4f93-a152-f78ac3ccc29a", + "metadata": { + "id": "f2bc9cc6-7642-4f93-a152-f78ac3ccc29a" + }, + "source": [ + "We check the results against a classical SVR." + ] + }, + { + "cell_type": "code", + "source": [ + "# Train classical SVR model using RBF kernel\n", + "classical = SVR(kernel='rbf')\n", + "classical.fit(x, y, w)\n", + "classical_score = classical.score(x, y, w)\n", + "print(f\"Classical SVR R² score on training data: {classical_score:.4f}\")\n", + "\n", + "# Predict and transform back to probabilities\n", + "pred = classical.predict(x)\n", + "p_hat = 1 / (1 + np.exp(-pred))\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# Sort data by age for smoother plots\n", + "group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", + "group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", + "group_0.sort()\n", + "group_1.sort()\n", + "\n", + "# Plot actual vs predicted transition probabilities\n", + "plt.figure(figsize=(10, 5))\n", + "plt.plot([a for a, _, _ in group_0], [p for _, p, _ in group_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_0], [p_hat for _, _, p_hat in group_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_1], [p for _, p, _ in group_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_1], [p_hat for _, _, p_hat in group_1], 'b', label='Group 1 model')\n", + "\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.title(\"Classical SVR Prediction vs Actual by Gender\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + }, + "id": "VU3uIjBZVdXQ", + "outputId": "ceb0ce3d-bd17-431c-ec88-7fd62ebb72f3" + }, + "id": "VU3uIjBZVdXQ", + "execution_count": 17, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Classical SVR R² score on training data: 0.8605\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "Side-by-side comparison of how well each model fits the transition probabilities across gender groups." + ], + "metadata": { + "id": "YLK8Srl7V5s1" + }, + "id": "YLK8Srl7V5s1" + }, + { + "cell_type": "code", + "source": [ + "# Quantum SVR predictions\n", + "pred_q = zzpc_svr.predict(f_matrix_train)\n", + "p_hat_q = 1 / (1 + np.exp(-pred_q))\n", + "p_q = 1 / (1 + np.exp(-y))\n", + "\n", + "# Classical SVR predictions\n", + "classical = SVR(kernel='rbf')\n", + "classical.fit(x, y, w)\n", + "pred_c = classical.predict(x)\n", + "p_hat_c = 1 / (1 + np.exp(-pred_c))\n", + "p_c = 1 / (1 + np.exp(-y))\n", + "\n", + "# Sort and group data by gender and age\n", + "def group_and_sort(x, p, p_hat):\n", + " group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", + " group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", + " return sorted(group_0), sorted(group_1)\n", + "\n", + "group_q_0, group_q_1 = group_and_sort(x, p_q, p_hat_q)\n", + "group_c_0, group_c_1 = group_and_sort(x, p_c, p_hat_c)\n", + "\n", + "# Plot both models side-by-side\n", + "plt.figure(figsize=(12, 5))\n", + "\n", + "# Quantum SVR\n", + "plt.subplot(1, 2, 1)\n", + "plt.plot([a for a, _, _ in group_q_0], [p for _, p, _ in group_q_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_q_0], [p_hat for _, _, p_hat in group_q_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_q_1], [p for _, p, _ in group_q_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_q_1], [p_hat for _, _, p_hat in group_q_1], 'b', label='Group 1 model')\n", + "plt.title(\"Quantum Kernel SVR\")\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "\n", + "# Classical SVR\n", + "plt.subplot(1, 2, 2)\n", + "plt.plot([a for a, _, _ in group_c_0], [p for _, p, _ in group_c_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_c_0], [p_hat for _, _, p_hat in group_c_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_c_1], [p for _, p, _ in group_c_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_c_1], [p_hat for _, _, p_hat in group_c_1], 'b', label='Group 1 model')\n", + "plt.title(\"Classical SVR\")\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 457 + }, + "id": "au5H9ebVVtIq", + "outputId": "490cb18e-835a-4dd7-a1da-ba140ec55f2e" + }, + "id": "au5H9ebVVtIq", + "execution_count": 18, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "id": "22f6ed9d-0b80-43c2-9a59-21bfb1d7a695", + "metadata": { + "id": "22f6ed9d-0b80-43c2-9a59-21bfb1d7a695" + }, + "source": [ + "The above analysis is done in-sample. Below, we use the leave-one-out cross-validation functionality from the sklearn module." + ] + }, + { + "cell_type": "code", + "source": [ + "from sklearn.model_selection import LeaveOneOut\n", + "from sklearn.metrics import r2_score\n", + "from sklearn.svm import SVR\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Quantum SVR LOO prediction\n", + "def predict_loo(K, y, w, svr_model):\n", + " cols = range(len(y))\n", + " loo = LeaveOneOut()\n", + " pred_loo = []\n", + " for train_index, test_index in loo.split(cols):\n", + " svr_model.fit(K[np.ix_(train_index, train_index)], y[train_index], w[train_index])\n", + " pred = svr_model.predict(K[np.ix_(test_index, train_index)])\n", + " pred_loo.extend(pred)\n", + " return np.array(pred_loo)\n", + "\n", + "zzpc_svr = SVR(kernel='precomputed')\n", + "statevector_loo = predict_loo(matrix_train, y, w, zzpc_svr)\n", + "\n", + "# Classical SVR LOO prediction\n", + "classical = SVR(kernel='rbf')\n", + "loo = LeaveOneOut()\n", + "pred_loo_classic = []\n", + "for train_index, test_index in loo.split(x):\n", + " classical.fit(x[train_index], y[train_index], w[train_index])\n", + " cpred = classical.predict(x[test_index])\n", + " pred_loo_classic.extend(cpred)\n", + "pred_loo_classic = np.array(pred_loo_classic)\n", + "\n", + "# Transform predictions to probabilities\n", + "p_hat_q = 1 / (1 + np.exp(-statevector_loo))\n", + "p_hat_c = 1 / (1 + np.exp(-pred_loo_classic))\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# R² scores\n", + "score_q = r2_score(p, p_hat_q, sample_weight=w)\n", + "score_c = r2_score(p, p_hat_c, sample_weight=w)\n", + "print(f\"Quantum SVR LOO R² score: {score_q:.4f}\")\n", + "print(f\"Classical SVR LOO R² score: {score_c:.4f}\")\n", + "\n", + "# Sort and group data by gender and age\n", + "def group_and_sort(x, p, p_hat):\n", + " group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", + " group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", + " return sorted(group_0), sorted(group_1)\n", + "\n", + "group_q_0, group_q_1 = group_and_sort(x, p, p_hat_q)\n", + "group_c_0, group_c_1 = group_and_sort(x, p, p_hat_c)\n", + "\n", + "# Plot both models side-by-side\n", + "plt.figure(figsize=(12, 5))\n", + "\n", + "# Quantum SVR LOO\n", + "plt.subplot(1, 2, 1)\n", + "plt.plot([a for a, _, _ in group_q_0], [p for _, p, _ in group_q_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_q_0], [p_hat for _, _, p_hat in group_q_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_q_1], [p for _, p, _ in group_q_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_q_1], [p_hat for _, _, p_hat in group_q_1], 'b', label='Group 1 model')\n", + "plt.title(\"Quantum SVR (LOO)\")\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "\n", + "# Classical SVR LOO\n", + "plt.subplot(1, 2, 2)\n", + "plt.plot([a for a, _, _ in group_c_0], [p for _, p, _ in group_c_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_c_0], [p_hat for _, _, p_hat in group_c_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_c_1], [p for _, p, _ in group_c_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_c_1], [p_hat for _, _, p_hat in group_c_1], 'b', label='Group 1 model')\n", + "plt.title(\"Classical SVR (LOO)\")\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 491 + }, + "id": "z-rdVMiSW65Q", + "outputId": "5992f530-6a3b-4a5d-beb9-f6f85f392235" + }, + "id": "z-rdVMiSW65Q", + "execution_count": 19, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Quantum SVR LOO R² score: 0.8584\n", + "Classical SVR LOO R² score: 0.8532\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "id": "8ecebea2-79c9-4903-8f1c-8ffbc5393330", + "metadata": { + "id": "8ecebea2-79c9-4903-8f1c-8ffbc5393330" + }, + "source": [ + "Quantum Support Vector Regression (QSVR) Score (0.9155345528008413): This score suggests that your QSVR model is doing a good job of capturing the relationship between your features and your target variable.\n", + "\n", + "Classical Support Vector Regression (SVR) Score (0.9295558682302361): This score is slightly higher than your QSVR score, suggesting that your classical SVR model might be fitting the data slightly better than your QSVR model.\n", + "\n", + "Leave-One-Out Cross-Validation Score (0.8977158412990511): This score is lower than both your QSVR and classical SVR scores. This isn’t surprising, as leave-one-out cross-validation can often result in lower scores because it’s a more rigorous form of validation. It’s a good way to get an unbiased estimate of how well your model will perform on unseen data.\n", + "\n", + "To compare these results, you can look at how much each score deviates from 1.0. The closer the score is to 1.0, the better the model is fitting your data. However, keep in mind that a high R-squared score doesn’t always mean your model will perform well on unseen data. It’s important to also look at other metrics and plots (like residuals) to assess your model’s performance." + ] + }, + { + "cell_type": "markdown", + "source": [ + "## 📊 Model Performance Summary\n", + "\n", + "This section compares the performance of Quantum and Classical Support Vector Regression models, both in-sample and using Leave-One-Out Cross-Validation (LOO).\n", + "\n", + "### **In-Sample R² Scores**\n", + "| Model | R² Score | Interpretation |\n", + "|-------|----------|----------------|\n", + "| **Quantum SVR (QSVR)** | **0.8609** | Captures the relationship between features and target well. |\n", + "| **Classical SVR (RBF Kernel)** | **0.8605** | Very similar to QSVR, suggesting the classical kernel is equally expressive for this dataset. |\n", + "\n", + "### **Leave-One-Out Cross-Validation (LOO)**\n", + "| Model | R² Score | Interpretation |\n", + "|-------|----------|----------------|\n", + "| **Quantum SVR (LOO)** | **0.8977** | Slightly lower than in-sample scores, as expected. This is a more rigorous test of generalization. |\n", + "\n", + "---\n", + "\n", + "### 🧠 Interpretation\n", + "\n", + "- The **QSVR and Classical SVR** models perform almost identically on this dataset, indicating that the quantum kernel does not yet offer a significant advantage over the classical RBF kernel.\n", + "- The **LOO score** is slightly lower, which is expected due to its stricter validation. It provides a more **unbiased estimate** of how well the model generalizes to unseen data.\n", + "- A high R² score indicates good fit, but it’s important to also examine **residuals**, **error distributions**, and **kernel structures** to fully assess model performance.\n", + "\n", + "To compare these results, you can look at how much each score deviates from 1.0. The closer the score is to 1.0, the better the model is fitting your data. However, keep in mind that a high R-squared score doesn’t always mean your model will perform well on unseen data. It’s important to also look at other metrics and plots to assess your model’s performance." + ], + "metadata": { + "id": "Ia52tUuWX6xP" + }, + "id": "Ia52tUuWX6xP" + }, + { + "cell_type": "markdown", + "source": [ + "### Exercise 2: Residuals\n", + "\n", + "> In regression analysis, **residuals** represent the difference between the observed (actual) and predicted values for each data point. They help us understand how well a model fits the data.\n", + ">\n", + "> Mathematically, for an observed value $$y_{\\text{obs}}$$ and a predicted value $$y_{\\text{pred}}$$ for a data point, the residual $$e$$ is calculated as:\n", + ">\n", + "> $$e = y_{\\text{obs}} - y_{\\text{pred}}$$\n", + ">\n", + "> In our case, we are working with **transition probabilities**, so we transform both actual and predicted values using the sigmoid function to interpret them as probabilities:\n", + ">\n", + "> $$p = \\frac{1}{1 + e^{-y}}, \\quad \\hat{p} = \\frac{1}{1 + e^{-y_{\\text{pred}}}}$$\n", + ">\n", + "> The residuals then become:\n", + ">\n", + "> $$e = p - \\hat{p}$$\n", + ">\n", + "> A good model will produce residuals that are:\n", + "> - **Close to zero**, indicating accurate predictions.\n", + "> - **Randomly distributed**, without patterns, which suggests the model captures the underlying data structure well.\n", + ">\n", + "> In this exercise, we will:\n", + "> 1. Compute residuals for the Quantum SVR model.\n", + "> 2. Plot a histogram to visualize their distribution.\n", + ">\n", + "> ### 🔍 Hints\n", + "> - Use `residuals = p - p_hat_q` for Quantum SVR.\n", + "> - Use `plt.hist(residuals, bins=20)` to plot.\n", + "> - Label your axes clearly.\n", + "> - *Advanced:* Compare with Classical SVR residuals or plot residuals vs. age to detect patterns.\n" + ], + "metadata": { + "id": "AgNktxzOCvwP" + }, + "id": "AgNktxzOCvwP" + }, + { + "cell_type": "code", + "source": [ + "# Transform actual values to probabilities\n", + "p =\n", + "\n", + "# Compute residuals\n", + "residuals_qsvr =\n", + "residuals_classical =\n", + "\n", + "# Plot histogram of Quantum SVR residuals\n", + "plt.figure(figsize=(12, 5))" + ], + "metadata": { + "id": "me-eoMwCH9JS" + }, + "id": "me-eoMwCH9JS", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "vgIIM-NPH9LX" + }, + "id": "vgIIM-NPH9LX", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "### ✅ Summary of Exercise 2: Residuals\n", + "\n", + "You've done a great job implementing Quantum Support Vector Regression (QSVR) and comparing it with classical SVR using **leave-one-out cross-validation (LOO)**—a robust method for estimating generalization error.\n", + "\n", + "#### 🔍 Residual Analysis\n", + "\n", + "You've plotted two types of residual histograms:\n", + "\n", + "1. **Raw residuals**: \n", + " $$e = y - \\hat{y}$$ \n", + " These show how far off the predicted values are from the actual targets. Ideally, residuals should be centered around zero with no clear pattern.\n", + "\n", + "2. **Probability residuals**: \n", + " $$e = p - \\hat{p}$$ \n", + " Here, both actual and predicted values are transformed using the sigmoid function to represent transition probabilities. This is especially relevant in your context of modeling disability insurance transitions.\n", + "\n", + "#### 📊 Interpretation\n", + "\n", + "- A **tight, symmetric distribution** around zero suggests good model performance.\n", + "- **Skewed or long-tailed distributions** may indicate systematic bias—either overestimation or underestimation.\n", + "- Comparing Quantum and Classical SVR residuals side-by-side helps assess which model generalizes better.\n", + "\n", + "#### 🧠 What You’ve Achieved\n", + "\n", + "- Implemented QSVR with a custom kernel matrix.\n", + "- Compared it with classical SVR using RBF kernel.\n", + "- Evaluated both using LOO cross-validation.\n", + "- Analyzed residuals both in raw and probability-transformed form.\n", + "\n", + "This is a **comprehensive and methodologically sound approach** to model evaluation. Excellent work! 😊" + ], + "metadata": { + "id": "G_ACDFHkLuCh" + }, + "id": "G_ACDFHkLuCh" + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bf6ece14-57fb-4ea5-85f5-5e5f3919414f", + "metadata": { + "id": "bf6ece14-57fb-4ea5-85f5-5e5f3919414f" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "8d6c503e-5292-4644-8155-b5e76134ebf1", + "metadata": { + "id": "8d6c503e-5292-4644-8155-b5e76134ebf1" + }, + "source": [ + "### We used the statevector simulator and now we'll run it on IQM simulator" + ] + }, + { + "cell_type": "code", + "source": [ + "pip install qrisp[iqm]" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "YGtkNXZwMhWx", + "outputId": "4579b418-f10a-4021-921f-832e4542d705" + }, + "id": "YGtkNXZwMhWx", + "execution_count": 21, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Requirement already satisfied: qrisp[iqm] in /usr/local/lib/python3.12/dist-packages 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In this case, it's creating a quantum circuit `qc` with 2 qubits. It then applies a rotation around the y-axis (`ry`) on each qubit. The rotation angle is determined by the input data `x` multiplied by `pi`. The `ParameterVector` is a way to create a list of parameters." + ] + }, + { + "cell_type": "markdown", + "id": "19f6461a-7bc1-47e9-bf5b-6bf606fbc586", + "metadata": { + "id": "19f6461a-7bc1-47e9-bf5b-6bf606fbc586" + }, + "source": [ + "First, we create some dummy data, but smaller (fewer data points) than it was before." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ed4cad78-d89f-4dff-981c-8113ca649e12", + "metadata": { + "id": "ed4cad78-d89f-4dff-981c-8113ca649e12" + }, + "outputs": [], + "source": [ + "nsamp = 10\n", + "x = np.array( [[0.0, x/nsamp] for x in range(nsamp)] + [[1.0, x/nsamp] for x in range(nsamp)] )\n", + "y = np.array([-4.5 + 0.2*a[0] + a[1]*(1+a[0]*0.2) + 0.1*np.random.normal() for a in x])\n", + "\n", + "p = 1/(1+np.exp(-y))\n", + "\n", + "n = [int(200 + 600*xj[1]/0.7) if xj[1] <= 0.7 else int(800 - 300*(xj[1]-0.7)/0.3) for xj in x]\n", + "\n", + "d = [nj*pj for nj,pj in zip(n,p)]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6b244442-219f-448c-bee8-21b566d906c4", + "metadata": { + "id": "6b244442-219f-448c-bee8-21b566d906c4" + }, + "outputs": [], + "source": [ + "# Create a DataFrame\n", + "df1 = pd.DataFrame({\n", + " 'gender': [a[0] for a in x],\n", + " 'age group (normalized)': [a[1] for a in x],\n", + " 'population size': n,\n", + " 'number of transitions': d\n", + "})\n", + "\n", + "# Write the DataFrame to a CSV file\n", + "df1.to_csv('fdata1.csv', index=False) # index=False argument is used to prevent pandas from writing row indices into the CSV file" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "670765b0-5135-4965-a15f-57e5ea90c130", + "metadata": { + "id": "670765b0-5135-4965-a15f-57e5ea90c130" + }, + "outputs": [], + "source": [ + "data1 = df1\n", + "# data1 = pd.read_csv('fdata1.csv')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f04e1346-2773-4918-9789-b72c9354f381", + "metadata": { + "id": "f04e1346-2773-4918-9789-b72c9354f381", + "outputId": "e0c43769-aa51-498c-88b0-a58e178903da" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 0. ]\n", + " [0. 0.1]\n", + " [0. 0.2]\n", + " [0. 0.3]\n", + " [0. 0.4]\n", + " [0. 0.5]\n", + " [0. 0.6]\n", + " [0. 0.7]\n", + " [0. 0.8]\n", + " [0. 0.9]\n", + " [1. 0. ]\n", + " [1. 0.1]\n", + " [1. 0.2]\n", + " [1. 0.3]\n", + " [1. 0.4]\n", + " [1. 0.5]\n", + " [1. 0.6]\n", + " [1. 0.7]\n", + " [1. 0.8]\n", + " [1. 0.9]]\n" + ] + } + ], + "source": [ + "# Transform and inspect data\n", + "x1 = np.array( [[a,b] for a,b in zip(data1['gender'], data1['age group (normalized)'])] )\n", + "print(x1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b74a992-8a26-481b-b40a-05cc775ce58f", + "metadata": { + "id": "3b74a992-8a26-481b-b40a-05cc775ce58f" + }, + "outputs": [], + "source": [ + "# raw transition frequency per group, used for plots\n", + "p_raw = [a/b for a,b in zip(d,n)]\n", + "\n", + "# logistic probability, used as input to SVR optimization\n", + "y = np.array([np.log( p / (1-p) ) for p in p_raw])\n", + "\n", + "# calculate weights for SVR based on population size\n", + "w = np.array([1./nj for nj in n])\n", + "\n", + "# normalize weights (equivalent to changing the hyperparameters of the SVR)\n", + "w = w/sum(w)*len(x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c4e5c7fd-1c28-4867-8e1a-4ba20b711f1f", + "metadata": { + "id": "c4e5c7fd-1c28-4867-8e1a-4ba20b711f1f", + "outputId": "9395a2e9-1d87-4e79-e6fd-5e448166e0fa" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "axs.plot([x1j[1] for x1j,p in zip(x1, p_raw) if x1j[0] == 0], [p for x1j,p in zip(x1, p_raw) if x1j[0] == 0], 'or')\n", + "axs.plot([x1j[1] for x1j,p in zip(x1, p_raw) if x1j[0] == 1], [p for x1j,p in zip(x1, p_raw) if x1j[0] == 1], 'ob')\n", + "axs.set_title(\"raw transition frequencies\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "08783390-fb9a-4d24-ae8b-02eb0923c632", + "metadata": { + "id": "08783390-fb9a-4d24-ae8b-02eb0923c632" + }, + "source": [ + "## Exercise 3: Implement and Visualize a Quantum Feature Map\n", + "\n", + "In this exercise, you will implement a quantum feature map using Qiskit and visualize the resulting quantum circuit. The feature map is a way of encoding classical data into quantum states. In this case, we will use a simple feature map that applies a rotation around the y-axis on each qubit.\n", + "\n", + "### Task 1: Implement the Feature Map\n", + "\n", + "First, let's implement the feature map. Here is the function you need to complete:\n", + "\n", + "```python\n", + "def feature_map(x1):\n", + " p = ParameterVector('x1', length=2)\n", + " qc = QuantumCircuit(2)\n", + "\n", + " # TODO: Apply a rotation around the y-axis on each qubit\n", + " # Hint: Use the ry gate and the input data x1\n", + "\n", + " return qc\n", + "```\n", + "\n", + "### Task 2: Visualize the Circuit\n", + "\n", + "After implementing the feature map, you visualize the resulting quantum circuit, as we did at the beginning of this lesson.\n", + "\n", + "Good luck with your exercise! If you have any questions or need further clarification, feel free to ask. 😊" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "24c26430-a283-4a99-8fb7-058c52bf4c7e", + "metadata": { + "id": "24c26430-a283-4a99-8fb7-058c52bf4c7e" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dc63aa1a-0bf0-4e1f-9bf2-580c12aadbdb", + "metadata": { + "id": "dc63aa1a-0bf0-4e1f-9bf2-580c12aadbdb" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "52aa44c7-40bc-4ec2-b273-94d6b457a8dc", + "metadata": { + "id": "52aa44c7-40bc-4ec2-b273-94d6b457a8dc" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "13cf3642-2745-4250-ac18-9006bb457793", + "metadata": { + "id": "13cf3642-2745-4250-ac18-9006bb457793" + }, + "source": [ + "The following part of the code implements a list of all possible quantum circuits for the given data `x1`. For each pair of data points `(x1[i], x1[j])`, it creates two circuits using the `feature_map` function. The feature map is a way of encoding classical data into quantum states. It then appends the inverse of `qc_j` to `qc_i` using the `compose` function. This function combines two circuits, and with `.inverse()`, it applies the inverse of the second circuit. After composing the circuits, it adds a measurement on all qubits using `measure_all()`. The circuit is then transpiled for a specific backend using the `transpile` function." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "051f839e-9306-44eb-b198-eaeafa837238", + "metadata": { + "id": "051f839e-9306-44eb-b198-eaeafa837238", + "outputId": "b753f105-a8a2-463d-f334-24d1d0f4ef40" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "190\n" + ] + } + ], + "source": [ + "# from qiskit import transpile\n", + "\n", + "# Initialize an empty list to store all circuits\n", + "all_circuits = []\n", + "\n", + "for i in range(len(x1)):\n", + " for j in range(i):\n", + " # Substitute parameters with values from your data\n", + " qc_i = feature_map(x1[i])\n", + " qc_j = feature_map(x1[j])\n", + "\n", + " # Append the inverse of qc_j to qc_i and measure\n", + " qc_ij = qc_i.compose(qc_j.inverse())\n", + " qc_ij.measure_all()\n", + "\n", + " # Transpile the circuit for the backend\n", + " qc_ij_transpiled = transpile(qc_ij, backend=backend)\n", + "\n", + " # Add the transpiled circuit to the list\n", + " all_circuits.append(qc_ij_transpiled)\n", + "\n", + "print(len(all_circuits))" + ] + }, + { + "cell_type": "markdown", + "id": "b50ea21e-efef-4102-82c5-9a36ecde6552", + "metadata": { + "id": "b50ea21e-efef-4102-82c5-9a36ecde6552" + }, + "source": [ + "This block of code defines a batch size and splits the transpiled circuits into batches. It then initializes a list to store job IDs. Each batch of circuits is executed on the backend with 1024 shots per circuit execution. Also, it can take some time to execute." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "23cde26c-9afe-42ca-80e1-657f120f26ac", + "metadata": { + "id": "23cde26c-9afe-42ca-80e1-657f120f26ac", + "outputId": "ed9bfcae-b340-42ef-cdd2-2c9010e12cd7" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tracking execution of job1:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job2:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job3:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job4:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job5:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job6:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job7:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job8:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job9:\n", + "Job Status: job has successfully run\n", + "Tracking execution of job10:\n", + "Job Status: job has successfully run\n" + ] + } + ], + "source": [ + "# Define the batch size\n", + "batch_size = 20\n", + "\n", + "# Split the transpiled circuits into batches\n", + "batches = [all_circuits[i:i + batch_size] for i in range(0, len(all_circuits), batch_size)]\n", + "\n", + "# Initialize a list to store job IDs\n", + "job_ids = []\n", + "\n", + "# Execute each batch of circuits\n", + "for batch in batches:\n", + " job = backend.run(batch, shots=1024)\n", + " job_ids.append(job.job_id())\n", + "\n", + "# This block of code executes each batch until it's successful or an exception occurs\n", + "# If an exception occurs, it waits for a random amount of time between 1 and 10 seconds before retrying\n", + "\n", + "import time\n", + "import random\n", + "\n", + "# Initialize a list to store results\n", + "results = []\n", + "n_shots = 1024\n", + "\n", + "# Initialize a counter for the job number\n", + "job_number = 1\n", + "\n", + "for batch in batches:\n", + " success = False\n", + " while not success:\n", + " try:\n", + " # Execute the batch of circuits\n", + " job = backend.run(batch, shots=n_shots)\n", + "\n", + " # Print job execution status\n", + " print(f\"Tracking execution of job{job_number}:\")\n", + " job_monitor(job)\n", + "\n", + " # Wait for the job to finish and get the result\n", + " result = job.result()\n", + "\n", + " # If successful, append the result and break the loop\n", + " results.append(result)\n", + " success = True\n", + "\n", + " except Exception as e:\n", + " print(f\"Execution failed with error: {e}\")\n", + "\n", + " # Sleep for a bit (random backoff) before retrying\n", + " time.sleep(random.randint(1, 10))\n", + "\n", + " # Increment the job number for the next iteration\n", + " job_number += 1" + ] + }, + { + "cell_type": "markdown", + "id": "fc8b2a3d-9729-4c20-acf5-f40d9851ef30", + "metadata": { + "id": "fc8b2a3d-9729-4c20-acf5-f40d9851ef30" + }, + "source": [ + "**Job Retrieval and Frequency Calculation**: The script starts by iterating over a list of `job_ids`. For each `job_id`, it retrieves the job result from the backend. It then calculates the frequency of the '00' state in the results and appends this frequency to the `estimates` list." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6f002a91-d87c-4278-905c-dbfacf9a03f0", + "metadata": { + "id": "6f002a91-d87c-4278-905c-dbfacf9a03f0", + "outputId": "390fbd69-02d5-434a-c90c-ddd9b617bb37" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Job1: ea63caca-9859-4988-afcc-4617a4422261\n", + "Job2: 4ea8454c-0146-47e3-a4f3-22e7098bf8b5\n", + "Job3: 29c17939-328b-46bd-bcf6-e2df758b4efd\n", + "Job4: 80e39182-931b-4bc9-83d7-f100a877d81b\n", + "Job5: bae16e48-b12a-4cea-bdf4-287bce4e11ab\n", + "Job6: ed7f15be-36d1-41c4-b0e1-794746789a48\n", + "Job7: b07bd0df-a786-4389-8def-ea0926f2fd17\n", + "Job8: d346a014-4afc-43ee-8ee4-d16e229e7c1e\n", + "Job9: baf11441-c6d0-4b0b-8641-068a929c72c4\n", + "Job10: 1895b727-95b8-4925-bc95-e7e2347493f7\n" + ] + } + ], + "source": [ + "# Initialize a counter for the job number\n", + "job_number = 1\n", + "\n", + "for job_id in job_ids:\n", + " print(f\"Job{job_number}: {job_id}\")\n", + " job_number += 1" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bacb231a-f8cc-4922-82fd-079a6b568dc9", + "metadata": { + "id": "bacb231a-f8cc-4922-82fd-079a6b568dc9" + }, + "outputs": [], + "source": [ + "estimates = []\n", + "\n", + "for job_id in job_ids:\n", + " job_res = backend.retrieve_job(job_id).result()\n", + " for res in job_res.results:\n", + " if '00' in res.data.counts:\n", + " freq = res.data.counts['00']/n_shots\n", + " else:\n", + " freq = 0.0\n", + " estimates.append(freq)" + ] + }, + { + "cell_type": "markdown", + "id": "3ab74e22-d559-46b8-8777-396d0af98e79", + "metadata": { + "id": "3ab74e22-d559-46b8-8777-396d0af98e79" + }, + "source": [ + "**Kernel Matrix Construction**: The script constructs a kernel matrix `K_helmi` using the estimates. The kernel matrix is a symmetric matrix where each element represents a measure of similarity between two data points." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "77466963-5ed7-4a93-adcd-4c9dd0867a18", + "metadata": { + "id": "77466963-5ed7-4a93-adcd-4c9dd0867a18" + }, + "outputs": [], + "source": [ + "K_helmi = np.identity(len(x1))\n", + "\n", + "cnt = 0\n", + "for i in range(len(x1)):\n", + " for j in range(i):\n", + " #print(i, ' ', j)\n", + " K_helmi[i,j] = estimates[cnt]\n", + " K_helmi[j,i] = estimates[cnt]\n", + " cnt += 1" + ] + }, + { + "cell_type": "markdown", + "id": "9f7f0f1d-bf79-45fd-9763-2b448c10c884", + "metadata": { + "id": "9f7f0f1d-bf79-45fd-9763-2b448c10c884" + }, + "source": [ + " **Kernel Matrix Visualization**: The kernel matrix is then visualized using matplotlib's `imshow` function. The color map 'Blues' is used, and a color bar is added for reference." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e09a4a10-61a5-4f02-92a3-2bdd33a5e7ba", + "metadata": { + "id": "e09a4a10-61a5-4f02-92a3-2bdd33a5e7ba", + "outputId": "226f709d-e913-4db8-b7c4-eb6c27ac180c" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(K_helmi),\n", + " interpolation='nearest', origin='upper', cmap='Blues')\n", + "axs.set_title(\"kernel matrix from Helmi\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0cc501ab-40c7-4b26-aefb-f20ff7369b72", + "metadata": { + "id": "0cc501ab-40c7-4b26-aefb-f20ff7369b72" + }, + "source": [ + "**Support Vector Regression (SVR)**: The script uses the Support Vector Regression (SVR) model from scikit-learn with a precomputed kernel. It fits the model to the data (`f_matrix_train` and `y`) and calculates the score of the model using the `score` method.\n", + "\n", + "**Prediction and Plotting**: The fitted model is used to predict outcomes, which are then plotted against the actual outcomes for two groups (Group 0 and Group 1)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "77e7a3fc-3bd0-4d7f-acb7-17e5fbb2132e", + "metadata": { + "id": "77e7a3fc-3bd0-4d7f-acb7-17e5fbb2132e", + "outputId": "e8f46872-0507-4837-920b-4046bad19bf8" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "score: 0.9001754733534563\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "f_matrix_train = K_helmi\n", + "\n", + "zzpc_svr = SVR(kernel='precomputed')\n", + "zzpc_svr.fit(f_matrix_train, y, w)\n", + "zzpc_score = zzpc_svr.score(f_matrix_train, y, w)\n", + "print(f'score: {zzpc_score}')\n", + "pred = zzpc_svr.predict(f_matrix_train)\n", + "\n", + "p_hat = 1/(1+np.exp(-pred))\n", + "p = 1/(1+np.exp(-y))\n", + "plt.figure()\n", + "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p) if a[0] == 0],'or')\n", + "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", + "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", + "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", + "plt.legend(['Group 0', 'Group 0 model', 'Group 1', 'Group 1 model'])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5e211b3e-7c28-4de0-967d-14bb3c502bd8", + "metadata": { + "id": "5e211b3e-7c28-4de0-967d-14bb3c502bd8" + }, + "source": [ + "**Error Calculation and Visualization**: Finally, the script calculates the absolute errors between `K_helmi` and `matrix_train`, visualizes these errors using `imshow`, and displays this with a color bar for reference." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8a3b538d-9deb-418a-9a3c-4e14590e6074", + "metadata": { + "id": "8a3b538d-9deb-418a-9a3c-4e14590e6074" + }, + "outputs": [], + "source": [ + "# redo the steps for statevector kernel to compare with the Helmi results\n", + "\n", + "zz_kernel = QuantumKernel(feature_map=qc, quantum_instance=Aer.get_backend('statevector_simulator'))\n", + "zz_circuit = zz_kernel.construct_circuit(ParameterVector('x_i', length=2),ParameterVector('x_j', length=2))\n", + "zz_circuit.decompose().draw(output='mpl')\n", + "matrix_train = zz_kernel.evaluate(x_vec=x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "errors = np.abs(K_helmi - matrix_train)\n", + "\n", + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(errors),\n", + " interpolation='nearest', origin='upper', cmap='Reds')\n", + "axs.set_title(\"erorrs\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "47fa3d94-0b0e-41f9-ba3b-4571be968882", + "metadata": { + "id": "47fa3d94-0b0e-41f9-ba3b-4571be968882" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3ca65f4a-c3b7-43da-b27b-35bf2a7c73d1", + "metadata": { + "id": "3ca65f4a-c3b7-43da-b27b-35bf2a7c73d1" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "30df1f84-8e4b-4e3b-a607-3ecf25e9d375", + "metadata": { + "id": "30df1f84-8e4b-4e3b-a607-3ecf25e9d375" + }, + "outputs": [], + "source": [ + "# solution ex2\n", + "residuals = y - pred\n", + "plt.hist(residuals, bins=20)\n", + "plt.xlabel('Residuals')\n", + "plt.ylabel('Frequency')\n", + "plt.title('Histogram of Residuals')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "97aab143-92b2-4765-853c-1c8757bd79b0", + "metadata": { + "id": "97aab143-92b2-4765-853c-1c8757bd79b0" + }, + "outputs": [], + "source": [ + "# solution1 ex2\n", + "residuals1 = p_hat-p\n", + "plt.hist(residuals1, bins=20)\n", + "plt.xlabel('Residuals')\n", + "plt.ylabel('Frequency')\n", + "plt.title('Histogram of Residuals')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c3a78eab-1e43-4f1b-a992-526d1c131b4a", + "metadata": { + "id": "c3a78eab-1e43-4f1b-a992-526d1c131b4a" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a26ddc57-a2fc-48ac-b3ae-f3ece0a2b507", + "metadata": { + "id": "a26ddc57-a2fc-48ac-b3ae-f3ece0a2b507" + }, + "outputs": [], + "source": [ + "# solution ex3\n", + "\n", + "def feature_map(x1):\n", + " p = ParameterVector('x1', length=2)\n", + " qc = QuantumCircuit(2)\n", + "\n", + " qc.ry(x1[0]*np.pi, 0)\n", + " qc.ry(x1[1]*np.pi, 1)\n", + "\n", + " return qc" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "681cbb1a-dcc1-4870-990f-7935e14b8d81", + "metadata": { + "id": "681cbb1a-dcc1-4870-990f-7935e14b8d81", + "outputId": "4679a728-38f0-4ada-e70e-b7fa1bcbac3c" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# solution1 ex3\n", + "# Draw the circuit\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "INefXmud-4fw" + }, + "id": "INefXmud-4fw", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "nNAylO7d-4iF" + }, + "id": "nNAylO7d-4iF", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "_mqodsqI-4kK" + }, + "id": "_mqodsqI-4kK", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "RoP5NvHh-4mp" + }, + "id": "RoP5NvHh-4mp", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d1960e7f-a57d-4047-b7eb-6054e37ee913", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "d1960e7f-a57d-4047-b7eb-6054e37ee913", + "outputId": "2412fed3-f003-4c32-c3d0-24478e6c35d3" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + " ┌──────────┐\n", + "q.0: ┤ Rx(π*x0) ├\n", + " ├──────────┤\n", + "q.1: ┤ Rz(π*x1) ├\n", + " └──────────┘\n" + ] + } + ], + "source": [ + "# solution ex1.1\n", + "\n", + "from qrisp import QuantumVariable, rx, rz\n", + "from sympy import symbols\n", + "import numpy as np\n", + "\n", + "def build_feature_map(sym):\n", + " n = 2\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n))\n", + " rx(np.pi * params[0], q[0])\n", + " rz(np.pi * params[1], q[1])\n", + " return q\n", + "\n", + "feature_map = build_feature_map('x')\n", + "print(feature_map.qs.transpile())\n" + ] + }, + { + "cell_type": "code", + "source": [ + "# solution ex1.2\n", + "\n", + "from qrisp import QuantumVariable, ry, h, cx\n", + "\n", + "def build_feature_map(sym):\n", + " n = 2\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n))\n", + " ry(np.pi * params[0], q[0])\n", + " ry(np.pi * params[1], q[1])\n", + " h(q[0])\n", + " cx(q[0], q[1])\n", + " return q\n", + "\n", + "feature_map = build_feature_map('x')\n", + "print(feature_map.qs.transpile())" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "__-88RBE-4_g", + "outputId": "da284955-5d98-42c5-b20f-5f075f7efb18" + }, + "id": "__-88RBE-4_g", + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + " ┌──────────┐┌───┐ \n", + "q.0: ┤ Ry(π*x0) ├┤ H ├──■──\n", + " ├──────────┤└───┘┌─┴─┐\n", + "q.1: ┤ Ry(π*x1) ├─────┤ X ├\n", + " └──────────┘ └───┘\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "# solution ex1.3\n", + "\n", + "from qrisp import QuantumVariable, ry\n", + "from sympy import symbols\n", + "import numpy as np\n", + "\n", + "def build_feature_map(sym):\n", + " n = 2\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n))\n", + " ry(np.sin(params[0] * np.pi), q[0])\n", + " ry(np.log1p(params[1]) * np.pi, q[1])\n", + " return q\n", + "\n", + "feature_map = build_feature_map('x')\n", + "print(feature_map.qs.transpile())" + ], + "metadata": { + "id": "eq41tPVY-5B2" + }, + "id": "eq41tPVY-5B2", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# solution ex1.4\n", + "\n", + "from qrisp import QuantumVariable, ry\n", + "from sympy import symbols\n", + "import numpy as np\n", + "\n", + "def build_feature_map(sym):\n", + " n = 3\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n))\n", + " for i in range(n):\n", + " ry(np.pi * params[i], q[i])\n", + " return q\n", + "\n", + "feature_map = build_feature_map('x')\n", + "print(feature_map.qs.transpile())\n" + ], + "metadata": { + "id": "kkFik42y_LIc" + }, + "id": "kkFik42y_LIc", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# solution ex2\n", + "\n", + "# Transform actual values to probabilities\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# Compute residuals\n", + "residuals_qsvr = p - p_hat_q\n", + "residuals_classical = p - p_hat_c\n", + "\n", + "# Plot histogram of Quantum SVR residuals\n", + "plt.figure(figsize=(12, 5))\n", + "\n", + "plt.subplot(1, 2, 1)\n", + "plt.hist(residuals_qsvr, bins=20, color='skyblue', edgecolor='black')\n", + "plt.xlabel('Residuals (Actual - Predicted)')\n", + "plt.ylabel('Frequency')\n", + "plt.title('Histogram of Residuals - Quantum SVR')\n", + "plt.grid(True)\n", + "\n", + "# Plot histogram of Classical SVR residuals\n", + "plt.subplot(1, 2, 2)\n", + "plt.hist(residuals_classical, bins=20, color='salmon', edgecolor='black')\n", + "plt.xlabel('Residuals (Actual - Predicted)')\n", + "plt.ylabel('Frequency')\n", + "plt.title('Histogram of Residuals - Classical SVR')\n", + "plt.grid(True)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "metadata": { + "id": "whov_4CX-5Di" + }, + "id": "whov_4CX-5Di", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "gyvxsT5A-5Fo" + }, + "id": "gyvxsT5A-5Fo", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "7GyO8oYR-5Hn" + }, + "id": "7GyO8oYR-5Hn", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "id": "eaae61c0-9258-4bf7-a929-065ab90d36aa", + "metadata": { + "id": "eaae61c0-9258-4bf7-a929-065ab90d36aa" + }, + "source": [ + "#### TEST CODE" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3397e118-363f-4cb2-b0aa-3166d83ae03f", + "metadata": { + "id": "3397e118-363f-4cb2-b0aa-3166d83ae03f" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6d2dad5d-6493-460a-a5d6-898448124f31", + "metadata": { + "id": "6d2dad5d-6493-460a-a5d6-898448124f31" + }, + "outputs": [], + 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f5ae09b0c1faa5588a0bf5d138617f077dd6a2b0 Mon Sep 17 00:00:00 2001 From: Anastasiia Andriievska <79667606+fomalhautn@users.noreply.github.com> Date: Wed, 5 Nov 2025 19:46:04 +0100 Subject: [PATCH 6/8] Delete content/QKE.ipynb --- content/QKE.ipynb | 1575 --------------------------------------------- 1 file changed, 1575 deletions(-) delete mode 100644 content/QKE.ipynb diff --git a/content/QKE.ipynb b/content/QKE.ipynb deleted file mode 100644 index b779326..0000000 --- a/content/QKE.ipynb +++ /dev/null @@ -1,1575 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "e4b10801-19d8-4751-8e31-a9bfd2df03d1", - "metadata": {}, - "source": [ - "# Tutorial - Quantum kernel estimation with application to disability insurance\n", - "\n", - "B. Djehiche and B. Löfdahl – KTH, Department of Mathematics / SEB – \n", - "Risks 2021, 9(12), 216; https://doi.org/10.3390/risks9120216\n", - "\n", - "Hands-on assistance: https://enccs.se/anastasiia-andriievska" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "b6f8b962-5fde-46f8-af33-dda094485734", - "metadata": {}, - "outputs": [], - "source": [ - "# install necessary packages via pip\n", - "\n", - "import pandas as pd\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from sklearn.svm import SVR\n", - "from copy import copy\n", - "from qrisp import QuantumVariable, QuantumCircuit\n", - "from sympy import symbols" - ] - }, - { - "cell_type": "markdown", - "id": "d9224010-d6e9-4d8a-a391-cd5350418491", - "metadata": {}, - "source": [ - "First, we create some dummy data. The x-variable holds the available data. x[1] represents gender (0 or 1). x[2] represents age, normalized to the [0,1] interval. The y-variable is the value that we seek to model. It represents the logistic transition probability between two states. The w-variable represents the weight that we assign to each data point." - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "id": "168cfc3c-d7ba-4b88-b60a-7cbd67738d83", - "metadata": {}, - "outputs": [], - "source": [ - "nsamp = 100\n", - "x = np.array( [[0.0, x/nsamp] for x in range(nsamp)] + [[1.0, x/nsamp] for x in range(nsamp)] )\n", - "y = np.array([-4.5 + 0.2*a[0]*(1-5*a[1]**2) + a[1]*(1+a[0]*0.2) + 0.1*np.random.normal() for a in x])\n", - "\n", - "p = 1/(1+np.exp(-y))\n", - "\n", - "n = [int(2000 + 6000*xj[1]/0.7) if xj[1] <= 0.7 else int(8000 - 3000*(xj[1]-0.7)/0.3) for xj in x]\n", - "\n", - "d = [nj*pj for nj,pj in zip(n,p)]" - ] - }, - { - "cell_type": "markdown", - "id": "6404a54d-b5d7-4395-96ab-d4bb9f75df61", - "metadata": {}, - "source": [ - "We can use the Pandas library to create a DataFrame and then save it as a CSV file, which support column headers. This will create a CSV file with each column labeled as ‘gender’, ‘age group (normalized)’, ‘population size’, and ‘number of transitions’ respectively. The index=False argument is used to prevent pandas from writing row indices into the file." - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "id": "98b3d891-41c2-4ead-90dd-a8419e79809e", - "metadata": {}, - "outputs": [], - "source": [ - "# Create a DataFrame\n", - "df = pd.DataFrame({\n", - " 'gender': [a[0] for a in x],\n", - " 'age group (normalized)': [a[1] for a in x],\n", - " 'population size': n,\n", - " 'number of transitions': [int(round(a)) for a in d]\n", - "})\n", - "\n", - "# Write the DataFrame to a CSV file\n", - "df.to_csv('fdata.csv', index=False) # index=False argument is used to prevent pandas from writing row indices into the CSV file" - ] - }, - { - "cell_type": "markdown", - "id": "79a2034c-1509-44c2-9fdb-ed63b301a727", - "metadata": {}, - "source": [ - "One can read the data back from the file like this:" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "id": "0da27f10-d9b1-4c75-afcd-cf69122586a6", - "metadata": {}, - "outputs": [], - "source": [ - "data = pd.read_csv('fdata.csv')" - ] - }, - { - "cell_type": "markdown", - "id": "e0d5741f-c5fb-4fb8-84a2-da56f6fa2ae9", - "metadata": {}, - "source": [ - "### Transform and inspect data" - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "id": "84552a98-075b-48de-b7a9-68e018e95e83", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[0. 0. ]\n", - " [0. 0.01]\n", - " [0. 0.02]\n", - " [0. 0.03]\n", - " [0. 0.04]\n", - " [0. 0.05]\n", - " [0. 0.06]\n", - " [0. 0.07]\n", - " [0. 0.08]\n", - " [0. 0.09]]\n" - ] - } - ], - "source": [ - "x = np.array( [[a,b] for a,b in zip(data['gender'], data['age group (normalized)'])] )\n", - "print(x[0:10])" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "id": "5bfef017-385e-47c0-8b46-89a280406102", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([-4.5444026 , -4.60062263, -4.34262549, -4.54103397, -4.40819711,\n", - " -4.54385044, -4.38964424, -4.41688114, -4.52361368, -4.24510111])" - ] - }, - "execution_count": 71, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "y[0:10]" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "id": "e7447d0f-64e9-4d56-8a41-299cdd3b044e", - "metadata": {}, - "outputs": [], - "source": [ - "# raw transition frequency per group, used for plots\n", - "p_raw = [a/b for a,b in zip(d,n)]\n", - "\n", - "# logistic probability, used as input to SVR optimization\n", - "y = np.array([np.log( p / (1-p) ) for p in p_raw])\n", - "\n", - "# calculate weights for SVR based on population size\n", - "w = np.array([1./nj for nj in n])\n", - "\n", - "# normalize weights (equivalent to changing the hyperparameters of the SVR)\n", - "w = w/sum(w)*len(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "id": "0fe05211-ed34-463f-81ea-37069c0fd93f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", - "axs.plot([xj[1] for xj,p in zip(x, p_raw) if xj[0] == 0], [p for xj,p in zip(x, p_raw) if xj[0] == 0], 'or')\n", - "axs.plot([xj[1] for xj,p in zip(x, p_raw) if xj[0] == 1], [p for xj,p in zip(x, p_raw) if xj[0] == 1], 'ob')\n", - "axs.set_title(\"raw transition frequencies\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "cd869a15-a44e-406c-9ef7-22009f1f4bd0", - "metadata": {}, - "source": [ - "The first step of the modelling is to define the mapping from data space to our quantum feature space. This is done by setting up the build_feature_map function. The circuit below is a very simplified two-variable circuit. Feel free to experiment!" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "id": "f6546726-7f76-4f7d-992c-95ee972abf17", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "QuantumCircuit:\n", - "---------------\n", - " ┌──────────┐\n", - "q.0: ┤ Ry(π*x0) ├\n", - " ├──────────┤\n", - "q.1: ┤ Ry(π*x1) ├\n", - " └──────────┘\n", - "Live QuantumVariables:\n", - "----------------------\n", - "QuantumVariable q\n" - ] - } - ], - "source": [ - "# set up 'kernel feature map' with sympy parameters\n", - "from qrisp import ry\n", - "\n", - "def build_feature_map(sym):\n", - " n = 2#number of qubits\n", - " q = QuantumVariable(n)\n", - " params = symbols(sym+':'+str(n))\n", - " ry(np.pi * params[0], q[0])\n", - " ry(np.pi * params[1], q[1])\n", - "\n", - " return q\n", - "\n", - "feature_map = build_feature_map('x')\n", - "print(feature_map.qs)\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "id": "2c128f3c-da92-4dd2-b94d-27dd25970626", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " ┌────────────┐\n", - "q.0: ┤ Ry(1.7798) ├\n", - " ├────────────┤\n", - "q.1: ┤ Ry(1.5008) ├\n", - " └────────────┘\n" - ] - } - ], - "source": [ - "# example, assign random data as parameters and print cirquit\n", - "\n", - "subs_dic = {a : np.random.rand() for a in feature_map.qs.abstract_params}\n", - "bound_qc = feature_map.qs.bind_parameters(subs_dic)\n", - "print(bound_qc)" - ] - }, - { - "cell_type": "markdown", - "id": "45f26e2c-cf15-4e67-a9b7-d774cb11c2eb", - "metadata": {}, - "source": [ - "For a data pair $(x, y)$, we create the kernel circuit by calling the build_feature_map twice, once for $x$ and once for $y$, inverting the latter, and joining them together" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "id": "ce778494-1f6a-40f0-89e9-02123cd6600a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " ┌──────────┐┌─────────────┐┌─┐ \n", - " q.0: ┤ Ry(π*x0) ├┤ Ry((-π)*y0) ├┤M├───\n", - " ├──────────┤├─────────────┤└╥┘┌─┐\n", - " q.1: ┤ Ry(π*x1) ├┤ Ry((-π)*y1) ├─╫─┤M├\n", - " └──────────┘└─────────────┘ ║ └╥┘\n", - "cb_0: ════════════════════════════╩══╬═\n", - " ║ \n", - "cb_1: ═══════════════════════════════╩═\n", - " \n" - ] - } - ], - "source": [ - "\n", - "kernel = build_feature_map('x')\n", - "y_inverse = build_feature_map('y').qs.inverse()\n", - "\n", - "kernel.qs.append(y_inverse.to_op(), kernel.qs.qubits)\n", - "\n", - "kernel.qs.measure(kernel.qs.qubits)\n", - "\n", - "print(kernel.qs.transpile())" - ] - }, - { - "cell_type": "markdown", - "id": "b9fefbd4-5e78-4b09-8e7f-8e5a9f342e60", - "metadata": {}, - "source": [ - "## Exercise 1 TODO rewrite to qrisp calls\n", - "\n", - "Experimenting with quantum circuits involves changing the structure of the circuit or the parameters used. Here are a few ways you can experiment with the given circuit:\n", - "\n", - "1. **Change the gates**: Instead of using `ry` gates, you could use other gates like `rx`, `rz`, `h` (Hadamard), etc.\n", - "\n", - "```python\n", - "qc.rx(p[0]*np.pi, 0)\n", - "qc.rz(p[1]*np.pi, 1)\n", - "```\n", - "\n", - "2. **Add more gates**: You can add more gates to your circuit to make it more complex.\n", - "\n", - "```python\n", - "qc.ry(p[0]*np.pi, 0)\n", - "qc.ry(p[1]*np.pi, 1)\n", - "qc.h(0)\n", - "qc.cx(0, 1) # CNOT gate\n", - "```\n", - "\n", - "3. **Change the parameters**: Instead of multiplying the parameters by `pi`, you could multiply them by other constants or use more complex functions of the parameters.\n", - "\n", - "```python\n", - "qc.ry(p[0], 0)\n", - "qc.ry(np.sin(p[1]), 1)\n", - "```\n", - "\n", - "4. **Increase the number of qubits**: You can increase the number of qubits in your circuit and see how that affects your results.\n", - "\n", - "Remember, when experimenting with quantum circuits, it's important to understand what each gate does and how changing the circuit might affect your results. Happy experimenting! 😊\n", - "\n", - "A few general guidelines for experimenting with quantum circuits:\n", - "\n", - "1. **Understand the problem**: Before you start experimenting, make sure you understand the problem you're trying to solve and how a quantum circuit could help solve it.\n", - "\n", - "2. **Start simple**: Start with a simple circuit and gradually add complexity. This makes it easier to understand what each part of your circuit is doing.\n", - "\n", - "3. **Use a variety of gates**: Different gates can have different effects on your quantum state, so try using a variety of gates in your experiments.\n", - "\n", - "4. **Test on a simulator first**: Before running your circuit on a real quantum computer, test it on a simulator to make sure it's working as expected.\n", - "\n", - "5. **Analyze your results**: After running your circuit, analyze the results to see if they make sense and if they're helping you solve your problem.\n", - "\n", - "6. **Iterate**: Experimenting with quantum circuits often involves a lot of trial and error. Don't be afraid to iterate on your design and try new things.\n", - "\n", - "In the context of the Quantum Support Vector Regression (QSVR) for disability insurance that you're working on, you might want to experiment with different ways of encoding your data into the quantum state or different types of quantum kernels. Remember, the goal is to find a quantum circuit that can effectively model your data and help you make accurate predictions." - ] - }, - { - "cell_type": "markdown", - "id": "3dc158a8-1035-47fa-80bd-4d0b4743eabe", - "metadata": {}, - "source": [ - "#### Hints\n", - "1. x[0] is a binary variable representing gender. Hence, flipping the first qubit from |0> to |1> based on gender will maximize the distance (wrt only the first qubit) between two subpopulations belong to different genders.\n", - "\n", - "2. x[1] is a representing age. For two sub-populations of similar age, the rotations of the second qubit will be similar, causing a low distance (wrt only the second qubit).\n", - "\n", - "3. One possible extension is to add a third qubit that would capture a first order interaction effect between x[0] and x[1], e.g. a cy or cx gate. We could also incorporate this by adding more gates to qubits 1 or 2." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "339246ed-877a-4235-9009-69f77e6e057b", - "metadata": {}, - "outputs": [], - "source": [ - "# Test code here\n", - "# Then rerun the following cells \n", - "\n" - ] - }, - { - "cell_type": "markdown", - "id": "7ed23841-0821-40bd-8a6e-0e7fd12ed22b", - "metadata": {}, - "source": [ - "#### Estimating the kernel matrix\n", - "\n", - "The train_kernel_matrix function prepares the kernel estimation by setting up inner product circuits, based on each combination of two data points. The kernel circuits are then run on a either a specified backend, or using statevector simulation." - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "id": "17cc99d0-a6b8-4e61-8d51-d89f582c7e77", - "metadata": {}, - "outputs": [], - "source": [ - "def train_kernel_matrix(x, f_feature_map, shots=1000, backend=None):\n", - " kernel = f_feature_map('x') #call feature map function\n", - " x_params = copy(kernel.qs.abstract_params)\n", - " adjoint_qs = f_feature_map('y').qs.inverse() #call feature map funciton again and apply inverse\n", - " y_params = adjoint_qs.abstract_params\n", - " kernel.qs.append(adjoint_qs.to_op(), kernel.qs.qubits) #create inner product circuit\n", - " kernel.qs = kernel.qs.transpile()\n", - " if backend is not None:#measurement only needed when running shots\n", - " kernel.qs.measure(kernel.qs.qubits)\n", - " n = len(x)\n", - " K = np.eye(n)\n", - " for i in range(n):\n", - " subs_dic = {p : x[i][int(p.name[1:])] for p in x_params}\n", - " for j in range(i+1,n):\n", - " for p in y_params:\n", - " subs_dic[p] = x[j][int(p.name[1:])]\n", - " bound_kernel = kernel.qs.bind_parameters(subs_dic) #bind parameters for data pair (x_i, x_j)\n", - " if backend is not None:\n", - " res = bound_kernel.run(shots=shots, backend=backend)\n", - " K_ij = res['0'*len(kernel.qs.qubits)] / shots if '0'*len(kernel.qs.qubits) in res else 0.0\n", - " else:#if no backend use statevector simulation\n", - " res = bound_kernel.statevector_array()\n", - " K_ij = np.abs(res[0])**2\n", - " \n", - " K[i,j] = K[j,i] = K_ij\n", - " return K\n", - " " - ] - }, - { - "cell_type": "markdown", - "id": "6684d892-b617-4556-926e-e23e10353aec", - "metadata": {}, - "source": [ - "We evaluate the kernel matrix based on our $x$ data and the build_feature_map helper function." - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "id": "908ec069-24b6-4d5b-bb47-e677339e3279", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " \u001b[2K" - ] - } - ], - "source": [ - "matrix_train = train_kernel_matrix(x, build_feature_map)" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "id": "cc7771e0-7f0c-4a32-b6bd-d6a7dd50da52", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plot the kernel matrix\n", - "\n", - "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", - "pos = axs.imshow(np.asmatrix(matrix_train),\n", - " interpolation='nearest', origin='upper', cmap='Blues')\n", - "axs.set_title(\"trained kernel matrix\")\n", - "fig.colorbar(pos, ax=axs)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "b5e309fb-7fb7-4fed-9e3f-05ff9aa6ea87", - "metadata": {}, - "source": [ - "Figure 1 displays the estimated kernel matrix. This matrix has an interesting structure: it is block-diagonal. This is due to the fact that the second quadrant of the matrix correspond to the inner products of the population groups with gender=0. These share the common characteristic gender=0, and each row is similar to its neighbours due to the encoding: similar ages are also similar in the quantum feature space. Analogously, the fourth quadrant of the matrix contains the gender=1 population groups. The first and third quadrants contain the inner products between gender=0 and gender=1 population groups and so are dissimilar in the quantum feature space." - ] - }, - { - "cell_type": "markdown", - "id": "5169b0dc-a666-4d0a-a19e-63de0ca8e6c2", - "metadata": {}, - "source": [ - "Next, we run a support vector regression (SVR) taking the kernel matrix, the weights, and the y-values as input." - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "id": "ab02281d-bcb6-4cf3-af08-a786e0f22b79", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "score: 0.8103104968457695\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "f_matrix_train = matrix_train\n", - "\n", - "zzpc_svr = SVR(kernel='precomputed')\n", - "zzpc_svr.fit(f_matrix_train, y, w)\n", - "zzpc_score = zzpc_svr.score(f_matrix_train, y, w)\n", - "print(f'score: {zzpc_score}')\n", - "pred = zzpc_svr.predict(f_matrix_train)\n", - "\n", - "p_hat = 1/(1+np.exp(-pred))\n", - "p = 1/(1+np.exp(-y))\n", - "plt.figure()\n", - "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p) if a[0] == 0],'or')\n", - "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", - "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", - "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", - "plt.legend(['Group 0', 'Group 0 model', 'Group 1', 'Group 1 model'])\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "ad0da92a-1f89-4289-a2c2-e0cb5d4e1bc6", - "metadata": {}, - "source": [ - "The score you see is the R-squared score from the SVR model. This score represents the proportion of the variance in the dependent variable that is predictable from the independent variables1. In other words, it gives you a measure of how well your model is fitting the data. A score of 1.0 indicates a perfect fit." - ] - }, - { - "cell_type": "markdown", - "id": "f2bc9cc6-7642-4f93-a152-f78ac3ccc29a", - "metadata": {}, - "source": [ - "We check the results against a classical SVR." - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "id": "df66e9a5-409b-4014-911e-c8880f081a7c", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "score: 0.8251845288722951\n" - ] - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "classical = SVR(kernel='rbf')\n", - "classical.fit(x, y, w)\n", - "classical_score = classical.score(x, y, w)\n", - "print(f'score: {classical_score}')\n", - "pred = classical.predict(x)\n", - "\n", - "p_hat = 1/(1+np.exp(-pred))\n", - "p = 1/(1+np.exp(-y))\n", - "plt.figure()\n", - "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p) if a[0] == 0],'or')\n", - "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", - "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", - "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", - "plt.legend(['Group 0', 'Group 0 model', 'Group 1', 'Group 1 model'])\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "22f6ed9d-0b80-43c2-9a59-21bfb1d7a695", - "metadata": {}, - "source": [ - "The above analysis is done in-sample. Below, we use the leave-one-out cross-validation functionality from the sklearn module." - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "id": "aed94e25-bbcc-473e-92f2-53b5ef265fa4", - "metadata": {}, - "outputs": [], - "source": [ - "from sklearn.model_selection import LeaveOneOut\n", - "from sklearn.metrics import r2_score\n", - "\n", - "zzpc_svr = SVR(kernel='precomputed')\n", - "classical = SVR(kernel='rbf')\n", - "\n", - "cols = range(len(x))\n", - "\n", - "loo = LeaveOneOut()\n", - "pred_loo = []\n", - "pred_loo_classic = []\n", - "used_K = matrix_train\n", - "for train_index, test_index in loo.split(cols):\n", - " #print(x[train_index])\n", - " zzpc_svr.fit(used_K[np.ix_(train_index,train_index)], y[train_index], w[train_index])\n", - " pred = zzpc_svr.predict(used_K[np.ix_(test_index,train_index)])\n", - " for p in pred:\n", - " pred_loo.append(p)\n", - " classical.fit(x[train_index], y[train_index], w[train_index])\n", - " cpred = classical.predict(x[test_index])\n", - " for p in cpred:\n", - " pred_loo_classic.append(p)\n", - "pred_loo = np.array(pred_loo)\n", - "pred_loo_classic = np.array(pred_loo_classic)" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "id": "d0936803-5081-44b5-9a13-2e46e05a819b", - "metadata": {}, - "outputs": [], - "source": [ - "from sklearn.model_selection import LeaveOneOut\n", - "from sklearn.metrics import r2_score\n", - "\n", - "def predict_loo(K, y, w, zzpc_svr):\n", - " cols = range(len(y))\n", - " loo = LeaveOneOut()\n", - " pred_loo = []\n", - " for train_index, test_index in loo.split(cols):\n", - " #print(x[train_index])\n", - " zzpc_svr.fit(K[np.ix_(train_index,train_index)], y[train_index], w[train_index])\n", - " pred = zzpc_svr.predict(K[np.ix_(test_index,train_index)])\n", - " for p in pred:\n", - " pred_loo.append(p)\n", - " return np.array(pred_loo)\n", - "\n", - "statevector_loo = predict_loo(matrix_train, y, w, SVR(kernel='precomputed'))" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "id": "b8d8628e-d9fd-4aff-b06a-f1db1df1c531", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "score: 0.7968219718898861\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "p_hat = 1/(1+np.exp(-statevector_loo))\n", - "p = 1/(1+np.exp(-y))\n", - "score = r2_score(p, p_hat, sample_weight=w)\n", - "print(f'score: {score}')\n", - "fig, ax = plt.subplots(1, 1)\n", - "plt.plot(np.array([a[1] for a in x if a[0] == 0])*100, [p for a,p in zip(x,p) if a[0] == 0],'or')\n", - "plt.plot(np.array([a[1] for a in x if a[0] == 1])*100, [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", - "plt.plot(np.array([a[1] for a in x if a[0] == 0])*100, [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", - "plt.plot(np.array([a[1] for a in x if a[0] == 1])*100, [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", - "plt.legend(['Group 0', 'Group 1', 'Group 0, statevector', 'Group 1, statevector'])\n", - "ax.axes.yaxis.set_ticklabels([])\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "8ecebea2-79c9-4903-8f1c-8ffbc5393330", - "metadata": {}, - "source": [ - "Quantum Support Vector Regression (QSVR) Score (0.9155345528008413): This score suggests that your QSVR model is doing a good job of capturing the relationship between your features and your target variable.\n", - "\n", - "Classical Support Vector Regression (SVR) Score (0.9295558682302361): This score is slightly higher than your QSVR score, suggesting that your classical SVR model might be fitting the data slightly better than your QSVR model.\n", - "\n", - "Leave-One-Out Cross-Validation Score (0.8977158412990511): This score is lower than both your QSVR and classical SVR scores. This isn’t surprising, as leave-one-out cross-validation can often result in lower scores because it’s a more rigorous form of validation. It’s a good way to get an unbiased estimate of how well your model will perform on unseen data.\n", - "\n", - "To compare these results, you can look at how much each score deviates from 1.0. The closer the score is to 1.0, the better the model is fitting your data. However, keep in mind that a high R-squared score doesn’t always mean your model will perform well on unseen data. It’s important to also look at other metrics and plots (like residuals) to assess your model’s performance." - ] - }, - { - "cell_type": "markdown", - "id": "dd9e815f-feef-465e-8f0b-3aefe268e477", - "metadata": {}, - "source": [ - "## Exercise 2: Residuals\n", - "In the context of regression analysis, residuals are the difference between the observed (actual) and predicted values for a data point. In other words, a residual is an error in prediction.\n", - "\n", - "Mathematically, if you have an observed value $$y_{\\text{obs}}$$ and a predicted value $$y_{\\text{pred}}$$ for a data point, the residual $$e$$ for that data point is calculated as:\n", - "\n", - "$$e = y_{\\text{obs}} - y_{\\text{pred}}$$\n", - "\n", - "Residuals are used to understand the accuracy of a regression model. If a model fits the data well, the residuals should be small and randomly distributed around zero. Patterns or trends in the residuals can indicate that the model is not adequately capturing some aspect of the data.\n", - "\n", - "In our case, we will plot a histogram of residuals from our QSVR model. This visualization can help us understand the distribution of errors made by the model.\n", - "If the model is performing well, we would expect to see most residuals close to zero, indicating that the predicted and actual values are close. Large residuals indicate that the model's predictions are far off from the actual values.\n", - "\n", - "#### Hints\n", - "1. use `residuals = y - pred`\n", - "2. in `plt.hist`use `bins=20` # bins parameter determines the number of bins (or bars) to divide your data into\n", - "3. use appropriate lables\n", - "4. *Advanced* – use `p_hat-p` for residuals" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "039e7e99-e44a-474d-bff8-08321ac03656", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "971cfa01-0662-4e8b-9b9b-6d7aa8a3ef52", - "metadata": {}, - "source": [] - }, - { - "cell_type": "markdown", - "id": "45284812-ff18-4017-a649-9276f0c071ea", - "metadata": {}, - "source": [ - "You've done a great job implementing the Quantum Support Vector Regression (QSVR) and comparing it with a classical SVR. You've also used leave-one-out cross-validation to evaluate the performance of your models, which is a robust method for estimating the generalization error.\n", - "\n", - "In terms of the residuals, you've plotted two histograms:\n", - "1. The first histogram represents the residuals calculated as `y - pred`, where `y` is the observed value and `pred` is the predicted value from your QSVR model. This gives you an idea of how well your model is predicting the actual `y` values. If your model is accurate, most residuals should be close to zero, indicating that the predicted and actual values are close. Large residuals indicate that the model's predictions are far off from the actual values.\n", - "2. The second histogram represents the residuals calculated as `p_hat - p`, where `p_hat` is the predicted probability and `p` is the actual probability. This gives you an idea of how well your model is predicting the actual probabilities. Again, if your model is accurate, most residuals should be close to zero.\n", - "\n", - "To describe the results, you would typically look at the distribution of residuals in your histograms. If your model is performing well, you would expect to see a distribution centered around zero, indicating that most predictions are close to the actual values or probabilities. If you see a skewed distribution or a distribution with a long tail, it might indicate that your model is systematically overestimating or underestimating the values or probabilities.\n", - "\n", - "In terms of what you've done here, you've implemented a QSVR for modeling transition probabilities in disability insurance, compared it with a classical SVR, and evaluated their performance using leave-one-out cross-validation and residual analysis. This is a comprehensive approach to developing and evaluating predictive models. Great work! 😊" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "ef5179d6-bb8c-46f7-a192-80d23beaf97e", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "bf6ece14-57fb-4ea5-85f5-5e5f3919414f", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "8d6c503e-5292-4644-8155-b5e76134ebf1", - "metadata": {}, - "source": [ - "### We used the statevector simulator and now we'll run it on Helmi." - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "95b0744c-60be-403a-ade5-0518b63c58df", - "metadata": {}, - "outputs": [], - "source": [ - "provider = IQMProvider(\"https://qc.vtt.fi/cocos\")\n", - "backend = provider.get_backend()" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "ceea2aee-3acf-4c85-998b-b08c6147d48c", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Native operations: ['r', 'id', 'cz', 'measure']\n", - "Number of qubits: 5\n", - "Coupling map: [[0, 2], [2, 0], [1, 2], [2, 1], [2, 3], [3, 2], [2, 4], [4, 2]]\n" - ] - } - ], - "source": [ - "print(f'Native operations: {backend.operation_names}')\n", - "print(f'Number of qubits: {backend.num_qubits}')\n", - "print(f'Coupling map: {backend.coupling_map}')" - ] - }, - { - "cell_type": "markdown", - "id": "15595412-8121-43a4-a786-083a9ed0e27a", - "metadata": {}, - "source": [ - "The `feature_map` function is a way to encode classical data into a quantum state. In this case, it's creating a quantum circuit `qc` with 2 qubits. It then applies a rotation around the y-axis (`ry`) on each qubit. The rotation angle is determined by the input data `x` multiplied by `pi`. The `ParameterVector` is a way to create a list of parameters." - ] - }, - { - "cell_type": "markdown", - "id": "19f6461a-7bc1-47e9-bf5b-6bf606fbc586", - "metadata": {}, - "source": [ - "First, we create some dummy data, but smaller (fewer data points) than it was before." - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "ed4cad78-d89f-4dff-981c-8113ca649e12", - "metadata": {}, - "outputs": [], - "source": [ - "nsamp = 10\n", - "x = np.array( [[0.0, x/nsamp] for x in range(nsamp)] + [[1.0, x/nsamp] for x in range(nsamp)] )\n", - "y = np.array([-4.5 + 0.2*a[0] + a[1]*(1+a[0]*0.2) + 0.1*np.random.normal() for a in x])\n", - "\n", - "p = 1/(1+np.exp(-y))\n", - "\n", - "n = [int(200 + 600*xj[1]/0.7) if xj[1] <= 0.7 else int(800 - 300*(xj[1]-0.7)/0.3) for xj in x]\n", - "\n", - "d = [nj*pj for nj,pj in zip(n,p)]" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "6b244442-219f-448c-bee8-21b566d906c4", - "metadata": {}, - "outputs": [], - "source": [ - "# Create a DataFrame\n", - "df1 = pd.DataFrame({\n", - " 'gender': [a[0] for a in x],\n", - " 'age group (normalized)': [a[1] for a in x],\n", - " 'population size': n,\n", - " 'number of transitions': d\n", - "})\n", - "\n", - "# Write the DataFrame to a CSV file\n", - "df1.to_csv('fdata1.csv', index=False) # index=False argument is used to prevent pandas from writing row indices into the CSV file" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "670765b0-5135-4965-a15f-57e5ea90c130", - "metadata": {}, - "outputs": [], - "source": [ - "data1 = df1\n", - "# data1 = pd.read_csv('fdata1.csv')" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "f04e1346-2773-4918-9789-b72c9354f381", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[0. 0. ]\n", - " [0. 0.1]\n", - " [0. 0.2]\n", - " [0. 0.3]\n", - " [0. 0.4]\n", - " [0. 0.5]\n", - " [0. 0.6]\n", - " [0. 0.7]\n", - " [0. 0.8]\n", - " [0. 0.9]\n", - " [1. 0. ]\n", - " [1. 0.1]\n", - " [1. 0.2]\n", - " [1. 0.3]\n", - " [1. 0.4]\n", - " [1. 0.5]\n", - " [1. 0.6]\n", - " [1. 0.7]\n", - " [1. 0.8]\n", - " [1. 0.9]]\n" - ] - } - ], - "source": [ - "# Transform and inspect data\n", - "x1 = np.array( [[a,b] for a,b in zip(data1['gender'], data1['age group (normalized)'])] )\n", - "print(x1)" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "3b74a992-8a26-481b-b40a-05cc775ce58f", - "metadata": {}, - "outputs": [], - "source": [ - "# raw transition frequency per group, used for plots\n", - "p_raw = [a/b for a,b in zip(d,n)]\n", - "\n", - "# logistic probability, used as input to SVR optimization\n", - "y = np.array([np.log( p / (1-p) ) for p in p_raw])\n", - "\n", - "# calculate weights for SVR based on population size\n", - "w = np.array([1./nj for nj in n])\n", - "\n", - "# normalize weights (equivalent to changing the hyperparameters of the SVR)\n", - "w = w/sum(w)*len(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "c4e5c7fd-1c28-4867-8e1a-4ba20b711f1f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", - "axs.plot([x1j[1] for x1j,p in zip(x1, p_raw) if x1j[0] == 0], [p for x1j,p in zip(x1, p_raw) if x1j[0] == 0], 'or')\n", - "axs.plot([x1j[1] for x1j,p in zip(x1, p_raw) if x1j[0] == 1], [p for x1j,p in zip(x1, p_raw) if x1j[0] == 1], 'ob')\n", - "axs.set_title(\"raw transition frequencies\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "08783390-fb9a-4d24-ae8b-02eb0923c632", - "metadata": {}, - "source": [ - "## Exercise 3: Implement and Visualize a Quantum Feature Map\n", - "\n", - "In this exercise, you will implement a quantum feature map using Qiskit and visualize the resulting quantum circuit. The feature map is a way of encoding classical data into quantum states. In this case, we will use a simple feature map that applies a rotation around the y-axis on each qubit.\n", - "\n", - "### Task 1: Implement the Feature Map\n", - "\n", - "First, let's implement the feature map. Here is the function you need to complete:\n", - "\n", - "```python\n", - "def feature_map(x1):\n", - " p = ParameterVector('x1', length=2)\n", - " qc = QuantumCircuit(2)\n", - "\n", - " # TODO: Apply a rotation around the y-axis on each qubit\n", - " # Hint: Use the ry gate and the input data x1\n", - "\n", - " return qc\n", - "```\n", - "\n", - "### Task 2: Visualize the Circuit\n", - "\n", - "After implementing the feature map, you visualize the resulting quantum circuit, as we did at the beginning of this lesson. \n", - "\n", - "Good luck with your exercise! If you have any questions or need further clarification, feel free to ask. 😊" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "24c26430-a283-4a99-8fb7-058c52bf4c7e", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "dc63aa1a-0bf0-4e1f-9bf2-580c12aadbdb", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "52aa44c7-40bc-4ec2-b273-94d6b457a8dc", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "13cf3642-2745-4250-ac18-9006bb457793", - "metadata": {}, - "source": [ - "The following part of the code implements a list of all possible quantum circuits for the given data `x1`. For each pair of data points `(x1[i], x1[j])`, it creates two circuits using the `feature_map` function. The feature map is a way of encoding classical data into quantum states. It then appends the inverse of `qc_j` to `qc_i` using the `compose` function. This function combines two circuits, and with `.inverse()`, it applies the inverse of the second circuit. After composing the circuits, it adds a measurement on all qubits using `measure_all()`. The circuit is then transpiled for a specific backend using the `transpile` function." - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "id": "051f839e-9306-44eb-b198-eaeafa837238", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "190\n" - ] - } - ], - "source": [ - "# from qiskit import transpile\n", - "\n", - "# Initialize an empty list to store all circuits\n", - "all_circuits = []\n", - "\n", - "for i in range(len(x1)):\n", - " for j in range(i):\n", - " # Substitute parameters with values from your data\n", - " qc_i = feature_map(x1[i])\n", - " qc_j = feature_map(x1[j])\n", - " \n", - " # Append the inverse of qc_j to qc_i and measure\n", - " qc_ij = qc_i.compose(qc_j.inverse())\n", - " qc_ij.measure_all()\n", - " \n", - " # Transpile the circuit for the backend\n", - " qc_ij_transpiled = transpile(qc_ij, backend=backend)\n", - " \n", - " # Add the transpiled circuit to the list\n", - " all_circuits.append(qc_ij_transpiled)\n", - "\n", - "print(len(all_circuits))" - ] - }, - { - "cell_type": "markdown", - "id": "b50ea21e-efef-4102-82c5-9a36ecde6552", - "metadata": {}, - "source": [ - "This block of code defines a batch size and splits the transpiled circuits into batches. It then initializes a list to store job IDs. Each batch of circuits is executed on the backend with 1024 shots per circuit execution. Also, it can take some time to execute." - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "id": "23cde26c-9afe-42ca-80e1-657f120f26ac", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Tracking execution of job1:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job2:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job3:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job4:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job5:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job6:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job7:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job8:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job9:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job10:\n", - "Job Status: job has successfully run\n" - ] - } - ], - "source": [ - "# Define the batch size\n", - "batch_size = 20\n", - "\n", - "# Split the transpiled circuits into batches\n", - "batches = [all_circuits[i:i + batch_size] for i in range(0, len(all_circuits), batch_size)]\n", - "\n", - "# Initialize a list to store job IDs\n", - "job_ids = []\n", - "\n", - "# Execute each batch of circuits\n", - "for batch in batches:\n", - " job = backend.run(batch, shots=1024)\n", - " job_ids.append(job.job_id())\n", - "\n", - "# This block of code executes each batch until it's successful or an exception occurs\n", - "# If an exception occurs, it waits for a random amount of time between 1 and 10 seconds before retrying\n", - "\n", - "import time\n", - "import random\n", - "\n", - "# Initialize a list to store results\n", - "results = []\n", - "n_shots = 1024\n", - "\n", - "# Initialize a counter for the job number\n", - "job_number = 1\n", - "\n", - "for batch in batches:\n", - " success = False\n", - " while not success:\n", - " try:\n", - " # Execute the batch of circuits\n", - " job = backend.run(batch, shots=n_shots)\n", - " \n", - " # Print job execution status\n", - " print(f\"Tracking execution of job{job_number}:\")\n", - " job_monitor(job)\n", - " \n", - " # Wait for the job to finish and get the result\n", - " result = job.result()\n", - " \n", - " # If successful, append the result and break the loop\n", - " results.append(result)\n", - " success = True\n", - " \n", - " except Exception as e:\n", - " print(f\"Execution failed with error: {e}\")\n", - " \n", - " # Sleep for a bit (random backoff) before retrying\n", - " time.sleep(random.randint(1, 10))\n", - " \n", - " # Increment the job number for the next iteration\n", - " job_number += 1" - ] - }, - { - "cell_type": "markdown", - "id": "fc8b2a3d-9729-4c20-acf5-f40d9851ef30", - "metadata": {}, - "source": [ - "**Job Retrieval and Frequency Calculation**: The script starts by iterating over a list of `job_ids`. For each `job_id`, it retrieves the job result from the backend. It then calculates the frequency of the '00' state in the results and appends this frequency to the `estimates` list." - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "id": "6f002a91-d87c-4278-905c-dbfacf9a03f0", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Job1: ea63caca-9859-4988-afcc-4617a4422261\n", - "Job2: 4ea8454c-0146-47e3-a4f3-22e7098bf8b5\n", - "Job3: 29c17939-328b-46bd-bcf6-e2df758b4efd\n", - "Job4: 80e39182-931b-4bc9-83d7-f100a877d81b\n", - "Job5: bae16e48-b12a-4cea-bdf4-287bce4e11ab\n", - "Job6: ed7f15be-36d1-41c4-b0e1-794746789a48\n", - "Job7: b07bd0df-a786-4389-8def-ea0926f2fd17\n", - "Job8: d346a014-4afc-43ee-8ee4-d16e229e7c1e\n", - "Job9: baf11441-c6d0-4b0b-8641-068a929c72c4\n", - "Job10: 1895b727-95b8-4925-bc95-e7e2347493f7\n" - ] - } - ], - "source": [ - "# Initialize a counter for the job number\n", - "job_number = 1\n", - "\n", - "for job_id in job_ids:\n", - " print(f\"Job{job_number}: {job_id}\")\n", - " job_number += 1" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "id": "bacb231a-f8cc-4922-82fd-079a6b568dc9", - "metadata": {}, - "outputs": [], - "source": [ - "estimates = []\n", - "\n", - "for job_id in job_ids:\n", - " job_res = backend.retrieve_job(job_id).result()\n", - " for res in job_res.results:\n", - " if '00' in res.data.counts:\n", - " freq = res.data.counts['00']/n_shots\n", - " else:\n", - " freq = 0.0\n", - " estimates.append(freq)" - ] - }, - { - "cell_type": "markdown", - "id": "3ab74e22-d559-46b8-8777-396d0af98e79", - "metadata": {}, - "source": [ - "**Kernel Matrix Construction**: The script constructs a kernel matrix `K_helmi` using the estimates. The kernel matrix is a symmetric matrix where each element represents a measure of similarity between two data points." - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "id": "77466963-5ed7-4a93-adcd-4c9dd0867a18", - "metadata": {}, - "outputs": [], - "source": [ - "K_helmi = np.identity(len(x1))\n", - "\n", - "cnt = 0\n", - "for i in range(len(x1)):\n", - " for j in range(i):\n", - " #print(i, ' ', j)\n", - " K_helmi[i,j] = estimates[cnt]\n", - " K_helmi[j,i] = estimates[cnt]\n", - " cnt += 1" - ] - }, - { - "cell_type": "markdown", - "id": "9f7f0f1d-bf79-45fd-9763-2b448c10c884", - "metadata": {}, - "source": [ - " **Kernel Matrix Visualization**: The kernel matrix is then visualized using matplotlib's `imshow` function. The color map 'Blues' is used, and a color bar is added for reference." - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "id": "e09a4a10-61a5-4f02-92a3-2bdd33a5e7ba", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", - "pos = axs.imshow(np.asmatrix(K_helmi),\n", - " interpolation='nearest', origin='upper', cmap='Blues')\n", - "axs.set_title(\"kernel matrix from Helmi\")\n", - "fig.colorbar(pos, ax=axs)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "0cc501ab-40c7-4b26-aefb-f20ff7369b72", - "metadata": {}, - "source": [ - "**Support Vector Regression (SVR)**: The script uses the Support Vector Regression (SVR) model from scikit-learn with a precomputed kernel. It fits the model to the data (`f_matrix_train` and `y`) and calculates the score of the model using the `score` method.\n", - "\n", - "**Prediction and Plotting**: The fitted model is used to predict outcomes, which are then plotted against the actual outcomes for two groups (Group 0 and Group 1)." - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "id": "77e7a3fc-3bd0-4d7f-acb7-17e5fbb2132e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "score: 0.9001754733534563\n" - ] - }, - { - "data": { - "image/png": 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5iczMTK3nqVevnvjPf/4jhBAiKipKNG/eXGfcOn/GiIjoiYr7/H6c3tNPkZGR+Oqrr7Bq1SqcPXsWb7zxBtLT0zFixAgAwNChQzFt2jRN/4iICOzYsQMLFy7EuXPnMGvWLBw7dgzjx48HAKSnp+Pdd9/FoUOHcPnyZcTFxeHVV1/F9evX0b9/fwBysfGiRYvwxx9/4OLFi1i9ejUmTZqEV155BdWrVy91Qmeujhw5gpMnT6JJkyaFpufatGmjdfvs2bMICgrSagsKCsLZs2f1ft3AwEDNdRcXFzRs2LBUz/MkzZo101xXr9dq2rRpoTb1SEtRX+M///yDvLw8nD17FpUqVULr1q019zdq1EjrgM4//vgDDx480CxqVl8SEhJw4cIFg3+NRESkP70rCg8YMAC3bt3Ce++9h6SkJLRo0QI7duzQfJBcuXIFVlYFuVL79u2xZs0azJgxA++++y6eeuop/PDDD3jmmWcAANbW1jh37hxWrVqF27dvw9XVFW3btsX+/fvRpEkTAHIqae3atZg1axaysrLg5+eHSZMmITIy0hDfA92qVAEePCi/53/Sa5dA/fr1oVKpEB8fr9Vet25dAEDlypULPUbfbfDq91I8MiVW1JSSPjw8PJCdnY2UlBSt5KG4qUy1Rxc3q6fXdLXl5+eXOU61Bw8ewNPTU7OO6FE8nZyIyDiU6piE8ePHa0ZaHqfrl37//v01oy6Ps7e3R3R0dLGv16pVq2IXj5YLlQow8jo4rq6u6Nq1KxYvXowJEyaUqm5P48aNceDAAQwbNkzTduDAATz99NMAgBo1agAAEhMT0bJlSwDQWjT8qEOHDsHHxwcAcO/ePfz9999o3Lixzr6tW7eGjY0N9uzZg5deegkAEB8fjytXrmiN+BiC+mt81IEDB9CgQQNYW1ujUaNGyM3NRVxcHNq2bauJJSUlRdO/VatWSEpKQqVKleDr62vQ+IiIyDB49pOJW7p0KYKCgtCmTRvMmjULzZo1g5WVFY4ePYpz585pTanoMnnyZISHh6Nly5YIDg7Gli1bEB0djd27dwOQoz3t2rXDvHnz4Ofnh5s3b2LGjBk6n2v27NlwdXWFu7s7pk+fDjc3N4SGhurs6+zsjJEjRyIyMhIuLi5wcnLChAkTEBgYiHbt2pXpe/K4t956C23btsUHH3yAAQMGIDY2FosXL8bSpUsBAA0bNkT37t0xZswYLFu2DJUqVcLEiRO1RrqCg4MRGBiI0NBQfPLJJ2jQoAFu3LiBbdu2oW/fvoWm9YiISAHlv8THOOi9UNiE3LhxQ4wfP174+fkJGxsb4ejoKPz9/cX8+fNFenq6ph8AsXnz5kKPX7p0qahbt66wsbERDRo0EN9++63W/WfOnBGBgYGicuXKokWLFmLnzp06Fwpv2bJFNGnSRNja2gp/f3/xxx9/FBv3w4cPxdixY0X16tVFlSpVRN++fTWLe4tSp04dzeLdor4uXYubN27cKJ5++mlhY2MjfHx8xPz587WeIzExUfTs2VPY2dkJHx8f8e233xZ6rbS0NDFhwgRRq1YtYWNjI7y9vcXgwYPFlStXhBBcKExEVB70WSisEqKE+4dNXFpaGpydnZGamlpoe3dmZiYSEhLg5+cHe3t7hSI0XXv37kXnzp1x7949ri8pAn/GiIhKp7jP78cZTfE9IiIiorJgUkNERERmgQuFqcw6deoEC5nFJCIiI8aRGiIiIjILTGqIiIjILDCpISIiIrPApIaIiIjMApMaIiIiMgtMaoiIiMgsMKkhIiIis8CkxsDy8oC9e4Hvv5f/5uWV/2smJSUhIiIC9evXh729Pdzd3REUFIRly5YhIyOj/AMopRUrVqBTp05wcnKCSqXSOhWbiIhIXyy+Z0DR0UBEBHDtWkGblxfw+edAWFj5vObFixcRFBSEatWqYc6cOWjatCns7Oxw6tQprFixArVr10bv3r11PjYnJwc2NjblE1gJZGRkoHv37ujevTumTZumWBxERGQeOFJjINHRQL9+2gkNAFy/Ltujo8vndceOHYtKlSrh2LFjCA8PR+PGjVG3bl306dMH27ZtQ69evTR9VSoVli1bht69e8PBwQEfffQRAGDZsmWoV68ebG1t0bBhQ3z33Xeax1y6dAkqlQonT57UtKWkpEClUmHv3r0A5IGWKpUK27ZtQ7NmzWBvb4927drh9OnTxcY+ceJETJ06Fe3atTPcN4SIiCwWkxoDyMuTIzS6TgpQt02caPipqDt37mDnzp0YN24cHBwcdPZRqVRat2fNmoW+ffvi1KlTePXVV7F582ZERETgrbfewunTpzFmzBiMGDECMTExesczefJkLFy4EEePHkWNGjXQq1cv5OTklOprIyIi0yEEkJgIXL6sbBycfjKA/fsLj9A8Sgjg6lXZr1Mnw73u+fPnIYRAw4YNtdrd3NyQmZkJABg3bhw+/vhjzX2DBg3CiBEjNLcHDhyI4cOHY+zYsQCAyMhIHDp0CAsWLEDnzp31iicqKgpdu3YFAKxatQpeXl7YvHkzwsPDS/X1ERGR8cjLk591588DFy7If9XXL1wA0tPlzMSGDcrFyKTGABITDduvrI4cOYL8/HwMHjwYWVlZWve1adNG6/bZs2cxevRorbagoCB8/vnner9uYGCg5rqLiwsaNmyIs2fP6v08RESWIi9P/sGbmAh4egIdOgDW1srFk5MDXLqknbCoryckANnZRT/Wygp4+LDCQtWJSY0BeHoatl9J1a9fHyqVCvHx8VrtdevWBQBUrly50GOKmqYqipWVnKF89BRuTikREZWdEptLAJl4XLyoO3G5cqX4pRK2toCfH1C/vrzUq1dwvU4deb+SmNQYQIcO8gfx+nXd62pUKnl/hw6GfV1XV1d07doVixcvxoQJE/ROWACgcePGOHDgAIYNG6ZpO3DgAJ5++mkAQI0aNQAAiYmJaNmyJQBoLRp+1KFDh+Dj4wMAuHfvHv7++280btxY75iIiMydenPJ458Z6s0lGzeWLbFJS9M9TXT+vHyN4lSpop2sPHrdy0vZkaQnYVJjANbWMrPu108mMI/+kKrX6S5aVD4/CEuXLkVQUBDatGmDWbNmoVmzZrCyssLRo0dx7tw5tG7dutjHT548GeHh4WjZsiWCg4OxZcsWREdHY/fu3QDkaE+7du0wb948+Pn54ebNm5gxY4bO55o9ezZcXV3h7u6O6dOnw83NDaGhoUW+dlJSEpKSknD+/HkAwKlTp1C1alX4+PjAxcWldN8QIiIj96TNJSqV3FzSp0/RnxtCAHfu6B5tuXABuHWr+BicnYGnntKdvHh4FHx2mRxhIVJTUwUAkZqaWui+hw8fijNnzoiHDx+W6TU2bRLCy0sI+eMmL97esr083bhxQ4wfP174+fkJGxsb4ejoKPz9/cX8+fNFenq6ph8AsXnz5kKPX7p0qahbt66wsbERDRo0EN9++63W/WfOnBGBgYGicuXKokWLFmLnzp0CgIiJiRFCCBETEyMAiC1btogmTZoIW1tb4e/vL/74449i446KihIACl2+/vrrsn5LjI6hfsaIyPTFxGh/ThR1+fVXIa5fF2LfPiFWrhTi3XeFCA8XolUrIZydn/z4mjWFaN9eiKFDhXj/fSFWrxbi8GEhbt8WIj9f6e9CyRX3+f04lRC6ckXzk5aWBmdnZ6SmpsLJyUnrvszMTCQkJMDPzw/29vZleh1jW/RVEfbu3YvOnTvj3r17qFatmtLhGCVD/owRkXT7tn4LU0vzaafvY0rS/6ef5EjNk9jaFr8wFwC8vXWPttSrB1StWrKYjV1xn9+P4/STgVlbG3bbNhERaXv4EBg7FvjmG6UjKV/Z2fIzxde38NqWevXkgl0d+0EsGpMaIiIyGZcvywW0x4/L23Z2+j+HvutFSrO+5EmPefiw+FEdNzfgwAGZuCh4mo3JYVJDZdapUydYyCwmESlozx5gwAC5QNbNDVi/HtCzRqjRUO9+AnRvLvnPf4AGDSo+LlPHYxKIiMioCQHMnw906yYTmjZtgLg4001oADnatHEjULu2druXV9m3c1syjtQQEZHRevAAGDlSjsoAwIgRwNKlgDmstw8Lk9u2LW1zSXliUkNEREbp/Hmgb1/g9Gm5ruTzz4HXXzfhGio6cHOJYTGpISIio7NtGzB4MJCaKkcwNm4E2rdXOioydlxTQ0RERiM/H5g9G+jVSyY0QUFy/QwTGioJjtQQEZFRSE0Fhg6VxekAYNw44NNPlT8kkUwHR2qIitCpUydMnDixxP2/+eYbVlQmKqUzZwB/f5nQ2NkBX38NLF7MhIb0w6TGDCQlJSEiIgL169eHvb093N3dERQUhGXLliEjI0Pp8Iq0YsUKdOrUCU5OTlCpVEhJSVE6JCJSwKZNQEAA8Pffsuz/778Dw4crHRWZIk4/mbiLFy8iKCgI1apVw5w5c9C0aVPY2dnh1KlTWLFiBWrXro3evXvrfGxOTg5sFCxVmZGRge7du6N79+6YNm2aYnEQkTLy8oAZM4B58+Tt558H1q4FatRQNi4yXRypMXFjx45FpUqVcOzYMYSHh6Nx48aoW7cu+vTpg23btqFXr16aviqVCsuWLUPv3r3h4OCAjz76CACwbNky1KtXD7a2tmjYsCG+++47zWMuXboElUqFkydPatpSUlKgUqmwd+9eAPJAS5VKhW3btqFZs2awt7dHu3btcPr06WJjnzhxIqZOnYp27dqV+Ovt1KkTJkyYgIkTJ6J69epwd3fHV199hfT0dIwYMQJVq1ZF/fr18fPPP2s9bt++ffD394ednR08PT0xdepU5Obmau5PT0/H0KFD4ejoCE9PTyxcuLDQa2dlZeHtt99G7dq14eDggICAAM33gIj0c+cO0KNHQULz9tvAL78woaGyYVJTBCGA9HRlLiU9ceDOnTvYuXMnxo0bBwcHB519VI8VdJg1axb69u2LU6dO4dVXX8XmzZsRERGBt956C6dPn8aYMWMwYsQIxMTE6P09mzx5MhYuXIijR4+iRo0a6NWrF3JycvR+nidZtWoV3NzccOTIEUyYMAFvvPEG+vfvj/bt2+P48ePo1q0bhgwZopl6u379Onr06IG2bdvijz/+wLJly7By5Up8+OGHWrHv27cPP/74I3bu3Im9e/fiuPpwmX+NHz8esbGxWLt2Lf7880/0798f3bt3xz///GPwr5HInJ08KasC79wJVKkiR2fmzwcqce6AykpYiNTUVAFApKamFrrv4cOH4syZM+Lhw4eatgcPhJDpRcVfHjwo2dd06NAhAUBER0drtbu6ugoHBwfh4OAg3nnnHU07ADFx4kStvu3btxejRo3Sauvfv7/o0aOHEEKIhIQEAUCcOHFCc/+9e/cEABETEyOEECImJkYAEGvXrtX0uXPnjqhcubJYt27dE78O9ePv3bv3xL4dO3YUzz77rOZ2bm6ucHBwEEOGDNG0JSYmCgAiNjZWCCHEu+++Kxo2bCjy8/M1fZYsWSIcHR1FXl6euH//vrC1tRXr168vFH9ERIQQQojLly8La2trcf36da14unTpIqZNmyaEEOLrr78Wzs7OOuPW9TNGZIn+9z8hKleWv+vq1RPizz+VjoiMXXGf34/jSI0ZOnLkCE6ePIkmTZogKytL6742bdpo3T579iyCgoK02oKCgnD27Fm9XzcwMFBz3cXFBQ0bNizV8zxJs2bNNNetra3h6uqKpk2batrc3d0BADdv3gQgv8bAwECtUaugoCA8ePAA165dw4ULF5CdnY2AgIBC8audOnUKeXl5aNCgARwdHTWXffv24cKFCwb/GonMTU4OMHEi8Mor8oTqF14Ajh4FHvmvS1RmHOwrQpUq8swRpV67JOrXrw+VSoX4+Hit9rp16wIAKleuXOgxRU1TFcXKSua94pE5sfKYUtLH44ubVSqVVps6ecnPzzfYaz548ADW1taIi4uD9WMHszg6OhrsdYjMUXIyEB4O/PabvD1jBjBrFs84IsPjSE0RVCrAwUGZS0nPNXF1dUXXrl2xePFipKenl+rrbNy4MQ4cOKDVduDAATz99NMAgBr/rtpLTEzU3P/oouFHHTp0SHP93r17+Pvvv9G4ceNSxWVIjRs3RmxsrFZiduDAAVStWhVeXl6oV68ebGxscPjwYc396vjVWrZsiby8PNy8eRP169fXunh4eFTo10NkSg4fBlq3lglN1arA5s3ABx8woaHywZEaE7d06VIEBQWhTZs2mDVrFpo1awYrKyscPXoU586dQ+vWrYt9/OTJkxEeHo6WLVsiODgYW7ZsQXR0NHbv3g1Ajva0a9cO8+bNg5+fH27evIkZM2bofK7Zs2fD1dUV7u7umD59Otzc3BAaGlrkayclJSEpKQnnz58HIKd4qlatCh8fH7i4uJTuG6LD2LFjsWjRIkyYMAHjx49HfHw8oqKiEBkZCSsrKzg6OmLkyJGYPHkyXF1dUbNmTUyfPl0zSgUADRo0wODBgzF06FAsXLgQLVu2xK1bt7Bnzx40a9YMPXv2NFi8RObiq6+A8eOB7GygUSOZ0DRqpHRUZNbKfYWPkdB3obApuXHjhhg/frzw8/MTNjY2wtHRUfj7+4v58+eL9PR0TT8AYvPmzYUev3TpUlG3bl1hY2MjGjRoIL799lut+8+cOSMCAwNF5cqVRYsWLcTOnTt1LhTesmWLaNKkibC1tRX+/v7ijz/+KDbuqKgoAaDQ5euvvy7yMR07dtQs3lWrU6eO+Oyzz7TaHv9a9+7dK9q2bStsbW2Fh4eHmDJlisjJydHcf//+ffHKK6+IKlWqCHd3d/HJJ58Ueq3s7Gzx3nvvCV9fX2FjYyM8PT1F3759xZ//rnTkQmEiKTNTiNGjCzY/hIUJkZamdFRkqvRZKKwSoqQbiE1bWloanJ2dkZqaCicnJ637MjMzkZCQAD8/P9jb2ysUoenau3cvOnfujHv37vGYgCLwZ4wsxfXrQL9+wKFDcir9o4+AqVNLPq1O9LjiPr8fx+knIiIyiP37gf795cLg6tWB778HQkKUjoosCRcKExFRmQgBfPGFPOYgORlo1gw4dowJDVU8jtRQmXXq1AkWMotJRI/JyABefx1Qn64ycKBcIKxn9Qgig2BSQ0REpXLpEtC3rzz2wNoaWLAAiIjg+hlSDpMaIiLS265dwMsvA3fvykMo168HOnVSOiqydFxT8whOoVB54c8WmQshgI8/Brp3lwlN27ZAXBwTGjIOTGpQUHZffaozkaFlZ2cDQKEjFohMyf378riDqVOB/Hxg5EhZKdjbW+nIiCROP0F+0FSrVk1zAGKVKlW0Dj8kKov8/HzcunULVapUQaVK/C9Hpumff4DQUODMGcDGBvjyS2D0aK6fIePC37D/Up/fo05siAzJysoKPj4+TJbJJG3dCgweDKSlAZ6ewKZNQGCg0lERFVaqpGbJkiWYP38+kpKS0Lx5c3z55Zfw9/cvsv+GDRswc+ZMXLp0CU899RQ+/vhj9OjRQ3P/rFmzsHbtWly9ehW2trZo3bo1PvroIwQEBGj63L17FxMmTMCWLVtgZWWFl156CZ9//rnBTkhWqVTw9PREzZo1FT+FmsyPra2t1llSRKYgPx+YPRt4/315OygI2LBBJjZExkjvpGbdunWIjIzE8uXLERAQgEWLFiEkJATx8fGoWbNmof4HDx7EwIEDMXfuXLz44otYs2YNQkNDcfz4cTzzzDMA5GGBixcvRt26dfHw4UN89tln6NatG86fP685JXrw4MFITEzErl27kJOTgxEjRmD06NFYs2ZNGb8F2qytrbnugYgsXkoKMGSIHKUB5MGUCxcCtraKhkVULL3PfgoICEDbtm2xePFiAHK9gLe3NyZMmICpU6cW6j9gwACkp6djq/p/BoB27dqhRYsWWL58uc7XUJ/zsHv3bnTp0gVnz57F008/jaNHj6JNmzYAgB07dqBHjx64du0aatWq9cS49Tk7gojIkv31l6w/888/gL09sHw5MGyY0lGRpdLn81uv8fDs7GzExcUhODi44AmsrBAcHIzY2Fidj4mNjdXqDwAhISFF9s/OzsaKFSvg7OyM5s2ba56jWrVqmoQGAIKDg2FlZYXDhw/rfJ6srCykpaVpXYiIqHgbNgABATKh8fEBDhxgQkOmQ6+k5vbt28jLy4O7u7tWu7u7O5KSknQ+JikpqUT9t27dCkdHR9jb2+Ozzz7Drl274ObmpnmOx6e2KlWqBBcXlyJfd+7cuXB2dtZcvLnnkIioSLm5wJQpcst2ejrQpYusP9OqldKREZWc0axc7Ny5M06ePImDBw+ie/fuCA8PL9NOpGnTpiE1NVVzuXr1qgGjJSIyH7dvAy+8AHzyibw9eTKwYwfw79+VRCZDr6TGzc0N1tbWSE5O1mpPTk7WbIl+nIeHR4n6Ozg4oH79+mjXrh1WrlyJSpUqYeXKlZrneDzByc3Nxd27d4t8XTs7Ozg5OWldiIhI2/HjQJs2wO7d8hDKdetkcsOSSmSK9Epq1Nut9+zZo2nLz8/Hnj17EFhE0YLAwECt/gCwa9euIvs/+rxZWVma50hJSUFcXJzm/l9//RX5+fla276JiKjkvvtObtO+fBmoVw84dEhOPxGZKr1z8cjISAwbNgxt2rSBv78/Fi1ahPT0dIwYMQIAMHToUNSuXRtz584FAERERKBjx45YuHAhevbsibVr1+LYsWNYsWIFACA9PR0fffQRevfuDU9PT9y+fRtLlizB9evX0b9/fwBA48aN0b17d4waNQrLly9HTk4Oxo8fj5dffrlEO5+IiKhATg7w1luyKjAA9OgBrF4NVKumaFhEZaZ3UjNgwADcunUL7733HpKSktCiRQvs2LFDsxj4ypUrWkXG2rdvjzVr1mDGjBl499138dRTT+GHH37Q1KixtrbGuXPnsGrVKty+fRuurq5o27Yt9u/fjyZNmmieZ/Xq1Rg/fjy6dOmiKb73xRdflPXrJyKyKMnJQP/+wP798vZ77wFRUQBrQ5I50LtOjalinRoisnSXL8tdTRcuAE5Ocvqpd2+loyIqnj6f31wKRkRkAf75RyY0V68Cfn7Azz8DDRsqHRWRYTGpISIyc6dPA8HBcuqpYUO508nLS+moiAyPs6hERGYsLg7o2FEmNM2aAb/9xoSGzBeTGiIiM3XgAPD888Ddu4C/PxATA+g4d5jIbDCpISIyQ7t3A926AWlpwHPPydsuLkpHRVS+mNQQEZmZLVuAF18EMjKA7t3louCqVZWOiqj8MakhIjIj69YBYWFAVhbQty/www9AlSpKR0VUMZjUEBGZia+/BgYNkiduDx4MrF8P2NkpHRVRxWFSQ0RkBhYvBl59FcjPB0aPBr79lodSkuXhjzwRkYn7+GNg6lR5fdIkYOFCQKVSNqZylZcnz3lITAQ8PYEOHQBra6WjIiPAkRoiIhMlBDBzZkFCM3OmBSQ00dGAry/QubOca+vcWd6OjlY6MjICTGqIiEyQEEBkJPDhh/L2xx8Ds2dbQELTrx9w7Zp2+/Xrsp2JjcVjUkNEZGLy8oAxY4BFi+TtxYuBd95RNKTyl5cHRETIbO5x6raJE2U/slhMaoiITEhuLjB0KPDVV4CVldzxNG6c0lFVgP37C4/QPEoIeVrn/v0VFxMZHS4UJiIyEVlZwMsvy9ozlSoBq1cD4eFKR1VBEhMN24/MEpMaIiITkJEhi+r98ousPbNxo6wabDE8PQ3bj8wSp5+IiIxcWhrwwgsyoalSBdi2zcISGkBu2/byKnoltEoFeHvLfmSxmNQQERmxu3eBrl2B334DnJyAnTuBLl2UjkoB1tbA55/L648nNurbixaxXo2FY1JDRGSkkpNlGZYjRwBXVyAmBggKUjoqBYWFyXm32rW12728ZHtYmDJxkdHgmhoiIiN07RoQHAzExwMeHsDu3UCTJkpHZQTCwoA+fVhRmHRiUkNEZGQuXpRTTJcuAT4+wJ49QP36SkdlRKytgU6dlI6CjBCnn4iIjMi5c3Lg4dIlmcjs38+EhqikmNQQERmJkyeB554DbtyQU02//SZHaoioZDj9RERkBA4fBrp3B1JSgFat5PZtNzfDvgYPtyZzx5EaIiKF7d0rFwWnpADt2wO//mr4hIaHW5MlYFJDRKSgHTtkYb0HD+Ti4J07AWdnw74GD7cmS8GkhohIIdHRQO/eQGamrBC8dSvg4GDY1+Dh1mRJmNQQESngf/+Th1Hm5Mh/o6MBe3vDvw4PtyZLwqSGiKiCrVgBDB0qR0eGDwfWrAFsbMrntXi4NVkSJjVERBXos8+AMWPkCMn48cDKleW7A4mHW5MlYVJDRFQBhAA++ACIjJS3p0wBvvgCsCrn38I83JosCZMaIqJyJgQwdSrw3nvy9ocfAnPnFp1oGBIPtyZLwqSGiKgc5efLaaZPPpG3P/sMmD69YhIaNR5uTZaCFYWJiMpJbi7w2mvAqlUyifnPf4BRo5SJhYdbkyVgUkNEVA6ys4FXXgE2bJCJw6pVwODBysbEw63J3DGpISIysMxMWal32zbA1hZYuxbo21fpqIjMH5MaIiIDevBATvP8+qsspvfDD0BIiNJREVkGJjVERAaSkgL07AkcPAg4OspjDzp2VDoqIsvBpIaIyABu3wa6dQNOnACqVQN++QXw91c6KiLLwqSGiKiMEhOB4GDgzBmgRg1g1y6geXOloyKyPExqiIjK4PJloEsX4MIFWQdm926gUSOloyKyTExqiIhK6Z9/ZEJz9Srg5wfs2SP/JSJlsKIwEVEpnD4ti9ddvSpHZvbvZ0JDpDQmNUREeoqLk7uakpPl2pl9+wofQUBEFY9JDRGRHn7/HXj+eeDuXSAgAIiJAWrWVDoqIgKY1BARldju3bKQXlqaHKnZtQuoXl3pqIhIjUkNEVEJbN8OvPgikJEBdO8ub1etqnRURPQoJjVERE/wxx9A//5AVpY8w+mHH4AqVZSOiogexy3dRETFuH1bnuWUkQF07QqsXw9U4m9OIqPEkRoioiLk5MgRmsuXgXr15GnbTGiIjBeTGiKiIkyaBOzdKw+n/OknwMVF6YiIqDhMaoiIdPjqK2DJEnl99Wrg6aeVjYeInoxJDRHRYw4cAMaNk9c/+ADo3VvZeIioZEqV1CxZsgS+vr6wt7dHQEAAjhw5Umz/DRs2oFGjRrC3t0fTpk2xfft2zX05OTmYMmUKmjZtCgcHB9SqVQtDhw7FjRs3tJ7D19cXKpVK6zJv3rzShE9EVKSrV4GwsIL1NNOnKx0REZWU3knNunXrEBkZiaioKBw/fhzNmzdHSEgIbt68qbP/wYMHMXDgQIwcORInTpxAaGgoQkNDcfr0aQBARkYGjh8/jpkzZ+L48eOIjo5GfHw8euv402j27NlITEzUXCZMmKBv+ERERcrIAEJDgZs3gWbNgK+/BlQqpaMiopJSCSGEPg8ICAhA27ZtsXjxYgBAfn4+vL29MWHCBEydOrVQ/wEDBiA9PR1bt27VtLVr1w4tWrTA8uXLdb7G0aNH4e/vj8uXL8PHxweAHKmZOHEiJk6cqE+4GmlpaXB2dkZqaiqcnJxK9RxEZL6EAF55BVizBnBzA44eBXx9lY6KiPT5/NZrpCY7OxtxcXEIDg4ueAIrKwQHByM2NlbnY2JjY7X6A0BISEiR/QEgNTUVKpUK1apV02qfN28eXF1d0bJlS8yfPx+5ubn6hE9EVKT582VCU6kSsHEjExoiU6RXxYXbt28jLy8P7u7uWu3u7u44d+6czsckJSXp7J+UlKSzf2ZmJqZMmYKBAwdqZWRvvvkmWrVqBRcXFxw8eBDTpk1DYmIiPv30U53Pk5WVhaysLM3ttLS0En2NRGR5tm8H1APNn38uz3UiItNjVGWkcnJyEB4eDiEEli1bpnVfZGSk5nqzZs1ga2uLMWPGYO7cubCzsyv0XHPnzsX7779f7jETkWmLjwcGDZLTT6NGAW+8oXRERFRaek0/ubm5wdraGsnJyVrtycnJ8PDw0PkYDw+PEvVXJzSXL1/Grl27njhvFhAQgNzcXFy6dEnn/dOmTUNqaqrmcvXq1Sd8dURkaVJT5REIqalAUBCweDEXBhOZMr2SGltbW7Ru3Rp79uzRtOXn52PPnj0IDAzU+ZjAwECt/gCwa9curf7qhOaff/7B7t274erq+sRYTp48CSsrK9SsWVPn/XZ2dnByctK6EBGp5eXJEZr4eMDLC9i0CbC1VToqIioLvaefIiMjMWzYMLRp0wb+/v5YtGgR0tPTMWLECADA0KFDUbt2bcydOxcAEBERgY4dO2LhwoXo2bMn1q5di2PHjmHFihUAZELTr18/HD9+HFu3bkVeXp5mvY2LiwtsbW0RGxuLw4cPo3PnzqhatSpiY2MxadIkvPLKK6hevbqhvhdEZEFmzJBraezt5anbjy39IyJTJErhyy+/FD4+PsLW1lb4+/uLQ4cOae7r2LGjGDZsmFb/9evXiwYNGghbW1vRpEkTsW3bNs19CQkJAoDOS0xMjBBCiLi4OBEQECCcnZ2Fvb29aNy4sZgzZ47IzMwsccypqakCgEhNTS3Nl0xEZmTNGiHkKhp5nYiMlz6f33rXqTFVrFNDRAAQFwc8+yyQmQlMmQKwMDmRAeTlAfv3A4mJgKcn0KEDYG1tkKfW5/PbqHY/ERGVp+RkWTE4MxPo0QP46COlIyIyA9HRQEQEcO1aQZuXl6yPEBZWoaHwQEsisgjZ2cBLL8nfuw0bykJ7BvpDkshyRUcD/fppJzQAcP26bI+OrtBwmNQQkdkTAhg/Xp6+7eQE/Pgj4OysdFREJi4vT47Q6FrFom6bOFH2qyBMaojI7C1fDnz1laxB8/33cqSGiMpo//7CIzSPEkIee79/f4WFxKSGiMzavn3Am2/K6/PmybU0RGQAiYmG7WcATGqIyGxduiSn9XNzgYEDgcmTlY6IyIx4ehq2nwEwqSEis5SeLnc63b4NtGoF/N//8QgEIoPq0EHucirqP5ZKBXh7y34VhEkNEZkdIYARI4A//gBq1pQVg6tUUToqIh3y8oC9e+Vir717K3RRbZlZW8tt20DhxEZ9e9GiCt1myKSGiMzOnDnAhg2AjY3cUertrXRERDpERwO+vkDnzvIgss6d5e0K3gZdJmFhwMaNQO3a2u1eXrK9guvUsKIwEZmVn36SJ28DwIoVwKhRysZDpJO6vsvjH8HqEQ4FEoIyMZKKwkxqiMhsnDkDtGsH3L8PjBsHLF5smOctx9/XZIny8uSITFHboVUqOdKRkMAfNOj3+c3pJyIyC3fvAr17y4SmUyfgs88M87zmMENARsYI67uYCyY1RGTycnOBl18GLlwA6tQpWE9TVkZWAZ7MhRHWdzEXTGqIyORNmQLs2iV3OP34I+DmVvbnNMIK8GQujLC+i7lgUkNEJu3bb4FPP5XXV60Cmjc3zPNyhoDKjRHWdzEXTGrIrJhyyQfS35EjwOjR8vrMmXJKyFA4Q0Dlxgjru5gLJjVkNrig07LcuCErBmdlyQXCs2YZ9vk5Q0Dlysjqu5gLbukms2BuJR+oeJmZcofT4cPA008DsbGAof9bq3fdXr+ue10Nd92SQbBewBOxTo0OTGrMF0s+WBYhgFdfBb75BqheHTh6FKhXr3xeS50sq19XjckyUcVhnRqyKFzQaVm++EImNFZWwLp15ZfQAJwhIDI1lZQOgKisuKDTcuzeDbz1lry+YAHQtWv5v2ZYmDx2gTMERMaPSQ2ZPC7otAwXLgDh4XK6cdgwWSOmolhbyzU8RGTcOP1EJo8lH8zf/ftytOTePcDfH1i+vOj3m4gsF5MaMnks+WDe8vOBoUOBv/6So22bNwP29kpHRUTGiEkNmQUu6DRf778P/PADYGsrE5patZSOiIiMFdfUkNnggk7zs2kTMHu2vL5iBRAQoGw8RGTcmNSQWeGCTvPx559yQTAgFwWrrxMRFYXTT0RkdG7flqNu6elAcDAwf77SERGRKWBSQ0RGJSdHbt2+dAmoW1cW2KvEMWUiKgEmNURkVN56C4iJARwdgZ9+AlxclI6IiEwFkxoiMhorVwJffimv/+9/QJMmysZDRKaFg7pEZBQOHgTeeENenz1brqkhIhMgBJCSAly+LOeKn3lGsVCY1BCR4q5dk1vyc3LkqdgzZigdERFp5OQAN24AV67IxOXKlcLXHzyQfUNDZUEphTCpISJFPXwofw8mJwPNmgFff80jEIgqVGpqQXKiK3G5cUOW9n6SGjUAB4fyj7cYTGqISDFCAKNGAXFxgKurrBzs6Kh0VERmJC9PViMtaoTlyhWZ1DyJra08RM/HR17q1NG+7u0NVK5c/l/PEzCpISLFLFwIrF4tiyZu3Aj4+SkdEZGJefCg6BGWK1fk3G5e3pOfx8VFO1F5PHFxdwesjH9vEZMaIlLEjh3AlCny+uefsxI0USH5+UBSUvFTQ/fuPfl5KlWSB+E9nqg8OspiJkOkTGqIjFBennmfYfX338DLL8vf2a+9Bowdq3RERBUsJ0eWzr55UyYuV68WTlyuXpX9nsTZufB00KOJi6enef0CKQaTGiIjEx0NRETIUWM1Ly85mmEOp42npsrt2qmpQFAQsGQJFwaTGRACSEuTScqjl+Rk3W1375bsea2sgNq1da9j8fGRoyzOzuX7tZkQJjVERiQ6Wm5pFkK7/fp12b5xo2knNnl5wODBwLlzMlHbtEmuPyQyStnZwK1bJUtUbt4EsrL0e34rK8DNDahZs2AR7uOJS61aPCdED/xOERmJvDw5QvN4QgPINpVKnlbdp4/pjiTPnAls2wbY28udTu7uSkdEFkVdJE5XQqIrUSnJepXHOTrKJKVmTfkDrr7+6EXd7uJiuv+ZjRSTGiIjsX+/9pTT44SQU+z795vmotp164C5c+X1lSuB1q2VjYfMRFaWHE0paprn8baSrFF5lLW1rL9SXKKibqtRA6hSpXy+TioRJjVERiIx0bD9jMnx48CIEfL6O+8AgwYpGw+ZOCFkPYBPPpEJjb6cnHQnJbqSlerVTWIrM0lMaoiMhKenYfsZi5s3ZcXghw+BF14A5sxROiIyaSkpwPDhwI8/FrRVqlT06MnjbTVqyPlPMktMaoiMRIcOcvHs9eu619WoVPL+Dh0qPrbSePgQ+PZb+cf01atAgwbAmjVcQkBlcPy4XDGfkCBXmH/2mawNUL06t9ARAIBjakRGwtpabtsGCv9+Vt9etMj4k4Lbt+Up23XqAK+/Dly8KP9I/vFHoFo1paMjkyQEsGIF0L69TGj8/OSx7mPHysW2TGjoX0xqiIxIWJjctl27tna7l5fxb+e+cAEYN07uRI2Kkksd6tSRidiFC0CjRkpHSCYpPR0YOhQYM0YuCu7dWx4WxpXmpAOnn4iMTFiY3LZtKhWFDx8G5s+XNXbU02atWgGTJ8uZApbYoFI7d07+EP31l/wPMHcu8PbbHJmhIvHXDZERsrY27m3b+fnA1q0ymfn994L2F16QyUynTvzcoTJau1aeoZGeLjP7tWuB555TOioyckxqiKjEMjOB776Tu2nj42WbjY2sEvzWW8AzzygbH5mBrCz5w7RkibzduTPw/fes1EglwqSGiJ7ozh1g2TLgyy/lFm1AHjfz+uvAhAmF1wARlcqlS0B4OHD0qLw9fTrw/vvGO/dKRodJDREVKSEB+PRT4L//BTIyZJu3NzBpkpwZqFpV2fjIjGzbBgwZIo8mcHGRQ4I9eigdFZkYJjVEVMjRo8CCBXLHVX6+bGvRQq6X6d9fTjkRGURuLvDeewVnaPj7A+vXy61zRHpiUkNEAGTysn27XPz7228F7SEhcsNJly5c/EsGlpQEDBwI7N0rb0+YILNpHt1OpVSqOjVLliyBr68v7O3tERAQgCNHjhTbf8OGDWjUqBHs7e3RtGlTbN++XXNfTk4OpkyZgqZNm8LBwQG1atXC0KFDcePGDa3nuHv3LgYPHgwnJydUq1YNI0eOxIMHD0oTPhE9IitLHjD5zDNAr14yoalUSc4E/PEHsGMHEBzMhIYMbN8+oGVLmdA4OsrdTV98wYSGykTvpGbdunWIjIxEVFQUjh8/jubNmyMkJAQ31asHH3Pw4EEMHDgQI0eOxIkTJxAaGorQ0FCcPn0aAJCRkYHjx49j5syZOH78OKKjoxEfH4/evXtrPc/gwYPx119/YdeuXdi6dSt+++03jB49uhRfMhEBcunCnDmAr69cH3P2rFwj8/bbci3Nt98CzZopHSWZnfx84OOPgeeflyM1TZoAx44BAwYoHRmZA6Enf39/MW7cOM3tvLw8UatWLTF37lyd/cPDw0XPnj212gICAsSYMWOKfI0jR44IAOLy5ctCCCHOnDkjAIijR49q+vz8889CpVKJ69evlyju1NRUAUCkpqaWqD+RuUpIECIiQggHByFkuTwhatcWYv58IVJSlI6OzNrdu0K8+GLBD96QIUI8eKB0VGTk9Pn81mukJjs7G3FxcQgODta0WVlZITg4GLGxsTofExsbq9UfAEJCQorsDwCpqalQqVSo9u9BMbGxsahWrRratGmj6RMcHAwrKyscPnxYny+ByGLFxcmz/+rVk2dMpafLkZhvv5XnM739ttymTVQujh2Tpaa3bgXs7ORZTqtWAQ4OSkdGZkSvhcK3b99GXl4e3B8rguTu7o5z587pfExSUpLO/klJSTr7Z2ZmYsqUKRg4cCCcnJw0z1GzZk3twCtVgouLS5HPk5WVhaysLM3ttLS04r84IjMkBPDzz3LtZUxMQXtwsNzJ1LUr18pQORMCWL4cmDgRyM4G6taV2+patlQ6MjJDRnWgZU5ODsLDwyGEwLJly8r0XHPnzoWzs7Pm4u3tbaAoiYxfVhbwzTdA06ZAz54yobG2lpV/T5wAdu0CunVjQkPl7MED4JVX5Gna2dlAaKgcMmRCQ+VEr6TGzc0N1tbWSE5O1mpPTk6Gh4eHzsd4eHiUqL86obl8+TJ27dqlGaVRP8fjC5Fzc3Nx9+7dIl932rRpSE1N1VyuXr1a4q+TyFSlpMg1mH5+wIgR8hxAR0cgMlJOMf3vf7LeDFG5O3NG1pxZs0Zm1AsWyFNP/11WQFQe9EpqbG1t0bp1a+zZs0fTlp+fjz179iAwMFDnYwIDA7X6A8CuXbu0+qsTmn/++Qe7d++Gq6troedISUlBXFycpu3XX39Ffn4+AgICdL6unZ0dnJyctC5E5uryZZm4eHsDU6fK071r1ZIJztWr8qwmHx+loySLsWYN0Lat3FJXq5bctv3WWxwapPKn7yrktWvXCjs7O/HNN9+IM2fOiNGjR4tq1aqJpKQkIYQQQ4YMEVOnTtX0P3DggKhUqZJYsGCBOHv2rIiKihI2Njbi1KlTQgghsrOzRe/evYWXl5c4efKkSExM1FyysrI0z9O9e3fRsmVLcfjwYfH777+Lp556SgwcOLDEcXP3E5mj48eFGDRICGvrgg0lzzwjxDffCPHIfx+iipGZKcQbbxT8MHbpIkRystJRkYnT5/Nb76RGCCG+/PJL4ePjI2xtbYW/v784dOiQ5r6OHTuKYcOGafVfv369aNCggbC1tRVNmjQR27Zt09yXkJAgAOi8xMTEaPrduXNHDBw4UDg6OgonJycxYsQIcf/+/RLHzKSGzEV+vhA7dsjPC/VnByDE888L8fPP8n6iCnfxohCtW8sfRpVKiJkzhcjNVToqMgP6fH6rhBBCqVGiipSWlgZnZ2ekpqZyKopMUna2LLq6YAFw6pRss7aWhxq//bbcLUukiC1bgKFD5aIuV1e5eKt7d6WjIjOhz+c3z34iMnKpqbKkx+efA9evyzYHB2DUKCAiQlYENlZ5ecD+/XKNj6cn0KGDTMTITOTmAjNmyMVbANCunTyMkrtNSSFMaoiM1LVrwKJFMqG5f1+2eXgAb74JvP46UL26ouE9UXS0TLquXSto8/KSyVlYmHJxkYEkJspqjurTTyMigE8+4dlNpCgmNURGJiEBmDtX1pnJyZFtjRvLKabBg2UxVmMXHQ306ydX+zzq+nXZvnEjExuTFhMjT9dOTpYHhq1cCfTvr3RURMZVfI/Ikv39NzB8OPDUU8BXX8mE5rnnZFX506eBV181jYQmL0/+0a5rtZ66beJE2Y9MTH6+zLiDg2VC07SpPP6ACQ0ZCSY1RAr76y9g0CA5GrNqlfyw79ZNjurv2ycrAluZ0P/U/fu1p5weJ4SsnbN/f8XFRAZw5w7Qqxfw7rsyuRk+HDh0CGjQQOnIiDQ4/USkkBMngA8/lFM1ai++KNddFlFT0iQkJhq2HxmBI0fkaMyVK4C9PbBkiRw6JDIyTGqIKtiRI8AHH8hpJbWwMJnMmMOROJ6ehu1HChJCJjCRkXI+tH59uSCqeXOlIyPSyYQGtYlM2++/AyEhchRm61Y5pTRwoFwvs2mTeSQ0gNy27eVVdEV8lUru+O3QoWLjIj3dvy9/QCdMkAnNSy/J9TNMaMiIMakhKkdCAHv2AJ06yQ/xnTtlnZZhw+SxOGvWAE2aKB2lYVlby23bQOHERn170SLWqzFqp0/Ls5vWrQMqVQI++wzYsAFwdlY6MqJiMakhKgdCAD//DAQFyY0i+/YBNjayYN7ff8vt2ua8vjIsTM5S1K6t3e7lxe3cRu+77+Tp2vHx8g3bt09uV+NhlGQCuKaGyIDy82XF+A8/lCP1gNyG/dprwJQpllVoNSwM6NOHFYVNRmamrOz41Vfydrdu8riDGjWUjYtID0xqiAwgL0+ui/noI+DPP2VblSqy8u/bb1vuolhrazn1RkbuwgW5u+nECTkiExUlV64zAyUTw6SGqAxyc+Uhkx99BJw7J9scHYHx4+WGEf6RS0bvhx9kzZnUVMDNTS706tpV6aiISoVJDVEp5OTIpQdz5wLnz8s2Z2dZSTciAnBxUTY+oifKyZGF9BYskLfbt5cLg728lI2LqAyY1BDpISsL+PprYN484PJl2ebqKkdlxo3j5hAyEdevy8Mof/9d3o6MlD/UNjbKxkVURkxqiEogI0Oun/zkE+DGDdnm7i7Xy7z+upxyIjJKubmyEvCFC8DFi/LfVauAmzcBJyeZpXM7GpkJJjVExXjwAFi2TI7Q37wp22rXBt55R27PrlxZ2fiIAMhCeRcuaCcu6n8vX9Z9emjz5nJ/ff36FR8vUTlhUkOkQ2oqsHixrDl2545sq1MHmDZNrqk0hdOyyYzk58t98Y8mK49ev327+Mfb2QF16wL16sl/mzQBhgxhVk5mh0kN0SPu3pXVbr/4QiY2gPxD9t13gVde4ZIDveXlsVBNSWVmAgkJukdbEhLk/cVxc5NJizpxefRfT0/TOuqdqJSY1BBBTi19+qk8u+/BA9nWuDEwfTowYICsFE96io6WW8GuXSto8/KSZyhY4hoOIeSwX1GjLdevF/94a2s5XPhosqK+XreuXB9DZOH4q5osWmIiMH8+sHw58PChbGveXNYdCwvjH7elFh0N9OsnP8gfdf26bDfXsxJ0Lcp99N+0tOIfX7Vq0aMtPj7MromeQCXE4791zFNaWhqcnZ2RmpoKJ/5FY/GuXAE+/hhYuVJu0waANm2AmTOBXr14zE2Z5OUBvr7aIzSPUqnkiE1CgmlORakX5eoabSlqUe6jatcuOnFxdeUPH9Fj9Pn8ZtpPFuXiRVkwb9UqWXsMkDXHZs4EQkL4eWIQ+/cXndAAcvTm6lXZz1TOUDh6VC60+uUX4Nat4vs+vij30QTGzw+wt6+YmIksEJMasgjx8cCcOcDq1QV/SHfuLJOZTp2YzBhUYqJh+yklJ0ce6PXFF0BsrPZ9NWoUTly4KJdIcUxqyKydPi1PzF6/vmB5R0iITGaCgpSNzWyV9PROYz3l89YtYMUKYOnSgkqLNjayAu/o0UCzZlyUS2SkmNSQWTpxAvjgA2Dz5oK23r3lbiZ/f+XisggdOsg1M9evF14oDBSsqenQoeJjK87Jk3JUZs2agoVW7u7AG28AY8YAHh6KhkdET8akhszKP//Iowt++kneVqmAl16SyUyLFoqGZjmsreW27X795BvwaGKjnudbtMg4Fgnn5gI//ijj3b+/oL1tW7kdvX9/wNZWufiISC+c+CWzkJYmjy5o0kQmNFZWwKBBcvppwwYmNBUuLExu265dW7vdy8s4tnPfvSu3v9WtK5Ov/fvldumBA+X6mcOHgcGDmdAQmRiO1JBJy88HvvsOmDoVSEqSbS+8IAvpNWqkbGwWLywM6NPHuCoKnz4tp5j+97+CwkRubvJU0tdfL5yEqbEyMpFJYFJDJuvIEWDCBPkvADz1lDyrqWdPZeOiR1hbK79tOy8P2LpVJjO//lrQ3qKFnGJ6+eXit1mzMjKRyWBSQyYnKUkeLPnNN/K2o6PczRQRwYMm6REpKcB//ytPJk1IkG1WVjIRefNN4Nlnn7yX31IrIxOZKFYUJgCmMbqenS3/OP7gA1nUFQCGDZPF9Ix1dzAp4Nw54MsvZYXF9HTZVr263I49dqw8bqAkzL0yMpGJYEVh0ospjK5v3w5MnCh3NwFyc8qXXwIBAYqGRcYiPx/YsaOg6q/aM8/IUZnBg4EqVfR7TnOsjExk5pjUWDhjH13/+29g0iSZ1ACybMi8ecDQoSzaSpBDdt98IzNcdcarUsmiRG++KctGl7ZctLlURiayIExqLFhenhyh0TUBKYT8LJg4UW5gqejR9bQ0WQl40SJZrd7GRsY6cyaLuRKA8+flWpn//rdgLtLZGRg5Ehg3Tm7VLitTr4ysiynMMxOVAZMaC2aMo+v5+cC338ot2snJsq1HD7mrqUGDiomBjJQQwO7dcopp27aCbLxhQzkqM3SoXDVuKKZaGbkopjDPTFRGHMC3YMY2un74MBAYCIwYIROap56SO3G3bWNCY9HS04Hly2VlxW7d5A+FEDLb/eUX4MwZuQDYkAkNUFAZGSg8hWVslZGfRD3P/PhfMep55uhoZeIiMjAmNRbMWEbXExOB4cOBdu1kzRlHR+CTT2SdNNacsWCXLgGTJ8vRhDfeAM6elT8cEybIxVbbtskkpzwXVxl7ZeSSeNI8MyDnmdXH1xOZMG7ptmDqHatPGl0vrx2r6i3as2cDDx7INm7R/pelrn0QAti3T/5g/PSTnI8EgPr1ZTIzfLgyi6pM+f3Yu1cumH6SmBju4iKjxC3dVCJKnju4bZvc1aTesOLvL5dKcIs2LHPtw8OH8nTsL74A/vyzoL1bN7le5oUXlN3uZgyVkUvL2OaZicoRp58sXEWPrsfHy6UQL74oExp3d7kjNzaWCQ0Ay1v7cPWqLA/t5QW89ppMaKpUkdNNf/0l18z07Mn9+2VhLPPMRBWA008EoPxH19PSZCXgzz8v2KI9cSIwYwa3aGtYSgVbIYCDB+UPQ3R0wVoOX19g/Hjg1VdlBWAyDKXnmYnKiNNPpLfyGl3nFm09GOMee0PKygLWrpVTTMePF7R37iynmHr14odqeVBynpmognFMl8qNri3a27Zxi3aRzHXtw7VrwHvvyTOXhg+XCY29vZxu+uMPeXJ2aCg/VMuTOeziIioBjtSQwSUmypGZb7+Vt6tWlZ9pb74J2NoqG5tRM6e1D3fvAps2ycW/+/YVjA54ecmKv6+9Bri5KRujpQkLk+XBTXUXF1EJMKkhg8nKKjhFW71Fe/hwuUXbw0PR0EyDqVewzcgAtmyRiczPP8vFU2rPPSfXy/TtC1Tirx3FmPIuLqIS4G8XMoht2+TC3/Pn5W1u0S4FU1z7kJMjjy5YswbYvFlW/1Vr3hwYNAh4+WU59UREVM6Y1FCZxMfLejM//yxve3jIU7SHDOEu3FJRr33QVadm0SLjWPuQny93L33/PbB+PXD7dsF9fn4ykRk4UB5rQERUgZjUUKmkpclKwJ9/DuTmyi3akyYB06dzi3aZGevahz//lCMy338PXLlS0F6zJjBggExmAgIKn5NERFRBmNSQXvLzgVWrZL009Rbtnj2BTz/ljiaDMpa1DwkJchv2mjXyMC61qlVl8jVoEPD881wnQ0RGgb+JqMQOHZI7mI4elbcbNJD1Znr0UDYuMrCbN4ENG2Qic/BgQbutrcxgBw2S/1aurFyMREQ6MKmhJ+IWbQtw/z7www8ykdm1q6DKr0olR2IGDZIjM9WqKRklEVGxmNRQkbKy5NrUDz8s2KI9YgQwZw63aJuFrCy5wvv77+WJ2JmZBfe1bSsTmfBwoFYt5WIkItIDkxoqRIiCU7TVW7QDAuQWbX9/ZWOjMsrLk8Xw1qyRxfFSUgrua9iwYOfSU08pFiIRUWmVatPtkiVL4OvrC3t7ewQEBODIkSPF9t+wYQMaNWoEe3t7NG3aFNu3b9e6Pzo6Gt26dYOrqytUKhVOnjxZ6Dk6deoElUqldXn99ddLEz4VQ32Kdq9eMqHx8JALgw8eZEJjsoQA4uKAyEjA2xvo0gVYuVImNLVqAW+9Je8/e1bOKzKhISITpXdSs27dOkRGRiIqKgrHjx9H8+bNERISgps3b+rsf/DgQQwcOBAjR47EiRMnEBoaitDQUJx+ZCdFeno6nn32WXz88cfFvvaoUaOQmJiouXzyySf6hk9FyMkBpkwBnnkG2LFDbtF+5x3g77+BoUNZc8Yk/f038P77QKNGQJs2clV3YqJcFzNqFBATI7dmL1gAtGrFrdhEZPJUQuiqx160gIAAtG3bFosXLwYA5Ofnw9vbGxMmTMDUqVML9R8wYADS09OxdetWTVu7du3QokULLF++XKvvpUuX4OfnhxMnTqBFixZa93Xq1AktWrTAokWL9AlXQ5+jyy1NRoYsM6J+i158UW7R5h/sJuj6dWDdOjm9FBdX0F65MtC7t5xeCgkB7OyUi5GISA/6fH7r9fd3dnY24uLiEBwcXPAEVlYIDg5GbGyszsfExsZq9QeAkJCQIvsXZ/Xq1XBzc8MzzzyDadOmISMjo8i+WVlZSEtL07pQYffuAd26yYTG3l7u5N2yhQmNSbl3D/i//5O7lLy9C6aTrK2BF14AvvtOFhVau1YmNkxoiMhM6bVQ+Pbt28jLy4O7u7tWu7u7O86dO6fzMUlJSTr7JyUl6RXooEGDUKdOHdSqVQt//vknpkyZgvj4eERHR+vsP3fuXLz//vt6vYaluXFD/tF++jTg7CwTm2efVToqKpGMDPmGrVkDbN+ufXhkUJAckenfH6hRQ7kYiYgqmMnsfho9erTmetOmTeHp6YkuXbrgwoULqFevXqH+06ZNQ2RkpOZ2WloavL29KyRWU/DPP3KE5tIlWYV/xw6gWTOlo6Ji5eZqHx6p3mcPAE2bFhwe6eurWIhERErSK6lxc3ODtbU1ktX18f+VnJwMjyIKl3h4eOjVv6QC/j3++fz58zqTGjs7O9hxmF2n48eB7t2BW7eA+vWBnTvlOYRkhIQAYmNlIrN+vXzT1OrUKdiC3bSpcjESERkJvdbU2NraonXr1tizZ4+mLT8/H3v27EFgYKDOxwQGBmr1B4Bdu3YV2b+k1Nu+PT09y/Q8lubXX+WRQrduAS1bAr//bmYJTV4esHevLCi3d29BZVxTc+ECMGMGULeunE5askS+aW5uwLhxwIED8lymOXOY0BAR/Uvv6afIyEgMGzYMbdq0gb+/PxYtWoT09HSMGDECADB06FDUrl0bc+fOBQBERESgY8eOWLhwIXr27Im1a9fi2LFjWLFiheY57969iytXruDGjRsAgPj4eABylMfDwwMXLlzAmjVr0KNHD7i6uuLPP//EpEmT8Nxzz6EZ50xKbNMm+Yd9djbQubOsim9WG8Gio4GICODatYI2Ly95lHhYmHJxldTDh/JNWrlSJmRqjo5A377yzevSRe63JyKiwkQpfPnll8LHx0fY2toKf39/cejQIc19HTt2FMOGDdPqv379etGgQQNha2srmjRpIrZt26Z1/9dffy0AFLpERUUJIYS4cuWKeO6554SLi4uws7MT9evXF5MnTxapqakljjk1NVUA0Osx5uQ//xHCykoIQIiwMCEePlQ6IgPbtEkIlUp+gY9eVCp52bRJ6Qh1y88X4uhRId54QwhnZ+24u3UT4vvvhUhPVzpKIiLF6PP5rXedGlNlqXVqhJAzFDNmyNujRgHLlsndvmYjL08ujn10hOZRKpUcsUlIMJ4v/M4dYPVqOSrz558F7b6+8oCt4cMBHx+loiMiMhr6fH6bzO4n0l9+vjy/6Ysv5O3p04EPPjDDwrH79xed0AAys7t6Vfbr1KnCwiokP1/uXlq5Us79ZWfLdjs7OT02cqScF2T5ZiKiUmFSY6ays+Uf/GvWyNuLFsnlJmYpMdGw/Qzt0iXgm2+Ar7+WxxKotWwpE5mBAwEXF2ViIyIyI0xqzFB6OtCvn6w9U6mS/DwdPFjpqMpRSXfAVeROucxMORqzciWwZ48cLQLkuUuDB8tkpmXLiouHiMgCMKkxM3fuAD17AocPy+N+Nm2SlfLNWocOcs3M9esFycOj1GtqOnQo/1hOnpSJzOrV8vgCtS5dZCITGirfGCIiMjgmNWbk2jVZJfjsWaB6dWDbNqCM5YBMg7W13Lbdr59MYB5NbNQLiBYtKr9FwvfuyXm+lSuBEycK2r29Cxb9mlUxICIi48SkxkycOycTmqtXgdq1gV9+AZo0UTqqChQWBmzcqLtOzaJFhq9Tk58va8msXCnr42RmynZbWzka8+qrQHCw8ey2IiKyAExqzMCRI0CPHnLqqWFDeeyBRe4GDgsD+vSRu5wSE+Uamg4dDJtYXL1asOg3IaGgvWlTOb00eLCs+ktERBWOSY2J27VLFptNTwfatJEHNlv0wczW1obftp2VBfz0kxyV2bmzYHrLyUlW+X31VfnNN7u98kREpoVJjQlbvx545RUgJ0fOdERHA1WrKh2VGTl9WiYy330nh8HUOnWSicxLLwFVqigWHhERaWNSY6KWLgXGj5eDBuHhwLffyhpuVEapqcDatTKZOXq0oL1WLbngd8QIebQ5EREZHSY1JkYI4P335QUA3ngD+PJLrkctEyGA336TiczGjfJgSUAW+endW66V6dZN3iYiIqPF39ImJC8PePNNOUoDAFFR8sKlHKV04wawahXw3/8C588XtDduLBOZIUOAmjWVi4+IiPTCpMZEZGUBQ4fKdTQqlRydGTdO6ahMUE4OsHWrHJX5+We5NRsAHB2Bl1+WyUxAADNFIiITxKTGBNy/L3cr794N2NjIdasDBigdlYk5e7Zg0e/NmwXtzz4rE5l+/WRiQ0REJotJjZG7dUsee3D0KODgAGzeDHTtqnRUJuL+fTm0tXIlEBtb0O7hAQwbJhf9NmyoXHxERGRQTGqM2OXLQEgIEB8PuLrKGjT+/kpHZeRycoDff5cjMuvXywI+gFxJ/eKLciv2Cy/IIS8iIjIrTGqM1F9/yYTm+nV5hNDOnUCjRkpHZaQuXZJHkv/yizwR+/79gvsaNJDTS0OHyhEaIiIyW0xqjFBsrJxyundPbsTZuVMeYUT/ysgA9u0rSGTi47Xvr1GjYFQmKIiLfomILASTGiPz889yzWpGBtCundyo4+qqdFQKE0Iu9N2xQ15++01uB1Oztgbat5dDW927Ay1bAlZWysVLRESKYFJjRFavlkVrc3Pl5/OmTXJxsEVKSZFTSerRmKtXte/38ZEJTEgI0KUL4OysSJhERGQ8mNQYiS++ACIi5PVBg+Qh0La2ysZUofLzgePHC0ZjDh2S1QbV7OzkmUvq0ZhGjTitREREWpjUKEwIYOZM4KOP5O033wQ++8xCZk+Sk+WCoR075L+3b2vf36hRwWjMc8/x8EgiIioWkxoF5eXJs5u++kre/vBD4N13zXgAIicHOHhQTift2AGcOKF9f9Wq8rhxdSJTp44ycRIRkUliUqOQzExg8GAgOlqOyixbBowerXRU5eDSpYIk5vHt1gDQqlVBEhMYyPoxRERUakxqFJCWBoSGAjExct3MmjXASy8pHZWBqLdbqxOZx7dbu7kVrIvp2hVwd1cmTiIiMjtMaipYcrIsaHvihDxq6McfgeefVzqqMnh0u/Uvv8iE5vHt1oGBMonhdmsiIipHTGoqUEIC0K0bcP68rA/3889A69ZKR1UK6u3W6tGYx7dbe3sXJDHcbk1ERBWESU1ZXb1aUFDGwUHu0FFff+RyKsERIf0ckZiogq+v3Ozz1FNKB19Cj263/uUXWfL48e3WHTsWJDLcbk1ERApgUlNWZ88CkyYV2+V3BKEXtiAFKjyjOo1f7oWj1vP3i02CStVepYrhkgn1dutffpEXXdut1WtjuN2aiIiMAJOasqpRA3j5ZXkadEaG/PeRy5a05xD+cBUyURlB+B1bRC9UT00BUsspnkeTHn0TI3t7udjnl1/kyMyj1NutQ0Lkxde3nL4AIiKi0lEJIYTSQVSEtLQ0ODs7IzU1FU5OThXymqtWyQOi8/KAni/kYf1/UlBFpBeZAJW47fH2hw/L5wto1apgNIbbrYmISAH6fH5zpKas8vKA/fuBxETA0xPo0AGwtsaCBcDkybLL0KHA//2fNWxsXAGUw+mU+fkyySltUvRoW506MpHp1o3brYmIyKQwqSmL6Gh5YNO1a5omUdsLU9vuxic/NAQAvPUW8Mkn5byL2cpK7g93dCzHFyEiIjJuTGpKKzoa6NdP1mn5Vy6sMfr6bHx9XSY0H38MvPOOUgESERFZFlZBK428PDlC80hC8xD2eAmb8DVGwAp5WFn9bbzzVl4xT0JERESGxKSmNPbv15pySoEzQvALfkIf2CET0QjDq/cWyn5ERERUITj9VBqJiQVX4YHu2IE/0RxOSMUW9MJz2F+oHxEREZUvJjWl4empufoj+uBPNIc7kvALQtAcf+rsR0REROWLSU1pdOgAeHkB16/jdfEfpMEJL2ET6uGivF+lkvd36KBsnERERBaEa2pKw9oa+PxzeV2lwjuYr53QAMCiRbIfERERVQgmNaUVFgZs3AjUrq3d7uUl28PClImLiIjIQnH6qSzCwoA+fXRWFDY5RVRGJiIiMhVMasrK2hro1EnpKMpGR2VkeHnJKTaOOBERkYng9JOlU1dGfjShAYDr12V7dLQycREREemJSY0l01EZWUPdNnGi7EdERGTkmNRYsscqIxciBHD1KisjExGRSeCamjIy6fW1Ja14zMrIRERkApjUlIHJr68tacVjVkYmIiITwOmnUjKL9bXqysjqgoGPU6kAb29WRiYiIpPApKYUzGZ97WOVkbWwMjIREZkYJjWlYFbra1kZmYiIzATX1JSC2a2vNafKyEREZLGY1JSCWa6vNYfKyEREZNE4/VQKXF9LRERkfEqV1CxZsgS+vr6wt7dHQEAAjhw5Umz/DRs2oFGjRrC3t0fTpk2xfft2rfujo6PRrVs3uLq6QqVS4eTJk4WeIzMzE+PGjYOrqyscHR3x0ksvITk5uTThlxnX1xIRERkfvZOadevWITIyElFRUTh+/DiaN2+OkJAQ3Lx5U2f/gwcPYuDAgRg5ciROnDiB0NBQhIaG4vTp05o+6enpePbZZ/Hxxx8X+bqTJk3Cli1bsGHDBuzbtw83btxAmIKLWLm+loiIyLiohNC1MbloAQEBaNu2LRYvXgwAyM/Ph7e3NyZMmICpU6cW6j9gwACkp6dj69atmrZ27dqhRYsWWL58uVbfS5cuwc/PDydOnECLFi007ampqahRowbWrFmDfv36AQDOnTuHxo0bIzY2Fu3atXti3GlpaXB2dkZqaiqcnJz0+ZKLZdIVhYmIiIycPp/feo3UZGdnIy4uDsHBwQVPYGWF4OBgxMbG6nxMbGysVn8ACAkJKbK/LnFxccjJydF6nkaNGsHHx6fI58nKykJaWprWpTyo19cOHCj/ZUJDRESkDL2Smtu3byMvLw/u7u5a7e7u7khKStL5mKSkJL36F/Uctra2qFatWomfZ+7cuXB2dtZcvL29S/x6REREZHrMdvfTtGnTkJqaqrlcvXpV6ZCIiIioHOlVp8bNzQ3W1taFdh0lJyfDw8ND52M8PDz06l/Uc2RnZyMlJUVrtKa457Gzs4OdnV2JX4OIiIhMm14jNba2tmjdujX27NmjacvPz8eePXsQGBio8zGBgYFa/QFg165dRfbXpXXr1rCxsdF6nvj4eFy5ckWv5yEiIiLzpXdF4cjISAwbNgxt2rSBv78/Fi1ahPT0dIwYMQIAMHToUNSuXRtz584FAERERKBjx45YuHAhevbsibVr1+LYsWNYsWKF5jnv3r2LK1eu4MaNGwBkwgLIERoPDw84Oztj5MiRiIyMhIuLC5ycnDBhwgQEBgaWaOcTERERmT+9k5oBAwbg1q1beO+995CUlIQWLVpgx44dmsXAV65cgZVVwQBQ+/btsWbNGsyYMQPvvvsunnrqKfzwww945plnNH1++uknTVIEAC+//DIAICoqCrNmzQIAfPbZZ7CyssJLL72ErKwshISEYOnSpaX6oomIiMj86F2nxlSVV50aIiIiKj/lVqeGiIiIyFgxqSEiIiKzoPeaGlOlnmUrr8rCREREZHjqz+2SrJaxmKTm/v37AMDKwkRERCbo/v37cHZ2LraPxSwUzs/Px40bN1C1alWoVCqDPndaWhq8vb1x9epVLkI2Anw/jAvfD+PC98P48D0pnhAC9+/fR61atbR2V+tiMSM1VlZW8PLyKtfXcHJy4g+kEeH7YVz4fhgXvh/Gh+9J0Z40QqPGhcJERERkFpjUEBERkVlgUmMAdnZ2iIqK4gGaRoLvh3Hh+2Fc+H4YH74nhmMxC4WJiIjIvHGkhoiIiMwCkxoiIiIyC0xqiIiIyCwwqSEiIiKzwKSmhJYsWQJfX1/Y29sjICAAR44cKbb/hg0b0KhRI9jb26Np06bYvn17BUVqGfR5P7766it06NAB1atXR/Xq1REcHPzE94/0o+//D7W1a9dCpVIhNDS0fAO0MPq+HykpKRg3bhw8PT1hZ2eHBg0a8HeWAen7fixatAgNGzZE5cqV4e3tjUmTJiEzM7OCojVxgp5o7dq1wtbWVvz3v/8Vf/31lxg1apSoVq2aSE5O1tn/wIEDwtraWnzyySfizJkzYsaMGcLGxkacOnWqgiM3T/q+H4MGDRJLliwRJ06cEGfPnhXDhw8Xzs7O4tq1axUcuXnS9/1QS0hIELVr1xYdOnQQffr0qZhgLYC+70dWVpZo06aN6NGjh/j9999FQkKC2Lt3rzh58mQFR26e9H0/Vq9eLezs7MTq1atFQkKC+OWXX4Snp6eYNGlSBUdumpjUlIC/v78YN26c5nZeXp6oVauWmDt3rs7+4eHhomfPnlptAQEBYsyYMeUap6XQ9/14XG5urqhatapYtWpVeYVoUUrzfuTm5or27duL//u//xPDhg1jUmNA+r4fy5YtE3Xr1hXZ2dkVFaJF0ff9GDdunHj++ee12iIjI0VQUFC5xmkuOP30BNnZ2YiLi0NwcLCmzcrKCsHBwYiNjdX5mNjYWK3+ABASElJkfyq50rwfj8vIyEBOTg5cXFzKK0yLUdr3Y/bs2ahZsyZGjhxZEWFajNK8Hz/99BMCAwMxbtw4uLu745lnnsGcOXOQl5dXUWGbrdK8H+3bt0dcXJxmiurixYvYvn07evToUSExmzqLOdCytG7fvo28vDy4u7trtbu7u+PcuXM6H5OUlKSzf1JSUrnFaSlK8348bsqUKahVq1ahxJP0V5r34/fff8fKlStx8uTJCojQspTm/bh48SJ+/fVXDB48GNu3b8f58+cxduxY5OTkICoqqiLCNluleT8GDRqE27dv49lnn4UQArm5uXj99dfx7rvvVkTIJo8jNWRR5s2bh7Vr12Lz5s2wt7dXOhyLc//+fQwZMgRfffUV3NzclA6HAOTn56NmzZpYsWIFWrdujQEDBmD69OlYvny50qFZpL1792LOnDlYunQpjh8/jujoaGzbtg0ffPCB0qGZBI7UPIGbmxusra2RnJys1Z6cnAwPDw+dj/Hw8NCrP5Vcad4PtQULFmDevHnYvXs3mjVrVp5hWgx9348LFy7g0qVL6NWrl6YtPz8fAFCpUiXEx8ejXr165Ru0GSvN/w9PT0/Y2NjA2tpa09a4cWMkJSUhOzsbtra25RqzOSvN+zFz5kwMGTIEr732GgCgadOmSE9Px+jRozF9+nRYWXEsojj87jyBra0tWrdujT179mja8vPzsWfPHgQGBup8TGBgoFZ/ANi1a1eR/ankSvN+AMAnn3yCDz74ADt27ECbNm0qIlSLoO/70ahRI5w6dQonT57UXHr37o3OnTvj5MmT8Pb2rsjwzU5p/n8EBQXh/PnzmuQSAP7++294enoyoSmj0rwfGRkZhRIXdcIpeFTjkym9UtkUrF27VtjZ2YlvvvlGnDlzRowePVpUq1ZNJCUlCSGEGDJkiJg6daqm/4EDB0SlSpXEggULxNmzZ0VUVBS3dBuQvu/HvHnzhK2trdi4caNITEzUXO7fv6/Ul2BW9H0/HsfdT4al7/tx5coVUbVqVTF+/HgRHx8vtm7dKmrWrCk+/PBDpb4Es6Lv+xEVFSWqVq0qvv/+e3Hx4kWxc+dOUa9ePREeHq7Ul2BSmNSU0Jdffil8fHyEra2t8Pf3F4cOHdLc17FjRzFs2DCt/uvXrxcNGjQQtra2okmTJmLbtm0VHLF50+f9qFOnjgBQ6BIVFVXxgZspff9/PIpJjeHp+34cPHhQBAQECDs7O1G3bl3x0Ucfidzc3AqO2nzp837k5OSIWbNmiXr16gl7e3vh7e0txo4dK+7du1fxgZsglRAczyIiIiLTxzU1REREZBaY1BAREZFZYFJDREREZoFJDREREZkFJjVERERkFpjUEBERkVlgUkNERERmgUkNERERmQUmNURERGQWmNQQERGRWWBSQ0RERGaBSQ0RERGZhf8H6n63EKcTiv4AAAAASUVORK5CYII=", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "f_matrix_train = K_helmi\n", - "\n", - "zzpc_svr = SVR(kernel='precomputed')\n", - "zzpc_svr.fit(f_matrix_train, y, w)\n", - "zzpc_score = zzpc_svr.score(f_matrix_train, y, w)\n", - "print(f'score: {zzpc_score}')\n", - "pred = zzpc_svr.predict(f_matrix_train)\n", - "\n", - "p_hat = 1/(1+np.exp(-pred))\n", - "p = 1/(1+np.exp(-y))\n", - "plt.figure()\n", - "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p) if a[0] == 0],'or')\n", - "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", - "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", - "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", - "plt.legend(['Group 0', 'Group 0 model', 'Group 1', 'Group 1 model'])\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "5e211b3e-7c28-4de0-967d-14bb3c502bd8", - "metadata": {}, - "source": [ - "**Error Calculation and Visualization**: Finally, the script calculates the absolute errors between `K_helmi` and `matrix_train`, visualizes these errors using `imshow`, and displays this with a color bar for reference." - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "id": "8a3b538d-9deb-418a-9a3c-4e14590e6074", - "metadata": {}, - "outputs": [], - "source": [ - "# redo the steps for statevector kernel to compare with the Helmi results\n", - "\n", - "zz_kernel = QuantumKernel(feature_map=qc, quantum_instance=Aer.get_backend('statevector_simulator'))\n", - "zz_circuit = zz_kernel.construct_circuit(ParameterVector('x_i', length=2),ParameterVector('x_j', length=2))\n", - "zz_circuit.decompose().draw(output='mpl')\n", - "matrix_train = zz_kernel.evaluate(x_vec=x)" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "id": "656b8465-c4a3-4794-b301-f50f68c61dc7", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "errors = np.abs(K_helmi - matrix_train)\n", - "\n", - "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", - "pos = axs.imshow(np.asmatrix(errors),\n", - " interpolation='nearest', origin='upper', cmap='Reds')\n", - "axs.set_title(\"erorrs\")\n", - "fig.colorbar(pos, ax=axs)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "47fa3d94-0b0e-41f9-ba3b-4571be968882", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3ca65f4a-c3b7-43da-b27b-35bf2a7c73d1", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "30df1f84-8e4b-4e3b-a607-3ecf25e9d375", - "metadata": {}, - "outputs": [], - "source": [ - "# solution ex2\n", - "residuals = y - pred\n", - "plt.hist(residuals, bins=20)\n", - "plt.xlabel('Residuals')\n", - "plt.ylabel('Frequency')\n", - "plt.title('Histogram of Residuals')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "97aab143-92b2-4765-853c-1c8757bd79b0", - "metadata": {}, - "outputs": [], - "source": [ - "# solution1 ex2\n", - "residuals1 = p_hat-p\n", - "plt.hist(residuals1, bins=20)\n", - "plt.xlabel('Residuals')\n", - "plt.ylabel('Frequency')\n", - "plt.title('Histogram of Residuals')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c3a78eab-1e43-4f1b-a992-526d1c131b4a", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "a26ddc57-a2fc-48ac-b3ae-f3ece0a2b507", - "metadata": {}, - "outputs": [], - "source": [ - "# solution ex3\n", - "\n", - "def feature_map(x1):\n", - " p = ParameterVector('x1', length=2)\n", - " qc = QuantumCircuit(2)\n", - "\n", - " qc.ry(x1[0]*np.pi, 0)\n", - " qc.ry(x1[1]*np.pi, 1)\n", - "\n", - " return qc" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "id": "681cbb1a-dcc1-4870-990f-7935e14b8d81", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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y8vIOrwMDAxk3bpz1ChWXNCADXFZWBnQ/fUhNTe3y9X333cdbb73Vr7WJ3rHbOfDFXCrAJpOpyz9XanhNpgvXfrfsfApDQ4359cVMy9Qw/6XRfFPxkbnt9Q+Xcc9zgUzL1FBZu79D/1UbE5j9hCfvF79iydIvmwTYDhSXbePNwtWcaT7J4WPfkpWbzummE5fc7+XFxUwIn2F+fWPUXby8+H+4zqPz3cvsh75g4qiZFq3bEgbkFOK3dRKqOdN8kvkvRfJLSzPDrvGnpe0XDCeqmTo2neSJC9Ftmkp1/QGey/gYx8Fajh0/jC5nKusWfYnP0CD+XpRN6dHPWJPxUZfHjwq6ycpndPkG5AisKhcnd6bE/IHZk5ezacV+Fs18hbCAicSFzeDLg/ncOv4BUuIX8XL+Ak43ncD/2pHMT1rLM1vncKCqiO1fvc7qtHf6Zb2HrdjPmQwQlXX7CfYdA8BR/XcEDx/D5Mg7mZ+UhauTByP949DNfdu8LHLKmDRCfGN59M3bWJ32jl39Sj0M0CmEyqr/LcDxETPNaznuvfWpTv3b2lqpMfzr118r6vmCIlXICKwQ46la0GjwusYXgGrDwUsug9z80Z/wGzaSdYuLySlYRa2x0hqlWo0EWCGVtfsIHj7G/NpF6872r9/otv+e8gL2Hv4HS+98HV+vYBamrOPZrXM433Kuy/6v5C8k7Vk/fjql59HNt3HfC8EWPwdL05h6ctFQWJU1VqNNy9TwwdONuDi593ifF9+7n2DfGGbfuLzTNvmWImFVHi7XsfKvN3e4kXExqzYmUFb9T7SOzv1cWe/ICHwFUnE9sIzAQvSBBFgoTQIslCZz4CuQfNl3z0mAhdJkCiGUJgEWSpMAC6VJgIXSJMBCaRJgoTQJsFCaBFgoTQIslCYBFkqTAAulSYCF0iTAQmkSYKE0CbBQmgRYKE0CLJQmARZKkwALpUmAhdIkwEJpEmChNAmwUJoEWChNAiyU9r//7E7Ul41AzwAAAABJRU5ErkJggg==", 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" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# solution1 ex3\n", - "# Draw the circuit\n", - "qc.draw('mpl')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "d1960e7f-a57d-4047-b7eb-6054e37ee913", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "eaae61c0-9258-4bf7-a929-065ab90d36aa", - "metadata": {}, - "source": [ - "#### TEST CODE" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3397e118-363f-4cb2-b0aa-3166d83ae03f", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6d2dad5d-6493-460a-a5d6-898448124f31", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.13.7" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} From 77bc9386d3ac29f91d529ce9e80727fba338274b Mon Sep 17 00:00:00 2001 From: Anastasiia Andriievska <79667606+fomalhautn@users.noreply.github.com> Date: Wed, 5 Nov 2025 19:46:14 +0100 Subject: [PATCH 7/8] Delete content/QKE_AA.ipynb --- content/QKE_AA.ipynb | 2835 ------------------------------------------ 1 file changed, 2835 deletions(-) delete mode 100644 content/QKE_AA.ipynb diff --git a/content/QKE_AA.ipynb b/content/QKE_AA.ipynb deleted file mode 100644 index 06ef0d2..0000000 --- a/content/QKE_AA.ipynb +++ /dev/null @@ -1,2835 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "e4b10801-19d8-4751-8e31-a9bfd2df03d1", - "metadata": { - "id": "e4b10801-19d8-4751-8e31-a9bfd2df03d1" - }, - "source": [ - "# Tutorial - Quantum kernel estimation with application to disability insurance\n", - "\n", - "B. Djehiche and B. Löfdahl – KTH, Department of Mathematics / SEB –\n", - "Risks 2021, 9(12), 216; https://doi.org/10.3390/risks9120216\n", - "\n", - "Hands-on assistance: [Anastasiia Andriievska](https://www.linkedin.com/in/aandriievska/)" - ] - }, - { - "cell_type": "code", - "source": [ - "!pip install qrisp==0.7.9 pandas numpy matplotlib scikit-learn sympy" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "YWc5tpIJbric", - "outputId": "efec0699-82c6-47d6-9d37-58ae5e24b10d" - }, - "id": "YWc5tpIJbric", - "execution_count": 1, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Collecting qrisp==0.7.9\n", - " Downloading qrisp-0.7.9-py3-none-any.whl.metadata (7.0 kB)\n", - "Requirement already satisfied: pandas in /usr/local/lib/python3.12/dist-packages (2.2.2)\n", - "Requirement already satisfied: numpy in /usr/local/lib/python3.12/dist-packages (2.0.2)\n", - "Requirement already satisfied: matplotlib in /usr/local/lib/python3.12/dist-packages (3.10.0)\n", - 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" Uninstalling sympy-1.13.3:\n", - " Successfully uninstalled sympy-1.13.3\n", - " Attempting uninstall: jaxlib\n", - " Found existing installation: jaxlib 0.7.2\n", - " Uninstalling jaxlib-0.7.2:\n", - " Successfully uninstalled jaxlib-0.7.2\n", - " Attempting uninstall: jax\n", - " Found existing installation: jax 0.7.2\n", - " Uninstalling jax-0.7.2:\n", - " Successfully uninstalled jax-0.7.2\n", - "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. 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The x-variable holds the available data. x[i][0] represents gender (0 or 1). x[i][1] represents age, normalized to the [0,1] interval. The y-variable is the value that we seek to model. It represents the logistic transition probability between two states. The w-variable represents the weight that we assign to each data point." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "168cfc3c-d7ba-4b88-b60a-7cbd67738d83", - "metadata": { - "id": "168cfc3c-d7ba-4b88-b60a-7cbd67738d83" - }, - "outputs": [], - "source": [ - "# Set random seed for reproducibility\n", - "np.random.seed(42)\n", - "\n", - "# Number of samples per gender\n", - "nsamp = 100\n", - "\n", - "# Create feature matrix: gender (0 or 1), normalized age [0, 1]\n", - "x = np.array([[0.0, i/nsamp] for i in range(nsamp)] + [[1.0, i/nsamp] for i in range(nsamp)])\n", - "\n", - "# Generate target values with noise\n", - "y = np.array([\n", - " -4.5 + 0.2*a[0]*(1 - 5*a[1]**2) + a[1]*(1 + a[0]*0.2) + 0.1*np.random.normal()\n", - " for a in x\n", - "])\n", - "\n", - "# Logistic transformation\n", - "p = 1 / (1 + np.exp(-y))\n", - "\n", - "# Population size based on age\n", - "n = [\n", - " int(2000 + 6000*xj[1]/0.7) if xj[1] <= 0.7 else int(8000 - 3000*(xj[1] - 0.7)/0.3)\n", - " for xj in x\n", - "]\n", - "\n", - "# Weighted transitions\n", - "d = [nj * pj for nj, pj in zip(n, p)]" - ] - }, - { - "cell_type": "markdown", - "id": "6404a54d-b5d7-4395-96ab-d4bb9f75df61", - "metadata": { - "id": "6404a54d-b5d7-4395-96ab-d4bb9f75df61" - }, - "source": [ - "We can use the Pandas library to create a DataFrame and then save it as a CSV file, which support column headers. This will create a CSV file with each column labeled as ‘gender’, ‘age group (normalized)’, ‘population size’, and ‘number of transitions’ respectively. The index=False argument is used to prevent pandas from writing row indices into the file." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "98b3d891-41c2-4ead-90dd-a8419e79809e", - "metadata": { - "id": "98b3d891-41c2-4ead-90dd-a8419e79809e" - }, - "outputs": [], - "source": [ - "# Create a DataFrame\n", - "df = pd.DataFrame({\n", - " 'gender': [a[0] for a in x],\n", - " 'age group (normalized)': [a[1] for a in x],\n", - " 'population size': n,\n", - " 'number of transitions': [int(round(a)) for a in d]\n", - "})\n", - "\n", - "# Write the DataFrame to a CSV file\n", - "df.to_csv('fdata.csv', index=False) # index=False argument is used to prevent pandas from writing row indices into the CSV file" - ] - }, - { - "cell_type": "markdown", - "id": "79a2034c-1509-44c2-9fdb-ed63b301a727", - "metadata": { - "id": "79a2034c-1509-44c2-9fdb-ed63b301a727" - }, - "source": [ - "One can read the data back from the file like this:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "0da27f10-d9b1-4c75-afcd-cf69122586a6", - "metadata": { - "id": "0da27f10-d9b1-4c75-afcd-cf69122586a6" - }, - "outputs": [], - "source": [ - "data = pd.read_csv('fdata.csv')" - ] - }, - { - "cell_type": "markdown", - "id": "e0d5741f-c5fb-4fb8-84a2-da56f6fa2ae9", - "metadata": { - "id": "e0d5741f-c5fb-4fb8-84a2-da56f6fa2ae9" - }, - "source": [ - "### Transform and inspect data" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "84552a98-075b-48de-b7a9-68e018e95e83", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "84552a98-075b-48de-b7a9-68e018e95e83", - "outputId": "859c109d-3ab3-4a3c-b673-355c8b43a60b" - }, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "[[0. 0. ]\n", - " [0. 0.01]\n", - " [0. 0.02]\n", - " [0. 0.03]\n", - " [0. 0.04]\n", - " [0. 0.05]\n", - " [0. 0.06]\n", - " [0. 0.07]\n", - " [0. 0.08]\n", - " [0. 0.09]]\n" - ] - } - ], - "source": [ - "x = np.array( [[a,b] for a,b in zip(data['gender'], data['age group (normalized)'])] )\n", - "print(x[0:10])" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "5bfef017-385e-47c0-8b46-89a280406102", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "5bfef017-385e-47c0-8b46-89a280406102", - "outputId": "846425a9-d74d-4427-a528-d2d8d9191bf4" - }, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "array([-4.45032858, -4.50382643, -4.41523115, -4.31769701, -4.48341534,\n", - " -4.4734137 , -4.28207872, -4.35325653, -4.46694744, -4.355744 ])" - ] - }, - "metadata": {}, - "execution_count": 7 - } - ], - "source": [ - "y[0:10]" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "e7447d0f-64e9-4d56-8a41-299cdd3b044e", - "metadata": { - "id": "e7447d0f-64e9-4d56-8a41-299cdd3b044e" - }, - "outputs": [], - "source": [ - "# raw transition frequency per group, used for plots\n", - "p_raw = [a/b for a,b in zip(d,n)]\n", - "\n", - "# logistic probability, used as input to SVR optimization\n", - "y = np.array([np.log( p / (1-p) ) for p in p_raw])\n", - "\n", - "# calculate weights for SVR based on population size\n", - "w = np.array([1./nj for nj in n])\n", - "\n", - "# normalize weights (equivalent to changing the hyperparameters of the SVR)\n", - "w = w/sum(w)*len(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "0fe05211-ed34-463f-81ea-37069c0fd93f", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 468 - }, - "id": "0fe05211-ed34-463f-81ea-37069c0fd93f", - "outputId": "6b8f90cb-61bc-4b51-e8da-375034d03537" - }, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ], - "source": [ - "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", - "axs.plot([xj[1] for xj,p in zip(x, p_raw) if xj[0] == 0], [p for xj,p in zip(x, p_raw) if xj[0] == 0], 'or')\n", - "axs.plot([xj[1] for xj,p in zip(x, p_raw) if xj[0] == 1], [p for xj,p in zip(x, p_raw) if xj[0] == 1], 'ob')\n", - "axs.set_title(\"raw transition frequencies\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "cd869a15-a44e-406c-9ef7-22009f1f4bd0", - "metadata": { - "id": "cd869a15-a44e-406c-9ef7-22009f1f4bd0" - }, - "source": [ - "The first step of the modelling is to define the mapping from data space to our quantum feature space. This is done by setting up the build_feature_map function. The circuit below is a very simplified two-variable circuit. Feel free to experiment!" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "f6546726-7f76-4f7d-992c-95ee972abf17", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "f6546726-7f76-4f7d-992c-95ee972abf17", - "outputId": "dff222f3-4d86-435c-b11e-defffd550a33" - }, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "QuantumCircuit:\n", - "---------------\n", - " ┌──────────┐\n", - "q.0: ┤ Ry(π*x0) ├\n", - " ├──────────┤\n", - "q.1: ┤ Ry(π*x1) ├\n", - " └──────────┘\n", - "Live QuantumVariables:\n", - "----------------------\n", - "QuantumVariable q\n" - ] - } - ], - "source": [ - "from qrisp import ry\n", - "\n", - "# Define a simple feature map using Ry rotations\n", - "def build_feature_map(sym):\n", - " n = 2 # Number of qubits\n", - " q = QuantumVariable(n)\n", - " params = symbols(sym + ':' + str(n)) # Create symbolic parameters: x:0, x:1\n", - " ry(np.pi * params[0], q[0]) # Apply Ry rotation to qubit 0\n", - " ry(np.pi * params[1], q[1]) # Apply Ry rotation to qubit 1\n", - " return q\n", - "\n", - "# Build the feature map\n", - "feature_map = build_feature_map('x')\n", - "\n", - "# Inspect the quantum state\n", - "print(feature_map.qs)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "2c128f3c-da92-4dd2-b94d-27dd25970626", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "2c128f3c-da92-4dd2-b94d-27dd25970626", - "outputId": "ae3bcf0e-c252-4faa-bc39-b81fa3c542ad" - }, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - " ┌────────────┐\n", - "q.0: ┤ Ry(2.3272) ├\n", - " ├────────────┤\n", - "q.1: ┤ Ry(2.7563) ├\n", - " └────────────┘\n" - ] - } - ], - "source": [ - "# example, assign random data as parameters and print cirquit\n", - "\n", - "subs_dic = {a : np.random.rand() for a in feature_map.qs.abstract_params}\n", - "bound_qc = feature_map.qs.bind_parameters(subs_dic)\n", - "print(bound_qc)" - ] - }, - { - "cell_type": "markdown", - "id": "45f26e2c-cf15-4e67-a9b7-d774cb11c2eb", - "metadata": { - "id": "45f26e2c-cf15-4e67-a9b7-d774cb11c2eb" - }, - "source": [ - "For a data pair $(x, y)$, we create the kernel circuit by calling the build_feature_map twice, once for $x$ and once for $y$, inverting the latter, and joining them together" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "ce778494-1f6a-40f0-89e9-02123cd6600a", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "ce778494-1f6a-40f0-89e9-02123cd6600a", - "outputId": "1ab5c81e-ed04-4d95-a115-89b324a1c45e" - }, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - " ┌──────────┐┌─────────────┐┌─┐ \n", - " q.0: ┤ Ry(π*x0) ├┤ Ry((-π)*y0) ├┤M├───\n", - " ├──────────┤├─────────────┤└╥┘┌─┐\n", - " q.1: ┤ Ry(π*x1) ├┤ Ry((-π)*y1) ├─╫─┤M├\n", - " └──────────┘└─────────────┘ ║ └╥┘\n", - "cb_0: ════════════════════════════╩══╬═\n", - " ║ \n", - "cb_1: ═══════════════════════════════╩═\n", - " \n" - ] - } - ], - "source": [ - "kernel = build_feature_map('x')\n", - "y_inverse = build_feature_map('y').qs.inverse()\n", - "\n", - "kernel.qs.append(y_inverse.to_op(), kernel.qs.qubits)\n", - "\n", - "kernel.qs.measure(kernel.qs.qubits)\n", - "\n", - "print(kernel.qs.transpile())" - ] - }, - { - "cell_type": "markdown", - "id": "b9fefbd4-5e78-4b09-8e7f-8e5a9f342e60", - "metadata": { - "id": "b9fefbd4-5e78-4b09-8e7f-8e5a9f342e60" - }, - "source": [ - "## Experimenting\n", - "\n", - "Remember, when experimenting with quantum circuits, it's important to understand what each gate does and how changing the circuit might affect your results. Happy experimenting! 😊\n", - "\n", - "A few general guidelines for experimenting with quantum circuits:\n", - "\n", - "1. **Understand the problem**: Before you start experimenting, make sure you understand the problem you're trying to solve and how a quantum circuit could help solve it.\n", - "\n", - "2. **Start simple**: Start with a simple circuit and gradually add complexity. This makes it easier to understand what each part of your circuit is doing.\n", - "\n", - "3. **Use a variety of gates**: Different gates can have different effects on your quantum state, so try using a variety of gates in your experiments.\n", - "\n", - "4. **Test on a simulator first**: Before running your circuit on a real quantum computer, test it on a simulator to make sure it's working as expected.\n", - "\n", - "5. **Analyze your results**: After running your circuit, analyze the results to see if they make sense and if they're helping you solve your problem.\n", - "\n", - "6. **Iterate**: Experimenting with quantum circuits often involves a lot of trial and error. Don't be afraid to iterate on your design and try new things.\n", - "\n", - "In the context of the Quantum Support Vector Regression (QSVR) for disability insurance that you're working on, you might want to experiment with different ways of encoding your data into the quantum state or different types of quantum kernels. Remember, the goal is to find a quantum circuit that can effectively model your data and help you make accurate predictions." - ] - }, - { - "cell_type": "markdown", - "source": [ - "### Exercise 1 – Experimenting with Quantum Feature Maps\n", - "\n", - "🧪 Goal:\n", - "Explore how different quantum circuit designs affect the feature mapping in quantum kernel estimation." - ], - "metadata": { - "id": "cStNolKC62xl" - }, - "id": "cStNolKC62xl" - }, - { - "cell_type": "markdown", - "source": [ - "#####1.1 Change the rotation gates\n", - "Try replacing ry with other single-qubit gates like rx, rz, or combinations:" - ], - "metadata": { - "id": "XUGk2fHP7CHo" - }, - "id": "XUGk2fHP7CHo" - }, - { - "cell_type": "code", - "source": [ - "from qrisp import rx, rz\n", - "rx(np.pi * params[0], q[0])\n", - "rz(np.pi * params[1], q[1])" - ], - "metadata": { - "id": "haddGeZA6gXM" - }, - "id": "haddGeZA6gXM", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "What to observe:\n", - "\n", - "How does the circuit look after transpiling?\n", - "Does the kernel matrix change significantly?\n", - "Does SVR performance improve or degrade?" - ], - "metadata": { - "id": "33oWLNjK8MPY" - }, - "id": "33oWLNjK8MPY" - }, - { - "cell_type": "markdown", - "source": [ - "1.2 Add entanglement\n", - "Introduce gates like cx or cz to create entanglement between qubits:" - ], - "metadata": { - "id": "-lBC_HZS7mJY" - }, - "id": "-lBC_HZS7mJY" - }, - { - "cell_type": "code", - "source": [ - "from qrisp import cx, h\n", - "h(q[0])\n", - "cx(q[0], q[1])" - ], - "metadata": { - "id": "yQnWPe_q7mZM" - }, - "id": "yQnWPe_q7mZM", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "What to observe:\n", - "\n", - "Does entanglement improve the expressiveness of the kernel?\n", - "Is the circuit still efficient to simulate?" - ], - "metadata": { - "id": "OVna9A--8Oiy" - }, - "id": "OVna9A--8Oiy" - }, - { - "cell_type": "markdown", - "source": [ - "1.3 Use nonlinear parameter functions\n", - "Instead of linear scaling, try nonlinear transformations:" - ], - "metadata": { - "id": "TKLmbiZ57m3K" - }, - "id": "TKLmbiZ57m3K" - }, - { - "cell_type": "code", - "source": [ - "ry(np.sin(params[0] * np.pi), q[0])\n", - "ry(np.log1p(params[1]) * np.pi, q[1])" - ], - "metadata": { - "id": "tSmjrs4-7nI2" - }, - "id": "tSmjrs4-7nI2", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "What to observe:\n", - "\n", - "Does the kernel matrix capture more subtle patterns?\n", - "Are the results more stable or more sensitive?" - ], - "metadata": { - "id": "jyhJD1TC8Qd3" - }, - "id": "jyhJD1TC8Qd3" - }, - { - "cell_type": "markdown", - "source": [ - "1.4 Increase the number of qubits\n", - "Modify n = 2 to n = 3 or more, and expand your feature map accordingly." - ], - "metadata": { - "id": "KTOBmogV7nSn" - }, - "id": "KTOBmogV7nSn" - }, - { - "cell_type": "code", - "source": [], - "metadata": { - "id": "ATwqZ79m7naC" - }, - "id": "ATwqZ79m7naC", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "What to observe:\n", - "\n", - "How does the circuit scale?\n", - "Does the SVR model benefit from higher-dimensional quantum features?" - ], - "metadata": { - "id": "Ys1Mm-iz8Slg" - }, - "id": "Ys1Mm-iz8Slg" - }, - { - "cell_type": "markdown", - "id": "3dc158a8-1035-47fa-80bd-4d0b4743eabe", - "metadata": { - "id": "3dc158a8-1035-47fa-80bd-4d0b4743eabe" - }, - "source": [ - "#### Hints\n", - "1. Use .transpile() to inspect how your circuit changes.\n", - "2. Try binding real data instead of random values to see how the circuit behaves.\n", - "3. Consider how each change might affect the kernel similarity between data points." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "339246ed-877a-4235-9009-69f77e6e057b", - "metadata": { - "id": "339246ed-877a-4235-9009-69f77e6e057b" - }, - "outputs": [], - "source": [ - "# Test code here\n", - "# Then rerun the following cells\n", - "\n" - ] - }, - { - "cell_type": "code", - "source": [], - "metadata": { - "id": "RcEnL1fJ_Z26" - }, - "id": "RcEnL1fJ_Z26", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "id": "7ed23841-0821-40bd-8a6e-0e7fd12ed22b", - "metadata": { - "id": "7ed23841-0821-40bd-8a6e-0e7fd12ed22b" - }, - "source": [ - "#### Estimating the kernel matrix\n", - "\n", - "The train_kernel_matrix function prepares the kernel estimation by setting up inner product circuits, based on each combination of two data points. The kernel circuits are then run on a either a specified backend, or using statevector simulation." - ] - }, - { - "cell_type": "code", - "source": [ - "def train_kernel_matrix(x, f_feature_map, shots=1000, backend=None):\n", - " # Build base kernel circuit\n", - " kernel = f_feature_map('x')\n", - " x_params = copy(kernel.qs.abstract_params)\n", - "\n", - " # Build inverse feature map for y\n", - " adjoint_qs = f_feature_map('y').qs.inverse()\n", - " y_params = adjoint_qs.abstract_params\n", - " # Combine circuits\n", - " kernel.qs.append(adjoint_qs.to_op(), kernel.qs.qubits)\n", - " kernel.qs = kernel.qs.transpile()\n", - "\n", - " # Add measurement if using backend\n", - " if backend is not None:\n", - " kernel.qs.measure(kernel.qs.qubits)\n", - "\n", - " # Initialize kernel matrix\n", - " n = len(x)\n", - " K = np.eye(n)\n", - "\n", - " # Loop over all pairs (i, j)\n", - " for i in range(n):\n", - " subs_dic = {p: x[i][int(p.name[1:])] for p in x_params}\n", - " for j in range(i + 1, n):\n", - " for p in y_params:\n", - " subs_dic[p] = x[j][int(p.name[1:])]\n", - "\n", - " # Bind parameters\n", - " bound_kernel = kernel.qs.bind_parameters(subs_dic)\n", - "\n", - " # Run circuit\n", - " if backend is not None:\n", - " res = bound_kernel.run(shots=shots, backend=backend)\n", - " K_ij = res.get('0' * len(kernel.qs.qubits), 0) / shots\n", - " else:\n", - " res = bound_kernel.statevector_array()\n", - " K_ij = np.abs(res[0]) ** 2\n", - "\n", - " # Fill symmetric matrix\n", - " K[i, j] = K[j, i] = K_ij\n", - "\n", - " return K" - ], - "metadata": { - "id": "N6x2RwdvLInI" - }, - "id": "N6x2RwdvLInI", - "execution_count": 13, - "outputs": [] - }, - { - "cell_type": "markdown", - "id": "6684d892-b617-4556-926e-e23e10353aec", - "metadata": { - "id": "6684d892-b617-4556-926e-e23e10353aec" - }, - "source": [ - "We evaluate the kernel matrix based on our $x$ data and the build_feature_map helper function." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "908ec069-24b6-4d5b-bb47-e677339e3279", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "908ec069-24b6-4d5b-bb47-e677339e3279", - "outputId": "0a444975-2c62-430b-a17c-2398e6c52a74" - }, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [] - } - ], - "source": [ - "matrix_train = train_kernel_matrix(x, build_feature_map)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "cc7771e0-7f0c-4a32-b6bd-d6a7dd50da52", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 468 - }, - "id": "cc7771e0-7f0c-4a32-b6bd-d6a7dd50da52", - "outputId": "171aeae9-7343-4c0f-df53-2f13a86b75f3" - }, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
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\n" - }, - "metadata": {} - } - ], - "source": [ - "# Plot the kernel matrix\n", - "\n", - "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", - "pos = axs.imshow(np.asmatrix(matrix_train),\n", - " interpolation='nearest', origin='upper', cmap='Blues')\n", - "axs.set_title(\"trained kernel matrix\")\n", - "fig.colorbar(pos, ax=axs)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "b5e309fb-7fb7-4fed-9e3f-05ff9aa6ea87", - "metadata": { - "id": "b5e309fb-7fb7-4fed-9e3f-05ff9aa6ea87" - }, - "source": [ - "Figure 1 displays the estimated kernel matrix. This matrix has an interesting structure: it is block-diagonal. This is due to the fact that the second quadrant of the matrix correspond to the inner products of the population groups with gender=0. These share the common characteristic gender=0, and each row is similar to its neighbours due to the encoding: similar ages are also similar in the quantum feature space. Analogously, the fourth quadrant of the matrix contains the gender=1 population groups. The first and third quadrants contain the inner products between gender=0 and gender=1 population groups and so are dissimilar in the quantum feature space." - ] - }, - { - "cell_type": "markdown", - "id": "5169b0dc-a666-4d0a-a19e-63de0ca8e6c2", - "metadata": { - "id": "5169b0dc-a666-4d0a-a19e-63de0ca8e6c2" - }, - "source": [ - "Next, we run a support vector regression (SVR) taking the kernel matrix, the weights, and the y-values as input." - ] - }, - { - "cell_type": "code", - "source": [ - "# Train SVR model using precomputed kernel\n", - "f_matrix_train = matrix_train\n", - "zzpc_svr = SVR(kernel='precomputed')\n", - "zzpc_svr.fit(f_matrix_train, y, w)\n", - "\n", - "# Evaluate model\n", - "zzpc_score = zzpc_svr.score(f_matrix_train, y, w)\n", - "print(f\"SVR model R² score on training data: {zzpc_score:.4f}\")\n", - "\n", - "# Predict and transform back to probabilities\n", - "pred = zzpc_svr.predict(f_matrix_train)\n", - "p_hat = 1 / (1 + np.exp(-pred))\n", - "p = 1 / (1 + np.exp(-y))\n", - "\n", - "# Sort data by age for smoother plots\n", - "group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", - "group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", - "group_0.sort()\n", - "group_1.sort()\n", - "\n", - "# Plot actual vs predicted transition probabilities\n", - "plt.figure(figsize=(10, 5))\n", - "plt.plot([a for a, _, _ in group_0], [p for _, p, _ in group_0], 'or', label='Group 0')\n", - "plt.plot([a for a, _, _ in group_0], [p_hat for _, _, p_hat in group_0], 'r', label='Group 0 model')\n", - "plt.plot([a for a, _, _ in group_1], [p for _, p, _ in group_1], 'ob', label='Group 1')\n", - "plt.plot([a for a, _, _ in group_1], [p_hat for _, _, p_hat in group_1], 'b', label='Group 1 model')\n", - "\n", - "plt.xlabel(\"Normalized Age\")\n", - "plt.ylabel(\"Transition Probability\")\n", - "plt.title(\"SVR Prediction vs Actual by Gender\")\n", - "plt.legend()\n", - "plt.grid(True)\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 504 - }, - "id": "HYtBGKbnQm0-", - "outputId": "385138d4-452f-446a-da42-5c11d1b551ac" - }, - "id": "HYtBGKbnQm0-", - "execution_count": 16, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "SVR model R² score on training data: 0.8609\n" - ] - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "markdown", - "id": "ad0da92a-1f89-4289-a2c2-e0cb5d4e1bc6", - "metadata": { - "id": "ad0da92a-1f89-4289-a2c2-e0cb5d4e1bc6" - }, - "source": [ - "The score you see is the R-squared score from the SVR model. This score represents the proportion of the variance in the dependent variable that is predictable from the independent variables. In other words, it gives you a measure of how well your model is fitting the data. A score of 1.0 indicates a perfect fit." - ] - }, - { - "cell_type": "markdown", - "id": "f2bc9cc6-7642-4f93-a152-f78ac3ccc29a", - "metadata": { - "id": "f2bc9cc6-7642-4f93-a152-f78ac3ccc29a" - }, - "source": [ - "We check the results against a classical SVR." - ] - }, - { - "cell_type": "code", - "source": [ - "# Train classical SVR model using RBF kernel\n", - "classical = SVR(kernel='rbf')\n", - "classical.fit(x, y, w)\n", - "classical_score = classical.score(x, y, w)\n", - "print(f\"Classical SVR R² score on training data: {classical_score:.4f}\")\n", - "\n", - "# Predict and transform back to probabilities\n", - "pred = classical.predict(x)\n", - "p_hat = 1 / (1 + np.exp(-pred))\n", - "p = 1 / (1 + np.exp(-y))\n", - "\n", - "# Sort data by age for smoother plots\n", - "group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", - "group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", - "group_0.sort()\n", - "group_1.sort()\n", - "\n", - "# Plot actual vs predicted transition probabilities\n", - "plt.figure(figsize=(10, 5))\n", - "plt.plot([a for a, _, _ in group_0], [p for _, p, _ in group_0], 'or', label='Group 0')\n", - "plt.plot([a for a, _, _ in group_0], [p_hat for _, _, p_hat in group_0], 'r', label='Group 0 model')\n", - "plt.plot([a for a, _, _ in group_1], [p for _, p, _ in group_1], 'ob', label='Group 1')\n", - "plt.plot([a for a, _, _ in group_1], [p_hat for _, _, p_hat in group_1], 'b', label='Group 1 model')\n", - "\n", - "plt.xlabel(\"Normalized Age\")\n", - "plt.ylabel(\"Transition Probability\")\n", - "plt.title(\"Classical SVR Prediction vs Actual by Gender\")\n", - "plt.legend()\n", - "plt.grid(True)\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 504 - }, - "id": "VU3uIjBZVdXQ", - "outputId": "ceb0ce3d-bd17-431c-ec88-7fd62ebb72f3" - }, - "id": "VU3uIjBZVdXQ", - "execution_count": 17, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Classical SVR R² score on training data: 0.8605\n" - ] - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "markdown", - "source": [ - "Side-by-side comparison of how well each model fits the transition probabilities across gender groups." - ], - "metadata": { - "id": "YLK8Srl7V5s1" - }, - "id": "YLK8Srl7V5s1" - }, - { - "cell_type": "code", - "source": [ - "# Quantum SVR predictions\n", - "pred_q = zzpc_svr.predict(f_matrix_train)\n", - "p_hat_q = 1 / (1 + np.exp(-pred_q))\n", - "p_q = 1 / (1 + np.exp(-y))\n", - "\n", - "# Classical SVR predictions\n", - "classical = SVR(kernel='rbf')\n", - "classical.fit(x, y, w)\n", - "pred_c = classical.predict(x)\n", - "p_hat_c = 1 / (1 + np.exp(-pred_c))\n", - "p_c = 1 / (1 + np.exp(-y))\n", - "\n", - "# Sort and group data by gender and age\n", - "def group_and_sort(x, p, p_hat):\n", - " group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", - " group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", - " return sorted(group_0), sorted(group_1)\n", - "\n", - "group_q_0, group_q_1 = group_and_sort(x, p_q, p_hat_q)\n", - "group_c_0, group_c_1 = group_and_sort(x, p_c, p_hat_c)\n", - "\n", - "# Plot both models side-by-side\n", - "plt.figure(figsize=(12, 5))\n", - "\n", - "# Quantum SVR\n", - "plt.subplot(1, 2, 1)\n", - "plt.plot([a for a, _, _ in group_q_0], [p for _, p, _ in group_q_0], 'or', label='Group 0')\n", - "plt.plot([a for a, _, _ in group_q_0], [p_hat for _, _, p_hat in group_q_0], 'r', label='Group 0 model')\n", - "plt.plot([a for a, _, _ in group_q_1], [p for _, p, _ in group_q_1], 'ob', label='Group 1')\n", - "plt.plot([a for a, _, _ in group_q_1], [p_hat for _, _, p_hat in group_q_1], 'b', label='Group 1 model')\n", - "plt.title(\"Quantum Kernel SVR\")\n", - "plt.xlabel(\"Normalized Age\")\n", - "plt.ylabel(\"Transition Probability\")\n", - "plt.legend()\n", - "plt.grid(True)\n", - "\n", - "# Classical SVR\n", - "plt.subplot(1, 2, 2)\n", - "plt.plot([a for a, _, _ in group_c_0], [p for _, p, _ in group_c_0], 'or', label='Group 0')\n", - "plt.plot([a for a, _, _ in group_c_0], [p_hat for _, _, p_hat in group_c_0], 'r', label='Group 0 model')\n", - "plt.plot([a for a, _, _ in group_c_1], [p for _, p, _ in group_c_1], 'ob', label='Group 1')\n", - "plt.plot([a for a, _, _ in group_c_1], [p_hat for _, _, p_hat in group_c_1], 'b', label='Group 1 model')\n", - "plt.title(\"Classical SVR\")\n", - "plt.xlabel(\"Normalized Age\")\n", - "plt.ylabel(\"Transition Probability\")\n", - "plt.legend()\n", - "plt.grid(True)\n", - "\n", - "plt.tight_layout()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 457 - }, - "id": "au5H9ebVVtIq", - "outputId": "490cb18e-835a-4dd7-a1da-ba140ec55f2e" - }, - "id": "au5H9ebVVtIq", - "execution_count": 18, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "markdown", - "id": "22f6ed9d-0b80-43c2-9a59-21bfb1d7a695", - "metadata": { - "id": "22f6ed9d-0b80-43c2-9a59-21bfb1d7a695" - }, - "source": [ - "The above analysis is done in-sample. Below, we use the leave-one-out cross-validation functionality from the sklearn module." - ] - }, - { - "cell_type": "code", - "source": [ - "from sklearn.model_selection import LeaveOneOut\n", - "from sklearn.metrics import r2_score\n", - "from sklearn.svm import SVR\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "# Quantum SVR LOO prediction\n", - "def predict_loo(K, y, w, svr_model):\n", - " cols = range(len(y))\n", - " loo = LeaveOneOut()\n", - " pred_loo = []\n", - " for train_index, test_index in loo.split(cols):\n", - " svr_model.fit(K[np.ix_(train_index, train_index)], y[train_index], w[train_index])\n", - " pred = svr_model.predict(K[np.ix_(test_index, train_index)])\n", - " pred_loo.extend(pred)\n", - " return np.array(pred_loo)\n", - "\n", - "zzpc_svr = SVR(kernel='precomputed')\n", - "statevector_loo = predict_loo(matrix_train, y, w, zzpc_svr)\n", - "\n", - "# Classical SVR LOO prediction\n", - "classical = SVR(kernel='rbf')\n", - "loo = LeaveOneOut()\n", - "pred_loo_classic = []\n", - "for train_index, test_index in loo.split(x):\n", - " classical.fit(x[train_index], y[train_index], w[train_index])\n", - " cpred = classical.predict(x[test_index])\n", - " pred_loo_classic.extend(cpred)\n", - "pred_loo_classic = np.array(pred_loo_classic)\n", - "\n", - "# Transform predictions to probabilities\n", - "p_hat_q = 1 / (1 + np.exp(-statevector_loo))\n", - "p_hat_c = 1 / (1 + np.exp(-pred_loo_classic))\n", - "p = 1 / (1 + np.exp(-y))\n", - "\n", - "# R² scores\n", - "score_q = r2_score(p, p_hat_q, sample_weight=w)\n", - "score_c = r2_score(p, p_hat_c, sample_weight=w)\n", - "print(f\"Quantum SVR LOO R² score: {score_q:.4f}\")\n", - "print(f\"Classical SVR LOO R² score: {score_c:.4f}\")\n", - "\n", - "# Sort and group data by gender and age\n", - "def group_and_sort(x, p, p_hat):\n", - " group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", - " group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", - " return sorted(group_0), sorted(group_1)\n", - "\n", - "group_q_0, group_q_1 = group_and_sort(x, p, p_hat_q)\n", - "group_c_0, group_c_1 = group_and_sort(x, p, p_hat_c)\n", - "\n", - "# Plot both models side-by-side\n", - "plt.figure(figsize=(12, 5))\n", - "\n", - "# Quantum SVR LOO\n", - "plt.subplot(1, 2, 1)\n", - "plt.plot([a for a, _, _ in group_q_0], [p for _, p, _ in group_q_0], 'or', label='Group 0')\n", - "plt.plot([a for a, _, _ in group_q_0], [p_hat for _, _, p_hat in group_q_0], 'r', label='Group 0 model')\n", - "plt.plot([a for a, _, _ in group_q_1], [p for _, p, _ in group_q_1], 'ob', label='Group 1')\n", - "plt.plot([a for a, _, _ in group_q_1], [p_hat for _, _, p_hat in group_q_1], 'b', label='Group 1 model')\n", - "plt.title(\"Quantum SVR (LOO)\")\n", - "plt.xlabel(\"Normalized Age\")\n", - "plt.ylabel(\"Transition Probability\")\n", - "plt.legend()\n", - "plt.grid(True)\n", - "\n", - "# Classical SVR LOO\n", - "plt.subplot(1, 2, 2)\n", - "plt.plot([a for a, _, _ in group_c_0], [p for _, p, _ in group_c_0], 'or', label='Group 0')\n", - "plt.plot([a for a, _, _ in group_c_0], [p_hat for _, _, p_hat in group_c_0], 'r', label='Group 0 model')\n", - "plt.plot([a for a, _, _ in group_c_1], [p for _, p, _ in group_c_1], 'ob', label='Group 1')\n", - "plt.plot([a for a, _, _ in group_c_1], [p_hat for _, _, p_hat in group_c_1], 'b', label='Group 1 model')\n", - "plt.title(\"Classical SVR (LOO)\")\n", - "plt.xlabel(\"Normalized Age\")\n", - "plt.ylabel(\"Transition Probability\")\n", - "plt.legend()\n", - "plt.grid(True)\n", - "\n", - "plt.tight_layout()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 491 - }, - "id": "z-rdVMiSW65Q", - "outputId": "5992f530-6a3b-4a5d-beb9-f6f85f392235" - }, - "id": "z-rdVMiSW65Q", - "execution_count": 19, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Quantum SVR LOO R² score: 0.8584\n", - "Classical SVR LOO R² score: 0.8532\n" - ] - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "markdown", - "id": "8ecebea2-79c9-4903-8f1c-8ffbc5393330", - "metadata": { - "id": "8ecebea2-79c9-4903-8f1c-8ffbc5393330" - }, - "source": [ - "Quantum Support Vector Regression (QSVR) Score (0.9155345528008413): This score suggests that your QSVR model is doing a good job of capturing the relationship between your features and your target variable.\n", - "\n", - "Classical Support Vector Regression (SVR) Score (0.9295558682302361): This score is slightly higher than your QSVR score, suggesting that your classical SVR model might be fitting the data slightly better than your QSVR model.\n", - "\n", - "Leave-One-Out Cross-Validation Score (0.8977158412990511): This score is lower than both your QSVR and classical SVR scores. This isn’t surprising, as leave-one-out cross-validation can often result in lower scores because it’s a more rigorous form of validation. It’s a good way to get an unbiased estimate of how well your model will perform on unseen data.\n", - "\n", - "To compare these results, you can look at how much each score deviates from 1.0. The closer the score is to 1.0, the better the model is fitting your data. However, keep in mind that a high R-squared score doesn’t always mean your model will perform well on unseen data. It’s important to also look at other metrics and plots (like residuals) to assess your model’s performance." - ] - }, - { - "cell_type": "markdown", - "source": [ - "## 📊 Model Performance Summary\n", - "\n", - "This section compares the performance of Quantum and Classical Support Vector Regression models, both in-sample and using Leave-One-Out Cross-Validation (LOO).\n", - "\n", - "### **In-Sample R² Scores**\n", - "| Model | R² Score | Interpretation |\n", - "|-------|----------|----------------|\n", - "| **Quantum SVR (QSVR)** | **0.8609** | Captures the relationship between features and target well. |\n", - "| **Classical SVR (RBF Kernel)** | **0.8605** | Very similar to QSVR, suggesting the classical kernel is equally expressive for this dataset. |\n", - "\n", - "### **Leave-One-Out Cross-Validation (LOO)**\n", - "| Model | R² Score | Interpretation |\n", - "|-------|----------|----------------|\n", - "| **Quantum SVR (LOO)** | **0.8977** | Slightly lower than in-sample scores, as expected. This is a more rigorous test of generalization. |\n", - "\n", - "---\n", - "\n", - "### 🧠 Interpretation\n", - "\n", - "- The **QSVR and Classical SVR** models perform almost identically on this dataset, indicating that the quantum kernel does not yet offer a significant advantage over the classical RBF kernel.\n", - "- The **LOO score** is slightly lower, which is expected due to its stricter validation. It provides a more **unbiased estimate** of how well the model generalizes to unseen data.\n", - "- A high R² score indicates good fit, but it’s important to also examine **residuals**, **error distributions**, and **kernel structures** to fully assess model performance.\n", - "\n", - "To compare these results, you can look at how much each score deviates from 1.0. The closer the score is to 1.0, the better the model is fitting your data. However, keep in mind that a high R-squared score doesn’t always mean your model will perform well on unseen data. It’s important to also look at other metrics and plots to assess your model’s performance." - ], - "metadata": { - "id": "Ia52tUuWX6xP" - }, - "id": "Ia52tUuWX6xP" - }, - { - "cell_type": "markdown", - "source": [ - "### Exercise 2: Residuals\n", - "\n", - "> In regression analysis, **residuals** represent the difference between the observed (actual) and predicted values for each data point. They help us understand how well a model fits the data.\n", - ">\n", - "> Mathematically, for an observed value $$y_{\\text{obs}}$$ and a predicted value $$y_{\\text{pred}}$$ for a data point, the residual $$e$$ is calculated as:\n", - ">\n", - "> $$e = y_{\\text{obs}} - y_{\\text{pred}}$$\n", - ">\n", - "> In our case, we are working with **transition probabilities**, so we transform both actual and predicted values using the sigmoid function to interpret them as probabilities:\n", - ">\n", - "> $$p = \\frac{1}{1 + e^{-y}}, \\quad \\hat{p} = \\frac{1}{1 + e^{-y_{\\text{pred}}}}$$\n", - ">\n", - "> The residuals then become:\n", - ">\n", - "> $$e = p - \\hat{p}$$\n", - ">\n", - "> A good model will produce residuals that are:\n", - "> - **Close to zero**, indicating accurate predictions.\n", - "> - **Randomly distributed**, without patterns, which suggests the model captures the underlying data structure well.\n", - ">\n", - "> In this exercise, we will:\n", - "> 1. Compute residuals for the Quantum SVR model.\n", - "> 2. Plot a histogram to visualize their distribution.\n", - ">\n", - "> ### 🔍 Hints\n", - "> - Use `residuals = p - p_hat_q` for Quantum SVR.\n", - "> - Use `plt.hist(residuals, bins=20)` to plot.\n", - "> - Label your axes clearly.\n", - "> - *Advanced:* Compare with Classical SVR residuals or plot residuals vs. age to detect patterns.\n" - ], - "metadata": { - "id": "AgNktxzOCvwP" - }, - "id": "AgNktxzOCvwP" - }, - { - "cell_type": "code", - "source": [ - "# Transform actual values to probabilities\n", - "p =\n", - "\n", - "# Compute residuals\n", - "residuals_qsvr =\n", - "residuals_classical =\n", - "\n", - "# Plot histogram of Quantum SVR residuals\n", - "plt.figure(figsize=(12, 5))" - ], - "metadata": { - "id": "me-eoMwCH9JS" - }, - "id": "me-eoMwCH9JS", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "code", - "source": [], - "metadata": { - "id": "vgIIM-NPH9LX" - }, - "id": "vgIIM-NPH9LX", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "### ✅ Summary of Exercise 2: Residuals\n", - "\n", - "You've done a great job implementing Quantum Support Vector Regression (QSVR) and comparing it with classical SVR using **leave-one-out cross-validation (LOO)**—a robust method for estimating generalization error.\n", - "\n", - "#### 🔍 Residual Analysis\n", - "\n", - "You've plotted two types of residual histograms:\n", - "\n", - "1. **Raw residuals**: \n", - " $$e = y - \\hat{y}$$ \n", - " These show how far off the predicted values are from the actual targets. Ideally, residuals should be centered around zero with no clear pattern.\n", - "\n", - "2. **Probability residuals**: \n", - " $$e = p - \\hat{p}$$ \n", - " Here, both actual and predicted values are transformed using the sigmoid function to represent transition probabilities. This is especially relevant in your context of modeling disability insurance transitions.\n", - "\n", - "#### 📊 Interpretation\n", - "\n", - "- A **tight, symmetric distribution** around zero suggests good model performance.\n", - "- **Skewed or long-tailed distributions** may indicate systematic bias—either overestimation or underestimation.\n", - "- Comparing Quantum and Classical SVR residuals side-by-side helps assess which model generalizes better.\n", - "\n", - "#### 🧠 What You’ve Achieved\n", - "\n", - "- Implemented QSVR with a custom kernel matrix.\n", - "- Compared it with classical SVR using RBF kernel.\n", - "- Evaluated both using LOO cross-validation.\n", - "- Analyzed residuals both in raw and probability-transformed form.\n", - "\n", - "This is a **comprehensive and methodologically sound approach** to model evaluation. Excellent work! 😊" - ], - "metadata": { - "id": "G_ACDFHkLuCh" - }, - "id": "G_ACDFHkLuCh" - }, - { - "cell_type": "code", - "execution_count": null, - "id": "bf6ece14-57fb-4ea5-85f5-5e5f3919414f", - "metadata": { - "id": "bf6ece14-57fb-4ea5-85f5-5e5f3919414f" - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "8d6c503e-5292-4644-8155-b5e76134ebf1", - "metadata": { - "id": "8d6c503e-5292-4644-8155-b5e76134ebf1" - }, - "source": [ - "### We used the statevector simulator and now we'll run it on IQM simulator" - ] - }, - { - "cell_type": "code", - "source": [ - "pip install qrisp[iqm]" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "YGtkNXZwMhWx", - "outputId": "4579b418-f10a-4021-921f-832e4542d705" - }, - "id": "YGtkNXZwMhWx", - "execution_count": 21, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Requirement already satisfied: qrisp[iqm] in /usr/local/lib/python3.12/dist-packages (0.7.9)\n", - 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In this case, it's creating a quantum circuit `qc` with 2 qubits. It then applies a rotation around the y-axis (`ry`) on each qubit. The rotation angle is determined by the input data `x` multiplied by `pi`. The `ParameterVector` is a way to create a list of parameters." - ] - }, - { - "cell_type": "markdown", - "id": "19f6461a-7bc1-47e9-bf5b-6bf606fbc586", - "metadata": { - "id": "19f6461a-7bc1-47e9-bf5b-6bf606fbc586" - }, - "source": [ - "First, we create some dummy data, but smaller (fewer data points) than it was before." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "ed4cad78-d89f-4dff-981c-8113ca649e12", - "metadata": { - "id": "ed4cad78-d89f-4dff-981c-8113ca649e12" - }, - "outputs": [], - "source": [ - "nsamp = 10\n", - "x = np.array( [[0.0, x/nsamp] for x in range(nsamp)] + [[1.0, x/nsamp] for x in range(nsamp)] )\n", - "y = np.array([-4.5 + 0.2*a[0] + a[1]*(1+a[0]*0.2) + 0.1*np.random.normal() for a in x])\n", - "\n", - "p = 1/(1+np.exp(-y))\n", - "\n", - "n = [int(200 + 600*xj[1]/0.7) if xj[1] <= 0.7 else int(800 - 300*(xj[1]-0.7)/0.3) for xj in x]\n", - "\n", - "d = [nj*pj for nj,pj in zip(n,p)]" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6b244442-219f-448c-bee8-21b566d906c4", - "metadata": { - "id": "6b244442-219f-448c-bee8-21b566d906c4" - }, - "outputs": [], - "source": [ - "# Create a DataFrame\n", - "df1 = pd.DataFrame({\n", - " 'gender': [a[0] for a in x],\n", - " 'age group (normalized)': [a[1] for a in x],\n", - " 'population size': n,\n", - " 'number of transitions': d\n", - "})\n", - "\n", - "# Write the DataFrame to a CSV file\n", - "df1.to_csv('fdata1.csv', index=False) # index=False argument is used to prevent pandas from writing row indices into the CSV file" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "670765b0-5135-4965-a15f-57e5ea90c130", - "metadata": { - "id": "670765b0-5135-4965-a15f-57e5ea90c130" - }, - "outputs": [], - "source": [ - "data1 = df1\n", - "# data1 = pd.read_csv('fdata1.csv')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "f04e1346-2773-4918-9789-b72c9354f381", - "metadata": { - "id": "f04e1346-2773-4918-9789-b72c9354f381", - "outputId": "e0c43769-aa51-498c-88b0-a58e178903da" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[0. 0. ]\n", - " [0. 0.1]\n", - " [0. 0.2]\n", - " [0. 0.3]\n", - " [0. 0.4]\n", - " [0. 0.5]\n", - " [0. 0.6]\n", - " [0. 0.7]\n", - " [0. 0.8]\n", - " [0. 0.9]\n", - " [1. 0. ]\n", - " [1. 0.1]\n", - " [1. 0.2]\n", - " [1. 0.3]\n", - " [1. 0.4]\n", - " [1. 0.5]\n", - " [1. 0.6]\n", - " [1. 0.7]\n", - " [1. 0.8]\n", - " [1. 0.9]]\n" - ] - } - ], - "source": [ - "# Transform and inspect data\n", - "x1 = np.array( [[a,b] for a,b in zip(data1['gender'], data1['age group (normalized)'])] )\n", - "print(x1)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3b74a992-8a26-481b-b40a-05cc775ce58f", - "metadata": { - "id": "3b74a992-8a26-481b-b40a-05cc775ce58f" - }, - "outputs": [], - "source": [ - "# raw transition frequency per group, used for plots\n", - "p_raw = [a/b for a,b in zip(d,n)]\n", - "\n", - "# logistic probability, used as input to SVR optimization\n", - "y = np.array([np.log( p / (1-p) ) for p in p_raw])\n", - "\n", - "# calculate weights for SVR based on population size\n", - "w = np.array([1./nj for nj in n])\n", - "\n", - "# normalize weights (equivalent to changing the hyperparameters of the SVR)\n", - "w = w/sum(w)*len(x)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c4e5c7fd-1c28-4867-8e1a-4ba20b711f1f", - "metadata": { - "id": "c4e5c7fd-1c28-4867-8e1a-4ba20b711f1f", - "outputId": "9395a2e9-1d87-4e79-e6fd-5e448166e0fa" - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", - "axs.plot([x1j[1] for x1j,p in zip(x1, p_raw) if x1j[0] == 0], [p for x1j,p in zip(x1, p_raw) if x1j[0] == 0], 'or')\n", - "axs.plot([x1j[1] for x1j,p in zip(x1, p_raw) if x1j[0] == 1], [p for x1j,p in zip(x1, p_raw) if x1j[0] == 1], 'ob')\n", - "axs.set_title(\"raw transition frequencies\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "08783390-fb9a-4d24-ae8b-02eb0923c632", - "metadata": { - "id": "08783390-fb9a-4d24-ae8b-02eb0923c632" - }, - "source": [ - "## Exercise 3: Implement and Visualize a Quantum Feature Map\n", - "\n", - "In this exercise, you will implement a quantum feature map using Qiskit and visualize the resulting quantum circuit. The feature map is a way of encoding classical data into quantum states. In this case, we will use a simple feature map that applies a rotation around the y-axis on each qubit.\n", - "\n", - "### Task 1: Implement the Feature Map\n", - "\n", - "First, let's implement the feature map. Here is the function you need to complete:\n", - "\n", - "```python\n", - "def feature_map(x1):\n", - " p = ParameterVector('x1', length=2)\n", - " qc = QuantumCircuit(2)\n", - "\n", - " # TODO: Apply a rotation around the y-axis on each qubit\n", - " # Hint: Use the ry gate and the input data x1\n", - "\n", - " return qc\n", - "```\n", - "\n", - "### Task 2: Visualize the Circuit\n", - "\n", - "After implementing the feature map, you visualize the resulting quantum circuit, as we did at the beginning of this lesson.\n", - "\n", - "Good luck with your exercise! If you have any questions or need further clarification, feel free to ask. 😊" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "24c26430-a283-4a99-8fb7-058c52bf4c7e", - "metadata": { - "id": "24c26430-a283-4a99-8fb7-058c52bf4c7e" - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "dc63aa1a-0bf0-4e1f-9bf2-580c12aadbdb", - "metadata": { - "id": "dc63aa1a-0bf0-4e1f-9bf2-580c12aadbdb" - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "52aa44c7-40bc-4ec2-b273-94d6b457a8dc", - "metadata": { - "id": "52aa44c7-40bc-4ec2-b273-94d6b457a8dc" - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "13cf3642-2745-4250-ac18-9006bb457793", - "metadata": { - "id": "13cf3642-2745-4250-ac18-9006bb457793" - }, - "source": [ - "The following part of the code implements a list of all possible quantum circuits for the given data `x1`. For each pair of data points `(x1[i], x1[j])`, it creates two circuits using the `feature_map` function. The feature map is a way of encoding classical data into quantum states. It then appends the inverse of `qc_j` to `qc_i` using the `compose` function. This function combines two circuits, and with `.inverse()`, it applies the inverse of the second circuit. After composing the circuits, it adds a measurement on all qubits using `measure_all()`. The circuit is then transpiled for a specific backend using the `transpile` function." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "051f839e-9306-44eb-b198-eaeafa837238", - "metadata": { - "id": "051f839e-9306-44eb-b198-eaeafa837238", - "outputId": "b753f105-a8a2-463d-f334-24d1d0f4ef40" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "190\n" - ] - } - ], - "source": [ - "# from qiskit import transpile\n", - "\n", - "# Initialize an empty list to store all circuits\n", - "all_circuits = []\n", - "\n", - "for i in range(len(x1)):\n", - " for j in range(i):\n", - " # Substitute parameters with values from your data\n", - " qc_i = feature_map(x1[i])\n", - " qc_j = feature_map(x1[j])\n", - "\n", - " # Append the inverse of qc_j to qc_i and measure\n", - " qc_ij = qc_i.compose(qc_j.inverse())\n", - " qc_ij.measure_all()\n", - "\n", - " # Transpile the circuit for the backend\n", - " qc_ij_transpiled = transpile(qc_ij, backend=backend)\n", - "\n", - " # Add the transpiled circuit to the list\n", - " all_circuits.append(qc_ij_transpiled)\n", - "\n", - "print(len(all_circuits))" - ] - }, - { - "cell_type": "markdown", - "id": "b50ea21e-efef-4102-82c5-9a36ecde6552", - "metadata": { - "id": "b50ea21e-efef-4102-82c5-9a36ecde6552" - }, - "source": [ - "This block of code defines a batch size and splits the transpiled circuits into batches. It then initializes a list to store job IDs. Each batch of circuits is executed on the backend with 1024 shots per circuit execution. Also, it can take some time to execute." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "23cde26c-9afe-42ca-80e1-657f120f26ac", - "metadata": { - "id": "23cde26c-9afe-42ca-80e1-657f120f26ac", - "outputId": "ed9bfcae-b340-42ef-cdd2-2c9010e12cd7" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Tracking execution of job1:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job2:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job3:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job4:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job5:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job6:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job7:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job8:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job9:\n", - "Job Status: job has successfully run\n", - "Tracking execution of job10:\n", - "Job Status: job has successfully run\n" - ] - } - ], - "source": [ - "# Define the batch size\n", - "batch_size = 20\n", - "\n", - "# Split the transpiled circuits into batches\n", - "batches = [all_circuits[i:i + batch_size] for i in range(0, len(all_circuits), batch_size)]\n", - "\n", - "# Initialize a list to store job IDs\n", - "job_ids = []\n", - "\n", - "# Execute each batch of circuits\n", - "for batch in batches:\n", - " job = backend.run(batch, shots=1024)\n", - " job_ids.append(job.job_id())\n", - "\n", - "# This block of code executes each batch until it's successful or an exception occurs\n", - "# If an exception occurs, it waits for a random amount of time between 1 and 10 seconds before retrying\n", - "\n", - "import time\n", - "import random\n", - "\n", - "# Initialize a list to store results\n", - "results = []\n", - "n_shots = 1024\n", - "\n", - "# Initialize a counter for the job number\n", - "job_number = 1\n", - "\n", - "for batch in batches:\n", - " success = False\n", - " while not success:\n", - " try:\n", - " # Execute the batch of circuits\n", - " job = backend.run(batch, shots=n_shots)\n", - "\n", - " # Print job execution status\n", - " print(f\"Tracking execution of job{job_number}:\")\n", - " job_monitor(job)\n", - "\n", - " # Wait for the job to finish and get the result\n", - " result = job.result()\n", - "\n", - " # If successful, append the result and break the loop\n", - " results.append(result)\n", - " success = True\n", - "\n", - " except Exception as e:\n", - " print(f\"Execution failed with error: {e}\")\n", - "\n", - " # Sleep for a bit (random backoff) before retrying\n", - " time.sleep(random.randint(1, 10))\n", - "\n", - " # Increment the job number for the next iteration\n", - " job_number += 1" - ] - }, - { - "cell_type": "markdown", - "id": "fc8b2a3d-9729-4c20-acf5-f40d9851ef30", - "metadata": { - "id": "fc8b2a3d-9729-4c20-acf5-f40d9851ef30" - }, - "source": [ - "**Job Retrieval and Frequency Calculation**: The script starts by iterating over a list of `job_ids`. For each `job_id`, it retrieves the job result from the backend. It then calculates the frequency of the '00' state in the results and appends this frequency to the `estimates` list." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6f002a91-d87c-4278-905c-dbfacf9a03f0", - "metadata": { - "id": "6f002a91-d87c-4278-905c-dbfacf9a03f0", - "outputId": "390fbd69-02d5-434a-c90c-ddd9b617bb37" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Job1: ea63caca-9859-4988-afcc-4617a4422261\n", - "Job2: 4ea8454c-0146-47e3-a4f3-22e7098bf8b5\n", - "Job3: 29c17939-328b-46bd-bcf6-e2df758b4efd\n", - "Job4: 80e39182-931b-4bc9-83d7-f100a877d81b\n", - "Job5: bae16e48-b12a-4cea-bdf4-287bce4e11ab\n", - "Job6: ed7f15be-36d1-41c4-b0e1-794746789a48\n", - "Job7: b07bd0df-a786-4389-8def-ea0926f2fd17\n", - "Job8: d346a014-4afc-43ee-8ee4-d16e229e7c1e\n", - "Job9: baf11441-c6d0-4b0b-8641-068a929c72c4\n", - "Job10: 1895b727-95b8-4925-bc95-e7e2347493f7\n" - ] - } - ], - "source": [ - "# Initialize a counter for the job number\n", - "job_number = 1\n", - "\n", - "for job_id in job_ids:\n", - " print(f\"Job{job_number}: {job_id}\")\n", - " job_number += 1" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "bacb231a-f8cc-4922-82fd-079a6b568dc9", - "metadata": { - "id": "bacb231a-f8cc-4922-82fd-079a6b568dc9" - }, - "outputs": [], - "source": [ - "estimates = []\n", - "\n", - "for job_id in job_ids:\n", - " job_res = backend.retrieve_job(job_id).result()\n", - " for res in job_res.results:\n", - " if '00' in res.data.counts:\n", - " freq = res.data.counts['00']/n_shots\n", - " else:\n", - " freq = 0.0\n", - " estimates.append(freq)" - ] - }, - { - "cell_type": "markdown", - "id": "3ab74e22-d559-46b8-8777-396d0af98e79", - "metadata": { - "id": "3ab74e22-d559-46b8-8777-396d0af98e79" - }, - "source": [ - "**Kernel Matrix Construction**: The script constructs a kernel matrix `K_helmi` using the estimates. The kernel matrix is a symmetric matrix where each element represents a measure of similarity between two data points." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "77466963-5ed7-4a93-adcd-4c9dd0867a18", - "metadata": { - "id": "77466963-5ed7-4a93-adcd-4c9dd0867a18" - }, - "outputs": [], - "source": [ - "K_helmi = np.identity(len(x1))\n", - "\n", - "cnt = 0\n", - "for i in range(len(x1)):\n", - " for j in range(i):\n", - " #print(i, ' ', j)\n", - " K_helmi[i,j] = estimates[cnt]\n", - " K_helmi[j,i] = estimates[cnt]\n", - " cnt += 1" - ] - }, - { - "cell_type": "markdown", - "id": "9f7f0f1d-bf79-45fd-9763-2b448c10c884", - "metadata": { - "id": "9f7f0f1d-bf79-45fd-9763-2b448c10c884" - }, - "source": [ - " **Kernel Matrix Visualization**: The kernel matrix is then visualized using matplotlib's `imshow` function. The color map 'Blues' is used, and a color bar is added for reference." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "e09a4a10-61a5-4f02-92a3-2bdd33a5e7ba", - "metadata": { - "id": "e09a4a10-61a5-4f02-92a3-2bdd33a5e7ba", - "outputId": "226f709d-e913-4db8-b7c4-eb6c27ac180c" - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", - "pos = axs.imshow(np.asmatrix(K_helmi),\n", - " interpolation='nearest', origin='upper', cmap='Blues')\n", - "axs.set_title(\"kernel matrix from Helmi\")\n", - "fig.colorbar(pos, ax=axs)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "0cc501ab-40c7-4b26-aefb-f20ff7369b72", - "metadata": { - "id": "0cc501ab-40c7-4b26-aefb-f20ff7369b72" - }, - "source": [ - "**Support Vector Regression (SVR)**: The script uses the Support Vector Regression (SVR) model from scikit-learn with a precomputed kernel. It fits the model to the data (`f_matrix_train` and `y`) and calculates the score of the model using the `score` method.\n", - "\n", - "**Prediction and Plotting**: The fitted model is used to predict outcomes, which are then plotted against the actual outcomes for two groups (Group 0 and Group 1)." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "77e7a3fc-3bd0-4d7f-acb7-17e5fbb2132e", - "metadata": { - "id": "77e7a3fc-3bd0-4d7f-acb7-17e5fbb2132e", - "outputId": "e8f46872-0507-4837-920b-4046bad19bf8" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "score: 0.9001754733534563\n" - ] - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "f_matrix_train = K_helmi\n", - "\n", - "zzpc_svr = SVR(kernel='precomputed')\n", - "zzpc_svr.fit(f_matrix_train, y, w)\n", - "zzpc_score = zzpc_svr.score(f_matrix_train, y, w)\n", - "print(f'score: {zzpc_score}')\n", - "pred = zzpc_svr.predict(f_matrix_train)\n", - "\n", - "p_hat = 1/(1+np.exp(-pred))\n", - "p = 1/(1+np.exp(-y))\n", - "plt.figure()\n", - "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p) if a[0] == 0],'or')\n", - "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", - "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", - "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", - "plt.legend(['Group 0', 'Group 0 model', 'Group 1', 'Group 1 model'])\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "5e211b3e-7c28-4de0-967d-14bb3c502bd8", - "metadata": { - "id": "5e211b3e-7c28-4de0-967d-14bb3c502bd8" - }, - "source": [ - "**Error Calculation and Visualization**: Finally, the script calculates the absolute errors between `K_helmi` and `matrix_train`, visualizes these errors using `imshow`, and displays this with a color bar for reference." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "8a3b538d-9deb-418a-9a3c-4e14590e6074", - "metadata": { - "id": "8a3b538d-9deb-418a-9a3c-4e14590e6074" - }, - "outputs": [], - "source": [ - "# redo the steps for statevector kernel to compare with the Helmi results\n", - "\n", - "zz_kernel = QuantumKernel(feature_map=qc, quantum_instance=Aer.get_backend('statevector_simulator'))\n", - "zz_circuit = zz_kernel.construct_circuit(ParameterVector('x_i', length=2),ParameterVector('x_j', length=2))\n", - "zz_circuit.decompose().draw(output='mpl')\n", - "matrix_train = zz_kernel.evaluate(x_vec=x)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "errors = np.abs(K_helmi - matrix_train)\n", - "\n", - "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", - "pos = axs.imshow(np.asmatrix(errors),\n", - " interpolation='nearest', origin='upper', cmap='Reds')\n", - "axs.set_title(\"erorrs\")\n", - "fig.colorbar(pos, ax=axs)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "47fa3d94-0b0e-41f9-ba3b-4571be968882", - "metadata": { - "id": "47fa3d94-0b0e-41f9-ba3b-4571be968882" - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3ca65f4a-c3b7-43da-b27b-35bf2a7c73d1", - "metadata": { - "id": "3ca65f4a-c3b7-43da-b27b-35bf2a7c73d1" - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "30df1f84-8e4b-4e3b-a607-3ecf25e9d375", - "metadata": { - "id": "30df1f84-8e4b-4e3b-a607-3ecf25e9d375" - }, - "outputs": [], - "source": [ - "# solution ex2\n", - "residuals = y - pred\n", - "plt.hist(residuals, bins=20)\n", - "plt.xlabel('Residuals')\n", - "plt.ylabel('Frequency')\n", - "plt.title('Histogram of Residuals')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "97aab143-92b2-4765-853c-1c8757bd79b0", - "metadata": { - "id": "97aab143-92b2-4765-853c-1c8757bd79b0" - }, - "outputs": [], - "source": [ - "# solution1 ex2\n", - "residuals1 = p_hat-p\n", - "plt.hist(residuals1, bins=20)\n", - "plt.xlabel('Residuals')\n", - "plt.ylabel('Frequency')\n", - "plt.title('Histogram of Residuals')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c3a78eab-1e43-4f1b-a992-526d1c131b4a", - "metadata": { - "id": "c3a78eab-1e43-4f1b-a992-526d1c131b4a" - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "a26ddc57-a2fc-48ac-b3ae-f3ece0a2b507", - "metadata": { - "id": "a26ddc57-a2fc-48ac-b3ae-f3ece0a2b507" - }, - "outputs": [], - "source": [ - "# solution ex3\n", - "\n", - "def feature_map(x1):\n", - " p = ParameterVector('x1', length=2)\n", - " qc = QuantumCircuit(2)\n", - "\n", - " qc.ry(x1[0]*np.pi, 0)\n", - " qc.ry(x1[1]*np.pi, 1)\n", - "\n", - " return qc" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "681cbb1a-dcc1-4870-990f-7935e14b8d81", - "metadata": { - "id": "681cbb1a-dcc1-4870-990f-7935e14b8d81", - "outputId": "4679a728-38f0-4ada-e70e-b7fa1bcbac3c" - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# solution1 ex3\n", - "# Draw the circuit\n", - "qc.draw('mpl')" - ] - }, - { - "cell_type": "code", - "source": [], - "metadata": { - "id": "INefXmud-4fw" - }, - "id": "INefXmud-4fw", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "code", - "source": [], - "metadata": { - "id": "nNAylO7d-4iF" - }, - "id": "nNAylO7d-4iF", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "code", - "source": [], - "metadata": { - "id": "_mqodsqI-4kK" - }, - "id": "_mqodsqI-4kK", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "code", - "source": [], - "metadata": { - "id": "RoP5NvHh-4mp" - }, - "id": "RoP5NvHh-4mp", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "d1960e7f-a57d-4047-b7eb-6054e37ee913", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "d1960e7f-a57d-4047-b7eb-6054e37ee913", - "outputId": "2412fed3-f003-4c32-c3d0-24478e6c35d3" - }, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - " ┌──────────┐\n", - "q.0: ┤ Rx(π*x0) ├\n", - " ├──────────┤\n", - "q.1: ┤ Rz(π*x1) ├\n", - " └──────────┘\n" - ] - } - ], - "source": [ - "# solution ex1.1\n", - "\n", - "from qrisp import QuantumVariable, rx, rz\n", - "from sympy import symbols\n", - "import numpy as np\n", - "\n", - "def build_feature_map(sym):\n", - " n = 2\n", - " q = QuantumVariable(n)\n", - " params = symbols(sym + ':' + str(n))\n", - " rx(np.pi * params[0], q[0])\n", - " rz(np.pi * params[1], q[1])\n", - " return q\n", - "\n", - "feature_map = build_feature_map('x')\n", - "print(feature_map.qs.transpile())\n" - ] - }, - { - "cell_type": "code", - "source": [ - "# solution ex1.2\n", - "\n", - "from qrisp import QuantumVariable, ry, h, cx\n", - "\n", - "def build_feature_map(sym):\n", - " n = 2\n", - " q = QuantumVariable(n)\n", - " params = symbols(sym + ':' + str(n))\n", - " ry(np.pi * params[0], q[0])\n", - " ry(np.pi * params[1], q[1])\n", - " h(q[0])\n", - " cx(q[0], q[1])\n", - " return q\n", - "\n", - "feature_map = build_feature_map('x')\n", - "print(feature_map.qs.transpile())" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "__-88RBE-4_g", - "outputId": "da284955-5d98-42c5-b20f-5f075f7efb18" - }, - "id": "__-88RBE-4_g", - "execution_count": null, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - " ┌──────────┐┌───┐ \n", - "q.0: ┤ Ry(π*x0) ├┤ H ├──■──\n", - " ├──────────┤└───┘┌─┴─┐\n", - "q.1: ┤ Ry(π*x1) ├─────┤ X ├\n", - " └──────────┘ └───┘\n" - ] - } - ] - }, - { - "cell_type": "code", - "source": [ - "# solution ex1.3\n", - "\n", - "from qrisp import QuantumVariable, ry\n", - "from sympy import symbols\n", - "import numpy as np\n", - "\n", - "def build_feature_map(sym):\n", - " n = 2\n", - " q = QuantumVariable(n)\n", - " params = symbols(sym + ':' + str(n))\n", - " ry(np.sin(params[0] * np.pi), q[0])\n", - " ry(np.log1p(params[1]) * np.pi, q[1])\n", - " return q\n", - "\n", - "feature_map = build_feature_map('x')\n", - "print(feature_map.qs.transpile())" - ], - "metadata": { - "id": "eq41tPVY-5B2" - }, - "id": "eq41tPVY-5B2", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "code", - "source": [ - "# solution ex1.4\n", - "\n", - "from qrisp import QuantumVariable, ry\n", - "from sympy import symbols\n", - "import numpy as np\n", - "\n", - "def build_feature_map(sym):\n", - " n = 3\n", - " q = QuantumVariable(n)\n", - " params = symbols(sym + ':' + str(n))\n", - " for i in range(n):\n", - " ry(np.pi * params[i], q[i])\n", - " return q\n", - "\n", - "feature_map = build_feature_map('x')\n", - "print(feature_map.qs.transpile())\n" - ], - "metadata": { - "id": "kkFik42y_LIc" - }, - "id": "kkFik42y_LIc", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "code", - "source": [ - "# solution ex2\n", - "\n", - "# Transform actual values to probabilities\n", - "p = 1 / (1 + np.exp(-y))\n", - "\n", - "# Compute residuals\n", - "residuals_qsvr = p - p_hat_q\n", - "residuals_classical = p - p_hat_c\n", - "\n", - "# Plot histogram of Quantum SVR residuals\n", - "plt.figure(figsize=(12, 5))\n", - "\n", - "plt.subplot(1, 2, 1)\n", - "plt.hist(residuals_qsvr, bins=20, color='skyblue', edgecolor='black')\n", - "plt.xlabel('Residuals (Actual - Predicted)')\n", - "plt.ylabel('Frequency')\n", - "plt.title('Histogram of Residuals - Quantum SVR')\n", - "plt.grid(True)\n", - "\n", - "# Plot histogram of Classical SVR residuals\n", - "plt.subplot(1, 2, 2)\n", - "plt.hist(residuals_classical, bins=20, color='salmon', edgecolor='black')\n", - "plt.xlabel('Residuals (Actual - Predicted)')\n", - "plt.ylabel('Frequency')\n", - "plt.title('Histogram of Residuals - Classical SVR')\n", - "plt.grid(True)\n", - "\n", - "plt.tight_layout()\n", - "plt.show()" - ], - "metadata": { - "id": "whov_4CX-5Di" - }, - "id": "whov_4CX-5Di", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "code", - "source": [], - "metadata": { - "id": "gyvxsT5A-5Fo" - }, - "id": "gyvxsT5A-5Fo", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "code", - "source": [], - "metadata": { - "id": "7GyO8oYR-5Hn" - }, - "id": "7GyO8oYR-5Hn", - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "id": "eaae61c0-9258-4bf7-a929-065ab90d36aa", - "metadata": { - "id": "eaae61c0-9258-4bf7-a929-065ab90d36aa" - }, - "source": [ - "#### TEST CODE" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3397e118-363f-4cb2-b0aa-3166d83ae03f", - "metadata": { - "id": "3397e118-363f-4cb2-b0aa-3166d83ae03f" - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6d2dad5d-6493-460a-a5d6-898448124f31", - "metadata": { - "id": "6d2dad5d-6493-460a-a5d6-898448124f31" - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.13.7" - }, - "colab": { - "provenance": [] - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file From 0b0f0172ff924e38705c85d0ab91b725784b3dfc Mon Sep 17 00:00:00 2001 From: Anastasiia Andriievska <79667606+fomalhautn@users.noreply.github.com> Date: Wed, 5 Nov 2025 19:46:43 +0100 Subject: [PATCH 8/8] Finalised notebook for QAS2025 --- .../template_folders/QKE_BL_AA_IQM_2025.ipynb | 3192 +++++++++++++++++ 1 file changed, 3192 insertions(+) create mode 100644 content/template_folders/QKE_BL_AA_IQM_2025.ipynb diff --git a/content/template_folders/QKE_BL_AA_IQM_2025.ipynb b/content/template_folders/QKE_BL_AA_IQM_2025.ipynb new file mode 100644 index 0000000..15f12f3 --- /dev/null +++ b/content/template_folders/QKE_BL_AA_IQM_2025.ipynb @@ -0,0 +1,3192 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e4b10801-19d8-4751-8e31-a9bfd2df03d1", + "metadata": { + "id": "e4b10801-19d8-4751-8e31-a9bfd2df03d1" + }, + "source": [ + "# Tutorial - Quantum Kernel Estimation with application to Disability Insurance\n", + "\n", + "B. Djehiche and B. Löfdahl – KTH, Department of Mathematics / SEB –\n", + "Risks 2021, 9(12), 216; https://doi.org/10.3390/risks9120216\n", + "\n", + "Hands-on assistance: [Anastasiia Andriievska](https://www.linkedin.com/in/aandriievska/)" + ] + }, + { + "cell_type": "markdown", + "id": "db9aaa0c-7b71-4cd4-bc42-78c9d9694f33", + "metadata": {}, + "source": [ + "## Quantum Support Vector Regression for Disability Insurance\n", + "\n", + "This notebook explores the application of **Quantum Support Vector Regression (QSVR)** to model and predict outcomes in **Disability Insurance**, inspired by the methodology presented in the paper *Quantum Support Vector Regression for Disability Insurance*.\n", + "\n", + "It serves as both a **research prototype** and a **teaching resource** for students and professionals interested in quantum machine learning, actuarial science, and insurance analytics.\n", + "\n", + "### 📘 What You'll Learn\n", + "- The fundamentals of Support Vector Regression and its quantum counterpart.\n", + "- How quantum kernels are constructed using parameterized quantum circuits.\n", + "- How to compute kernel matrices using **statevector simulation** and **real quantum hardware** (IQM backends).\n", + "- How to train SVR models on quantum kernels and interpret predictions in terms of transition probabilities." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "YWc5tpIJbric", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "YWc5tpIJbric", + "outputId": "efec0699-82c6-47d6-9d37-58ae5e24b10d" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Requirement already satisfied: scikit-learn in /srv/conda/envs/notebook/lib/python3.11/site-packages (1.7.2)\n", + "Requirement already satisfied: numpy>=1.22.0 in /srv/conda/envs/notebook/lib/python3.11/site-packages (from scikit-learn) (2.3.4)\n", + "Requirement already satisfied: scipy>=1.8.0 in /srv/conda/envs/notebook/lib/python3.11/site-packages (from scikit-learn) (1.15.3)\n", + "Requirement already satisfied: joblib>=1.2.0 in /srv/conda/envs/notebook/lib/python3.11/site-packages (from scikit-learn) (1.5.2)\n", + "Requirement already satisfied: threadpoolctl>=3.1.0 in /srv/conda/envs/notebook/lib/python3.11/site-packages (from scikit-learn) (3.6.0)\n" + ] + } + ], + "source": [ + "!pip install scikit-learn\n", + "#qrisp==0.7.9 pandas numpy matplotlib sympy" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "b6f8b962-5fde-46f8-af33-dda094485734", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "b6f8b962-5fde-46f8-af33-dda094485734", + "outputId": "e4bc7ea9-0e86-4c20-ba97-38a87027d057" + }, + "outputs": [], + "source": [ + "# install necessary packages via pip\n", + "\n", + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.svm import SVR\n", + "from copy import copy\n", + "from qrisp import QuantumVariable, QuantumCircuit\n", + "from sympy import symbols" + ] + }, + { + "cell_type": "markdown", + "id": "d9224010-d6e9-4d8a-a391-cd5350418491", + "metadata": { + "id": "d9224010-d6e9-4d8a-a391-cd5350418491" + }, + "source": [ + "First, we create some synthetic data. The x-variable holds the available data. x[i][0] represents gender (0 or 1). x[i][1] represents age, normalized to the [0,1] interval. The y-variable is the value that we seek to model. It represents the logistic transition probability between two states. The w-variable represents the weight that we assign to each data point." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "168cfc3c-d7ba-4b88-b60a-7cbd67738d83", + "metadata": { + "id": "168cfc3c-d7ba-4b88-b60a-7cbd67738d83" + }, + "outputs": [], + "source": [ + "# Set random seed for reproducibility\n", + "np.random.seed(42)\n", + "\n", + "# Number of samples per gender\n", + "nsamp = 100\n", + "\n", + "# Create feature matrix: gender (0 or 1), normalized age [0, 1]\n", + "x = np.array([[0.0, i/nsamp] for i in range(nsamp)] + [[1.0, i/nsamp] for i in range(nsamp)])\n", + "\n", + "# Generate target values with noise\n", + "y = np.array([\n", + " -4.5 + 0.2*a[0]*(1 - 5*a[1]**2) + a[1]*(1 + a[0]*0.2) + 0.1*np.random.normal()\n", + " for a in x\n", + "])\n", + "\n", + "# Logistic transformation\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# Population size based on age\n", + "n = [\n", + " int(2000 + 6000*xj[1]/0.7) if xj[1] <= 0.7 else int(8000 - 3000*(xj[1] - 0.7)/0.3)\n", + " for xj in x\n", + "]\n", + "\n", + "# Weighted transitions\n", + "d = [nj * pj for nj, pj in zip(n, p)]" + ] + }, + { + "cell_type": "markdown", + "id": "6404a54d-b5d7-4395-96ab-d4bb9f75df61", + "metadata": { + "id": "6404a54d-b5d7-4395-96ab-d4bb9f75df61" + }, + "source": [ + "We can use the Pandas library to create a DataFrame and then save it as a CSV file, which support column headers. This will create a CSV file with each column labeled as ‘gender’, ‘age group (normalized)’, ‘population size’, and ‘number of transitions’ respectively. The index=False argument is used to prevent pandas from writing row indices into the file." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "98b3d891-41c2-4ead-90dd-a8419e79809e", + "metadata": { + "id": "98b3d891-41c2-4ead-90dd-a8419e79809e" + }, + "outputs": [], + "source": [ + "# Create a DataFrame\n", + "df = pd.DataFrame({\n", + " 'gender': [a[0] for a in x],\n", + " 'age group (normalized)': [a[1] for a in x],\n", + " 'population size': n,\n", + " 'number of transitions': [int(round(a)) for a in d]\n", + "})\n", + "\n", + "# Write the DataFrame to a CSV file\n", + "df.to_csv('fdata.csv', index=False) # index=False argument is used to prevent pandas from writing row indices into the CSV file" + ] + }, + { + "cell_type": "markdown", + "id": "79a2034c-1509-44c2-9fdb-ed63b301a727", + "metadata": { + "id": "79a2034c-1509-44c2-9fdb-ed63b301a727" + }, + "source": [ + "One can read the data back from the file like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "0da27f10-d9b1-4c75-afcd-cf69122586a6", + "metadata": { + "id": "0da27f10-d9b1-4c75-afcd-cf69122586a6" + }, + "outputs": [], + "source": [ + "data = pd.read_csv('fdata.csv')" + ] + }, + { + "cell_type": "markdown", + "id": "e0d5741f-c5fb-4fb8-84a2-da56f6fa2ae9", + "metadata": { + "id": "e0d5741f-c5fb-4fb8-84a2-da56f6fa2ae9" + }, + "source": [ + "### Transform and inspect data" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "84552a98-075b-48de-b7a9-68e018e95e83", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "84552a98-075b-48de-b7a9-68e018e95e83", + "outputId": "859c109d-3ab3-4a3c-b673-355c8b43a60b" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 0. ]\n", + " [0. 0.01]\n", + " [0. 0.02]\n", + " [0. 0.03]\n", + " [0. 0.04]\n", + " [0. 0.05]\n", + " [0. 0.06]\n", + " [0. 0.07]\n", + " [0. 0.08]\n", + " [0. 0.09]]\n" + ] + } + ], + "source": [ + "x = np.array( [[a,b] for a,b in zip(data['gender'], data['age group (normalized)'])] )\n", + "print(x[0:10])" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "5bfef017-385e-47c0-8b46-89a280406102", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "5bfef017-385e-47c0-8b46-89a280406102", + "outputId": "846425a9-d74d-4427-a528-d2d8d9191bf4" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-4.45032858, -4.50382643, -4.41523115, -4.31769701, -4.48341534,\n", + " -4.4734137 , -4.28207872, -4.35325653, -4.46694744, -4.355744 ])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y[0:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "e7447d0f-64e9-4d56-8a41-299cdd3b044e", + "metadata": { + "id": "e7447d0f-64e9-4d56-8a41-299cdd3b044e" + }, + "outputs": [], + "source": [ + "# raw transition frequency per group, used for plots\n", + "p_raw = [a/b for a,b in zip(d,n)]\n", + "\n", + "# logistic probability, used as input to SVR optimization\n", + "y = np.array([np.log( p / (1-p) ) for p in p_raw])\n", + "\n", + "# calculate weights for SVR based on population size\n", + "w = np.array([1./nj for nj in n])\n", + "\n", + "# normalize weights (equivalent to changing the hyperparameters of the SVR)\n", + "w = w/sum(w)*len(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "0fe05211-ed34-463f-81ea-37069c0fd93f", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 468 + }, + "id": "0fe05211-ed34-463f-81ea-37069c0fd93f", + "outputId": "6b8f90cb-61bc-4b51-e8da-375034d03537" + }, + "outputs": [ + { + "data": { + "image/png": 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xxx14/vnnYTKZ0Lt3b2zdurXFuDwAWLFiBYYNG4b+/fvjvvvuwzXXXIPq6moUFxfjxIkT+OKLLxR/nmeffRb33nsvBg8e7Jhr7YsvvsCFCxfw+uuvy75u+PDhmDFjBvLy8rB//36MGjUK7du3x7fffouNGzfiueeeQ1ZWFl5//XW8+OKLuP3229G7d2+cO3cOL7/8MiIiIvCb3/xGUV2JiLzKb/kFiYiCjD1t+unTp1s8d+LECXH77beLqKgoERkZKe644w5x8uRJAUDk5uY6la2trRVms1l07NjRKQ33P//5TwFATJo0yaP6NDQ0iNmzZ4uuXbsKk8nkSKFuT7Etl8q8sbFRPPXUU6JXr14iLCxM3HTTTWLr1q0tUmG3to6mn+nMmTNi5syZok+fPqJDhw4iMjJSJCcniw0bNji9pnnadCGkFOw33nijaNeunVNK8OZ1EUJKUf7AAw+IHj16iPbt24trr71WLFmyxCmdt71uzdOeCyFEr169xJQpU2S2YsvP5iptuqt034WFhSI9PV1ERkaK8PBw0bt3b3H33XeLvXv3OpXbvHmzuOGGG0RYWJi48cYbhdVqlf2sp0+fFuPGjRNXXnml6NSpk5gxY4Y4cOCAbJr5f//732Ly5MkiNjZWtG/fXsTFxYnbbrtNbNq0yW39XaVof+edd8TQoUPFFVdcISIiIkRSUpJYu3at43m5OgshxOrVq8XAgQPFFVdcITp27Cj69+8vHnnkEXHy5EkhhDQdQHZ2tujZs6cICwsT3bp1E7fddluL7URE5GsmIdo4mpSIiIj84u6770ZRURHKy8v9XRUioqDFMVREREREREQqMaAiIiIiIiJSiQEVERERERGRShxDRUREREREpBJbqIiIiIiIiFRiQEVERERERKQSJ/ZtorGxESdPnkTHjh1hMpn8XR0iIiIiIvITIQTOnTuHHj16ICTEdTsUA6omTp48CYvF4u9qEBERERGRThw/fhzx8fEun2dA1UTHjh0BSBstIiLCz7UhIiIiIiJ/qa2thcViccQIrjCgasLezS8iIoIBFRERERERuR0KxKQUREREREREKqkKqFasWIGEhASEh4cjOTkZe/bsabX8xo0b0adPH4SHh6N///7Ytm2b0/OLFy9Gnz590KFDB3Tq1AlpaWn47LPPnMqcPXsWd911FyIiIhAVFYVp06bhP//5j1OZL7/8EqmpqQgPD4fFYsEzzzyj5uMRERERERF5RHFAtX79euTk5CA3NxclJSUYMGAA0tPTcerUKdnyu3fvRnZ2NqZNm4bS0lJkZGQgIyMDBw4ccJS57rrr8MILL+Crr77Cxx9/jISEBIwaNQqnT592lLnrrrtw8OBBFBQUYOvWrfjoo48wffp0x/O1tbUYNWoUevXqhX379mHJkiVYvHgxVq9erfQjEhERERERecQkhBBKXpCcnIzBgwfjhRdeACClGrdYLJg9ezbmz5/fovyECRNw/vx5bN261bFsyJAhSExMxKpVq2Tfo7a2FpGRkdixYwd++ctf4ptvvsGNN96Izz//HIMGDQIAbN++Hb/5zW9w4sQJ9OjRAytXrsSf/vQnVFVVITQ0FAAwf/58bNmyBYcOHfLos9nft6amhmOoiIiIiIiCmKexgaIWqvr6euzbtw9paWmXVxASgrS0NBQXF8u+pri42Kk8AKSnp7ssX19fj9WrVyMyMhIDBgxwrCMqKsoRTAFAWloaQkJCHF0Di4uLccsttziCKfv7HD58GD/88IOSj0lEREREROQRRVn+zpw5A5vNhpiYGKflMTExLluBqqqqZMtXVVU5Ldu6dSvuvPNOXLhwAd27d0dBQQGio6Md6+jWrZtzxdu1Q+fOnR3rqaqqwtVXX93ifezPderUqUXd6urqUFdX5/h/bW2ty89ORERERETUnG6y/I0cORL79+/H7t27ceutt2L8+PEux2V5S15eHiIjIx0PTupLRERERERKKAqooqOjYTabUV1d7bS8uroasbGxsq+JjY31qHyHDh3ws5/9DEOGDMErr7yCdu3a4ZVXXnGso3lw1dDQgLNnzzrW4+p97M/JWbBgAWpqahyP48ePt/bxiYiIiIiInCgKqEJDQzFw4EDs3LnTsayxsRE7d+5ESkqK7GtSUlKcygNAQUGBy/JN12vvjpeSkoIff/wR+/btczz/4YcforGxEcnJyY4yH330ES5duuT0Ptdff71sdz8ACAsLc0ziy8l8iYiIiIhIKcVd/nJycvDyyy/j9ddfxzfffIM//OEPOH/+PKZOnQoAmDx5MhYsWOAoP2fOHGzfvh3Lli3DoUOHsHjxYuzduxezZs0CAJw/fx6PPvooPv30Uxw9ehT79u3DPffcg4qKCtxxxx0AgBtuuAG33nor7rvvPuzZsweffPIJZs2ahTvvvBM9evQAAEycOBGhoaGYNm0aDh48iPXr1+O5555DTk5OmzcSERERERGRHEVJKQApDfrp06exaNEiVFVVITExEdu3b3ckgDh27BhCQi7HaUOHDkV+fj4ee+wxPProo7j22muxZcsW9OvXDwBgNptx6NAhvP766zhz5gy6dOmCwYMHY9euXejbt69jPW+++SZmzZqFX/7ylwgJCcG4cePwv//7v47nIyMj8cEHH2DmzJkYOHAgoqOjsWjRIqe5qoiIiIiIDMlmA3btAiorge7dgdRUwGz2d60IKuahCmSch4qIiIiIdMdqBebMAU6cuLwsPh547jkgM9N/9QpwmsxDRUREREREPmS1AllZzsEUAFRUSMutVv/UixwYUBERERER6ZHNJrVMyXUosy+bO1cqR37DgIqIiIiISI927WrZMtWUEMDx41I58hvFSSmIiIiIiMgHKiu9W85XgiyBBgMqIiIiIiI96t7du+V8IQgTaLDLHxERERGRHqWmSsGIyST/vMkEWCxSOT0I0gQaDKiIiIiIiPTIbJZadoCWQZX9/8uX66M7XRAn0GBARURERESkV5mZwKZNQFyc8/L4eGm5P7rR2WxAURGwdq301z5mKkgTaHAMFRERERGRnmVmAmPH6iPRg6sxUllZnr1ebwk0vIABFRERERGR3pnNwIgR/q2DfYxU8259FRVS10NP6CmBhpewyx8REREREbXOkzFSZrNxEmh4EVuoiIiIiIiode7GSAGXE06YTM6BV9MEGoA07srfXRe9iC1URERERETUOk/HPs2d6zqBBgAkJAAjRwITJ0p/ExIMn06dARUREREREbXO07FPY8cC5eVAYSGQny/9LSuTngvQOapMQsh1hAxOtbW1iIyMRE1NDSIiIvxdHSIiIiIifbDZpNakigr5cVQmk9QSVVbWsguf/bWuugy29lo/8jQ2YAsVERERERG1ri2TDAf4HFUMqIiIiIiIyD21kwx7Ov7KoHNUMcsfERERERF5Rs0kw56OvzLoHFUMqIiIiIhI/2w2ZRfxpB2lkwynpkqtWO7GXw0dasiU6gyoiIiIiEjfrFZpUtmm43Di46UxPa66mZF+2MdfZWW5nqPqzjuB3r0NuY85hoqIiIiI9MtqDdh020GltfFXDz0ELF1q2H3MtOlNMG06ERERkY4YNN02taJ5182hQ1u2TDXlx33saWzALn9EREREpE9K0m0rGdND/tN8/FVRkeH3Mbv8EREREZE+BXi6bUJA7GMGVERERESkTwGebpsQEPuYARURERER6ZM93bY9E1xzJhNgsUjlyJgCYB8zoCIiIiIifbKn2wZaXnDb/798uTbJCmw2aXzP2rXSX5vN++9B/t3HXsKAioiIiIj0q7V025s2aTNHkdUqZRccORKYOFH6m5Cg+/TdhuWPfexFTJveBNOmExEREelU83TbqanatFrY571qfolsby0xwAW+YflqH3vI09iAAVUTDKiIiIiIghjnvaImPI0N2OWPiIiIiAhQNu8V0U84sS8REREREeCbOZF01q2N2o4BFRERERERoP2cSFYrMGeOcytYfLyU5Y7jsgyLXf6IiIiIiABt50SyJ7to3qWwokJazgyChsWAioiIiIgI0G5OJJtNapmSywVnXzZ3Lue6MihVAdWKFSuQkJCA8PBwJCcnY8+ePa2W37hxI/r06YPw8HD0798f27Ztczx36dIlzJs3D/3790eHDh3Qo0cPTJ48GSdPnnSUKSoqgslkkn18/vnnAIDy8nLZ5z/99FM1H5GIiIiIgpEWcyIx2UVAUxxQrV+/Hjk5OcjNzUVJSQkGDBiA9PR0nDp1Srb87t27kZ2djWnTpqG0tBQZGRnIyMjAgQMHAAAXLlxASUkJFi5ciJKSElitVhw+fBhjxoxxrGPo0KGorKx0etx77724+uqrMWjQIKf327Fjh1O5gQMHKv2IRERERBTMMjOB8nKgsBDIz5f+lpWpH+fki2QX5DeK56FKTk7G4MGD8cILLwAAGhsbYbFYMHv2bMyfP79F+QkTJuD8+fPYunWrY9mQIUOQmJiIVatWyb7H559/jqSkJBw9ehQ9e/Zs8fylS5cQFxeH2bNnY+HChQCkFqqrr74apaWlSExMVPKRHDgPFRERERF5XVERMHKk+3KFhcCIEVrXhjykyTxU9fX12LdvH9LS0i6vICQEaWlpKC4uln1NcXGxU3kASE9Pd1keAGpqamAymRAVFSX7/DvvvIPvv/8eU6dObfHcmDFj0K1bNwwbNgzvvPNOq5+nrq4OtbW1Tg8iIiIiIq/SMtkF+Z2igOrMmTOw2WyIiYlxWh4TE4OqqirZ11RVVSkqf/HiRcybNw/Z2dkuI8FXXnkF6enpiI+Pdyy76qqrsGzZMmzcuBHvvvsuhg0bhoyMjFaDqry8PERGRjoeFovFZVkiIiIiIlW0SnZBuqCrLH+XLl3C+PHjIYTAypUrZcucOHEC77//PqZNm+a0PDo6Gjk5OY4uiU8//TR+97vfYcmSJS7fb8GCBaipqXE8jh8/7tXPQ0REREQEQJtkF6QLiib2jY6OhtlsRnV1tdPy6upqxMbGyr4mNjbWo/L2YOro0aP48MMPXbZOrVmzBl26dHFKWuFKcnIyCgoKXD4fFhaGsLAwt+shIiIiImqzzExg7Fgpm19lpTRBcGoqW6YMTlELVWhoKAYOHIidO3c6ljU2NmLnzp1ISUmRfU1KSopTeQAoKChwKm8Ppr799lvs2LEDXbp0kV2XEAJr1qzB5MmT0b59e7f13b9/P7qrncmaiIiIiMjbzGYp8UR2tvSXwZThKWqhAoCcnBxMmTIFgwYNQlJSEpYvX47z5887EkRMnjwZcXFxyMvLAwDMmTMHw4cPx7JlyzB69GisW7cOe/fuxerVqwFIwVRWVhZKSkqwdetW2Gw2x/iqzp07IzQ01PHeH374IcrKynDvvfe2qNfrr7+O0NBQ3HTTTQAAq9WKV199FX//+9+VfkQiIiIiIiKPKA6oJkyYgNOnT2PRokWoqqpCYmIitm/f7kg8cezYMYSEXG74Gjp0KPLz8/HYY4/h0UcfxbXXXostW7agX79+AICKigpH4ojm6c4LCwsxoknqyFdeeQVDhw5Fnz59ZOv25JNP4ujRo2jXrh369OmD9evXIysrS+lHJCIiIiIi8ojieagCGeehIiIiIiIiwPPYQHELFRERERERacBmY8IKA2JARURERETkb1YrMGcOcOLE5WXx8dL8VUyprmu6moeKiIiIiCjoWK1AVpZzMAUAFRXScqvVP/UijzCgIiIiIiLyF5tNapmSS2tgXzZ3rlSOdIkBFRERERGREjYbUFQErF0r/W1LsLNrV8uWqaaEAI4fl8qRLnEMFRERERGRp7w91qmy0rvllGASDK9gCxURERERkSe0GOvUvbt3yzXnqjXNagUSEoCRI4GJE6W/CQkcr6UC56FqgvNQEREREZEsm00KOFx1zzOZpJaqsjJlrTz29VZUyI+jUrtewHVrWnY2sHRpy/czmaS/mzYxsyA8jw3YQkVERERE5I5WY53MZqm7IHA5oLGz/3/5cnXBlFxr2okTwJIlTILhRQyoiIiIiIjc0XKsU2am1CoUF+e8PD5eXWtRa5kD3WESDMWYlIKIiIiIyB2txzplZgJjx3onSYS71jRPaJEEI0AxoCIiIiIyAmZk86/UVKnFyN1Yp9RU9e9hNgMjRqh/vZ03giG1gWEQYpc/IiIiIr1jRjb/02qskxbaEgyZTIDF0rbAMMgwoCIiIiLSMy1SdZM63h7rpBV7a1rzwK85vQeGBsG06U0wbToRERHpilapuqltjND90h6IA85dFO1B00MPSXNTNT22LBYpmNJLYOhnnsYGDKiaYEBFREREulJUJHXvc6ew0DtjbyiwyM1D1TRoMkJg6EeexgZMSkFERESkV1qm6qbA5y5zoLeSYAQ5BlREREREeqV1qm4KfAyaNMekFERERER65S65ADOyEfkdAyoiIiIivTJSqm6iIMWAioiIiEjPjJKqmyhIcQwVERERkd65Sy5ARH7DgIqIiIjIV9qSpprJBYh0iQEVERERkS/IzQkUHy+NkWK3PSLD4hgqIiIiIq1ZrUBWlnMwBQAVFdJyq9U/9SKiNmNARURERKQlm01qmRKi5XP2ZXPnSuWIyHAYUBERERFpadeuli1TTQkBHD8ulSMiw2FARURERKSlykrvliMiXWFSCiIiIiItde/u3XJEzbUleyS1GVuoiIiIiLSUmipl8zOZ5J83mQCLRSpHpJTVCiQkACNHAhMnSn8TEpjoxIcYUBERERFpyWyWUqMDLYMq+/+XL2eLAiC1tBQVAWvXSn+ZqKN1zB6pCwyoiIiIiLSWmQls2gTExTkvj4+XlnMeKra0KMXskbphEkJuLwSn2tpaREZGoqamBhEREf6uDhEREQUajnWRZ29paX5Zam/BY9DZUlGRFHS6U1gIjBihdW0CkqexAZNSEBEREfmK2cyL2+bctbSYTFJLy9ixDD6bYvZI3WCXPyIiIiLyH87TpQ6zR+qGqoBqxYoVSEhIQHh4OJKTk7Fnz55Wy2/cuBF9+vRBeHg4+vfvj23btjmeu3TpEubNm4f+/fujQ4cO6NGjByZPnoyTJ086rSMhIQEmk8np8fTTTzuV+fLLL5Gamorw8HBYLBY888wzaj4eEREREfkKW1rUYfZI3VAcUK1fvx45OTnIzc1FSUkJBgwYgPT0dJw6dUq2/O7du5GdnY1p06ahtLQUGRkZyMjIwIEDBwAAFy5cQElJCRYuXIiSkhJYrVYcPnwYY8aMabGuJ554ApWVlY7H7NmzHc/V1tZi1KhR6NWrF/bt24clS5Zg8eLFWL16tdKPSERERBQ49J45jy0t6jB7pG4oTkqRnJyMwYMH44UXXgAANDY2wmKxYPbs2Zg/f36L8hMmTMD58+exdetWx7IhQ4YgMTERq1atkn2Pzz//HElJSTh69Ch69uwJQGqhmjt3LubOnSv7mpUrV+JPf/oTqqqqEBoaCgCYP38+tmzZgkOHDnn02ZiUgoiIiAKK1SqNT2rapS4+XroQ10uSB5tNyuZXUSE/jspkkupcVsbgQI7cPrZYpGBKL/vYoDyNDRS1UNXX12Pfvn1IS0u7vIKQEKSlpaG4uFj2NcXFxU7lASA9Pd1leQCoqamByWRCVFSU0/Knn34aXbp0wU033YQlS5agoaHB6X1uueUWRzBlf5/Dhw/jhx9+kH2furo61NbWOj2IiIiIAoJR5igKtJYWX7cIZmYC5eVSNr/8fOlvWRmDKR9SFFCdOXMGNpsNMTExTstjYmJQVVUl+5qqqipF5S9evIh58+YhOzvbKRL84x//iHXr1qGwsBAzZszAU089hUceecTt+9ifk5OXl4fIyEjHw2KxuPjkRERERAZitDmKAmWeLn/NpWXPHpmdLf01SvAZIHSVNv3SpUsYP348hBBYuXKl03M5OTmOf//85z9HaGgoZsyYgby8PISFhal6vwULFjitt7a2lkEVERERGZ+SzHl6SeOemSmlRjfqPF2u5tKytwgaKTAkRRQFVNHR0TCbzaiurnZaXl1djdjYWNnXxMbGelTeHkwdPXoUH374odsxTMnJyWhoaEB5eTmuv/56l+9jr4OcsLAw1cEYERERkW4ZNXOeUefp4lxaQU1Rl7/Q0FAMHDgQO3fudCxrbGzEzp07kZKSIvualJQUp/IAUFBQ4FTeHkx9++232LFjB7p06eK2Lvv370dISAi6devmeJ+PPvoIly5dcnqf66+/Hp06dVLyMYmIiIiMjZnzfItzaQU1xWnTc3Jy8PLLL+P111/HN998gz/84Q84f/48pk6dCgCYPHkyFixY4Cg/Z84cbN++HcuWLcOhQ4ewePFi7N27F7NmzQIgBVNZWVnYu3cv3nzzTdhsNlRVVaGqqgr19fUApIQTy5cvxxdffIHvvvsOb775Jh544AH87ne/cwRLEydORGhoKKZNm4aDBw9i/fr1eO6555y69BEREREFBc5R5FtGbREkr1A8hmrChAk4ffo0Fi1ahKqqKiQmJmL79u2OBBDHjh1DSMjlOG3o0KHIz8/HY489hkcffRTXXnsttmzZgn79+gEAKioq8M477wAAEhMTnd6rsLAQI0aMQFhYGNatW4fFixejrq4OV199NR544AGnYCkyMhIffPABZs6ciYEDByI6OhqLFi3C9OnTFW8UIiIiIkOzZ87LypKCp6Zd0YyYOU/v2CIY1BTPQxXIOA8VERERBRTOUeQbnEsrIHkaG+gqyx8REREReZHRM+cZBVsEgxoDKiIiIqJAZtTMeUZjn0ureYtgfDxbBAMcAyoiIiIiIm8IpBZBmy0wPocPMKAiIiIiIvKWQGgRlBt7Fx8vdWtkS1sLitOmExEREREFBJsNKCoC1q6V/tps/q6R/1mt0liw5vNqVVRIy61W/9RLxxhQEREREVHwsVqlzHwjRwITJ0p/ExKCO2Cw2aSWKblMhfZlc+cy8GyGARUREREReY0hGn3YCiNv166W26QpIYDjx6Vy5MCAioiIiIi8whCNPmyFca2y0rvlggQDKiIiIiJqM8M0+rAVxrXu3b1bLkgwoCIiIiIiZZr167PV24zT6MNWGNdSU6VsfvbJiJszmQCLRSpHDgyoiIiIyPgMMXAnQMj069sVd6dxGn3YCuOa2SylRgdaBlX2/y9fzvmommFARURERMZmiIE7AcJFv77KM+09erkuGn3YCtO6zExg0yYgLs55eXy8tJzzULXAgIqIiIiMyzADdwJAK8kcuuOkR6vQRaMPW2Hcy8wEysuBwkIgP1/6W1bGYMoFkxByvV2DU21tLSIjI1FTU4OIiAh/V4eIiIhaY7NJLVGu+pqZTNJd9bKy4L449paiIqn1T4YNIUhAOSoQByFzv95pV8Am9f2rrJQirNTUtu8fm4p1Wq1SgNj0+LFYpGCKgQPB89iALVRERERkTMzW5lut9NczoxHPYQ4AwATne/VOjT5va9A9U22XT7bCkJcwoCIiIiJjYrY233LTXy8Tb2ETshDXtc5puWPoDTTontnWLp9mMzBiBJCdLf1lSyapwC5/TbDLHxERkYG00gXNSWGhdLFMbWPvYllRIZ8f/ad+fbYjZdi12+zc+w4adM9kl0/SmKexQTsf1omIiIjIe+zZ2txc4LearU3N2JtAouTz25M5ZGVJ27bpNm/Sr88cam4ZvxYp6J7pafCrpMsnA2rSELv8ERERkTG1NVtbsKdbV/P51abU1qJ7Jrt8kk4woCIiIiLjUnuBH+zp1tvy+dUkc9BiMl1O0Es6wTFUTXAMFRERkUEp6boW7GNv/PH5PRx/pWoMlTfXSdQE06YTERFR8FCSrS3Y06374/NrMZmup+sEpAQma9dKf202z9+DyAMMqIiIiCi4BPvYG399frXdM9uyTiC4x8mRTzDLHxEREQWXYB9748/Pn5kJjB3r3cyKrtb59tvSeLDm3QHt48TUBnFEzXAMVRMcQ0VERBQEgn3sTTB8/mAfJ0dewTFURERERHK0GM9jJMHw+YN9nBz5FAMqIiIiCj5ajOcxkkD//ME+To58imOoiIiIAoCSrOH0k8xM2G4bi10vfoXKf19A995XIvX+/jCHBsmG02I8k14E+zg58imOoWqCY6iIiMiIrFZgzhznHk7x8VKvLqM3NGiJ2y2ABcM4MdIcx1AREREFAatVSljWfLiIPZEZs0PL43bzgM1m3PmbgmGcGOkGAyoiIiKDstmkFha5G/D2ZXPnGus62Be43TxgtRp//qZAHydGusEuf02wyx8RERlJUZF0netOYSEwYoTWtTEOzbeb0Qe02Zvvml8i2lt2jBaMGH1/kN94GhswKQUREZFBMZGZOppuN6MPzHLXfGcySc13Y8caJygxm3lHgTTFLn9EREQGxURm6mi23QJhYBbnbyJSTFVAtWLFCiQkJCA8PBzJycnYs2dPq+U3btyIPn36IDw8HP3798e2bdscz126dAnz5s1D//790aFDB/To0QOTJ0/GyZMnHWXKy8sxbdo0XH311bjiiivQu3dv5Obmor6+3qmMyWRq8fj000/VfEQiIiLdS02VGj+aj7m3M5kAi0UqR5dpst0CZWAWmz2JFFMcUK1fvx45OTnIzc1FSUkJBgwYgPT0dJw6dUq2/O7du5GdnY1p06ahtLQUGRkZyMjIwIEDBwAAFy5cQElJCRYuXIiSkhJYrVYcPnwYY8aMcazj0KFDaGxsxEsvvYSDBw/i2WefxapVq/Doo4+2eL8dO3agsrLS8Rg4cKDSj0hERGQITGSmjibbLVBadtjsSaSY4qQUycnJGDx4MF544QUAQGNjIywWC2bPno358+e3KD9hwgScP38eW7dudSwbMmQIEhMTsWrVKtn3+Pzzz5GUlISjR4+iZ8+esmWWLFmClStX4rvvvgMgtVBdffXVKC0tRWJiopKP5MCkFEREZERyw3YsFikoMMKwHX/x6nZbu1bKhudOfj6Qna1w5T7E+ZuIHDSZh6q+vh779u1DWlra5RWEhCAtLQ3FxcWyrykuLnYqDwDp6ekuywNATU0NTCYToqKiWi3TuXPnFsvHjBmDbt26YdiwYXjnnXfcfCIiIiLjy8wEysulrHT5+dLfsrIADKa8PC+SV7dboLTssNmTSDFFWf7OnDkDm82GmJgYp+UxMTE4dOiQ7Guqqqpky1dVVcmWv3jxIubNm4fs7GyXkeCRI0fw/PPPY+nSpY5lV111FZYtW4abb74ZISEh2Lx5MzIyMrBlyxan7oNN1dXVoa6uzvH/2tpa2XJERER6F/CJzDTKnue17WYfmOWuZccIA9rs8zfJbW82exK1oKu06ZcuXcL48eMhhMDKlStly1RUVODWW2/FHXfcgfvuu8+xPDo6Gjk5OY7/Dx48GCdPnsSSJUtcBlR5eXl4/PHHvfshiIiIyLtczYtkz56n1bxISuYvsrfsZGVJwVPTuipp2dHLnEmZmVJqdD3UhUjnFHX5i46OhtlsRnV1tdPy6upqxMbGyr4mNjbWo/L2YOro0aMoKCiQbZ06efIkRo4ciaFDh2L16tVu65ucnIwjR464fH7BggWoqalxPI4fP+52nURERORD/sqeZ7VKY4lGjpTGRo0cKf2/tdTn9paduDjn5fHxngV9at5TS/bmu+xs6S+DKSJZigKq0NBQDBw4EDt37nQsa2xsxM6dO5GSkiL7mpSUFKfyAFBQUOBU3h5Mffvtt9ixYwe6dOnSYj0VFRUYMWIEBg4ciDVr1iAkxH3V9+/fj+6t9FUOCwtDRESE04OIiIh0xB/Z89oyn5TagVmBMIcVUZBS3OUvJycHU6ZMwaBBg5CUlITly5fj/PnzmDp1KgBg8uTJiIuLQ15eHgBgzpw5GD58OJYtW4bRo0dj3bp12Lt3r6OF6dKlS8jKykJJSQm2bt0Km83mGF/VuXNnhIaGOoKpXr16YenSpTh9+rSjPvaWrtdffx2hoaG46aabAABWqxWvvvoq/v73v7dh8xAREZFf+XpeJHctYiaT1CI2dmzr3f+UDMzyxnsSkd8oDqgmTJiA06dPY9GiRaiqqkJiYiK2b9/uSDxx7Ngxp9ajoUOHIj8/H4899hgeffRRXHvttdiyZQv69esHQGp5smfja57uvLCwECNGjEBBQQGOHDmCI0eOID4+3qlM06zvTz75JI4ePYp27dqhT58+WL9+PbKyspR+RCIiItILX2fPU9Ii5q0sIP54TyLyGsXzUAUyzkNFRESkM76eF8kf80kFyhxWRAFGk3moiIiIiHzK1/Mi+WM+qUCZw4ooSDGgIiIiIn1ra/Y8JezzSTUP3uxMJsBi8e58Uv54TyLyGgZUREREpH9qs+cp5esWMX+9JxF5DQMqIiIiMgZfzYvkyxYxf74nEXkFk1I0waQURERE5GCzSZn1Kiul8Uupqdq3EvnjPYlIlqexgeK06URERBQkgv3iXul8UkZ9TyJqEwZURERE1JLVKk0223R+pPh4aawPu58RETlwDBURERE5s1qBrKyWk81WVEjLrVb/1IuISIcYUBEREdFlNpvUMiU3xNq+bO5cqRwRETGgIiIioiZ27WrZMtWUEMDx41I5Cmg2G1BUBKxdK/1lDE0kj2OoiIiI6LLKSu+WaybY81wYBYfQEXmOLVRERER0Wffu3i3XhNUKJCQAI0cCEydKfxMSOCRLbziEjkgZzkPVBOehIiKioGezSVFORYX8OCqTSWqqKCtT1LRkv0hvvkqTSfrLuWv1wb77XfX6VLn7iQzJ09iALVRERER0mdks9esCLkc7dvb/L1+u6GqaeS6Mg0PoiJRjQEVERETOMjOlJqO4OOfl8fGqmpJ4kW4cGg+hIwpITEpBRERELWVmAmPHeiWDBC/SjUPDIXREAYsBFREREckzm4ERI9q8Gl6kG0dqqtQQ6W4IXWqq7+tGpFcMqIhIE0yNHBi4H8kbvHWRzuNRe/YhdFlZ0n5pur9UDqEjCngcQ0VEXsfUyK0zymSZ3I/kLd7Ic9Gm49EoXzqd8PIQOqKAx7TpTTBtOlHbMTVy64wyWSb3I2lB7vi3WKRgqrXjqU3Ho1G+dDrEFkEKdp7GBgyommBARdQ2nL+kdUYJUrgfSUtKL9LbdDwa5UtHRLrEgEoFBlREbVNUJHXDcaew0Cvj3A3FSEEK9yPpierj0UhfOiLSJU7sS0Q+x9TIrhlpHh7uRz9yN9YnCMcCqT4ejfSlIyJDY5Y/IvIapkZ2zUhBCvejn7gb62OgsUDeHHuj+nhs8mWyIQS7kIpKdEd3VCIVu2BGY4tyRERqsIWKiLzGnhq5eRYvO5NJGoAejPOXGClI4X70A/tYn+YtKhUV0vJHHmn9eR2lXvR2dkjVx+NPXyYrbkcCyjESRZiItRiJIiSgHFbc7lSOiEgtBlRE5DXeSI0cqIwUpHA/+pjNJrU8yQ1pFkJ6/O1vrp8HgLlzddH9z11cqCaoUn08pqbC2uVeZGETTsA5/3cF4pCFTbB2uU8fXzoiMjQGVETkVZy/RJ7RghTuRx9yN9YHaD1Y0slYIHdxIaA+7lNzPNpgxhw8B+mtnS93xE//n4vlsEEnXzoiMixm+WuCWf6IvIfzl8hTOw+Pv3A/+sDatVLfuLbKzweys9u+HpV8kR1SyfHIbJVE1FaexgZMSkFEmjCbeZEiJzMTGDvWOEEK96MPeGsMjwZjgZQEML5IvKLkeNS8PrzbQEQ/YUBFRORjDFLIiX2AXUWFfH85QDpoGhvln7fPp+TlsUBKkwrqLfGKpvUxUMZFItIex1ARERH5k7sBdiYTkJPj+nnA6wPw1CSX0FviFc3qo0XmDY0F4fRlRD7FgIqIiMjf3GVdeOYZn2UJUZtcQm+JVzSpj5aZNzTi7TT2RNQSk1I0waQURET+FfTDUtxtAB9soLYmc9Bb4hWv1sdgmS7sjWnNr/TsASUzdhK1jkkpiIjIUDgsBe4H2GkxAK9ZkFZZcQs86cDiKpmD3hKveLU+vsi84SXuGtNMJqkxbezYILtpQaQBBlREROR3ru6k24el8E66RmSi2O7RWQA2un1pa8kc9JZ4xWv10VvmjVa4m96s6fRletpXREakagzVihUrkJCQgPDwcCQnJ2PPnj2tlt+4cSP69OmD8PBw9O/fH9u2bXM8d+nSJcybNw/9+/dHhw4d0KNHD0yePBknT550WsfZs2dx1113ISIiAlFRUZg2bRr+85//OJX58ssvkZqaivDwcFgsFjzzzDNqPh4REfmQAYelGI5sUgIXyRVSz7yFeByHCfIjAnydXEJX9JZ5oxUGakwjMjzFAdX69euRk5OD3NxclJSUYMCAAUhPT8epU6dky+/evRvZ2dmYNm0aSktLkZGRgYyMDBw4cAAAcOHCBZSUlGDhwoUoKSmB1WrF4cOHMWbMGKf13HXXXTh48CAKCgqwdetWfPTRR5g+fbrj+draWowaNQq9evXCvn37sGTJEixevBirV69W+hGJiMiHlNxJJ+XkkxIIWKe/JxvFmmHDc5gLQMBkcn7eH8kldEVvmTdaYaDGNCLjEwolJSWJmTNnOv5vs9lEjx49RF5enmz58ePHi9GjRzstS05OFjNmzHD5Hnv27BEAxNGjR4UQQnz99dcCgPj8888dZd577z1hMplERUWFEEKIF198UXTq1EnU1dU5ysybN09cf/31Hn+2mpoaAUDU1NR4/BoiImqb/HwhpCv71h/5+f6uqfFs3iyEydRyW5rQKEywic243eUG34zbRXzX/zottlikdQa9zZuFiI8Xet44DQ1SFeX2PyAtt1ikckQkz9PYQFELVX19Pfbt24e0tDTHspCQEKSlpaG4uFj2NcXFxU7lASA9Pd1leQCoqamByWRCVFSUYx1RUVEYNGiQo0xaWhpCQkLw2WefOcrccsstCA0NdXqfw4cP44cffpB9n7q6OtTW1jo9iIjIt3xxJz0Y5+FptSslpNaUuVgOm4vOKpl4C+XPbkFhIZCfLyWuKyvT71g2n+7jzEygvBx63jgGakwjMjxFAdWZM2dgs9kQExPjtDwmJgZVVVWyr6mqqlJU/uLFi5g3bx6ys7Md6QmrqqrQrVs3p3Lt2rVD586dHetx9T725+Tk5eUhMjLS8bBYLLLliIhIO1oPSwnWeXjcdqVECI6jJ3bB9YY1x8VixAggO1tKXKDXi2+/7GN7pgsdbxx305vpKP4jMjRdTex76dIljB8/HkIIrFy5UvP3W7BgAWpqahyP48ePa/6eRERaMWorjJZ30l3kXXBkD/RLUOWjHeVxUgLINP21NYr14cGoy32sI35pTDPqjxGRSooCqujoaJjNZlRXVzstr66uRmxsrOxrYmNjPSpvD6aOHj2KgoICp8mzYmNjWyS9aGhowNmzZx3rcfU+9ufkhIWFISIiwulBRGRERm+F0eJOui6zB/pwR3nclRLNenF4I4r10WfU5T7WIZ82phn9x4hIBUUBVWhoKAYOHIidO3c6ljU2NmLnzp1ISUmRfU1KSopTeQAoKChwKm8Ppr799lvs2LEDXbp0abGOH3/8Efv27XMs+/DDD9HY2Ijk5GRHmY8++giXLl1yep/rr78enTp1UvIxKQjxZhoZWaDcoff2nXStswcq/t3wYEd587fIo66UXS4gNe475yfaEsX6+GBkhkidCZQfIyKllGa7WLdunQgLCxOvvfaa+Prrr8X06dNFVFSUqKqqEkIIMWnSJDF//nxH+U8++US0a9dOLF26VHzzzTciNzdXtG/fXnz11VdCCCHq6+vFmDFjRHx8vNi/f7+orKx0PJpm7Lv11lvFTTfdJD777DPx8ccfi2uvvVZkZ2c7nv/xxx9FTEyMmDRpkjhw4IBYt26duPLKK8VLL73k8Wdjlr/gJJesKT5eV8maiFyyZ/JylRkvmDN5aZk9UPHvhgc7anOX+0R8fKNXf4vsWf6aZ3qzL9u8+ae6FRZKG6KwUP3B4oeDkRkidUTB/vfWIUekNU9jA8UBlRBCPP/886Jnz54iNDRUJCUliU8//dTx3PDhw8WUKVOcym/YsEFcd911IjQ0VPTt21e8++67jufKysoEANlHYWGho9z3338vsrOzxVVXXSUiIiLE1KlTxblz55ze54svvhDDhg0TYWFhIi4uTjz99NOKPhcDquDjMqVw04sNIh0rLPTsgrLJz2nQ0GrbqPrdcFOZzbhdmGATQKPn61RQX59k+PbDwcjjX0c83BmbH/+KNzHJMDyNDUxCyPU8Dk61tbWIjIxETU0Nx1MFAZtN6tbtqruIyST1fCkr02XyJiIAUtewiRPdl8vPl8ZPBBP7d7yiArJjbOzf8SNHgN27pSQO3btLXeVcfedV/2402VE2hGAXUlGJ7uiOSgzFJ+iN73ACcZDrie+N3yKbTer25slnVM0PB6On+zhQfsd9sh/V8mD/W3E7srDZkbbfzt4tlZkHSW88jQ3a+bBORLqipO/9iBE+qxaRIr6Yw8kwml1tmlNT8dxzZmRlSRdsTS+47Rdwd94J9O7t/FsQHy9lHczMbHkBa7Op/N34aQdYcTvm4DmcwOVpOqJxCmfgPDWIR+tUwJ6UQFN+OBjtGSJb28eBMteS1Sol4HB1rPqdm/1qQwjm4DnI3cUXQtpfc+cCY8cGxv6i4KKrtOlEvuRxSmEPyxH5g9ZzOBmGi8ximbC6zB740EPA0qWux88/8kjLVY4f71l1WvxupKbC2uVeZGHTTy1Rl51BtLp16o2fDsZgmGvJELke3Oz/XbjlpxsJ8s83vXFAZDQMqCho8c4+BQIt53AyDDdXm5mwtsgeeOSI1ENJrpuYfWTHkiUtV3n2rGdVav67YYO5yd355qdez07Fuv8t8uPB6Je5lnzE09Tw9fV+zlbrZv/Lzncmw9c3Dpjll7yBY6ia4Biq4BJsfe8psMl1B7JYpOvXQLiodEnloKaiIqnFydtc/W605f0M91sUtAejNjw9drp2BU6fvvx/v3UHdLH/i+79J0bm3uL25YWFvutmr/tulOR3nsYGDKiaYEAVfOw3tgH5vveB0l2EgoOuB6xrxdOrzWZXaZ7mT1Citd8Nte9n2N+ioDwYtWHIY0dm/9tg1tVNTPv5v3ldDPudI00wKQWRB+x97+XuUPFmKhmNTxIPeIFXr7VVDob0Rve5zp2duwC29rvh6fvJtTIY8rfIKAejAag9Vv2a6EFm/5uhnwQi7rpRMkEGKcUWqibYQhW8eDOVyDe83sVGZQuVuy6/ntixQ/qdUJJu3Zsp3Ck4eONY9WU3Onf00CNU5c8GBSG2UBEpEOw3UxlQki+46mJjz1SmqouNPbOYu0ilWWa51tJtu2Nf5YgRnn9PPE3vHRoa3L9F1FJbjlU7PWWIzMyUWn68fc5Rch5jll/yNmb5IwpyLrJN6yMNLwUMTzOVKc6w1YbMcq7SbVsswMMPSy/3ZrK6gEvvzfRoPuPq2Ona1bPX6y1DpP0mZna2shsTrig9jzHLL3kbu/w1wS5/FGw4KJe0Ijchblqa+9ep7mLThn5Eru5sa9U1KSBahJkezS+aHztDh0oTU+sl0YM/qDmPGTXLb0D8dhgMs/ypwICKgonKbNNEbsldazdP4OBKfr5011oVDa42eAEjg3didCWYs9W25TxmtO3Gexj+wYBKBQZUFEw4KJfsvBk0uLrW9hSPN53jnRhd0kOiB39o63nMKNuN9zD8h0kpiKhVHJRLgHfverY2TsodF7kjyFu8FTXv2uU6mAKknX/8uFSOkbHPaJXoQe/aeh5zt9300ELNFO/GwICKKEhxUC55O+ueu2ttV3w9B03Q8WbUzDsxmlN7Ea82W60egga1vHEec7Xd9NLFjvcwjIFZ/oiClD3bdPMsZnYmk9T1gS0Grhk5yZkWWfc8vYbu3Nn5/4bNcmcE9qi5+RWZPWpWms6Td2I05eusq0bP8qrVeczbX5u24D0MY2BARRSk2pBtmmD8CxEldz095ek19IYN0piG/Hzpb1mZjoMpRs3OeCdGM76+iNdT0KCWFucxzaZ4UIn3MIyBARVREAu4eXF8JBAuRLS46+nptfaIEd6dg0YzjJpbCrI7Mb6Kp319Ea+3oKEtvH0e0+Jr0xa8h2EMDKiIglxmJlBebqAWAz8LlAsRLe56BtS1NqNm14LkTowv42lfX8TrLWhoK2+ex/TWxS6gflcDGAMqIvL6rPWBLFAuRLS66xkQ19qMmt0L8Dsxvo6nfX0Rr7egwRu8dR7TYxe7gPhdDXDM8kdEpECgXIjY73pmZUnBk9zElmrveho+hXOgpNWyR80VFfLBYVtz1atNK6dz/khT7euLeD0GDXqh9ddGLcP/rgY4tlARESkQSBciWt711F2rp5LBMIEWNQPsK6SAP1qhfT1OhuNyXNPz10Z3v6vkwICKiEiBQLsQCfCeWxKlg2EYNQc1f8TTvr6I13PQoAf82pBSJiHUzGkfmGpraxEZGYmamhpERET4uzpEpFP28RWAfFc5nnB1xNXsxa3tLJtNCrjc9fkpKzPOFaeeZm91Vxc/17WoSIq53Sks9H6PR7nJZC0WKbjR4jfF1+9nNHr62pB/eBobMKBqggEVEXmKFyIGYA+MXPXfai0wYtSsDbkvTny81FySmen+eR/wdzzt64t4Bg1ErjGgUoEBFREpwQsRnWtrUwOjZu9y11r40EPA0qXKWhM1wniaiAAGVKowoCIiCiBr10pjptzJz5dGecth1Owd7loLAWm7ukoW4oduloynW8evBgUDT2MDpk0n0hmepIi8xBvJJQI0NbjPuUudB7SeedEPqeqZpto1HfTMJNIVBlREOsKTlJ8wig1Mep1QJhj5ekZaL2E83ZKrnpv2SY/ZHZKCEdOmE+mE/STV/Cau/STlKsMztZHSlNpkHMwNrR++npGWNOFu0mNAmvS4tcZGokDEgIpIB4x6klIyV6ouMYoNfJxQRh/cTeAGSIFtoEzwFqD8MekxkREwoCLSASOepAzfsGPUKJaU88PsxVrdbDDsTQx3rYUmE5CT4/p5gK2JOuCPSY+JjIABFZEOGO0kFRANO02iWBtCUIThWIs7UYThsCFEn1EsqWcfDJOdLf3V8MJcq5sNhr+J4a618Jln2Jqoc97I80IUiJg2vQmmTSd/aet0OXa+yK3QlrlSdeWnlNpW3I45eA4nYHE8FY/jeA5zkIm3Wk+pTdSMu6mW1MYFWq3XL9z8UNnqbdj14leo/PcFdO99JVLv7w9zqJ5/THTCBycAf096rJYWm0ZvuYz0Vp9A4XFsIMihpqZGABA1NTX+rgoFmYYGIeLjhTCZhJBOU84Pk0kIi0Uq58rmzdI6mr4uPl5a7k2FhfJ1bP4oLPTu+3pdYaHYjNuFCTYB2Jy3N2zCBJvYjNt190EaGqQq5edLf1s7Jvy70uBj/x67+k548j1u03rrjL8fffU75g26+tr4cMNt3iwdc83PV/ZlettXWmwavR2nWtVHV8e4n3gaGzCgaoIBFflTW05S9tfKXWh5+wSXn+9ZQJWf77331EJDXYOIN1e0CKaaBlUW8wnpIlUnNDlp6u3KwEiaXW0U7mjQ5GaDxzcxorMMvR99+TvWVrr62vhhw8l9fotFX/tICG02jd6OU63qo6tj3I80DaheeOEF0atXLxEWFiaSkpLEZ5991mr5DRs2iOuvv16EhYWJfv36iXfffdfp+c2bN4tf/epXonPnzgKAKC0tdXq+rKxMAJB9bNiw4fKHkXl+7dq1Hn8uBlTkb2pOUlrdFXfFny1U3rxbZrSWNk1Omnq7MjASmS9rfueZmtxs8PgmBu407H709e9YW+jqa+PHDaf31gstNo3ejlOt6qOrY9zPNAuo1q1bJ0JDQ8Wrr74qDh48KO677z4RFRUlqqurZct/8sknwmw2i2eeeUZ8/fXX4rHHHhPt27cXX331laPMP/7xD/H444+Ll19+WTagamhoEJWVlU6Pxx9/XFx11VXi3Llzlz8MINasWeNU7r///a/Hn40BFelBaycpued8HRh4o3uiGt6+W2akljZNTpp6uzIwEhdXG4UYocl30ePvOIYbdj8a5QaHN742Xg1EjLLh/ECLTaO3za1FfXhqcKZZQJWUlCRmzpzp+L/NZhM9evQQeXl5suXHjx8vRo8e7bQsOTlZzJgxo0VZe0tU84BKTmJiorjnnnuclgEQb731lvsP4QIDKtIzVwHF3Lm+Dwx83Ydei7tlejsxtkaTuhppA+hJK1cbDQgR8Tj207g8712IuL2JAZuw4KhoQIhP96M3AwOj3ODw9GuzY4f8tvF6NyqjbDg/0GLT6G1ze6M+zb/HO3bw1NCUp7GBorTp9fX12LdvH9LS0hzLQkJCkJaWhuLiYtnXFBcXO5UHgPT0dJflPbFv3z7s378f06ZNa/HczJkzER0djaSkJLz66qsQQrhcT11dHWpra50eRHrUWpry5cs9W4c309j6cq5UraaLcjfPqJ7mEdUkrb7RcvXrRSuTxpnRiOcwBwBggvMB25aplFqdwumn91mOuTCj0fVKvLwfvZ3C3SjpuD3djOPHt9w2jzyiwXQTRtlwfqDFptHb5m5rfeS+x+PHe7ZOnhqcKQqozpw5A5vNhpiYGKflMTExqKqqkn1NVVWVovKeeOWVV3DDDTdg6NChTsufeOIJbNiwAQUFBRg3bhzuv/9+PP/88y7Xk5eXh8jISMfDYrG4LEvyDDvJpIF4ElCYzb4PDHw1V6pWkx67m2cU0M88opqcxPV2ZWAUbq4iMvEWNiELcZ0vOC1v680GlzcxutZhE7KkFP+t8eJ+1GIeOqPc4PB0M5496/z/EyeAJUu8f2PIMBvOD7TYNHrb3G2pj6vvcfNj1xWeGppR0uxVUVEhAIjdu3c7LX/44YdFUlKS7Gvat28v8pu1Na5YsUJ069atRVlPuvxduHBBREZGiqVLl7qt78KFC0V8fLzL5y9evChqamocj+PHj3vUrEcSZoDxDU+7mNi7FDX/v9EHkGrdxcII2ao0Gbfmr8FwRufhF7Lh/R2i8NlSkT/rE1H4bKnXskW26GZX59v9qOX4CiOk43b3tWnrQ1U3KiNsOD/RYtPobXOrqY+777G764xgOjVoMoaqrq5OmM3mFuOUJk+eLMaMGSP7GovFIp599lmnZYsWLRI///nPW5T1JKD6xz/+Idq3by9OnTrltr5bt24VAMTFixfdlhWCY6iUYAYY3/E0oJg7V/+BgRq+GOqj92xVQmh0EtfblYEReBKIduni27tNPtyPWn8fjXCDw9Xm9sZD9dgbI2w4P9Fi0+htcyutj5IbtcF+atA0KcWsWbMc/7fZbCIuLq7VpBS33Xab07KUlBTVSSmGDx8uxo0b51Fd//znP4tOnTp5VFYIBlSeYgYY31JyAWOEwEApNqRcpslJXG9XBkbQWgDjrysRH+1HXwzKN8LvmNzm7ty57QFVmwb6G2HD+YkWm0Zvm1tJfTz9Hjc/poPx1OBpbGASQgglXQTXr1+PKVOm4KWXXkJSUhKWL1+ODRs24NChQ4iJicHkyZMRFxeHvLw8AMDu3bsxfPhwPP300xg9ejTWrVuHp556CiUlJejXrx8A4OzZszh27BhOnjzpKHP99dcjNjYWsbGxjvc+cuQIrrvuOmzbtg233nqrU73+9a9/obq6GkOGDEF4eDgKCgrw0EMP4aGHHsLjjz/u0Werra1FZGQkampqEBERoWSzBJWiImngojuFhcCIEVrXJvDZbNKg0YoK6SetOZNJ6kNdVqaP8T5asPf1Bpy3gb3fuLcTYeiZzSaNF6uslPqwp6Z6Yb9rstIAZ7VKgxubDkCIjwf++1/g++/lX6P1l9UH+5G//5c139w2G9AsB5fHguF3nPTD0+/xjh3S8RjMpwaPYwM10drzzz8vevbsKUJDQ0VSUpL49NNPHc8NHz5cTJkyxan8hg0bxHXXXSdCQ0NF3759W0zsu2bNGgG0nJQ3NzfXqdyCBQuExWIRNputRZ3ee+89kZiYKK666irRoUMHMWDAALFq1SrZsq6whcozeksbGgzYM4sNKaRDAZJvWMmdbbYYu+bp+Kpg/h0nffDF91hvLXhqadZCFcjYQuUZ3qH0D7kb4haLlImOrTNEOrB2rZR72J38fCA7W/v6eMBVQ9tzz7n+XWGLsWvuts1DD0mHSTD/jpM+aPk9VvO7oleexgYMqJpgQOUZdkHzHwYURDpmsLtN9guq5r/jnlxQ8QaPa+62DX/HSS+0+B635XdFjxhQqcCAynO8Q0lE1IyB7jbZq+pqjjdPqsrAwDVuG/W47XzLm9vbG78resOASgUGVMrwDiVREODVjTIGudtksMY0ChKB1FVMLSP/5Abi74qnsUE7H9aJAkxmJjB2rHG/+ESaUnlW1NXJlFc3ymVmSkGT3HbT0d2mykrvliNqK1ddxSoqpOU6uRehKaP/5Abz7wpbqJpgCxUReYXKs6KuTqaB1hHe13QVGbcUiHeSybgCsauYUoHwkxuI6djZ5U8FBlRE1GYqz4q6Opnq+OpG53GKYRhouBcFgWAP8HX8k6uIJ78rnTsDV1yhkxuHHvA0NgjxYZ2IiDRls0kn5rVrpb82mx8qMGeO/JnEvmzu3BYVU/ky7eza5frMDkiVOn5cKudDViuQkCAwcqSUnXzkSOn/VqtPqxEQzGbpAga4HLTb2f+/fLm+L94ocARzVzFAtz+5irn7XRFCmve8+We1d+s08m85AyoiCgjSxTaaXWz7+Ada5VnRJydTJdGmp1ctFRU+i2CtViBrnMCJE85RZ8UJgaxxUlDl94DaYOzDveLinJfHxxujexEFju7dvVvOaAIpoHT1uxIXB3TpIv8av9w49DImpSAiw9PNYGaVZ0XNT6ZKB2d5etXywAPA6dOerbMNbDZgzvQLEAhH8/uAAiEwoRHTp9RjTlSYYbqR6AWTC5EepKZK31d3XVBTU31fN18ItIBS7nfFZgPS0ly/pumNQyN262QLFREZmq66y6k8K2p6MrVHm0r6WNivbpr32WiuaTDlbp1tsKvIhhPfXwlXpyyBEHz/n7CWrVcB0I3EF8xm6QImO1v6y2CKfM3TLqhAYLZCu/vJNZmkaWmMFFA2/105dcqz1xmhFU4OAyoiMjRd9T1vcla0IQRFGI61uBNFGA4bQlyeFTU7maqNNlu7umlN03XW13vtyqey6LCHJZ3rGgjdSIiChbsuqIAOunVrJBjGNAZaK1xzDKiIyNB01ff8p7OiVdyOBJRjJIowEWsxEkVIQDms4nbZs6JmJ9O2RJuurm66dm39Pe3rjI/32pVPd6jfeUYZzE1E0s9OebmUzS8/X/pbViY9p7Sh3Z/UjOcM9DGNgdgK1xQDKiLSFaUnIr3d9bIiE1nYhBNwPitWIA5Z2AQr5M+KmpxMm0SRsi1mMuVaVKr51c2zz3r23l7sDpg6wox4HIcJjYpfa2fUbiREwaZ5VzFAR926PdCWBEmuAkqjB1NA4LfCcR6qJjgPFZF/qZnYVk/z6XhjLhGvzrP00+QuVtyOOXgOJ2BxPBWP43gOc5CJt5RN7uLphDFy1O4Mmw3WmN8j6/uXAEhjpi5rhCf3BgN1/hqiQGekOap0NZ+gTsmd5y0WKZjS47bhxL4qMKAipTjJqPe05URkfy3g/Hpfn8R0d+JvEohIm+Vy4GFv7dnU5ffIrF7p+YHrLoL1hJoNYLXCOu5NzMHyZoHhMfwXV+IsukCgZV8So0yISUTy1q6VWnrcyc+XWrX8JVAm5/UFI107cWJfIo3pYt6jANHWTH166XvulfFcXpxMyQYz5uC5FsEUcLmVZy6WwwYFZzK1CSuaUtP/LjMTmZvvQnncMBRiBPKRjUKMQHn8LVj98BHAZArIbiREwU5v3bpd0VWCJJ0LxMyiDKiIVFCTiZpc88aJSA99z9t84vdylL5rF9ymGz/+/ZXKT/BqE1bYtbahWgsoMzNhPvodRhQuRnb+GIwoXAxz+b+R+cwQXQTUROR9RklmoKsESeRznNiXSCF3rSkmk9SaMnZsYNx18QVvnYjsd728SUnXhDZNTqnB7MSanuDlZm4cOhTo3Vv97JyeDKJzsZM5QS1RYLI3imdlST8hct269dAKbZSWNNIGW6iIFGKzvvfp9USktMFIdRYjjWYn1ny7Nu+3ERqqPo2TF5p9A7EbCRHpp1t3a4zSkkbaYEBFpBCb9b1Pjycitdf3qk78GkXpWm9X2d55ajaARgElEQUOPXTrbk2gpwWn1jGgIlJIr60pRqa3E5E3kmQoOvFrFKVruV1bbb1TugHY7EtEHtB7K7QRWtJIGxxDRaSQp+Nkhg6V7tpzPIdn7CciuSE0vp6fQsn1vasxW4rGc2kYpWuxXT0b7qVgA7DZl4gCBMdzBicGVEQKeTJA9s47pbH5SiaoJf2ciHx+fd+mbBbueXO7apKUhc2+RBRAtEiQRPrGLn9EKrTWrP/QQ8DSpUyprpYeunT4/PreB30evbVdNemdp8dBdERERB5iQEWkktwwkSNHpAH6HFtvbH65vjdI53tNWu/0NoiOiIhIAXb5I2qD5s36RUVtH3vTJkomTfIjvVfTb/Oe6KXPYys0a73T0yA6IiIiBRhQEXmRX8fWezIpqg4YpJr+u77Xeed7TYd7GSCgJCIi/d8Y9TWTEHKnxOBUW1uLyMhI1NTUICIiwt/VIQMqKpLSR7tTWOjla2ZXadfszSk66TJmkGo64UmjJft+BORb7/S4H4mIyDuMcmPUGzyNDRhQNcGAKrD54sLYZpPm4nF3976szIvvbX9TV30NNXlT5QxSTfKQ3AnVYmHvPCKiQGbEG6Nt4WlswKQUFBRanYTUi/wytt4gk6IapJrkIcWTFxMRkaG1ddL7QMaAigKe/W6K2jTmNpvUlW/tWumvux8KnydrM8ikqAapJimghxT3RETkG7wx6hqTUlBAa+skpGr7Cft0bL1BJkU1SDWJiIg05euxud56P94YdY0tVBTQ2nI3pa0tWz67e2+QSVENUk0iIiLN+GoIghbvxxujrjGgooAh1zVP7d0UQ/UT9nDglg1mRV0Xvc2wc7cq7fNJREQko603av39frwx6pqqgGrFihVISEhAeHg4kpOTsWfPnlbLb9y4EX369EF4eDj69++Pbdu2OT1vtVoxatQodOnSBSaTCfv372+xjhEjRsBkMjk9fv/73zuVOXbsGEaPHo0rr7wS3bp1w8MPP4yGhgY1H5E05u1rVFd3YL791rPXN7+bYrh+wm4GblmR6dM7YiqrqWlCA1XHnK9vJZJ/MGgmIo35+katFu9n2BujviAUWrdunQgNDRWvvvqqOHjwoLjvvvtEVFSUqK6uli3/ySefCLPZLJ555hnx9ddfi8cee0y0b99efPXVV44y//jHP8Tjjz8uXn75ZQFAlJaWtljP8OHDxX333ScqKysdj5qaGsfzDQ0Nol+/fiItLU2UlpaKbdu2iejoaLFgwQKPP1tNTY0A4LRe8r7Nm4WIjxdC+kpLj/h4abna9ZlMzusDLi/r0kX+eXsZi0WIhgbndebny5dv/sjPb/v28KqGBiEKC6WKFRYK0dDQ6vYxmdRvdy9XU1Oqjjk9bjjyPm//IBERySgs9Oy6orBQ/+8n97NpsQTmz6ansYHigCopKUnMnDnT8X+bzSZ69Ogh8vLyZMuPHz9ejB492mlZcnKymDFjRouyZWVlrQZUc+bMcVmvbdu2iZCQEFFVVeVYtnLlShERESHq6urcfCoJAyrtefsataGh5Ze6+XrtAVXz923tPX39w6cVT7aPXEDpV16OtlQdc4bccKQYg2Yi8hFf36jV+v18fWPUXzyNDRR1+auvr8e+ffuQlpbmWBYSEoK0tDQUFxfLvqa4uNipPACkp6e7LN+aN998E9HR0ejXrx8WLFiACxcuOL1P//79ERMT4/Q+tbW1OHjwoOL3Iu/TovnZk655338PLF6srJtZoPQTNlzXRS93sVN9zBluw5FihhooSURG5+uEDlq/H6fNcKYobfqZM2dgs9mcghYAiImJwaFDh2RfU1VVJVu+qqpKUUUnTpyIXr16oUePHvjyyy8xb948HD58GNafLrRcvY/9OTl1dXWoq6tz/L+2tlZRnYKFt9JtKrlGHTHCs3V6mnTi2mulSUg9/Rz2fsJZWVLw1PSay0j9hA2V4tTV9Ov20bMqBlmpPuYMteFIFS1+kIiIXLDfqK2okL+PYzJJz3vrRq2v3y/YGWYequnTpzv+3b9/f3Tv3h2//OUv8e9//xu9e/dWtc68vDw8/vjj3qpiQFI7DxPQMhCrqPDsPZVcoyq5A2O/m+IpewIFuc+/fLm2CRS8xTApTts6YZgLquMiw2w4Uo1BMxH5kK9v1AbKjWGjUNTlLzo6GmazGdXV1U7Lq6urERsbK/ua2NhYReU9lZycDAA4cuRIq+9jf07OggULUFNT43gcP368TXUKNG1JtynXc2vuXM/et1s3zxNuad01LzNTatkqLATy86W/ZWXGCKYAA3Vd1KiLneq4yDAbzqD0kFWPQTMR+ZivM936M7OuWno4PaiidHBWUlKSmDVrluP/NptNxMXFtZqU4rbbbnNalpKSojgpRXMff/yxACC++OILIcTlpBRNsw2+9NJLIiIiQly8eNGTj8akFE20ZUy+q3He7h72BBJKE27Z309J0olgYojto9HoWftxrDTLoxDCIBvOgPSSVa9NBwcRkXq+TuhglAQSejk9NKVZlr9169aJsLAw8dprr4mvv/5aTJ8+XURFRTmy602aNEnMnz/fUf6TTz4R7dq1E0uXLhXffPONyM3NbZE2/fvvvxelpaXi3XffFQDEunXrRGlpqaisrBRCCHHkyBHxxBNPiL1794qysjLx9ttvi2uuuUbccsstjnXY06aPGjVK7N+/X2zfvl107dqVadNVUpvlzl0g1vRapbX/K71+DaYUnmq0Zfv45IdYw7SKbYqLeGB5l96y6jFoJiLSBb2dHuw0C6iEEOL5558XPXv2FKGhoSIpKUl8+umnjueGDx8upkyZ4lR+w4YN4rrrrhOhoaGib9++4t1333V6fs2aNQJAi0dubq4QQohjx46JW265RXTu3FmEhYWJn/3sZ+Lhhx9u8eHKy8vFr3/9a3HFFVeI6Oho8eCDD4pLly55/LkYUF2mtsHA0+virl1b3oHo0qX1oMrdzWKj3IHxFzXbx2d3izRuLWhTXMQDyzv0moqeQTMRkV/p9fQghOexgUkIIfzR1VCPamtrERkZiZqaGkRERPi7On5VVCSNe3KnsNA50cPatdKYKXf++U+pT689YYXNBjTLru/R+5F2XCXdsw8r8nr/a/sbAs5v6qU39Fa2SlJJ7Y+KL/DgICLyGz2fHjyNDQyT5Y98S226TU/Hb8fFtQzEPMGEW76hUdK91mmcVlFplkfyMj1n1ePBQUTkN3o+PXhKUZY/Ch72dJtAy0RnraXbVJscjQm39MVv89oaPa0iucYvORERyQiE0wMDKnJJTbpNXwdipA2/3i3i9OuBiV9yIiKSEQinBwZU1Co1DQa+DMRIG165W+SPySQMO4FFEOCXnIiIZATC6YFJKZpgUgrvUjPO22ptOYTGYvHKEBpd0fsYeJtNmpjZ3Ri6sjIX9ZbbkfHx0i+mVjvSH+9JygXLl5yIiBTR4+nB09iAAVUTDKj0Qe/BRlsZ5bpfddI9n6cH9NN7knqB/iUnIiJV9HZ6YEClAgMq0prRrvsV3y2yN225ymjhtmlLBX+8JxEREQU8BlQqMKAiLRn1ul/R3SJ/TCah5wksfE1vt/aIiIgMjPNQEemMklTkerruVzRFjz/SA3q6rooKKfgK1GDDKH1JiYiIAgwDKiIfCYSJ69zyx2QSnq7rgQeA06cv/z+Qgg1XfUkrKqTleutLSkREFECYNp3IRwJh4jq3/DGZhLv3tGsaTAGXgw2r1Xt18QebTWqZkuu9bV82dy5TyBMREWmEARUB4PQ9vhAIE9e55Y/JJFp7z9b4M9jw5hdOSV9SIiIi8joGVASrVUqWMHIkMHGi9Dchwfg37vVG1xPXefMCX83Mzm3l6j27dm39dW0NNtRsN29/4YKiLykREZF+MctfE8GY5c9oabwDge4mrtMqmYEWGefcrbP58xUVwO9+5369+flAdrayuqjZblp84ZjlkIiISBNMm65CsAVUXknjzTTNquhmsxkpolYTwGgVbKjZblrlzbevt6JCfhyVXvPxExER6RwDKhWCLaBq87Um0zQbm5EmxlIb+GkRbKjdblq2JNm3D+D8OfUYGBMRERmEp7EBx1AFsTYNvbBfwDW/qAyUzGnBwCjJDNqSxU6LgWtqt5uWY538MW6NiIiIADCgCmqq03gzTXNgMEoyg7YGft4ONtRuN63z5mdmAuXlUgtXfr70t6yMwRQREZHGOLFvELOn8XbXG6pFGm8lF7gcBC9PD4OojDIxljcCv8xMYOxY72xztdtN9RdOAbOZ3zkiIiIfYwtVEFPdG8ooLRt6pZc89UaZGMtbgZ892MjOlv6qDWDVbjdd580nIiIitRhQBTlVvaGM0rKhR3oae2aUC3y9BX5t2W4c60RERBRwmOWvCaNn+WtLLzJFr2WaZnX8nVXP1U7W3cRYMvSYxa4t200PXT6JiIioVUybroKRAyqPMph78yJOjxe4eufPCVjdHSBqjw1fBgZ6DPwYGBEREQUsBlQqGDWg8miKHmgwZ5QeL3D1bO1aacyUO/n50jgfb9Fq8l5/zEPGAIaIiIh8hAGVCkYMqDzqRdb5Asq+j4AZtpZPAm1rTeIFruf80UKlVTdDrYI0co/fOSIiIp9gQKWCEQKq5tdSNhuQlub+dYUYgRH4v5ZPcLyT7/hj7JkWQZy/x4IFM3+0ChIREQUpT2MDZvkzELls2+PHe/baSrjIuOduUlTyHn9k1dMixX1bJ9oldfSUIZKIiIgcGFAZhKtrqbNnPXt9d7i5YOacUb7h67TZWqS45zxkvmezSS1Tci2b9mVz50rliIiIyKfa+bsC5F5r11LumCAQj+NIhZvWAs4Z5TuZmcDYsb4ZB2Ofw8ldN0MlczhxHjLfU9Iq6O0MkURERNQqBlQG4O5ayhVHL7LOT8J8VsAmQrALqahEd3RHJVKxC2aTUH5BTW1nNvvmwtfezTArSzog5FLcK+1mqEWQRq1jqyAREZFuscufAXh6jdS5s/P/pV5kJmSu/jWs4nYkoBwjUYSJWIuRKEICymEVt3t/3A7pi7e7GfpjLFiwY6sgERGRbjHLXxN6zfLnaaK2HTuka9jmvcisViBrnICAQNMY2oRGACZs2mzSJkGY3iaLDfZ0097+/G2ZhyzY94VS/sgQSUREFOSYNl0FvQZUbbmW8luGa7XpnbVKC81009pQExhxX6hjz0wDyHfd5NxfREREXsWASgW9BlSA+mspf8wlq3rSV60mi+UktPrBfdE2bWkVJCIiIkUYUKmg54AKUHcttXatNGeVO/n5QHa2FyqptklMq6Y0TkKrH9wX3sHukkRERD6h6cS+K1asQEJCAsLDw5GcnIw9e/a0Wn7jxo3o06cPwsPD0b9/f2zbts3peavVilGjRqFLly4wmUzYv3+/0/Nnz57F7Nmzcf311+OKK65Az5498cc//hE1NTVO5UwmU4vHunXr1HxEXcrMBMrLpdak/Hzpb1lZ6zemfT6WXe2kr1pNFstJaPWD+8I77Bkis7OlvwymiIiI/EpxQLV+/Xrk5OQgNzcXJSUlGDBgANLT03Hq1CnZ8rt370Z2djamTZuG0tJSZGRkICMjAwcOHHCUOX/+PIYNG4a//vWvsus4efIkTp48iaVLl+LAgQN47bXXsH37dkybNq1F2TVr1qCystLxyMjIUPoRdU3ptZQ9w3XzZGx2JpPUyuW1DNdq0ztrlRaa6ab1g/uCiIiIApDieaj+9re/4b777sPUqVMBAKtWrcK7776LV199FfPnz29R/rnnnsOtt96Khx9+GADw5JNPoqCgAC+88AJWrVoFAJg0aRIAoLy8XPY9+/Xrh82bNzv+37t3b/zlL3/B7373OzQ0NKBdu8sfIyoqCrGxsUo/VsDSYhqiVqltEvPwdbZu3bGrSEFvJ6ab1g/uCyIiIgpAilqo6uvrsW/fPqSlpV1eQUgI0tLSUFxcLPua4uJip/IAkJ6e7rK8p+x9GZsGUwAwc+ZMREdHIykpCa+++ipaGyJWV1eH2tpap0cg8vY0RK1S2yTmweusXe5Dwt3DMXKkNC5s5EhpSI7VqkF9yPu4L4iIiCgAKQqozpw5A5vNhpiYGKflMTExqKqqkn1NVVWVovKe1uPJJ5/E9OnTnZY/8cQT2LBhAwoKCjBu3Djcf//9eP75512uJy8vD5GRkY6HxWJRXSe9UzP+ShW1k766eZ1V3I6s71/CiRPOz1VUSK1vLoMqTkKrH9wXREREFIBUJaXwp9raWowePRo33ngjFi9e7PTcwoULcfPNN+Omm27CvHnz8Mgjj2DJkiUu17VgwQLU1NQ4HsePH9e49v7ls7HsapvEXLzOFtcTc7q8AYGWLRv2Bsi5c6XkZ16tD3kf9wUREREFGEVjqKKjo2E2m1FdXe20vLq62uW4pdjYWEXlW3Pu3Dnceuut6NixI9566y20b9++1fLJycl48sknUVdXh7CwsBbPh4WFyS4nL8jMBMaOVZ7eWeZ1u2ypOJHm+nVNk8O5nEtLbX3I+7gviIiIKIAoCqhCQ0MxcOBA7Ny505E9r7GxETt37sSsWbNkX5OSkoKdO3di7ty5jmUFBQVISUlRVNHa2lqkp6cjLCwM77zzDsLDw92+Zv/+/ejUqRODJn+xN4m18XWVaz17mdvkcGrr0xrOCaSOFvuCiIiIyA8UZ/nLycnBlClTMGjQICQlJWH58uU4f/68I+vf5MmTERcXh7y8PADAnDlzMHz4cCxbtgyjR4/GunXrsHfvXqxevdqxzrNnz+LYsWM4efIkAODw4cMApNat2NhY1NbWYtSoUbhw4QL++c9/OiWQ6Nq1K8xmM/71r3+huroaQ4YMQXh4OAoKCvDUU0/hoYceatsWIr/TbXI4uZmW4+OlcUJt6brGII2IiIjIOIQKzz//vOjZs6cIDQ0VSUlJ4tNPP3U8N3z4cDFlyhSn8hs2bBDXXXedCA0NFX379hXvvvuu0/Nr1qwRAFo8cnNzhRBCFBYWyj4PQJSVlQkhhHjvvfdEYmKiuOqqq0SHDh3EgAEDxKpVq4TNZvP4c9XU1AgAoqamRs1m8b+GBiEKC4XIz5f+NjT4u0Ze0dAgRHy8ECaTEFIHP+eHySSExeLjj7t5s3yFTCbpsXmz+vXGxzuvMz5e/fq8IUCPKyIiIqLWeBobmIRoJa94kKmtrUVkZKQjJbuhaNVaohNWq5TND5CfS8un+QxsNilfe9Nt3ZTJJG37sjJlLUv2D9n8K+mXD9mkTgF8XBERERG54mlsYLgsfyTDfiHe/ALfbU5x49BVcrhdu1wHU4BzlgxP2WxS4CJ3f8OjVIYaCILjioiIiKitGFAZnR4vxDXis7m03HGb/UJhOUCbIK0tgui4IiIiImoLxUkpSGeUXIgHQFY1XSSH0yJLhhZBWlsE2XFFREREpBYDKqPT24W4P/kqO15qqtTXsKJCvgXHPoYqNdXzdeotlSGPKyIiIiKPsMufDtlsQFERsHat9LfVXlV6uxD3F6tVShQxciQwcaL0NyFBm3E+ZrOUlAG4nDDCzv7/5culv57uSHuQ1nx9TddrsSgL0tqCxxURERGRRxhQ6YziuEBvF+Jak4s2/ZE8wV2WDEDZjvQ0SPPVfFTBdlwRERERqcS06U34O2365azZAsDlC1mTSfq/y2x2usopriG5FN5xccDFi8D338u/Rm0Kc0/JdTN8+2316c/lPqPFIgVTmZm+nfQ3WI4rIiIiIhmexgYMqJrwZ0B1eWoj52DKzgSBeIvJdVzg7kLc6FzN0eSpwkLfJE/wxhxVroImf8wJFejHFREREZELDKhU8GdAVVQk9Qpzp9W4wJetF77kLkjxRH4+kJ3ttSq55JUdKcOfk/4G6nFFRERE1ApPYwNm+dOJyopGeDKkrdVyusgp7iElF+nuUnh7wsjZ8dzNCWUySXNCjR2rTaBjpOOKiIiIyMeYlEInup/+0qvldE1p5o22pOYOhOx4epv0l4iIiIgcGFDpRGrXQ4jHcZjQKPu8CY2w4BhSux7ycc2gMI+7G2oy8qltXQqU7HicE4qIiIhItxhQ6YQ5LhbPYQ4AtAiq7P9fjrkwx8X6tmLenN/JXdc1QOq61jxg8yRI6dJFKtOUPYW5L5MnaJH+nHNCEREREekWAyq9SE1FZvzn2IQ7EIcKp6ficQKbcAcyLXu167rmi/md1HZd8yRIWb0aKC+Xkj3k50t/y8r8k4nO3RxVSuvEOaGIiIiIdItZ/prw9zxU9gDGJkKwC8NQie7ojkqk4mOYTY3atbb4an6ntWulVi53XGXkM1oKb29mx+OcUEREREQ+xbTpKvg9oAJ8HzT4cn4nb6QUD+YU3kYLKImIiIgMjAGVCroIqADfBQ2+nt/J/n4VFfIBnJpWr2ATzAElERERkQ9xHioja23eH29eUPt6fif7WKisLCl4kuu65suMfEbEOaGIiIiIdIVJKYzEmxn3AP/M7+TthA1ERERERH7EFiqjcDXWyZ5xT00w4q/5nTIzgbFj2XWNiIiIiAyPY6ia0M0YqubcjXVSO/bIkzFNnTsDV1zBRAhEREREFFQ8jQ3Y5c8I1M7f5I7R5nciIiIiItIZdvkzAk/HOqkZE2Uf09Q8HXd8vHMrVDAnQmBmPSIiIiJygQGVEXg61kntmCiOaXJNbu6n+HipZY+tdERERERBj2OomtD9GCrO3+RbrhKB2LtDMishERERUcDiGKpA4slYJ87f5F02m9QyJRfA2pfNnSuVIyIiIqKgxYDKKDh/k29plQiEiIiIiAIKx1AZCcc6+Y6WiUCIiIiIKGAwoDIaszm4M+5ppXkmv27dPHud2kQgRERERBQQGFARyWXyi4sDunQBzp5tPRFIaqrv6klEREREusOAioKbq0x+J09eXmYyOT/PRCBERERE9BMmpaDg5S6Tn8kktVIxEQgRERERucAWKgpenmTy+/57YMcOqSWKiUCIiIiIqBkGVBS8PM3Qd+oUkJ2tbV2IiIiIyJDY5Y+Cl6cZ+pjJj4iIiIhcUBVQrVixAgkJCQgPD0dycjL27NnTavmNGzeiT58+CA8PR//+/bFt2zan561WK0aNGoUuXbrAZDJh//79LdZx8eJFzJw5E126dMFVV12FcePGobq62qnMsWPHMHr0aFx55ZXo1q0bHn74YTQ0NKj5iBQMUlOl8VD2JBPNmUyAxcJMfkRERETkkuKAav369cjJyUFubi5KSkowYMAApKen49SpU7Lld+/ejezsbEybNg2lpaXIyMhARkYGDhw44Chz/vx5DBs2DH/9619dvu8DDzyAf/3rX9i4cSP+7//+DydPnkRmk6QANpsNo0ePRn19PXbv3o3XX38dr732GhYtWqT0I1KwMJuB556T/t08qGImPyIiIiLygEkIuRRnriUnJ2Pw4MF44YUXAACNjY2wWCyYPXs25s+f36L8hAkTcP78eWzdutWxbMiQIUhMTMSqVaucypaXl+Pqq69GaWkpEhMTHctramrQtWtX5OfnIysrCwBw6NAh3HDDDSguLsaQIUPw3nvv4bbbbsPJkycRExMDAFi1ahXmzZuH06dPIzQ01O1nq62tRWRkJGpqahAREaFks5CRyc1DZbFIwRQz+REREREFJU9jA0UtVPX19di3bx/S0tIuryAkBGlpaSguLpZ9TXFxsVN5AEhPT3dZXs6+fftw6dIlp/X06dMHPXv2dKynuLgY/fv3dwRT9vepra3FwYMHZddbV1eH2tpapwcFocxMoLwcKCwE8vOlv2VlDKaIiIiIyC1FWf7OnDkDm83mFLQAQExMDA4dOiT7mqqqKtnyVVVVHr9vVVUVQkNDERUV5XI9rt7H/pycvLw8PP744x7XgwKY2QyMGOHvWhARERGRwQR1lr8FCxagpqbG8Th+/Li/q0RERERERAaiqIUqOjoaZrO5RXa96upqxMbGyr4mNjZWUXlX66ivr8ePP/7o1ErVdD2xsbEtsg3a39fVe4WFhSEsLMzjehARERERETWlqIUqNDQUAwcOxM6dOx3LGhsbsXPnTqSkpMi+JiUlxak8ABQUFLgsL2fgwIFo376903oOHz6MY8eOOdaTkpKCr776yinbYEFBASIiInDjjTd6/F5ERERERESeUtRCBQA5OTmYMmUKBg0ahKSkJCxfvhznz5/H1KlTAQCTJ09GXFwc8vLyAABz5szB8OHDsWzZMowePRrr1q3D3r17sXr1asc6z549i2PHjuHkyZMApGAJkFqWYmNjERkZiWnTpiEnJwedO3dGREQEZs+ejZSUFAwZMgQAMGrUKNx4442YNGkSnnnmGVRVVeGxxx7DzJkz2QpFRERERESaUBxQTZgwAadPn8aiRYtQVVWFxMREbN++3ZEA4tixYwgJudzwNXToUOTn5+Oxxx7Do48+imuvvRZbtmxBv379HGXeeecdR0AGAHfeeScAIDc3F4sXLwYAPPvsswgJCcG4ceNQV1eH9PR0vPjii47XmM1mbN26FX/4wx+QkpKCDh06YMqUKXjiiSeUfkQiIiIiIiKPKJ6HKpBxHioiIiIiIgI0moeKiIiIiIiILmNARUREREREpBIDKiIiIiIiIpUUJ6UIZPbhZLW1tX6uCRERERER+ZM9JnCXcoIBVRPnzp0DAFgsFj/XhIiIiIiI9ODcuXOIjIx0+Tyz/DXR2NiIkydPomPHjjCZTH6tS21tLSwWC44fP86Mg6QIjx1Sg8cNqcHjhtTisUNq+Pq4EULg3Llz6NGjh9O0UM2xhaqJkJAQxMfH+7saTiIiIvhDQ6rw2CE1eNyQGjxuSC0eO6SGL4+b1lqm7JiUgoiIiIiISCUGVERERERERCoxoNKpsLAw5ObmIiwszN9VIYPhsUNq8LghNXjckFo8dkgNvR43TEpBRERERESkEluoiIiIiIiIVGJARUREREREpBIDKiIiIiIiIpUYUBEREREREanEgMqPVqxYgYSEBISHhyM5ORl79uxptfzGjRvRp08fhIeHo3///ti2bZuPakp6ouS4efnll5GamopOnTqhU6dOSEtLc3ucUeBS+ptjt27dOphMJmRkZGhbQdIlpcfNjz/+iJkzZ6J79+4ICwvDddddx/NVEFJ63CxfvhzXX389rrjiClgsFjzwwAO4ePGij2pLevDRRx/ht7/9LXr06AGTyYQtW7a4fU1RURF+8YtfICwsDD/72c/w2muvaV5POQyo/GT9+vXIyclBbm4uSkpKMGDAAKSnp+PUqVOy5Xfv3o3s7GxMmzYNpaWlyMjIQEZGBg4cOODjmpM/KT1uioqKkJ2djcLCQhQXF8NisWDUqFGoqKjwcc3J35QeO3bl5eV46KGHkJqa6qOakp4oPW7q6+vxq1/9CuXl5di0aRMOHz6Ml19+GXFxcT6uOfmT0uMmPz8f8+fPR25uLr755hu88sorWL9+PR599FEf15z86fz58xgwYABWrFjhUfmysjKMHj0aI0eOxP79+zF37lzce++9eP/99zWuqQxBfpGUlCRmzpzp+L/NZhM9evQQeXl5suXHjx8vRo8e7bQsOTlZzJgxQ9N6kr4oPW6aa2hoEB07dhSvv/66VlUknVJz7DQ0NIihQ4eKv//972LKlCli7NixPqgp6YnS42blypXimmuuEfX19b6qIumQ0uNm5syZ4n/+53+cluXk5Iibb75Z03qSfgEQb731VqtlHnnkEdG3b1+nZRMmTBDp6eka1kweW6j8oL6+Hvv27UNaWppjWUhICNLS0lBcXCz7muLiYqfyAJCenu6yPAUeNcdNcxcuXMClS5fQuXNnrapJOqT22HniiSfQrVs3TJs2zRfVJJ1Rc9y88847SElJwcyZMxETE4N+/frhqaeegs1m81W1yc/UHDdDhw7Fvn37HN0Cv/vuO2zbtg2/+c1vfFJnMiY9XRu38/k7Es6cOQObzYaYmBin5TExMTh06JDsa6qqqmTLV1VVaVZP0hc1x01z8+bNQ48ePVr8AFFgU3PsfPzxx3jllVewf/9+H9SQ9EjNcfPdd9/hww8/xF133YVt27bhyJEjuP/++3Hp0iXk5ub6otrkZ2qOm4kTJ+LMmTMYNmwYhBBoaGjA73//e3b5o1a5ujaura3Ff//7X1xxxRU+qwtbqIiCxNNPP41169bhrbfeQnh4uL+rQzp27tw5TJo0CS+//DKio6P9XR0ykMbGRnTr1g2rV6/GwIEDMWHCBPzpT3/CqlWr/F010rGioiI89dRTePHFF1FSUgKr1Yp3330XTz75pL+rRuQRtlD5QXR0NMxmM6qrq52WV1dXIzY2VvY1sbGxispT4FFz3NgtXboUTz/9NHbs2IGf//znWlaTdEjpsfPvf/8b5eXl+O1vf+tY1tjYCABo164dDh8+jN69e2tbafI7Nb853bt3R/v27WE2mx3LbrjhBlRVVaG+vh6hoaGa1pn8T81xs3DhQkyaNAn33nsvAKB///44f/48pk+fjj/96U8ICeH9f2rJ1bVxRESET1unALZQ+UVoaCgGDhyInTt3OpY1NjZi586dSElJkX1NSkqKU3kAKCgocFmeAo+a4wYAnnnmGTz55JPYvn07Bg0a5Iuqks4oPXb69OmDr776Cvv373c8xowZ48ikZLFYfFl98hM1vzk333wzjhw54gjAAeD//b//h+7duzOYChJqjpsLFy60CJrsQbkQQrvKkqHp6trY52kwSAghxLp160RYWJh47bXXxNdffy2mT58uoqKiRFVVlRBCiEmTJon58+c7yn/yySeiXbt2YunSpeKbb74Rubm5on379uKrr77y10cgP1B63Dz99NMiNDRUbNq0SVRWVjoe586d89dHID9Reuw0xyx/wUnpcXPs2DHRsWNHMWvWLHH48GGxdetW0a1bN/HnP//ZXx+B/EDpcZObmys6duwo1q5dK7777jvxwQcfiN69e4vx48f76yOQH5w7d06UlpaK0tJSAUD87W9/E6WlpeLo0aNCCCHmz58vJk2a5Cj/3XffiSuvvFI8/PDD4ptvvhErVqwQZrNZbN++3ed1Z0DlR88//7zo2bOnCA0NFUlJSeLTTz91PDd8+HAxZcoUp/IbNmwQ1113nQgNDRV9+/YV7777ro9rTHqg5Ljp1auXANDikZub6/uKk98p/c1pigFV8FJ63OzevVskJyeLsLAwcc0114i//OUvoqGhwce1Jn9TctxcunRJLF68WPTu3VuEh4cLi8Ui7r//fvHDDz/4vuLkN4WFhbLXLPZjZcqUKWL48OEtXpOYmChCQ0PFNddcI9asWePzegshhEkItqUSERERERGpwTFUREREREREKjGgIiIiIiIiUokBFRERERERkUoMqIiIiIiIiFRiQEVERERERKQSAyoiIiIiIiKVGFARERERERGpxICKiIiIiIhIJQZUREREREREKjGgIiIiIiIiUokBFRERERERkUoMqIiIiIiIiFT6/9eBJ52T5uwoAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "axs.plot([xj[1] for xj,p in zip(x, p_raw) if xj[0] == 0], [p for xj,p in zip(x, p_raw) if xj[0] == 0], 'or')\n", + "axs.plot([xj[1] for xj,p in zip(x, p_raw) if xj[0] == 1], [p for xj,p in zip(x, p_raw) if xj[0] == 1], 'ob')\n", + "axs.set_title(\"raw transition frequencies\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cd869a15-a44e-406c-9ef7-22009f1f4bd0", + "metadata": { + "id": "cd869a15-a44e-406c-9ef7-22009f1f4bd0" + }, + "source": [ + "The first step of the modelling is to define the mapping from data space to our quantum feature space. This is done by setting up the build_feature_map function. The circuit below is a very simplified two-variable circuit. Feel free to experiment!" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "f6546726-7f76-4f7d-992c-95ee972abf17", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "f6546726-7f76-4f7d-992c-95ee972abf17", + "outputId": "dff222f3-4d86-435c-b11e-defffd550a33" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "QuantumCircuit:\n", + "---------------\n", + " ┌──────────┐\n", + "q.0: ┤ Ry(π*x0) ├\n", + " ├──────────┤\n", + "q.1: ┤ Ry(π*x1) ├\n", + " └──────────┘\n", + "Live QuantumVariables:\n", + "----------------------\n", + "QuantumVariable q\n" + ] + } + ], + "source": [ + "from qrisp import ry\n", + "\n", + "# Define a simple feature map using Ry rotations\n", + "def build_feature_map(sym):\n", + " n = 2 # Number of qubits\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n)) # Create symbolic parameters: x:0, x:1\n", + " ry(np.pi * params[0], q[0]) # Apply Ry rotation to qubit 0\n", + " ry(np.pi * params[1], q[1]) # Apply Ry rotation to qubit 1\n", + " return q\n", + "\n", + "# Build the feature map\n", + "feature_map = build_feature_map('x')\n", + "\n", + "# Inspect the quantum state\n", + "print(feature_map.qs)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "2c128f3c-da92-4dd2-b94d-27dd25970626", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "2c128f3c-da92-4dd2-b94d-27dd25970626", + "outputId": "ae3bcf0e-c252-4faa-bc39-b81fa3c542ad" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " ┌────────────┐\n", + "q.0: ┤ Ry(2.7563) ├\n", + " ├────────────┤\n", + "q.1: ┤ Ry(2.3272) ├\n", + " └────────────┘\n" + ] + } + ], + "source": [ + "# example, assign random data as parameters and print cirquit\n", + "\n", + "subs_dic = {a : np.random.rand() for a in feature_map.qs.abstract_params}\n", + "bound_qc = feature_map.qs.bind_parameters(subs_dic)\n", + "print(bound_qc)" + ] + }, + { + "cell_type": "markdown", + "id": "45f26e2c-cf15-4e67-a9b7-d774cb11c2eb", + "metadata": { + "id": "45f26e2c-cf15-4e67-a9b7-d774cb11c2eb" + }, + "source": [ + "For a data pair $(x, y)$, we create the kernel circuit by calling the build_feature_map twice, once for $x$ and once for $y$, inverting the latter, and joining them together" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "ce778494-1f6a-40f0-89e9-02123cd6600a", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "ce778494-1f6a-40f0-89e9-02123cd6600a", + "outputId": "1ab5c81e-ed04-4d95-a115-89b324a1c45e" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " ┌──────────┐┌───────────┐┌─┐ \n", + " q.0: ┤ Ry(π*x0) ├┤ Ry(-π*y0) ├┤M├───\n", + " ├──────────┤├───────────┤└╥┘┌─┐\n", + " q.1: ┤ Ry(π*x1) ├┤ Ry(-π*y1) ├─╫─┤M├\n", + " └──────────┘└───────────┘ ║ └╥┘\n", + "cb_0: ══════════════════════════╩══╬═\n", + " ║ \n", + "cb_1: ═════════════════════════════╩═\n", + " \n" + ] + } + ], + "source": [ + "kernel = build_feature_map('x')\n", + "y_inverse = build_feature_map('y').qs.inverse()\n", + "\n", + "kernel.qs.append(y_inverse.to_op(), kernel.qs.qubits)\n", + "\n", + "kernel.qs.measure(kernel.qs.qubits)\n", + "\n", + "print(kernel.qs.transpile())" + ] + }, + { + "cell_type": "markdown", + "id": "b9fefbd4-5e78-4b09-8e7f-8e5a9f342e60", + "metadata": { + "id": "b9fefbd4-5e78-4b09-8e7f-8e5a9f342e60" + }, + "source": [ + "## Experimenting\n", + "\n", + "Remember, when experimenting with quantum circuits, it's important to understand what each gate does and how changing the circuit might affect your results. Happy experimenting! 😊\n", + "\n", + "A few general guidelines for experimenting with quantum circuits:\n", + "\n", + "1. **Understand the problem**: Before you start experimenting, make sure you understand the problem you're trying to solve and how a quantum circuit could help solve it.\n", + "\n", + "2. **Start simple**: Start with a simple circuit and gradually add complexity. This makes it easier to understand what each part of your circuit is doing.\n", + "\n", + "3. **Use a variety of gates**: Different gates can have different effects on your quantum state, so try using a variety of gates in your experiments.\n", + "\n", + "4. **Test on a simulator first**: Before running your circuit on a real quantum computer, test it on a simulator to make sure it's working as expected.\n", + "\n", + "5. **Analyze your results**: After running your circuit, analyze the results to see if they make sense and if they're helping you solve your problem.\n", + "\n", + "6. **Iterate**: Experimenting with quantum circuits often involves a lot of trial and error. Don't be afraid to iterate on your design and try new things.\n", + "\n", + "In the context of the Quantum Support Vector Regression (QSVR) for disability insurance that you're working on, you might want to experiment with different ways of encoding your data into the quantum state or different types of quantum kernels. Remember, the goal is to find a quantum circuit that can effectively model your data and help you make accurate predictions." + ] + }, + { + "cell_type": "markdown", + "id": "cStNolKC62xl", + "metadata": { + "id": "cStNolKC62xl" + }, + "source": [ + "### Exercise 1 – Experimenting with Quantum Feature Maps\n", + "\n", + "🧪 Goal:\n", + "Explore how different quantum circuit designs affect the feature mapping in quantum kernel estimation." + ] + }, + { + "cell_type": "markdown", + "id": "XUGk2fHP7CHo", + "metadata": { + "id": "XUGk2fHP7CHo" + }, + "source": [ + "#####1.1 Change the rotation gates\n", + "Try replacing ry with other single-qubit gates like rx, rz, or combinations:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "haddGeZA6gXM", + "metadata": { + "id": "haddGeZA6gXM" + }, + "outputs": [], + "source": [ + "from qrisp import rx, rz\n", + "rx(np.pi * params[0], q[0])\n", + "rz(np.pi * params[1], q[1])" + ] + }, + { + "cell_type": "markdown", + "id": "33oWLNjK8MPY", + "metadata": { + "id": "33oWLNjK8MPY" + }, + "source": [ + "What to observe:\n", + "\n", + "How does the circuit look after transpiling?\n", + "Does the kernel matrix change significantly?\n", + "Does SVR performance improve or degrade?" + ] + }, + { + "cell_type": "markdown", + "id": "-lBC_HZS7mJY", + "metadata": { + "id": "-lBC_HZS7mJY" + }, + "source": [ + "1.2 Add entanglement\n", + "Introduce gates like cx or cz to create entanglement between qubits:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "yQnWPe_q7mZM", + "metadata": { + "id": "yQnWPe_q7mZM" + }, + "outputs": [], + "source": [ + "from qrisp import cx, h\n", + "h(q[0])\n", + "cx(q[0], q[1])" + ] + }, + { + "cell_type": "markdown", + "id": "OVna9A--8Oiy", + "metadata": { + "id": "OVna9A--8Oiy" + }, + "source": [ + "What to observe:\n", + "\n", + "Does entanglement improve the expressiveness of the kernel?\n", + "Is the circuit still efficient to simulate?" + ] + }, + { + "cell_type": "markdown", + "id": "TKLmbiZ57m3K", + "metadata": { + "id": "TKLmbiZ57m3K" + }, + "source": [ + "1.3 Use nonlinear parameter functions\n", + "Instead of linear scaling, try nonlinear transformations:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "tSmjrs4-7nI2", + "metadata": { + "id": "tSmjrs4-7nI2" + }, + "outputs": [], + "source": [ + "ry(np.sin(params[0] * np.pi), q[0])\n", + "ry(np.log1p(params[1]) * np.pi, q[1])" + ] + }, + { + "cell_type": "markdown", + "id": "jyhJD1TC8Qd3", + "metadata": { + "id": "jyhJD1TC8Qd3" + }, + "source": [ + "What to observe:\n", + "\n", + "Does the kernel matrix capture more subtle patterns?\n", + "Are the results more stable or more sensitive?" + ] + }, + { + "cell_type": "markdown", + "id": "KTOBmogV7nSn", + "metadata": { + "id": "KTOBmogV7nSn" + }, + "source": [ + "1.4 Increase the number of qubits\n", + "Modify n = 2 to n = 3 or more, and expand your feature map accordingly." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ATwqZ79m7naC", + "metadata": { + "id": "ATwqZ79m7naC" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "Ys1Mm-iz8Slg", + "metadata": { + "id": "Ys1Mm-iz8Slg" + }, + "source": [ + "What to observe:\n", + "\n", + "How does the circuit scale?\n", + "Does the SVR model benefit from higher-dimensional quantum features?" + ] + }, + { + "cell_type": "markdown", + "id": "3dc158a8-1035-47fa-80bd-4d0b4743eabe", + "metadata": { + "id": "3dc158a8-1035-47fa-80bd-4d0b4743eabe" + }, + "source": [ + "#### Hints\n", + "1. Use .transpile() to inspect how your circuit changes.\n", + "2. Try binding real data instead of random values to see how the circuit behaves.\n", + "3. Consider how each change might affect the kernel similarity between data points." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "339246ed-877a-4235-9009-69f77e6e057b", + "metadata": { + "id": "339246ed-877a-4235-9009-69f77e6e057b" + }, + "outputs": [], + "source": [ + "# Test code here\n", + "# Then rerun the following cells\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "RcEnL1fJ_Z26", + "metadata": { + "id": "RcEnL1fJ_Z26" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "7ed23841-0821-40bd-8a6e-0e7fd12ed22b", + "metadata": { + "id": "7ed23841-0821-40bd-8a6e-0e7fd12ed22b" + }, + "source": [ + "#### Estimating the kernel matrix\n", + "\n", + "The train_kernel_matrix function prepares the kernel estimation by setting up inner product circuits, based on each combination of two data points. The kernel circuits are then run on a either a specified backend, or using statevector simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "N6x2RwdvLInI", + "metadata": { + "id": "N6x2RwdvLInI" + }, + "outputs": [], + "source": [ + "def train_kernel_matrix(x, f_feature_map, shots=1000, backend=None):\n", + " # Build base kernel circuit\n", + " kernel = f_feature_map('x')\n", + " x_params = copy(kernel.qs.abstract_params)\n", + "\n", + " # Build inverse feature map for y\n", + " adjoint_qs = f_feature_map('y').qs.inverse()\n", + " y_params = adjoint_qs.abstract_params\n", + " # Combine circuits\n", + " kernel.qs.append(adjoint_qs.to_op(), kernel.qs.qubits)\n", + " kernel.qs = kernel.qs.transpile()\n", + "\n", + " # Add measurement if using backend\n", + " if backend is not None:\n", + " kernel.qs.measure(kernel.qs.qubits)\n", + "\n", + " # Initialize kernel matrix\n", + " n = len(x)\n", + " K = np.eye(n)\n", + "\n", + " # Loop over all pairs (i, j)\n", + " for i in range(n):\n", + " subs_dic = {p: x[i][int(p.name[1:])] for p in x_params}\n", + " for j in range(i + 1, n):\n", + " for p in y_params:\n", + " subs_dic[p] = x[j][int(p.name[1:])]\n", + "\n", + " # Bind parameters\n", + " bound_kernel = kernel.qs.bind_parameters(subs_dic)\n", + "\n", + " # Run circuit\n", + " if backend is not None:\n", + " res = bound_kernel.run(shots=shots, backend=backend)\n", + " K_ij = res.get('0' * len(kernel.qs.qubits), 0) / shots\n", + " else:\n", + " res = bound_kernel.statevector_array()\n", + " K_ij = np.abs(res[0]) ** 2\n", + "\n", + " # Fill symmetric matrix\n", + " K[i, j] = K[j, i] = K_ij\n", + "\n", + " return K" + ] + }, + { + "cell_type": "markdown", + "id": "6684d892-b617-4556-926e-e23e10353aec", + "metadata": { + "id": "6684d892-b617-4556-926e-e23e10353aec" + }, + "source": [ + "We evaluate the kernel matrix based on our $x$ data and the build_feature_map helper function." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "908ec069-24b6-4d5b-bb47-e677339e3279", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "908ec069-24b6-4d5b-bb47-e677339e3279", + "outputId": "0a444975-2c62-430b-a17c-2398e6c52a74" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " \u001b[2K" + ] + } + ], + "source": [ + "matrix_train = train_kernel_matrix(x, build_feature_map)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "cc7771e0-7f0c-4a32-b6bd-d6a7dd50da52", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 468 + }, + "id": "cc7771e0-7f0c-4a32-b6bd-d6a7dd50da52", + "outputId": "171aeae9-7343-4c0f-df53-2f13a86b75f3" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the kernel matrix\n", + "\n", + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(matrix_train),\n", + " interpolation='nearest', origin='upper', cmap='Blues')\n", + "axs.set_title(\"trained kernel matrix\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b5e309fb-7fb7-4fed-9e3f-05ff9aa6ea87", + "metadata": { + "id": "b5e309fb-7fb7-4fed-9e3f-05ff9aa6ea87" + }, + "source": [ + "Figure 1 displays the estimated kernel matrix. This matrix has an interesting structure: it is block-diagonal. This is due to the fact that the second quadrant of the matrix correspond to the inner products of the population groups with gender=0. These share the common characteristic gender=0, and each row is similar to its neighbours due to the encoding: similar ages are also similar in the quantum feature space. Analogously, the fourth quadrant of the matrix contains the gender=1 population groups. The first and third quadrants contain the inner products between gender=0 and gender=1 population groups and so are dissimilar in the quantum feature space." + ] + }, + { + "cell_type": "markdown", + "id": "5169b0dc-a666-4d0a-a19e-63de0ca8e6c2", + "metadata": { + "id": "5169b0dc-a666-4d0a-a19e-63de0ca8e6c2" + }, + "source": [ + "Next, we run a support vector regression (SVR) taking the kernel matrix, the weights, and the y-values as input." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "HYtBGKbnQm0-", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + }, + "id": "HYtBGKbnQm0-", + "outputId": "385138d4-452f-446a-da42-5c11d1b551ac" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SVR model R² score on training data: 0.8609\n" + ] + }, + { + "data": { + "image/png": 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oE4lEaNOmDaZMmSJ3HfHFqjHL359JVZ06dYK1tTV27dol6V9oYmIiFTBYWVnhzJkziI2NxcGDB3HkyBHs3LkTX3zxBY4dO1bo/sVBWFBQkNznHz16pDBRiSoU1bIVTJQiFArRpk0bvH//HlOnToWvry9sbGyQlJSEQYMGqVxDqKoBAwbgxx9/xL59+9C7d29s27YNHTt2hIODQ6Hr+fr6AuBr3PIfS09PT3h6egKApJZYTCQSoXbt2li2bJncbYrXE1P0PuavXVWWSCSSjHknb7sFb4RoI9sqIcSwUYBGCCFqEGfxe/nypdT8zp07w87ODtu2bYOZmRlSUlKUyt4I8Bdms2bNwuDBg7Fr1y706tVL4+XOr2rVqvj06VORAV6lSpVw4sQJfPr0SeriUZm05VWrVoVIJMKdO3dQr149hcsp21SvUqVKkn2Lm6PlL4/4eU2wsbFBx44dsXv3bixbtgw7d+5E8+bNZYYuMDExQevWrdG6dWssW7YM8+fPx7fffovY2FiFx/bx48e4cOECxo4dK6mhEhOJROjfvz+2bduGGTNmSJrW3b59G97e3grLq+gYihPOFMy6WbC28datW7h//z62bNmCAQMGSObHxMQo3KcyXrx4ITN0wP379wFAkmkS4GsI69evj61bt8LDwwOJiYmSweAL07FjRyxcuBBbt25VGOwWVLVqVfz9999o3bq1RpqJli1bFlZWVnjw4IHMcwU/J1WrVgVjDJUrVy4RN0EIIZpHTRwJIaQQsbGxcu+SHzp0CIBs8yUrKyt07doVhw4dwtq1a2FjY4MuXboovb++ffvCw8MDixYtKl7BlRAeHi5JUV7Qhw8fkJubCwDo0KEDcnNzsXbtWsnzQqFQqYvn0NBQmJiYYO7cuTI1MPmPq42Njdy0/QU1bNgQ5cqVw7p166TSoR8+fBh3797FV199VeQ2VNGzZ0+8ePECv/76K/7++2+p5o0A8P79e5l1xIFowXTt+Ylrz6ZMmYLu3btLTeHh4QgODpYs07ZtW9jZ2WHBggWSprNiBY+hvGaI4gBP3KcQ4N+/9evXSy0nrs3Jv03GmGRAdnXl5uZKpZvPzs7GL7/8grJly8Lf319q2f79++PYsWNYsWIFnJ2d8eWXXxa5/aCgILRp0wbr169XOERBwc9weHg4kpKSsGHDBpllP3/+jPT0dGVemoRAIEC7du2wb98+JCYmSubfvXtX5vMVFhYGgUCAOXPmyJSLMYZ3796ptG9CSMlDNWiEEFKIcePGISMjA127doWvry+ys7Nx4cIF7Ny5E15eXnI77/fr1w//93//h6NHj6Jv374qDTpsZmaGiIgITJ48GUeOHEH79u01+XKkTJ48Gfv370fHjh0xaNAg+Pv7Iz09Hbdu3cKff/6JJ0+ewMXFBZ06dUJQUBCmTZuGJ0+eoEaNGoiOjlaqT5K3tze+/fZbzJs3D82bN0dYWBgsLCxw5coVVKhQQTK+lb+/P9auXYvvv/8e3t7eKFeunEwNGcAfn0WLFmHw4MEIDg5G7969JWn2vby88M0332j0GHXo0AF2dnaYNGkSBAIBunXrJvX83LlzcebMGXz11VeoVKkSXr9+jTVr1sDDw0MqKUVBW7duRb169WSa0ol17twZ48aNw7Vr19CgQQMsX74cw4YNQ6NGjdCnTx+UKVMGf//9NzIyMrBlyxYA/DHcuXMnIiMj0ahRI9ja2qJTp06oWbMmAgICEBUVhffv38PJyQk7duyQBOBivr6+qFq1KiZNmoSkpCTY29tjz549SvXXK0yFChWwaNEiPHnyBNWrV8fOnTtx48YNrF+/HmZmZlLL9unTB1OmTMHevXsxatQomecV+eOPP9C+fXuEhobiyy+/REhICMqUKYPk5GQcP34cZ86ckQr2+vfvj127duHrr79GbGwsgoKCIBQKce/ePezatUsyZqAq5syZgyNHjqB58+YYPXo0cnNzsWrVKtSsWRM3b96ULFe1alV8//33iIqKwpMnTxAaGgo7Ozs8fvwYe/fuxYgRIzBp0iSV9k0IKWH0kjuSEEKMxOHDh9mQIUOYr68vs7W1Zebm5szb25uNGzeOvXr1Su46ubm5rHz58gwAO3TokNxlxGnK5aVnT01NZQ4ODkWmFxen2S9KpUqV2FdffSX3uY8fP7KoqCjm7e3NzM3NmYuLC2vatClbsmSJ1FAC7969Y/3792f29vbMwcGB9e/fn12/fr3INPtiGzduZPXr12cWFhasTJkyLDg4mMXExEieT05OZl999RWzs7NjACSvXV4qeMYY27lzp2R7Tk5OrG/fvuz58+dKHR9lU8SL9e3blwFgISEhMs+dOHGCdenShVWoUIGZm5uzChUqsN69e8sMXZBffHw8A8C+++47hcs8efKEAWDffPONZN7+/ftZ06ZNmZWVFbO3t2eNGzdm27dvlzz/6dMn1qdPH+bo6MgASKXc//fff1lISAizsLBgrq6ubPr06SwmJkbm2N65c4eFhIQwW1tb5uLiwoYPHy5JKa/M+1xQcHAwq1mzJrt69SoLDAxklpaWrFKlSmz16tUK1+nQoQMDwC5cuFDk9vP7/PkzW7FiBQsMDGT29vbM1NSUubm5sY4dO7KtW7ey3NxcqeWzs7PZokWLWM2aNSXnpb+/P5szZw5LTU2VLAeAjRkzRmZ/lSpVYgMHDpSad/r0aebv78/Mzc1ZlSpV2Lp16xQeqz179rBmzZoxGxsbZmNjw3x9fdmYMWNYQkKCZBnx8SOElC4cY2r0cCWEEEII0YKuXbvi1q1bePjwob6LQgghekF90AghhBBiEF6+fImDBw+if//++i4KIYToDfVBI4QQQohePX78GOfPn8evv/4KMzMzqYGtCSGktKEaNEIIIYTo1enTp9G/f388fvwYW7ZsgZubm76LRAghekN90AghhBBCCCHEQFANGiGEEEIIIYQYCArQCCGEEEIIIcRAUJIQLRKJRHjx4gXs7OzAcZy+i0MIIYQQQgjRE8YYPn78iAoVKsDERHE9GQVoWvTixQt4enrquxiEEEIIIYQQA/Hs2TN4eHgofJ4CNC2ys7MDwL8J9vb2ei1LTk4Ojh07hrZt28LMzEyvZSHGg84bog46b4i66Nwh6qDzhqhDH+dNWloaPD09JTGCIhSgaZG4WaO9vb1BBGjW1tawt7enLy+iNDpviDrovCHqonOHqIPOG6IOfZ43RXV9oiQhhBBCCCGEEGIgDCJA+/nnn+Hl5QVLS0s0adIEly9fLnT53bt3w9fXF5aWlqhduzYOHTok9fzs2bPh6+sLGxsblClTBiEhIbh06ZLUMu/fv0ffvn1hb28PR0dHDB06FJ8+fZJa5ubNm2jevDksLS3h6emJxYsXa+YFE0IIIYQQQogceg/Qdu7cicjISMyaNQvXrl1D3bp10a5dO7x+/Vru8hcuXEDv3r0xdOhQXL9+HaGhoQgNDcXt27cly1SvXh2rV6/GrVu3cO7cOXh5eaFt27Z48+aNZJm+ffvin3/+QUxMDA4cOIAzZ85gxIgRkufT0tLQtm1bVKpUCfHx8fjxxx8xe/ZsrF+/XnsHgxBCCCGEEFKq6b0P2rJlyzB8+HAMHjwYALBu3TocPHgQGzduxLRp02SWX7lyJdq3b4/JkycDAObNm4eYmBisXr0a69atAwD06dNHZh+//fYbbt68idatW+Pu3bs4cuQIrly5goYNGwIAVq1ahQ4dOmDJkiWoUKECtm7diuzsbGzcuBHm5uaoWbMmbty4gWXLlkkFcsXBGENubi6EQqFGtleYnJwcmJqaIjMzUyf7I/olEAhgampKwzsQQgghhBgZvQZo2dnZiI+PR1RUlGSeiYkJQkJCEBcXJ3eduLg4REZGSs1r164d9u3bp3Af69evh4ODA+rWrSvZhqOjoyQ4A4CQkBCYmJjg0qVL6Nq1K+Li4tCiRQuYm5tL7WfRokVISUlBmTJlZPaVlZWFrKwsyeO0tDQAfHCUk5MjtWxOTg5evXqFz58/yy23pjHG4ObmhsTERLpoLyWsrKzg6uparI6v4vO24PlLSGHovCHqonOHqIPOG6IOfZw3yu5LrwHa27dvIRQK4erqKjXf1dUV9+7dk7tOcnKy3OWTk5Ol5h04cAC9evVCRkYGypcvj5iYGLi4uEi2Ua5cOanlTU1N4eTkJNlOcnIyKleuLLMf8XPyArQFCxZgzpw5MvOPHTsGa2trmW3Z2trCyckJpqZ6r8gkJUxubi7ev3+Pmzdv4tWrV8XeXkxMjAZKRUobOm+IuujcIeqg84aoQ5fnTUZGhlLLldjIoFWrVrhx4wbevn2LDRs2IDw8HJcuXZIJzDQpKipKqnZPPNZB27ZtpdLsZ2VlITExERUrVpQJ3LRFPHK5nZ0d1aCVEvb29khMTEStWrVgYWGh1jZycnIQExODNm3aUOpiojQ6b4i66Nwh6qDzhqhDH+eNuHVdUfQaoLm4uEAgEMjc4X/16hXc3NzkruPm5qbU8jY2NvD29oa3tzcCAgJQrVo1/Pbbb4iKioKbm5tMEhJxjYN4O4r2I35OHgsLC7kXwmZmZlJvvFAoBMdxMDU1hYmJbvK0iEQiAPy4C7raJ9EvcR80U1PTYn/xFDyHCVEGnTdEXXTuEHXQeUPUocvzRtn96PVK3dzcHP7+/jhx4oRknkgkwokTJxAYGCh3ncDAQKnlAb5qUtHy+bcr7h8WGBiIDx8+ID4+XvL8yZMnIRKJ0KRJE8kyZ86ckWorGhMTAx8fH7nNGwkhhBBCCCGkuPRelRIZGYkNGzZgy5YtuHv3LkaNGoX09HRJVscBAwZIJRGJiIjAkSNHsHTpUty7dw+zZ8/G1atXMXbsWABAeno6pk+fjosXL+Lp06eIj4/HkCFDkJSUhB49egAA/Pz80L59ewwfPhyXL1/G+fPnMXbsWPTq1QsVKlQAwGeCNDc3x9ChQ/HPP/9g586dWLlypUyCEkIIIYQQQoyKUAicOgVs387/pQzfBkXvfdB69uyJN2/eYObMmUhOTka9evVw5MgRSUKOxMREqSZ5TZs2xbZt2zBjxgxMnz4d1apVw759+1CrVi0AfHrxe/fuYcuWLXj79i2cnZ3RqFEjnD17FjVr1pRsZ+vWrRg7dixat24NExMTdOvWDT/99JPkeQcHBxw7dgxjxoyBv78/XFxcMHPmTI2l2NcYoRA4exZ4+RIoXx5o3hwQCPRdKkIIIYQQYoiio4GICOD587x5Hh7AypVAWJj+ykUk9B6gAcDYsWMlNWAFnTp1SmZejx49JLVhBVlaWiI6OrrIfTo5OWHbtm2FLlOnTh2cPXu2yG3pjZ4+YMnJyViwYAEOHjyI58+fw8HBAd7e3ujXrx8GDhyos8QnqsrMzMTEiROxY8cOZGVloV27dlizZo1MVlBCCCGEkBIpOhro3h1gTHp+UhI//88/KUgzAHpv4kjUJP6A5Q/OgLwPmBJBqjoePXqE+vXr49ixY5g/fz6uX7+OuLg4TJkyBQcOHMDx48cVrqvv8Um++eYb/PXXX9i9ezdOnz6NFy9eIIy+hAghhBBSGgiF/I39gsEZkDdvwgRq7mgAKEAzRnr8gI0ePRqmpqa4evUqwsPD4efnhypVqqBLly44ePAgOnXqJFmW4zisXbsWnTt3ho2NDX744QcAwNq1a1G1alWYm5vDx8cHv//+u2SdJ0+egOM43LhxQzLvw4cP4DhOUpt66tQpcByHgwcPok6dOrC0tERAQABu376tsNypqan47bffsGzZMnzxxRfw9/fHpk2bcOHCBVy8eFGzB4kQQgghxNCcPSt7Yz8/xoBnz/jliF5RgGaM9PQBe/funaRfno2NjdxlCo6xNnv2bHTt2hW3bt3CkCFDsHfvXkRERGDixIm4ffs2Ro4cicGDByM2Nlbl8kyePBlLly7FlStXULZsWXTq1ElhLV18fDxycnIQEhIimefr64uKFSsiLi5O5X0TQgghhBiVly81uxzRGgrQjJGePmAPHz4EYww+Pj5S811cXGBrawtbW1tMnTpV6rk+ffpg8ODBqFKlCipWrIglS5Zg0KBBGD16NKpXr47IyEiEhYVhyZIlKpdn1qxZaNOmDWrXro0tW7bg1atX2Lt3r9xlk5OTYW5uDkdHR6n5rq6uSE5OVnnfhBBCCCFGpXx5zS6nK6Uw4yQFaMbIwD5gly9fxo0bN1CzZk3JWHNiDRs2lHp89+5dBAUFSc0LCgrC3bt3Vd5v/rHvnJyc4OPjo9Z2CCGEEEJKvObN+WRyBVo7SXAc4OnJL2cooqMBLy+gVSugTx/+r5eX1nItGAoK0IyRnj5g3t7e4DgOCQkJUvOrVKkCb29vWFlZyayjqCmkIuIhFVi+/nWaSC7i5uaG7OxsfPjwQWr+q1ev4ObmVuztE0IIIYQYNIGAz/QNyF5Dih+vWGE4wzXpKSGeIaAAzRjp6QPm7OyMNm3aYPXq1UhPT1drG35+fjh//rzUvPPnz6NGjRoAgLJlywIAXuZrnpk/YUh++ZN7pKSk4P79+/Dz85O7rL+/P8zMzHDixAnJvISEBCQmJkrVxBFCCCGElFhhYXwqfXd36fkeHvpNsV+wGWN2dqnOOGkQ46ARNYg/YPLGQVuxQmsfsDVr1iAoKAgNGzbE7NmzUadOHZiYmODKlSu4d+8e/P39C11/8uTJCA8PR/369RESEoK//voL0dHRkvT8VlZWCAgIwMKFC1G5cmW8fv0aM2bMkLutuXPnwtnZGa6urvj222/h4uKC0NBQucs6ODhg6NChiIyMhJOTE+zt7TFu3DgEBgYiICCgWMeEEEIIIcRohIUBXbrwyeRevuS7xDRvrr+aM3nj+rq4AG/fKl4nf0K8li21XkRdowDNmOnhA1a1alVcv34d8+fPR1RUFJ4/fw4LCwvUqFEDkyZNwujRowtdPzQ0FCtXrsSSJUsQERGBypUrY9OmTWiZ78O1ceNGDB06FP7+/vDx8cHixYvRtm1bmW0tXLgQERERePDgAerVq4e//voL5ubmCve9fPlymJiYoFu3blIDVRNCCCGElCoCgWEENooGzi4sOMuvhGacpADN2OnhA1a+fHmsWrUKq1atKnQ5Jq9aGsCoUaMwatQohev5+fnhwoULRW6rWbNmhY59VpClpSV+/vln/Pzzz0qvQwghhBBCtKCwcX2VZWgZJzWEAjRCCCGEEEKIbhU1rm9hOI7v1mNIGSc1iAI0QgghhBBCiG6p2zwxf0I8gE8qYgh96TSIAjRidFq2bKmw+SQhhBBCCDECyjZPLFsWePMm77E4IR7Aj4lWMFneypX6y0apIZRmnxBCCCGEEKJbyo7r+/w5EBsLbNvG/338mH++BI+RRgEaIYQQQgghRLeUHdfX3JxPiNe7d15ivBI+RhoFaIQQQgghhBDdU2fg7KKSi+QfI81IUR80QgghhBBCiH6oOq6vsslFjHiMNArQCCGEEEJI6SIUKh8QEO1TZVxfZZOLGPEYaRSgEUIIIYSQ0iM6mu/DVAKz/5UK4uQiSUny+6GJx0hr2tRoU/BTHzRCDISXlxdWiNPGKmH27NmoV6+e1spDCCGElDjR0SU6+1+poExykV69gKpVgVatgD59+L9eXkbz/lKARlSWnJyMiIgIeHt7w9LSEq6urggKCsLatWuRkZGh7+IplJmZiTFjxsDZ2Rm2trbo1q0bXr16pe9iEUIIIUQXhMISn/2v1CgsucikScCSJUYdhFOARlTy6NEj1K9fH8eOHcP8+fNx/fp1xMXFYcqUKThw4ACOHz+ucN2cnBwdllTWN998g7/++gu7d+/G6dOn8eLFC4RRUwZCCCGkdCgF2f9KlbAw4MkT6THSHj4Etm83+iCcAjRDwRiQnq6fSd5JrMDo0aNhamqKq1evIjw8HH5+fqhSpQq6dOmCgwcPolOnTpJlOY7D2rVr0blzZ9jY2OCHH34AAKxduxZVq1aFubk5fHx88Pvvv0vWefLkCTiOw40bNyTzPnz4AI7jcOrUKQDAqVOnwHEcDh48iDp16sDS0hIBAQG4ffu2wnKnpqbit99+w7Jly/DFF1/A398fmzZtwoULF3Dx4kWF63l5eeH777/HgAEDYGtri0qVKmH//v148+YNunTpAltbW9SpUwdXr16VWm/Pnj2oWbMmLCws4OXlhaVLl0o9//r1a3Tq1AlWVlaoXLkytm7dKrPvDx8+YNiwYShbtizs7e3xxRdf4O+//1ZYVkIIIYQUohRk/yt1xMlFxGOkXbhQIoJwCtAMRUYGYGurtcnE3h6OHh4wsbeXfV7JZonv3r3DsWPHMGbMGNjY2MhdhivQFnj27Nno2rUrbt26hSFDhmDv3r2IiIjAxIkTcfv2bYwcORKDBw9GbGysyods8uTJWLp0Ka5cuYKyZcuiU6dOCmvp4uPjkZOTg5CQEMk8X19fVKxYEXFxcYXuZ/ny5QgKCsL169fx1VdfoX///hgwYAD69euHa9euoWrVqhgwYADYf4FufHw8wsPD0atXL9y6dQuzZ8/Gd999h82bN0u2OWjQIDx79gyxsbH4888/sWbNGrx+/Vpqvz169MDr169x+PBhxMfHo0GDBmjdujXev3+v8rEihBBCSr1SkP2v1CshQTgFaERpDx8+BGMMPj4+UvNdXFxga2sLW1tbTJ06Veq5Pn36YPDgwahSpQoqVqyIJUuWYNCgQRg9ejSqV6+OyMhIhIWFYcmSJSqXZ9asWWjTpg1q166NLVu24NWrV9i7d6/cZZOTk2Fubg5HR0ep+a6urkhOTi50Px06dMDIkSNRrVo1zJw5E2lpaWjUqBF69OiB6tWrY+rUqbh7966kP9uyZcvQunVrfPfdd6hevToGDRqEsWPH4scffwQA3L9/H4cPH8aGDRsQEBAAf39//Pbbb/j8+bNkn+fOncPly5exe/duNGzYENWqVcOSJUvg6OiIP//8U+VjRQghhJR64ux/BRNLiHEc4OnJL0eMUwkJwinNvqGwtgY+fdLa5kUiEdLS0mBvbw8TkwJxubV1sbZ9+fJliEQi9O3bF1lZWVLPNWzYUOrx3bt3MWLECKl5QUFBWCnOxqOCwMBAyf9OTk7w8fHB3bt3Vd5OUerUqSP539XVFQBQu3ZtmXmvX7+Gm5sb7t69iy5dukhtIygoCCtWrIBQKMTdu3dhamoKf39/yfO+vr5SwePff/+NT58+wdnZWWo7nz9/xr///qux10YIIYSUGuLsf92788FY/i4e4qBtxQrtpWKnsde0T9kU/M2bAyKR7sunJArQDAXHAQqaDWqESMR/MdjYAAUDNCV5e3uD4zgkJCRIza9SpQoAwMrKSmYdRU0hFREHjyzfh0oTyUXc3NyQnZ2NDx8+SAVCr169gpubW6HrmpmZSf4XN+GUN0+kwQ/6p0+fUL58eUm/u/wK1gISQgghREni7H/yxkFbsUJ746DR2Gu6oUoQbsABGjVxJEpzdnZGmzZtsHr1aqSnp6u1DT8/P5w/f15q3vnz51GjRg0AQNmyZQEAL/O1Dc6fMCS//Mk9UlJScP/+ffj5+cld1t/fH2ZmZjhx4oRkXkJCAhITE6Vq4jRB0WusXr06BAIBfH19kZubi/j4eKmyfPjwQfK4QYMGSE5OhqmpKby9vaUmFxcXjZaXEEIIKVXkZf97/Fi7wRmNvaY7haXg//NPowiIqQaNqGTNmjUICgpCw4YNMXv2bNSpUwcmJia4cuUK7t27J9VsT57JkycjPDwc9evXR0hICP766y9ER0dL0vNbWVkhICAACxcuROXKlfH69WvMmDFD7rbmzp0LZ2dnuLq64ttvv4WLiwtCQ0PlLuvg4IChQ4ciMjISTk5OsLe3x7hx4xAYGIiAgIBiHZOCJk6ciEaNGmHevHno2bMn4uLisHr1aqxZswYA4OPjg/bt22PkyJFYu3YtTE1NMWHCBKkayJCQEAQGBiI0NBSLFy9G9erV8eLFCxw8eBBdu3aVaTpKCCGEEBWIs/9pW1Fjr3Ecn/a9Sxdq7qhJYWH8MTXSJqVUg0ZUUrVqVVy/fh0hISGIiopC3bp10bBhQ6xatQqTJk3CvHnzCl0/NDQUK1euxJIlS1CzZk388ssv2LRpE1rm+5LcuHEjcnNz4e/vjwkTJuD777+Xu62FCxciIiIC/v7+SE5Oxl9//QVzc3OF+16+fDk6duyIbt26oUWLFnBzc0O0Fu5aNWjQALt27cKOHTtQq1YtzJw5E3PnzsWgQYMky2zatAkVKlRAcHAwwsLCMGLECJQrV07yPMdxOHToEFq0aIHBgwejevXq6NWrF54+fSrp80YIIYQQA0djr+lPwRT8RhKcAQDHmAqDYBGVpKWlwcHBAampqbC3t5fMz8zMxOPHj1G5cmVYWlrqpCyFJgkxMqdOnUKrVq2QkpJC/bEKoYnzLCcnB4cOHUKHDh2k+t0RUhg6b4i66Nwh6jDo82b7dqBPn6KX27aNDyRURYlH1KaP80ZRbFAQNXEkhBBCCCFEG7SZ9p0Sj5RYxl2VQgghhBBCiKHS1thrlHikRKMAjRidli1bgjFGzRsJIYQQYtjEad8B2SBN3bHXiko8AvCJR4RCVUtLDAQFaIQQQgghhGiLptO+U+KREs8gArSff/4ZXl5esLS0RJMmTXD58uVCl9+9ezd8fX1haWmJ2rVr49ChQ5LncnJyMHXqVNSuXRs2NjaoUKECBgwYgBcvXkiWOXXqFDiOkztduXIFAPDkyRO5z+cfe4sQQgghhJAiaXLstXxjxWpkOWJw9B6g7dy5E5GRkZg1axauXbuGunXrol27dnj9+rXc5S9cuIDevXtj6NChuH79OkJDQxEaGorbt28DADIyMnDt2jV89913uHbtGqKjo5GQkIDOnTtLttG0aVO8fPlSaho2bBgqV64sM77U8ePHpZYrapwvQgghhBBCZGgq7bs2E48Qg6D3LI7Lli3D8OHDMXjwYADAunXrcPDgQWzcuBHTpk2TWX7lypVo3749Jk+eDACYN28eYmJisHr1aqxbtw4ODg6IiYmRWmf16tVo3LgxEhMTUbFiRZibm8PNzU3yfE5ODv73v/9h3Lhx4Aq0D3Z2dpZalhBCCCGEEL0RJx5JSpLfD43j+OdVTTxCDIZeA7Ts7GzEx8cjKipKMs/ExAQhISGIi4uTu05cXBwiIyOl5rVr1w779u1TuJ/U1FRwHKcwqcT+/fvx7t07SZCYX+fOnZGZmYnq1atjypQpUjVxBWVlZSErK0vyOC0tDQAfAObk5Ejm5+TkgDEGkUgEkUikcHuaJB7uTrxfUvKJRCIwxpCTkwOBmnfpxOdt/vOXkKLQeUPURecOUUdpPG+4pUsh6NUL4Dhw+YI09l9Fg3DJEjCRCKBrPoX0cd4ouy+9Bmhv376FUCiEq6ur1HxXV1fcu3dP7jrJyclyl09OTpa7fGZmJqZOnYrevXsrHBDut99+Q7t27eDh4SGZZ2tri6VLlyIoKAgmJibYs2cPQkNDsW/fPoVB2oIFCzBnzhyZ+ceOHYO1tbXksampKdzc3PDp0ydkZ2fL3Za2fPz4Uaf7I/qTnZ2Nz58/48yZM8jNzS3WtgrWShOiDDpviLro3CHqKFXnjYUFyk+Zgtq//gqrd+8ksz87O+P20KF4aWEB5MvRQBTT5XmTkZGh1HJ6b+KoTTk5OQgPDwdjDGvXrpW7zPPnz3H06FHs2rVLar6Li4tUTV2jRo3w4sUL/PjjjwoDtKioKKl10tLS4OnpibZt20oFh5mZmXj27BlsbW1haWlZnJeo9ADyjDF8/PgRdnZ2Ms04ScmUmZkJKysrtGjRQu3zLCcnBzExMWjTpg3MzMw0XEJSUtF5Q9RF5w5RR6k9bzp0AGbPRu65c5ILQbNmzVBfIEB9fZfNCOjjvBG3riuKXgM0FxcXCAQCvHr1Smr+q1evFPb7cnNzU2p5cXD29OlTnDx5UmHt2aZNm+Ds7Fxo00WxJk2aFBplW1hYwMLCQma+mZmZ1BsvFArBcRxMTExgYqJ+nhZVBpAXN2sU77c4kpOTsWDBAhw8eBDPnz+Hg4MDvL290a9fPwwcOFCqttCQrF+/Htu2bcO1a9fw8eNHpKSklOix1ExMTMBxnMz5pw5NbIOUPnTeEHXRuUPUUSrPGzMzICRE36Uwaro8b5Tdj16zOJqbm8Pf3x8nTpyQzBOJRDhx4gQCAwPlrhMYGCi1PMBXTeZfXhycPXjwAMePH4ezs7PcbTHGsGnTJgwYMECpA3bjxg2UN5CMOPoaQP7Ro0eoX78+jh07hvnz5+P69euIi4vDlClTcODAARw/flzhuvpuG56RkYH27dtj+vTpei0HIYQQQgghiug9zX5kZCQ2bNiALVu24O7duxg1ahTS09MlCTsGDBgglUQkIiICR44cwdKlS3Hv3j3Mnj0bV69exdixYwHwQUD37t1x9epVbN26FUKhEMnJyUhOTpbp73Xy5Ek8fvwYw4YNkynXli1bsH37dty7dw/37t3D/PnzsXHjRowbN06LR0M5+hxAfvTo0TA1NcXVq1cRHh4OPz8/VKlSBV26dMHBgwfRqVMnybIcx2Ht2rXo3LkzbGxs8MMPPwAA1q5di6pVq8Lc3Bw+Pj74/fffJeuIx5+7ceOGZN6HDx/AcRxOnToFIG8cu4MHD6JOnTqwtLREQECAZKgFRSZMmIBp06YhICBAcweEEEIIIYQQDdJ7H7SePXvizZs3mDlzJpKTk1GvXj0cOXJEkggkMTFRqkle06ZNsW3bNsyYMQPTp09HtWrVsG/fPtSqVQsAkJSUhP379wMA6tWrJ7Wv2NhYtGzZUvL4t99+Q9OmTeHr6yu3bPPmzcPTp09hamoKX19f7Ny5E927d9fgq1ePKgPI53u5xfbu3TtJzZmNjY3cZQr2b5s9ezYWLlyIFStWwNTUFHv37kVERARWrFiBkJAQHDhwAIMHD4aHhwdatWqlUnkmT56MlStXws3NDdOnT0enTp1w//790te8gRBCCCGElBh6D9AAYOzYsZIasILEtSb59ejRAz169JC7vJeXlySlfFG2bdum8LmBAwdi4MCBSm1H1/Q1gPzDhw/BGIOPj4/UfBcXF2RmZgIAxowZg0WLFkme69Onj9TwBb1798agQYMwevRoAHwN6sWLF7FkyRKVA7RZs2ahTZs2APgaTw8PD+zduxfh4eFqvT5CCCGEEEL0Te9NHInqDG0A+cuXL+PGjRuoWbOm1DhwANCwYUOpx3fv3kVQUJDUvKCgINy9e1fl/ebvd+jk5AQfHx+1tkMIIYQQUuIIhcCpU8D27fxfbfR9IVphEDVoRDX6GkDe29sbHMchISFBan6VKlUAAFZWVjLrKGoKqYi4OWv+WlB9JxchhBBCCDEqqqT6JgaHatCMkEDAf74APhjLT/x4xQr546EVh7OzM9q0aYPVq1cjPT1drW34+fnh/PnzUvPOnz+PGjVqAADKli0LAHiZr31m/oQh+V28eFHyf0pKCu7fvw8/Pz+1ykUIIYQQUiLoK9U30RiqQTNSYWHAn3/KvzmyYoX2bo6sWbMGQUFBaNiwIWbPno06derAxMQEV65cwb179+Dv71/o+pMnT0Z4eDjq16+PkJAQ/PXXX4iOjpak57eyskJAQAAWLlyIypUr4/Xr15gxY4bcbc2dOxfOzs5wdXXFt99+CxcXF4SGhirctzib58OHDwEAt27dgp2dHSpWrAgnJyf1DgghhBBCSHEJhXx2t/8GnEbz5urdaS8q1TfH8am+u3TR/J18fWMMyMwEPnwAUlOl/wYF8RfJRoICNCMWFsZ/vjTxeVZW1apVcf36dcyfPx9RUVF4/vw5LCwsUKNGDUyaNEmS/EOR0NBQrFy5EkuWLEFERAQqV66MTZs2SWXX3LhxI4YOHQp/f3/4+Phg8eLFaNu2rcy2Fi5ciIiICDx48AD16tXDX3/9BXNzc4X7XrduHebMmSN53KJFCwD8YOWDBg1S7UAQQgghhGiCJpsj6ivVt5imAk0xkQh4/Zov84sX/P+vXvGT+P/Xr4G3b/lgrMCQWhK7d/O1h0aCAjQjJxBo5/NVmPLly2PVqlVYtWpVocspyqY5atQojBo1SuF6fn5+uHDhQpHbatasWZFjn+U3e/ZszJ49W+nlCSGEEEK0StwcseB1jrg54p9/qhak6SvVN6BeoCkS8a/14UN+evKED8YSE/m/z58rDroU4TjAwQFwdOQnBwd+MiIUoBFCCCGEEKJr2miOqItU3/Jqyf73v8IDzU2bgCpVgDt3gAcP+GDswQPg33+BAhnAZXAcvx93d8DVlZ/KlZP+6+IClCnDB2K2toCJcafZoACNEEIIIYQQXdNGc0Rtp/qWV0vm7s73/VIUaAJAYV1JTE2BypUBb2/+b8WKgKdn3t8KFQAzM/XKa6QoQCNGp2XLlkoPRk4IIYQQYpC00RxRnOq7e3c+GMt/vVTcVN+FNcdUhqsr0KAB4OvLB2PiqWJFPkgjEnQ0CCGEEEII0TVtNUfURqrv9HTg66/l15Ipa/lyoHdv9dcvRShAI4QQQgghRNe02RyxuKm+ExOBc+eAixf56fp1IDdX9XLkV5x+b6UMBWiEEEIIIaWNptOhE9VpszmiePvK9F1jjE/aceYMP50+DTx9qt4+5Sluv7dSiAI0QgghhJDSRJPjbpHi0UZzRGU8fgzExAAnT/JBWcF+bgIB31+saVMgIICfp07zRE0EmqUQBWiEEEIIIaWFpsfdIsVX3OaIynj/ng/Gjh/nA7NHj6SfNzcHmjQBWrTgp6ZN+XT1YkIhMHly4c0xnZwAKyvdBpolFAVohBBCCCGlgTbG3SKaoWxzRGUJhcCVK8DBg8DRo8DVq9Lvu6kpXzMWEsLvt3FjPrgqrHxFNcdcv177gWYpQQEaIQaiZcuWqFevHlasWKHU8ps3b8aECRPw4cMHrZaLEEJICaGNcbeI4Xj/Hjh2jA/KjhwB3r6Vfr5GDaBNGz4oCw4G7OxU276yzTHp3Ck2CtCIypKTk7FgwQIcPHgQz58/h4ODA7y9vdGvXz8MHDgQ1tbW+i6iXOvXr8e2bdtw7do1fPz4ESkpKXB0dNR3sQghhBDd0Ma4W0S/7t8H9u0D/voLuHABEInynnNwANq1Azp04AOzChWKvz9dNMckFKAR1Tx69AhBQUFwdHTE/PnzUbt2bVhYWODWrVtYv3493N3d0blzZ7nr5uTkwEyPI8FnZGSgffv2aN++PaKiovRWDkIIIUQvtDXuFtEdxoD4eD4o27sXuHNH+vmaNYGvvuKnwEBAG9ddmm6OSWSY6LsAhMcYPwagPiZVxhwcPXo0TE1NcfXqVYSHh8PPzw9VqlRBly5dcPDgQXTq1EmyLMdxWLt2LTp37gwbGxv88MMPAIC1a9eiatWqMDc3h4+PD37//XfJOk+ePAHHcbhx44Zk3ocPH8BxHE6dOgUAOHXqFDiOw8GDB1GnTh1YWloiICAAt2/fLrTsEyZMwLRp0xAgzkakhJYtW2LcuHGYMGECypQpA1dXV2zYsAHp6ekYPHgw7Ozs4O3tjcOHD0utd/r0aTRu3BgWFhYoX748pk2bhtx844ekp6djwIABsLW1Rfny5bF06VKZfWdlZWHSpElwd3eHjY0NmjRpIjkGhBBCiMrE426J+wwVxHGApyelQzc0QiFw6hQwbhxQsSLQqBHwww98cGZqCrRtC/z8M/DkCXD7NrBoEZ/oQ483xUnxUIBmIDIy+GQ52prs7U3g4eEIe3sTmecyMpQr47t373Ds2DGMGTMGNjY2cpfhCnzpz549G127dsWtW7cwZMgQ7N27FxEREZg4cSJu376NkSNHYvDgwYiNjVX5mE2ePBlLly7FlStXULZsWXTq1Ak5OTkqb6coW7ZsgYuLCy5fvoxx48Zh1KhR6NGjB5o2bYpr166hbdu26N+/PzL+O5BJSUno0KEDGjVqhL///htr167Fb7/9hu+//16q7KdPn8b//vc/HDt2DKdOncK1a9ek9jt27FjExcVhx44duHnzJnr06IH27dvjwYMHGn+NhBBCSgFxogdANkijdOiGRSTi09+PHQu4uwOtWgGrV/N9v2xs+GQdW7cCb97wSUBGjwYqVdJ3qYmmMKI1qampDABLTU2Vmv/582d2584d9vnzZ8m8T58Y4+uydD99+qTc67l48SIDwKKjo6XmOzs7MxsbG2ZjY8OmTJkimQ+ATZgwQWrZpk2bsuHDh0vN69GjB+vQoQNjjLHHjx8zAOz69euS51NSUhgAFhsbyxhjLDY2lgFgO3bskCzz7t07ZmVlxXbu3Fnk6xCvn5KSUuSywcHBrFmzZpLHubm5zMbGhvXv318y7+XLlwwAi4uLY4wxNn36dObj48NEIpFkmZ9//pnZ2toyoVDIPn78yMzNzdmuXbtkyh8REcEYY+zp06dMIBCwpKQkqfK0bt2aRUVFMcYY27RpE3NwcFBYdnnnmaqys7PZvn37WHZ2ttrbIKUPnTdEXXTu6MiePYx5eEhfDHh68vONUIk5b4RCxs6fZ2z8eMYqVJB+f8qUYWzwYMb++ouxjAx9l7RE0Md5oyg2KIj6oBkIa2vg0yftbV8kEiEtLQ329vYwMZGuOC1uTo/Lly9DJBKhb9++yMrKknquYcOGUo/v3r2LESNGSM0LCgrCSvEdPRUEBgZK/ndycoKPjw/u3r2r8naKUqdOHcn/AoEAzs7OqF27tmSeq6srAOD169cA+NcYGBgoVZsYFBSET58+4fnz50hJSUF2djaaNGkiU36xW7duQSgUonr16lJlycrKgrOzs2ZfICGEEOMlFKqesIESPRiWf/4B/viDrxF79ixvvoMD0LUrEB7OZ16kJoulBgVoBoLj+BprbRGJ+O9wGxvARM2Grd7e3uA4DgkJCVLzq1SpAgCwkjN+hqKmkIqIg0eWr2OcNpotqqJgYhOO46TmiQMxUf7MScX06dMnCAQCxMfHQ1DgB9M2/8CRhBBCSq/oaPkpz1euLHpgYEr0oF8vXgDbt/OBWb5+97Cz44Pnnj35zIsWFnorItEf6oNGlObs7Iw2bdpg9erVSE9PV2sbfn5+OH/+vNS88+fPo0aNGgCAsmXLAgBe5kvxmz9hSH4XL16U/J+SkoL79+/Dz89PrXJpkp+fH+Li4qSCzPPnz8POzg4eHh6oWrUqzMzMcOnSJcnz4vKL1a9fH0KhEK9fv4a3t7fU5ObmptPXQwghxABFR/P9kAqOa5aUxM+PjtZPuYhi6enA//0fH3h5eACTJvHBmZkZH5Tt3g28egX8/jvQsSMFZ6UY1aARlaxZswZBQUFo2LAhZs+ejTp16sDExARXrlzBvXv34O/vX+j6kydPRnh4OOrXr4+QkBD89ddfiI6OxvHjxwHwtXABAQFYuHAhKleujNevX2PGjBlytzV37lw4OzvD1dUV3377LVxcXBAaGqpw38nJyUhOTsbDhw8B8M0I7ezsULFiRTg5Oal3QOQYPXo0VqxYgXHjxmHs2LFISEjArFmzEBkZCRMTE9ja2mLo0KGYPHkynJ2dUa5cOXz77bdSTU+rV6+Ovn37YsCAAVi6dCnq16+PN2/e4MSJE6hTpw6++uorjZWXEEKIkREK+ZozeWmYGeOb5UyYwF/0U7NF/WKMH59s0yZg507p/ixBQUC/fkCPHgB1XyD5UIBGVFK1alVcv34d8+fPR1RUFJ4/fw4LCwvUqFEDkyZNwujRowtdPzQ0FCtXrsSSJUsQERGBypUrY9OmTWiZr5nFxo0bMXToUPj7+8PHxweLFy9G27ZtZba1cOFCRERE4MGDB6hXrx7++usvmJubK9z3unXrMGfOHMnjFi1aAAA2bdqEQYMGqXYgCuHu7o5Dhw5h8uTJqFu3LpycnDB06FCpQPPHH3/Ep0+f0KlTJ9jZ2WHixIlITU2V2s6mTZvw/fffY+LEiUhKSoKLiwsCAgLQsWNHjZWVEEKIETp7VrbmLD/G+L5MZ89SM0Z9efGCry3btIkfTFqsalVgwAA+MPuviwghBXGMybv9QjQhLS0NDg4OSE1Nhb29vWR+ZmYmHj9+jMqVK8PS0lInZSksSYixOXXqFFq1aoWUlBQ4OjrquzgGSxPnWU5ODg4dOoQOHTrodZBxYlzovCHqonNHSdu3A336FL3ctm1A797aL4+eGcx5k5sLHDwIbNgAHD7MJwAA+Gxs4eHA4MF8MhZF49ARndLHeaMoNiiIatAIIYQQQoxJ+fKaXY4UT2Ii8OuvwG+/8TVnYkFBwJAhfBNGOzv9lY8YHQrQCCGEEEKMSfPmfJKJpCT5/dA4jn++eXPdl620yM3la8l++UW6tszFha8pGzoUyDd8jlFRZ+gGolEUoBGj07JlS1DLXEIIIaWWQMCn0u/enQ/G8v8mipvPrVhBF9XaCDReveKbMP7yi3Q/wFatgBEj+HHLjDn7YnGGbiAaY9ydkQghhBBCSqOwMODPPwF3d+n5Hh78/NJ+MR0dDXh58YFTnz78Xy8v9YYfYAyIi+MTe3h6At99xwcwzs7AxIlAQgJw8iTQq5fxB2c0dINBoBo0PaJaIKJNdH4RQkgJFxbGp9Kn5mjSxIFGwd9BcaChbAD7+TOwYwewejVw7Vre/CZNgDFj+L5lOkr2pnU0dINBoQBND8SZYjIyMmBlZaXn0pCSKiMjAwAoExohhJRkAgGl0s9PE4FGUhIflK1fD7x/z8+zsOAzYo4ZAzRsqLXi6w0N3WBQKEDTA4FAAEdHR7x+/RoAYG1tDU7LKVdFIhGys7ORmZlp9Gn2SeEYY8jIyMDr16/h6OgIAd3pIoQQUloUJ9C4cgVYvhzYvZtPAgIAlSoBo0fz2RhdXLRWbL17+VKzy5FioQBNT9zc3ABAEqRpG2MMnz9/hpWVldaDQWIYHB0dJecZIYQQUiqoGmjk5gL/+x8fmJ0/n/d8cDBf09apU+lo0kdDNxgUgwjQfv75Z/z4449ITk5G3bp1sWrVKjRu3Fjh8rt378Z3332HJ0+eoFq1ali0aBE6dOgAgB90bsaMGTh06BAePXoEBwcHhISEYOHChahQoYJkG15eXnj69KnUdhcsWIBp06ZJHt+8eRNjxozBlStXULZsWYwbNw5TpkzRyGvmOA7ly5dHuXLlkJOTo5FtFiYnJwdnzpxBixYtqMlbKWBmZkY1Z4QQQrTDkNOwKxtAODrymS5XrADE14NmZnyijwkTgAYNtFM+Q0VDNxgUvQdoO3fuRGRkJNatW4cmTZpgxYoVaNeuHRISElCuXDmZ5S9cuIDevXtjwYIF6NixI7Zt24bQ0FBcu3YNtWrVQkZGBq5du4bvvvsOdevWRUpKCiIiItC5c2dcvXpValtz587F8OHDJY/t8g0imJaWhrZt2yIkJATr1q3DrVu3MGTIEDg6OmLEiBEae/0CgUAnF9ICgQC5ubmwtLSkAI0QQggh6jH0NOxFBRoAP2h0nz7Ahw/8YxcX4Ouv+aaMpbWGiIZuMCh674y0bNkyDB8+HIMHD0aNGjWwbt06WFtbY+PGjXKXX7lyJdq3b4/JkyfDz88P8+bNQ4MGDbB69WoAgIODA2JiYhAeHg4fHx8EBARg9erViI+PR2JiotS27Ozs4ObmJplsbGwkz23duhXZ2dnYuHEjatasiV69emH8+PFYtmyZ9g4GIYQQQoihMoY07OJAA8gLLAr6+JEPzqpX58czS0wE5s0rvcGZGA3dYDD0WoOWnZ2N+Ph4REVFSeaZmJggJCQEcXFxcteJi4tDZGSk1Lx27dph3759CveTmpoKjuPg6OgoNX/hwoWYN28eKlasiD59+uCbb76BqampZD8tWrSAubm51H4WLVqElJQUlClTRmY/WVlZyMrKkjxOS0sDwDcv1EUzxsKI96/vchDjQucNUQedN0RddO4YMKEQpuPHA4xBJuxhDIzjgIgI5HbooPNaFpnzplMncDt2QBAZCS4pSWZ5UWAgRJGRYJ06AeLEaYZ8zgmF4M6dkzQpZc2aae8Yd+oEdOggf3+GfIzUoI/vG2X3pdcA7e3btxAKhXB1dZWa7+rqinv37sldJzk5We7yycnJcpfPzMzE1KlT0bt3b9jb20vmjx8/Hg0aNICTkxMuXLiAqKgovHz5UlJDlpycjMqVK8vsR/ycvABtwYIFmDNnjsz8Y8eOwdraWm75dC0mJkbfRSBGiM4bog46b4i66NwxPM63bqGZnGBHjGMMeP4cl5YswbvatXVYsjyS84YxlL1zB9UdHeHyX5kZxyG5YUM8DAvDez8/frkjR/RSTlWUj4tD7V9/hdW7d5J5n52dcWvYMLwMDNTuzu3tgfR04OhR7e5Hz3T5fSMeAqkoeu+Dpk05OTkIDw8HYwxr166Vei5/LVydOnVgbm6OkSNHYsGCBbBQcxT4qKgoqe2mpaXB09MTbdu2lQoO9SEnJwcxMTFo06YN9UEjSqPzhqiDzhuiLjp3DBf3X6ugogRUqgT2X+I2XZGcN61bw/zgQQgWLQJ3/ToAgJmZgfXvD+E338DFxwfGlCif27sXgsWLZfrSWb5/j0aLF0O4YwdY1656Kp3x08f3TZqSnyO9BmguLi4QCAR49eqV1PxXr14pTA/u5uam1PLi4Ozp06c4efJkkQFSkyZNkJubiydPnsDHx0fhfsRlkMfCwkJucGdmZmYwPzSGVBZiPOi8Ieqg84aoi84dA+TpqdRipp6efDZEXcrJgefJk7CaOhVcQgI/z9oaGDkSXGQkOA8P/SddUJVQCEycKDfRCfffgNumkyYB3bpR4o5i0uX3jbL70ev5am5uDn9/f5w4cUIyTyQS4cSJEwhUUG0bGBgotTzAV03mX14cnD148ADHjx+Hs7NzkWW5ceMGTExMJJkjAwMDcebMGam2ojExMfDx8ZHbvJEQQgghpMQSZ0dUlHiD4/ggTpdp2LOygF9+gWmNGmjw0098cOboCMycyafOX7aML7MxUmXAbVLi6P2GQmRkJDZs2IAtW7bg7t27GDVqFNLT0zF48GAAwIABA6SSiERERODIkSNYunQp7t27h9mzZ+Pq1asYO3YsAD446969O65evYqtW7dCKBQiOTkZycnJyM7OBsAnAFmxYgX+/vtvPHr0CFu3bsU333yDfv36SYKvPn36wNzcHEOHDsU///yDnTt3YuXKlTIJSgghhBBCSrzCsiPqOg17ZiawejXg7Q18/TW4p0+R6egI4YIFfGA2Zw6fOt+YqTrgNilR9N4HrWfPnnjz5g1mzpyJ5ORk1KtXD0eOHJEk5EhMTISJSV4c2bRpU2zbtg0zZszA9OnTUa1aNezbtw+1atUCACQlJWH//v0AgHr16kntKzY2Fi1btoSFhQV27NiB2bNnIysrC5UrV8Y333wjFXw5ODjg2LFjGDNmDPz9/eHi4oKZM2dqdAw0QgghhBCjIU7DLm8ctBUrtJ+GPSMDWL8eWLw4LzCpUAHCyZMRU6EC2nftCkFJaRqrbMr/0j40QAml9wANAMaOHSupASvo1KlTMvN69OiBHj16yF3ey8sLTNHAhP9p0KABLl68WGS56tSpg7NUdUwIIYQQwgsLA7p04ZvW/ZeGHc2ba7fmLCMDWLMG+PFH4PVrfp6nJxAVBQweDJFAANGhQ9rbvz4UNeA2x/HP67JJKdEZgwjQCCGEEEKIkRAIgJYttb+fz5+BdeuARYsAceK2ypWB6dOBAQMA8Vi1JWx8LgB5TUq7d+eDsfxBmq6blBKd03sfNEIIIYQQQiQyM4GffgKqVgUiI/ngrHJlYONGICEBGDYsLzgrycRNSt3dped7ePDztd2klOgN1aARQgghhBD9y8oCfvsNmD+fb9oHAJUqAd99x9eYlZT+ZarQR5NSbREKS8br0AEK0AghhBBCiP7k5gJbtvDZF5894+d5egLffgsMHlw6assKo6smpdoUHS0/uczKlVQTKAcFaIQQQgghRPdEImDXLn7csgcP+HkVKvCB2dChgIWFfsunDqolkhUdzfelK5jsJCmJn0/NNWVQgEYIIYQQQnSHMeDAAWDGDODmTX6eiwuf/OPrrwErK6nFjSbmoVoiWUIhf0zkZaJkjE94MmEC34zTIN9U/aAkIYQQQgghRDdOngQCA4HOnfngzN4emDcPePQI+OYbmeAsOhrw8gJatQL69OH/ennx8w2KuJYof3AG5NUSGVyBdeTsWdljkh9jfLNWGtZKCgVohBBCCCFEu65dA9q2BVq3Bi5d4gOxadOAx4/5mjQ7O5lVjCbmKaqWCOBriYRCnRbLIIgHFNfUcqUEBWiEEEIIIUQ7Hj4EevUC/P2BmBg+E+PYsXyN2YIFgJMTv5xQCJw6BWzfDpw6BWG20HhiHqolUqx8ec0uV0pQHzRCCCGEEKJZycnA3LnAhg18lkaO49sozp0LVKkivaycvltnXbrj+dvdCjefP+YJCtLWi1AS1RIp1rw53w8vKUl+tM1x/PPNm+u+bAaMAjRCCCGEkPyMJiuFAUpNBX78EVi+HMjI4Od9+SVfW1a3ruzyCjL8vXyr3JhnBhHzUC2RYgIBnySle3c+GMv/PnMc/3fFCvp8FUBNHAkhhBBCxIwmK4WByc4GVq0CvL2BH37gg7MmTfhmi4cOyQ/OCum7VR4vlNqtQcQ84loiccBREMfx47qV1lqisDA+lb67u/R8Dw9Ksa8ABWiEEEIIIYARZaUwIIzxF9k1awLjxwNv3wI+PvyxiosDgoMVr1tI363mOAsPPAMHkdznDSrmEdcSAbJBGtUS8cLCgCdPgNhYYNs2/u/jxxScKUABGiGEEEIIZeJT3blzfMr8Hj34ZCCursC6dcDt20DXroprlMQKaZ8ogAgrEQEA4CD9nkjFPBCCO30a7mfOgDt9WjPvT4GEJUptk2qJiiYQAC1bAr17839Lc8BaBArQCCGEEEIoE5/yEhKA0FC++urSJcDaGpg1C3jwABg5EjBVMsVBEe0Tw7AXf6I73MtmSc2XxDzgm6OatmmDhsuWwbRNm+I3Ry1OE1eqJSIaonKA5uXlhblz5yIxMVEb5SGEEEII0T3KxFe0t2+BceOAWrWA//2PrwEZOZKvPZs9W+5YZoVSou9WmOdVPHluJhvzQAvNUTXRxJVqiYgGqBygTZgwAdHR0ahSpQratGmDHTt2ICsrq+gVCSGEEEIMlaYy8anTPM7QZWXxmRm9vYHVq/m0+Z06Abdu8U0a1c3UoWTfLYG5QDrmgRaao1ITV2JA1ArQbty4gcuXL8PPzw/jxo1D+fLlMXbsWFy7dk0bZSSEEEII0S5NZOIraRkgGQN27QJ8fYEpU/gU+vXqASdOAPv3A35+suuoGqCq03dLG81RqYkrMSBq90Fr0KABfvrpJ7x48QKzZs3Cr7/+ikaNGqFevXrYuHEjmLw7EIQQQgghhqi4mfhKWgbIixf5EaB79uT7VVWoAGzaBFy9Cnzxhfx11A1QVe27pY3mqNTElRgQtQO0nJwc7Nq1C507d8bEiRPRsGFD/Prrr+jWrRumT5+Ovn37arKchBBCCCHapW4mvpLUPO7ZM6BvXz47Y1wcnwBkzhzg/n1g0CDtBaiq9N3SxsDQNNg0MSBKptnJc+3aNWzatAnbt2+HiYkJBgwYgOXLl8PX11eyTNeuXdGoUSONFpQQQgghROvCwoAuXfimbC9f8hfkzZsXHjCo0jyuZUuNF1kj0tOBxYv5vmafP/O1hoMGAd9/z9eeFaaoAJXj+AC1SxfNJM0QN0dNSpK/T47jn1dlkDRtbJMQNakcoDVq1Aht2rTB2rVrERoaCjMzM5llKleujF69emmkgIQQQgghOiWuzVGWMTePE4n4ZoXTpvHBCcAHIStWAA0aKLcNXQeo4uao3bvzgVP+gErdgaFV2aZQqFoAT4iKVG7i+OjRIxw5cgQ9evSQG5wBgI2NDTZt2lTswhFCCCGEGDxjbR4XF8c3Zezfnw/OvLz4ppynTysfnAH6CVC1MTC0MtssaYlgiEFSOUBr1aoV3r17JzP/w4cPqFKlikYKRQghhBBiNDSRAVKXkpL4oKxpU+DyZcDWFli4ELh7F+jWTfHrUERfAep/yUVyY2JwNTISuTExxR8YurCEJSUtEQwxWCo3cXzy5AmEcjq5ZmVlIUlcNU4IIYQQUlpoo8mdNmRmAkuXAvPnAxkZfNkGDwZ++AFwc1N/u/rsvyUQgAUHIyk9HXWDgzVzjOU1cdV1PztSqikdoO3fv1/y/9GjR+Hg4CB5LBQKceLECXh5eWm0cIQQQgghRkHcPC4iQrqGxcODD86KU6tTXIwBe/cCEyfytUMAX3u2ciXQsGHxt28sAWpxlIREMMRoKB2ghYaGAgA4jsPAgQOlnjMzM4OXlxeWLl2q0cIRQgghhBgNdTJAatutW3zQGBvLP3Z357M19u6telPGwhhygKoJxpwIhhgdpQM0kUgEgM/QeOXKFbi4uGitUIQQQgjRH0pSpz4hBDiLlngJoDyA5gD0cuhSUoCZM4E1a/hMjRYWwOTJfLZGGxvt7NMQA1RNMdZEMMQoqdwH7fHjx9ooByGEEEIMQHS0/EqQlSuNvxJE2wzi2AmFwMaNwPTpwNu3/LywML7vmS66oqg6RIGxoHHSiA4pFaD99NNPGDFiBCwtLfHTTz8Vuuz48eM1UjBCCCGE6JY4SV3B609xkjp1s5eXBgZx7C5eBMaOBeLj+cd+fsBPPwEhIVresZKMuWq2NPSzIwZDqQBt+fLl6Nu3LywtLbF8+XKFy3EcRwEaIYQQYoQoSZ36tH7sigpskpP5potbtvCP7e2BOXOAMWMABWPW6pxBVC8WU0nvZ0cMhlIBWv5mjdTEkRBCCCl5KEmd+rR67AoLbDp1AlavBmbNAj5+5J8bMoRPo+/qqurL0B6DqF7UkJLcz44YDJX7oBFCCCGk5KEkderT2rErLLDp1o0f/PrZM35eo0Z8sNa4sYo70bKSWDVbUvvZEYOhVIAWGRmp9AaXLVumdmEIIYQQoh+UpE59Wjl2RQU2AB+cOTsDCxfyNWcmJirsQEeoapYQlSn1Sb5+/bpS040bN9QqxM8//wwvLy9YWlqiSZMmuHz5cqHL7969G76+vrC0tETt2rVx6NAhyXM5OTmYOnUqateuDRsbG1SoUAEDBgzAixcvJMs8efIEQ4cOReXKlWFlZYWqVati1qxZyM7OllqG4ziZ6eLFi2q9RkIIIcSQiZPUKRoai+P4ChtKUidLK8euqMBGbONGYNgwwwzOAKqaJUQNStWgxYoHN9SCnTt3IjIyEuvWrUOTJk2wYsUKtGvXDgkJCShXrpzM8hcuXEDv3r2xYMECdOzYEdu2bUNoaCiuXbuGWrVqISMjA9euXcN3332HunXrIiUlBREREejcuTOuXr0KALh37x5EIhF++eUXeHt74/bt2xg+fDjS09OxZMkSqf0dP34cNWvWlDx2dnbW2rEghBBC9IWS1KlPK8dO2YAlPV2FjeoBVc0SojK9325ZtmwZhg8fjsGDB6NGjRpYt24drK2tsXHjRrnLr1y5Eu3bt8fkyZPh5+eHefPmoUGDBli9ejUAwMHBATExMQgPD4ePjw8CAgKwevVqxMfHIzExEQDQvn17bNq0CW3btkWVKlXQuXNnTJo0CdHR0TL7c3Z2hpubm2QyM5RsSIQQQoiGiZPUubtLz/fwMK48DkoRCoFTp4Dt2/m/QmGxNqfxY1dSAhuqmiVEZUrVoIWFhWHz5s2wt7dHWBHfMPKCHEWys7MRHx+PqKgoyTwTExOEhIQgLi5O7jpxcXEyfeLatWuHffv2KdxPamoqOI6Do6Njocs4OTnJzO/cuTMyMzNRvXp1TJkyBZ07d1a4jaysLGRlZUkep6WlAeCbXebk5ChcTxfE+9d3OYhxofOGqIPOG+PWqRPQoQNw7hwnSVLXrBmDQABo+y3V1bnD7d0LQWQkuKQkyTzm7g7hsmVgXbuqvV2NHbucHJhcvAgTjgMnrw8aAMZxgLs7cgMCtP/GFBO3dCkEvXoBBV4P+y9oEy5ZAiYSASKRWtun7xyiDn2cN8ruS6kAzcHBAdx/HyIHBwf1S1XA27dvIRQK4VogFayrqyvu3bsnd53k5GS5yycnJ8tdPjMzE1OnTkXv3r1hb28vd5mHDx9i1apVUs0bbW1tsXTpUgQFBcHExAR79uxBaGgo9u3bpzBIW7BgAebMmSMz/9ixY7C2tpa7jq7FxMTouwjECNF5Q9RB543xs7fnW9AdParb/Wrz3CkfF4dGixbJPpGUBEHPnrgydSpeBgYWez9yj51QCOc7d2CZkoLMMmXwrkYNmXaPzrdvo8769bD/r9WPOJzJX//EAIAxXOnbFy8Le3OU2J9OWFig/JQpqP3rr7B6904y+7OzM24PHYqXFhZAvnwC6qLvHKIOXZ43GRkZSi3HMabg1owOvHjxAu7u7rhw4QIC830ZTpkyBadPn8alS5dk1jE3N8eWLVvQu3dvybw1a9Zgzpw5ePXqldSyOTk56NatG54/f45Tp07JDdCSkpIQHByMli1b4tdffy20vAMGDMDjx49x9uxZuc/Lq0Hz9PTE27dvFQaHupKTk4OYmBi0adOGmmkSpdF5Q9RB5w1Rl9bPHaEQpt7eQFIS5DW4k9RKPXig8UCmyFq75GQIpk2DybZt/HPOzhDOnw/Y20MwaZL0eh4eEC5dWmhtn7ZqCYtFKAR37pxk/DDWrJlGjjN95xB16OO8SUtLg4uLC1JTUwuNDdQeB+3169dISEgAAPj4+MhN6FEUFxcXCAQCmcDq1atXcHNzk7uOm5ubUsvn5OQgPDwcT58+xcmTJ+UehBcvXqBVq1Zo2rQp1q9fX2R5mzRpUmiUbWFhAQsLC5n5ZmZmBvOFYUhlIcaDzhuiDjpviLq0du6cP8+PIaYAxxjw/DnMLl7UbMr36GigVy+ZlPncixcw7dmTz8K4ezeQmsr3yRoxAtz8+TAVd73o0UNqYGSueXOYFhbYFLa/Xr3016HQzAwICdHi5uk7h6hOl+eNsvtROUlIWloa+vfvD3d3dwQHByM4OBju7u7o168fUlNTVdqWubk5/P39ceLECck8kUiEEydOSNWo5RcYGCi1PMBXTeZfXhycPXjwAMePH5ebeTEpKQktW7aEv78/Nm3aBBMl0tPeuHED5Q29My4hhBBC5NNHyndlxjP79Vc+OPP3By5eBNatA/L3ixcPjNy7N/+3sOBMmf1NmFDspCiEEO1RuQZt+PDhuH79Og4cOCAJiuLi4hAREYGRI0dix44dKm0vMjISAwcORMOGDdG4cWOsWLEC6enpGDx4MAC+WaG7uzsWLFgAAIiIiEBwcDCWLl2Kr776Cjt27MDVq1clNWA5OTno3r07rl27hgMHDkAoFEr6pzk5OcHc3FwSnFWqVAlLlizBmzdvJOUR18Rt2bIF5ubmqF+/PgA++cnGjRuLbAZJCCGEEAOlj8yIyo5nFhEBLF1a/CZ/NDA0IUZP5QDtwIEDOHr0KJo1ayaZ165dO2zYsAHt27dXuQA9e/bEmzdvMHPmTCQnJ6NevXo4cuSIJBFIYmKiVO1W06ZNsW3bNsyYMQPTp09HtWrVsG/fPtSqVQsAXzO2f/9+AEC9evWk9hUbG4uWLVsiJiYGDx8+xMOHD+Hh4SG1TP4uefPmzcPTp09hamoKX19f7Ny5E927d1f5NRJCCCHEAIhTviclya9h4jj+eU2mfFe2Nq5JE830e6OBoQkxeioHaM7OznIzOTo4OKBMmTJqFWLs2LEYO3as3OdOnTolM69Hjx7o0aOH3OW9vLxQVN6TQYMGYdCgQYUuM3DgQAwcOLDQZQghhBBiRPQxGreua+1KyvhphJRiKvdBmzFjBiIjI6XS2icnJ2Py5Mn47rvvNFo4QgghhBCN0vVo3P7+gJ2d4uc1PVAzDQxNiNFTqgatfv36knHQAODBgweoWLEiKlasCIBvhmhhYYE3b95g5MiR2ikpIYQQQogmhIUBXbpIZUZE8+aaHyPswAFg7Fjg40f5z2uj1k4ftYSEEI1SKkALDQ3VcjEIIYQQQnRInBlRGxIT+aQf+/bxjytWBPr0Af74QzqBh4cHHyxputZOXEsYEaGb/RFCNEqpAG3WrFnaLgchhBBCiHHLyQF++gmYNQtITwdMTYHISGDmTMDGBvj+e+3X2onpqpaQEKJxag9UTQghhBCiEqGw5AYMFy8CI0cCN2/yj5s1A9auBf7LMg1Au7V28uh6f4QQjVA5QBMKhVi+fDl27dqFxMREZGdnSz3//v17jRWOEEIIISVEdLT8JncrVxp3k7uUFCAqCli/nu/v5ewM/PgjMHAgYKJyLjZCCFE9i+OcOXOwbNky9OzZE6mpqYiMjERYWBhMTEwwe/ZsLRSREEIIIUYtOppPWlFwAOWkJH5+dLR+ylUcjAFbtwK+vsAvv/CPBw8G7t3j/1JwRghRk8rfHlu3bsWGDRswceJEmJqaonfv3vj1118xc+ZMXLx4URtlJIQQQoixEgr5mjN5Y5SK502YwC9nLO7fB9q0Afr1A16/Bvz8gNOngY0bARcXfZeOEGLkVA7QkpOTUbt2bQCAra0tUlNTAQAdO3bEwYMHNVs6QgghhBi3s2dla87yYwx49oxfztBlZQFz5gC1awMnTgCWlsD8+cCNG0CLFvouHSGkhFC5D5qHhwdevnyJihUromrVqjh27BgaNGiAK1euwMLCQhtlJIQQQoixevlSs8sVoLO8I7GxwKhRQEIC/7hdO2DNGqBKFS3srGQqyTliCNEklWvQunbtihMnTgAAxo0bh++++w7VqlXDgAEDMGTIEI0XkBBCCCFGrHx5zS6XT3Q04OUFtGrFDzPWqhX/WKNd2t684RN+fPEFH5y5uQE7dwKHD1NwpgKdvFeElBAq16AtXLhQ8n/Pnj1RsWJFxMXFoVq1aujUqZNGC0cIIYQQI9e8OZ+tMSlJfj80juOfb94cEImU3qw470jBTYrzjvz5ZzGTQzIGbNoETJ4MvH/Pl3PUKOCHHwBHx2JsuPTR+ntFSAlT7BRDgYGBiIyMpOCMEEIIIbIEAj6VPsAHOfmJH69YoVJbN63nHbl7lx8/bOhQPjirWxeIiwN+/pmCMxWVxBwxhGibWgFaQkICxo4di9atW6N169YYO3YsEsRtsgkhhBBC8gsL46tJ3N2l53t4qFV9orW8I5mZwMyZfEB25gxgbQ0sWQJcvQo0aaLixghQsnLEEKIrKjdx3LNnD3r16oWGDRsiMDAQAHDx4kXUqlULO3bsQLdu3TReSEIIIYQYubAwoEsXjWSJ0ErekePH+SaMDx/yjzt2BFavBipVUrl8JI+Wc8QQUiKpHKBNmTIFUVFRmDt3rtT8WbNmYcqUKRSgEUIIIUQ+gYBvOlhMGs078vo1MHEi8Mcf/OMKFYBVq4CuXWWbZBKVaTFHDCEllspNHF++fIkBAwbIzO/Xrx9e0u0PQoiWCIXAqVPA9u38X+qvQEjpJc47oih+4jjA05NfTiGRCPjtN8DXlw/OOA4YN47vfxYWRsGZhmjkvSKklFE5QGvZsiXOymkofO7cOTSnTxchRAsoPXPJQYE20YRi5x25exfC4C9watjv2J7SDqeqDoXw/EXgp58Ae3ttFbtU0kKOGEJKPKWaOO7fv1/yf+fOnTF16lTEx8cjICAAAN8Hbffu3ZgzZ452SkkIKbUoPXPRjGXw1+hoPptb/oQBHh78xVtpfw+J6sR5R+SdUytWKDinMjOB+fMRPf8eIoS/4zk8+fn/Ah7hSp6LxvKBMyBqvVeElGJKBWihoaEy89asWYM1a9ZIzRszZgy+/vprjRSMEEKKSs/McXx65i5dSu/1kbEEPRRoE21QKe/IyZPA118j+kEtdMefYJCuzlHqXDSWD5wB0mCOGEJKPKUCNJEKA0cSQoimqJKeWQN5B4yOsQQ9FGgTbSoy78jbt8CkScCWLRDCBBEmp8BEHFAgQCvyXDSWD5wB01COGEJKvGIPVE0IIdpC6ZkVM6bBX2kcJD0qrNNfSe8QyBiweTOfBGTLFoDjcLbLUjwXVUDB4Cz/KnLPRWP6wBFCjJ5aAdrp06fRqVMneHt7w9vbG507d5abOIQQQoqD0jMrZkxBDwXaelJYdp2Snnnn/n2gdWtg8GDg3Tugdm3gwgW87DlBqdVlzkVj+sARQoyeygHaH3/8gZCQEFhbW2P8+PEYP348rKys0Lp1a2zbtk0bZSSElFKUnlkxYwp6KNDWA3FzvIJBRVIS0K0bP8l7rnt3gwzSlK7sy8oC5s7lA7LYWMDKCli0CIiPBwIC1D8X832QhDDBKQRjO3rhFIIhzH8pZQgfOEKI0VM5QPvhhx+wePFi7Ny5UxKg7dy5EwsXLsS8efO0UUZCSClF6ZkVM6aghwJtHVOmOZ48BtpUT+nKvrNngXr1gFmzgOxsoF074PZtYMoUwMwMQDHOxf8+SNHoCi88QSucQh9sRyucgheeIBpdpZYjhJDiUDlAe/ToETp16iQzv3Pnznj8+LFGCkUIIWLi9Mzu7tLzPTxKd598Ywp6KNDWsaKa4xXGwJrqFVYRKKnse/8eGDYMaNECuHcPcHXlq9oOHwaqVJFaT+1zsXlzRDsPQ3f8ieeQ/jJKgju6409EOw83jA8cIcToqRygeXp64sSJEzLzjx8/Dk9PT40UihBC8gsLA5484VssbdvG/338uPQGZ4DxBT0UaOuQJprZGUBTvaIrAhkmDE+H0KcG8Ntv/BMjRgB37wK9eim8e6HOuSiEABFYCb4o0pdO7L/HE7ACQhjIB44QYtSUSrOf38SJEzF+/HjcuHEDTZs2BQCcP38emzdvxkrx1QIhhGgYpWeWZWyDv9I4SDqiiWZ2BtBUr+i8HByevbfBWfiiZQ1n4JdfgGbNlNq2qufi2bPA83fWissCEzx7Z11qh/wghGiWygHaqFGj4ObmhqVLl2LXrl0AAD8/P+zcuRNdunTReAEJIYQoZmxBDwXaOiBu/5qUVHifM3k4jl9XS031hELlz1WlE+H0iAD++AowN1epLKqcizpJyqPKwSGElGgqBWi5ubmYP38+hgwZgnPnzmmrTIQQQlRAQQ+RIm7/2r07H3DlD9LyP5b3HKC1trHR0fJre1eulF/bq3QinNFdAdViM5VpPSmPqgeHEFKiqdQHzdTUFIsXL0Zubq62ykMIIYSQ4iqso9WePfykww6BSiX7KCAvEY78WkCOYzpLhKPVpDzqHBw9K+ljnBOibyonCWndujVOnz6tjbIQQgghGlWqLyQLy66jw8w7ymT9l5fZX2DCsDL8PMAYOIiknuMDJU5niXC0lpRH3YOjRyV9jHNCDIHKfdC+/PJLTJs2Dbdu3YK/vz9sbGyknu/cubPGCkcIIYSoi1qNofD2r9pqG1ugL9VZYXM8f644csmf2T8o6L+Zjx8DEyYg7PBh/ImuiDD9Gc9z89oP6iMRjlaS8hSdCSXv4BhAO2ZxZV/BeFJc2UcZWQnRDJUDtNGjRwMAli1bJvMcx3EQGtBdHkIIIaUTXUjqiZyo+KXTGACri1z15UsAOTnwjo6G6e7dwOfPgLk5wr6thy6TnHD2sv7zZ2g8KY9Oso9oRlGVfRzHV/Z16UK5TQgpLpUDNJFIVPRChBBCiJ7QhaR2KUw2qCAqLv/+H6W2Wz7lDkwDeqHmrVv8jJYtgXXrAB8fCGAQFUgANFzxqPXsI5pjZJV9hBg1lfqgPXnyBBs2bMCaNWvwzz/KfeEq4+eff4aXlxcsLS3RpEkTXL58udDld+/eDV9fX1haWqJ27do4dOiQ5LmcnBxMnToVtWvXho2NDSpUqIABAwbgxYsXUtt4//49+vbtC3t7ezg6OmLo0KH49OmT1DI3b95E8+bNYWlpCU9PTyxevFhjr5kQQoh2qHIhSVSjsP/Rn4qj4uY4Aw88k+lHJsZxDJ6279F8TB1wt24h284Oub/+Cpw8Cfj4aPcF6ZtWs49olhFV9hFi9JQO0GJjY1GzZk2MHDkSY8eORf369fHHH38UuwA7d+5EZGQkZs2ahWvXrqFu3bpo164dXr9+LXf5CxcuoHfv3hg6dCiuX7+O0NBQhIaG4vbt2wCAjIwMXLt2Dd999x2uXbuG6OhoJCQkyPSN69u3L/755x/ExMTgwIEDOHPmDEaMGCF5Pi0tDW3btkWlSpUQHx+PH3/8EbNnz8b69euL/ZoJIYRoD11IakehyQZ7mCD6eSO56wkgwkpEAAA4SAdwHBjAGFZ8GgYBhBD1748Tq1eDDRigOGgpSbSWfUTzjKiyjxDjx5QUFBTEunTpwl68eMHev3/PRo8ezcqXL6/s6go1btyYjRkzRvJYKBSyChUqsAULFshdPjw8nH311VdS85o0acJGjhypcB+XL19mANjTp08ZY4zduXOHAWBXrlyRLHP48GHGcRxLSkpijDG2Zs0aVqZMGZaVlSVZZurUqczHx0fp15aamsoAsNTUVKXX0Zbs7Gy2b98+lp2dre+iECNC5w1Rh77Pm9hYxl/1FzHFxuqleEYpN5cxDw/Fx5KDiHniKcuFicKF9qAr83D6JDXbE0/ZHnRlrFo1xk6e1Pu5k//1xsYytm0b/zc3V8s73LNH9gB7evLzDYT4HOA4BecAxxdZ68dKDkM5b4hx0cd5o2xsoHQftNu3b+PChQso/9+tkR9//BG//PIL3r17B2dnZ7WCw+zsbMTHxyMqKkoyz8TEBCEhIYiLi5O7TlxcHCIjI6XmtWvXDvv27VO4n9TUVHAcB0dHR8k2HB0d0bBhQ8kyISEhMDExwaVLl9C1a1fExcWhRYsWMDfPG/2yXbt2WLRoEVJSUlCmTBmZ/WRlZSErK0vyOC0tDQDf7DInJ0fxgdAB8f71XQ5iXOi8IerQ93kTEAC4u5vixQs+dCiI4xjc3YGAgFyoU0ShEDh3jpP0wWrWjBlCBYdWnT7N4flzxZcMDByeoSLOojlaQv5QPGHYi6/+7yzO/e89Xm0+igo5T9HM7BK4qZOQM2ULYGmp93MHAPbu5RAZKUBSUt654+7OsGyZEF27yh+Trdg6dQI6dAB37pykcx9r1oyvOTOg79+lSzn06iX4b4zzvOMjHqtuyRIhRCIGXacrMITzhhgffZw3yu5L6QAtLS0NLi4uksfW1tawsrJCamqq2gHa27dvIRQK4erqKjXf1dUV9+7dk7tOcnKy3OWTk5PlLp+ZmYmpU6eid+/esLe3l2yjXLlyUsuZmprCyclJsp3k5GRUrlxZZj/i5+QFaAsWLMCcOXNk5h87dgzW1tZyy6drMTEx+i4CMUJ03pQ+QiFw544zUlIsUaZMJmrUeKdyEKLP86Zfv/JYtKgRAAYgf5DGwBjQt+8VHD2qehvHuLjy+PXX2nj3zkoyz9n5M4YNu4XAwJLbZvLMGXcADYtc7gXkt29jALIcHJA1eiRaJyYCAN7WrInTo5bgk4cH398sH32dO3Fx4vNGWlIS0LOnAFOnXtH++2xvD6SnA0ePanc/arCwAKZMkf8ZGDr0NiwsXiJfWgCdo98qog5dnjcZGRlKLadSFsejR4/CwcFB8lgkEuHEiROS/l+AYY2DlpOTg/DwcDDGsHbtWq3vLyoqSqp2Ly0tDZ6enmjbtq0kONSXnJwcxMTEoE2bNjAzM9NrWYjxoPOmdCpuDYIhnDcdOgANGgj/ex158z08gKVLhejatT6A+iptc+9eDosXC2TyYLx/b4nFixthxw4t1rAURiiUX/OiQTY2HOSMriOjPJLBOA5cvoMk/s8iLQ2WqalgTk4QLloEhwED0KJAvyuF544OXqNQCIwZI74sKljzyoHjGLZubYTZs3NLfI1pYTp0AGbPBs6dy81Xi2wGgUD1z5TSinj/DeE7hxgffZw34tZ1RVEpQBs4cKDMvJEjR0r+V3UcNBcXFwgEArx69Upq/qtXr+Dm5iZ3HTc3N6WWFwdnT58+xcmTJ6UCJDc3N5kkJLm5uXj//r1kO4r2I35OHgsLC1hYWMjMNzMzM5gvDEMqCzEedN6UHtHRQK9essn4Xrzg0KuXqUrjh+n7vAkPB7p1K5gSnoNAoPIIMxAKgYkTFaXu58BxwKRJpujWTcf5HHQ0GnerVvxmk5LkHwOO459vsXQcuMiHUuXhTEwAkYhfceBAcD/+CNOyZQvdn9S5o6PXeP48pIL5ghjj8Pw5cPGiWalPI29mBoSE6GhnKrz/+v7OIcZJl+eNsvtROoujSCQqclJ1kGpzc3P4+/vjxIkTUvs5ceIEAgMD5a4TGBgotTzAV03mX14cnD148ADHjx+XaYIZGBiIDx8+ID4+XjLv5MmTEIlEaNKkiWSZM2fOSLUVjYmJgY+Pj9zmjYSICYXAqVPA9u38Xxq7nRiLosYPA/jxw4zpnBaPWdW7N/9X3eBJF6n7Vf7uKDStYncgOlpj30dKJxvsEQY8eQL88QdQuzb/hEgEVK/ON2PcvBkoIjiTosRr1BTK/mmAdPj+E2JQdJOzRLEdO3YwCwsLtnnzZnbnzh02YsQI5ujoyJKTkxljjPXv359NmzZNsvz58+eZqakpW7JkCbt79y6bNWsWMzMzY7du3WKM8RlZOnfuzDw8PNiNGzfYy5cvJVP+jIzt27dn9evXZ5cuXWLnzp1j1apVY71795Y8/+HDB+bq6sr69+/Pbt++zXbs2MGsra3ZL7/8ovRroyyOpY+8RFweHgaViEsldN6ULprKflgSz5tt25Q7Ntu2qbd9lb87ikyryLE9zsOZh4dIo99HRSYbzMpibP58xiwt+SfNzRmbM4exzEylti917ijxGjWZNpCyfxoYJd//3KxcFhOTwyIjr7CYmBy9ZJEkxsmQszjqPUBjjLFVq1axihUrMnNzc9a4cWN28eJFyXPBwcFs4MCBUsvv2rWLVa9enZmbm7OaNWuygwcPSp57/PgxA9/kXWaKzfet+u7dO9a7d29ma2vL7O3t2eDBg9nHjx+l9vP333+zZs2aMQsLC+bu7s4WLlyo0uuiAK102bNHfvphjuMnYwzS6LwpXTQVhJTE80abF+9qfXfkK1AuTFgsgtk29GKxCGa5MGF70JVxEDJApPHvI4Up6M+cYaxGjbydffEFYwkJKm1b6tzRccRkyGnkSyUl3v896Mo8yn4uMTdFiW4ZcoCmekN8LRg7dizGjh0r97lTp07JzOvRowd69Oghd3kvLy8wee1zCnBycsK2bdsKXaZOnTo4W5z2KqTUKKppGMfxTcO6dDGI8UYJkYsGos1HKJTqvNa8aXN4eAiK7IPVtCnflDCvz1vhn3m1vzv+a2cXja6IwEo8h6fkKXc8Qyas/kvOId0eURPfR+JmoxJv3wJTpgCbNvGPy5YFli0D+vYt3mDTOm5zKG7G2b07/ksjn/ecgY0ZrREFTvEiz1WdK+J9jUZXdMefYG+kzzFx60dV+ssSYmiU7oNGCFFMF/1TCNG25s35IEPRNTXHAZ6e/HIlWnQ04OXFZ8bo0wdo1QqCql5Y2fsiAMV9sHr1AqpWlVoNXl7S3WQK9gk7dUrN747y5SUXqM/hLvVUEtzxDi5Q9BOvse8jxvg+Zb6+ecHZiBFAQgLQr1/xgjNAL3cMwsL4C3t36UMKD4+SdcEv5xSXOVf1rpD3VQgTRGClwpsQgPH1lyUkP4OoQSPE2FHnclISlLYaBLnESQkKVmklJSFsSVP8OekCIrYHyCSU69ULWLJE7mqSu/mAbDI6JyflilXwu0PYtDkiBNXBhIBsIKbcvddifR/dvQt8/TVw5gz/uHZtYN06vgpRU8R3DIqqttTwHYOwML520aBrl4qhkFPcsGqeCnn/z6K5VK1xQflvQpT2jJvEOKkdoGVnZ+P169cQFRguvmLFisUuFCHGhpqGkZJCXIMgL6v1ihUGcuGmLUq0NwzbEY4u/z7G2QsCycV706Z8zVlhzRRHjADev5dd5v175YpW8Lvj7AUBngsrKLeykttUSkYG8MMPwI8/Ajk5gLU1PyjWhAl87nVN0uMdA5lmnCWEsk1qO3YELlzQc4BayPv/Esqd+/q4KWrwTUeJUVA5QHvw4AGGDBmCCxcuSM1njKk8DhohJYWebvQSohUlvQZBISXbKgsunEXLfFfvyjRTfPdOvSIp+u4ozoWn2t9Hhw4BY8cCjx/zjzt1AlatAipVUr8wRSnVdww0T9nm+B4ewJs3efO1MOycchS8/+XL5gJvCllPvJyOb4rqaMg+UgqoHKANGjQIpqamOHDgAMqXLw+uuG3MCSkBqGkYKWlKag1CodRsq6ytu/SFfXeoe+Gp1vfR8+d8tcqePfxjT08+MOvSRb1CqKrU3jHQPGXP1TcFgh+9Nn+U8/43b9ocHlUN66ao0TQdJUZB5QDtxo0biI+Ph6+vrzbKQ4jRohu9hOiHxpoUqdlWWVN36Z2cpJs8FvbdoUytvZMTYGVVjO+j3Fw+EJs5E/j0iT+okZH8Y1tbFV9dMZXKOwaap+65qvdsxAXefwEM66YoZXImmqZygFajRg28fftWG2UhxOjRjV5qf090S6NNitRsq1zUasratYv/rCjz2VGm1n79+mJ8H128CIwaBdy4wT9u2hRYuxaoU0f9F0j0rjjnqqEl3tDmTVFVf8dUyeRsCMeOGD6VA7RFixZhypQpmD9/PmrXrg2zAp2C7e3tNVY4QoxRab7RS+3viS5pvEmRmm2Vi1qNMcDZWX6SEPEyHh7894YqNzOUvUBV6fvo/Xtg2jRgwwb+cZkywOLFwJAhgIn87JBCIZCZKTtlZ/N5RORNIpGcKVeEnNsJSLyZjg9xCTCrVQOcwAQcxx8jExP++Jia8vlITE2l/zc3BywtAQsL2b+mpsXP+l8SFHauKsuQshGLb4rGxubi8OEb+PLLemjVyrRYNwXV+R2jTM5E01QO0EJCQgAArVu3lppPSUIIKd2o/T3RpoJ3tJs21VKTIjVvyxe1GqCd5ljq1NozBnz+DKSk8PHYhw9AaooIaQfPInXrAaSll0EqfkCabxOk1Q5C+mFLfNoNpKfzLR3z/83M5AMuzTABUIufjmhqmzyBALCx4Sdr67z/bWz41pp2doC9fd6U/3GZMtKTtbVxB3uKztWyZWX7nsljaNmIBQIgOJghPT0JwcF1ix2cqfM7ZoyZnKm1i2FTOUCLjY3VRjkIIUaM2t8TbZJ3R9vFBSistX2xmhSp2Va5qNW01RwrNxeoUoUPNN68AbZu5Y/Nmzd5f9+944MxcVCWlVVwKyYAgv+b/nPvv0kFpqZ5tVbm5nztlpmZ9P9mZvwxMTHhJ+7tG5j8cxMmEIH7b+hhBi5vqlUbzKUcRCL+uyY3lw8KC/7NzuZfV2Ym/zc3N69cQiGQlsZPxWVmlhesubgonsqVA1xd+cnSsvj71SR556p4uAhDSryhS8X5HTO2TM7U2sXwqRygBQcHF70QIaRUofb3RFsU3dFWtiu02k2K1GyrXNhqqsZ9Hz/yF3wvXvB/k5KA5OS86dUr/u+HDyoXEwBgaspQxiwdZT4nwQGpsDdJh0MNd9g38IZDGRNJTZKtLT+Ja5vy1z5ZWfHBh3gyVfWqQigEvBoAUPAFwnFAqgdw47HKd3eEwryA7fNnfgi39HR+yv//p0/8sRYHcPmn1FQ+qBVPQiEfDL5+zU8JCcqVxd4+L1hzc+Pf+woVpCd3d345XdXOyTtXDSnxhq4V53fMmDI5U2sX46DWQNUfPnzAb7/9hrt37wIAatasiSFDhsDBwUGjhSOEGAdqf0/EhELg9GkOZ864w8aGQ6tW6l+UFHZHW1mG1KQIyLsoTk/nL/ZOnOD/Jibm/RUHYx8/Kr9dMzO+xqZsWb72pmxZ6f+dnfmpTBnAqQyD05l9sI0aB+5FEr+BsDD+CtLTUxsvWzEt3t0RCPjmiNbWxSti/qKkp+cFa+/f8zWTb9/KTm/e8AH0q1d8QCcO+B48KHwf1tZ8oObpKX+qVIkPmrWlNGcjLu7vmDEcO2rtYjxUDtCuXr2Kdu3awcrKCo0bNwYALFu2DD/88AOOHTuGBg0aaLyQhBDDZozt74nm5TWbMQXQEMuWFa/ZTFHX7oXRd5OijAzgyRN+evxY9m/+dPqFsbfPq11xd+c/Q25ueTUx4v/LlFGy5uXBA2DkWODYMf5xlSp8Kv0OHZR/cZrsvGJEd3c4Lq82Udk4ljG+hlMcrImnly/5mlHxlJTEL5eRwb9FhQVyTk6Alxc/VaqU93/lyvzbaWOTt6w6b1VpzUasid+xoo6dvvt9UWsX46FygPbNN9+gc+fO2LBhA0z/a8uQm5uLYcOGYcKECThz5ozGC0kIMWzG1v7eUOn7x7s4tNFsRt1rcl01KUpJAR4+BP79V/avMmW3swMqVsybxLUkHh55AZnGhhv7/BmYP5/PyJidzXcSmzYNmDqVb6eoLE13Xinhd3c4Lq+/WlHDx2Zk5AVrz57JTomJeTV3798D167J346rK9+XzMwMuH5dut+dsm9VcbIRG+v3mKZ+xxQdO0Po92VE90NKPbVq0PIHZwBgamqKKVOmoGHDhhotHCHEOBhT+3tDZQg/3urSVrMZZa/JC2af02STos+f+aDr/v28KSGB//vuXeHr2tvztRri2g0vL6ByJSG83l1DJTyFQ1UX3Vy9HjwIjBvHV90BQPv2fK2Zt7dq29FGFE53dySsrfm3pLC35eNH4OnTvNrZ/LW0jx/zAZy4lk6e58+Bbt2AFi2AkBCgevW8KX/Nm7qM+XtMm79jhtLvq4TfDylRVA7Q7O3tkZiYCN8Ct4KePXsGO202jCaEGDRjaH9vqAzlx1td2mo2o+y1+8OHwIULxbtj/+4dcPcucO8e/1c8PX1aeB+48uX52gpvb+m/VavKaXYYHQ2M0+HV6+PHfGS8f7/0vrp2VT0Thbai8FJ2d6e4tUt2dkCtWvwkT0oK3zzyyy8Lb0Z75gw/5VexIl/L5+fH/xVPrq7KnS7G/j0GaOd3zJD6fdH9EOOhcoDWs2dPDB06FEuWLEHTpk0BAOfPn8fkyZPRu3dvjReQEGI8SmvfheIwpB9vdWmr2Yyy1+7m5soHfu/fA//8w0+3b+f9X9j4T46OgI+PdG1D9ep8MKZ0E0RdXr1mZgI//sg3aczM5FMrfvMNMHOm+m0mtdl5pZTc3dFF7VKZMnxTSWX6OLZvz9fIJSTwiU0SE/lJ3D1RzMkJqFkzb6pRg/9brlze57AkfI+Jafp3zJD6fZWy+yFGTeUAbcmSJeA4DgMGDEDuf4OMmJmZYdSoUVi4cKHGC0gIMS7F6btQGhnSj7e6tNlsRt1r98xMvgbs5k3g77/5YOz27cKDxIoV82oP/PzyJheXYqY+1+XV6+HDfHPGf//lH3/xBbB6Nf9CikPbnVf+uyrOjY3FjcOHUe/LL2FanBSgBkaX8bmyb8GAAYD4vvq7d3ztcf7p7t28hDZnz/JTfi4uQO3a/GRubvzfY/lp8nfM0Pp9lZL7IUZP5QDN3NwcK1euxIIFC/Dvfz8AVatWhbWm8tgSQkgpYmg/3urQdrOZwu5oM8bPu3GDD8Ru3uSnhAQ+LpKnYkW+iVjNmvzfGjX4oExjCTkK0kUU/vQpH+Tt28c/rlABWLYMCA/XzMBauui8IhCABQcjKT0ddYODS0xwpuvaJXXeKmdnICiIn/L7/Jn/LIlrmsXTo0d8rVtsLD8py5C/x7TFEPt9UWsXw6fWOGgAYG1tjdq1a2uyLIQQUuoY4o+3qnTRbEYg4C8gHj7kM9N9+y3/98YNfsBgeZycgLp1gTp1+ECsdm0+GNN5d2ltRuHi5owLFvBX06am/NX+zJmafaHUeUVtuq4l1+RbZWUF1KvHT/llZPA1bLdu8TdETp9WnFUyv337+IC1fn2+2bDKA5sbIUP96FBrF8Om1EcjLCwMmzdvhr29PcKKqPuMjo7WSMEIIaQ0MNQfb1VputmMUMjfuY+Pz5uuX+cHCi7IxISvAatbNy8gq1uXD2o1UXkkt3Cq3HrWVhR+4AB/wB894h+3bMk3Z6xZU7XtKIM6r6hN17XkunirrK0Bf39+AviPhJdX0eMW7trFT0Be8OfvDzRowP/18+OHByhJ6KND1KFUgObg4ADuv7PI3t5e8j8hhJDiKUk/3uJmM7GxuTh8+Aa+/LIeWrUyLbLsIhFfM3blCj9dvcrXjMkLxqys+ACsfn3+4q5+fb5mTJWhvIpFnUwPmo7C//2XryU7cIB/XKECsHQp0LOnliLS/xhj5xUDGJRLH7Xkun6r8n+PAfJP81Gj+OXENd/p6UBcHD+JWVjwN1caNcqbfHyM4/uvMMb40SH6pVSAtmnTJsn/mzdv1lZZCCGkVCpJP94CARAczJCenoTg4LpyL6xevAAuX+aDscuX+YDswwfZ5ayt+QBMfKfe31/PzaLUzfSgqSg8IwNYuJAfbDori69q+OYb4LvvtNiBrgBD7LyiKAgzkEG59FVLruu3StH3mKen7PeYUMgPB3DtGl87fu0aP6Wl8d8Jly/nLWtry3/2GzUCGjcGmjTht2lsdQWG+NEhhkvln7kvvvgC0dHRcHR0lJqflpaG0NBQnDx5UlNlI4SQUqOk/nh//sxfgF28CFy6xP+V1wzKwoIPxsR3zcXBmMG8/uJmeihOFM4YH2xERvJ50AGgTRvgp5/4tp26ZkidVxQFYb17A0uWGMSgXPqsJdf1W6Xs95hAkDfOWp8+/DyRiK8cvno1rzb92jXg0ye+j9vp03nru7nxgZp4KthHzlAZ0keHGDaVA7RTp04hOztbZn5mZibOFszBSgghRGnG/uPNGJ+W++xZDjt31sHcuQLcvAn8NyKLhIkJ302qceO8u+K1ahl43xNNZHpQJwr/5x8+ADlxgn9csSKwfLl6g02XNIpqNJ8/5xOnyKOnQblKUi15UdT9HmOMj58BoHNn/i1kjE9GIg7YLl/mk5IkJwP/+x8/AQDHmcLTsxUOHDBBUBDQtClQrRp9RIjxUjpAu3nzpuT/O3fuIDk5WfJYKBTiyJEjcHd312zpCCHFZgBdMEgJlZnJ3+G+cCFvevUK4H9aKkuWK18eCAjg73QHBPC1Y7pqkacxmsr0oOzV64cPwJw5wKpV/IfYwgKYMgWYNo1v+1naFVajWRQ9DcpVUmvJNaGo1qi1awNDhvDzMzL4751Ll/KmxEQOiYn2+PVX4Ndf+eWcnfnvm6ZNgcBA/kaQjY3uXxsh6lA6QKtXrx44jgPHcfjiiy9knreyssKqVas0WjhCSPEYSBeM0qUER8Tv3gHnz/PTuXN8U6SCDSrMzIAGDURwdX2EXr280KyZKTw8SsCdbF1lehCJgM2bgaiovPEDQkP5JCBVqhRv2yVJUTWaytDDoFzGXkuuDap27bS2Bpo14yexxMQcrF17HdnZ/rh8WYArV/jvq4MH+Qng+67Wr8+vJx7zzc1N+6+PEHUoHaA9fvwYjDFUqVIFly9fRtmyZSXPmZubo1y5chCUkIsQQkoCdfMZkGIoQRExY8CTJ/x18Llz/HT3ruxyrq78HWrx1KABIBAIcejQP+jQoZJhN1tUhS4yPVy6BIwfn5chwceH72fWtq362yypNBFcGfLggqWEpgbx5mvpX6JDBxHMzATIzuYzRV64wGeJPH+e/+iKm0ouX86vV7UqH7A1bw60aAF4e5eAm0mkRFA6QKtUqRIAQCQSaa0whBDN0NSPnq4ZdeWTkUfEjAH37gFnzuRN8iooatSQvgNdpYrsBU1Ojm7KrFPazPTw8iVfY7ZlC//Yzg6YNQsYNw4wNy920Uuk4gRXxjK4YCmgrUG8zc35Jo2NG/O/dYzx+XXEtf/nz/ODbP/7Lz+JP3qurnygJg7YatUyot8gUqIoFaDt378fX375JczMzLB///5Cl+3cubNGCkYIUZ+2fvS0yagrn4wwIhaJ+M724uxoZ88Cb99KL2NmBjRsyF+sNGvG15A5O+unvAZB05kesrL4E3zePD5VHQAMGgTMny8TgGjj5oVR3xApqkZTzNgHFyzhdDWIN8cBlSrxkzhr5IcPfFbZs2f56dIlvg/t7t38BACOjvx3X3Aw/1tZr54eh/kgpYpSp1loaCiSk5NRrlw5hIaGKlyO4zgIhUJNlY0QoiZd/ehpipFXPklFxEKY4Cya4yXKozxeojnOQsBEeo+IxQHZqVP8dOYMkJIivYyVFd+ZvkULfmrShPJRyNBEpgfG+EGmIyP5EboB/mD/9BN/y78Abdy8MOobIoByNZqTJgHbt5f8tIlGTB+DeIs5OgLt2/MTwCc9unKF/248e5avZfvwgf+oiseEt7PjA7aWLfmgzd+fAjaiHUqdVvmbNVITR0IMnyZ+9IRC4PRpDmfOuMPGhkOrVtq54WyElU+y/ot0o9EVEViJ5/CUPOWBZ1iJCIRhr04jYpGIz9B+8iQ/nTkjOxi0rW3e3WHxxQa1qFNCcTI93L3LB2ZHjvCP3dyARYuAfv348QcK0MbNC6O/ISKmTI3mggVGXE1Y8ulrEG95LC35/Yj3lZvL92MTtzI4cwZITQUOH+YngL+pVacOf6q1bs3XsKl7ehlSjbYhlaW00kjc/+HDB5mBqwkh+lPcH728u+umABpi2TLt3V03xuaYMsqXRzS6ojv+RMHDnQR3dMef+BPdEabFpASMAffvA7GxfEAWGyvbZDH/3d+WLfmEHnT3V0fev+fT5v/8M3/1Y27OB2rTp/NvjBzauHmh9DY7CiG4YARXaEXUaAohwFm0xEsA5QE0B2CArwKAgV0U66gw+hzEuyimpnwT74YNgYkT+UNy8yY/8sX27XyN2+fPean+Ab5WLjgYaNUK+OILvg+bMklHDKlGW5tlMahz3NAxFS1cuJDt2LFD8rh79+6M4zhWoUIFduPGDVU3V6KlpqYyACw1NVXfRWHZ2dls3759LDs7W99FITqyZw9jHMdP/M8eP4nn7dlT+Hr511FmPXVt2ya7L3nTtm2a3a8m5WblMg9BEgOEcsvOQcg8Bc9ZblauRvf7/DljW7Yw1r8/Y+7usvu1tmasXTvGFi1i7NIlxnJyCpQ7l7HYWP7Yxsbyj4stN5flxMSwK5GRLCcmRkMbNWI5OYytXs2Yk1PeG9OlC2MPHhS5amyscp+N2Fjli6P0Nl26S8/w8ND8h18OTf5W7dnDF1sPL0NlBlVWPRRG3i49PZXfpa6ucRT9PiqaypVjrFcvxjZsYOzRI9W2qa3fXHVenybKYlDn+H/0cW2sbGygcoDm5eXFzp8/zxhj7NixY8zR0ZEdPXqUDR06lLVp00a90pZQFKARfVP1Ry83V3b5gl/Snp6avebWxkWorunqNbx/z1h0NGOjRzPm4yO7fQsLxlq1YmzuXMbOnWMsK0vxtrTyY2mIv8D6dOwYYzVr5h2LWrUYO35c8fIFIuZtf8gP+Itz80LpGyLopZerRU39VhnSRW9RDKqseixMcW4Y6eIap6jfR3FANn8+Y23b8jfICj5fuTJjw4YxtmMHY2/e6Oc3V93XV5yyGNQ5nk+JCtAsLS1ZYmIiY4yx8ePHsxEjRjDGGEtISGCOjo4qF3T16tWsUqVKzMLCgjVu3JhdunSp0OV37drFfHx8mIWFBatVqxY7ePCg1PN79uxhbdq0YU5OTgwAu379utTzjx8/ZgDkTrt27ZIsJ+/57du3q/TaKEAjhqCwH72Czx0/rvtgSfyjoOiupDZ/oDRVg6StWsCsLL5c06cz1qgRYyYm0tszMeHnR0Xx711GhnLb1cqPpaH+AutDQgJjnTrlHQNnZ8bWrJGtwsxPTnAb69Jd459HpW8mIFgvV4ua+K0ypIteXZRVYzXhxnTgCtDFNY6qN+IyMxk7fZqxmTMZCwpizNRUdtlq1XT/m6up16csQz6tSlSAVr58eUkNWvXq1SVBzb1795idnZ1K29qxYwczNzdnGzduZP/88w8bPnw4c3R0ZK9evZK7/Pnz55lAIGCLFy9md+7cYTNmzGBmZmbs1q1bkmX+7//+j82ZM4dt2LCByQvQcnNz2cuXL6WmOXPmMFtbW/bx40fJcgDYpk2bpJb7/PmzSq+PAjRiyORVduRvhaXJQEOZsqjTHLO4+9RUZY+mfthEIsZu3WJs2TLGvvxS/h1YX1/GxoxhbO9exlJSVC+rVn4sDfkXWJfevWMsIiLvSszUlLEJE/iqz8IoCG5zIWAeSGQcRBo7rEXeEIGQeeIpy4WJ4vdTS1eLubmMxcTksMjIKywmJkft08WYauWLW1aNVlob04ErQBfXOMW9EZeWxtjBg4xFRjJWp45y29LWb642Xp8ihnxaGXKApnL38LCwMPTp0wfVqlXDu3fv8OWXXwIArl+/Dm9vb5W2tWzZMgwfPhyDBw8GAKxbtw4HDx7Exo0bMW3aNJnlV65cifbt22Py5MkAgHnz5iEmJgarV6/GunXrAAD9+/cHADx58kTuPgUCAdzc3KTm7d27F+Hh4bC1tZWa7+joKLNsYbKyspCVlSV5nJaWBgDIyclBjp5HbhXvX9/lIIZh714OvXoJwBgA5PVgfv+eST1WpGzZXOTkMI2Vp1MnYMcODpGRAiQl5e3f3Z1h6VIhOnViGh38WNHrT0pi6N4d2LFDiK5dlX99AQGAu7spXrzgL3EL4jgGd3cgICBX5nW8fQscP87h+HETHD/O4cUL6fXLlWP44guGkBARvviCwcNDen1Vj8vp09x/yV/kY4xPyhIbm4vgYOWOAXf6NEyVyPSSGxsLFhysWoGNQU4OTH75BSbffw/u/XsAgKhDBwgXLgR8fSXLyCUUwnT8eIAxmU+eAEKswAT0wO7/EijkLcFx/HuzZIkQIhGDKgmWly7lz3+Zbf6X4mYFJkAAxRvMffYMTMO/JXv3ij//eYmJ3N0Zli1T7bMIAM+ecVAmB9qzZ5r9HlOHsmV9+jQXx4/nJVdo1oxh/37Nfo9xz54plTlOG+9/ceniGqdsWeXeK0W/j5aWQJs2/ATwY679/LMJFi4sOkuGiYn2z9Xivj4xoRA4d46TnKtJSVBqu/r4POrj2ljZfakcoC1fvhxeXl549uwZFi9eLAlqXr58idGjRyu9nezsbMTHxyMqKkoyz8TEBCEhIYiLi5O7TlxcHCIjI6XmtWvXDvv27VP1ZUjEx8fjxo0b+Pnnn2WeGzNmDIYNG4YqVarg66+/xuDBg8EVko5nwYIFmDNnjsz8Y8eOwdpABhOKiYnRdxEUEgqBO3eckZJiiTJlMlGjxjvK7qMFQiEwenRbMCaAbDDGAZI8hPLOdQYXl89IS4vBoUOaLZeFBT8MlLxzQJP7Kuz18xerDGPGZMPUNEal869fv/JYtKgR+OOXf7sMjAF9+17B0aMvkZvLISHBCdevl8P16+Xw6JGD1EWyubkQNWq8Q716r1G37htUqpQmyb5+8yY/FceZM+4AGha53OHDN5CenqTUNt3PnFFii8CNw4eRlJ6u1DaNAmNwvXoVNTdvhh1/FYK0ihVxe8gQvKlXD3j0iJ8K4XzrFpolKT7O3RCNP9EdX9ttxps0+7z1nD9j6NDbsLB4qfLnw8ICmDKlPH79tTbevbOSzC/rkIa1qYP5ISEKcfHpU7zT4IcyLk782ZGWlAT07CnA1KlXEBio/BAVT586A2imxHIXcejQO1WKqnHKlnX8eCHS0iwkj52cPiMnx0Sj32POT58qURLNv/+apM1rHKEQcHZui3fvLKGp38dGjYraJq9XL1NUqpSKevXeoEGD1/Dzewdzc80Oe6WJ1xcXJ/u9Ym+fBeVuQujv86jLa+OMjAylluMYY3q5ffTixQu4u7vjwoULCAwMlMyfMmUKTp8+jUvinKX5mJubY8uWLejdu7dk3po1azBnzhy8evVKatknT56gcuXKuH79OurVq6ewHKNHj8apU6dw584dqfnz5s3DF198AWtraxw7dgyzZs3C4sWLMX78eIXbkleD5unpibdv38Le3l7hev/f3p2HRVX9fwB/X4ZVBRdQQEBJzZ1cU8iFLJXSTCUztdTKNMvKMi1tc6u0MtP6WmZp+quMMtEs0URTcyvLtCyXXFMQXEsURWA4vz+OMzDMDMw+d2ber+e5D3Lnzr1nLse593PPOZ/jCkVFRcjMzESPHj0QEBDg1rKYUvr01LD1xJanp1SxzZsV9OhhybMZw0BD98Te2qeyamPp58/MtLwFScdUPY6NFXj+eS0URcG6dQo2blRw6ZLhxS8hQaBHjxL06CHQqZNAcLBVh7WKMz6/snkz/HWPhStQnJnpPS1of/wBzfPPw2/DBgCAqF0bJVOmoOShh6yau0BJS4P/sGGVbndt8afYEjPIoAXF3gdY5Z90d04qRlCTRsCpU1BM3BoIRQFiYlB86JDDcmNrtUCjRv7Xn7Kbb30+dKjYqqkEGjWqvEXbmn06S2VlhcHEHUq59ZX3drDqe0yrhX8j1/79HcVV9zi63heA6RZtW66P5vap+9s3aAAcO2b4WkiIwK23CvToIdCzZwluvNGydP62lsWSz2euZ4r5Oly6b3f9f3THvXFeXh4iIiJw8eLFCmMDm2bAOXToEDZu3IgzZ84YTVz9yiuv2LJLt7h69SqWLl2Kl19+2ei1suvatGmD/Px8vPXWWxUGaEFBQQgKCjJaHxAQoJqgSE1l0UlPBwYNAspfD06dUjBokL/nTJrqIc6etWy7WrUUXO+tBQCIjVWuz/3q2RNnWfr5z571h7X/VQYOBO65B1i/Xs5Ddvgw8OefCp580vCc1a4N9Owplx49gOhoBa6analbN8vmyOvWzd/yi6WFO/V31mznrnTqFPDKK8CiRfKzBgYCzzwDZdIkaKpXt/6vGBdX+TYAgmKj0V2zFfDPAfyjgQD7JxAKCAC6dy+7xl82Y5uZlEoBgLlzEeDAJwjbtum6QJkmhIKsLOCnnwIsngcxIKDCjwFAwdy5QHCw+6+FFZVVMnfXbdnduFXfY5WcOGf8/R3N2fc4AwfK5y/G84TZfn00t8+4OEU/37rsCg+sWyfnuM/JUbBmjXJ9wmwNbrgBSEkB7rxTzr9WbsSO0z+fVivnijPd5FM20FPn/0dX3htbfBxrB7ctWLBAaDQaERkZKVq1aiVat26tX9q0aWPxfq5duyY0Go1YsWKFwfphw4aJu+++2+R74uLixDvvvGOw7pVXXhE33XST0ba6bI3lk4SU9X//938iICBAnDlzptLyfvfddwKAKCgoqHRbHSYJqRxzC7iepQN21693zIB9tXHWgOW//xZi7lwh7rhDiOBgw31pNEJ06SLEa68JsWuXEFqtMz6Z5ZySlMUdmV5c6fJlIaZMMczccu+9Qhw5Yt9+LUljGh7u2ukL7J2UygrOnAfRhR/DbqbKWru2dYkkHJZ4wZNO3HWuvsdxxhySlu6zpESI338X4s03hbjtNiECAw3/VAEBcv1bbwnx559ye2eVRcfS62r5Ou3uaqXmJCFWB2j16tUTM2fOtLlgZXXo0EE88cQT+t+1Wq2IiYkRM2bMMLn9wIEDxV133WWwLikpSTz66KNG21oSoCUnJ4t77rnHorK++uqrombNmhZtq8MArXJqzu7jraxJa6/WemMPR6X1v3JFiIwMIZ58UohGjYz3ExcnxMiR8uLz33+u+WzWcMo9mAfe2FWquFiIhQuFiI4u/UyJiUJs3+64Y1QU3Jr7UnR24OuUWcyNOfsa4KKP4RDly/rZZ7YHZnY/3PSkEye881plqUuXhPj2W5ndt0ED09eiUaOEWLlSbusMlj5o+ewzdVUrrwrQQkNDxRF7nxhel5aWJoKCgsTixYvFvn37xKhRo0SNGjVEbm6uEEKIoUOHiokTJ+q337Ztm/D39xezZs0S+/fvF5MnTzZKs3/+/Hmxe/dusXr1agFApKWlid27d4ucnByDYx86dEgoiiLWrFljVK5Vq1aJjz76SOzdu1ccOnRIvP/++6JKlSrilVdeserzMUCrnDOfnpJ5ljZ2qLXe2MvWxp5jx4T43/+E6NXLuJXMEU8tXc0p92DFxaIoM1P8Mm6cKMrMdP8V2B6ZmYb5sG+4QYgvv3TOH9dcvvTwcCfehTuHNfXKnfMgqp2lwaurY3c18tZrlbVKSuQ0jHPmCJGSIkRQkGHdCAwUont3OZXLgQOO+yrz1IftXhWgPfzww+KDDz6wuWDlvffee6JevXoiMDBQdOjQQfz000/615KTk8Xw4cMNtv/qq69E48aNRWBgoGjRooXRRNWffPKJAIwnmZ48ebLBdpMmTRJxcXFCa6Kv0Zo1a0Tr1q1FtWrVRNWqVUWrVq3E/PnzTW5bEQZolfPU/9TewJLGDrXWG0ew5PNfuybEDz8I8eyzQjRrZv7J5IoVco4bkjy+3vz+u7y70f2hq1cXYtYsOfOsM6lh5ng72TIvl7f3jrWVrb1fPb3R2hYe/53jJPn5pT09TLWuNWwoX1uzRggrp/o14OwHLc5q0FVzgGZ1FscZM2Zg9uzZ6N27NxISEowGu1WURMPX5OXloXr16pVmanGFoqIiZGRkoFevXqpKEqLVAvHxlScsOHbM83MLqJFWC2zZUjq3TpdyeQfUWm8cxdTnP3cOWLMG+O47OSD70qXS7TUaoFMnoFcvoHdvoEULx2TO8jYeW2+ysoCXXwaWLJFfSAEBwGOPyXUREa4vzxdfAEOGVL7d0qVAmezG7pKeLvNLlP8u1/0fqSjhU3q6qSQJ0CdJ8FW6cwoYntey57Rv34q/x32Bx37nuJAQwN9/y2lrMjKAzZsNp2esUkUmDerdW17jys+5WRlL6qot/5dNfTfExgJz59r/3eCOemNpbGB1gHbDDTeY35mi4Gglc774EgZolnHWf2qyn5rrjaOUlAC7dwOrV8tl507D1+vUkZmxevWSWRdr1HBLMT2Kx9WbixeBN94A3nkHKCiQ6wYOBF5/HWjY0H3l2rRJZsiszMaNsDjFoZPoHraZm6/ckodtWq2cIH3Nmj24887W1mUS9WIMXitn7junsoeQvuzSJeCHH0qvfadOGb7eqpUM1u66C+jQwbLz5ui6as9DH0uoOUCzOh/osWPH7CoYUXmpqfI/maknJLwAkTPk5wMbNshWsu++kxfvstq1kxem3r2B9u2hnyiaHEBNd0yFhcCHHwLTpsmmU0CW5623gI4d3VOmsrp0sWxOhC5dXF+2crZsMR+cAbL4J0/K7czFkhoNkJwskJ+fjeTkVryRvi41la1ktnBmy4s3CA2V9apvX/n/8/ffS4O1n36Sv//+u3xOVbu2fEh5113yQaW5uMKRdVWrlX8/U199Qsivv6eflsfzxv8Lnj2hEXkNXoDI2U6eLA3IfvihtKEEAKpWlRcdXdeO6Gj3ldPR1BQPqeaOqaQE+PJL4KWXAF2vj6ZNZStanz7q6beq0chzY35CL/kUSwVflOUfcti7HRnSaNzeSOpRzLW8ZGfL9b7SM8fS739FAVq3lsuLL8r5Qr//Xl4v166Vvy9ZIpeAAKBrVxms9elj3MnAUXXVEQ99PJlNAVpWVhZWrVqFEydOoLCw0OC12bNnO6Rg5Ht4ASJHKikBdu0CVq0Cvv1WPgksKz5eXlzuugtITgZMzDGvLjZEWmqJh/SFUcMdU2Ym8Pzzsl8rAERFAVOmACNGyBla1cZDuhhY+lDDmx5+kDr5esuLjj3f/7VrAw88IJeiIjmhvO4B58GDsgfKhg3AM88AzZrJa2mfPkBSkuPOqaUPc7KzZW9wVTyEdCCrr0YbNmzA3XffjQYNGuDAgQNo2bIljh8/DiEE2rZt64wyEhFZ5MoVYP16GZB99x2Qm1v6mp+fvHjonvo1b66ehpJK2XClVUs8BEAdd0y//QZMnCgDNAAIDYV2wkRsaf8Mcv4LQfRWFV/YPaCLgQf1xiQv5+stL4Bjv/8DAuR5uvVWYNYs4NAheX399lt5Dvfvl8ubbwLh4bIXSp8+QEqK+a6QlrD0Yc4zz8gWPh1v6cZq9ciKSZMmYfz48di7dy+Cg4OxfPlynDx5EsnJybj33nudUUYiIrNycoCPPpIXhPBweR/78ccyOKtWTV6MliyRv2/dKu/RLcm+qNXKp3JffCF/arWu+DQm6K605e84dFfa9HSjt1QWDwEyHnLZZ7LmjsnRDh+WmRDbtZPBWUAA8PTTSH83C/ELJqFbrxAMGSJzccTHC1OnUx10XQwGD5Y/VRScAaW9MQHj/1sq641JXs7Xu9s6+/v/xhtlUPTDDzIw0iWbrVkTOH8e+PRTmWMpIkIGafPmASdOWH8c3UOfyq7VZYMzoMJLo0exOkDbv38/hg0bBgDw9/fH1atXUa1aNUybNg1vvPGGwwtIRFSWEMCff8qByx07AnXrAqNGySd6BQVAvXrAE0/I/vPnzgHLlgHDhskuG5ZKT5ddILt1Q5mbdzd84dt4pXVnPGSSO+6YTp2SKfKbNZN3EIoi++scPIj0Lu9gwEOhyMoyPK/ZWQID7pFBmmoCdA+i640ZE2O4PjbWd8b8kPv5endbV37/16gBDBoEfP45cOaM/K589lkZxBUVyalqnngCqF8faNMGmDxZDj2wJH98RQ99KuKWh5BOYHUXx6pVq+rHnUVHR+PIkSNo0aIFAOCcLgsWEZEDFRXJi8mqVXIpn0y2Qwfg7rtlK1pCgn1dF1XVNdDGvjpOj4esHQ9n6Z1QnTr2Dyb491+Z7OPdd4GrV+W6Xr2A114DWreWMe/NVyAQjPLPKAX8oKAEo4YXYmyNIHWM3fMwHtAbk7ycr3e3dVcLor+/HM+dnCy7Qh48WHrN3r4d2LNHLtOmyYc4ffrI74pu3cyPATc3BLd2beOWs7K8oRur1QFaYmIitm7dimbNmqFXr1549tlnsXfvXqSnpyMxMdEZZSQiH5SXJ1vBvvlGpv3977/S14KC5ISaffvKMWWOehKqhqFSBmy80jr1CbItI88tuWOqVQt48EHbM5rk58ug7M03SytLp07AjBkGd2JbNmmRdb6K2d0I+OH85SDgsgBQGun7WvY3ezDhE7mTpclPAe9MLqGWFsQmTYAJE+Ry9qycHPvbb2VWyOxsYP58uYSGAnfcIR+y9uolLwVlmXrok50tO0RUxpO7sVodoM2ePRuXL18GAEydOhWXL1/Gl19+iRtvvJEZHInILtnZ8mnbN9/IuXfLJomNiJDBWN++QI8eMjW+o6lucHmZK6gWftiCLshBNKKRgy7YAg1KjLYDnPgE2dbmxcrumISQgxfKK7tfc80y167JQYivvVaaFSYhQfaB7d3bqDk1Z9NBAM0t+LCG7/Ol7G9Enq6y5KeA8cTq3tJKrsYWxNq1geHD5VJQIK/v33wjr/c5OXIowrJl8nu1SxegXz/5PRsfL99f/qHPpk2WHdeju7EKKxQXF4vNmzeLf//915q3+ayLFy8KAOLixYvuLoooLCwUK1euFIWFhe4uCnkQZ9ebkhIh9u4V4tVXhbj5ZiHk5aR0ufFGIcaPF2LLFiGKi51SBANLlxqXwdSydKnzyyKEkB86NlYsR6qIxQmDMsTihFiOVCHi4kyenOXLhVAUuZR9n27d8uW2lcXsSVEUfVnM1pvly433ERsrRHh4xfsNDzd+X0yMEI8/LkS9eqXrbrhBiM8+q7CybHxpvUV/44qWjRutPHdkMV6ryBbm6k1xsfz/unSp/FlcXPrdaOqrxqbvRhcw9Tkq4vDvfyfRaoXYuVOIF18UomVL47/JTTcJ8fLLQuzaJe8XdHSXI1N/x3KXowq54/vG0tjAqgBNCCGCgoLE0aNHbS6YL2GARp7OGfWmuFiIH38UYtw4IRo2NP5STUwUYsYMIfbtM/xCtud4ll7YNm5U3w368gk7hAKtALSG5wpaoUArlk/YYf69JuKhuDgbL85lTk4x/MRGJIulGCQ2IlkUw8/g5FRYb8r/Qdavty9aAoSoW1eIDz4Q4tq1Sj9G8fqNIhYnrp9T2w7nsgDdB/FaRbawtN5Y8ZxJNcw916rse9yh3/8ucuSIELNnC5GcLISfn3HZx4wRIjNTiMJCxwShag7QrO7i2LJlSxw9ehQ33HCDoxvziMhLXb0qM5yvXCn7oJfNJ1R2PFmfPnLeYEexdriU2rqGaLXA2C8SISBg1OUOflAg8HRaIvrOMN3lzqEJG6535k9Hf4zFXGQhTv9SLE5iLsYiFSsq7/Rfvq/KF1/YUJgyqleXo9GrVbNoc82tXTA3fDQGnP8QCkogDBKFlMCS5MYe3W2GyIeprht7JexJWuWJCXsaNJAp/J95Rt4nrF4tu0J+/738u8ybJ5caNWQP9mefBZYulUl7dXTdWD29q6rVAdqrr76K8ePHY/r06WjXrh2qlhsIEmbPrHREPs7a5Hhqdv68/HJduVJ+uV65UvpazZql48lSUiy+t7aKLRc2SweXu+pvUnozYTotpYBS6c2EwxI2REcjHf0xAF+jfOyajRgMwNf4GgOQam30Ym+0c/Ei8Ouvln9IjQapC+7E1/fci7GYUy7QzMJVVMEFhEOYOOfenv2NyNt50hxpjkha5ckJeyIiSsetXb0KrF9fOm7t7FmZ2h8AAgPllDsJCcCdd3rPGGGLA7Rp06bh2WefRa9evQAAd999N5Qyg6+FEFAUBVpPnnSAyI1sSY6nNidOyIBs5Urgxx8N5yCpV08O/O3XD+jcWc4X7Cz2XNgqG1zuyr+Fmm4mtLd0wVhNYwgtYC49/dOa99D3lihAl7zEEpU1W1rC2hOQmorU5UDfpzpjS/YNpYlXYo/jm8FpGDArAgrcH6ATkWOpJcOhJTyttc+ZQkJkD5s+feT1/aefSu81Dh8Gfv5ZLgsXAklJpfcaN97o3nLbw+IAberUqRg9ejQ2btzozPIQ+SRVzb1lBSHkpNG6L8rffjN8/aabSr8oW7e2b34ya9h7YVNL1xCH3Ew4qFl2y3YNsrR1zb4u4IeT2hhs2Q506mRFgFZRs6WlbLmbSk2Fpm9f3Fru3KRqNPg6UR0BOhE5ltq6sVdETQ/o1ESjkTOodOokZ1XZv7/0HuSXX+Sca9u3A889B7RoUXoP0q6d6+5BHMHiAE1cr8nJyclOKwyRL1Ld3FuV0GqBHTtKvxCPHCl9zc9Pfmn27y/L26CBe8roiAubM7qGWBsr2X0z4cBmWafeLOiaLUePNp59NDhY5mU2xZK7qYpOupk/sloCdCJyLLV1Y6+IJ7X2uYuiAM2by+WFF+SlbtUqeW+ycSPw119yee01GcxNmODuEluu8tHQZSieFHoSeQhrWnvcpaBATjI5ciRQt668WX37bRmcBQXJbgcLF8qb2R9/lAN83RWcAeq8sKWnyzldunUDhgyRP+Pj5XpzdDcTgPGTv0pvJnTNsuUrl65ZtqIDm+DUc7ptG/DBB6XBmUYjZy09flwONFAUG04AbDvpKC3CrbcCgwfLn2q4YSMi++meB8XEGK6PjVVXbxXdAzpzt96KAsTFqaO1Ty1iY4HHHwfWrQPOnAE++0xe7qpWlePdPYlVSUIaN25caZB24cIFuwpE5GvU2o3h4kVg1SoFH37YHg884I/r89MDkInz7rpLdhu44w7nJPmwh9q6sdibicvqMXFOaJa15pyWWNrDcetWYOpUOfobAPz9gYceko9CdTOU1q9v26BAT+03TERO5wmt5J7U2qdGNWsC998vl4IC+TDZk1gVoE2dOhXVq1d3VlmIfJKaWntyc2WWpJUrgQ0bgKIifwDyMWPduqV9uW+91blJPuylpgubI2Ilq28mnDC63JpzWmmAtnUrMGWKrGSADMwefhja5yZhy8l45OwAoo+X+YzWngBP6zdMRC7nCRkO1ZS0ypMFB7u7BNazKkAbNGgQ6tSp46yyEPkkS1smbrkF2LTJ8U/7jhwBVqyQy44dhmVo3FggIeEQxo1rgMREf/hZ1SnavdRyYXNUrGTVzYSTmmXtOqdCyAo8bZr8Ccgo/6GHgEmTkP5bPMbeWsFwOWtOANOfEZGX8ITWPnI8iwM0jj8jcg5LWiYGDQIaNnRMCn4hgD17ZEC2ciWwd6/h6zffLJN89O8PNGxYjIyM/bj55hs8KjjTUcOFzS1dWJ3YLGv1ORVCDgiYPl2ONQNkYPbww8CkSUD9+o7vjajWfsNERDbwhNY+ciyrszgSkeNV1DIxaBAwa5Z9N69arbw31gVlx4+XvqbRAMnJMiDr108eU6eoyM4PpgLuvrC5pQurkwfhWXROhYDy3XfAzJnAzp1yXVAQ8MgjMv9xvXoAnNQbUU39homIiKxkcYBWYvGobyKyhamWiVtukS1ntty8FhTIIT4rVsi0s2Wzl4eEyIxG/fvLZB+1ajn1o/k0tyQscecgvJISKOnpSH7hBfgfPSrXhYTIFPrjx8vBjGU4pTei2rLEEBERWcGqMWhE5FzlWyY2bbLu5jUvT6bDX7FC/iybebFmTZkOv39/oGdPoEoVJ30IMuC2WMnVg/CKioClS4GZM+F/4ABqABDVqkEZMwYYNw4wM37ZKb0R1ZQlhoiIyEoM0IhUzNKb0s8/l5MwbtgAFBaWro+Jkd0W+/cHuna1MvOiVgtl82bE/PgjlKpV5RxSKr2htXYCaFdzW8ISVwzCu3oVWLRIVsATJwAAokYN/N2zJxrMnYuAqKgK3+603ohqyRJDRERkJQZoRCpm6U3pxx+X/rtJk9IkH+3bw7bkHunpwNix8M/KQnsAmD3b9qwkTna9qA5JoOJMbktY4qxBeHl5cnLp2bPljKAAEBkJPPssikeMwIEtW9AgPLzS3Ti1N6IassQQEVGl1P6g1dUYoBGpmO7mtaJujoAMxFJTZWtZs2Z2HtSDJvj1oKICcH/CEofIzZXR7wcfyNnMATmZ9HPPyZT5ISFWZZdxem9ErzjpRETey1MetLqSBybOJnI/rVaOD/viC/lTq3XOMbZtA1q3rni7BQuAX36RGcvtDs4qS6kHyKwkzvjAVvKgonqHw4dloo/4eJmZ8eJFoGlTYMkS4NAh4PHHZXBmA11vxJgYw/WxseoLsomIyHF0D1rLP4jWPWhNT3dPudyNLWhEVrLnSU9lTfgFBcD69aWZF8+dK32tfOtCXJwThtJ40AS/HlRUz7ZrF/DGG8Dy5YAum29iIjBxosw646AJ8tgbkYjItzhlmhUvwQCNyAr2dKkzF9i9/rq8x125ElizBsjPL329bObF22+X98pOvXn1oAl+Paionkc3ufRbb8nMMzq9egHPPy8rn67/oQOxNyIRkfo5arwYH7SaxwCNyEL2POkxF9hlZQHDhhmuqyjzotO/oDxogl8PKqrnKCwE0tLkzOh798p1Go2cLf2554CbbnJv+YiIyICrk2s4crwYH7SaxwCNyEK2PumpKLDT8feXc/jecw/Qrp1TGics40ET/HpQUUupNU3VxYtyMOPcufKEAkDVqsDIkbLyxse7tXhERGTM1ck1HJ2Yiw9azWOARl7BGfe95fepu2+tjO5JT0kJsHMn8O67lWdhLC4GUlJkNka3sjClnhYabNnk3jjDnXMR21Tf1Jim6p9/ZAX96CPg0iW5LjoaeOop4NFHZR9bIiJSHVdnMXbGeDGPfNDqIm7P4jhv3jzEx8cjODgYHTt2xM6dOyvcftmyZWjatCmCg4ORkJCAjIwMg9fT09PRs2dPhIeHQ1EU7Nmzx2gft956KxRFMVhGjx5tsM2JEyfQu3dvVKlSBXXq1MGECRNQXFxs9+clx0tPlw/4u3UDhgyRP+Pj7cv8Y2qfTz9t2XtPnpTJ7mJigKQkmenREqppwq8kpV46Uh1+vp1UVKc9QbT686stTdWOHcDAgUCDBnIes0uXgBYtgE8+AY4dkwlAGJzZxhUpXonIp7kji7E1vYgspXvQChj3HHL2g1bVE26UlpYmAgMDxaJFi8Rff/0lRo4cKWrUqCFOnz5tcvtt27YJjUYj3nzzTbFv3z7x0ksviYCAALF37179Nv/3f/8npk6dKj766CMBQOzevdtoP8nJyWLkyJEiJydHv1y8eFH/enFxsWjZsqXo3r272L17t8jIyBARERFi0qRJVn2+ixcvCgAG+3aXwsJCsXLlSlFYWOjuojjU8uVCKIoQ8quhdFEUuSxf7rh9WrKUf19oqBC33WbZezdudPjpsU9xsSjKzBS/jBsnijIzhSgudsr5dlBRxcaNQixdKn8WF1v6onVs+vzFxULExlZcaeLi7CqXRYqKhPjySyESEw2P3727EKtXC1FS4rBDeev3TaWWLzf+W8fGuu8/hgfy2bpDdvG1erNxo+vvK5YuteyYS5dav29TX51xcc7/6nRHvbE0NnBrgNahQwcxZswY/e9arVbUrVtXzJgxw+T2AwcOFL179zZY17FjR/Hoo48abXvs2LEKA7SxY8eaLVdGRobw8/MTubm5+nUffPCBCAsLE9euXavkU5VigOZczrjvrWyflizR0UKMHi3EmjVCFBSU7tNc0Oeq+3NblK03aokzrOLAG2abP787rqRl/fuvELNmCVGvXumxAgOFeOghIf74wymH9Mbvm0qp9emFh/HJukN287V648xgyRxnX8oc+CzVYmoO0Nw2Bq2wsBC7du3CpEmT9Ov8/PzQvXt37Nixw+R7duzYgXHjxhmsS0lJwcqVK60+/ueff47PPvsMUVFR6NOnD15++WVUqVJFf5yEhARERkYaHOexxx7DX3/9hTZt2pjc57Vr13Dt2jX973l5eQCAoqIiFBUVWV1GR9Id393lcKTNmxVkZZmvwkLI5vaNG4uRnCwcsk9z/P0F7rpLYMKEErRrJwymhiopAd5+W8GgQZrrY6VK2/EVRZZr1iwtSkqEfpoptShbb7Zvd/z5diZlxQpoBg0ChEDZnhPierdCbVoaRP/+Fu/P1vqmnDxp0WDf4pMnIRz5/3P/fvi9/z78Pv0UypUrsowRESh59FGUjB4N6L7fnPCd4I3fNxXSauH/1FNGdQ0AIASEogBjx6K4Vy8f7atjOZ+rO+QQvlZvatdWYEkaidq1i1FU5JjrcWIiEBPjj1OnDO9jdBRFICYGSEwstvmy0qlT6b9LSuD0eyJ31BtLj+W2AO3cuXPQarUGQRAAREZG4sCBAybfk5uba3L73Nxcq449ZMgQ1K9fH3Xr1sUff/yB559/HgcPHkT69XEg5o6je82cGTNmYOrUqUbr161bpw/+3C0zM9Otx9dqgX37wvHvv8GoWbMAzZuft/h+pfx7z58PBlB5Vo01a/YgP9+yDB8//hhj0T4BgXr1LqF+/Ty0aXMayclZ0GiAs2eBtWuNtw4KAp57Lhoff5yA8+dD9OvDw69ixIg/ERSUg3LDKVUlMzPT4nNjzfl2Gq0WPR9/HBoTN8yKEBAACseMQaa/v8U3zLZ+/vB//kFnC/b/0z//4Ly9laCkBJG//YYG332HOmXG3+bVq4cjffogq2tXlAQFyQn1XMDd3zeuEr53LzpXkEVIEQLIysLPs2bhfEKCC0vmuXyl7pBj+Uq90WqB8PCe1++DTKV9FoiIuIq8vEyH3ls88EA03njjZgCi3HEFhADuv/8XfP+9WgbUW86V9ebK9QemlfHJLI6jRo3S/zshIQHR0dG4/fbbceTIETRs2NDm/U6aNMmghS8vLw9xcXHo2bMnwsLC7CqzvYqKipCZmYkePXogoOzEWi60YoWCceM0yM4u/U8dEyMwe7YW/ftX/ITH1HsjIix7KtSzZ2toNK31Gfc6dxZm78kVRcHs2ZXv86uvtOjXLwRACIBIAJXPD9WrFzBlCrB1a3GZsgRAo2kDwHSrrLuVrTdVqwZadG7uvLM1kpNbOb9wFVA2b4b/+fPmXwdQ5dw59A4Lg0hOtmifVataVjeMPn9KCsT8+cCpU/JGvRyhKEBMDDqOH29768rFi/D79FP4vf8+lMOH9fsVd92FkiefREhyMloqClratnerufz7RquFsnWrPq2m6NzZpS1VyvXeEpVJrF8folcvJ5fGs6nhWkWexxfrzfvvKxg0CJDBkXHPnHnzAtGnj2O/b3r1Atq21V6/HytdHxsLvP22Fv37q+t+RqsFtm5VzN7/uaPe5Fl4vXBbgBYREQGNRoPTp08brD99+jSioqJMvicqKsqq7S3VsWNHAMDhw4fRsGFDREVFGWWT1B23omMFBQUhKCjIaH1AQIBqvjDcVZb0dDnXbfn701OnFAwa5F9hxj1z7z13ruLJwhQFqFULeOQR/wozm586BXz7LfDNN8CGDRV/Dl3K19RUf5vu/wICgO7drX+fuwUEBKBbN3+L0uF262bbuXGos2ct2sz/7FnDmcAr0K2bZemAjT5/QIBMZW9mPgAFAObORUBwsEXlMPDnn8C8ecCnnwL5+XJd9erAI49AGTMGyg03uDVVr0u+b9QwfUFcnEWb+cfFWVzffJ2arpvkOXyp3gwcKOdQNf76UzBnjrxPcdZx77mn/FQzCjQadbX5WHNpcGW9sfQ4brt2BwYGol27dthQ5o64pKQEGzZsQFJSksn3JCUlGWwPyGZJc9tbSpeKP/r6THhJSUnYu3cvzpw5Y3CcsLAwNG/e3K5j+SJ70sFaMskzYDo9qxDA+fPGaWGzsuSXy+DBwM03yxTto0cDa9YAhYWAuRjc11O+elQ6XCfMfmnX53fkfABFRcCyZXI29IQEYP58GZw1ayaDtawsYNYs4IYbLN+np1LL9AW6yXzMzTCvKDKI88XJfIjIaVJTgePHgY0bgaVL5c9jx5z/bEqjkZegwYPlT1Vc98tQy6XBLi5KWmJSWlqaCAoKEosXLxb79u0To0aNEjVq1NBnTxw6dKiYOHGifvtt27YJf39/MWvWLLF//34xefJkozT758+fF7t37xarV68WAERaWprYvXu3yMnJEUIIcfjwYTFt2jTx66+/imPHjolvvvlGNGjQQHTt2lW/D12a/Z49e4o9e/aItWvXitq1azPNvo3syfxj6Xtr1zZO1Bcebtl7FUWIjh2FeP11If76S2Ybd1fKV7UxVW/sOTcuy9LkxNSZdtUNe05AdrYQU6cKUbdu6YE1GiHuuUeIH35waJp8e7nk+0ZtaUV1WRzL1zlmcbSKr2XjI8dgvSEday4Nas7i6NYATQgh3nvvPVGvXj0RGBgoOnToIH766Sf9a8nJyWL48OEG23/11VeicePGIjAwULRo0UKsXr3a4PVPPvlEQI5eNFgmT54shBDixIkTomvXrqJWrVoiKChINGrUSEyYMMHoRB0/flzceeedIiQkRERERIhnn31WFBUVWfXZGKBJ9qSDtfS9n31meN+7fr1l7xs/XojrsbsRd6R8VRtz9caWc+PyKaKceMPssrqh1Qqxbp0QqakyGNN9hjp1hHjpJSFOnnTSge3jku8bd09fYAqf7NiNN9pkC9Yb0rHm0qDmAM3tHUafeOIJPPHEEyZf27Rpk9G6e++9F/fee6/Z/T344IN48MEHzb4eFxeHzZs3V1qu+vXrI0PNafU8iD29zSx9b0yMbGY/eFCOJ1u40LL3tW1rvkujrgmfjFl7bnTdDcp3VdV1N7C2l59FdN0KTXVClx30bd610+vGuXPA4sXAhx8C15N+AAA6dwYee0z20TUx3tWn5FiYKczS7RwhNRXo27f84Az19f8hIvJSarw02MLtARp5P93wjMqSK5ganlHZewGgdm2Z4GPUKODQIevKZsUQJLJRZWMQFUWOQezb1wn3sZ50wyyELOeCBXKMWWGhXB8WBgwbBjz6KNDSVXkYPYATxhk6BJ/sEBG5jVovDdZyZ4Iv8hH2JFeo6L06Z8/K9x86JBOk9eghf4+K4ph9NdiyxXigbllCyAmet2xxUgHUPpr53Dng7bdlko/kZODzz2Vw1rYt8NFH8unEe+8xOCuPiTmIiKgcb7k0MEAjl7AniV3//jLgMjeVXEQEMHw48NVX8l533TrZYjNvnnxd9RkHvZzDuhtotcCmTcAXX8ifptJ+OpIzj1dSIud0GDQIqFsXGD9e9s+tWhUYMQLYuVNOJv3II0C1ao47rjfxqLSiRETkCt5yaWAXR3IZa3qbXbsGbN4MfPedXI4dM3z9hhvkXBx33w107Gh6H04cgqQ6Wq16e/E5pLuBq+e6ctbxsrOBJUuARYuAI0dK17dvD4wcKVv5QkNt37+v8aX/5EREZBFvuDQwQCOXqmh4xqlTQEaGXNatK513FwACA4HbbgN69wbuuguIj7fseJ40BMlWapintyL2jEEE4PoMI44+3rVrMnPNokXA99/L1jNANgnff78MzNq0cVz5fY0v/CcnIiKrePqlgQEauY1WC/zyC7B6tVx27zZ8PTq6NCC7/Xbbe3p585h9t2RHtJKuu8GAAaUTiOtU2t3A1RlGHHm8vXtlUPbpp3LGdJ2uXYGHHgLuvVd2aST7efN/ciIisoknXxoYoJFLXbggW8dWrwbWrpVjxnQUBbj5ZqBXLxmUtWkD+HGUpFluzY5oJZu7G1iTYcQR38L2Hu/sWTlmbckS4LffStfXrQs8+KBcbrzR/nK6gpr7zRIREXkxBmjkVEIAv/9e2nVxx47SHl4AUL06kJIiW8ruuAOoU8d9ZfU0ro5d7GVTdwNXT2hiy/EKC+VAySVLZCUvLpbrAwLkIMmHHwZ69gT8PejrVu39ZomIiLyYB90xkKe4eBFYvx5Ys0ber5a/523ZErjzThmU3XKLvI8l63niZIxWdzdw9YQmlu6ndm3ggw+AFSuAn38G8vJKX2vfXqYVHTRIphj1NJ7Qb5aIiMiLMUAju+laydaskcv27YYZyatWBbp3l0HZnXcC9eq5r6zexFsmY6yQ3RlGHHw8AAgJkRVZ11IGyL64d98NvPYa0Ly5Y8riDp7Ub5aIiMhLMUAjm1y4IFvJ1q6VS/lWmnr1gBYtZHKPxx4DqlRxTzm9matjF7ewK8OIg4+nc/Wq8bqSEuCbb4ChQz07QPO0frNEREReiCkYyCJarezJNXWq7JZYuzZw333AJ5/I4KxKFaBPH5kxPCoKOHFCtqaNHw80aSJ7TZFjqXYyRkdP8GzPLOe2Hu/TT4EaNax/79NPO38CbVMcdc49sd8sERGRl2ELGpl16pTMuPj99/LnhQuGr7doIRN83HmnbKVZvZpDV1xNdZMxOiu5hCsmNLl6VQ6aTEuTST8KCkpfa9JENge//7759zuidcmWzImOPOc+0W+WiIhI3RigkV5Bgbw3/P57ufz5p+Hr1asDPXrIoCwlBYiLK33NIUNXmNbbJqqZjNHZySWcMaHJ1avAu+/Kpwu7dgFXrpS+1rgxMHiwTPbRtKlsnaooQNOxtXXJlkDL0efcJ/rNEhERqRsDNB8mBPDXX0BmpgzINm82bDRQFJmQLiVFpsDv2NF8pnC7h64wrbdd3D4ZoycllygsBDZsAGbNAjZuNCyzRiMn4Zs8GWjd2rDvqDNbl2wJtJxxzl095o+IiIiMcAyajzl9Gvj8c5kFPCYGSEgAxo2TAVpBgZxP96GHZC+vs2eBnTuB6dOBTp0qnsbJrqErupvT8hGe7uaUA9jUz5oI3R0KC+WgyIcfloMke/UCfvjBOLjRaoFVq4Bjx4wH9ulal8qv11EU2axsbetSZYEWYHpsm7POuavH/BEREZEBtqD5gL/+AhYt8kN6+q04ftxw0rGQEKBrVzmPbkqKTEBn7v6zIjY3LnhSywuZp8bkElevysGT6eky6Prvv9LX/PwMZ0wvz1Sdc1brkq3Nz84856rpN0tEROR7GKD5gIMHgdmzNQCqAwDatJEBWY8esmUsONj+Y9g8dIVpvR3D3eP31JJcIi9PJvpYvly2mOXnl74WGSmDq0aNgGeeMb+PiuqcM7Ky2BpoOfucu73fLBERkW9igOYDbrsNGDasBBERv2HcuFaIiQmo/E1WsrlxQY0tL55GDeP33JlcIjcX+PZbOQ9ZZqbszqhTr548B/fcAyQlyQr4xReW7ddcnXN065KtgRYTehAREXklBmg+oEYN4OOPtcjIyEadOq2cdhybGhfU0vLiqZydOdFSrkwuIQRw4IAMyL75Rk7QV/Z4TZrIgCw1FWjb1rjPriPqnCNbl2wNtJjQg4iIyCsxQCOzbOk1Z3XjAlsBbKe28XvOnJStqAjYvl3OT/bNN8ChQ4avd+ggP2e/fnIgZUXUVufsCbRUNxEeERER2YsBGplkT685qxoX2ApgO3eO3zMXvdvb/a/sfqtUAS5elGPJ1q41TPIRGCgnju7bF+jTR6YftZQa65w9gRYTehAREXkVBmhkxKJec30dmJSCrQC2cdf4vcqid1u7/y1fDjz+OHDmjOnXIyKAO+8E7r5bphwNDbWp+ADUWefsCbSY0IOIiMhrMEAjAxb1mht1BX2fagZN9onSF+1NSsFWAOu5Y/yeo8e8/fuvTOzx4YdyXjJzXn8deO45x9YHNdY5BlpEREQ+jwEaGbCo19z5KtiCG3ArygRojkhKwZtT67h6LJUjxrxptcCuXXJ+sjVrgJ9+qng+MkDu94MPZIDmaL5e59w9PQMREREZYYDm48rfn2VnW/a+HJRrleGk0q7n6rFUto55O3ZMtpJlZgIbNshWs7Lq1wf++cf6/ZJ91DA9AxERERlhgObDTN2fRURY9t5omBjXxBtp13PlWCpLx7IdOgRcuACsXy+DssOHDV+vXl1OznfHHXLZtg0YMsRxx6fKqWV6BiIiIjLCAM1Hmbs/O3eu4vcpKEEsstAFW8xvxBtp13LVWCpLx7I9+qhhxdJo5CTRPXoAPXsC7dsD/mW+eo4edezxqWJqm56BiIiIDDBA80EV3Z+VZdRrDvKXOXgaALAJychBNKKRgy7YAg2ujyXijbTruWIslW7MW0XdHAFZaZo3B7p1kwHZrbcCYWGV71ct85J5O3dOz0BERESVYoDmgyq7P9OJiADOni39PTYWmHP1UeC8gngcRxbiSl/DSczF00iN+4U30l7GPz8fSkaG7IoYElLxxk8/LZN5WBOkq3FeMm/mrukZiIiIyCIM0HyQpfdd77wDxMSU7TWn4JtJIzDgrQ4o386RjRgMwDJ8PWgnUp11I82Mc66RnQ1s3Qps3Qr/rVvR648/oJTPtKjRyL+HTlycfWPe1Dgvmbdyx/QMREREZDEGaD7I0vuumBjDHk5aLTD2i0QICACKwbYCflAg8HRaIvrOcELcZE/GOWcEdt4SLGq1wL59snVs61b58/hx/cu6v7Jo1AhKcjKQnAx07SrPvaM/vz1j6bzl7+EK7FJKRESkagzQfJCt92elXSMV4zcBEFCcM3TFnoxzzkgl7snpyc+dA37+GdixQ85BtnMncOmS4TZ+fkDr1kCnTihOTMSGggLcNnQoAgICDLdzxvgkW8bSefLfwx3YpZSIiEjVGKD5IFvvz9wydMWejHPOSCXuSenJCwqAPXtkEPbLLzIgK5/yHgCqVQM6dgQ6d5ZLx45AaCgAQBQVoSAjw7XltoYn/T3UhF1KiYiIVIsBmo+y5f7MLUNXbM0454xU4mpOT15UBOzfLwMxXUC2dy9QXGy8bdOmMu19YqJcWrTwzNYSNf89PIGrpmcgIiIiq/i5uwDz5s1DfHw8goOD0bFjR+zcubPC7ZctW4amTZsiODgYCQkJyCj3dD89PR09e/ZEeHg4FEXBnj17DF6/cOECnnzySTRp0gQhISGoV68ennrqKVy8eNFgO0VRjJa0tDSHfGa1SE2Vw402bgSWLpU/jx0z//Bc1zVSMd3DEYoic0U4dOiKrc121gR2lnLGPm1RUAD8+iuwYAEwejTQoYNs8WrVCnjkEbl+924ZnNWpA/TuDUydCqxZIyeQ3r8fWLQIGDUKuOkmz70hV8vfw5PpupQOHix/empdICIi8iJubUH78ssvMW7cOMyfPx8dO3bEnDlzkJKSgoMHD6JOnTpG22/fvh2DBw/GjBkzcNddd2Hp0qXo168ffvvtN7Rs2RIAkJ+fj86dO2PgwIEYOXKk0T5OnTqFU6dOYdasWWjevDn++ecfjB49GqdOncLXX39tsO0nn3yCO+64Q/97jRo1HHsCVMCaIT9uGbpia7OdM/pjuqOP59mzwO+/Gy779pluGQsLA9q1A26+WS4dOsiI2VxE7emYLp6IiIi8kFsDtNmzZ2PkyJF46KGHAADz58/H6tWrsWjRIkycONFo+7lz5+KOO+7AhAkTAADTp09HZmYm/ve//2H+/PkAgKFDhwIAjpfJRFdWy5YtsXz5cv3vDRs2xGuvvYYHHngAxcXF8PcvPSU1atRAVFSUQz6rt3D50BVbM5pYGNhp60RjyyYLe3g5s4/n1avAgQPAn3/KRReM5eaa3j48XAZjbdoAbdvKpUEDmeDDVzBdPBEREXkhtwVohYWF2LVrFyZNmqRf5+fnh+7du2PHjh0m37Njxw6MGzfOYF1KSgpWrlxpV1kuXryIsLAwg+AMAMaMGYNHHnkEDRo0wOjRo/HQQw9BqaA14tq1a7h27Zr+97y8PABAUVERioqK7CqjvXTHd0Q5+vQBevUCtm5V9IFN584CGo0cCuVoyttvQzNoEKAoUMoEaeL630I7axZESQlQdq6uxET4x8QAp04ZvKfse9NrjcDY4cnIzi5dHxMjMHu2Fv37mwgGLdgnYmJQnJho/kQUFAB//w3lwAEof/0FZd8+KH/9BRw9ajzXmG6/jRpBJCTI5aabINq0Md3XVKs1nJvMARxZbxzOEX8PcgpV1xtSNdYdsgXrDdnCHfXG0mO5LUA7d+4ctFotIiMjDdZHRkbiwIEDJt+Tm5trcvtcc60MFpZj+vTpGDVqlMH6adOm4bbbbkOVKlWwbt06PP7447h8+TKeeuops/uaMWMGpk6darR+3bp1qFKlis1ldKTMzEyH7i8sDMjPB77/3qG7NRQUhOjnnkPCxx8j5Px5/eqr4eH4c8QI5AQFASYyDUY/8ABufuMNo1nbBIB00Q8Dzi8wek92NnDffRo8//wvSEoy7hpX0T4hBH65/37krF2LwLw8VDt1CtWyshCalaX/WeXMGZPBBAAUhoYir149XIqLQ158PC7GxyOvfn1oQ0IMN9y7Vy4u5Oh64ygW/T2cWjmpImqtN6R+rDtkC9YbsoUr682VK1cs2s6nszjm5eWhd+/eaN68OaZMmWLw2ssvv6z/d5s2bZCfn4+33nqrwgBt0qRJBi18eXl5iIuLQ8+ePREWFubw8lujqKgImZmZ6NGjh/F8Vp6gVy9gyhQUb92q748Y0Lkz2mg0aFPBe7Rt20IzbhzKNpNpY+rh6aufARcA4zndFCiKwOef34wpU4qNuzvq9vnMM8CpU6XrQ0MhbroJ7devhzJ/PpRySWfKEjVqQDRtCjRvDtGiBcT1n0pkJKorCqpbflacTvX1xszfGLGx0L79Ntr072++fpDTqL7ekGqx7pAtWG/IFu6oN7redZVxW4AWEREBjUaD06dPG6w/ffq02XFfUVFRVm1fkUuXLuGOO+5AaGgoVqxYUekfpmPHjpg+fTquXbuGoKAgk9sEBQWZfC0gIEA1XxhqKovVAgKA7t2te8/AgcA99xikEt+q7YKs7uYzmQihICsL+OlHgVtv+Eemtjx61HDJzzd4j3LpEpRt28qsuJ7SslkzmdZe97NpUyh16lTYVVaNVF1vTPyNlS5d4M+MhG6n6npDqsa6Q7ZgvSFbuLLeWHoctwVogYGBaNeuHTZs2IB+/foBAEpKSrBhwwY88cQTJt+TlJSEDRs24Omnn9avy8zMRFJSklXHzsvLQ0pKCoKCgrBq1SoEBwdX+p49e/agZs2aZoMzUrFyqSpzvrDsbTkpwwFUMrVCdDRw441yady49N8NGwLluyZaQqvlvFS2sCYdKREREZGKubWL47hx4zB8+HC0b98eHTp0wJw5c5Cfn6/P6jhs2DDExMRgxowZAICxY8ciOTkZb7/9Nnr37o20tDT8+uuvWLCgdCzRhQsXcOLECZy63v3s4MGDAGTrW1RUFPLy8tCzZ09cuXIFn332GfLy8vTNjbVr14ZGo8G3336L06dPIzExEcHBwcjMzMTrr7+O8ePHu/L0kC2EkHN95eTIDIhlf2ZnA9nZiD4ci0oDLwDRyAGqVAHi42XA1aCB4RIfL193lPR00+kx5861Lz2mmoI+NZWFiIiISIXcGqDdd999OHv2LF555RXk5uaidevWWLt2rT4RyIkTJ+BXJm34LbfcgqVLl+Kll17CCy+8gBtvvBErV67Uz4EGAKtWrdIHeAAwaNAgAMDkyZMxZcoU/Pbbb/j5558BAI0aNTIoz7FjxxAfH4+AgADMmzcPzzzzDIQQaNSokX5KAJ+ihpvpwkLg339l0KVbzp4Fzpwx/Kn79+nTlWbs6wI/xOItZCMGwsRc7QoEYiOL0OWP5UDtWq6ZRyw9XU4wVz6BSHa2XP/117YFac4K+myhprIQERERqZQihJmUcmS3vLw8VK9eXZ/G352KioqQkZGBXr16Wdb/1Z6baSGAa9eAK1fkWK3Ll0sX3e+XLgEXLxou//1X+m9dMHb5sm0fODwciIqSgWVUlFxiYuQSG4v0vTdiwOhwAIrJCbdtjYdsotXK1riy57os3Vxvx45ZFyCbC/qs+JBW1xsnloU8h8PqDfkc1h2yBesN2cId9cbS2MCnszj6jD/+gGb2bLTOyoJm5Up5k6+7MVYUuQghA4WSEuD4cWDTJuP9ZGXJZAzNmsn8+oWFcrl6VS4FBaU/HUlRgBo1gFq15FK7NlCnjvxZ/t9RUUBkJBAYWOEuU5OAryNcOOF2RbZsMR+cAfJvc/Kk3M7ScVZarfxwpp6/CCHP6dNPA337Or9VVE1lISIiIlI5Bmi+ICsLfkuWoL6j9rd/v+XbBgYC1arJpWrV0n9XqwZUr25+0QVj4eHydyfcuKemypjA3b04kWM835pd2wHOCfpspaayEBEREakcAzRf0KQJtK++ioMHD6JJ48bQ+PnJm+Kyi5+fXP75B1hgPIGzkenTgXbtZAAWEiKX4ODSf+t+r6Qly90qTP7nqjF40dGO3Q5wTtBnKzWVhYiIiEjlGKD5AG18Q2zs+DzWXNiDOxNbo1s3f/NxxhdfWBagNWwI3HmnQ8upKq5MaNGli9x3drbpboC6MWi33CK7nloSMDoj6LOVmspCREREpHLGKezIq6Sny/wTPXr4Y/bs9ujRwx/x8XK9Sb52M63VyqDniy/kT622NKFF+W55uoyKZk+ejTQaGfgBxhkjdb8PGiSD4m7dgCFD5M+K/pC6oM9cBkrdRNpdujjkI1RITWUhIiIiUjkGaF6sNM4wbJXJzhbm4wxfupnWRa9lg5769YFRo8wntABkQgut1rFlSU2VmQxjYgzXx8YC48cDs2ZZFzBaEvTNmeOaAXdqKgsRERGRyjFA81KlifMEAMObYiFk1kaTcYav3ExX1Ep2/rz595VNaOFoqakyg+bGjcDSpfLn4cOydc+WgLGioE+X1t5UC6IzWFIWIiIiIuIYNG9VmjjPdEuYgGI+cZ7uZloVOeidoKK075ZyVkKL8llLNm2yLwNiRakqXT1xtGrSZhIRERGpFwM0L5WTXQJLGkjNbufNN9OVpX23hKvG4DkiA6KpVJXmJo7WdZt0VqtWhWkziYiIiIgBmpeKPvsHgNb2bedJN9PWpMS3p/VLl1HRVWPwnJG0xZqJo4mIiIjIpTgGzUt1qX0AsTgJBSUmX1dQgjicQJfaB1xbMGeMeTKV7KOiDIe2tn65YwyeM5K2WDNxNBERERG5FAM0L6WJicJcjAUAoyBN9/scPA1NTJTrCmVtIGXpPq1NiW9J0BMeLrcpyx0JLZyRtIUTRxMRERGpFgM0b9WlC1Jjf8HXuBcxyDZ4KRZZ+Br3IjXuV+d01XPV3GKVddUDTGc4tCToWbDAOKPisWPuSZDi6AyIvjbXHREREZEH4Rg0b3U9CEkdMAB9xTfYgs7IQTSikYMu2AqNUgLM+drxXfVMZQaMiQEKCiwb82RNeazpqld+LJ2lmSrVMgbPkUlbdC2I2dmm/yZlx9mVmO4iS0RERETOwQDNm10PQjRjx+LWrM2l6+PinJMuv6LMgBWpLFW8OfZ21fO0TJWOStqia0EcMEAGY2X/XuW7TTJAIyIiInIpBmje7noQUrxxI/asWYPWd94J/27dHB+EuGNuMUd01fOkTJWO5O1z3RERERF5KAZovkCjgUhORnZ+PlolJxsGZ9akp6+IO+YWs6arHhnztBZEIiIiIh/AAM2XmRovFhsru79Z24LijrnFrOmqR6b5agsiERERkUoxi6OvcnRWRXfNLeboDIdERERERG7EAM0X2ZqeviLunFssNVU9KfGJiIiIiOzALo6+yJ709OZY0t1wwQLnjXliVz0iIiIi8gIM0HyRvenpzfG0ucWIiIiIiFSGAZovckR6enOYGbBijsqaSUREREReiQGaL3J2enp2NzTNkVkziYiIiMgrMUmIL9KNFwOMk3owPb1zODprJhERERF5JQZovorp6V3HGVkziYiIiMgrsYujL+N4MddwRtZMIiIiIvJKDNB8HceLOV75RCDZ2Za9z9qsmURERETkdRigETmSqUQgERGWvdeWrJlERERE5FUYoBE5ii4RSPmxZufOVfw+e7NmEhEREZHXYJIQIkeoKBFIWcyaSUREREQVYIBG5AiVJQLRKd/dkVkziYiIiKgMdnEkcgRLE3y8846c2oBZM4mIiIjIBAZoRI5gaYKPmBhmzSQiIiIis9jFkcgRunSR3RXLjzHTURQgLo6JQIiIiIioQm4P0ObNm4f4+HgEBwejY8eO2LlzZ4XbL1u2DE2bNkVwcDASEhKQkZFh8Hp6ejp69uyJ8PBwKIqCPXv2GO2joKAAY8aMQXh4OKpVq4Z77rkHp0+fNtjmxIkT6N27N6pUqYI6depgwoQJKC4utvvzkpfSaIC5c+W/mQiEiIiIiGzk1gDtyy+/xLhx4zB58mT89ttvaNWqFVJSUnDmzBmT22/fvh2DBw/GiBEjsHv3bvTr1w/9+vXDn3/+qd8mPz8fnTt3xhtvvGH2uM888wy+/fZbLFu2DJs3b8apU6eQWiZJg1arRe/evVFYWIjt27djyZIlWLx4MV555RXHfXjyPqmpMuFHTIzheiYCISIiIiILuXUM2uzZszFy5Eg89NBDAID58+dj9erVWLRoESZOnGi0/dy5c3HHHXdgwoQJAIDp06cjMzMT//vf/zB//nwAwNChQwEAx48fN3nMixcvYuHChVi6dCluu+02AMAnn3yCZs2a4aeffkJiYiLWrVuHffv2Yf369YiMjETr1q0xffp0PP/885gyZQoCAwNN7vvatWu4du2a/ve8vDwAQFFREYqKimw4Q46jO767y+H1+vQBevWCsnWrPhGI6NxZtpx54LlnvSFbsN6QrVh3yBasN2QLd9QbS4/ltgCtsLAQu3btwqRJk/Tr/Pz80L17d+zYscPke3bs2IFx48YZrEtJScHKlSstPu6uXbtQVFSE7t2769c1bdoU9erVw44dO5CYmIgdO3YgISEBkZGRBsd57LHH8Ndff6FNmzYm9z1jxgxMnTrVaP26detQpUoVi8voTJmZme4ugu8ICwPy84Hvv3d3SezGekO2YL0hW7HukC1Yb8gWrqw3V65csWg7twVo586dg1arNQiCACAyMhIHDhww+Z7c3FyT2+fm5lp83NzcXAQGBqJGjRpm92PuOLrXzJk0aZJBAJmXl4e4uDj07NkTYWFhFpfRGYqKipCZmYkePXogICDArWUhz8F6Q7ZgvSFbse6QLVhvyBbuqDe63nWVYZp9BwoKCkJQUJDR+oCAANV8YaipLOQ5WG/IFqw3ZCvWHbIF6w3ZwpX1xtLjuC1JSEREBDQajVH2xNOnTyMqKsrke6Kioqza3tw+CgsL8d9//5ndj7nj6F4jIiIiIiJyBrcFaIGBgWjXrh02bNigX1dSUoINGzYgKSnJ5HuSkpIMtgdkv1Fz25vSrl07BAQEGOzn4MGDOHHihH4/SUlJ2Lt3r0E2yczMTISFhaF58+YWH4uIiIiIiMgabu3iOG7cOAwfPhzt27dHhw4dMGfOHOTn5+uzOg4bNgwxMTGYMWMGAGDs2LFITk7G22+/jd69eyMtLQ2//vorFixYoN/nhQsXcOLECZw6dQqADL4A2fIVFRWF6tWrY8SIERg3bhxq1aqFsLAwPPnkk0hKSkJiYiIAoGfPnmjevDmGDh2KN998E7m5uXjppZcwZswYk10YiYiIiIiIHMGtAdp9992Hs2fP4pVXXkFubi5at26NtWvX6hNynDhxAn5+pY18t9xyC5YuXYqXXnoJL7zwAm688UasXLkSLVu21G+zatUqfYAHAIMGDQIATJ48GVOmTAEAvPPOO/Dz88M999yDa9euISUlBe+//77+PRqNBt999x0ee+wxJCUloWrVqhg+fDimTZvmzNNBREREREQ+zu1JQp544gk88cQTJl/btGmT0bp7770X9957r9n9Pfjgg3jwwQcrPGZwcDDmzZuHefPmmd2mfv36yMjIqHA/REREREREjuS2MWhERERERERkiAEaERERERGRSjBAIyIiIiIiUgm3j0HzZkIIAJbPGu5MRUVFuHLlCvLy8jiJI1mM9YZswXpDtmLdIVuw3pAt3FFvdDGBLkYwhwGaE126dAkAEBcX5+aSEBERERGRGly6dAnVq1c3+7oiKgvhyGYlJSU4deoUQkNDoSiKW8uSl5eHuLg4nDx5EmFhYW4tC3kO1huyBesN2Yp1h2zBekO2cEe9EULg0qVLqFu3rsFUYuWxBc2J/Pz8EBsb6+5iGAgLC+OXF1mN9YZswXpDtmLdIVuw3pAtXF1vKmo502GSECIiIiIiIpVggEZERERERKQSDNB8RFBQECZPnoygoCB3F4U8COsN2YL1hmzFukO2YL0hW6i53jBJCBERERERkUqwBY2IiIiIiEglGKARERERERGpBAM0IiIiIiIilWCARkREREREpBIM0LzIvHnzEB8fj+DgYHTs2BE7d+6scPtly5ahadOmCA4ORkJCAjIyMlxUUlITa+rNRx99hC5duqBmzZqoWbMmunfvXmk9I+9k7feNTlpaGhRFQb9+/ZxbQFIta+vOf//9hzFjxiA6OhpBQUFo3Lgxr1c+yNp6M2fOHDRp0gQhISGIi4vDM888g4KCAheVltTgxx9/RJ8+fVC3bl0oioKVK1dW+p5Nmzahbdu2CAoKQqNGjbB48WKnl9MUBmhe4ssvv8S4ceMwefJk/Pbbb2jVqhVSUlJw5swZk9tv374dgwcPxogRI7B7927069cP/fr1w59//unikpM7WVtvNm3ahMGDB2Pjxo3YsWMH4uLi0LNnT2RnZ7u45ORO1tYbnePHj2P8+PHo0qWLi0pKamNt3SksLESPHj1w/PhxfP311zh48CA++ugjxMTEuLjk5E7W1pulS5di4sSJmDx5Mvbv34+FCxfiyy+/xAsvvODikpM75efno1WrVpg3b55F2x87dgy9e/dGt27dsGfPHjz99NN45JFH8P333zu5pCYI8godOnQQY8aM0f+u1WpF3bp1xYwZM0xuP3DgQNG7d2+DdR07dhSPPvqoU8tJ6mJtvSmvuLhYhIaGiiVLljiriKRCttSb4uJiccstt4iPP/5YDB8+XPTt29cFJSW1sbbufPDBB6JBgwaisLDQVUUkFbK23owZM0bcdtttBuvGjRsnOnXq5NRyknoBECtWrKhwm+eee060aNHCYN19990nUlJSnFgy09iC5gUKCwuxa9cudO/eXb/Oz88P3bt3x44dO0y+Z8eOHQbbA0BKSorZ7cn72FJvyrty5QqKiopQq1YtZxWTVMbWejNt2jTUqVMHI0aMcEUxSYVsqTurVq1CUlISxowZg8jISLRs2RKvv/46tFqtq4pNbmZLvbnllluwa9cufTfIo0ePIiMjA7169XJJmckzqene2N/lRySHO3fuHLRaLSIjIw3WR0ZG4sCBAybfk5uba3L73Nxcp5WT1MWWelPe888/j7p16xp9oZH3sqXebN26FQsXLsSePXtcUEJSK1vqztGjR/HDDz/g/vvvR0ZGBg4fPozHH38cRUVFmDx5siuKTW5mS70ZMmQIzp07h86dO0MIgeLiYowePZpdHKlC5u6N8/LycPXqVYSEhLisLGxBIyKbzJw5E2lpaVixYgWCg4PdXRxSqUuXLmHo0KH46KOPEBER4e7ikIcpKSlBnTp1sGDBArRr1w733XcfXnzxRcyfP9/dRSMV27RpE15//XW8//77+O2335Ceno7Vq1dj+vTp7i4akUXYguYFIiIioNFocPr0aYP1p0+fRlRUlMn3REVFWbU9eR9b6o3OrFmzMHPmTKxfvx433XSTM4tJKmNtvTly5AiOHz+OPn366NeVlJQAAPz9/XHw4EE0bNjQuYUmVbDlOyc6OhoBAQHQaDT6dc2aNUNubi4KCwsRGBjo1DKT+9lSb15++WUMHToUjzzyCAAgISEB+fn5GDVqFF588UX4+bF9goyZuzcOCwtzaesZwBY0rxAYGIh27dphw4YN+nUlJSXYsGEDkpKSTL4nKSnJYHsAyMzMNLs9eR9b6g0AvPnmm5g+fTrWrl2L9u3bu6KopCLW1pumTZti79692LNnj365++679Vmy4uLiXFl8ciNbvnM6deqEw4cP64N6APj7778RHR3N4MxH2FJvrly5YhSE6YJ8IYTzCkseTVX3xi5PS0JOkZaWJoKCgsTixYvFvn37xKhRo0SNGjVEbm6uEEKIoUOHiokTJ+q337Ztm/D39xezZs0S+/fvF5MnTxYBAQFi79697voI5AbW1puZM2eKwMBA8fXXX4ucnBz9cunSJXd9BHIDa+tNeczi6LusrTsnTpwQoaGh4oknnhAHDx4U3333nahTp4549dVX3fURyA2srTeTJ08WoaGh4osvvhBHjx4V69atEw0bNhQDBw5010cgN7h06ZLYvXu32L17twAgZs+eLXbv3i3++ecfIYQQEydOFEOHDtVvf/ToUVGlShUxYcIEsX//fjFv3jyh0WjE2rVrXV52Bmhe5L333hP16tUTgYGBokOHDuKnn37Sv5acnCyGDx9usP1XX30lGjduLAIDA0WLFi3E6tWrXVxiUgNr6k39+vUFAKNl8uTJri84uZW13zdlMUDzbdbWne3bt4uOHTuKoKAg0aBBA/Haa6+J4uJiF5ea3M2aelNUVCSmTJkiGjZsKIKDg0VcXJx4/PHHxb///uv6gpPbbNy40eQ9i66uDB8+XCQnJxu9p3Xr1iIwMFA0aNBAfPLJJy4vtxBCKEKwrZeIiIiIiEgNOAaNiIiIiIhIJRigERERERERqQQDNCIiIiIiIpVggEZERERERKQSDNCIiIiIiIhUggEaERERERGRSjBAIyIiIiIiUgkGaERERERERCrBAI2IiMhOmzZtgqIo+O+//wAAixcvRo0aNZx6zAcffBD9+vVz6jGIiMj1GKAREZFqPPjgg1AUBTNnzjRYv3LlSiiK4qZSWe++++7D33//7e5i6DVt2hRBQUHIzc11d1GIiKgSDNCIiEhVgoOD8cYbb+Dff/916H4LCwsdur+KhISEoE6dOi47XkW2bt2Kq1evYsCAAViyZIm7i0NERJVggEZERKrSvXt3REVFYcaMGRVut3z5crRo0QJBQUGIj4/H22+/bfB6fHw8pk+fjmHDhiEsLAyjRo3Sdz387rvv0KRJE1SpUgUDBgzAlStXsGTJEsTHx6NmzZp46qmnoNVq9fv69NNP0b59e4SGhiIqKgpDhgzBmTNnzJatfBfH+Ph4KIpitOicPHkSAwcORI0aNVCrVi307dsXx48f17+u1Woxbtw41KhRA+Hh4XjuuecghLDofC5cuBBDhgzB0KFDsWjRIqPXc3Jy0Lt3b4SEhOCGG27A0qVLER8fjzlz5ui3+e+///DII4+gdu3aCAsLw2233Ybff//douMTEZF1GKAREZGqaDQavP7663jvvfeQlZVlcptdu3Zh4MCBGDRoEPbu3YspU6bg5ZdfxuLFiw22mzVrFlq1aoXdu3fj5ZdfBgBcuXIF7777LtLS0rB27Vps2rQJ/fv3R0ZGBjIyMvDpp5/iww8/xNdff63fT1FREaZPn47ff/8dK1euxPHjx/Hggw9a/Jl++eUX5OTkICcnB1lZWUhMTESXLl30+05JSUFoaCi2bNmCbdu2oVq1arjjjjv0rX5vv/02Fi9ejEWLFmHr1q24cOECVqxYUelxL126hGXLluGBBx5Ajx49cPHiRWzZssVgm2HDhuHUqVPYtGkTli9fjgULFhgFn/feey/OnDmDNWvWYNeuXWjbti1uv/12XLhwweJzQEREFhJEREQqMXz4cNG3b18hhBCJiYni4YcfFkIIsWLFClH2kjVkyBDRo0cPg/dOmDBBNG/eXP97/fr1Rb9+/Qy2+eSTTwQAcfjwYf26Rx99VFSpUkVcunRJvy4lJUU8+uijZsv5yy+/CAD692zcuFEAEP/++6/+ONWrVzf53qeeekrUr19fnDlzRgghxKeffiqaNGkiSkpK9Ntcu3ZNhISEiO+//14IIUR0dLR488039a8XFRWJ2NhY/bkyZ8GCBaJ169b638eOHSuGDx+u/33//v0CgPjll1/06w4dOiQAiHfeeUcIIcSWLVtEWFiYKCgoMNh3w4YNxYcffljh8YmIyHpsQSMiIlV64403sGTJEuzfv9/otf3796NTp04G6zp16oRDhw4ZdE1s37690XurVKmChg0b6n+PjIxEfHw8qlWrZrCubCvSrl270KdPH9SrVw+hoaFITk4GAJw4ccKqz7RgwQIsXLgQq1atQu3atQEAv//+Ow4fPozQ0FBUq1YN1apVQ61atVBQUIAjR47g4sWLyMnJQceOHfX78ff3N/nZylu0aBEeeOAB/e8PPPAAli1bhkuXLgEADh48CH9/f7Rt21a/TaNGjVCzZk3977///jsuX76M8PBwffmqVauGY8eO4ciRI1Z9fiIiqpy/uwtARERkSteuXZGSkoJJkyZZ1Z2wrKpVqxqtCwgIMPhdURST60pKSgAA+fn5SElJQUpKCj7//HPUrl0bJ06cQEpKilWJRzZu3Ignn3wSX3zxBW666Sb9+suXL6Ndu3b4/PPPjd6jC+JssW/fPvz000/YuXMnnn/+ef16rVaLtLQ0jBw50qL9XL58GdHR0di0aZPRa86eSoCIyBcxQCMiItWaOXMmWrdujSZNmhisb9asGbZt22awbtu2bWjcuDE0Go1Dy3DgwAGcP38eM2fORFxcHADg119/tWofhw8fxoABA/DCCy8gNTXV4LW2bdviyy+/RJ06dRAWFmby/dHR0fj555/RtWtXAEBxcbF+LJg5CxcuRNeuXTFv3jyD9Z988gkWLlyIkSNHokmTJiguLsbu3bvRrl07fVnLZtBs27YtcnNz4e/vj/j4eKs+NxERWY9dHImISLUSEhJw//3349133zVY/+yzz2LDhg2YPn06/v77byxZsgT/+9//MH78eIeXoV69eggMDMR7772Ho0ePYtWqVZg+fbrF77969Sr69OmDNm3aYNSoUcjNzdUvAHD//fcjIiICffv2xZYtW3Ds2DFs2rQJTz31lD5JytixYzFz5kysXLkSBw4cwOOPP66fFNuUoqIifPrppxg8eDBatmxpsDzyyCP4+eef8ddff6Fp06bo3r07Ro0ahZ07d2L37t0YNWoUQkJC9Fkmu3fvjqSkJPTr1w/r1q3D8ePHsX37drz44otWB6pERFQ5BmhERKRq06ZN03c31Gnbti2++uorpKWloWXLlnjllVcwbdo0m7tCVqR27dpYvHgxli1bhubNm2PmzJmYNWuWxe8/ffo0Dhw4gA0bNqBu3bqIjo7WL4AcE/fjjz+iXr16SE1NRbNmzTBixAgUFBToW9SeffZZDB06FMOHD0dSUhJCQ0PRv39/s8dctWoVzp8/b3KbZs2aoVmzZli4cCEA4P/+7/8QGRmJrl27on///hg5ciRCQ0MRHBwMQHb3zMjIQNeuXfHQQw+hcePGGDRoEP755x9ERkZafB6IiMgyihAWTqRCREREXi8rKwtxcXFYv349br/9dncXh4jI5zBAIyIi8mE//PADLl++jISEBOTk5OC5555DdnY2/v77b6PkKURE5HxMEkJEROTDioqK8MILL+Do0aMIDQ3FLbfcgs8//5zBGRGRm7AFjYiIiIiISCWYJISIiIiIiEglGKARERERERGpBAM0IiIiIiIilWCARkREREREpBIM0IiIiIiIiFSCARoREREREZFKMEAjIiIiIiJSCQZoREREREREKvH/5YubwsdZWsUAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Train SVR model using precomputed kernel\n", + "f_matrix_train = matrix_train\n", + "zzpc_svr = SVR(kernel='precomputed')\n", + "zzpc_svr.fit(f_matrix_train, y, w)\n", + "\n", + "# Evaluate model\n", + "zzpc_score = zzpc_svr.score(f_matrix_train, y, w)\n", + "print(f\"SVR model R² score on training data: {zzpc_score:.4f}\")\n", + "\n", + "# Predict and transform back to probabilities\n", + "pred = zzpc_svr.predict(f_matrix_train)\n", + "p_hat = 1 / (1 + np.exp(-pred))\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# Sort data by age for smoother plots\n", + "group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", + "group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", + "group_0.sort()\n", + "group_1.sort()\n", + "\n", + "# Plot actual vs predicted transition probabilities\n", + "plt.figure(figsize=(10, 5))\n", + "plt.plot([a for a, _, _ in group_0], [p for _, p, _ in group_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_0], [p_hat for _, _, p_hat in group_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_1], [p for _, p, _ in group_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_1], [p_hat for _, _, p_hat in group_1], 'b', label='Group 1 model')\n", + "\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.title(\"SVR Prediction vs Actual by Gender\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ad0da92a-1f89-4289-a2c2-e0cb5d4e1bc6", + "metadata": { + "id": "ad0da92a-1f89-4289-a2c2-e0cb5d4e1bc6" + }, + "source": [ + "The score you see is the R-squared score from the SVR model. This score represents the proportion of the variance in the dependent variable that is predictable from the independent variables. In other words, it gives you a measure of how well your model is fitting the data. A score of 1.0 indicates a perfect fit." + ] + }, + { + "cell_type": "markdown", + "id": "f2bc9cc6-7642-4f93-a152-f78ac3ccc29a", + "metadata": { + "id": "f2bc9cc6-7642-4f93-a152-f78ac3ccc29a" + }, + "source": [ + "We check the results against a classical SVR." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "VU3uIjBZVdXQ", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + }, + "id": "VU3uIjBZVdXQ", + "outputId": "ceb0ce3d-bd17-431c-ec88-7fd62ebb72f3" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Classical SVR R² score on training data: 0.8605\n" + ] + }, + { + "data": { + "image/png": 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Lln379gEArl27hvv372Pw4MFIS0uTnPtZWVno2LEjTp48KZOg6H//+5/U7cDAQKSlpUn2L34uEyZMkCpXtDWMMYbdu3ejZ8+eYIxJvfe6du2KjIwMmWM9dOjQElvfCSGqowCNEKJXtra2AFBsGviSiEQiLFu2DDVr1oSFhQWcnJzg7OyMGzduSAU+U6dOhY2NDVq0aIGaNWti3LhxMuM6Fi5ciFu3bsHDwwMtWrRAVFRUiT+Y//33X1SpUgUODg7Fljtz5gw6deoEa2tr2Nvbw9nZWZLgQ9UADeAD02+//RZ37tzBixcvsHXrVrRq1UqmKyMASRIQ8Xi758+f49SpUxg0aJDc7HG9e/dGXFwcDh48KBnrkp2drVICgFGjRiEuLg7Hjh3D5cuXkZqaiilTpsiU8/Lykrp9//59APyYtcI/Yp2dnXHkyBHJWLonT54AAGrWrCmzzdq1axdbt1evXiEzMxP169dX+vmU5MmTJ6hZs6bMMRJ3iRTXV6xatWpSt8XB2tu3b4vdT6NGjVCnTh1s375dsm779u1wcnKSjPMD1DuXAf4ix7Zt29ChQwc8evQIDx48wIMHD9CyZUukpKTg2LFjkrL//vuvRo9hcTZv3oyGDRvC0tISjo6OcHZ2xsGDB9V674gVPXc4jkONGjWkLmQMHDgQFhYWkjF4GRkZOHDgAIYMGVJsECoO/N6/fy9z3x9//IG4uDgsXrxYar343B86dKjMuf/LL78gNzdX5vmWdB49efIEJiYmMt2Ti75HXr16hfT0dKxbt05m32FhYQAgM4616HuXEKIZNAaNEKJXtra2qFKlCm7duqX2NubOnYvvv/8ew4cPx5w5c+Dg4AATExNMnDhR6mqzr68v7t27hwMHDuCvv/7C7t27sXr1asyYMQOzZs0CwI/nCAwMxJ49e3DkyBEsWrQICxYsQGxsLLp37652Hf/991907NgRderUwdKlS+Hh4QFzc3McOnQIy5YtK3Xafjc3NwwaNAh9+/ZFvXr1sGPHDmzatEkyNs3Pzw916tTB1q1bMX36dGzduhWMMZnsjWLu7u7o1KkTAKBHjx5wcnJCeHg4OnToINMCpkjNmjUl2yhO0Svw4mPx22+/wdXVVaa8qqnyDZWitOqMsRIfO3DgQPz44494/fo1KlasiH379iEkJETq2Kh7Lh8/fhwvX77Etm3bsG3bNpn7t2zZgi5duijxDEumKMARCoVSx+f333/HsGHDEBQUhMmTJ6Ny5coQCASYN29eqRLXKKNSpUr47LPPsGXLFsyYMQO7du1Cbm6uVIZSeWrUqAFTU1O5n23ilrei57L43F+0aJHCcXVFW+RKcx7J2/fnn38uM75RrGHDhlK3qfWMEO0oG99yhBCj9tlnn2HdunVITEyEv7+/yo/ftWsXOnTogF9//VVqfXp6OpycnKTWWVtbY+DAgRg4cCDy8vIQHByMH3/8EdOmTZMM9ndzc8PYsWMxduxYpKamomnTpvjxxx8V/qj18fHB4cOH8ebNG4WtaPv370dubi727dsndcW7tFnoijIzM0PDhg1x//59vH79WirAGTJkCL7//nvcuHEDMTExqFmzplTCh+KMHj0ay5Ytw3fffYc+ffpotPtaUeIr/ZUrVy42wBMnShG3OhR27969Yvfh7OwMW1vbEi8MqPI8q1evjhs3bkAkEkm1ooknDRfXVxMGDhyIWbNmYffu3XBxcUFmZiYGDRokU07VcxngA7DKlStj1apVMvfFxsZiz549WLt2LaysrODj41OqY1ipUiWp7rhiT548gbe3t+T2rl274O3tjdjYWKntlTbtf9FzhzGGBw8eyAQioaGh6N27Ny5evIgtW7agSZMmqFevXrHbtra2Rvv27XHixAkkJSWhatWqJdZHfO7b2toqdXFDGdWrV4dIJMK///4r1WpW9D0izvAoFAo1tm9CiHqoiyMhRO+mTJkCa2trfPnll0hJSZG5/99//0V0dLTCxwsEApmrxTt37kRSUpLUurS0NKnb5ubmqFu3LhhjyM/Ph1AolOk+VLlyZVSpUgW5ubkK99+3b18wxiStcIWJ6yW+yl24nhkZGdi4caPC7Rbn/v37ePr0qcz69PR0JCYmolKlSnB2dpa6T9xaNmPGDFy7dk1h65k8pqammDRpEu7cuYM//vhDrTorq2vXrrC1tcXcuXORn58vc7845bmbmxsaN26MzZs3S71ucXFxuH37drH7MDExQVBQEPbv3y81FYKY+HUSz8kmL4goqkePHkhOTpbqelhQUIAVK1bAxsam2PFKqvL19UWDBg2wfft2bN++HW5ubmjbtq3kfnXP5Q8fPiA2NhafffYZ+vXrJ7OEh4fj3bt3kjFTffv2xfXr1+VObaDMMfTx8cG5c+eQl5cnWXfgwAGpVPeA/PfP+fPnkZiYqPC5KOP//u//pLpX79q1Cy9fvpQJYLt37w4nJycsWLAAJ06cKLH1TGzGjBkQCoX4/PPP5XZ1LPq55efnBx8fHyxevFhueXnp/ksifi4//fST1Prly5dL3RYIBOjbty92794tN+hWZ9+EEPVQCxohRO98fHwQExODgQMHwtfXF6Ghoahfvz7y8vJw9uxZSapyRT777DPMnj0bYWFhaN26NW7evIktW7ZIXYEHgC5dusDV1RUBAQFwcXHBnTt3sHLlSnz66aeoWLEi0tPT4e7ujn79+qFRo0awsbHB0aNHcfHiRSxZskTh/jt06IAvvvgCP/30E+7fv49u3bpBJBLh1KlT6NChA8LDw9GlSxeYm5ujZ8+eGD16NN6/f4/169ejcuXKePnypcrH7Pr16xg8eDC6d++OwMBAODg4ICkpCZs3b8aLFy+wfPlyma5PXl5eaN26tSTAUiVAA/j532bMmIEFCxYgKChI5Tory9bWFmvWrMEXX3yBpk2bYtCgQXB2dsbTp09x8OBBBAQEYOXKlQCAefPm4dNPP0WbNm0wfPhwvHnzRjLXnbwfuIXNnTsXR44cQbt27TBq1Cj4+vri5cuX2LlzJ06fPg17e3s0btwYAoEACxYsQEZGBiwsLCRz2RU1atQo/Pzzzxg2bBguX74MT09P7Nq1C2fOnMHy5ctLlQhHnoEDB2LGjBmwtLTEiBEjpFrt3r17p9a5vG/fPrx7907hvHitWrWCs7MztmzZgoEDB2Ly5MnYtWsX+vfvj+HDh8PPzw9v3rzBvn37sHbtWjRq1Ag+Pj6wt7fH2rVrUbFiRVhbW6Nly5bw8vLCl19+iV27dqFbt24YMGAA/v33X/z+++8y46U+++wzxMbGok+fPvj000/x6NEjrF27FnXr1i3xdS6Og4MD2rRpg7CwMKSkpGD58uWoUaMGRo4cKVXOzMwMgwYNwsqVKyEQCKQSwRQnMDAQK1euxPjx41GzZk0MGTIEderUQV5eHv755x9s2bIF5ubmkpZuExMT/PLLL+jevTvq1auHsLAwVK1aFUlJSYiPj4etrS3279+v0nNs3LgxQkJCsHr1amRkZKB169Y4duwYHjx4IFN2/vz5iI+PR8uWLTFy5EjUrVsXb968wZUrV3D06FG8efNGpX0TQtSkh8yRhBAi1z///MNGjhzJPD09mbm5OatYsSILCAhgK1asYDk5OZJy8tLsT5o0ibm5uTErKysWEBDAEhMTZVJ1//zzz6xt27bM0dGRWVhYMB8fHzZ58mSWkZHBGONTlU+ePJk1atSIVaxYkVlbW7NGjRqx1atXS9WzaJp9xvg04IsWLWJ16tRh5ubmzNnZmXXv3p1dvnxZUmbfvn2sYcOGzNLSknl6erIFCxawDRs2MADs0aNHknLKpNlPSUlh8+fPZ+3atWNubm7M1NSUVapUiX3yySds165dCh+3atUqBoC1aNFCYRkACtOzR0VFlZheXJxGvqSU/OI0+/LS3DPGp/Lu2rUrs7OzY5aWlszHx4cNGzaMXbp0Sarc7t27ma+vL7OwsGB169ZlsbGxcl8jyEm//uTJExYaGsqcnZ2ZhYUF8/b2ZuPGjZNK6b5+/Xrm7e3NBAKB1HOX9zqlpKSwsLAw5uTkxMzNzVmDBg1k0ssXd3zk1VGR+/fvMwAMADt9+rTUfcqey0X17NmTWVpasqysLIVlhg0bxszMzCSp2NPS0lh4eDirWrUqMzc3Z+7u7mzo0KFSqdr/+OMPVrduXWZqaiqTcn/JkiWsatWqzMLCggUEBLBLly7JHFuRSMTmzp3LqlevziwsLFiTJk3YgQMHlH6dixKnid+6dSubNm0aq1y5MrOysmKffvqp3KkqGGPswoULDADr0qVLsduW5+rVqyw0NJRVq1aNmZubM2tra9awYUM2adIk9uDBA7nlg4ODJZ9V1atXZwMGDGDHjh2TlBGn2X/16pXUY8Xvq8KfKR8+fGATJkxgjo6OzNramvXs2ZM9e/ZM7rFKSUlh48aNYx4eHszMzIy5urqyjh07snXr1skcv507d6p8LAghJeMYU3EUKSGEEEJIOXP9+nU0btwY//d//4cvvvhC39UhhJRhNAaNEEIIIaQE69evh42NjdJZTAkhRF00Bo0QQgghRIH9+/fj9u3bWLduHcLDwyVJTwghRFuoiyMhhBBCiAKenp5ISUlB165d8dtvv2k82QshhBRFARohhBBCCCGEGAgag0YIIYQQQgghBoICNEIIIYQQQggxEJQkRItEIhFevHiBihUrguM4fVeHEEIIIYQQoieMMbx79w5VqlSBiYnidjIK0LToxYsX8PDw0Hc1CCGEEEIIIQbi2bNncHd3V3g/BWhaJM709OzZM9ja2uq1Lvn5+Thy5Ai6dOkCMzMzvdaFGA86b4g66Lwh6qJzh6iDzhuiDn2cN5mZmfDw8CgxGywFaFok7tZoa2trEAFahQoVYGtrSx9eRGl03hB10HlD1EXnDlEHnTdEHfo8b0oa+kRJQgghhBBCCCHEQBhEgLZq1Sp4enrC0tISLVu2xIULF4otv3PnTtSpUweWlpZo0KABDh06JHV/VFQU6tSpA2tra1SqVAmdOnXC+fPnpcq8efMGQ4YMga2tLezt7TFixAi8f/9eqsyNGzcQGBgIS0tLeHh4YOHChZp5woQQQgghhBAih94DtO3btyMyMhIzZ87ElStX0KhRI3Tt2hWpqalyy589exYhISEYMWIErl69iqCgIAQFBeHWrVuSMrVq1cLKlStx8+ZNnD59Gp6enujSpQtevXolKTNkyBD8/fffiIuLw4EDB3Dy5EmMGjVKcn9mZia6dOmC6tWr4/Lly1i0aBGioqKwbt067R0MQgghhBBCSLmm9zFoS5cuxciRIxEWFgYAWLt2LQ4ePIgNGzbgm2++kSkfHR2Nbt26YfLkyQCAOXPmIC4uDitXrsTatWsBAIMHD5bZx6+//oobN26gY8eOuHPnDv766y9cvHgRzZo1AwCsWLECPXr0wOLFi1GlShVs2bIFeXl52LBhA8zNzVGvXj1cu3YNS5culQrkSoMxhoKCAgiFQo1srzj5+fkwNTVFTk6OTvZH9EsgEMDU1JSmdyCEEEIIMTJ6DdDy8vJw+fJlTJs2TbLOxMQEnTp1QmJiotzHJCYmIjIyUmpd165dsXfvXoX7WLduHezs7NCoUSPJNuzt7SXBGQB06tQJJiYmOH/+PPr06YPExES0bdsW5ubmUvtZsGAB3r59i0qVKsnsKzc3F7m5uZLbmZmZAPjgKD8/X6psfn4+UlJS8OHDB7n11jTGGFxdXfH06VP60V5OWFlZwcXFpVQDX8XnbdHzl5Di0HlD1EXnDlEHnTdEHfo4b5Tdl14DtNevX0MoFMLFxUVqvYuLC+7evSv3McnJyXLLJycnS607cOAABg0ahOzsbLi5uSEuLg5OTk6SbVSuXFmqvKmpKRwcHCTbSU5OhpeXl8x+xPfJC9DmzZuHWbNmyaw/cuQIKlSoILMtGxsbODg4wNRU7w2ZpIwpKCjAmzdvcOPGDaSkpJR6e3FxcRqoFSlv6Lwh6qJzh6iDzhuiDl2eN9nZ2UqVK7ORQYcOHXDt2jW8fv0a69evx4ABA3D+/HmZwEyTpk2bJtW6J57roEuXLlJp9nNzc/H06VNUq1ZNJnDTFvHM5RUrVqQWtHLC1tYWT58+Rf369WFhYaHWNvLz8xEXF4fOnTtT6mKiNDpviLro3CHqoPOGqEMf5424d11J9BqgOTk5QSAQyFzhT0lJgaurq9zHuLq6KlXe2toaNWrUQI0aNdCqVSvUrFkTv/76K6ZNmwZXV1eZJCTiFgfxdhTtR3yfPBYWFnJ/CJuZmUm98EKhEBzHwdTUFCYmusnTIhKJAPDzLuhqn0S/xGPQTE1NS/3BU/QcJkQZdN4QddG5Q9RB5w1Rhy7PG2X3o9df6ubm5vDz88OxY8ck60QiEY4dOwZ/f3+5j/H395cqD/BNk4rKF96ueHyYv78/0tPTcfnyZcn9x48fh0gkQsuWLSVlTp48KdVXNC4uDrVr15bbvZEQQgghhBBCSkvvTSmRkZFYv349Nm/ejDt37mDMmDHIysqSZHUMDQ2VSiISERGBv/76C0uWLMHdu3cRFRWFS5cuITw8HACQlZWF6dOn49y5c3jy5AkuX76M4cOHIykpCf379wcA+Pr6olu3bhg5ciQuXLiAM2fOIDw8HIMGDUKVKlUA8Jkgzc3NMWLECPz999/Yvn07oqOjZRKUEEIIIYQQYlSEQiAhAdi6lf9LGb4Nit7HoA0cOBCvXr3CjBkzkJycjMaNG+Ovv/6SJOR4+vSpVJe81q1bIyYmBt999x2mT5+OmjVrYu/evahfvz4APr343bt3sXnzZrx+/RqOjo5o3rw5Tp06hXr16km2s2XLFoSHh6Njx44wMTFB37598dNPP0nut7Ozw5EjRzBu3Dj4+fnByckJM2bM0FiKfY0RCoFTp4CXLwE3NyAwEBAI9F0rQgghhBBiiGJjgYgI4Pnzj+vc3YHoaCA4WH/1IhJ6D9AAIDw8XNICVlRCQoLMuv79+0taw4qytLREbGxsift0cHBATExMsWUaNmyIU6dOlbgtvdHTGyw5ORnz5s3DwYMH8fz5c9jZ2aFGjRr4/PPPMXToUJ0lPlFVTk4OJk2ahG3btiE3Nxddu3bF6tWrZbKCEkIIIYSUSbGxQL9+AGPS65OS+PW7dlGQZgD03sWRqEn8BiscnAEf32BKBKnqePjwIZo0aYIjR45g7ty5uHr1KhITEzFlyhQcOHAAR48eVfhYfc9P8tVXX2H//v3YuXMnTpw4gRcvXiCYPoQIIYQQUh4IhfyF/aLBGfBx3cSJ1N3RAFCAZoz0+AYbO3YsTE1NcenSJQwYMAC+vr7w9vZG7969cfDgQfTs2VNSluM4rFmzBr169YK1tTV+/PFHAMCaNWvg4+MDc3Nz1K5dG7/99pvkMY8fPwbHcbh27ZpkXXp6OjiOk7SmJiQkgOM4HDx4EA0bNoSlpSVatWqFW7duKax3RkYGfv31VyxduhSffPIJ/Pz8sHHjRpw9exbnzp3T7EEihBBCCDE0p07JXtgvjDHg2TO+HNErCtCMkZ7eYGlpaZJxedbW1nLLFJ1jLSoqCn369MHNmzcxfPhw7NmzBxEREZg0aRJu3bqF0aNHIywsDPHx8SrXZ/LkyViyZAkuXrwIZ2dn9OzZU2Er3eXLl5Gfn49OnTpJ1tWpUwfVqlVDYmKiyvsmhBBCCDEqL19qthzRGgrQjJGe3mAPHjwAYwy1a9eWWu/k5AQbGxvY2Nhg6tSpUvcNHjwYYWFh8Pb2RrVq1bB48WIMGzYMY8eORa1atRAZGYng4GAsXrxY5frMnDkTnTt3RoMGDbB582akpKRgz549cssmJyfD3Nwc9vb2UutdXFyQnJys8r4JIYQQQoyKm5tmy+lKOcw4SQGaMTKwN9iFCxdw7do11KtXTzLXnFizZs2kbt+5cwcBAQFS6wICAnDnzh2V91t47jsHBwfUrl1bre0QQgghhJR5gYF8MrkivZ0kOA7w8ODLGYrYWMDTE+jQARg8mP/r6am1XAuGggI0Y6SnN1iNGjXAcRzu3bsntd7b2xs1atSAlZWVzGMUdYVURDylAis0vk4TyUVcXV2Rl5eH9PR0qfUpKSlwdXUt9fYJIYQQQgyaQMBn+gZkf0OKby9fbjjTNekpIZ4hoADNGOnpDebo6IjOnTtj5cqVyMrKUmsbvr6+OHPmjNS6M2fOoG7dugAAZ2dnAMDLQt0zCycMKaxwco+3b9/in3/+ga+vr9yyfn5+MDMzw7FjxyTr7t27h6dPn0q1xBFCCCGElFnBwXwq/apVpde7u+s3xX7Rbox5eeU646RBzING1CB+g8mbB235cq29wVavXo2AgAA0a9YMUVFRaNiwIUxMTHDx4kXcvXsXfn5+xT5+8uTJGDBgAJo0aYJOnTph//79iI2NlaTnt7KyQqtWrTB//nx4eXkhNTUV3333ndxtzZ49G46OjnBxccG3334LJycnBAUFyS1rZ2eHESNGIDIyEg4ODrC1tcX48ePh7++PVq1aleqYEEIIIYQYjeBgoHdvPpncy5f8kJjAQP21nMmb19fJCXj9WvFjCifEa99e61XUNQrQjJke3mA+Pj64evUq5s6di2nTpuH58+ewsLBA3bp18fXXX2Ps2LHFPj4oKAjR0dFYvHgxIiIi4OXlhY0bN6J9oTfXhg0bMGLECPj5+aF27dpYuHAhunTpIrOt+fPnIyIiAvfv30fjxo2xf/9+mJubK9z3smXLYGJigr59+0pNVE0IIYQQUq4IBIYR2CiaOLu44KywMppxkgI0Y6eHN5ibmxtWrFiBFStWFFuOyWuWBjBmzBiMGTNG4eN8fX1x9uzZErfVpk2bYuc+K8rS0hKrVq3CqlWrlH4MIYQQQgjRguLm9VWWoWWc1BAK0AghhBBCCCG6VdK8vsXhOH5YjyFlnNQgCtAIIYQQQgghuqVu98TCCfEAPqmIIYyl0yAK0IjRad++vcLuk4QQQgghxAgo2z3R2Rl49erjbXFCPICfE61osrzoaP1lo9QQSrNPCCGEEEII0S1l5/V9/hyIjwdiYvi/jx7x95fhOdIoQCOEEEIIIYTolrLz+pqb8wnxQkI+JsYr43OkUYBGCCGEEEII0T11Js4uKblI4TnSjBSNQSOEEEIIIYToh6rz+iqbXMSI50ijAI0QQgghhJQvQqHyAQHRPlXm9VU2uYgRz5FGARohhBBCCCk/YmP5MUxlMPtfuSBOLpKUJH8cmniOtNatjTYFP41BI8RAeHp6Yrk4bawSoqKi0LhxY63VhxBCCClzYmPLdPa/ckGZ5CKDBgE+PkCHDsDgwfxfT0+jeX0pQCMqS05ORkREBGrUqAFLS0u4uLggICAAa9asQXZ2tr6rp1BOTg7GjRsHR0dH2NjYoG/fvkhJSdF3tQghhBCiC0Jhmc/+V24Ul1zk66+BxYuNOginAI2o5OHDh2jSpAmOHDmCuXPn4urVq0hMTMSUKVNw4MABHD16VOFj8/PzdVhTWV999RX279+PnTt34sSJE3jx4gWCqSsDIYQQUj6Ug+x/5UpwMPD4sfQcaQ8eAFu3Gn0QTgGaoWAMyMrSzyLvJFZg7NixMDU1xaVLlzBgwAD4+vrC29sbvXv3xsGDB9GzZ09JWY7jsGbNGvTq1QvW1tb48ccfAQBr1qyBj48PzM3NUbt2bfz222+Sxzx+/Bgcx+HatWuSdenp6eA4DgkJCQCAhIQEcByHgwcPomHDhrC0tESrVq1w69YthfXOyMjAr7/+iqVLl+KTTz6Bn58fNm7ciLNnz+LcuXMKH+fp6YkffvgBoaGhsLGxQfXq1bFv3z68evUKvXv3ho2NDRo2bIhLly5JPW737t2oV68eLCws4OnpiSVLlkjdn5qaip49e8LKygpeXl7YsmWLzL7T09Px5ZdfwtnZGba2tvjkk09w/fp1hXUlhBBCSDHKQfa/ckecXEQ8R9rZs2UiCKcAzVBkZwM2NlpbTGxtYe/uDhNbW9n7leyWmJaWhiNHjmDcuHGwtraWW4Yr0hc4KioKffr0wc2bNzF8+HDs2bMHERERmDRpEm7duoXRo0cjLCwM8fHxKh+yyZMnY8mSJbh48SKcnZ3Rs2dPha10ly9fRn5+Pjp16iRZV6dOHVSrVg2JiYnF7mfZsmUICAjA1atX8emnn+KLL75AaGgoPv/8c1y5cgU+Pj4IDQ0F+y/QvXz5MgYMGIBBgwbh5s2biIqKwvfff49NmzZJtjls2DA8e/YM8fHx2LVrF1avXo3U1FSp/fbv3x+pqan4888/cfnyZTRt2hQdO3bEmzdvVD5WhBBCSLlXDrL/lXtlJAinAI0o7cGDB2CMoXbt2lLrnZycYGNjAxsbG0ydOlXqvsGDByMsLAze3t6oVq0aFi9ejGHDhmHs2LGoVasWIiMjERwcjMWLF6tcn5kzZ6Jz585o0KABNm/ejJSUFOzZs0du2eTkZJibm8Pe3l5qvYuLC5KTk4vdT48ePTB69GjUrFkTM2bMQGZmJpo3b47+/fujVq1amDp1Ku7cuSMZz7Z06VJ07NgR33//PWrVqoVhw4YhPDwcixYtAgD8888/+PPPP7F+/Xq0atUKfn5++PXXX/HhwwfJPk+fPo0LFy5g586daNasGWrWrInFixfD3t4eu3btUvlYEUIIIeWeOPtf0cQSYhwHeHjw5YhxKiNBOKXZNxQVKgDv32tt8yKRCJmZmbC1tYWJSZG4vEKFUm37woULEIlEGDJkCHJzc6Xua9asmdTtO3fuYNSoUVLrAgICEC3OxqMCf39/yf8ODg6oXbs27ty5o/J2StKwYUPJ/y4uLgCABg0ayKxLTU2Fq6sr7ty5g969e0ttIyAgAMuXL4dQKMSdO3dgamoKPz8/yf116tSRCh6vX7+O9+/fw9HRUWo7Hz58wL///qux50YIIYSUG+Lsf/368cFY4SEe4qBt+XLtpWKnude0T9kU/IGBgEik+/opiQI0Q8FxgIJugxohEvEfDNbWQNEATUk1atQAx3G4d++e1Hpvb28AgJWVlcxjFHWFVEQcPLJCbypNJBdxdXVFXl4e0tPTpQKhlJQUuLq6FvtYMzMzyf/iLpzy1ok0+EZ///493NzcJOPuCivaCkgIIYQQJYmz/8mbB235cu3Ng0Zzr+mGKkG4AQdo1MWRKM3R0RGdO3fGypUrkZWVpdY2fH19cebMGal1Z86cQd26dQEAzs7OAICXhfoGF04YUljh5B5v377FP//8A19fX7ll/fz8YGZmhmPHjknW3bt3D0+fPpVqidMERc+xVq1aEAgEqFOnDgoKCnD58mWpuqSnp0tuN23aFMnJyTA1NUWNGjWkFicnJ43WlxBCCClX5GX/e/RIu8EZzb2mO8Wl4N+1yygCYmpBIypZvXo1AgIC0KxZM0RFRaFhw4YwMTHBxYsXcffuXalue/JMnjwZAwYMQJMmTdCpUyfs378fsbGxkvT8VlZWaNWqFebPnw8vLy+kpqbiu+++k7ut2bNnw9HRES4uLvj222/h5OSEoKAguWXt7OwwYsQIREZGwsHBAba2thg/fjz8/f3RqlWrUh2ToiZNmoTmzZtjzpw5GDhwIBITE7Fy5UqsXr0aAFC7dm1069YNo0ePxpo1a2BqaoqJEydKtUB26tQJ/v7+CAoKwsKFC1GrVi28ePECBw8eRJ8+fWS6jhJCCCFEBeLsf9pW0txrHMenfe/dm7o7alJwMH9MjbRLKbWgEZX4+Pjg6tWr6NSpE6ZNm4ZGjRqhWbNmWLFiBb7++mvMmTOn2McHBQUhOjoaixcvRr169fDzzz9j48aNaF/oQ3LDhg0oKCiAn58fJk6ciB9++EHutubPn4+IiAj4+fkhOTkZ+/fvh7m5ucJ9L1u2DJ999hn69u2Ltm3bwtXVFbFauGrVtGlT7NixA9u2bUP9+vUxY8YMzJ49G8OGDZOU2bhxI6pUqYJ27dohODgYo0aNQuXKlSX3cxyHQ4cOoW3btggLC0OtWrUwaNAgPHnyRDLmjRBCCCEGjuZe05+iKfiNJDgDAI4xFSbBIirJzMyEnZ0dMjIyYGtrK1mfk5ODR48ewcvLC5aWljqpS7FJQoxMQkICOnTogLdv39J4rGJo4jzLz8/HoUOH0KNHD6lxd4QUh84boi46d4g6DPq82boVGDy45HIxMXwgoSpKPKI2fZw3imKDoqiLIyGEEEIIIdqgzbTvlHikzDLuphRCCCGEEEIMlbbmXqPEI2UaBWjE6LRv3x6MMereSAghhBDDJk77DsgGaerOvVZS4hGATzwiFKpaW2IgKEAjhBBCCCFEWzSd9p0Sj5R5BhGgrVq1Cp6enrC0tETLli1x4cKFYsvv3LkTderUgaWlJRo0aIBDhw5J7svPz8fUqVPRoEEDWFtbo0qVKggNDcWLFy8kZRISEsBxnNzl4sWLAIDHjx/Lvb/w3FuEEEIIIYSUSJNzrxWaK1Yj5YjB0XuAtn37dkRGRmLmzJm4cuUKGjVqhK5duyI1NVVu+bNnzyIkJAQjRozA1atXERQUhKCgINy6dQsAkJ2djStXruD777/HlStXEBsbi3v37qFXr16SbbRu3RovX76UWr788kt4eXnJzC919OhRqXIlzfNFCCGEEEKIDE2lfddm4hFiEPSexXHp0qUYOXIkwsLCAABr167FwYMHsWHDBnzzzTcy5aOjo9GtWzdMnjwZADBnzhzExcVh5cqVWLt2Lezs7BAXFyf1mJUrV6JFixZ4+vQpqlWrBnNzc7i6ukruz8/Pxx9//IHx48eDK9I/2NHRUaosIYQQQggheiNOPJKUJH8cGsfx96uaeIQYDL0GaHl5ebh8+TKmTZsmWWdiYoJOnTohMTFR7mMSExMRGRkpta5r167Yu3evwv1kZGSA4ziFSSX27duHtLQ0SZBYWK9evZCTk4NatWphypQpUi1xReXm5iI3N1dyOzMzEwAfAObn50vW5+fngzEGkUgEkUikcHuaJJ7uTrxfUvaJRCIwxpCfnw+BmlfpxOdt4fOXkJLQeUPURecOUUd5PG+4JUsgGDQI4DhwhYI09l9Dg3DxYjCRCKDffArp47xRdl96DdBev34NoVAIFxcXqfUuLi64e/eu3MckJyfLLZ+cnCy3fE5ODqZOnYqQkBCFE8L9+uuv6Nq1K9zd3SXrbGxssGTJEgQEBMDExAS7d+9GUFAQ9u7dqzBImzdvHmbNmiWz/siRI6hQoYLktqmpKVxdXfH+/Xvk5eXJ3Za2vHv3Tqf7I/qTl5eHDx8+4OTJkygoKCjVtoq2ShOiDDpviLro3CHqKFfnjYUF3KZMQYNffoFVWppk9QdHR9waMQIvLSyAQjkaiGK6PG+ys7OVKqf3Lo7alJ+fjwEDBoAxhjVr1sgt8/z5cxw+fBg7duyQWu/k5CTVUte8eXO8ePECixYtUhigTZs2TeoxmZmZ8PDwQJcuXaSCw5ycHDx79gw2NjawtLQszVNUegJ5xhjevXuHihUrynTjJGVTTk4OrKys0LZtW7XPs/z8fMTFxaFz584wMzPTcA1JWUXnDVEXnTtEHeX2vOnRA4iKQsHp05IfgmZt2qCJQIAm+q6bEdDHeSPuXVcSvQZoTk5OEAgESElJkVqfkpKicNyXq6urUuXFwdmTJ09w/Phxha1nGzduhKOjY7FdF8VatmxZbJRtYWEBCwsLmfVmZmZSL7xQKATHcTAxMYGJifp5WlSZQF7crVG839JITk7GvHnzcPDgQTx//hx2dnaoUaMGPv/8cwwdOlSqtdCQrFu3DjExMbhy5QrevXuHt2/flum51ExMTMBxnMz5pw5NbIOUP3TeEHXRuUPUUS7PGzMzoFMnfdfCqOnyvFF2P3rN4mhubg4/Pz8cO3ZMsk4kEuHYsWPw9/eX+xh/f3+p8gDfNFm4vDg4u3//Po4ePQpHR0e522KMYePGjQgNDVXqgF27dg1uBpIRR18TyD98+BBNmjTBkSNHMHfuXFy9ehWJiYmYMmUKDhw4gKNHjyp8rL77hmdnZ6Nbt26YPn26XutBCCGEEEKIInpPsx8ZGYn169dj8+bNuHPnDsaMGYOsrCxJwo7Q0FCpJCIRERH466+/sGTJEty9exdRUVG4dOkSwsPDAfBBQL9+/XDp0iVs2bIFQqEQycnJSE5Olhnvdfz4cTx69AhffvmlTL02b96MrVu34u7du7h79y7mzp2LDRs2YPz48Vo8GsrR5wTyY8eOhampKS5duoQBAwbA19cX3t7e6N27Nw4ePIiePXtKynIchzVr1qBXr16wtrbGjz/+CABYs2YNfHx8YG5ujtq1a+O3336TPEY8/9y1a9ck69LT08FxHBISEgB8nMfu4MGDaNiwISwtLdGqVSvJVAuKTJw4Ed988w1atWqluQNCCCGEEEKIBul9DNrAgQPx6tUrzJgxA8nJyWjcuDH++usvSSKQp0+fSnXJa926NWJiYvDdd99h+vTpqFmzJvbu3Yv69esDAJKSkrBv3z4AQOPGjaX2FR8fj/bt20tu//rrr2jdujXq1Kkjt25z5szBkydPYGpqijp16mD79u3o16+fBp+9elSZQL7Q0y21tLQ0ScuZtbW13DJFx7dFRUVh/vz5WL58OUxNTbFnzx5ERERg+fLl6NSpEw4cOICwsDC4u7ujQ4cOKtVn8uTJiI6OhqurK6ZPn46ePXvin3/+KX/dGwghhBBCSJmh9wANAMLDwyUtYEWJW00K69+/P/r37y+3vKenpySlfEliYmIU3jd06FAMHTpUqe3omr4mkH/w4AEYY6hdu7bUeicnJ+Tk5AAAxo0bhwULFkjuGzx4sNT0BSEhIRg2bBjGjh0LgG9BPXfuHBYvXqxygDZz5kx07twZAN/i6e7ujj179mDAgAFqPT9CCCGEEEL0Te9dHInqDG0C+QsXLuDatWuoV6+e1DxwANCsWTOp23fu3EFAQIDUuoCAANy5c0fl/RYed+jg4IDatWurtR1CCCGEkDJHKAQSEoCtW/m/2hj7QrTCIFrQiGr0NYF8jRo1wHEc7t27J7Xe29sbAGBlZSXzGEVdIRURd2ct3Aqq7+QihBBCCCFGRZVU38TgUAuaERII+PcXwAdjhYlvL18ufz600nB0dETnzp2xcuVKZGVlqbUNX19fnDlzRmrdmTNnULduXQCAs7MzAOBlof6ZhROGFHbu3DnJ/2/fvsU///wDX19ftepFCCGEEFIm6CvVN9EYakEzUsHBwK5d8i+OLF+uvYsjq1evRkBAAJo1a4aoqCg0bNgQJiYmuHjxIu7evQs/P79iHz958mQMGDAATZo0QadOnbB//37ExsZK0vNbWVmhVatWmD9/Pry8vJCamorvvvtO7rZmz54NR0dHuLi44Ntvv4WTkxOCgoIU7luczfPBgwcAgJs3b6JixYqoVq0aHBwc1DsghBBCCCGlJRTy2d3+m3AagYHqXWkvKdU3x/Gpvnv31vyVfKIxFKAZseBg/v2lifezsnx8fHD16lXMnTsX06ZNw/Pnz2FhYYG6devi66+/liT/UCQoKAjR0dFYvHgxIiIi4OXlhY0bN0pl19ywYQNGjBgBPz8/1K5dGwsXLkSXLl1ktjV//nxERETg/v37aNy4Mfbv3w9zc3OF+167di1mzZolud22bVsA/GTlw4YNU+1AEEIIIYRogia7I+or1beYpgJNZTAGZGUBGRn835wcIDf341L4dkAAUK2aduqhBRSgGTmBQDvvr+K4ublhxYoVWLFiRbHlFGXTHDNmDMaMGaPwcb6+vjh79myJ22rTpk2Jc58VFhUVhaioKKXLE0IIIYRolbg7YtHfOeLuiLt2qRak6SvVN1C6QDMvD3jxAkhJAV69kr+8fQtkZkovSmZux/btFKARQgghhBBCiqGN7oi6SPUtr5Xsjz8UB5p9+wIbNgB16gAPHwJPn/JBXFIS//f5cz4wU5dAAFhbA5aW/GJh8XER33Z0VH/7ekABGiGEEEIIIbqmje6I2k71La+VrGpVvjuhokATAIYPL3nb5uaAqyvg7Cx/cXAA7OwAW1vpxcpKNmuekaMAjRid9u3bKz0ZOSGEEEKIQdJGd0Rxqu9+/figpfDvpdKm+i6uO6YyKlcGfH0BT08+qHN3l16cnMpcoKUuCtAIIYQQQgjRNW11R9RUqm/GgEePgGvXgMuXgaVLlR/zJc/y5UBIiPqPL0coQCOEEEIIIUTXtNkdUZ1U3ykpwPnzH5dLl/gMiZpSmnFv5QwFaIQQQggh5Y0u06ET+bTZHVG8fUVj1woKgKtXgdOnPwZkjx/LljM3B+rX58d6JSSoV4/SjnsrhyhAI4QQQggpTzQ57xYpHU11RyxJTg5w4QJw8iS/nD3Lzx1WGMfxY8Ratvy41KsHmJnxwZk6AZomAs1yiAI0QgghhJDyQtPzbpHSU6c7Ykny84Fz54CjR4H4eL6FLC9Puoy9PdCmDeDvzwdjzZrxWRLlUaY7poMDn1FRm4FmOUEBGiGEEEJIeaCNebeIZhTXHVEZjAG3bwNxcXxQduIE8P69dBlXV6Bt249LvXqAiYny9SupO+a6dZoPNMspCtAIMRDt27dH48aNsXz5cqXKb9q0CRMnTkR6erpW60UIIaSM0Ma8W0R/0tP5gOzgQeDIEdl0/E5OQMeO/NK+PVCjRunS2CvbHZPOnVKjAI2oLDk5GfPmzcPBgwfx/Plz2NnZoUaNGvj8888xdOhQVKhQQd9VlGvdunWIiYnBlStX8O7dO7x9+xb29vb6rhYhhBCiG9qYd4voDmPAnTt8QHbwIHDmDJ/sQ8zSkm8Z69QJ6NwZaNhQ+RYyZWmjOyaRQQEaUcnDhw8REBAAe3t7zJ07Fw0aNICFhQVu3ryJdevWoWrVqujVq5fcx+bn58PMzEzHNf4oOzsb3bp1Q7du3TBt2jS91YMQQgjRC23Nu0W0p6CAT+qxdy+wf79spsU6dYBPPwW6dwcCAvggTdtK2x2TlEjDYTVRF2N8Mh19LKrMOTh27FiYmpri0qVLGDBgAHx9feHt7Y3evXvj4MGD6Nmzp6Qsx3FYs2YNevXqBWtra/z4448AgDVr1sDHxwfm5uaoXbs2fvvtN8ljHj9+DI7jcO3aNcm69PR0cByHhP+yByUkJIDjOBw8eBANGzaEpaUlWrVqhVu3bhVb94kTJ+Kbb75Bq1atlH6+7du3x/jx4zFx4kRUqlQJLi4uWL9+PbKyshAWFoaKFSuiRo0a+PPPP6Ued+LECbRo0QIWFhZwc3PDN998g4JCV7mysrIQGhoKGxsbuLm5YcmSJTL7zs3Nxddff42qVavC2toaLVu2lBwDQgghRGXiRA+KurlxHODhQenQ9e3DB2DfPiAsjB831rEjsGIFH5xZWABduwI//QT8+y/forZ4MV9GF8EZ0QkK0AxEdjZgY6O9xdbWBO7u9rC1NZG5LztbuTqmpaXhyJEjGDduHKytreWW4Yp86EdFRaFPnz64efMmhg8fjj179iAiIgKTJk3CrVu3MHr0aISFhSE+Pl7lYzZ58mQsWbIEFy9ehLOzM3r27In8/HyVt1OSzZs3w8nJCRcuXMD48eMxZswY9O/fH61bt8aVK1fQpUsXfPHFF8j+70AmJSWhR48eaN68Oa5fv441a9bg119/xQ8//CBV9xMnTuCPP/7AkSNHkJCQgCtXrkjtNzw8HImJidi2bRtu3LiB/v37o1u3brh//77GnyMhhJByQJzoAZAN0igdun69ewfExPBJOJyd+W6EmzYBaWmAoyMwfDjwxx/87b/+AsaPB7y99V1roi2MaE1GRgYDwDIyMqTWf/jwgd2+fZt9+PBBsu79e8b4tizdL+/fK/d8zp07xwCw2NhYqfWOjo7M2tqaWVtbsylTpkjWA2ATJ06UKtu6dWs2cuRIqXX9+/dnPXr0YIwx9ujRIwaAXb16VXL/27dvGQAWHx/PGGMsPj6eAWDbtm2TlElLS2NWVlZs+/btJT4P8ePfvn1bYtl27dqxNm3aSG4XFBQwa2tr9sUXX0jWvXz5kgFgiYmJjDHGpk+fzmrXrs1EIpGkzKpVq5iNjQ0TCoXs3bt3zNzcnO3YsUOm/hEREYwxxp48ecIEAgFLSkqSqk/Hjh3ZtGnTGGOMbdy4kdnZ2Smsu7zzTFV5eXls7969LC8vT+1tkPKHzhuiLjp3dGT3bsbc3aV/DHh48OuNkNGeN1lZjO3cyVjfvoxZWsq+HhMmMBYfz1h+vr5rWibp47xRFBsURWPQDESFCrLZUDVJJBIhMzMTtra2MCkyYLS0OT0uXLgAkUiEIUOGIDc3V+q+Zs2aSd2+c+cORo0aJbUuICAA0eIreirw9/eX/O/g4IDatWvjzp07Km+nJA0bNpT8LxAI4OjoiAYNGkjWubi4AABSU1MB8M/R399fqjUxICAA79+/x/Pnz/H27Vvk5eWhZcuWMvUXu3nzJoRCIWrVqiVVl9zcXDg6Omr2CRJCCDFeQqHqCRso0YP+5OYChw8D27fzLWKFJ4uuWRPo359/fZo2LV3GRWLUKEAzEBwHKOg1qBEiEf8Zbm2tfkKfGjVqgOM43Lt3T2q9939N7FZWVjKPUdQVUhFx8MgKDYzTRrdFVRRNbMJxnNQ6cSAmEok0ts/3799DIBDg8uXLEBT5wrSxsdHYfgghhBix2Fj5Kc+jo0ueGJgSPegOY8Dp08BvvwE7d/Lp8cWqVwcGDuSXJk0oKCMAaAwaUYGjoyM6d+6MlStXIqvwFR8V+Pr64syZM1Lrzpw5g7p16wIAnJ2dAQAvC6X4LZwwpLBz585J/n/79i3++ecf+Pr6qlUvTfL19UViYqJUkHnmzBlUrFgR7u7u8PHxgZmZGc6fPy+5X1x/sSZNmkAoFCI1NRU1atSQWlxdXXX6fAghhBig2Fh+vFLRec2Skvj1sbH6qRf56P59YMYMwMeHT3+/fj0fnFWpwk8InpgIPHoELFhALWZECrWgEZWsXr0aAQEBaNasGaKiotCwYUOYmJjg4sWLuHv3Lvz8/Ip9/OTJkzFgwAA0adIEnTp1wv79+xEbG4ujR48C4FvhWrVqhfnz58PLywupqan47rvv5G5r9uzZcHR0hIuLC7799ls4OTkhKChI4b6Tk5ORnJyMBw8eAOC7EVasWBHVqlWDg4ODegdEjrFjx2L58uUYP348wsPDce/ePcycORORkZEwMTGBjY0NRowYgcmTJ8PR0RGVK1fGt99+K9X1tFatWhgyZAhCQ0OxZMkSNGnSBK9evcKxY8fQsGFDfPrppxqrLyGEECMjFPItZ/LSMDPG/9CfOJHvxkjdFnXr7Vtg61bg//4PKHQhFjY2fOD8xRd8y6Wm5ycjZQoFaEQlPj4+uHr1KubOnYtp06bh+fPnsLCwQN26dfH1119j7NixxT4+KCgI0dHRWLx4MSIiIuDl5YWNGzeifaFuFhs2bMCIESPg5+eH2rVrY+HChejSpYvMtubPn4+IiAjcv38fjRs3xv79+2Fubq5w32vXrsWsWbMkt9u2bQsA2LhxI4YNG6bagShG1apVcejQIUyePBmNGjWCg4MDRowYIRVoLlq0CO/fv0fPnj1RsWJFTJo0CRkZGVLb2bhxI3744QdMmjQJSUlJcHJyQqtWrfDZZ59prK6EEEKM0KlTsi1nhTEGPHvGl6NujNonEgEJCcAvv/Atl+Lx+CYmQJcuQGgoHyyXdtA/KTc4xuRdfiGakJmZCTs7O2RkZMDW1layPicnB48ePYKXlxcsdTRnRXFJQoxNQkICOnTogLdv38Le3l7f1TFYmjjP8vPzcejQIfTo0UOvk4wT40LnDVEXnTtK2roVGDy45HIxMUBIiPbro2d6O2+eP+dT4W/YwHdVFGvQABg2jH+NaFiCwdLHeaMoNiiKWtAIIYQQQoyJm5tmyxHlFRQAhw4BP//Mz0cmThBma8sHwyNGAM2a0XgyUioUoBFCCCGEGJPAQD5bY1KS/HFoHMffHxio+7qVVS9f8l0Y162T7l7ati0flPXrV3a6MKozdQPRKArQiNFp3749qGcuIYSQcksg4FPp9+vHB2OFvxPFLTfLl9OP6tIGGowBx48Da9bwc5YVFPDrHR2B4cOBkSP5ucvKktJM3UA0xrgHIxFCCCGElEfBwcCuXUDVqtLr3d359eX9x3RsLODpCXTowI8F69CBv63M9AOZmcBPPwF16gCdOgG7d/PBWUAA8PvvfPCycGHZDM5o6gaDQC1oekStQESb6PwihJAyLjiYzw5I3dGkiQONot+D4kBDUQD7zz/AypXAxo3A+/f8uooV+dT4//sfn/yjrKKpGwwKBWh6IM4Uk52dDSsrKz3XhpRV2dnZAECZ0AghpCwTCCiVfmGqBhoiEXDkCN9i9uefH8v6+gLjxwOff84HaWUdTd1gUChA0wOBQAB7e3ukpqYCACpUqABOy9l+RCIR8vLykJOTY/Rp9knxGGPIzs5Gamoq7O3tIaArXYQQQsoLZQONuDjg4UN+bNU///D3cRzw6ad8gNexY/nKxPjypWbLkVKhAE1PXP+bF0McpGkbYwwfPnyAlZWV1oNBYhjs7e0l5xkhhBBSLigbQPTv/7Ebo60tn/Rj3DigRg3t1c2Q0dQNBsUgArRVq1Zh0aJFSE5ORqNGjbBixQq0aNFCYfmdO3fi+++/x+PHj1GzZk0sWLAAPXr0AMBPOvfdd9/h0KFDePjwIezs7NCpUyfMnz8fVapUkWzD09MTT548kdruvHnz8M0330hu37hxA+PGjcPFixfh7OyM8ePHY8qUKRp5zhzHwc3NDZUrV0Z+fr5Gtlmc/Px8nDx5Em3btqUub+WAmZkZtZwRQgjRDkNOw65sAPH+PeDtzXd3HDasfHRjLA5N3WBQ9B6gbd++HZGRkVi7di1atmyJ5cuXo2vXrrh37x4qV64sU/7s2bMICQnBvHnz8NlnnyEmJgZBQUG4cuUK6tevj+zsbFy5cgXff/89GjVqhLdv3yIiIgK9evXCpUuXpLY1e/ZsjBw5UnK7YqE3Z2ZmJrp06YJOnTph7dq1uHnzJoYPHw57e3uMGjVKY89fIBDo5Ie0QCBAQUEBLC0tKUAjhBBCiHoMPQ17SYEGAJib89kYg4MNJ7DUN5q6waDofTDS0qVLMXLkSISFhaFu3bpYu3YtKlSogA0bNsgtHx0djW7dumHy5Mnw9fXFnDlz0LRpU6xcuRIAYGdnh7i4OAwYMAC1a9dGq1atsHLlSly+fBlPnz6V2lbFihXh6uoqWaytrSX3bdmyBXl5ediwYQPq1auHQYMGYcKECVi6dKn2DgYhhBBCiKEyhjTsAgGwbJni4AwAtm7luzhSsCGNpm4wGHptQcvLy8Ply5cxbdo0yToTExN06tQJiYmJch+TmJiIyMhIqXVdu3bF3r17Fe4nIyMDHMfB3t5eav38+fMxZ84cVKtWDYMHD8ZXX30FU1NTyX7atm0Lc3Nzqf0sWLAAb9++RaVKlWT2k5ubi9zcXMntzMxMAHz3Ql10YyyOeP/6rgcxLnTeEHXQeUPUReeOARMKYTphAsAYZEayMwbGcUBEBAp69NB54CM5b7KywO3eDcGiRbJ1BMDc3SFcsgSsZ0/AmM4xoRDc6dOSLqWsTRvtHeOePYEePeTvz5iOmRL08Xmj7L70GqC9fv0aQqEQLi4uUutdXFxw9+5duY9JTk6WWz45OVlu+ZycHEydOhUhISGwtbWVrJ8wYQKaNm0KBwcHnD17FtOmTcPLly8lLWTJycnw8vKS2Y/4PnkB2rx58zBr1iyZ9UeOHEGFChXk1k/X4uLi9F0FYoTovCHqoPOGqIvOHcPjePMm2iQlKbyfYwx4/hznFy9Gmo7nCxPk5MD7yBFwI0bANC0NAJBfoQIedeuGtzVrQpCfj5xKlZBWty4faBw6pNP6lYZbYiIa/PILrP57XgDwwdERN7/8Ei/9/bW7c1tbICsLOHxYu/vRM11+3oinQCqJ3segaVN+fj4GDBgAxhjWrFkjdV/hVriGDRvC3Nwco0ePxrx582BhYaHW/qZNmya13czMTHh4eKBLly5SwaE+5OfnIy4uDp07d6YxaERpdN4QddB5Q9RF547h4v7rFVSSVtWrg/2XuE3rMjNhsno1TKKjwf0XwDBXV4giIoCRI+FlawuvEjZhyLg9eyBYuFCmu6blmzdovnAhhNu2gfXpo6faGT99fN5kKvk+0muA5uTkBIFAgJSUFKn1KSkpCtODu7q6KlVeHJw9efIEx48fLzFAatmyJQoKCvD48WPUrl1b4X7EdZDHwsJCbnBnZmZmMF80hlQXYjzovCHqoPOGqIvOHQPk4aFUMVMPD0Dbr93bt3xCi+hoID0dAPDe1RWWM2bANCwMAktLGP3oMqEQmDRJ7lg67r8Jt02//hro25fG0pWSLj9vlN2PXpOEmJubw8/PD8eOHZOsE4lEOHbsGPwVNNv6+/tLlQf4psnC5cXB2f3793H06FE4OjqWWJdr167BxMREkjnS398fJ0+elOorGhcXh9q1a8vt3kgIIYQQUmaJsyMqmkuV4/ggTptp2F+9AqZNA6pXB2bN4oMzX18UbNqE46tWgX35JWBpqb3965KyE26fOqW7OhGd0XsWx8jISKxfvx6bN2/GnTt3MGbMGGRlZSEsLAwAEBoaKpVEJCIiAn/99ReWLFmCu3fvIioqCpcuXUJ4eDgAPjjr168fLl26hC1btkAoFCI5ORnJycnIy8sDwCcAWb58Oa5fv46HDx9iy5Yt+Oqrr/D5559Lgq/BgwfD3NwcI0aMwN9//43t27cjOjpaJkEJIYQQQkiZJ07DDsgGadpOw56SAnz9NeDpCcyfD7x7BzRsCOzYAdy6BTZ4MFhZa0VSdsJtZcsRo6L3MWgDBw7Eq1evMGPGDCQnJ6Nx48b466+/JAk5nj59ChOTj3Fk69atERMTg++++w7Tp09HzZo1sXfvXtSvXx8AkJSUhH379gEAGjduLLWv+Ph4tG/fHhYWFti2bRuioqKQm5sLLy8vfPXVV1LBl52dHY4cOYJx48bBz88PTk5OmDFjhkbnQCOEEEIIMRriNOzy5kFbvlzzadhfvQIWLQJWrQLEyRWaNQO+/x747DNA/PtQKNTsfg2BshNuK1uOGBW9B2gAEB4eLmkBKyohIUFmXf/+/dG/f3+55T09PcGKm/sCQNOmTXHu3LkS69WwYUOcoqZjQgghhBBecDDQuzffte6/NOwIDNRsy1laGrB4MbBiBZ9FEABatACiooBu3RR3syxLSppwm+P4+7XZpZTojUEEaIQQQgghxEgIBED79prf7ps3wJIlwE8/Ae/f8+v8/PjxZj16lI/ATEzcpbRfP/55Fw7StN2llOid3segEUIIIYSQcuzdO2D2bMDLC5g7lw/OGjcG/vgDuHgR+PTT8hWciYm7lFatKr3e3Z1fr+kupcRgUAsaIYQQQgjRvQ8fgNWr+cQfr1/z6xo25LsyBgWVz6CsKF10KdUVobBsPA8doACNEEIIIYToTn4+sGED32r24gW/rmZNYM4coH//j8k/CE9bXUp1KTZWfnKZ6GhqCZSDAjRCCCGEEKJ9QiGwdSswcybw8CG/zsODbzELDQVMy8DPUmolkhUby4+lK5rsJCmJX0/dNWXQJQpCCCGEEKI9jAGHDgFNmwJffMEHZ5Ur88lA7t8Hhg8vNjgTCoGEBD62S0gw4Kz6sbH8XG0dOgCDB/N/PT359eWVUMi3nMnLRCleN3GiAb+o+kEBGiGEEEII0Y5z5/hA5dNPgRs3ADs7PhHIw4fA+PGAhUWxDzeamEfcSlS4Cx/wsZXI4CqsI6dOyR6TwhgDnj3jyxEJCtAIIYQQQohm3b0L9O0L+PsDJ07wgdjkyXxgNm0aYG1d4iaMJuahViLFXr7UbLlyggI0QgghhBCiGS9eAKNGAfXr8xGUiQkQFsZ3ZVy4EHBwkP+4Iv0YhXlC44l5qJVIMTc3zZYrJ8rAaExCCCGEEKJX798DixYBixcD2dn8ul69+O6M9eoV/1g5Gf5OOfXD89c7FT6kcMwTEKCJJ1AK1EqkWGAgn60xKUl+tM1x/P2BgbqvmwGjAI0QQgghpDDKxKe8ggI+Zf6MGUBKCr/O359vLWvTpuTHK8jw9/K1mVK7N4iYh1qJFBMI+FT6/frxwVjh11k8z93y5fT+KoK6OBJCCCGEiBlNVgo9Yww4cICfWHr0aD448/EBdu4EzpxRLjgrZuyWG14oVQ2DiHnErUSKJtbmOH46gfLaShQczKfSr1pVer27O6XYV4ACNEIIIYQQwIiyUujZlSvAJ58APXsCd+4Ajo58K8nt2x9bSpRRzNitQJyCO56Bg0ju/QYV84hbiQDZ506tRLzgYODxYyA+HoiJ4f8+ekTBmQIUoBFCCCGEUCa+kr14wSf8aNaMT+hhYQFMnQo8eABMmACYm6u2vWL6JwogQjQiAAAcpF8TqZgHQnAnTqDqyZPgTpzQzOujzsRr1EpUMoEAaN8eCAnh/5bngLUEFKARQgghhFAmPsWys4HZs4GaNYFNm/hjMWQIcO8eMH8+YG+v3nZL6J8YjD3YhX6o6pwrtV4S84DvjmrauTOaLV0K086dS98dtTRdXKmViGiIyklCPD09MXz4cAwbNgzVqlXTRp0IIYQQQnSLMvHJEomALVv4ecuSkvh1rVsDS5cCLVuWfvtKZPgLdr+E3g/McOpskZwtf8hPLiLpjqpOq5WChCUqbVPcSkRIKajcgjZx4kTExsbC29sbnTt3xrZt25Cbm1vyAwkhhBBCDJWmMvGp0z3OEJ05wwdhoaF8gFK9OrBtG3D6tGaCM0DpsVsCc4F0zzhooTsqdXElBkStAO3atWu4cOECfH19MX78eLi5uSE8PBxXrlzRRh0JIYQQQrRLE5n4ykIGyKdP+UioTRvg0iWgYkVg3jzg7l1g4MCSE4CoGqCqM3ZLG91RqYsrMSBqj0Fr2rQpfvrpJ7x48QIzZ87EL7/8gubNm6Nx48bYsGEDmLwrEIQQQgghhqi0mfiMPQNkdjYwaxZQpw7fUsZxwJdfAvfvA998A1halrwNdQNUVcduaaM7KnVxJQZE7QAtPz8fO3bsQK9evTBp0iQ0a9YMv/zyC/r27Yvp06djyJAhmqwnIYQQQoh2qZuJz5i7xzHGB2R16gBRUcCHD3wr4eXLwPr1gIuLctspbYCqSoY/bUwMTZNNEwOicpKQK1euYOPGjdi6dStMTEwQGhqKZcuWoU6dOpIyffr0QfPmzTVaUUIIIYQQrQsOBnr35ruySWWlKCZgUKV7nCElkLhyhU+Pf+YMf7taNWDRIqB/f+XnMgNKDlA5jg9Qe/fWTGp1JZKLwN1dtUnStLFNQtSkcoDWvHlzdO7cGWvWrEFQUBDMzMxkynh5eWHQoEEaqSAhhBBCiE6pmonP2LrHvX4NfPst30LGGGBlxWdq/Ppr/n9V6TpAFXdHFU+KXTigUndiaFW2KRSqFsAToiKVuzg+fPgQf/31F/r37y83OAMAa2trbNy4sdSVI4QQQggxeMbSPa6gAFi1CqhVC1i3jg9CQkL4+cy+/1694AzQT4CqjYmhldlmWUgEQwyeygFahw4dkJaWJrM+PT0d3t7eGqkUIYQQQojR0EQGSG07eRLw8wPCw4G3b4FGjfh1MTF83UpDXwHqf8lFCuLicCkyEgVxcaWfGLq4hCXGngiGGA2VA7THjx9DKGeQa25uLpLEkxgSQgghhJQXpc0AqU3Pn/OtZO3aATduAJUq8a1oly5pLmDUZ4AqEIC1a4ektm3B2rXTzDGWl7DEmBPBEKOj9Bi0ffv2Sf4/fPgw7OzsJLeFQiGOHTsGT09PjVaOEEIIIcQoiLvHRURIt7C4u/PBWWladdSRlwcsWwbMmQNkZfFB0ujRwA8/AI6Omt2XNsaEGRpjTQRDjJLSAVpQUBAAgOM4DB06VOo+MzMzeHp6YsmSJRqtHCGEEEKI0VAnA6Q2xMUB48fzY8sAoHVrYOVKoEkT7e3T0AJUTTO2RDDEqCkdoIlEIgB8hsaLFy/CyclJa5UihBBCiP5Qkjr1CSHAKbTHSwBuAAIB6OzQPXsGREbygRIAVK7Mp83/4gvV0uary1ACVG0wlkQwpExQOc3+o0ePtFEPQgghhBiA2Fj5jSDR0cbfCKJtejt2ubnA0qV898XsbMDEhE8GMmsWYG+vxR3LoeoUBcaC5kkjOqRUgPbTTz9h1KhRsLS0xE8//VRs2QkTJmikYoQQQgjRLXGSuqK/P8VJ6tTNXl4e6O3YHT0KjBsH/PMPf7tNGz4JSMOGWthZKRlz02x5GGdHDIZSAdqyZcswZMgQWFpaYtmyZQrLcRxHARohhBBihEpKUsdxfJK63r3pN2hRWj928gKb5GRg0iRg+3a+jIsL353x8891051RVWWhabasj7MjBkOpAK1wt0bq4kgIIYSUPZSkTn1aPXbyAhs7O75bY07Ox+6Ms2fz6w1RWWqaLcvj7IjBUHkMGiGEEELKHkpSpz6tHTtFgU1GBv+3Vi1g2zbtZmcsrbLYNFtWx9kRg6FUgBYZGan0BpcuXap2ZQghhBCiH5SkTn1aOXbFBTZi2dmGOdasMGqaJURlJsoUunr1qlLLtWvX1KrEqlWr4OnpCUtLS7Rs2RIXLlwotvzOnTtRp04dWFpaokGDBjh06JDkvvz8fEydOhUNGjSAtbU1qlSpgtDQULx48UJS5vHjxxgxYgS8vLxgZWUFHx8fzJw5E3l5eVJlOI6TWc6dO6fWcySEEEIMmThJnaLhSxwHeHhQkjp5tHLsSgpsAP7+U6dU2KgeUNMsISpTqgUtPj5eaxXYvn07IiMjsXbtWrRs2RLLly9H165dce/ePVSuXFmm/NmzZxESEoJ58+bhs88+Q0xMDIKCgnDlyhXUr18f2dnZuHLlCr7//ns0atQIb9++RUREBHr16oVLly4BAO7evQuRSISff/4ZNWrUwK1btzBy5EhkZWVh8eLFUvs7evQo6tWrJ7nt6OiotWNBCCGE6AslqVOfVo7d+fPKlTP0wIaaZglRmVItaNq0dOlSjBw5EmFhYahbty7Wrl2LChUqYMOGDXLLR0dHo1u3bpg8eTJ8fX0xZ84cNG3aFCtXrgQA2NnZIS4uDgMGDEDt2rXRqlUrrFy5EpcvX8bTp08BAN26dcPGjRvRpUsXeHt7o1evXvj6668RGxsrsz9HR0e4urpKFjMzM+0dDEIIIUSPxEnqqlaVXu/ublx5HJQiFAIJCcDWrfxfobBUm9PYsXv/Hpg8GZg+Xbnyhh7YUNMsISpTqgUtODgYmzZtgq2tLYJL+ISRF+QokpeXh8uXL2PatGmSdSYmJujUqRMSExPlPiYxMVFmTFzXrl2xd+9ehfvJyMgAx3GwL2ayxoyMDDg4OMis79WrF3JyclCrVi1MmTIFvXr1UriN3Nxc5ObmSm5nZmYC4Ltd5ufnK3ycLoj3r+96EONC5w1RB503xq1nT6BHD+D0aU6SpK5NGwaBAND2S6qrc4fbsweCyEhwSUmSdaxqVQiXLgXr00ft7Zb22HH79kHw1Vfgnj3j62RpCeTkQF5owzgOqFoVBa1aaf+FKSVuyRIIBg0COA5coeZF9l/QJly8GEwkAkQitbZPnzlEHfo4b5Tdl1IBmp2dHbj/3kR2Gkzh+vr1awiFQri4uEitd3Fxwd27d+U+Jjk5WW755ORkueVzcnIwdepUhISEwNbWVm6ZBw8eYMWKFVLdG21sbLBkyRIEBATAxMQEu3fvRlBQEPbu3aswSJs3bx5mzZols/7IkSOoUKGC3MfoWlxcnL6rQIwQnTdEHXTeGD9bWyArCzh8WLf71ea545aYiOYLFsjekZQEwcCBuDh1Kl76+5d6P3KPnVAIx9u3Yfn2LXIqVUJa3bqAQACrV6/QYP16uP03Bj+rcmXcHDUKJvn5aL5gARggFaQxAGAMF4cMwcviXhwF+9M5Cwu4TZmCBr/8Aqu0NMnqD46OuDViBF5aWACF8gmoiz5ziDp0ed5kZ2crVY5jrLj0QNr14sULVK1aFWfPnoV/oQ/DKVOm4MSJEzgvp/+1ubk5Nm/ejJCQEMm61atXY9asWUhJSZEqm5+fj759++L58+dISEiQG6AlJSWhXbt2aN++PX755Zdi6xsaGopHjx7hlIIBufJa0Dw8PPD69WuFwaGu5OfnIy4uDp07d6ZumkRpdN4QddB5Q9Sl9XNHKIRpjRpAUlLxrVL372s8kJHbalelCkQdO8IkNhZcVhaYqSlEX30F0bffAv9d2JX7OHd3CJcsKba1T1uthKUiFII7fVoyfxhr00Yjx5k+c4g69HHeZGZmwsnJCRkZGcXGBmrPg5aamop79+4BAGrXri03oUdJnJycIBAIZAKrlJQUuLq6yn2Mq6urUuXz8/MxYMAAPHnyBMePH5d7EF68eIEOHTqgdevWWLduXYn1bdmyZbFRtoWFBSwsLGTWm5mZGcwHhiHVhRgPOm+IOui8IerS2rlz5gw/ObICHGPA8+cwO3dOsynfY2OBQYNkUuZzL15A8Ntv/I2AAHA//wxBvXqQClkGDAD69pWaGJkLDIRpcYFNMfszHTRIfwMKzcyATp20uHn6zCGq0+V5o+x+VE4SkpmZiS+++AJVq1ZFu3bt0K5dO1StWhWff/45MsQTJyrJ3Nwcfn5+OHbsmGSdSCTCsWPHpFrUCvP395cqD/BNk4XLi4Oz+/fv4+jRo3IzLyYlJaF9+/bw8/PDxo0bYWJS8qG4du0a3Ax9MC4hhBBC5NNHyndl5jOrVAmIjwcKZY2WIp4YOSSE/1tccFbSxNAAPzF0KZOiEEK0R+UAbeTIkTh//jwOHDiA9PR0pKen48CBA7h06RJGjx6tcgUiIyOxfv16bN68GXfu3MGYMWOQlZWFsLAwAHy3wsJJRCIiIvDXX39hyZIluHv3LqKionDp0iWEh4cD4IOzfv364dKlS9iyZQuEQiGSk5ORnJwsmedMHJxVq1YNixcvxqtXryRlxDZv3oytW7fi7t27uHv3LubOnYsNGzZg/PjxKj9HQgghhBgAfaR8V2Y+s7dv+dY9Xeyv8MTQhBCDpHIXxwMHDuDw4cNo06aNZF3Xrl2xfv16dOvWTeUKDBw4EK9evcKMGTOQnJyMxo0b46+//pIkAnn69KlU61br1q0RExOD7777DtOnT0fNmjWxd+9e1K9fHwAffO3btw8A0LhxY6l9xcfHo3379oiLi8ODBw/w4MEDuLu7S5UpPCRvzpw5ePLkCUxNTVGnTh1s374d/fr1U/k5EkIIIcQAiFO+JyXJb2HiOP5+TaZ813WrHU0MTYjRUzlAc3R0lJvJ0c7ODpUqVVKrEuHh4ZIWsKISEhJk1vXv3x/9+/eXW97T0xMl5T0ZNmwYhg0bVmyZoUOHYujQocWWIYQQQogR0fVs3AUFyrdUaarVjiaGJsToqdzF8bvvvkNkZKRUd8Dk5GRMnjwZ33//vUYrRwghhBCiUbqajfvyZaBlS2DNmuLLaXqiZpoYmhCjp1QLWpMmTSTzoAHA/fv3Ua1aNVSrVg0A3w3RwsICr169UmscGiGEEEKIzgQHA717S2VGRGCgZlrO3r8Hvv8e+OknfuJle3s+o+LatbpptdN1KyEhROOUCtCCgoK0XA1CCCGEEB0SZ0bUpIMHgbFjgadP+duDBgHLlgGurkDnznx2xcIJPNzd+WBJ0ynvxa2EutofIUSjlArQZs6cqe16EEIIIYQYp+RkPhjasYO/7enJd20snDxNm6128uh6f4QQjVF7ompCCCGEEJUIhWUrYBCJgA0bgMmTgfR0/rl89RUQFQVYW8uW10arXXF0vT9CiEaoHKAJhUIsW7YMO3bswNOnTyVzi4m9efNGY5UjhBBCSBkRGyu/y110tHF2ubt7Fxg9Gjh5kr/t5wesXw80aaLfehFCjJ7KWRxnzZqFpUuXYuDAgcjIyEBkZCSCg4NhYmKCqKgoLVSREEIIIUYtNpZPWlF0AuWkJH59bKx+6qWOvDxg9mygUSM+OKtQAVi6FDh3joIzQohGqBygbdmyBevXr8ekSZNgamqKkJAQ/PLLL5gxYwbOnTunjToSQgghxFgJhXzLmbw5SsXrJk7kyxm6s2f5IGzmTD5Q694d+PtvvlujKY0aIYRohsoBWnJyMho0aAAAsLGxQUZGBgDgs88+w8GDBzVbO0IIIYQYt1OnZFvOCmMMePZM+Qmd9SEzEwgPB9q0AW7fBpydga1b+ayNnp76rh0hpIxROUBzd3fHy5cvAQA+Pj44cuQIAODixYuwsLDQbO0IIYQQYtz++82gsXJFCIVAQgIfLyUkaKEhbt8+oG5dYNUqPpgcNgy4c4dPoa9oMmgil9ZfK0LKCJUDtD59+uDYsWMAgPHjx+P7779HzZo1ERoaiuHDh2u8goQQQggxYm5umi1XSGws34DVoQMweDD/19NTQ0PakpOB/v35VPVJSYCPD3D0KLBxI+DoqIEdlC9afa0IKWNU7jA9f/58yf8DBw5EtWrVkJiYiJo1a6Jnz54arRwhhBBCjFxgIJ+tMSlJ/jg0juPvDwzk09YrSZx3pOgmxXlHdu1SMzkkY3zq/K+//pg6/+uv+XFnVlZqbJBo7bUipIwq9YhWf39/+Pv7a6IuhBBCCClrBAI+lX6/fnwwVvhXuriL4PLlfDklA7SS8o5wHJ93pHdvFadZu3+fT50fH8/f9vMDfvkFaNxYhY2QwrT2WhFShqncxREA7t27h/DwcHTs2BEdO3ZEeHg47t27p+m6EUIIIaQsCA7mm0mqVpVe7+6uVvOJxvOO5OcD8+cDDRvywZmVFbBkCZ86n4KzUikLOWII0TWVW9B2796NQYMGoVmzZpKWs3PnzqF+/frYtm0b+vbtq/FKEkIIIcTIBQfzzSSnTvEJQdzc+G6NajSbaDTvyKVLwJdfAtev87c7dwbWrgW8vVWuF5Gl5RwxhJRJKgdoU6ZMwbRp0zB79myp9TNnzsSUKVMoQCOEEEKIfAIB0L59qTejkbwjWVn8uLJly/iulQ4O/P9ffEHZGTVIizliCCmzVO7i+PLlS4SGhsqs//zzzyXp9wkhRNMoPTMhREycd0RRHMVxgIcHX06uo0eBBg34bowiEZ9W8M4dIDSUgjMNK/VrRUg5pHKA1r59e5yS01H49OnTCKR3FyFECyg9c9lBgTbRBHHeEUD2h3/RvCNS3rwBwsKAzp0hfPQECc79sXXyFSSM3AKhY2VtV7tcUvu1IqQcU6qL4759+yT/9+rVC1OnTsXly5fRqlUrAPwYtJ07d2LWrFnaqSUhpNyi9MwlEwo1MqxH62Jj+WxuhRMGuLvzP97K+2tIVCfOOyLvnFq+vMg5xRiwcycwfjyQmopYBCPC5hc8f1UJWARgkQrnorG84QyISq8VIUS5AC0oKEhm3erVq7F69WqpdePGjcP//vc/jVSMEEIoPXPJjCXooUCbaINSeUeePwfGjgX27wcAxLpPQL/ny8HeSzfnKHUuGssbzgBpMEcMIWWeUl0cRSKRUouQ+qoQQjSI0jMXTxz0FD1G4h+ahtIFtKRAG+ADbfoKIeoQ5x0JCeH/Sn7wi0TAmjVA3bp8cGZmBuGMWYhgy8EgOyCqxHPRWN5wBkzha0UIkaLWPGiEEKILlJ5ZMWMKeijQ1qPiBv2V5QGBd+8C7drxLWfv3gH+/sC1azjVYQaeJylOAqLwXDSmNxwhxOipFaCdOHECPXv2RI0aNVCjRg306tVLbuIQQggpDUrPrJgxBT0UaOtJcdl1ymrmnbw84IcfgEaNgNOnAWtr4Kef+DdC3brqn4vG9IYjhBg9lQO033//HZ06dUKFChUwYcIETJgwAVZWVujYsSNiYmK0UUdCSDlF6ZkVM6aghwJtPSiuO17fvvxiRF31lGrsu3gRaNYM+P57PlDr3h24fZtPDPJfXzq1z8VCbyQhTJCAdtiKQUhAOwgL/5QyhDccIcToqRyg/fjjj1i4cCG2b98uCdC2b9+O+fPnY86cOdqoIyGknKL0zIoZU9BDgbaOKdMdTx4D7apXYmNfVhYQGQm0agXcvAk4OgK//w4cPAhUqya1LbXPxf/eSLHoA088RgckYDC2ogMS4InHiEUfqXKEEFIaKgdoDx8+RM+ePWXW9+rVC48ePdJIpQghREycnrlqVen17u7lO/OfMQU9FGjrWEnd8YpjYF31SszLMeMaUL8+sGwZnxRkyBB+wukhQ+S+OdQ+FwMDEev4JfphF55D+sMoCVXRD7sQ6zjSMN5whBCjp3KA5uHhgWPHjsmsP3r0KDw8PDRSKUIIKSw4GHj8GIiPB2Ji+L+PHpXf4AwwvqCHAm0d0kQ3OwPoqldiQyATYeIcBwgfP+WvRhw8yLecOTsXu111zkUhBIhANPiqSP90Yv/dnojlEMJA3nCEEKOm1DxohU2aNAkTJkzAtWvX0Lp1awDAmTNnsGnTJkSLfy0QQoiGidMzk4+MbfJXmgdJRzTRzc4AuuqVmJcDJniGajjVZxnabw4DKlZUetuqnounTgHP0yoUX5e0Cjh1ij6nCCGlp3KANmbMGLi6umLJkiXYsWMHAMDX1xfbt29H7969NV5BQgghihlb0EOBtg6I+78mJRU/5kwejuMfq6WuekKh8ueq0olw+k8AlI/NJFQ5F3WSlEeVg0MIKdNUCtAKCgowd+5cDB8+HKdPn9ZWnQghhKiAgh4iRdz/tV8/PuAqHKQVvi3vPkBrfWNjY+W39kZHy2/tNaREOFqvi6oHhxBSpqk0Bs3U1BQLFy5EQUGBtupDCCGEkNIqbqDV7t38osMBgSUm+5CT2T8wEHB3zQcHkdxt6jIRjlaT8qhzcPSsLM9xToghULmLY8eOHXHixAl4enpqoTqEEEKI5pTrXmMl9X/VUd/YkpJ9cByf2V9qlEReHgTLFiD69Q30wzZwEEmScQC6T4RTUqOk2nVR5eAYyIlLjX2EaJ/KAVr37t3xzTff4ObNm/Dz84O1tbXU/b169dJY5QghhBB10Q9JFN//VVt9Y4tExaeEgXj+XHFwUTizf0AAYP/PPzD97jvg1i0EA9jVpCEikr/B85cfAzR9JMLRSlKeEjOhFDo4BtCPWdzYVzSeFDf2UUZWQjRD5QBt7NixAIClS5fK3MdxHITUzk0IIUTP6IeknsiJil86jAOwssSHvnyUA5M9U9F2xQpwjAFOTkB0NIJDQtBbxBlES6jGk/LoJPuIZhhhYx8hRkvlAE0kkt8XnBBCCDEE9ENSuxR2G1UQFbu9+Vup7bpNGwZBynYAgGjwYJhER/NBGgwrEY5G62JImVBKYGSNfYQYNZWShDx+/Bjr16/H6tWr8fffyn3gKmPVqlXw9PSEpaUlWrZsiQsXLhRbfufOnahTpw4sLS3RoEEDHDp0SHJffn4+pk6digYNGsDa2hpVqlRBaGgoXrx4IbWNN2/eYMiQIbC1tYW9vT1GjBiB9+/fS5W5ceMGAgMDYWlpCQ8PDyxcuFBjz5kQQoh2qPJDkqgmNhbw9AQ6dAAGD+b/enoCsbsUR8WBOAl3PFOc7AMieOApAlN2glWvjsQZMyDctEkSnJVpWs0+ollG1NhHiNFTOkCLj49HvXr1MHr0aISHh6NJkyb4/fffS12B7du3IzIyEjNnzsSVK1fQqFEjdO3aFampqXLLnz17FiEhIRgxYgSuXr2KoKAgBAUF4datWwCA7OxsXLlyBd9//z2uXLmC2NhY3Lt3T2Zs3JAhQ/D3338jLi4OBw4cwMmTJzFq1CjJ/ZmZmejSpQuqV6+Oy5cvY9GiRYiKisK6detK/ZwJIYRoD/2Q1I5ikw32N0Hs8+ZyHyeACNGIAABwkA7gxEHbcnwFwcQJKLh6FalNm2q+8oZKnH0EkA3SdJ0JpQRG1NhHiPFjSgoICGC9e/dmL168YG/evGFjx45lbm5uyj5coRYtWrBx48ZJbguFQlalShU2b948ueUHDBjAPv30U6l1LVu2ZKNHj1a4jwsXLjAA7MmTJ4wxxm7fvs0AsIsXL0rK/Pnnn4zjOJaUlMQYY2z16tWsUqVKLDc3V1Jm6tSprHbt2ko/t4yMDAaAZWRkKP0YbcnLy2N79+5leXl5+q4KMSJ03hB16Pu8iY9njG/KKX6Jj9dL9YxSQQFj7u6KjyUHEfPAE1YAE4WFdqMPc3d4L7XaA0/Y7moTGTt3jjGm/3On8PONj2csJob/W1Cg5R3u3i17gD08+PUGQnwOcJyCc4Djq6z1YyWHoZw3xLjo47xRNjZQegzarVu3cPbsWbj9d2lk0aJF+Pnnn5GWlgZHR0e1gsO8vDxcvnwZ06ZNk6wzMTFBp06dkJiYKPcxiYmJiIyMlFrXtWtX7N27V+F+MjIywHEc7O3tJduwt7dHs2bNJGU6deoEExMTnD9/Hn369EFiYiLatm0Lc3Nzqf0sWLAAb9++RaVKlWT2k5ubi9zcXMntzMxMAHy3y/z8fMUHQgfE+9d3PYhxofOGqEPf502rVkDVqqZ48YIPHYriOIaqVYFWrQqgThWFQuD0aU4yBqtNG2YIDRxadeIEh+fPFf9kYODwDNVwCoFojxNyywRjDz7rPwVnNj9Eco49XM3SEPBtW3CTf0S+mRlQ6LtSn585e/ZwiIwUICnp47lTtSrD0qVC9OkjZ2CjJvTsCfToAe70acngPtamDd9yZkCfv0uWcBg0SPDfVAMfjw/H8cdl8WIhRCIGXacrMITzhhgffZw3yu5L6QAtMzMTToX6g1eoUAFWVlbIyMhQO0B7/fo1hEIhXFxcpNa7uLjg7t27ch+TnJwst3xycrLc8jk5OZg6dSpCQkJga2sr2UblypWlypmamsLBwUGyneTkZHh5ecnsR3yfvABt3rx5mDVrlsz6I0eOoEKFCnLrp2txcXH6rgIxQnTelD9CIXD7tiPevrVEpUo5qFs3TeUgRJ/nzeefu2HBguYAGIDCQRoDY8CQIRdx+LDqfRwTE93wyy8NkJZmJVnn6PgBX355E/7+ZbfP5MmTVQE0K7HcC8jv38YAiExNYf7zanQA8LpuXVwfNw5/Vq0KyDlP9HXuJCaKzxtpSUnAwIECTJ16Ufuvs60tkJUFHD6s3f2owcICmDJF/ntgxIhbsLB4iUJpAXSOvquIOnR53mRnZytVTqUsjocPH4adnZ3ktkgkwrFjxyTjvwDDmgctPz8fAwYMAGMMa9as0fr+pk2bJtW6l5mZCQ8PD3Tp0kUSHOpLfn4+4uLi0LlzZ5iZmem1LsR40HlTPpW2BcEQzpsePYCmTYX/PY+P693dgSVLhOjTpwmAJiptc88eDgsXCmTyYLx5Y4mFC5tj2zYttrAURyiU3/KiQdbWHOTMriPDDclgHMenyf+P+D9BQQGYnR2E8+bBbvhwtDWRHQav8NzRwXMUCoFx48Q/i4q2vHLgOIYtW5ojKqqgzLeYFqdHDyAqCjh9uqBQK7IZBALV31NKK+H1N4TPHGJ89HHeiHvXlUSlAG3o0KEy60aPHi35X9V50JycnCAQCJCSkiK1PiUlBa6urnIf4+rqqlR5cXD25MkTHD9+XCpAcnV1lUlCUlBQgDdv3ki2o2g/4vvksbCwgIWFhcx6MzMzg/nAMKS6EONB5035ERsLDBokm4zvxQsOgwaZqjR/mL7PmwEDgL59i6aE5yAQqDzDDIRCYNIkRan7OXAc8PXXpujbV8f5HHQ0G3eHDvxmk5LkHwOO4+9vu2Q8uMgHUvWRhDrBweBWrIBplSol7k/q3NHRczxzBlLBfFGMcXj+HDh3zqzcp5E3MwM6ddLRzlR4/fX9mUOMky7PG2X3o3QWR5FIVOKi6iTV5ubm8PPzw7Fjx6T2c+zYMfj7+8t9jL+/v1R5gG+aLFxeHJzdv38fR48elemC6e/vj/T0dFy+fFmy7vjx4xCJRGjZsqWkzMmTJ6X6isbFxaF27dpyuzcSIiYUAgkJwNat/F+au50Yi5LmDwP4+cOM6ZwWz1kVEsL/VTd40kXqfpU/O4pNq9gPiI3V2OeR0skG+wcDV68Cn376sYCbG1/X3bsBJYIzKUo8R02h7J8GSIevPyEGRTc5SxTbtm0bs7CwYJs2bWK3b99mo0aNYvb29iw5OZkxxtgXX3zBvvnmG0n5M2fOMFNTU7Z48WJ2584dNnPmTGZmZsZu3rzJGOMzsvTq1Yu5u7uza9eusZcvX0qWwhkZu3Xrxpo0acLOnz/PTp8+zWrWrMlCQkIk96enpzMXFxf2xRdfsFu3brFt27axChUqsJ9//lnp50ZZHMsfeYm43N0NKhGXSui8KV80lf2wLJ43MTHKHZuYGPW2r/JnR4lpFTm223Ekc3cXafTzqNhkgyIRY9u3M+bi8vHO//2PsfR0pbcvde4o8Rw1mTaQsn8aGCVf/4LcAhYXl88iIy+yuLh8vWSRJMbJkLM46j1AY4yxFStWsGrVqjFzc3PWokULdu6/dLuMMdauXTs2dOhQqfI7duxgtWrVYubm5qxevXrs4MGDkvsePXrEwHd5l1niC32qpqWlsZCQEGZjY8NsbW1ZWFgYe/fundR+rl+/ztq0acMsLCxY1apV2fz581V6XhSglS+7d8tPP8xx/GKMQRqdN+WLpoKQsnjeaPPHu1qfHYUqVAATFo92LAaDWDzasQKYsN3owzgIGSDS+OeR3BT0T54w9tlnH3dUpw5jJ0+qvG2pc0fHEZMhp5Evl5R4/XejD3N3/lBmLooS3TLkAE31jvhaEB4ejvDwcLn3JSQkyKzr378/+vfvL7e8p6cnmLz+OUU4ODggJiam2DINGzbEqdL0VyHlRkldwziO7xrWu7dBzDdKiFw0EW0hQqHU4LXA1oFwdxeUOAardWu+K+HHMW/Fv+fV/uz4r59dLPogAtF4Dg/JXVXxDDmw+i85h3R/RE18Hom7jUqewMqVwLff8pkHzcyA6dOBadP4lH+loeM+h+JunP364b808h/vM7A5ozWiyCle4rmqcyW8rrHog37YBfZK+hwX935UZbwsIYZG6TFohBDFdDE+hRBtCwzkg4yiY4zEOA7w8ODLlWmxsYCnJ58ZY/BgoEMHCHw8ER1yDoDiMViDBgE+PlIPg6en9DCZomPCEhLU/Oxwc5P8QH2OqlJ3JaEq0uAERV/xGvs8un4d8Pfno72sLCAggF8XFVX64AzQyxWD4GD+h31V6UMKd/ey9YNfzikuc67qXTGvqxAmiEC0wosQgPGNlyWkMINoQSPE2NHgclIWlLcWBLnESQmKNmklJSF4cWvs+vosIra2kkkoN2gQsHix3IdJruYDssnoHByUq1bRzw5h60BECGqBCQHZQEy5a69qfx5lZwOzZ/NPWCjk5+1auBAYORKQkzpfbeIrBiU1W2r4ikFwMN+6aNCtS6VQzCluWC1Pxbz+pxAo1WpcVOGLEOU94yYxTmoHaHl5eUhNTYWoyHTx1apVK3WlCDE21DWMlBXiFgR5Wa2XLzeQH27aokR/w+BtA9D730c4dVYg+fHeujXfclZcN8VRo4A3b2TLvHmjXNWKfnacOivAc6GKGRFL2KZSjhwB/vc/4NEj/nbfvsBPP6menVEZerxiINWNswxRtkvtZ58BZ8/qOUAt5vV/CeXON31cFDX4rqPEKKgcoN2/fx/Dhw/H2bNnpdYzxlSeB42QskJPF3oJ0Yqy3oKgkJJ9lQVnT6F9oV/vynRTTEtTr0qKPjtK88NTrc+j1FQgMhLYsoW/7e4OrFoF9OqlfkWUUa6vGGiest3x3d2BV68+rtfCtHPKUfD6uzkXAK+KeZy4nI4viupoyj5SDqgcoA0bNgympqY4cOAA3NzcwCkarEBIOUJdw0hZU1ZbEIqlZl9lbV2lL+6zQ90fnip/HjEGbNoEfP0139zHccD48cAPPwAVK6pXCVWV2ysGmqfsufqqSPCj1+6Pcl7/wNaBcPcxrIuiRtN1lBgFlQO0a9eu4fLly6hTp4426kOI0aILvYToh8a6FKnZV1lTV+kdHKS7PBb32aFMq72DA2BlVYrPo3/+4bszxsfztxs1AtavB5o3V+FZaUi5vGKgeeqeq3rPRlzk9RfAsC6KUiZnomkqB2h169bF69evtVEXQoweXeil/vdEtzTapUjNvsolPUxZO3bw7xVl3jvKtNqvW6fm51FuLrBgAfDjj0BeHh/lzZ7N/8I0pdxixqw056qhJd7Q5kVRVb/HVMnkbAjHjhg+lT9pFyxYgClTpmDu3Llo0KABzMzMpO63tbXVWOUIMUbl+UIv9b8nuqTxLkVq9lUu6WGMAY6O8pOEiMu4u/OfG6pczFD2B6pKn0cnTgCjRwP37vG3u3YF1qwBvLxU2Ih8jAEFBUB+PiASyVnyhcg7lQiL41eRmlcJ5oEB4EwF4Dj+GJmY8MfHzIyPEwUCxVNCEPmKO1eVZUjZiMUXRePjC/Dnn9fQvXtjdOhgWqqLgup8j1EmZ6JpKgdonTp1AgB07NhRaj0lCSGkfKP+90Sbil7Rbt1aS12K1LwsX9LDAO10x9JEqz1jQNbTNGRM+RGZO/5EJuyQad8fmWERyKzfGlkHOWRlAe/f89OdFV5ychQveXl8MCZeSv55IADQll9+Vq7upqb8YmYGmJvz069ZWkr/tbDgGwGtrfmlQoWP/1tbAzY2/EwBFSvyf4suVlbKH0tjoOhcdXaWHXsmj6FlIxYIgHbtGLKyktCuXaNSB2fqfI8ZYyZn6u1i2FQO0OLFfdEJIeQ/1P+eaJO8K9pOTkBxve1L1aVIzainpIdpqzuWuNWeMSAzE3j8mD82r17xf1+/5rNIvn3LL2/efPz/7VuGjHQGEXMEsPS/BUA6gGXq10lXCgr4JSdHe/uwsAAqVZK/ODl9XJydP/7v6MgHjIZK3rkqni7CkBJv6FJpvseMLZMz9XYxfCoHaO3atdNGPQghRoz63xNtUXRFW9mh0Gp3KVKzr3JxD1Mn7mMMyMgAXrzgl+RkICVF/vLqFR+sqIb7bwEEKICdLYOtg5mk9ahiRb6FqXCLk7jVqUIFvnXJ0lJ2sbDgAxQzM/mLQMB3WTRhQnA1fGCS9BQcGAr3WGQAGEzA3D3AHvwLESeAUPixm2TRv3l5/PC5nBzZvx8+8PNrF20BFLcMvnvHB7eZmR//f/eOP/65ufxxT05W7chWqgS4uMgurq78a1+1Kj99nKOjZuf3Vpa8c9WQEm/oWmm+x4wpkzP1djEOao32TU9Px6+//oo7d+4AAOrVq4fhw4fDzs5Oo5UjhBgH6n9PxIRC4MQJDidPVoW1NYcOHdT/UVLcFW1lGVKXIkD6R7FQyP/of/aM/2H47Bm/iIMx8fLhg2r7sLaWbdFxcOCXSpUAh4p5qBS3E5V2rkOlglTYW+TAbvo4WE2dAM5Cx80+CaeApCdy7+JDRxHw/AmQqPurOyIRH7x9bG2UXt684Vsmxa2U4hbLtDT+seJyd+8Wvx8zMz5QEy/u7kC1aoCHB79Uq8YHdrr4cV+esxGX9nvMGI4d9XYxHioHaJcuXULXrl1hZWWFFi1aAACWLl2KH3/8EUeOHEHTpk01XklCiGEzxv73RPM+dpsxBdAMS5eWrttMSVe0i2MIXYpycoCnT/kuh0+eSP8VB2LKtnhVqsS/f1xd+UVey4w4ICt2zNTx43zq/Pv3+dvduvETTnt7K//ENDl4xYCv7piYfByHVr268o8TB2fyWjnFLaDi4Ds1lW/9e/KEXxQxNeVb3KpXBzw9+Zwtnp4fF3d3+Qk21Xmpyms2Yk18j5V07PQ97ot6uxgPlQO0r776Cr169cL69eth+t+nQUFBAb788ktMnDgRJ0+e1HglCSGGzdj63xsqfX95l4Y2us2o+5tcV12KRCL+B/fDh/zy778f/3/4ULkucQIB32ri4cG/Rzw8PnZ9K7yUOlFFaiowaRLw++/8bVdXPnLu31+1VIiaHrxSBq/umJjw3RYdHYG6dYsvm5fHnyfigC0p6WNL6rNnfIAvDuTFQZy8n1kCAd/S5uPzcXn9mp9jPDX1YzllX6rSZCM21s8xTX2PKTp2hjDuy4Cvh5Ai1GpBKxycAYCpqSmmTJmCZs2aabRyhBDjYEz97w2VIXx5q0tb3WaU/U1eNPucJrsUMcb/QL5/X3Z5+LDk7ofW1h9bOapXBzyriVA9+w6qCZLg4WsD194tITDXchT5yy/A1KlAejr/YowbB/zwA6DqsARtROHl/OqOuTkfWFWrprhMQQEfxD19+rEF9vFj4NGjj62yeXn87UePgKNHFW/r+XOgb1/gm2+AoUP5hlNNJjMx5s8xbX6PGcq4rzJ4PaTMUjlAs7W1xdOnT1GnTh2p9c+ePUPFihU1VjFCiHExhv73hspQvrzVpa1uM8r+dn/wADh7tnRX7LOzgX/+4ccL3b3LTwN29y4fiGVlKX6cicnHlgtvb37x8eG7oHl58eO+JA1Uuv71ev06MGYMkJjI327SBPj5Z6B5c9W3pa0ovJxd3VGndcnUlD9N3N35TItFiUT89sStuPfvA8uWFX/xYP58fjEx4c9TX1/ZxRDid13TxveYIY37KufXQ4wLU9H48eOZu7s727ZtG3v69Cl7+vQp27p1K3N3d2cRERGqbq5My8jIYABYRkaGvqvC8vLy2N69e1leXp6+q0KMiDrnTUEBY/HxjMXE8H8LCrRWvTKhoIAxd3fG+K9L2YXjGPPwMOzjGBOjuP6Fl5gY1be9ezd/DDhO9rhwHH+/Kt6+ZezMGcbWr2fsq68Y69qVsWrViq+3iQlj3t582fBwxqKjGTt0iLH79xlT+q0hfiLyXmB1nkhxMjP5JycQ8PuwsWFs2TLG8vPV32Z8vHIvcny8etvfvVv2jeDhodnjomfynqK7u+aforIvlZVV8fe7uTH2ySeMTZjA2M8/8++b9HT5+9T355imf+No8ntM228dVWn6M9WY6eO3sbKxgcotaIsXLwbHcQgNDUXBf6ObzczMMGbMGMyfP1/D4SMhxNiUZuxCeVQWBm1rs9uMule0378H/v4buHkTuHWL///2bb67oiIODkCdOh+X2rX5xcurlN3AdHUJnbGPrXRJSfy6/v355pSqVdXfLqD9wSv/ZVcoiI/HtT//ROPu3WFamhSgBkaXrUvKvgS//AJ06MC3FN+5I728eMFv5+VLPq9MYe7uQP36QL16QMOG/JKaavyfY4Vp8nvM0MZ9UW8X46BygGZubo7o6GjMmzcP//77LwDAx8cHFSpU0HjlCCGkrDO0L291aLvbTHGZ0YRCvkvX9et8MCZeHj1SvD13dz55g3jx9eUDMicn9epXIl1E4Q8fAuHhwJ9/8re9vfnsjN26qbe9onQxeEUgAGvXDklZWWjUrl2ZCc503cVN2ZegShW+rJsbH6gVlpHBB263b/MXN/7+m7/Q8fz5x+Wvvz6WV7behvw5pi2GOO6rvGbqNCZqzYMGABUqVECDBg00WRdCCCl3DPHLW1W6GEYkEABNmwI3bgDXrgFbtvBB2a1bisfauLoCDRp8vNpfr556Y2tKTZtReE4OsGgRMHcu/7+5OZ8QZNo0DaR+LIQGr6hN163kmnip7OyAli35pbD0dD5ou3Xr48WQ69f59coQifhFHxNz64uhvnWot4thUypACw4OxqZNm2Bra4vgEto+Y2NjNVIxQggpDwz1y1tVmu42k5oKXL3KL1eu8H8fPJBftkIFPhBr2JD/Kw7KtNYipmqmB21F4YcP861m4gPzySfA6tV8v0xNK2fJPDRJ163k2nyp7O35RCWFk5UwxmeSbNaMn6S7OJ9/DowdCzRuzJf38+OXmjXLbtBGbx2iDqUCNDs7O3D/nUW2traS/wkhhJROWfryFnebiY8vwJ9/XkP37o3RoYNpiXVPSQEuXeKXy5f5gEw8hKood3f+x12jRh8XHx8dHh91MjFqOgp//hz46is+Igb4wG7pUmDgQNXmNFOVMQ5eMYBJufTRSq7Ll4rj+Gkk1q3jP8cA+ae5jw9fl8xMfi63wvO5VazIt5D7+fFJRps353vplpWfm8b41iH6pVSAtnHjRsn/mzZt0lZdCCGkXCpLX94CAdCuHUNWVhLatWsk81s4LQ24ePFjMHbpkvzuXxzHX1Vv2pTPDi/+6+iom+chl7qZHjQVhefn8+VmzeJz/wsEwPjx/G1b29I8M+UZ4uAVRUGYgUzKpa9Wcl2/VIo+xzw8Pn6OFRTwSUiuXPn4GXD1KvDuHXDiBL+IOTgALVrwwZr4r4uLduquC4b41iGGS+UxaJ988gliY2Nhb28vtT4zMxNBQUE4XjTdDyGEkBKVxS/vDx/4YOzChY/Lf7mlpHAcPzZM3N3Jz49vGTOoqTVLm+mhtFH4iRP8BNN//83fbt2a787YqJG6z0h9hjR4RVEQFhICLF5sEJNy6bOVXNcvVUmfY6amH7shDx3KrxMHbeILNhcv8uNM37zhE5EUTkZSvTrQqtXHpUkTwMJCd8+vtAzprUMMm8oBWkJCAvLy8mTW5+Tk4NSpUxqpFCGElEfG/OXNGJ9N8dw54OxZE8TFtcPTp6b4bzYWKTVr8lfDmzXjlyZNABsb3ddZJZrI9KBOFP7iBTB5MhATw992cgIWLuR/3ZbVQTvKUtSi+fw5nzhFHl3PDPyfstRKXhJVP8fEQVvdunxXyYAAvqXczo4P2sQXd+7e5ce6PXkCbN/OP9bMjP/8aNHCBObmVVG/ftnqGknKL6UDtBs3bkj+v337NpKTkyW3hUIh/vrrL1Qt7TwrhBCNM4AhGKQMyswEzp/nAzLx8uaN+F4BAHsAfJekli35LkotWvABWaVKeqp0aWgq04Oyv17z84EVK4CZM/lJ3TgOGD0a+PFHvu9XeVdci2ZJ9DQpV1lsJdeU4nqjikfWZGbyLWyFP3NevRIHcAIAzbB0KT/lnziRSevW/JjVUs1jSIgeKB2gNW7cGBzHgeM4fPLJJzL3W1lZYcWKFRqtHCGkdAxkCEb5UgYjYsb4ecXOnuWXM2f49NpFfxtbWPABWIsWQpiZXcbo0U3g5WVWNq5m6zLTQ9HujC1b8nOa+fmVfttlRUktmsrQw6RcxtxKri3KDu20teUTlYp/goo/l/hWeyEOH87Eo0f2SErisHMnsHMnX87Skm+xDwwE2rQB/P35bJSEGDKlA7RHjx6BMQZvb29cuHABzs7OkvvMzc1RuXJlCIz8RwghZYm6+QxIKZSRiDg/nx8Dcvo0v5w9CxTqNCHh5cX/2BGPB2nUiL9SnZ8vwqFDL+Hh0aRsBGeAbjI9FO3O6OgILFgAhIVRd8aiNBFcGfLkguVEaYZ2chzfndHbG+jfX4RDh06iXbseuH7dTHIx6exZvmX/1Cl+ET+uQQM+WBMvHh5af6qEqETpAK169eoAAJFIpLXKEEI0o7T5DPTFqBufjDgifv+evwotDsjOneOTBBZmZsY34LRuzY8R8fcvZ79vtZnpIS+P3/bs2R+7M/7vf8APP1B3RkVKc/IZy+SC5YCmJ/G2tgbateMX8ePv3eMDNfHn2/37/IT3N27weXYAfuxb27b8EhjIj5MtMxeXiFFSKkDbt28funfvDjMzM+zbt6/Ysr169dJIxQgh6tP0l54uGHXjk5FFxG/f8q+9eC6iK1f4p1BYpUr8leWAAH5p1ozvKlSuaSPTw5EjwIQJ/K9IgG+KXLlSpjujNi5eGPUFkZJaNMWMfXLBMk7bk3hzHFCnDr8MH86vS0nhu2mLA7YrV4DHj/nl//6PL+Pi8jFga9cOqFePGrGJbikVoAUFBSE5ORmVK1dGUFCQwnIcx0FY9FueEKJz2v7S0zQjbnziFYqIhTDBKQTiJdzghpcIxCkImEivEXFqKh+InTjB/5U3fqxatY9jNAID+bT39INEDk1lenj8GIiMBPbs4W9XrsxnZ/ziC5kDr42LF0Z9QQRQrkXz66+BrVvLftpEI6aPSbxdXPiXX3wKvH8PJCZ+vGB1/jwfxBUex+bo+LFlrn17oH59+nwk2qVUgFa4WyN1cSTE8GniS08oBE6c4HDyZFVYW3Po0EE7F5yNrPFJvv8i3Vj0QQSi8RwfBzS44xmiEYFg7NFZRJyaygdjCQn8cvu2bJnatfkfG+IuPdWq6aRqZUNpMj18+MAHYvPnAzk5/LYmTOCzNdrZyRTXxsULo78gIqZMi+a8eUbcTFj26WsS78JsbIDOnfkF4N+WFy9+vKh15gyQlsa/b2Jj+TIODvy0AN7e/OfoF1/w3cBLw5BatA2pLuUW04C3b99qYjNlTkZGBgPAMjIy9F0VlpeXx/bu3cvy8vL0XRWiAwUFjLm7M8ZxjPFfe9ILxzHm4cGXk2f3bv7xhR/j7s6v17T4ePl1LLrEx2t+3xoTH892ow/jIGSAUPpYQ8g4CNlu9NHak3j9mrFduxgbN46xevXkH78GDRgLD2ds507GkpO1Ug0J+ryRQyTiX6Tq1T++KJ98wtitWwofIn4fK3pPlPQ+LtU2cwv48zUmhv+ryk5KQa1zp0BxXYu5y+AYVF11WJndu/nzruj3lXidMt872vzMyc1l7OxZxubOZaxLF8YsLWXfNyYmjPn7M7Z6NWN37/Jvd1Xo8jtXn3UxqHOc6ee7StnYQOUAbf78+Wzbtm2S2/369WMcx7EqVaqwa9euqV7TMowCNKJP6n7piR8n74ebsl+WqoiJUS5Ai4nR7H41qSC3gLkLkmSCs8JBmofgOf+jVwMyMxk7eJCxyEjGGjeW/3o1bMjYhAmMxcbyAZzcemvjy7KggOXHxbGLkZEsPy5O/9/AhuDGDcY6dPj44nh4MLZ9e4m/4rRx8ULpbTr108uvRU1+VxnSj96SGFRd9VAZebv08FB+l7r6jbN7t3LvnypVGBsyhLENGxh78qTkberyO1dfdTGoc/w/ZSpA8/T0ZGfOnGGMMXbkyBFmb2/PDh8+zEaMGME6d+6sXm3LKArQiL6p+qWnjSv2JSkLLWjafg45Ofxjv/2Wv0orEMhuu149voVs927GXr0qeZta+bI0xG9gfUpL418UExP+WFhaMjZjBmNZWfLLF4mYY36XH/CX5uKF0hdEMEgvvxY19V1lSD96S2JQddVjZUpzwUgXv3FK+n4EGLOw4Jei6318GBs1ir8uk5qq/Da18Z2r7vMrTV0M6hwvpEwFaJaWluzp06eMMcYmTJjARo0axRhj7N69e8ze3l7liq5cuZJVr16dWVhYsBYtWrDz588XW37Hjh2sdu3azMLCgtWvX58dPHhQ6v7du3ezzp07MwcHBwaAXb16Ver+R48eMQBylx07dkjKybt/69atKj03CtCIISjuS6/ofUeP6j5YKm13zNLuWxMtSJpuBRQKGbtyhbGFCxnr2pUxKyv5X/gjRzK2davqXRa18mVpqN/A+lBQwNiaNYw5On48Dn37MvbokeLHyAlu4536afz9qPTFBLTTy69FTXxXGdKPXl3UVWMt4cZ04IrQxW8cZd87hw8zduwYf0GtVSv5F9QaNWJs0iTGFizQ/XduaZ+fqnUx5NOqTAVobm5ukha0WrVqSYKau3fvsooVK6q0rW3btjFzc3O2YcMG9vfff7ORI0cye3t7lpKSIrf8mTNnmEAgYAsXLmS3b99m3333HTMzM2M3b96UlPm///s/NmvWLLZ+/XomL0ArKChgL1++lFpmzZrFbGxs2Lt37yTlALCNGzdKlfvw4YNKz48CNGLI5DV2ODhoNtBQpS6lHYOgzj411dijiS+2x48ZW7+esQEDpH/XixdXV77LzMaNfFl1aeXL0pC/gXXt+HG+f6n4uderx/9aK46C4LYAAuaOp4yDSGOHtcQLIhAyDzxhBTDR+a/FggLG4uLyWWTkRRYXl6/26WJMrfKlratGG62N6cAVoYvfOOpeiMvIYGz/fsYmTuTHAiuzDW1/52ry+ZXEkE8rQw7QlJ6oWiw4OBiDBw9GzZo1kZaWhu7duwMArl69iho1aqi0raVLl2LkyJEICwsDAKxduxYHDx7E/7d353FRVf0fwD+XYRMFcQcBJTVzLbdUTOWxVFxzzdRy6XFpsUfLsrTNrdJ61LSyfCzNNqNUNEs00dBcSM2wn+W+K4ILLrgDw/n9cZyBYRbuDLPcgc/79ZoXcOcuZ2YOc+/3nnO+Z/HixZg4caLZ+vPmzUOXLl0wYcIEAMD06dORlJSEjz/+GAsWLAAADBkyBABw4sQJi8fU6XQICwszWbZy5UoMGDAA5cqVM1keGhpqtq4td+7cwZ07d4x/Z2VlAQBycnKQk5Ojej+uYDi+p8tB2rBypYKBA3UQAgDyZ+O8dEmY/G1NlSq5yMkRTitPz55AfLyC8eN1SEvLP35EhMDs2Xr07CngzKpr7fWnpQn07w/Ex+vRp4/619e6NRAR4YuzZ+UlbmGKIhARAbRunWt8HdeuySyZGzYoSEryweHDptuVKyfQvr3AI48IPPxwHho0MJ041dH3Y/NmBWfOWP/qF0LOCJCcnIvYWHXvgbJ5M3xVTLyXm5wMYZhBtqQ5dgy6V1+Fz48/AgBEaCjypkxB3ujRgK+v9Q9Mr4fv2LGAEGb/eTroMRcv4DEsu5tJPn8NRZGfzaxZeuTlCdiTYHn2bFn/zfYJuc+5eAE6WN9h7unTEE4+l6xcafj/9wXQAnPmyP//OXPs+18EgNOnFahJUn36tHO/xxyhtqwnT+Ziw4b8rHpt2wqsXu3c7zHl9GlVqb1d8fkXlzuucapUUfdZFT4/likDxMXJByCz7CYnK/j1Vx+sWaPg/Hn3n3MtH8Ox11eYXg9s3aoY62paGlTt1xP/j564NlZ7LLsDtA8++ADR0dE4ffo03n//fWNQk56ejueee071frKzs7F7925MmjTJuMzHxwcdO3ZESkqKxW1SUlIwfvx4k2VxcXFYtWqVvS/DaPfu3dizZw/mz59v9tyYMWMwcuRI1KpVC8888wyeeuopKDamlp8xYwamTp1qtnz9+vUICgpyuIzOlJSU5OkiWKXXA/v2VcLly4GoUOE2GjTIZFpXF9Drgeee6wwhdDAPxhQAosDvhQlUrnwLWVlJSEx0brkCAoAPP7RcB5x5LFuvX16sCowZkw1f3yS76t+TT4bjvfcehHz/Cu5XQAhg8OBdmD//FlJTqyI1tQoOHqwIvT5/Ih0fnzzUrXsZDzxwAU2aXMC9916Gr6/8LE6elA9n+O23CAAtilxv7do9uHEjTdU+I377TcUegT1r1yLtxg1V+/QWvrduoe6yZai1ejV8cnOR5+ODE1264MDAgcgJCZETUdtQae9etE2z/j73QwKWoz+eCV6CC1kh+dtVuoURI/5GQEC63f8fAQHAK6+E4/PPGyMzs4xxeZXyWfj06lNySggbfj95EplO/KdMSTH875hKSwMef1yHV1/dhZgY9VNUnDxZCUBbFev9jsTETHuK6nRqyzp2rB5ZWQHGvytWvIWcHB+nfo9VOnlSRUmc//k7kyuvcfR6oFKlzsjMDERxz4/BwXLqmO7dgZEj43DlSoCVfcpzw3//expJSRdw//0XUa6ca4IJZ7y+lBTz75WQkDtQdxPCc/+P7rw2vnnzpqr1FCGER24fnT17FhEREdi+fTtiYmKMy1955RVs3rwZO3bsMNvG398fX375JQYNGmRc9sknn2Dq1Kk4d+6cybonTpzAPffcg9TUVDRp0sRqOZ577jls2rQJ+wpNFDR9+nQ8/PDDCAoKwvr16zF58mS8//77GDt2rNV9WWpBi4qKwsWLFxESEmJ1O3fIyclBUlISOnXqBL/iTtbhAvl3T01bTxy5e0q2bd6soFMnNfdmTAMNwx17e+/Kao3a15+UpL4FycBSPa5QQaBBA4GDBxVcvGh60qtdW6Bjxzx07Cjwr38JS9NgOZ0rXr+yeTN8DZMI2ZCblFRyWtDy8qB89RV0b74J5e75J69jR+j/+1+gYUPVu1Hi4+E7dGiR691Z8jW2RAw0aUEp7g2swne628bkIuC+OsDZs1AsXBoIRQEiIpB7+LDTJkXS64E6dXzv3mW33vp8+HCu6kMa9llUi7Y9+3SVosqaf8MMKHzjR01vB7u+x/R6+NZx7+fvLO66xjH0vgAst2g7cn60tk9LN0t9fAQefFCgUyf5ePBBAV+7m1rsL4ua12etZ4r1Opy/b0/9P3ri2jgrKwuVK1fG1atXbcYGDn2shw8fRnJyMs6fP282cfVbb73lyC494tatW1i6dCnefPNNs+cKLmvatClu3LiB//73vzYDtICAAAQEBJgt9/Pz00xQpKWyGCQkAAMHAoXPB2fPKhg40Nd7Jk31EhcuqFuvYkUFly7l/x0Zqdyd+9WJZwMPUPv6L1zwtXvi0T59gMqVgc8/B7Zvl61ely8r2LZNnpSCg4FHHpFdXTp3BmrVUgC494zUoYO6iWE7dPBVf7JUuVNfV8127m6bNwMvvgikpsq/69QB5syBT48e8LHRy8KiqKii1wEQEBmOjrqtgG864BsO+BV/5lg/P6Bjx4JLfGUzdv/+uNv/Mf8pRZGXVvPmwS8wsFjHLWjbNkMXKMuEUHDmDPD7736q5wb387P5MgAomDcPCAz0/LnQVlkla/VJXT2z63usiDfOFZ+/s7n6GmfAANlj2XxudMfPj9b2GRWlYMYMIDRUNsSvXw8cOKBgxw4FO3YAb78NhITIc0rnzvK8cs89nnl9ej3w0kuWv/5Nb/Rq8//RndfGqo9j7+C2hQsXCp1OJ6pVqyYeeOAB0aRJE+OjadOmqvdz584dodPpxMqVK02WDx06VDz66KMWt4mKihIffPCBybK33npL3H///WbrGrI1Fk4SUtBXX30l/Pz8xPmCOU+t+PnnnwUAcfv27SLXNWCSkKIxt4D7qR2wu2GDcwbsa42zByyfPCnE//4nRJ8+QgQHm9ffFi1kNq/ffhNCK/9+LknK4olML+52+LD8oA2vLSREiP/+V85k6yg1aUwrVXLv9AXFnZTKDq6cB9GNL6PYLJW1ShXHEkoUO/GCN71xd7n7GscVc0iq2eepU0J8/rlMJlWhgvnnfe+9cmaPn38W4vp115alILXn1cJ12tPVSstJQuwO0GrUqCFmzpzpcMEKatmypXj++eeNf+v1ehERESFmzJhhcf0BAwaIHj16mCyLiYkRTz/9tNm6agK02NhY0a9fP1Vlffvtt0WFChVUrWvAAK1oWs7uU1LZk9Zeq/WmOIqb1v/OHZmo7+WXhWjQwPIJaMgQIb791nS+G61xyTWYF17YqXL5ssyJ7ecnX5OPjxDPPuu8D9hWcGvtS9HVga9LZjE35+pzgJtehlMULus33zgemBX75qY3vXGiZJ6ripKbK8SOHUJMny5E27bm6fz9/YV4+GE5XctffwmRl+e6sqi90fLNN9qqViUqQAsODhZHjx51uGAFxcfHi4CAALFkyRKxb98+MXr0aBEaGioy7k7qM2TIEDFx4kTj+tu2bRO+vr5i1qxZYv/+/WLy5MlmafYzMzNFamqqWLNmjQAg4uPjRWpqqkhPTzc59uHDh4WiKGLt2rVm5Vq9erX47LPPxN69e8Xhw4fFJ598IoKCgsRbb71l1+tjgFY0V949JevUNnZotd4Ul72NPWlp8q5l377mrWQ+PkK0aSNPkrt2yTnMvIVLrsFyc0VOUpLYNX68yElK8vwZuDhycoT4+GPTeQ/i4oT4+2/nH8tavnRLcy447SrcNeypV56cB1Hr1Aav7o7dtaiknqvsceWKEAkJQjz9tBDR0eb1onp1IZ56Sk6WnZnp3GN76832EhWg/fvf/xaffvqpwwUr7KOPPhI1atQQ/v7+omXLluL33383PhcbGyuGDRtmsv4PP/wg6tatK/z9/UXDhg3NJqr+4osvBGA+yfTkyZNN1ps0aZKIiooSegtXU2vXrhVNmjQR5cqVE2XLlhUPPPCAWLBggcV1bWGAVjRv/acuCdQ0dmi13jiDrdefmytESorsmti0qXl9rFpViGHDhIiPd/6JriTw+nqTlycnLqpXL/9Db9BACAs39JxKCzPHF5Mj83KVht6xjnC092tJaLS2l9d/5zhZXp4QBw4IMW+eEN26CREUZH5jMSZGiKlTZStccW+AuPpGi6sadLUcoNmdxXHGjBmYM2cOunfvjsaNG5sNdrOVRKO0ycrKQvny5YvM1OIOOTk5SExMRLdu3TSVJESvB6Kji05YcPx4ycgtoDV6PbBlS/7cOu0K5R3Qar1xloKvPzgYuH4dWLtWpvW/eDF/PUUBHnwQ6NZNPpo3B3x8rO+3tPPqevPnn8DLLwPJyfLvypWBqVMBw3xm7vTdd8DgwUWvt3QpUCC7sackJMj8EoW/yw15U2wlfEpIsJQkAXcTE7ikuF7B8J4Cpu9rwfe0Vy/b3+OlgVd/57jB7dvA1q3AunXy8c8/ps9XqiSTjHTpIn9WrWr/MdTUVUf+ly19N0RGAvPmFf+7wRP1Rm1sYHeAdo+NFDGKouDYsWP27K5EY4Cmjqv+qan4tFxvnOHQIeCnn4A1a+QFTm5u/nPly8sTVffu8qTlyAmrtPLKenP6NPD668DXX8u/AwKAF14AJk2CW+Y/sGTTJpkhsyjJyVCd4tBFDDfbrM1XruZmm14vJ0hfu3YPunZtYl8m0RKMwWvRrH3nFHUTsrQ6fRr45Rf5WL8eyMoyfb5FC3ne69oVaNlS/b0pZ9fV4tz0UUPLAZrdtwOPHz9erIIRFda3r/wns3SHhCcgcqacHJnW+6ef5OPwYdPn69UDevSQQdlDD8HuNPukgtaumLKygPfeA+bMkbeZAeCJJ4B33gFq1vRcuQD53qiZE6FdO/eXrZAtW6wHZ4As/unTcj1rsaROB8TGCty4kYbY2Ad4IX1X375sJXOEK1tevF1UFDBypHzk5AC//y57j6xbJ2cP+eMP+Xj7baBCBaBTJxmsdekChIVZ368z66peLz8/S199QsivvxdekMcrif8L3j2hEZUYPAGRq1y+LE88P/0kTz5XruQ/5+cHxMbKoKxHD6B2bY8V02U0FQ9p6YopOxtYuBCYNi1/crz27YFZs2R/Vi3Q6eR7Y31CL3kXSwNflOnpzl2PTOl0Hm8k9SrWWl7S0uTy0tIzR833v5+fXN6uHfDuu3Ld9evleXP9enkO/eEH+QCApk1lsNa1K9C6tXnrmrPqqjNu+ngzhwK0M2fOYPXq1Th16hSys7NNnpszZ45TCkalD09A5CzHjgGrV8vHb7/Jk5RB5cpyHFnPnnJyTw/3PlbPgUhLS/GQZq6YhJDHeu014MgRuaxuXeD994FHH80PfLTCS7oYhIc7dz0iR5X2lhcDR7//w8OBYcPkIzcX2LlTBmtr1wK7d8sWttRUGcyFhsrzqJrWNXupvZmTliZ7g2viJqQT2R2gbdy4EY8++ihq1aqFAwcOoFGjRjhx4gSEEGjWrJkrykhEZFNenjyJGIKywgOgGzSQAVnPnvKOn9d9eTtwptVKPARAO1dMv/0GvPIKsGOHLFaVMGx5YgHSm3VHeHlftMvTaN3wgi4GXtQbk0q40t7yAjjv+9/XF2jTRj6mTwfOnZPj1tatkz8vXTJtXWvWLL91rVWr4uVVUnsz58UX8ztBACWnG6vdecgmTZqEl19+GXv37kVgYCBWrFiB06dPIzY2Fo899pgrykhEZOb2bZncY/RooHp1ICYGmDFDBmc6ncyt8MEHspHkn3+AmTPluDK117R6vbwr99138mfBVji3MpxpC19xGM60CQlmmxQVDwEyHnLba7LniskV9u2TAU5srAzOypZFwoB4RPulocPcXhg81BcdOgDR0cLS26kNhi4GgwbJnxoKzoD83piAeSOkxnpjUglX2rvbuvL7v1o1YOhQmTj2/Hlg+3bgzTdlZmNAJsF95x2gbVuZWGvgQOCrr+S69jLc9CmqU0PB4AyweWr0KnYHaPv378fQoUMBAL6+vrh16xbKlSuHadOm4b333nN6AYmIDDIz5Zd9v36yq2KPHsBnn8m7eiEhwIABwLffyi/sX3+VJyFHxpUlJMiMdB06yCzn8uLdA1/4Dp5pPR0PmfHUFdPp08CIEUDjxrJpVacDnnkGCfNOo/8PA3DmrOnqaWcE+veTQZpmAnQvYuiNGRFhujwysvSM+SHPK+3dbd31/a/TyRuj06bJhCIZGcCXXwKPPy4Ti1y+DHz/vewqWa2aHNr71lsyIYma71NbN31s8chNSBewu/GxbNmyxnFn4eHhOHr0KBo2bAgAuFhw4iAiIic4cQL48Udg1Sp5Qin4hRsRIRtGevWSjQr+/sU/nqa6BjrYV8fl8ZC94+HUXglVreqcwQSZmbLJ9KOPgDt35LI+fYAZM6Cvcx/GVbsJAYHC9ygFfKAgD6OHZWNcaIA2xu55GS/ojUklXGnvbuup+2GG1rWhQ+XYtR078ucVLZgZcvr0/HnXunaVP6tUsbxPa0Nwq1QxbzkrqCR0Y7U7QGvdujW2bt2K+vXro1u3bnjppZewd+9eJCQkoHXr1q4oIxGVIkIAe/fKgGzVKvnFXlDjxkDv3vIisFkz5+Z00MpQKSMHz7QuvYPsyMhzNVdMFSsCw4cXL6PJjRty/fffB65elctiY2Wwdvf8tGWjHmcyg6zuQsAHmdcDgOsCQH7lKm3Z34qDCZ/Ik9QmPwVKZnIJLbQg+vrKIQUPPSRT9aenyzFriYkyM2RmpuwmuXSp/EwefFAm7+raVc7B5lPg3pmlmz5pacCTTxZdDm/uxmp3gDZnzhxcv34dADB16lRcv34d33//Pe69915mcCQih+j1si/7ypUyKCs43aKPj+zPbgjKatVyXTk0N7i8wBlUDx9sQTukIxzhSEc7bIEOeWbrAS68g+xo82JRV0xCyDN2YQX3a6tZJicHWLQImDpV9rMBgPvvl4FZly4mUXz6poMAGqh4saaRf2nK/kbk7YpKfgqYT6xeUlrJtdiCGB4u778NHy5b11JS8lvX/vpLJvnauROYMkUOXzBMkt25s/y78E2fTZvUH9drCTvk5uaKzZs3i8uXL9uzWal19epVAUBcvXrV00UR2dnZYtWqVSI7O9vTRSEv4sp6c/u2ED//LMSIEUJUqSKEPJXIR2CgEI8+KsTixUKcP+/0Q1u1dKlpOaw9li51U4Fyc4WIjBQr0FdE4pRJGSJxSqxAXyGiouR6haxYIYSiyEfB7QzLVqxwrCxW3xRFMZbFar1ZscJ8H5GRQlSqZHu/lSpZ3u6HH4T45hshatXKXx4dLcTXXwuh11t8GclvbFD1Gdt6JCfb+d6RajxXkSOs1ZvcXPn/unSp/Jmbm//daOmrxqHvRjew9Dpscfr3vwulpQmxaJEQ/foJERJiXt5WrYSYOlWInTvzv9YNpyNLn2Oh05FNnvi+URsb2BWgCSFEQECAOHbsmMMFK00YoJG3c3a9ycoSIj5eiAEDhChXzvQLNTRUiCeflCeO69edcjghhH0ntuRk7V2gr5iQIhToBaA3PQFBLxToxYoJKda3tRAPRUU5eHIu8ObkwkckI1YsxUCRjFiRCx+TN8dmvSn8gWzYULxoyfCoWlWIefNk5G9D7oZkEYlTd99Txw7ltgC9FOK5ihyhtt7YcZ9JM6zd1yrqe9yp3/9ukp0txObNQkycKMT995t/PlWqyOuEb78VYsmS4gehWg7Q7O7i2KhRIxw7dgz33HOPsxvziKgEunhRJtBbuRJISsrP2QDI9Pi9e8vHv/4F+Pk599j2DpfSWtcQvR4Y913ruwktCnW5gw8UCLwQ3xq9ZljucufUhA13O/MnoA/GYR7OIMr4VCROYx7GoS9WFt3pv3Bfle++c6AwBSiKHHU+bhxQrlyRq+v+1Q7zKj2D/pn/g4I8CJNEIXlQk9zYq7vNEJVimuvGXoTiJK3yxoQ9fn5A+/byMWOG/KzWrZPdIZOSZGKQb76RD0UB6tSRWZyzsvL3YejG6u1dVe0O0N5++228/PLLmD59Opo3b46yZcuaPB8SEuK0whGVNvYmx9OqM2fkWLKEBGDzZjmRtEGdOvKLs29fOTDYp+jrYYc4cmJTO7jcXZ9J/sWE5UwoAkqRFxNOS9gQHo4E9EF/LEfh2DUNEeiP5ViO/uhrb/RS3GhHCDkSXUVwBgDQ6dB3YVcs7/cYxmFuoUDzDG4hCJdQCcLCe17Ss78RlXTeNEeaM5JWeXvCnshIYORI+cjJkWPVExNlwLZ3L3D4cP66wcFycuyhQ0vGd7TqAG3atGl46aWX0K1bNwDAo48+CqXAwGshBBRFgd6bJx0g8iBHkuNpydGj8jWsWCHT6xbUpIl8DX36AA0bOjfzoiXFObEVNbjcnZ+Fli4m9G3aYZyuLoQesJae/gXdR+jVJgxAnqVdWFZUs6Ua9r4Bffui7wqg19i22JJ2T37ilcgT+HFQPPrPqgwFng/Qici5tJDhUC1va+1zNT8/mZQ3NhZ47z3z1rVr14ANG+RDUWQ2yK5dZcKRli2973tbdYA2depUPPPMM0hOTnZleYhKJU3NvaWSEMC+fTIgS0iQmZgMFEVOYNmvnwzK3N0jurgnNq10DXHKxYSTmmW3bNfhjL661ecFfHBaH4Et24GHHrIjQLPVbKmWI1dTfftC16sX/lXovemr02F5a20E6ETkXFrrxm6Llm7QaVHh1jVDZsi1a+X1yK5d8jFtmpw4e948YMgQT5daPdUBmrhbk2NjY11WGKLSSHNzb9kghJyXbMUK+Th4MP85Q1eKfv3kmDJP3oF0xonNFV1D7I2Vin0x4cRmWZdeLFhrtiyKmqspW2+6lQ9ZKwE6ETmX1rqx2+JNrX2eVnjs2tmzct61devkvGuXL3vf+2TX6A/F1f2SiEohe1p7PCEvD/j9dwUvvyznIGveHHj3XRmc+fsDPXoAixfLgbobNgDPPuv5L0ItntgSEuS8Ox06AIMHy5/R0XK5NYaLCcC8W2iRFxOGZtnClcvQLGvrwBa4/D1t1Ej2XSk4KPGxx+QboCgOvAFw7E2/yxC7DRokf2rhgo2Iis9wPygiwnR5ZKS2eqsYbtBZu/RWFCAqShutfVpTvTrw1FPA99/LxCLbtnnf+2RXkpC6desWGaRdunSpWAUiKm202I1Brwe2bgV++MEH33/fGZmZ+V8VQUGyX3e/fkD37oAW8wJprRtLcTNx2T0mzgXNsva8p3l29HDEoUPA228D336bv2GvXrJfyv33y78jI+3vc+iN/YaJyC28oZXcm1r7tMzXF2jTxtOlsJ9dAdrUqVNRvnx5V5WFqFTSSmtPTo7MuLh8uUyJf/48AOgAlEFwsEDPngr69ZMDboOCXFuW4tLSic0ZsZLdFxMuGF1uz3uqKkCzEJjpe/bGlh7vIT24LsIvAe30d1+jvW+AN/UbJiKP8IYMh1pKWkXuZVeANnDgQFStWtVVZSEqldS2TLRpA2za5Ny7fdnZwMaN8gSwahVQsAG8QgWgZ888REXtxMSJzVGunJMnKXMxrZzYnBUr2XUx4aJmWae8p4cOAe+8IyeyMURyPXsiod0HGPdhbZz5yXS/xuFy9rwBTH9GRCWEN7T2kfOpDtA4/ozINdS0TAwcCNSu7ZwU/Ldvy5S0y5cDP/4IXL2a/1zlyjLrYv/+crgOoEdi4jkEBDj66jxLCyc2j3RhdWGzrMPv6T//yMDs++/zA7MePYApU5BwsrlzeyNqsd8wEZGDvKG1j5zL7iyOROR8tlomBg4EZs0q3sXrrVsym9Hy5cBPP8n5QgzCwuT2/fvLC23fAt8KOTnFf22e5ukTm0e6sLp4EJ5d7+lff8mujCtW5JelRw/grbeABx+UvRF7O7k3olb6DRMRETlAdYCWZ9eobyKyl6WWiTZtZMuZIxevN24AiYkyKFuzRv5tEBEhA7L+/eV8Zewq4ToeSViigUF4oUeOQNe3L/Dzz/kL+/YF3ngDaNrUuMglvRG1liWGiIjIDnaNQSMi1yrcMrFpk30Xr9evy2Bs2TIZnN26lb9ujRryev2xx4CWLU2zmZPreCxW8tQgvC1boHvnHcT+8ov8W1GAAQOA118HGjc2W90lvRE1EKASERE5igEakYapvShdvhz48ENg7Vo5xszgnntkQNa/P9CihfX5VCzS66Fs3oyI336DUrasHJSm0QtaeyeAdjePJSxx1yA8IeSsoO+8A2zdCh8AwscHYtAg+LzxBlCvntVNXdYbUStZYoiIiOzEAI1Iw9RelM6fn/97nTr5QVnTpnYGZQYJCcC4cfA9cwYtAGDOHMezkrjY3aI6JYGKK3ksYYkrB+Hl5ckP4N13gdRUuczfH/phw/Brs2b414gR8PGznf3Tpb0RtZAlhoiIiqT1G63uxgCNSMOKung1uO++/KDs/vsdDMoMvGiCXy8qKgDPJyxxmuxsYOlS4L33gAMH5LKgIOCZZ4Dx45FXtSpuJiaq2pXLeyOWmDediKhk8pYbre7EUShEDtDr5fiw776TP/V61xzn6lXZAGArOPvgA2D/fmD6dOCBB4oZnBU1wS8gs5K46gXbwYuKWnJcuyZbU2vXBp56SgZnoaEyI+OpU8Ds2TIDjZ0MvRELbxoZqb0gm4iInMdwo7XweHvDjdaEBM+Uy9PYgkZkp+Lc6VHThJ+ZKSeNXrZMTiKdm2t5X1FRLhhK40UT/HpRUb3f+fNykOP8+cCVK3JZeDjw4ovA008DISHFPgR7IxIRlS5F3Wh1aJqVEoIBGpEditOlzlZg165dflD266+mrT6NG8vui336ABcvuvji1Ysm+PWionqvY8dkq9jixfnZZ+rWBSZMAIYMgbNnMGdvRCIi7XPWeDHeaLWOARqRSsW502MtsDtzBujXT6a8LzjVYJMm+fOU3Xefs1+JDV40wa8XFdX77NghZ0dPSMivmC1bAq++WjpvZRIRaZS7k2s4c7wYb7RaxwCNSCVH7/TYCuwM8vKAZs3yg7J773Vase3jRRP8elFR82k5TVVeHvDTTzIw27o1f3mXLjIwi40t5gBHIiJyJncn13B2Yi7eaLWOARqVCK647i28z7Q0ddsVvtOzapXtwM5g9mwNNOGrTKmnhw5bNnk2zvDkXMQO1Tetpqm6dQv46iuZ/OPQIbnMzw944gngpZeARo08VzYiIrLI3VmMXTFezCtvtLqJx7M4zp8/H9HR0QgMDESrVq2wc+dOm+svW7YM9erVQ2BgIBo3bozEQqmcExIS0LlzZ1SqVAmKomDPnj1m+/jXv/4FRVFMHs8884zJOqdOnUL37t0RFBSEqlWrYsKECci1lq2BPCohAYiOlvMoDx4sf0ZHFy/zj6V9vvCCum0NwdyHHwLt28vxY2popgm/iJR6Cejr9PfbRUV12R1Eu1+/FtNUpacDb74J1Kgh0+MfOiQzMk6cCJw4AXzxBYMzR7grxSsRlVqeyGJsTy8itQw3WgHzDhquvtGqecKD4uPjhb+/v1i8eLH4559/xKhRo0RoaKg4d+6cxfW3bdsmdDqdeP/998W+ffvEG2+8Ifz8/MTevXuN63z11Vdi6tSp4rPPPhMARGpqqtl+YmNjxahRo0R6errxcfXqVePzubm5olGjRqJjx44iNTVVJCYmisqVK4tJkybZ9fquXr0qAJjs21Oys7PFqlWrRHZ2tqeL4lQrVgihKELIr4b8h6LIx4oVztunmkdoqBAxMY5tm5zs9LeneHJzRU5Sktg1frzISUoSIjfXJe+3k4oqkpOFWLpU/szNVfukfRx6/bm5QkRGWv/gFUWIqKhilcsuqalCDB0qhJ9ffhlq1hRi7lwhsrKccoiS+n1TpBUrzD/ryEjP/WN4oVJbd6hYSlu9SU52/3XF0qXqjrl0qf37tvTVGRXl+q9OT9QbtbGBRwO0li1bijFjxhj/1uv1onr16mLGjBkW1x8wYIDo3r27ybJWrVqJp59+2mzd48eP2wzQxo0bZ7VciYmJwsfHR2RkZBiXffrppyIkJETcuXOniFeVjwGaa7niureofRbcd1HrPPSQvOY9flzu09o27r4+t0fBeqO1OEMVJ14wO/z6PXEmtVT4VauEiI01PWabNkIsWyZETo5TD1cSv2+KpNW7F16mVNYdKrbSVm9cGSxZ4+pTmRPvpaqm5QDNY2PQsrOzsXv3bkyaNMm4zMfHBx07dkRKSorFbVJSUjB+/HiTZXFxcVi1apXdx//222/xzTffICwsDD179sSbb76JoKAg43EaN26MatWqmRzn2WefxT///IOmTZta3OedO3dw584d499ZWVkAgJycHOTk5NhdRmcyHN/T5XCmzZsVnDljvQoLIZvbk5NzERsrnLJPgzJlBG7eNG2PVxSBtm0F+vUT6NUrz6Tb3ezZCgYO1N0dK6WYbAMAs2bpkZcnTDI5akHBerN9u/Pfb1dSVq6EbuBAQAgU/KTE3W6F+vh4iD59VO/P0fqmnD6tarBv7unTEM7+/7x6FT5ffgmfTz+FcvSoLKdOB9G/P/LGjoV48MH8wjvx2CXx+8YmvR6+Y8ea1TUAgBAQigKMG4fcbt1KaV8d9Upd3SGnKG31pkoVBWrSSFSpkoucHOecj1u3BiIifHH2rOl1jIGiCEREAK1b5zp8Onnoofzf8/Lg8msiT9QbtcfyWIB28eJF6PV6kyAIAKpVq4YDBw5Y3CYjI8Pi+hkZGXYde/DgwahZsyaqV6+O//u//8Orr76KgwcPIuHuOBBrxzE8Z82MGTMwdepUs+Xr1683Bn+elpSU5NHj6/XAvn2VcPlyICpUuI0GDTJVX68U3jYzMxBAiyK3W7t2D27cUJfh47ffIlTt0xCcKYrAPfdcxSOPnESbNumoUEEG6H/9JR8GAQHAK6+E4/PPGyMzs4xxeaVKtzBixN8ICEhHoeGUmpKUlKT6vbHn/XYZvR6dn3sOOgsXzIoQEACyx4xBkq+v6gtmR19/pZMn0VbF/n8/eRKZTqoE5U6fRq3EREQlJ0N3d/6y7HLlcLJzZxzr1g23K1cGLlyAqyudp79v3KXS3r1oayOLkCIEcOYMdsyahczGjd1YMu9VWuoOOVdpqTd6PVCpUue710GWsusKVK58C1lZSU79mn/yyXC8996DAESh4woIATzxxC788otWBtSr5856c/PmTVXrlcosjqNHjzb+3rhxY4SHh+ORRx7B0aNHUbt2bYf3O2nSJJMWvqysLERFRaFz584ICQkpVpmLKycnB0lJSejUqRP8/Pw8UoaVKxWMH69DWlr+P3VEhMCcOXr06WP7Do+lbStXVndXqHPnJtDpmhgz7rVtK6xek5ctq2DOnKL32axZHkaOzMOjjwpUrVoWQIO7D+u6dQOmTAG2bs0tUBY/6HRNAVhulfW0gvWmbFl/Ve9N165NEBv7gOsLZ4OyeTN8MzOtPw8g6OJFdA8JgYiNVbVPtXXD7PXHxUEsWACcPSsv1AsRigJERKDVyy8Xr3UlLw/K2rXw+eQT+BQ42YgGDZA3ZgyUwYMRXbYsoh0/gmpu/77R66Fs3WpMqynatnVrS5Vyt7dEUVrXrAnRrZuLS+PdtHCuIu9TGuvNJ58oGDgQkMGRec+c+fP90bOnc79vunUDmjXT370ey18eGQnMnq1Hnz7aup7R64GtWxWr13+eqDdZKs8XHgvQKleuDJ1Oh3PnzpksP3fuHMLCwixuExYWZtf6arVq1QoAcOTIEdSuXRthYWFm2SQNx7V1rICAAAQEBJgt9/Pz08wXhqfKkpAA3O1tZuLsWQUDB/razLhnbduLF23PyaQoQMWKwMiRvqoymwshk9gFBwPXrlnfb/XqwM6dPtDp7E+C6ucHdOxo92Ye5+fnhw4dfFWlw+3QwdfzvbguXFC1mu+FC/JDUaFDB3XpgM1ev5+fTOlpZT4ABQDmzYNfYKCqcpjJzASWLAE+/RS4240RigI8+igwdiyUDh2gUxR44iNxy/eNFqYviIpStZpvVJTq+lbaaem8Sd6jNNWbAQMAX19LX38K5s4F+vZ1zSX+gAFAv36Fp5pRoNNpq83HnlODO+uN2uN4LM2+v78/mjdvjo0bNxqX5eXlYePGjYiJibG4TUxMjMn6gGyWtLa+WoZU/OF3Z8KLiYnB3r17cf78eZPjhISEoEED260kZK446WDVTPIMWE7PKoS8drWV2VwIYMcO4JVXgNq1gQcftB6cKYp8fPRR6RxG4lXpcF0w+2WxXr8r5gPYtQt46im5j5dflsFZaGj+76tWAQ8/XLInl9bK9AWGyXysvdeKIoO40jiZDxG5TN++claU5GRg6VL58/hx19+b0unkvK2DBsmfmjjvF6CVU0OxuClpiUXx8fEiICBALFmyROzbt0+MHj1ahIaGGrMnDhkyREycONG4/rZt24Svr6+YNWuW2L9/v5g8ebJZmv3MzEyRmpoq1qxZIwCI+Ph4kZqaKtLT04UQQhw5ckRMmzZN/PHHH+L48ePixx9/FLVq1RLt27c37sOQZr9z585iz549Yt26daJKlSpMs++g4mT+UbttlSrmifoqVbK9Tbly5ln5ypQRol8/IV54QYjq1U2fc0fKV62xVG+Kkw7XbVmaDCkXXZA6s1jpgIv7Bty8KcQXXwjx4IOmBWjSRIjPPhPi+nW7X48ruOX7RmtpRQ1ZHAvXOWZxtEtpy8ZHzsF6Qwb2nBq0nMXRowGaEEJ89NFHokaNGsLf31+0bNlS/P7778bnYmNjxbBhw0zW/+GHH0TdunWFv7+/aNiwoVizZo3J81988YWAHL1o8pg8ebIQQohTp06J9u3bi4oVK4qAgABRp04dMWHCBLM36sSJE6Jr166iTJkyonLlyuKll14SOXamomaAJhUnHazabb/5xvS6d8MGddsZArXHH5fZxgte33oi5avWWKs3jrw3bp8iyoUXzG6vG/v3C/Hii0JUrJj/Ovz9hXjySSFSUoTIy3NxAezjlu8bLUxfUJinJvMpQXihTY5gvSEDe04NWg7QPN5h9Pnnn8fzzz9v8blNmzaZLXvsscfw2GOPWd3f8OHDMXz4cKvPR0VFYfPmzUWWq2bNmkjUclo9L1Kc3mZqt42IkM3sBt99p267l14C3n4bsDT8x9CET+bsfW8M3Q0Kd1U1dDdwtJefTYZuhZY6ocsO+g7v2i11484d+cb9739Awe+smjWBZ58F/v1voEoVFxdCw9JVZgpTu54z9O0L9OpVeHCG9vr/EBGVUFo8NTjC4wEalXyG4RlFJVewNDzD3m2vXwfWrgU++0xd2Xr0sByckfMUNQZRUeQYxF69XHAd640XzIcPAwsXysQfFy/KZT4+srI+/TQQF6ft8ruLC8YZOgXv7BAReYxWTw32YoBGLmdIrmAliR0A68kV1Gw7fTrwzTfAypXAL78Ad6d9sslWUEjOtWWL+UDdgoSQEzxv2eKi61pvuGC+dUu2ln3+OVCw50BEBDByJDBihOpMgaVGce78EBFRiWTPqcHVE2EXBwM0covi9Daztm358kCNGvLatWAGyNq1ZQrYihWBiRPtDwrJuZzW3UCvd29LmDuOt2ePDMq+/Ra4ckUuUxSga1fZWtatm8yjTOaKc+eHiIhKJHtODQzQiFC83mZ9+wINGwIffAD8+qvsBXblSv417f33A336yPUaN87/J7z3XpcMQdIcd8cu9nBKdwN3z3XlyuNduQLEx8vAbPfu/OU1a8pxZcOHyzsPVDQXjjMkIiLvVBJODQzQyK3s6W0mBJCaKqdzWrkS+Ptv0+djYmRQ1qcPUKeO5X144xAke2lhnl5bit0Tzd0ZRlxxPL0e2LhRjitbuTK/H66fn6zAI0cCjzwix5qRfUrDPzkREdnF208NDNBIU3Jzga1bZVC2ahVw8mT+c76+Mrjr0wfo3RuoXl3dPr1hCJKjPJId0U7F6onm7gwjzj7e4cMyKPvqK9MIumFD2Td3yBCgcuXil7u0K8n/5ERE5BBvPjUwQCOPu3kTWL8e+PFH4KefgMzM/OeCgoAuXWRQ1r07UKGC58qpNR7Njmgnh7sbuDvDiDOOd+UKsGyZDMq2bs1fXqECMHiw7MLYvHl+dKpVWu43S0REVIIxQCOPuHgR+Pln2Uq2fr1MYmdQsSLQs6cMyjp1kkEamfN4dkQ7OdTdwN0Tmjh6vOxsYN064Ouv5V2GO3fkch8fmRb/qadkpfaWOR203m+WiIioBGOARm5z9KhsJfvxR9mwUDB7Ts2aMiDr1Qto25aJ69TwxskY7e5u4O4JTdTup2pVIDlZVuQ//5RRZ8Gm34YNZffFIUPU98XVCm/oN0tERFSC8TKYXCYvD9i1Kz8o27fP9PkmTeRYst69ZRZGrff40pqSMhmjTe6e60rN8cqXl3cTrl0zfS40VLaUDRkiK7c3Vmhv6jdLRERUQjFAI6e6dUt2Wfz8c9m4YEiDD8jrudhYeW336KNAdLSnSlkylIp5et0915Wt4wHy74KVuqArV2Tzb9OmzimLJ3hbv1kiIqISiDmdqdjOnQMWLZKBV2iobBH7+ef869gyZeRN+QsXZKbxsWMZnDmDIZYAzBtrPDpPr14PbNoEfPed/FlwFnFHGDKMRESYLo+MdE13O8PxwsLs287QulTc1+sIZ73n3thvloiIqIRhCxrZTQhg716ZC+Gnn4CdOy234Bjcvg18+CHQvj2Hrjib5iZjdFVyCXdNaHLpkpyn7IcfgPPnTZ9r1Mh8Mr6CnNG65EjmRGe+56Wi3ywREZG2MUAjVW7fljkRfv5ZPk6dMn2+RQvg0CEgK8t8W9VDV5jW2yGamYzR1cklXDGhiV4PrF0rK/WePcDu3XIyPoNmzYABA4CBA4Ht22Wa/KI42rrkSKDl7Pe8VPSbJSIi0jYGaGTV2bNAYqK8dk1KkvOVGQQGAh07Aj16yOzhhw4BHTpY31eRjQtM610sHp+M0duSS1y8CLz1FrB4cX5KfIPoaGDUKBmY1amTv/z4cXX7dqR1yZFAyxXvubvH/BEREZEZjkEjo7w8YMcOed3arJkc8jNqlMzAePOm/Pvpp2XAlpkpuzc+/bTMIl6soSuGi9PCyQkMF6cJCcV+beRi9iSX8JT0dOCTT4BHHgGqVQM+/dQ8OAOAkyeBevVMgzMgv3XJWnZGRQGiouxvXSoq0AIsj21z1Xvu7jF/REREZIItaKXc5cuydWzNGtnT68KF/OcUBXjwQaB7d9lKZitzuMNDV7yt5YUs02pyiSNH5Gzoq1bJLoq2BksWZKnOuap1ydHMia58zzXTb5aIiKj0YYBWygghh9qsXSu7L6akmN6YDwkB4uJkUNa1q5yPVw2Hh64wrbdzeHr8nlaSSwgB/PGHbPZdtQr45x/T51u3lncaFiywvQ9rdc4VWVkcDbRc/Z57vN8sERFR6cQArRTIygLWrlXw+edN8Nxzvjh71vT5+vWBbt1kUNa2LeDnZ/8xHG5c0GrLizfRwvg9TyaXMGSw+eknYPVqWQYDX18ZZPTuLVuEIiNlKnpbAZqBtTrn7NYlRwMtJvQgIiIqkRiglQLLlgEjR/oCqAkACAqSw3C6dpUPZ81J5lDjglZaXryVqzMnquXu5BLp6bIJ+KefzDPYlCsnK3bv3vLOQ2io6bbOqHPObF1yNNBiQg8iIqISiQFaKdC1K3DvvQL16h3DM8/UxMMP+yIwsOjtHOk1Z3fjAlsBHKe18XuunJQtL0+mwF+7VgZlf/xh+nxERH5K0Ucegc0KrrU6V5xAS3MT4REREVFxMUArBapXB/75JxeJiX+jU6caqrowFqfXnF2NC2wFcJwnx+9Zi96L2/2v4H6DgoDr14FffgHWrTPNYAMALVvKoKxHD9sZbArTYp0rTqDFhB5EREQlCgM0MqOq11wvJyalYCuAYzw1fq+o6N3R7n/LlgFjxpgHYgbBwXLyve7d5SMszKHiA9BmnStOoMWEHkRERCUGAzQyoarX3Oib6DW2PnRpp/KfLG5SCrYC2M8T4/ecPebtxAk5huyLL2RKUWumTgUmTgT8/R0qtkVarHMMtIiIiEo9BmhkQlWvucwgbME9+BcKBGjOSErBi1P7uHsslTPGvF2+DGzeDGzYAKxfDxw+XPRxFQX4/HPg9deLVXyLSnud8/T0DERERGSGAVopV/j6rGCGclvSUahVhpNKu5+7x1I5Mubt5k1g61Zg40bg11+BP/+UCT8Kvob69YG//7Zvv1R8WpiegYiIiMwwQCvFLF2fVa6sbttwWBjXxAtp93PnWCq1Y9k2bAA2bZJzk6WkADk5ps/fdx/w8MNA585Ahw4yXf7gwc47PhVNK9MzEBERkRkGaKWUteuzixdtb6cgD5E4g3bYYn0lXki7l7vGUqkdy/bOO6Z/R0XJ1PcPPywfERGO7Zdz4TmH1qZnICIiIhMM0EohW9dnBZn1moP8Yy5eAABsQizSEY5wpKMdtkCHu13XeCHtfu4YS9WunfxsiwrAw8NlWWJjZWBWu7btFPham5espPPk9AxERERUJAZopVBR12cGlSubZjyPjATm3noayFQQjRM4g6j853Aa8/AC+kbt4oV0SSEEcPQoIpOT4fPzz8C2bUUHZx99JFPlq52TDNDmvGQlmaemZyAiIiJVGKCVQmqvuz74QPZGy+81p+DHSSPQ/78tUbidIw0R6I9lWD5wJ/q66kKaGedc68YN4I8/5LixlBTg99/hd/48mhdeLzJSZmO8cSN/WVRU8ca8aXFespKKXUqJiIg0jQFaKaT2uisiwrSHk14PjPuuNQQEANMWEgEfKBB4Ib41es1wQdxUnIxzrgjsvD1Y1OuBAweAXbvkIyUF+L//k8sLEH5+uFyrFsp37w5d+/ZAmzZAlSquef3FGUvn7Z+HO7FLKRERkaYxQCuFHL0+y+8aabn7moDimqErxck454pU4t6WnlwI4NQpGYjt3Cl//vEHcP26+boREUBMjPGR26gRtvz6K7p16wadn1/+eq4a8+bIfr3t8/A0diklIiLSNAZopZCj12ceGbpSnIxzrkglrvX05EIAx47J+cZ275Y///wTyMw0XzcoCGjRAnjwQaBlSxmURUWZrlM4Rb7WaP3z0Cp2KSUiItIsBmillCPXZx4ZuuJoxjlXpBLXWnry7Gxg3z7gr7+APXvkzz//BK5eNV/X1xdo3FgGYi1byqCsfn253Ftp7fPwNu6anoGIiIjs4uPpAsyfPx/R0dEIDAxEq1atsHPnTpvrL1u2DPXq1UNgYCAaN26MxMREk+cTEhLQuXNnVKpUCYqiYM+ePSbPX7p0Cf/5z39w3333oUyZMqhRowbGjh2Lq4UuahVFMXvEx8c75TVrRd++wIkTcj7hpUvlz+PHrd88N3SNtJagT1FkA4xTh6442mxnT2Cnliv2qYYQwNmzwPr1wOzZwNChwAMPAGXLAk2bAsOHy6g6OVkGZ/7+smVs9Gjgf/+TXRqvX5fB24IFwL//LYM1bw7OAM99HiWJoUvpoEHyJ4MzIiIij/PoFdr333+P8ePHY8GCBWjVqhXmzp2LuLg4HDx4EFWrVjVbf/v27Rg0aBBmzJiBHj16YOnSpejduzf+/PNPNGrUCABw48YNtG3bFgMGDMCoUaPM9nH27FmcPXsWs2bNQoMGDXDy5Ek888wzOHv2LJYvX26y7hdffIEuXboY/w4NDXXuG6AB9gz58cjQFUeb7VzRH9MdfTwvXAD27wf+/tv0cfmy5fVDQ2WwZng0awY0aCCDtJKO6eKJiIioBPJogDZnzhyMGjUKTz31FABgwYIFWLNmDRYvXoyJEyearT9v3jx06dIFEyZMAABMnz4dSUlJ+Pjjj7FgwQIAwJAhQwAAJ06csHjMRo0aYcWKFca/a9eujXfeeQdPPvkkcnNz4VugVSE0NBRhYWFOea0lhduHrjia0URlYKevGo4tm1T28HJWH8+8PPnm7d+f/9i3T/60NFYMAHx8gLp1gYYN84OxJk1kk6U9c46VJEwXT0RERCWQxwK07Oxs7N69G5MmTTIu8/HxQceOHZGSkmJxm5SUFIwfP95kWVxcHFatWlWssly9ehUhISEmwRkAjBkzBiNHjkStWrXwzDPP4KmnnoJi42L4zp07uHPnjvHvrKwsAEBOTg5yPJxswXB8Z5SjZ0+gWzdg61bFGNi0bSug07kmp4QyezZ0AwcCigKlQJAm7n4W+lmzIPLyZOBj0Lo1fCMigLNnTbYpuG1CxREYNywWaWn5yyMiBObM0aNPHwvBoIp9IiICua1byzciMxPK4cPAoUNQDh82PnDkCJRbt6y+XlGzJkTDhhANGsifDRsC9eoBgYHmK+fmWt2PMziz3jidvZ8HuY2m6w1pGusOOYL1hhzhiXqj9lgeC9AuXrwIvV6PatWqmSyvVq0aDhw4YHGbjIwMi+tnZGQUqxzTp0/H6NGjTZZPmzYNDz/8MIKCgrB+/Xo899xzuH79OsaOHWt1XzNmzMDUqVPNlq9fvx5BQUEOl9GZkpKSnLq/kBA5X/Evvzh1t6YCAhD+yito/PnnKFOghelWpUr4e8QIpAcEAIXGIgJA+JNP4sH33jObtU0ASBC90T9zodk2aWnA44/r8OqruxATY941ztY+IQQulSsHXaNGCMrIgH/BiZwLydPpcCM8HNciI3EtKgrXIyNxLTIS1yMioC8ciJ09Kx8e5Ox64yxFfR67nngC6S6tnGSLVusNaR/rDjmC9YYc4c56c/PmTVXreXmWgOLJyspC9+7d0aBBA0yZMsXkuTfffNP4e9OmTXHjxg3897//tRmgTZo0yaSFLysrC1FRUejcuTNCQkKcXn575OTkICkpCZ06dYJfwfmsvEW3bsCUKcjdutXYH9GvbVs01enQ1MY2+mbNoBs/HgWbyfQRNfDCrW+AS4D5nG4KFEXg228fxJQ3bkN3Ph3K6dPAiRNQTpyAcv48RKNGUPbvN5nU2bCXSoVuLoioKIh774W4917g7k9x771AdDQCfX0RCKBK8d4Zl9J8vbHyGSMyEvrZs9G0Tx/r9YNcRvP1hjSLdYccwXpDjvBEvTH0riuKxwK0ypUrQ6fT4dy5cybLz507Z3XcV1hYmF3r23Lt2jV06dIFwcHBWLlyZZEfTKtWrTB9+nTcuXMHAQEBFtcJCAiw+Jyfn59mvjC0VBa7+fkBHTvat82AAUC/fiapxLfq2+FMR+uZTIRQcOYM8HtId/xLJNvev04HhIXJsWF16gC1a+c/atWCEhRkZVpv76LpemPhM1batYMvMxJ6nKbrDWka6w45gvWGHOHOeqP2OB4L0Pz9/dG8eXNs3LgRvXv3BgDk5eVh48aNeP755y1uExMTg40bN+KFF14wLktKSkJMTIxdx87KykJcXBwCAgKwevVqBFoa21PInj17UKFCBavBGWmAEDLb4blz+Y+MjPzf09OBs2eRfqwVgP8Vubt0UU0GhZGRQHS05Uf16s5NV6/Xc14qR9iTjpSIiIhIwzzaxXH8+PEYNmwYWrRogZYtW2Lu3Lm4ceOGMavj0KFDERERgRkzZgAAxo0bh9jYWMyePRvdu3dHfHw8/vjjDyxcmD+W6NKlSzh16hTO3h2zc/DgQQCy9S0sLAxZWVno3Lkzbt68iW+++QZZWVnG5sYqVapAp9Php59+wrlz59C6dWsEBgYiKSkJ7777Ll5++WV3vj2lW26uDLYuXwYuXZIPw+8XL8rHhQv5vxseKgZfhiNUVRHCl38M9PlWZlB0h4QEy+kx580rXnpMLQV9WioLERERkQZ5NEB7/PHHceHCBbz11lvIyMhAkyZNsG7dOmMikFOnTsGnwMVxmzZtsHTpUrzxxht47bXXcO+992LVqlXGOdAAYPXq1cYADwAGDhwIAJg8eTKmTJmCP//8Ezt27AAA1KlTx6Q8x48fR3R0NPz8/DB//ny8+OKLEEKgTp06xikBShV7LqZzcoBbt4CbN+XPW7dk9pDr1y0/rl2TkypfvQpkZeX/bnhcu+Z4uUNDgWrV8h9hYfJneDhQvTraVauOyB56pKX7QAjzDojGzP29K7lvKveEBDnBXOFshGlpcvny5Y4Faa4K+hyhpbIQERERaZQihKXJpcgZsrKyUL58eWMaf4/55x/oP/kEp44fR40aNaADZEr6vDwZEOTlyWAsJ0e2XOXmAqdPywmSC0wbAD8/Gej4+wPZ2fK527dlMOaqdO/lywMVKgAVK8qfFSoAVaoAlSvLR8HfK1cGqlYFVHRDNcRDgOUJtx2Nhxyi18vukgUDl4IMEePx4/a1NlkL+ux4kTk5OUhMTES3bt2K1z/bCWUh7+G0ekOlDusOOYL1hhzhiXqjNjYo1VkcS42TJ6H75BPcU9z95ORYDyIKCgoCypSRP8uVy38EB5v+Xb68zNNfvrz5o0IF2RLmzPFdBbh9wm1btmyx/b4KIQPmLVvUj7PS6+WLs3T/RQgZGL3wAtCrl+u7GGqpLEREREQaxwCtNKhTB/rXXsPho0dxb9260Pn6ynFVPj7y4lhRZCBkWD55MnDlivX9Va0K/PSTDMACAkwDsoCA/FYRjevbV8YEHh8SlW4+31qx1gNcE/Q5SktlISIiItI4BmilQd26yJsyBQcTE1G7WzfobDXjbtpkOzgDgPPn5Vizli2dWUqPsJn8z10JLcLDnbse4Jqgz1FaKgsRERGRxjFAKwX0emDzZgW//RaBsmUVdOhgI87gxbTkzoQW7drJfaelWe4GaBiD1qaNDKDVBIyuCPocpaWyEBEREWmcu3LUkYckJMj8E506+WLOnBbo1MkX0dFyuUWl7WJar5dBz3ffyZ96fX5Ci8Ld8gwZFa2+eQ7S6WTgB5h3DzX8PXCgnPy6Qwdg8GD509YHaQj6rHU3VRQgKkqu52paKgsRERGRxjFAK8Hy4wzTVpm0NGE9zihNF9OG6LVg0FOzJjB6tPWEFoBMaKHXO7cshqwlERGmyyMjgZdfBmbNsi9gVBP0zZ3rngF3WioLERERkcYxQCuh8hPnCQCmF8VCKIAQluOM0nIxbauVLDPT+nYFE1o4W9++wIkTQHIysHSp/HnkiGzdcyRgtBX0GdLaW2pBdAU1ZSEiIiIijkErqfIT51luCRNQrCfO01QOehewlfZdLVeNwSuctWTTpuJlQLSVqtLdE0drJm0mERERkXYxQCuh0tPyoKaB1Op6Jfliuqi072q4awyeM5K2WEpVaW3iaEO3SVe1atlMm0lEREREDNBKqPAL/wegSfHW86aLaXtS4hen9cuQUdFdY/BckbTFnomjiYiIiMitOAathGpX5QAicRoK8iw+ryAPUTiFdlUOuLdgrhjzZCnZh60Mh462fnliDJ4rkrbYM3E0EREREbkVA7QSShcRhnkYBwBmQZrh77l4AbqIMPcVyt5ASu0+7U2JryboqVRJrlOQJxJauCJpC+e6IyIiItIsBmglVbt26Bu5C8vxGCKQZvJUJM5gOR5D36g/XNNVz11zixXVVQ+wnOFQTdCzcKF5RsXjxz2TIMXZGRBL21x3RERERF6EY9BKqrtBSN/+/dFL/IgtaIt0hCMc6WiHrdApecDc5c7vqmcpM2BEBHD7troxT/aUx56ueoXH0qnNVKmVMXjOTNpiaEFMS7P8mRQcZ5dnuYssEREREbkGA7SS7G4Qohs3Dv86szl/eVSUa9Ll28oMaEtRqeKtKW5XPW/LVOmspC2GFsT+/WUwVvDzKtxtkgEaERERkVsxQCvp7gYhucnJ2LN2LZp07QrfDh2cH4R4Ym4xZ3TV86ZMlc5U0ue6IyIiIvJSDNBKA50OIjYWaTdu4IHYWNPgzJ709LZ4Ym4xe7rqkTlva0EkIiIiKgUYoJVmlsaLRUbK7m/2tqB4Ym4xe7rqkWWltQWRiIiISKOYxbG0cnZWRU/NLebsDIdERERERB7EAK00cjQ9vS2enFusb1/tpMQnIiIiIioGdnEsjYqTnt4aNd0NFy503ZgndtUjIiIiohKAAVppVNz09NZ429xiREREREQawwCtNHJGenprmBnQNmdlzSQiIiKiEokBWmnk6vT07G5omTOzZhIRERFRicQkIaWRYbwYYJ7Ug+npXcPZWTOJiIiIqERigFZaMT29+7giayYRERERlUjs4liacbyYe7giayYRERERlUgM0Eo7jhdzvsKJQNLS1G1nb9ZMIiIiIipxGKAROZOlRCCVK6vb1pGsmURERERUojBAI3IWQyKQwmPNLl60vV1xs2YSERERUYnBJCFEzmArEUhBzJpJRERERDYwQCNyhqISgRgU7u7IrJlEREREVAC7OBI5g9oEHx98IKc2YNZMIiIiIrKAARqRM6hN8BERwayZRERERGQVuzgSOUO7drK7YuExZgaKAkRFMREIEREREdnk8QBt/vz5iI6ORmBgIFq1aoWdO3faXH/ZsmWoV68eAgMD0bhxYyQmJpo8n5CQgM6dO6NSpUpQFAV79uwx28ft27cxZswYVKpUCeXKlUO/fv1w7tw5k3VOnTqF7t27IygoCFWrVsWECROQm5tb7NdLJZROB8ybJ39nIhAiIiIicpBHA7Tvv/8e48ePx+TJk/Hnn3/igQceQFxcHM6fP29x/e3bt2PQoEEYMWIEUlNT0bt3b/Tu3Rt///23cZ0bN26gbdu2eO+996we98UXX8RPP/2EZcuWYfPmzTh79iz6FkjSoNfr0b17d2RnZ2P79u348ssvsWTJErz11lvOe/FU8vTtKxN+RESYLmciECIiIiJSyaNj0ObMmYNRo0bhqaeeAgAsWLAAa9asweLFizFx4kSz9efNm4cuXbpgwoQJAIDp06cjKSkJH3/8MRYsWAAAGDJkCADgxIkTFo959epVLFq0CEuXLsXDDz8MAPjiiy9Qv359/P7772jdujXWr1+Pffv2YcOGDahWrRqaNGmC6dOn49VXX8WUKVPg7+9vcd937tzBnTt3jH9nZWUBAHJycpCTk+PAO+Q8huN7uhwlXs+eQLduULZuNSYCEW3bypYzL3zvWW/IEaw35CjWHXIE6w05whP1Ru2xPBagZWdnY/fu3Zg0aZJxmY+PDzp27IiUlBSL26SkpGD8+PEmy+Li4rBq1SrVx929ezdycnLQsWNH47J69eqhRo0aSElJQevWrZGSkoLGjRujWrVqJsd59tln8c8//6Bp06YW9z1jxgxMnTrVbPn69esRFBSkuoyulJSU5OkilB4hIcCNG8Avv3i6JMXGekOOYL0hR7HukCNYb8gR7qw3N2/eVLWexwK0ixcvQq/XmwRBAFCtWjUcOHDA4jYZGRkW18/IyFB93IyMDPj7+yM0NNTqfqwdx/CcNZMmTTIJILOyshAVFYXOnTsjJCREdRldIScnB0lJSejUqRP8/Pw8WhbyHqw35AjWG3IU6w45gvWGHOGJemPoXVcUptl3ooCAAAQEBJgt9/Pz08wXhpbKQt6D9YYcwXpDjmLdIUew3pAj3Flv1B7HY0lCKleuDJ1OZ5Y98dy5cwgLC7O4TVhYmF3rW9tHdnY2rly5YnU/1o5jeI6IiIiIiMgVPBag+fv7o3nz5ti4caNxWV5eHjZu3IiYmBiL28TExJisD8h+o9bWt6R58+bw8/Mz2c/Bgwdx6tQp435iYmKwd+9ek2ySSUlJCAkJQYMGDVQfi4iIiIiIyB4e7eI4fvx4DBs2DC1atEDLli0xd+5c3Lhxw5jVcejQoYiIiMCMGTMAAOPGjUNsbCxmz56N7t27Iz4+Hn/88QcWLlxo3OelS5dw6tQpnD17FoAMvgDZ8hUWFoby5ctjxIgRGD9+PCpWrIiQkBD85z//QUxMDFq3bg0A6Ny5Mxo0aIAhQ4bg/fffR0ZGBt544w2MGTPGYhdGIiIiIiIiZ/BogPb444/jwoULeOutt5CRkYEmTZpg3bp1xoQcp06dgo9PfiNfmzZtsHTpUrzxxht47bXXcO+992LVqlVo1KiRcZ3Vq1cbAzwAGDhwIABg8uTJmDJlCgDggw8+gI+PD/r164c7d+4gLi4On3zyiXEbnU6Hn3/+Gc8++yxiYmJQtmxZDBs2DNOmTXPl20FERERERKWcx5OEPP/883j++ectPrdp0yazZY899hgee+wxq/sbPnw4hg8fbvOYgYGBmD9/PubPn291nZo1ayIxMdHmfoiIiIiIiJzJY2PQiIiIiIiIyBQDNCIiIiIiIo1ggEZERERERKQRHh+DVpIJIQConzXclXJycnDz5k1kZWVxEkdSjfWGHMF6Q45i3SFHsN6QIzxRbwwxgSFGsIYBmgtdu3YNABAVFeXhkhARERERkRZcu3YN5cuXt/q8IooK4chheXl5OHv2LIKDg6EoikfLkpWVhaioKJw+fRohISEeLQt5D9YbcgTrDTmKdYccwXpDjvBEvRFC4Nq1a6hevbrJVGKFsQXNhXx8fBAZGenpYpgICQnhlxfZjfWGHMF6Q45i3SFHsN6QI9xdb2y1nBkwSQgREREREZFGMEAjIiIiIiLSCAZopURAQAAmT56MgIAATxeFvAjrDTmC9YYcxbpDjmC9IUdoud4wSQgREREREZFGsAWNiIiIiIhIIxigERERERERaQQDNCIiIiIiIo1ggEZERERERKQRDNBKkPnz5yM6OhqBgYFo1aoVdu7caXP9ZcuWoV69eggMDETjxo2RmJjoppKSlthTbz777DO0a9cOFSpUQIUKFdCxY8ci6xmVTPZ+3xjEx8dDURT07t3btQUkzbK37ly5cgVjxoxBeHg4AgICULduXZ6vSiF7683cuXNx3333oUyZMoiKisKLL76I27dvu6m0pAW//fYbevbsierVq0NRFKxatarIbTZt2oRmzZohICAAderUwZIlS1xeTksYoJUQ33//PcaPH4/Jkyfjzz//xAMPPIC4uDicP3/e4vrbt2/HoEGDMGLECKSmpqJ3797o3bs3/v77bzeXnDzJ3nqzadMmDBo0CMnJyUhJSUFUVBQ6d+6MtLQ0N5ecPMneemNw4sQJvPzyy2jXrp2bSkpaY2/dyc7ORqdOnXDixAksX74cBw8exGeffYaIiAg3l5w8yd56s3TpUkycOBGTJ0/G/v37sWjRInz//fd47bXX3Fxy8qQbN27ggQcewPz581Wtf/z4cXTv3h0dOnTAnj178MILL2DkyJH45ZdfXFxSCwSVCC1bthRjxowx/q3X60X16tXFjBkzLK4/YMAA0b17d5NlrVq1Ek8//bRLy0naYm+9KSw3N1cEBweLL7/80lVFJA1ypN7k5uaKNm3aiM8//1wMGzZM9OrVyw0lJa2xt+58+umnolatWiI7O9tdRSQNsrfejBkzRjz88MMmy8aPHy8eeughl5aTtAuAWLlypc11XnnlFdGwYUOTZY8//riIi4tzYcksYwtaCZCdnY3du3ejY8eOxmU+Pj7o2LEjUlJSLG6TkpJisj4AxMXFWV2fSh5H6k1hN2/eRE5ODipWrOiqYpLGOFpvpk2bhqpVq2LEiBHuKCZpkCN1Z/Xq1YiJicGYMWNQrVo1NGrUCO+++y70er27ik0e5ki9adOmDXbv3m3sBnns2DEkJiaiW7dubikzeSctXRv7uv2I5HQXL16EXq9HtWrVTJZXq1YNBw4csLhNRkaGxfUzMjJcVk7SFkfqTWGvvvoqqlevbvaFRiWXI/Vm69atWLRoEfbs2eOGEpJWOVJ3jh07hl9//RVPPPEEEhMTceTIETz33HPIycnB5MmT3VFs8jBH6s3gwYNx8eJFtG3bFkII5Obm4plnnmEXR7LJ2rVxVlYWbt26hTJlyritLGxBIyKHzJw5E/Hx8Vi5ciUCAwM9XRzSqGvXrmHIkCH47LPPULlyZU8Xh7xMXl4eqlatioULF6J58+Z4/PHH8frrr2PBggWeLhpp2KZNm/Duu+/ik08+wZ9//omEhASsWbMG06dP93TRiFRhC1oJULlyZeh0Opw7d85k+blz5xAWFmZxm7CwMLvWp5LHkXpjMGvWLMycORMbNmzA/fff78piksbYW2+OHj2KEydOoGfPnsZleXl5AABfX18cPHgQtWvXdm2hSRMc+c4JDw+Hn58fdDqdcVn9+vWRkZGB7Oxs+Pv7u7TM5HmO1Js333wTQ4YMwciRIwEAjRs3xo0bNzB69Gi8/vrr8PFh+wSZs3ZtHBIS4tbWM4AtaCWCv78/mjdvjo0bNxqX5eXlYePGjYiJibG4TUxMjMn6AJCUlGR1fSp5HKk3APD+++9j+vTpWLduHVq0aOGOopKG2Ftv6tWrh71792LPnj3Gx6OPPmrMkhUVFeXO4pMHOfKd89BDD+HIkSPGoB4ADh06hPDwcAZnpYQj9ebmzZtmQZghyBdCuK6w5NU0dW3s9rQk5BLx8fEiICBALFmyROzbt0+MHj1ahIaGioyMDCGEEEOGDBETJ040rr9t2zbh6+srZs2aJfbv3y8mT54s/Pz8xN69ez31EsgD7K03M2fOFP7+/mL58uUiPT3d+Lh27ZqnXgJ5gL31pjBmcSy97K07p06dEsHBweL5558XBw8eFD///LOoWrWqePvttz31EsgD7K03kydPFsHBweK7774Tx44dE+vXrxe1a9cWAwYM8NRLIA+4du2aSE1NFampqQKAmDNnjkhNTRUnT54UQggxceJEMWTIEOP6x44dE0FBQWLChAli//79Yv78+UKn04l169a5vewM0EqQjz76SNSoUUP4+/uLli1bit9//934XGxsrBg2bJjJ+j/88IOoW7eu8Pf3Fw0bNhRr1qxxc4lJC+ypNzVr1hQAzB6TJ092f8HJo+z9vimIAVrpZm/d2b59u2jVqpUICAgQtWrVEu+8847Izc11c6nJ0+ypNzk5OWLKlCmidu3aIjAwUERFRYnnnntOXL582f0FJ49JTk62eM1iqCvDhg0TsbGxZts0adJE+Pv7i1q1aokvvvjC7eUWQghFCLb1EhERERERaQHHoBEREREREWkEAzQiIiIiIiKNYIBGRERERESkEQzQiIiIiIiINIIBGhERERERkUYwQCMiIiIiItIIBmhEREREREQawQCNiIiIiIhIIxigERERFdOmTZugKAquXLkCAFiyZAlCQ0Ndeszhw4ejd+/eLj0GERG5HwM0IiLSjOHDh0NRFMycOdNk+apVq6AoiodKZb/HH38chw4d8nQxjOrVq4eAgABkZGR4uihERFQEBmhERKQpgYGBeO+993D58mWn7jc7O9up+7OlTJkyqFq1qtuOZ8vWrVtx69Yt9O/fH19++aWni0NEREVggEZERJrSsWNHhIWFYcaMGTbXW7FiBRo2bIiAgABER0dj9uzZJs9HR0dj+vTpGDp0KEJCQjB69Ghj18Off/4Z9913H4KCgtC/f3/cvHkTX375JaKjo1GhQgWMHTsWer3euK+vv/4aLVq0QHBwMMLCwjB48GCcP3/eatkKd3GMjo6GoihmD4PTp09jwIABCA0NRcWKFdGrVy+cOHHC+Lxer8f48eMRGhqKSpUq4ZVXXoEQQtX7uWjRIgwePBhDhgzB4sWLzZ5PT09H9+7dUaZMGdxzzz1YunQpoqOjMXfuXOM6V65cwciRI1GlShWEhITg4Ycfxl9//aXq+EREZB8GaEREpCk6nQ7vvvsuPvroI5w5c8biOrt378aAAQMwcOBA7N27F1OmTMGbb76JJUuWmKw3a9YsPPDAA0hNTcWbb74JALh58yY+/PBDxMfHY926ddi0aRP69OmDxMREJCYm4uuvv8b//vc/LF++3LifnJwcTJ8+HX/99RdWrVqFEydOYPjw4apf065du5Ceno709HScOXMGrVu3Rrt27Yz7jouLQ3BwMLZs2YJt27ahXLly6NKli7HVb/bs2ViyZAkWL16MrVu34tKlS1i5cmWRx7127RqWLVuGJ598Ep06dcLVq1exZcsWk3WGDh2Ks2fPYtOmTVixYgUWLlxoFnw+9thjOH/+PNauXYvdu3ejWbNmeOSRR3Dp0iXV7wEREakkiIiINGLYsGGiV69eQgghWrduLf79738LIYRYuXKlKHjKGjx4sOjUqZPJthMmTBANGjQw/l2zZk3Ru3dvk3W++OILAUAcOXLEuOzpp58WQUFB4tq1a8ZlcXFx4umnn7Zazl27dgkAxm2Sk5MFAHH58mXjccqXL29x27Fjx4qaNWuK8+fPCyGE+Prrr8V9990n8vLyjOvcuXNHlClTRvzyyy9CCCHCw8PF+++/b3w+JydHREZGGt8raxYuXCiaNGli/HvcuHFi2LBhxr/3798vAIhdu3YZlx0+fFgAEB988IEQQogtW7aIkJAQcfv2bZN9165dW/zvf/+zeXwiIrIfW9CIiEiT3nvvPXz55ZfYv3+/2XP79+/HQw89ZLLsoYcewuHDh026JrZo0cJs26CgINSuXdv4d7Vq1RAdHY1y5cqZLCvYirR792707NkTNWrUQHBwMGJjYwEAp06dsus1LVy4EIsWLcLq1atRpUoVAMBff/2FI0eOIDg4GOXKlUO5cuVQsWJF3L59G0ePHsXVq1eRnp6OVq1aGffj6+tr8bUVtnjxYjz55JPGv5988kksW7YM165dAwAcPHgQvr6+aNasmXGdOnXqoEKFCsa///rrL1y/fh2VKlUylq9cuXI4fvw4jh49atfrJyKiovl6ugBERESWtG/fHnFxcZg0aZJd3QkLKlu2rNkyPz8/k78VRbG4LC8vDwBw48YNxMXFIS4uDt9++y2qVKmCU6dOIS4uzq7EI8nJyfjPf/6D7777Dvfff79x+fXr19G8eXN8++23ZtsYgjhH7Nu3D7///jt27tyJV1991bhcr9cjPj4eo0aNUrWf69evIzw8HJs2bTJ7ztVTCRARlUYM0IiISLNmzpyJJk2a4L777jNZXr9+fWzbts1k2bZt21C3bl3odDqnluHAgQPIzMzEzJkzERUVBQD4448/7NrHkSNH0L9/f7z22mvo27evyXPNmjXD999/j6pVqyIkJMTi9uHh4dixYwfat28PAMjNzTWOBbNm0aJFaN++PebPn2+y/IsvvsCiRYswatQo3HfffcjNzUVqaiqaN29uLGvBDJrNmjVDRkYGfH19ER0dbdfrJiIi+7GLIxERaVbjxo3xxBNP4MMPPzRZ/tJLL2Hjxo2YPn06Dh06hC+//BIff/wxXn75ZaeXoUaNGvD398dHH32EY8eOYfXq1Zg+fbrq7W/duoWePXuiadOmGD16NDIyMowPAHjiiSdQuXJl9OrVC1u2bMHx48exadMmjB071pgkZdy4cZg5cyZWrVqFAwcO4LnnnjNOim1JTk4Ovv76awwaNAiNGjUyeYwcORI7duzAP//8g3r16qFjx44YPXo0du7cidTUVIwePRplypQxZpns2LEjYmJi0Lt3b6xfvx4nTpzA9u3b8frrr9sdqBIRUdEYoBERkaZNmzbN2N3QoFmzZvjhhx8QHx+PRo0a4a233sK0adMc7gppS5UqVbBkyRIsW7YMDRo0wMyZMzFr1izV2587dw4HDhzAxo0bUb16dYSHhxsfgBwT99tvv6FGjRro27cv6tevjxEjRuD27dvGFrWXXnoJQ4YMwbBhwxATE4Pg4GD06dPH6jFXr16NzMxMi+vUr18f9evXx6JFiwAAX331FapVq4b27dujT58+GDVqFIKDgxEYGAhAdvdMTExE+/bt8dRTT6Fu3boYOHAgTp48iWrVqql+H4iISB1FCJUTqRAREVGJd+bMGURFRWHDhg145JFHPF0cIqJShwEaERFRKfbrr7/i+vXraNy4MdLT0/HKK68gLS0Nhw4dMkueQkRErsckIURERKVYTk4OXnvtNRw7dgzBwcFo06YNvv32WwZnREQewhY0IiIiIiIijWCSECIiIiIiIo1ggEZERERERKQRDNCIiIiIiIg0ggEaERERERGRRjBAIyIiIiIi0ggGaERERERERBrBAI2IiIiIiEgjGKARERERERFpxP8DTIw4Y/hDTfIAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Train classical SVR model using RBF kernel\n", + "classical = SVR(kernel='rbf')\n", + "classical.fit(x, y, w)\n", + "classical_score = classical.score(x, y, w)\n", + "print(f\"Classical SVR R² score on training data: {classical_score:.4f}\")\n", + "\n", + "# Predict and transform back to probabilities\n", + "pred = classical.predict(x)\n", + "p_hat = 1 / (1 + np.exp(-pred))\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# Sort data by age for smoother plots\n", + "group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", + "group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", + "group_0.sort()\n", + "group_1.sort()\n", + "\n", + "# Plot actual vs predicted transition probabilities\n", + "plt.figure(figsize=(10, 5))\n", + "plt.plot([a for a, _, _ in group_0], [p for _, p, _ in group_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_0], [p_hat for _, _, p_hat in group_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_1], [p for _, p, _ in group_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_1], [p_hat for _, _, p_hat in group_1], 'b', label='Group 1 model')\n", + "\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.title(\"Classical SVR Prediction vs Actual by Gender\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "YLK8Srl7V5s1", + "metadata": { + "id": "YLK8Srl7V5s1" + }, + "source": [ + "Side-by-side comparison of how well each model fits the transition probabilities across gender groups." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "au5H9ebVVtIq", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 457 + }, + "id": "au5H9ebVVtIq", + "outputId": "490cb18e-835a-4dd7-a1da-ba140ec55f2e" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Quantum SVR predictions\n", + "pred_q = zzpc_svr.predict(f_matrix_train)\n", + "p_hat_q = 1 / (1 + np.exp(-pred_q))\n", + "p_q = 1 / (1 + np.exp(-y))\n", + "\n", + "# Classical SVR predictions\n", + "classical = SVR(kernel='rbf')\n", + "classical.fit(x, y, w)\n", + "pred_c = classical.predict(x)\n", + "p_hat_c = 1 / (1 + np.exp(-pred_c))\n", + "p_c = 1 / (1 + np.exp(-y))\n", + "\n", + "# Sort and group data by gender and age\n", + "def group_and_sort(x, p, p_hat):\n", + " group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", + " group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", + " return sorted(group_0), sorted(group_1)\n", + "\n", + "group_q_0, group_q_1 = group_and_sort(x, p_q, p_hat_q)\n", + "group_c_0, group_c_1 = group_and_sort(x, p_c, p_hat_c)\n", + "\n", + "# Plot both models side-by-side\n", + "plt.figure(figsize=(12, 5))\n", + "\n", + "# Quantum SVR\n", + "plt.subplot(1, 2, 1)\n", + "plt.plot([a for a, _, _ in group_q_0], [p for _, p, _ in group_q_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_q_0], [p_hat for _, _, p_hat in group_q_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_q_1], [p for _, p, _ in group_q_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_q_1], [p_hat for _, _, p_hat in group_q_1], 'b', label='Group 1 model')\n", + "plt.title(\"Quantum Kernel SVR\")\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "\n", + "# Classical SVR\n", + "plt.subplot(1, 2, 2)\n", + "plt.plot([a for a, _, _ in group_c_0], [p for _, p, _ in group_c_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_c_0], [p_hat for _, _, p_hat in group_c_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_c_1], [p for _, p, _ in group_c_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_c_1], [p_hat for _, _, p_hat in group_c_1], 'b', label='Group 1 model')\n", + "plt.title(\"Classical SVR\")\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "22f6ed9d-0b80-43c2-9a59-21bfb1d7a695", + "metadata": { + "id": "22f6ed9d-0b80-43c2-9a59-21bfb1d7a695" + }, + "source": [ + "The above analysis is done in-sample. Below, we use the leave-one-out cross-validation functionality from the sklearn module." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "z-rdVMiSW65Q", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 491 + }, + "id": "z-rdVMiSW65Q", + "outputId": "5992f530-6a3b-4a5d-beb9-f6f85f392235" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum SVR LOO R² score: 0.8584\n", + "Classical SVR LOO R² score: 0.8532\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.model_selection import LeaveOneOut\n", + "from sklearn.metrics import r2_score\n", + "from sklearn.svm import SVR\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Quantum SVR LOO prediction\n", + "def predict_loo(K, y, w, svr_model):\n", + " cols = range(len(y))\n", + " loo = LeaveOneOut()\n", + " pred_loo = []\n", + " for train_index, test_index in loo.split(cols):\n", + " svr_model.fit(K[np.ix_(train_index, train_index)], y[train_index], w[train_index])\n", + " pred = svr_model.predict(K[np.ix_(test_index, train_index)])\n", + " pred_loo.extend(pred)\n", + " return np.array(pred_loo)\n", + "\n", + "zzpc_svr = SVR(kernel='precomputed')\n", + "statevector_loo = predict_loo(matrix_train, y, w, zzpc_svr)\n", + "\n", + "# Classical SVR LOO prediction\n", + "classical = SVR(kernel='rbf')\n", + "loo = LeaveOneOut()\n", + "pred_loo_classic = []\n", + "for train_index, test_index in loo.split(x):\n", + " classical.fit(x[train_index], y[train_index], w[train_index])\n", + " cpred = classical.predict(x[test_index])\n", + " pred_loo_classic.extend(cpred)\n", + "pred_loo_classic = np.array(pred_loo_classic)\n", + "\n", + "# Transform predictions to probabilities\n", + "p_hat_q = 1 / (1 + np.exp(-statevector_loo))\n", + "p_hat_c = 1 / (1 + np.exp(-pred_loo_classic))\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# R² scores\n", + "score_q = r2_score(p, p_hat_q, sample_weight=w)\n", + "score_c = r2_score(p, p_hat_c, sample_weight=w)\n", + "print(f\"Quantum SVR LOO R² score: {score_q:.4f}\")\n", + "print(f\"Classical SVR LOO R² score: {score_c:.4f}\")\n", + "\n", + "# Sort and group data by gender and age\n", + "def group_and_sort(x, p, p_hat):\n", + " group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", + " group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", + " return sorted(group_0), sorted(group_1)\n", + "\n", + "group_q_0, group_q_1 = group_and_sort(x, p, p_hat_q)\n", + "group_c_0, group_c_1 = group_and_sort(x, p, p_hat_c)\n", + "\n", + "# Plot both models side-by-side\n", + "plt.figure(figsize=(12, 5))\n", + "\n", + "# Quantum SVR LOO\n", + "plt.subplot(1, 2, 1)\n", + "plt.plot([a for a, _, _ in group_q_0], [p for _, p, _ in group_q_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_q_0], [p_hat for _, _, p_hat in group_q_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_q_1], [p for _, p, _ in group_q_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_q_1], [p_hat for _, _, p_hat in group_q_1], 'b', label='Group 1 model')\n", + "plt.title(\"Quantum SVR (LOO)\")\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "\n", + "# Classical SVR LOO\n", + "plt.subplot(1, 2, 2)\n", + "plt.plot([a for a, _, _ in group_c_0], [p for _, p, _ in group_c_0], 'or', label='Group 0')\n", + "plt.plot([a for a, _, _ in group_c_0], [p_hat for _, _, p_hat in group_c_0], 'r', label='Group 0 model')\n", + "plt.plot([a for a, _, _ in group_c_1], [p for _, p, _ in group_c_1], 'ob', label='Group 1')\n", + "plt.plot([a for a, _, _ in group_c_1], [p_hat for _, _, p_hat in group_c_1], 'b', label='Group 1 model')\n", + "plt.title(\"Classical SVR (LOO)\")\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "Ia52tUuWX6xP", + "metadata": { + "id": "Ia52tUuWX6xP" + }, + "source": [ + "## 📊 Model Performance Summary\n", + "\n", + "This section compares the performance of Quantum and Classical Support Vector Regression models, both in-sample and using Leave-One-Out Cross-Validation (LOO).\n", + "\n", + "### **In-Sample R² Scores**\n", + "| Model | R² Score | Interpretation |\n", + "|-------|----------|----------------|\n", + "| **Quantum SVR (QSVR)** | **0.8609** | Captures the relationship between features and target well. |\n", + "| **Classical SVR (RBF Kernel)** | **0.8605** | Very similar to QSVR, suggesting the classical kernel is equally expressive for this dataset. |\n", + "\n", + "### **Leave-One-Out Cross-Validation (LOO)**\n", + "| Model | R² Score | Interpretation |\n", + "|-------|----------|----------------|\n", + "| **Quantum SVR (LOO)** | **0.8977** | Slightly lower than in-sample scores, as expected. This is a more rigorous test of generalization. |\n", + "\n", + "---\n", + "\n", + "### 🧠 Interpretation\n", + "\n", + "- The **QSVR and Classical SVR** models perform almost identically on this dataset, indicating that the quantum kernel does not yet offer a significant advantage over the classical RBF kernel.\n", + "- The **LOO score** is slightly lower, which is expected due to its stricter validation. It provides a more **unbiased estimate** of how well the model generalizes to unseen data.\n", + "- A high R² score indicates good fit, but it’s important to also examine **residuals**, **error distributions**, and **kernel structures** to fully assess model performance.\n", + "\n", + "To compare these results, you can look at how much each score deviates from 1.0. The closer the score is to 1.0, the better the model is fitting your data. However, keep in mind that a high R-squared score doesn’t always mean your model will perform well on unseen data. It’s important to also look at other metrics and plots to assess your model’s performance." + ] + }, + { + "cell_type": "markdown", + "id": "AgNktxzOCvwP", + "metadata": { + "id": "AgNktxzOCvwP" + }, + "source": [ + "### Exercise 2: Residuals\n", + "\n", + "> In regression analysis, **residuals** represent the difference between the observed (actual) and predicted values for each data point. They help us understand how well a model fits the data.\n", + ">\n", + "> Mathematically, for an observed value $$y_{\\text{obs}}$$ and a predicted value $$y_{\\text{pred}}$$ for a data point, the residual $$e$$ is calculated as:\n", + ">\n", + "> $$e = y_{\\text{obs}} - y_{\\text{pred}}$$\n", + ">\n", + "> In our case, we are working with **transition probabilities**, so we transform both actual and predicted values using the sigmoid function to interpret them as probabilities:\n", + ">\n", + "> $$p = \\frac{1}{1 + e^{-y}}, \\quad \\hat{p} = \\frac{1}{1 + e^{-y_{\\text{pred}}}}$$\n", + ">\n", + "> The residuals then become:\n", + ">\n", + "> $$e = p - \\hat{p}$$\n", + ">\n", + "> A good model will produce residuals that are:\n", + "> - **Close to zero**, indicating accurate predictions.\n", + "> - **Randomly distributed**, without patterns, which suggests the model captures the underlying data structure well.\n", + ">\n", + "> In this exercise, we will:\n", + "> 1. Compute residuals for the Quantum SVR model.\n", + "> 2. Plot a histogram to visualize their distribution.\n", + ">\n", + "> ### 🔍 Hints\n", + "> - Use `residuals = p - p_hat_q` for Quantum SVR.\n", + "> - Use `plt.hist(residuals, bins=20)` to plot.\n", + "> - Label your axes clearly.\n", + "> - *Advanced:* Compare with Classical SVR residuals or plot residuals vs. age to detect patterns.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "me-eoMwCH9JS", + "metadata": { + "id": "me-eoMwCH9JS" + }, + "outputs": [], + "source": [ + "# Transform actual values to probabilities\n", + "p =\n", + "\n", + "# Compute residuals\n", + "residuals_qsvr =\n", + "residuals_classical =\n", + "\n", + "# Plot histogram of Quantum SVR residuals\n", + "plt.figure(figsize=(12, 5))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "vgIIM-NPH9LX", + "metadata": { + "id": "vgIIM-NPH9LX" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "G_ACDFHkLuCh", + "metadata": { + "id": "G_ACDFHkLuCh" + }, + "source": [ + "### ✅ Summary of Exercise 2: Residuals\n", + "\n", + "You've done a great job implementing Quantum Support Vector Regression (QSVR) and comparing it with classical SVR using **leave-one-out cross-validation (LOO)**—a robust method for estimating generalization error.\n", + "\n", + "#### 🔍 Residual Analysis\n", + "\n", + "You've plotted two types of residual histograms:\n", + "\n", + "1. **Raw residuals**: \n", + " $$e = y - \\hat{y}$$ \n", + " These show how far off the predicted values are from the actual targets. Ideally, residuals should be centered around zero with no clear pattern.\n", + "\n", + "2. **Probability residuals**: \n", + " $$e = p - \\hat{p}$$ \n", + " Here, both actual and predicted values are transformed using the sigmoid function to represent transition probabilities. This is especially relevant in your context of modeling disability insurance transitions.\n", + "\n", + "#### 📊 Interpretation\n", + "\n", + "- A **tight, symmetric distribution** around zero suggests good model performance.\n", + "- **Skewed or long-tailed distributions** may indicate systematic bias—either overestimation or underestimation.\n", + "- Comparing Quantum and Classical SVR residuals side-by-side helps assess which model generalizes better.\n", + "\n", + "#### 🧠 What You’ve Achieved\n", + "\n", + "- Implemented QSVR with a custom kernel matrix.\n", + "- Compared it with classical SVR using RBF kernel.\n", + "- Evaluated both using LOO cross-validation.\n", + "- Analyzed residuals both in raw and probability-transformed form.\n", + "\n", + "This is a **comprehensive and methodologically sound approach** to model evaluation. Excellent work! 😊" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bf6ece14-57fb-4ea5-85f5-5e5f3919414f", + "metadata": { + "id": "bf6ece14-57fb-4ea5-85f5-5e5f3919414f" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "8d6c503e-5292-4644-8155-b5e76134ebf1", + "metadata": { + "id": "8d6c503e-5292-4644-8155-b5e76134ebf1" + }, + "source": [ + "### We used the statevector simulator and now we'll run it on IQM simulator and compare all three runs:\n", + "### Simulator vs Mock vs Real Hardware" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "9XF9kpZxM53H", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "9XF9kpZxM53H", + "outputId": "efafafd9-8d9f-4e47-adfd-cac57eef5fd7" + }, + "outputs": [], + "source": [ + "from qrisp import *\n", + "from qrisp.interface import IQMBackend" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "MYB6f3nHM55c", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "MYB6f3nHM55c", + "outputId": "296bc9fa-8cc8-4bd0-a46d-3bc6425db975" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " \u001b[2K" + ] + }, + { + "data": { + "text/plain": [ + "{2: 1.0}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = QuantumFloat(2)\n", + "a[:] = 2\n", + "a.get_measurement()" + ] + }, + { + "cell_type": "markdown", + "id": "xSxaCW_KxjS0", + "metadata": { + "id": "xSxaCW_KxjS0" + }, + "source": [ + "## Running on IQM Resonance\n", + "\n", + "Now let's run circuits on IQM Resonance. IQM provides both real quantum hardware and a mock backend for testing.\n", + "\n", + "### Token Authentication\n", + "\n", + "To access IQM quantum computers, you need an API Token. Get one at\n", + "\n", + "🔗 [resonance.meetiqm.com](https://resonance.meetiqm.com/)\n", + "\n", + "by clicking \"Create Token\" in the side panel." + ] + }, + { + "cell_type": "markdown", + "id": "b45cb38b-6689-419e-b5f5-2c0365c7ad51", + "metadata": {}, + "source": [ + "### Step 1: Load Your IQM Token\n", + "\n", + "First, let's load your authentication token from the file:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "Tev0tk-1xoVf", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Tev0tk-1xoVf", + "outputId": "6f954088-5589-4375-9d53-4385feed0fbf" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "✓ Token loaded successfully!\n", + "✓ Token length: 64 characters\n" + ] + } + ], + "source": [ + "# Load your IQM authentication token\n", + "with open('token.txt', 'r') as f:\n", + " iqm_token = f.read().strip()\n", + "\n", + "print(\"✓ Token loaded successfully!\")\n", + "print(f\"✓ Token length: {len(iqm_token)} characters\")" + ] + }, + { + "cell_type": "markdown", + "id": "00c02e6d-5081-41c2-bcad-315fd9de9133", + "metadata": {}, + "source": [ + "### Step 2: Configure IQM Backends\n", + "\n", + "Qrisp provides a convenient interface to IQM quantum computers. Let's set it up:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "73c0fbb4-2cc4-4d4b-a0bd-2ed46c348e36", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "✓ Connected to: sirius:mock (IQM simulator)\n", + "✓ Connected to: sirius (IQM 24-qubit real hardware)\n", + "✓ Connected to: garnet (IQM 20-qubit real hardware)\n", + "✓ All IQM backends configured successfully!\n" + ] + } + ], + "source": [ + " # Import IQM backend support\n", + "# Note: This requires qrisp[iqm] to be installed\n", + "try:\n", + " from qrisp.interface import IQMBackend\n", + "\n", + " # Configure IQM backends\n", + " iqm_mock = IQMBackend(api_token=iqm_token, device_instance=\"sirius:mock\")\n", + " print(\"✓ Connected to: sirius:mock (IQM simulator)\")\n", + "\n", + " iqm_sirius = IQMBackend(api_token=iqm_token, device_instance=\"sirius\")\n", + " print(\"✓ Connected to: sirius (IQM 24-qubit real hardware)\")\n", + "\n", + " iqm_garnet = IQMBackend(api_token=iqm_token, device_instance=\"garnet\")\n", + " print(\"✓ Connected to: garnet (IQM 20-qubit real hardware)\")\n", + "\n", + " print(\"✓ All IQM backends configured successfully!\")\n", + " \n", + "except ImportError:\n", + " print(\"⚠ IQM backend not available\")\n", + " print(\"To install: pip install qrisp[iqm]\")\n", + " iqm_mock = iqm_sirius = iqm_garnet = None\n", + "\n", + "except Exception as e:\n", + " print(f\"⚠ Could not connect to IQM: {e}\")\n", + " print(\"Check your token and internet connection\")\n", + " iqm_mock = iqm_sirius = iqm_garnet = None" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "iI2K9GZGM57h", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "iI2K9GZGM57h", + "outputId": "cb7bc62f-2e8b-4cbf-e2a2-37467522bcee" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Qrisp Simulator: {2: 1.0} \u001b[2K\n", + "Simulator: Perfect (no noise)\n" + ] + } + ], + "source": [ + "# local simulator\n", + "a = QuantumFloat(2)\n", + "a[:] = 2\n", + "sim_result = a.get_measurement()\n", + "print(f\"Qrisp Simulator: {sim_result}\")\n", + "print(\"Simulator: Perfect (no noise)\")" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "8G-vyVI7Mha5", + "metadata": { + "id": "8G-vyVI7Mha5" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "IQM Mock Backend: {0: 1.0}\n", + "Mock: Simulates IQM backend behavior (with noise model), zero credits used\n" + ] + } + ], + "source": [ + "# mock backend on IQM resonance\n", + "a = QuantumFloat(2)\n", + "a[:] = 2\n", + "mock_result = a.get_measurement(backend=iqm_mock, shots=500)\n", + "print(f\"IQM Mock Backend: {mock_result}\")\n", + "print(\"Mock: Simulates IQM backend behavior (with noise model), zero credits used\")" + ] + }, + { + "cell_type": "markdown", + "id": "15595412-8121-43a4-a786-083a9ed0e27a", + "metadata": { + "id": "15595412-8121-43a4-a786-083a9ed0e27a" + }, + "source": [ + "### Step 3. Synthetic Data Preparation\n", + "The `feature_map` function is a way to encode classical data into a quantum state. In this case, it's creating a quantum circuit `qc` with 2 qubits. It then applies a rotation around the y-axis (`ry`) on each qubit. The rotation angle is determined by the input data `x` multiplied by `pi`. The `ParameterVector` is a way to create a list of parameters." + ] + }, + { + "cell_type": "markdown", + "id": "19f6461a-7bc1-47e9-bf5b-6bf606fbc586", + "metadata": { + "id": "19f6461a-7bc1-47e9-bf5b-6bf606fbc586" + }, + "source": [ + "First, we create some synthetic data, but smaller (fewer data points) than it was before." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "4e2855b6-00ff-4e1d-9d84-ef796d64ca26", + "metadata": {}, + "outputs": [], + "source": [ + "# Smaller dataset for quantum simulation\n", + "nsamp = 10\n", + "\n", + "# Create feature matrix\n", + "x = np.array([[0.0, i/nsamp] for i in range(nsamp)] + [[1.0, i/nsamp] for i in range(nsamp)])\n", + "\n", + "# Generate target values with noise\n", + "y = np.array([\n", + " -4.5 + 0.2*a[0] + a[1]*(1 + a[0]*0.2) + 0.1*np.random.normal()\n", + " for a in x\n", + "])\n", + "\n", + "# Logistic transformation\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# Population size based on age\n", + "n = [\n", + " int(200 + 600*xj[1]/0.7) if xj[1] <= 0.7 else int(800 - 300*(xj[1] - 0.7)/0.3)\n", + " for xj in x\n", + "]\n", + "\n", + "# Weighted transitions\n", + "d = [nj * pj for nj, pj in zip(n, p)]\n", + "\n", + "# Create a DataFrame\n", + "df1 = pd.DataFrame({\n", + " 'gender': [a[0] for a in x],\n", + " 'age group (normalized)': [a[1] for a in x],\n", + " 'population size': n,\n", + " 'number of transitions': d\n", + "})\n", + "\n", + "# Save to CSV\n", + "df1.to_csv('fdata1.csv', index=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "670765b0-5135-4965-a15f-57e5ea90c130", + "metadata": { + "id": "670765b0-5135-4965-a15f-57e5ea90c130" + }, + "outputs": [], + "source": [ + "data1 = df1\n", + "# data1 = pd.read_csv('fdata1.csv')" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "f04e1346-2773-4918-9789-b72c9354f381", + "metadata": { + "id": "f04e1346-2773-4918-9789-b72c9354f381", + "outputId": "e0c43769-aa51-498c-88b0-a58e178903da" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 0. ]\n", + " [0. 0.1]\n", + " [0. 0.2]\n", + " [0. 0.3]\n", + " [0. 0.4]\n", + " [0. 0.5]\n", + " [0. 0.6]\n", + " [0. 0.7]\n", + " [0. 0.8]\n", + " [0. 0.9]\n", + " [1. 0. ]\n", + " [1. 0.1]\n", + " [1. 0.2]\n", + " [1. 0.3]\n", + " [1. 0.4]\n", + " [1. 0.5]\n", + " [1. 0.6]\n", + " [1. 0.7]\n", + " [1. 0.8]\n", + " [1. 0.9]]\n" + ] + } + ], + "source": [ + "# Transform and inspect data\n", + "x1 = np.array( [[a,b] for a,b in zip(data1['gender'], data1['age group (normalized)'])] )\n", + "print(x1)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "3b74a992-8a26-481b-b40a-05cc775ce58f", + "metadata": { + "id": "3b74a992-8a26-481b-b40a-05cc775ce58f" + }, + "outputs": [], + "source": [ + "# raw transition frequency per group, used for plots\n", + "p_raw = [a/b for a,b in zip(d,n)]\n", + "\n", + "# logistic probability, used as input to SVR optimization\n", + "y = np.array([np.log( p / (1-p) ) for p in p_raw])\n", + "\n", + "# calculate weights for SVR based on population size\n", + "w = np.array([1./nj for nj in n])\n", + "\n", + "# normalize weights (equivalent to changing the hyperparameters of the SVR)\n", + "w = w/sum(w)*len(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "c4e5c7fd-1c28-4867-8e1a-4ba20b711f1f", + "metadata": { + "id": "c4e5c7fd-1c28-4867-8e1a-4ba20b711f1f", + "outputId": "9395a2e9-1d87-4e79-e6fd-5e448166e0fa" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "axs.plot([x1j[1] for x1j,p in zip(x1, p_raw) if x1j[0] == 0], [p for x1j,p in zip(x1, p_raw) if x1j[0] == 0], 'or')\n", + "axs.plot([x1j[1] for x1j,p in zip(x1, p_raw) if x1j[0] == 1], [p for x1j,p in zip(x1, p_raw) if x1j[0] == 1], 'ob')\n", + "axs.set_title(\"raw transition frequencies\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "08783390-fb9a-4d24-ae8b-02eb0923c632", + "metadata": { + "id": "08783390-fb9a-4d24-ae8b-02eb0923c632" + }, + "source": [ + "## Exercise 3: Implement and Visualize a Quantum Feature Map\n", + "\n", + "In this exercise, you will implement a quantum feature map using Qiskit and visualize the resulting quantum circuit. The feature map is a way of encoding classical data into quantum states. In this case, we will use a simple feature map that applies a rotation around the y-axis on each qubit.\n", + "\n", + "### Task 1: Implement the Feature Map\n", + "\n", + "First, let's implement the feature map. Here is the function you need to complete:\n", + "\n", + "```python\n", + "def build_feature_map(sym):\n", + " n = 2 # Number of qubits\n", + " q = QuantumVariable(n)\n", + " \n", + " # TODO: Apply a rotation around the y-axis on each qubit\n", + " # Hint: Use the ry gate and the input data x1\n", + " \n", + " return q\n", + "```\n", + "\n", + "### Task 2: Visualize the Circuit\n", + "\n", + "After implementing the feature map, you visualize the resulting quantum circuit, as we did at the beginning of this lesson.\n", + "\n", + "Good luck with your exercise! If you have any questions or need further clarification, feel free to ask. 😊" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "24c26430-a283-4a99-8fb7-058c52bf4c7e", + "metadata": { + "id": "24c26430-a283-4a99-8fb7-058c52bf4c7e" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "QuantumCircuit:\n", + "---------------\n", + " ┌──────────┐\n", + "q.0: ┤ Ry(π*x0) ├\n", + " ├──────────┤\n", + "q.1: ┤ Ry(π*x1) ├\n", + " └──────────┘\n", + "Live QuantumVariables:\n", + "----------------------\n", + "QuantumVariable q\n" + ] + } + ], + "source": [ + "from qrisp import ry\n", + "\n", + "# Define a simple feature map using Ry rotations\n", + "def build_feature_map(sym):\n", + " n = 2 # Number of qubits\n", + " q = QuantumVariable(n)\n", + "\n", + " return q\n", + "\n", + "# Build the feature map\n", + "feature_map = build_feature_map('x')\n", + "\n", + "# Inspect the quantum state\n", + "print(feature_map.qs)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2aba5629-9030-4878-87c6-dba479d289eb", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f444fdcf-4ec3-4d22-a790-a7cc4e8febb2", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dc63aa1a-0bf0-4e1f-9bf2-580c12aadbdb", + "metadata": { + "id": "dc63aa1a-0bf0-4e1f-9bf2-580c12aadbdb" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "52aa44c7-40bc-4ec2-b273-94d6b457a8dc", + "metadata": { + "id": "52aa44c7-40bc-4ec2-b273-94d6b457a8dc" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "a3634fcb-4416-4760-a116-568287dc025e", + "metadata": {}, + "source": [ + "The following part of the code implements a list of all possible quantum circuits for the given data `x1`. For each pair of data points `(x1[i], x1[j])`, it creates two circuits using the `feature_map` function. The feature map encodes classical data into quantum states using symbolic Ry rotations. It then appends the inverse of the second circuit to the first using Qrisp’s circuit composition. This allows us to measure the overlap between quantum states, which is used to compute the quantum kernel. The circuits can be evaluated symbolically or numerically, and run on simulators or quantum hardware." + ] + }, + { + "cell_type": "markdown", + "id": "3d96b4b7-43d9-4926-adb5-c84f320f5b76", + "metadata": {}, + "source": [ + "### Step 4: Compose Kernel Circuit and Prepare for Execution\n", + "\n", + "The following part of the code implements a list of all possible quantum circuits for the given data `x1`. For each pair of data points `(x1[i], x1[j])`, it creates two circuits using the `feature_map` function. The feature map encodes classical data into quantum states using symbolic Ry rotations.\n", + "\n", + "It then appends the inverse of the second circuit to the first using Qrisp’s circuit composition. This allows us to measure the overlap between quantum states, which is used to compute the quantum kernel. The circuits can be evaluated symbolically or numerically, and run on simulators or quantum hardware." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "23821649-5ff3-4939-bb5a-c9298ec2a69c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " ┌─────────────┐\n", + "q.0: ┤ Ry(0.59388) ├\n", + " └┬────────────┤\n", + "q.1: ─┤ Ry(1.4003) ├\n", + " └────────────┘\n" + ] + } + ], + "source": [ + "# example, assign random data as parameters and print cirquit\n", + "\n", + "subs_dic = {a : np.random.rand() for a in feature_map.qs.abstract_params}\n", + "bound_qc = feature_map.qs.bind_parameters(subs_dic)\n", + "print(bound_qc)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "a5a848cf-f061-40ae-a04e-50d45333c26f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " ┌──────────┐┌───────────┐┌─┐ \n", + " q.0: ┤ Ry(π*x0) ├┤ Ry(-π*y0) ├┤M├───\n", + " ├──────────┤├───────────┤└╥┘┌─┐\n", + " q.1: ┤ Ry(π*x1) ├┤ Ry(-π*y1) ├─╫─┤M├\n", + " └──────────┘└───────────┘ ║ └╥┘\n", + "cb_0: ══════════════════════════╩══╬═\n", + " ║ \n", + "cb_1: ═════════════════════════════╩═\n", + " \n" + ] + } + ], + "source": [ + "kernel = build_feature_map('x')\n", + "y_inverse = build_feature_map('y').qs.inverse()\n", + "\n", + "kernel.qs.append(y_inverse.to_op(), kernel.qs.qubits)\n", + "\n", + "kernel.qs.measure(kernel.qs.qubits)\n", + "\n", + "print(kernel.qs.transpile())" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "aaffb693-08f8-4cb3-9ec4-ea29bd0d3f78", + "metadata": {}, + "outputs": [], + "source": [ + "from copy import deepcopy\n", + "from qrisp import QuantumVariable, ry\n", + "from sympy import symbols\n", + "import numpy as np\n", + "\n", + "# Optional: tqdm for progress bar\n", + "try:\n", + " from tqdm import tqdm\n", + "except ImportError:\n", + " tqdm = lambda x: x # fallback if tqdm not installed\n", + "\n", + "def build_feature_map(sym):\n", + " \"\"\"\n", + " Builds a quantum feature map using Ry rotations.\n", + " Each classical feature is encoded as a rotation angle.\n", + " \"\"\"\n", + " n = 2 # Must match number of features in x1\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n)) # e.g., x:0, x:1\n", + " ry(np.pi * params[0], q[0])\n", + " ry(np.pi * params[1], q[1])\n", + " return q\n", + "\n", + "def safe_param_index(p):\n", + " \"\"\"\n", + " Extracts index from parameter name like 'x0' or 'x:0'.\n", + " \"\"\"\n", + " name = p.name\n", + " if ':' in name:\n", + " parts = name.split(':')\n", + " if len(parts) == 2 and parts[1].isdigit():\n", + " return int(parts[1])\n", + " elif name[-1].isdigit():\n", + " return int(name[-1])\n", + " raise ValueError(f\"Unexpected parameter format: {name}\")\n", + "\n", + "def train_kernel_matrix_x1(x1, f_feature_map, shots=100, backend=None):\n", + " \"\"\"\n", + " Computes the quantum kernel matrix for input data x1 using a feature map.\n", + " If a backend is provided, runs on quantum hardware or simulator.\n", + " \"\"\"\n", + " # Build base kernel circuit\n", + " kernel = f_feature_map('x')\n", + " x_params = deepcopy(kernel.qs.abstract_params)\n", + "\n", + " # Build inverse feature map for y\n", + " adjoint_qs = f_feature_map('y').qs.inverse()\n", + " y_params = deepcopy(adjoint_qs.abstract_params)\n", + "\n", + " # Combine circuits\n", + " kernel.qs.append(adjoint_qs.to_op(), kernel.qs.qubits)\n", + " kernel.qs = kernel.qs.transpile()\n", + "\n", + " # Add measurement if using backend\n", + " if backend is not None:\n", + " kernel.qs.measure(kernel.qs.qubits)\n", + "\n", + " # Initialize kernel matrix\n", + " n = len(x1)\n", + " K = np.eye(n)\n", + "\n", + " # Loop over all pairs (i, j)\n", + " for i in tqdm(range(n)):\n", + " for j in range(i + 1, n):\n", + " subs_dic = {}\n", + "\n", + " # Assign x parameters from x1[i]\n", + " for p in x_params:\n", + " idx = safe_param_index(p)\n", + " subs_dic[p] = x1[i][idx]\n", + "\n", + " # Assign y parameters from x1[j]\n", + " for p in y_params:\n", + " idx = safe_param_index(p)\n", + " subs_dic[p] = x1[j][idx]\n", + "\n", + " # Bind parameters\n", + " bound_kernel = kernel.qs.bind_parameters(subs_dic)\n", + "\n", + " # Run circuit\n", + " if backend is not None:\n", + " res = bound_kernel.run(shots=shots, backend=backend)\n", + " K_ij = res.get('0' * len(kernel.qs.qubits), 0) / shots\n", + " else:\n", + " res = bound_kernel.statevector_array()\n", + " K_ij = np.abs(res[0]) ** 2\n", + "\n", + " # Fill symmetric matrix\n", + " K[i, j] = K[j, i] = K_ij\n", + " return K\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "3f479106-7170-41cf-9962-1fc86f56910d", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 0/20 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(matrix_train_statevector),\n", + " interpolation='nearest', origin='upper', cmap='Blues')\n", + "axs.set_title(\"Quantum Kernel Matrix (Statevector Simulation)\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "bc30d10d-ea4d-4447-8fc4-b383ba823fd8", + "metadata": {}, + "outputs": [], + "source": [ + "matrix_train_iqm_mock = train_kernel_matrix_x1(x1, build_feature_map, backend=iqm_mock)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "8aa22e4f-4c78-43e9-ba9b-40f1f3da0bef", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(matrix_train_iqm_mock),\n", + " interpolation='nearest', origin='upper', cmap='Blues')\n", + "axs.set_title(\"Quantum Kernel Matrix (IQM Mock Simulator)\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "42a006f1-3f97-4f11-ba45-cc7e13b40210", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Shape of matrix_train: (20, 20)\n", + "First few rows:\n", + " [[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n", + " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n", + " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n", + " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n", + " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]\n" + ] + } + ], + "source": [ + "\n", + "print(\"Shape of matrix_train:\", matrix_train.shape)\n", + "print(\"First few rows:\\n\", matrix_train[:5])\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "52daacc0-63d0-4856-aa5d-ac20e7854546", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 20/20 [22:54<00:00, 68.71s/it]\n" + ] + } + ], + "source": [ + "matrix_train_sirius = train_kernel_matrix_x1(x1, build_feature_map, backend=iqm_sirius)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "0f196a9b-0355-4f4f-a64f-44d452141104", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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4448bzDIAgOvXr+OJJ56Ak5MToqKi9Ou7du2KvLw8g7/WLl++jM8++8xg/6q/rG/+qz8vLw8bN26sd31bt24NoPovt6p67du3z2Dd+vXrTbZcKO3tt9/G/fffj9WrV+t/mQYHB8PJyQkvv/wyysvLq+1z9epVace3sbHBlClT8O9//xsnTpxQ5FgqlQpvvPEGYmJi8PDDD9dYF6Bu74XWrVsb/fma64cffsDKlSsxf/58/OMf/8Czzz6LtWvXYu/evbXuGxgYiD/++KNOY23q8xm6VZs2bbBu3TrExsYiNDS09pO7SVZWltG7gJaVlSE5ORlqtbpONwKri6rk+ObPWWVlJdavX29QLj8/HxUVFQbr+vfvD7VajdLSUoP1R48ehUqlQmBgoJQ6ErHlwgp069YN77//PsLCwtC/f3/Mnj0bnTt3xvnz57Fhwwb88ccf2Lx5s0E/9/Tp07FgwQJMnjwZTz75JIqLi7Fu3Tr06NHDYIDg2LFjYW9vj9DQUDz++OMoLCzEO++8Azc3t3q3JgwcOBA2NjZYvnw58vLyoNFo9PdOePTRR/HEE09gypQpuPvuu/HTTz/hm2++abTmVrVajY8++gh5eXlYvHgx2rdvj7lz52LdunV4+OGHMWjQIEyfPh2urq7IzMzE9u3bMWzYMKxdu1ZaHV555RXs2bMHAQEBiIyMRJ8+fXD9+nUcO3YMu3btknJvgYkTJ2LixIk1ljHnveDv749169bhxRdfRLdu3eDm5oa77rrLrDqVlJQgIiIC3bt3x0svvQQAWLp0Kb788kvMmjULv/zyiz5RNWb8+PGwtbXFrl278Nhjj9V4rPp8howx1XVVm0uXLmHIkCG46667MGbMGHh4eODKlSv4+OOP8dNPP2H+/PnSPgN9+/bFHXfcgYULF+L69ev6Ab23JhK7d+9GVFQUpk6dih49eqCiogIffPCBPuG92c6dOzFs2LBq94IhqrdGmqVCRvzyyy/iwQcfFB4eHkKtVgsAQqvVipMnTxot/+2334p+/foJe3t70bNnT/Hhhx8anYr6xRdfiAEDBgitVit8fX3F8uXLRWJiYrXpbKam3N06FU4IId555x3RpUsXYWNjYzD9rbKyUixYsEC4uLgIBwcHERwcLNLS0kxORf3xxx8N4lbV/9a7TkZERIjWrVvXcgWNT78U4sZdJO+44w6hVqvFRx99JIS4MXUvODhYODs7C61WK7p27Spmzpwpjhw5UqfjAhDz5s2rtv7WcxXixt0m582bJ7y9vYWdnZ3w8PAQY8aMEevXr9eXqc9U1JoYuxZ1fS9kZWWJ8ePHC0dHRwFA//M39XO7eVtVnKefflrY2NiIH374waDckSNHhK2trZgzZ06N9RfixvTRMWPG1Pn8zfkM1XQuN6vLVNT8/Hzx+uuvi+DgYNGxY0dhZ2cnHB0dRWBgoHjnnXcMplubmopq6m6qxj5/6enpIigoSGg0GuHu7i4WLVokdu7caRD33Llz4pFHHhFdu3YVWq1WtG/fXowePVrs2rXLIFZubq6wt7evdidUIkuohLBwpB4p5v3338fMmTPx0EMPGdwlk6il+O677zBq1CicPn0a3bt3N3t/foZqt2bNGrz66qtIT083a6AuUU045sKKhYeHIy4uDh988IF+uiBRSzJixAiMHTsWr776ar3252eoZuXl5Vi9ejWef/55JhYkFVsuiIiISCq2XBAREZFUTC6IiIiaqX379iE0NBReXl5QqVTYtm1brfukpKRg0KBB0Gg06NatG5KSksw+LpMLIiKiZqqoqAh+fn5Gn4JtTEZGBsaPH4/Ro0cjNTUV8+fPx6OPPopvvvnGrONyzAUREVELoFKp8Nlnn2HSpEkmyyxYsADbt283uOnf9OnTkZubix07dtT5WM3iJlo6nQ6///47HB0d+eAdIqIWRgiBgoICeHl5mXwOUGMqKSlBWVmZlFhCiGrfcxqNBhqNRkr8gwcPVntUQXBwMObPn29WnGaRXPz+++/VnqJJREQty8WLF00+wbixlJSUoJXjbUBFzY+9r6s2bdqgsLDQYF1MTAxiY2OlxM/KyoK7u7vBOnd3d+Tn5+PPP/+s85TlZpFcVD1y2b5PBFQ2Eh5ZbCfvscdoX/2R3JZo7e4qLVaf/vI+hM4OdtJiTRlY/UmllnCyl1e3vp7O0mJpbOX9hSW7wc7WRl7dbNXyKqeWGIuaj4L8fHTr7K3/LrAmZWVlQEUxNH0iAEu/nyrLUPjre7h48SKcnJz0q2W1WsjULJKLqiYilY29nOTCRuIPyk4rLxYAtX3tj6quK1ut6ec6mMuulbyEzKGN3F8QDhKTC8ebPtCWkplcyP7OZXJBTZFVd4vbai3+fhKqG59LJycng+RCJg8PD2RnZxusy87OhpOTk1k3WmsWyQUREZFVU8HyJsYGyJ0CAwPx9ddfG6zbuXOn2U/Mtb6RL0RERCRFYWEhUlNTkZqaCuDGVNPU1FRkZmYCABYuXIjw8HB9+SeeeALnzp3DP//5T5w+fRpvvfUWPvnkEzz99NNmHVex5CI+Ph6+vr7QarUICAjA4cOHayy/detW9OrVC1qtFv3796+WORERETVZKrWcxUxHjhzB7bffjttvvx0AEB0djdtvvx1LliwBAFy+fFmfaABA586dsX37duzcuRN+fn5YtWoV3n33XQQHB5t1XEW6RbZs2YLo6GgkJCQgICAAa9asQXBwMM6cOQM3N7dq5Q8cOICwsDDExcXh3nvvxaZNmzBp0iQcO3YM/fr1U6KKREREDUelktAtYv7+o0aNQk23szJ2981Ro0bh+PHjZh/rZoq0XKxevRqRkZGYNWsW+vTpg4SEBDg4OCAxMdFo+ddffx3jxo3Ds88+i969e2PZsmUYNGgQ1q5dq0T1iIiISEHSk4uysjIcPXrU4CYcarUaQUFBOHjwoNF9TN20w1R5IiKiJqWRukUai/RukZycHFRWVhq9Ccfp06eN7mPqph1ZWVlGy5eWlqK0tFT/Oj8/38JaExERKaiRukUaS9NJg24SFxcHZ2dn/cK7cxIREVkP6cmFi4sLbGxsjN6Ew8PD+J0XTd20w1T5hQsXIi8vT79cvHhRTuWJiIgUIaNLpOm0B0ivqb29Pfz9/ZGcnKxfp9PpkJycbPImHIGBgQblgZpv2qHRaPR3KFPyTmVERERSVHWLWLo0EYpMRY2OjkZERAQGDx6MIUOGYM2aNSgqKsKsWbMAAOHh4ejQoQPi4uIAAE899RRGjhyJVatWYfz48di8eTOOHDmC9evXK1E9IiIiUpAiycW0adNw9epVLFmyBFlZWRg4cCB27NihH7SZmZlp8FjcoUOHYtOmTXj++eexaNEidO/eHdu2beM9LoiIqHmQMdujJc8WqRIVFYWoqCij21JSUqqtmzp1KqZOnapUdYiIiBoPZ4sQERER1R+fikpERKQ0dosQERGRVC2sW6R5JRd29oCNxvI45aW1l6mr4jx5sQAU5rWWFiv1SIa0WFNC/aTF+ubMdWmxAKCPp7xr5mxvJy1WG628j1839zbSYslWoTP90CRzWfMvLJnnqZb4HaKW+IWkllkxatas+bNKRETUPLBbhIiIiKRSqSQkF02n5ajppEFERETUJLDlgoiISGlqleWDaZrQmBcmF0REREprYWMumk5NiYiIqElgywUREZHSeJ8LIiIikordIkRERET1x5YLIiIipbFbhIiIiKRitwgRERFR/bHlgoiISGnsFiEiIiKp2C1CREREVH9suSAiIlIau0WIiIhILgndIk2os6Hp1JSIiIiahObVctG+E2CntTxOcZ7lMarkZcuLBQAlBfJCuXaWFuvfX/4kLVaXHl7SYgGAva28HLpn+9bSYuWVlUuL1cVNXr1k0+mEvFgSW4VtbeT+bWUv8XHYFZU6abFkkl0v2T8Dq8ZuESIiIpJKpZIwW6TpJBctKG0kIiKihsCWCyIiIqW1sPtcMLkgIiJSWgsbc9F00iAiIiJqEthyQUREpDR2ixAREZFU7BYhIiIiqj+2XBARESmN3SJEREQkFbtFiIiIiOqPLRdEREQKU6lUULWglgsmF0RERAprackFu0WIiIhIKrZcEBERKU31v8XSGE2E9JaLuLg4/O1vf4OjoyPc3NwwadIknDlzpsZ9kpKS9E1GVYtWq5VdNSIiokZx63dcfZemQnpysXfvXsybNw+HDh3Czp07UV5ejrFjx6KoqKjG/ZycnHD58mX9cuHCBdlVIyIiogYgvVtkx44dBq+TkpLg5uaGo0eP4s477zS5n0qlgoeHh+zqEBERNToO6JQsLy8PANC+ffsayxUWFsLHxwfe3t6YOHEiTp48abJsaWkp8vPzDRYiIiJr1dK6RRQd0KnT6TB//nwMGzYM/fr1M1muZ8+eSExMxIABA5CXl4eVK1di6NChOHnyJDp27FitfFxcHJYuXVptfWt3V6jtHSyud2Fea4tj6JUUyIsFAKXF8mJlp0kLVVJ0m7RYOe2dpMUCgDO/aaTF8nC0lxYrt6RCWqwR3VykxQIAnZAXS2tvIy1WRaXOKmMBgLoJ/eKvL1sbTjCkulH0nTJv3jycOHECmzdvrrFcYGAgwsPDMXDgQIwcORKffvopXF1d8fbbbxstv3DhQuTl5emXixcvKlF9IiIiKdhyIUlUVBS++uor7Nu3z2jrQ03s7Oxw++23Iy3N+F/WGo0GGo28v0aJiIgUxamolhFCICoqCp999hl2796Nzp07mx2jsrISv/zyCzw9PWVXj4iIiBQmveVi3rx52LRpEz7//HM4OjoiKysLAODs7IxWrVoBAMLDw9GhQwfExcUBAF544QXccccd6NatG3Jzc7FixQpcuHABjz76qOzqERERNbiWNltEenKxbt06AMCoUaMM1m/cuBEzZ84EAGRmZkKt/qvR5I8//kBkZCSysrLQrl07+Pv748CBA+jTp4/s6hERETW4G09ctzS5kFOXhiA9uRCi9mHmKSkpBq9fe+01vPbaa7KrQkRERI2AzxYhIiJSmAoyZns0naYLJhdEREQKa2ljLnhHFCIiIpKKLRdERERKa2H3uWByQUREpDQJ3SKC3SJERETUUrHlgoiISGEyBnTy2SJERESk19KSC3aLEBERNWPx8fHw9fWFVqtFQEAADh8+XGP5NWvWoGfPnmjVqhW8vb3x9NNPo6SkxKxjMrkgIiJSmkrSYqYtW7YgOjoaMTExOHbsGPz8/BAcHIwrV64YLb9p0yY899xziImJwalTp7BhwwZs2bIFixYtMuu4TC6IiIgUVtUtYulirtWrVyMyMhKzZs1Cnz59kJCQAAcHByQmJhotf+DAAQwbNgwPPvggfH19MXbsWISFhdXa2nErJhdERERNSH5+vsFSWlpqtFxZWRmOHj2KoKAg/Tq1Wo2goCAcPHjQ6D5Dhw7F0aNH9cnEuXPn8PXXX+Oee+4xq47NakBnn/4dYattbXGc1CMZEmpzQ4lrZ2mxAADZafJilRt/Q9ZLaZG0UFd+PSUt1g29pUX65XimtFgTxvWVFks2e1t5f3fodLU/zLCu1BIHtJVV6KTFAgBbG3mxZJ6nTDJ/lgBQISme7J+lEmQO6PT29jZYHxMTg9jY2Grlc3JyUFlZCXd3d4P17u7uOH36tNFjPPjgg8jJycHw4cMhhEBFRQWeeOIJs7tFmlVyQUREZI1kJhcXL16Ek5OTfr1Go7Eo7s1SUlLw8ssv46233kJAQADS0tLw1FNPYdmyZVi8eHGd4zC5ICIiakKcnJwMkgtTXFxcYGNjg+zsbIP12dnZ8PDwMLrP4sWL8fDDD+PRRx8FAPTv3x9FRUV47LHH8H//939Qq+vWqskxF0RERAprjAGd9vb28Pf3R3Jysn6dTqdDcnIyAgMDje5TXFxcLYGwsbnR5ydE3bux2HJBRESktEZ6cFl0dDQiIiIwePBgDBkyBGvWrEFRURFmzZoFAAgPD0eHDh0QFxcHAAgNDcXq1atx++2367tFFi9ejNDQUH2SURdMLoiIiJqpadOm4erVq1iyZAmysrIwcOBA7NixQz/IMzMz06Cl4vnnn4dKpcLzzz+P3377Da6urggNDcVLL71k1nGZXBARESmsMW//HRUVhaioKKPbUlJSDF7b2toiJiYGMTEx9TqWPo5FexMREVGt+GwRIiIiIguw5YKIiEhhbLkgIiIisgBbLoiIiJTWSFNRGwuTCyIiIoWxW4SIiIjIAmy5ICIiUlhLa7lgckFERKQwFSQkF01o0AW7RYiIiEgqtlwQEREpjN0iREREJBenojZdzg52sGtlb3GcKaF+Empzw7+//ElaLAAoKbpNXrDSInmxivPkxXJ0kRcLwJVjP0qLpfXtKS3W8TNXpcVSS/6LRqcT0mJVSIyllniaMusFAGqJlZN5njLrVVahkxYLkHeeMq8XydGskgsiIiJrxG4RIiIikqqlJRecLUJERERSseWCiIhIYSrVjcXSGE0FkwsiIiKF3UguLO0WkVSZBiC9WyQ2Nlbft1S19OrVq8Z9tm7dil69ekGr1aJ///74+uuvZVeLiIiIGogiYy769u2Ly5cv65f9+/ebLHvgwAGEhYVh9uzZOH78OCZNmoRJkybhxIkTSlSNiIio4an+6hqp79Li73Nha2sLDw+POpV9/fXXMW7cODz77LMAgGXLlmHnzp1Yu3YtEhISlKgeERFRg+JsEQnOnj0LLy8vdOnSBTNmzEBmZqbJsgcPHkRQUJDBuuDgYBw8eNDkPqWlpcjPzzdYiIiIyDpITy4CAgKQlJSEHTt2YN26dcjIyMCIESNQUFBgtHxWVhbc3d0N1rm7uyMrK8vkMeLi4uDs7KxfvL29pZ4DERGRTJZ2iciYbdKQpHeLhISE6P8/YMAABAQEwMfHB5988glmz54t5RgLFy5EdHS0/nV+fj4TDCIislpqtcriW7GLJnSfc8WnorZt2xY9evRAWlqa0e0eHh7Izs42WJednV3jmA2NRgONRiO1nkRERCSH4nfoLCwsRHp6Ojw9PY1uDwwMRHJyssG6nTt3IjAwUOmqERERNYiW1i0iPbl45plnsHfvXpw/fx4HDhzA5MmTYWNjg7CwMABAeHg4Fi5cqC//1FNPYceOHVi1ahVOnz6N2NhYHDlyBFFRUbKrRkRE1Chuvf9TfZemQnq3yKVLlxAWFoZr167B1dUVw4cPx6FDh+Dq6goAyMzMhFr9V04zdOhQbNq0Cc8//zwWLVqE7t27Y9u2bejXr5/sqhEREVEDkJ5cbN68ucbtKSkp1dZNnToVU6dOlV0VIiIiq8BnixAREZFUvIkWERERkQWaVcvFlIEecGjjaHGcb85cl1CbG7r08JIWCwBy2jtJi3Xl11PSYsHRRV6s7HR5sQCgnbyfQUlBkbRYubl/Soslm6Xz8W9mrb9k2mjl1kynE/JiCXmxoJMXyt7WOv8etbWxznrdrKW1XFjr556IiKjZaGljLqw/3SMiIqImhS0XREREClNBQrdIE3rmOpMLIiIihbFbhIiIiMgCbLkgIiJSGGeLEBERkVTsFiEiIiKyAFsuiIiIFMZuESIiIpKK3SJEREREFmDLBRERkcLYLUJERERySegWaUI36GS3CBEREcnFlgsiIiKFsVuEiIiIpOJsESIiIiILsOWCiIhIYewWISIiIqlaWrdIs0ounOzt4GBvZ3GcPp6tJdTmBntbuT1PZ37TSIzWW1qkK8d+lBYL7bzkxQKAP36XF6s4V1qorJIiabHU6vHSYgGATiekxVKr5f1GrKjUSYsFiaEAoELiNbOVec0k1ktXIfei2drIOU+p7wuSolklF0RERNaI3SJEREQkVUtLLjhbhIiIiKRiywUREZHCOKCTiIiIpGK3CBEREZEF2HJBRESkMHaLEBERkVTsFiEiIiKyAFsuiIiIFKaChG4RKTVpGEwuiIiIFKZWqaC2MLuwdP+GxG4RIiIikootF0RERArjbBEiIiKSirNFLOTr66u/iDcv8+bNM1o+KSmpWlmtViu7WkRERC1SfHw8fH19odVqERAQgMOHD9dYPjc3F/PmzYOnpyc0Gg169OiBr7/+2qxjSm+5+PHHH1FZWal/feLECdx9992YOnWqyX2cnJxw5swZ/eumlJ0RERHVRq26sVgaw1xbtmxBdHQ0EhISEBAQgDVr1iA4OBhnzpyBm5tbtfJlZWW4++674ebmhn/961/o0KEDLly4gLZt25p1XOnJhaurq8HrV155BV27dsXIkSNN7qNSqeDh4SG7KkRERNZBJeEP53rsvnr1akRGRmLWrFkAgISEBGzfvh2JiYl47rnnqpVPTEzE9evXceDAAdjZ2QG40SNhLkVni5SVleHDDz/EI488UuNFLSwshI+PD7y9vTFx4kScPHmyxrilpaXIz883WIiIiFqCW7//SktLjZYrKyvD0aNHERQUpF+nVqsRFBSEgwcPGt3niy++QGBgIObNmwd3d3f069cPL7/8skGPRF0oOqBz27ZtyM3NxcyZM02W6dmzJxITEzFgwADk5eVh5cqVGDp0KE6ePImOHTsa3ScuLg5Lly6ttr6vpzMcnZwsrrezvZ3FMar0bN9aWiwA8HC0lxbrl+OZ0mJpfXtKi1VSUCQtFgCgOFderNJiebGuX5IWSqcT0mJZM5nz/Cus+JrphLy6yXxvyKwXAFSY931VQxzr/VlWkTlbxNvb22B9TEwMYmNjq5XPyclBZWUl3N3dDda7u7vj9OnTRo9x7tw57N69GzNmzMDXX3+NtLQ0zJ07F+Xl5YiJialzXRVNLjZs2ICQkBB4eXmZLBMYGIjAwED966FDh6J37954++23sWzZMqP7LFy4ENHR0frX+fn51S42ERGRtVD975+lMQDg4sWLcLrpD2mNRmNR3JvpdDq4ublh/fr1sLGxgb+/P3777TesWLHCOpKLCxcuYNeuXfj000/N2s/Ozg6333470tLSTJbRaDRSLyYREVFT4eTkZJBcmOLi4gIbGxtkZ2cbrM/OzjY5ztHT0xN2dnawsbHRr+vduzeysrJQVlYGe/u6tZ4rNuZi48aNcHNzw/jx483ar7KyEr/88gs8PT0VqhkREVHDqpotYuliDnt7e/j7+yM5OVm/TqfTITk52aDH4GbDhg1DWloadDqdft1///tfeHp61jmxABRKLnQ6HTZu3IiIiAjY2ho2joSHh2PhwoX61y+88AK+/fZbnDt3DseOHcNDDz2ECxcu4NFHH1WiakRERA3O2P2f6rOYKzo6Gu+88w7ee+89nDp1CnPmzEFRUZF+9sit38lz5szB9evX8dRTT+G///0vtm/fjpdfftnkvapMUaRbZNeuXcjMzMQjjzxSbVtmZibU6r9ymj/++AORkZHIyspCu3bt4O/vjwMHDqBPnz5KVI2IiKjFmDZtGq5evYolS5YgKysLAwcOxI4dO/SDPG/9Tvb29sY333yDp59+GgMGDECHDh3w1FNPYcGCBWYdVyWE5OG/jSA/Px/Ozs44deGqlNkiF67Km61wraRMWiwAOPq7vGm3az8+Ki2WudOUaiJ9tkiW6fE7ZpM5W8RO3riha/tXSoslm9rSOwfdRObMB2ueLSLxkkmdSSF7tois2T/5+fnw8WyPvLy8Oo1FaEhV30/3vLEHdq3aWBSr/M9CfP3kaKs8z1vx2SJEREQK4yPXiYiIiCzAlgsiIiKF8ZHrREREJBUfuU5ERERkAbZcEBERKYzdIkRERCQVZ4sQERERWYAtF0RERApT/W+xNEZTweSCiIhIYZwtQkRERGQBtlwQEREprD6PTDcWo6loVsmFxlYNja3ljTFttPIuS15ZubRYAJBbUiEt1oRxfaXFOn7mqrRYubl/SosFAFklEh+Edv2SvFjlpdJCyXw4mGwyHzYm8zzVVvoQLkDyeaqs9wFtsthL+L2vNHaLEBEREVmgWbVcEBERWasm1PBgMSYXRERECmO3CBEREZEF2HJBRESkMM4WISIiIqnYLUJERERkAbZcEBERKYzPFiEiIiKp+Mh1IiIiIguw5YKIiEhhKpXlN9FqQg0XTC6IiIiUxtkiRERERBZgywUREZHC2C1CREREUnG2CBEREZEF2HJBRESkMHaLEBERkVQtbbZIs0ouVBKeOgcA3dzbWB7kf7q4tZYWCwBGdHORGk8Wa+4LVKvHS4ul0wlpsdQSH3HY7m9R0mIBANQ28mJ595UWqlPPTtJieXs7S4sFAP2820qL1du9lbRYfdvLO8/2beylxQIAr7ZaKXHKKnRS4pA8zSq5ICIiskZqWD7IsSkNkmRyQUREpLCW1i3SlBIhIiIiagLYckFERKQwGWMCm1DDBZMLIiIipaklJBcSx4ArzuxukX379iE0NBReXl5QqVTYtm2bwXYhBJYsWQJPT0+0atUKQUFBOHv2bK1x4+Pj4evrC61Wi4CAABw+fNjcqhEREZEVMDu5KCoqgp+fH+Lj441uf/XVV/HGG28gISEBP/zwA1q3bo3g4GCUlJSYjLllyxZER0cjJiYGx44dg5+fH4KDg3HlyhVzq0dERGR1qgZ0Wro0FWYnFyEhIXjxxRcxefLkatuEEFizZg2ef/55TJw4EQMGDMD777+P33//vVoLx81Wr16NyMhIzJo1C3369EFCQgIcHByQmJhobvWIiIisTlW3iKVLUyF1tkhGRgaysrIQFBSkX+fs7IyAgAAcPHjQ6D5lZWU4evSowT5qtRpBQUEm9yktLUV+fr7BQkRERNZBanKRlZUFAHB3dzdY7+7urt92q5ycHFRWVpq1T1xcHJydnfWLt7e3hNoTEREpo+rZIpYuTUWTvM/FwoULkZeXp18uXrzY2FUiIiIyqeqR65YuTYXU5MLDwwMAkJ2dbbA+Oztbv+1WLi4usLGxMWsfjUYDJycng4WIiIisg9TkonPnzvDw8EBycrJ+XX5+Pn744QcEBgYa3cfe3h7+/v4G++h0OiQnJ5vch4iIqClRS1qaCrNvolVYWIi0tDT964yMDKSmpqJ9+/bo1KkT5s+fjxdffBHdu3dH586dsXjxYnh5eWHSpEn6fcaMGYPJkycjKurGkxyjo6MRERGBwYMHY8iQIVizZg2Kioowa9Ysy8+QiIiokckYM9GEekXMTy6OHDmC0aNH619HR0cDACIiIpCUlIR//vOfKCoqwmOPPYbc3FwMHz4cO3bsgFb716N109PTkZOTo389bdo0XL16FUuWLEFWVhYGDhyIHTt2VBvkSURERNbP7ORi1KhREEKY3K5SqfDCCy/ghRdeMFnm/Pnz1dZFRUXpWzKIiIiaEzUsH5CpRtNpuuCzRYiIiBTW0rpFmtL4ECIiImoC2HJBRESksJb2VNRmlVzY2qhha9O8G2N0poe7mM3eVt610kmsmFryJ0hm3ayW2kZuPF2lvFhXL0gLlWkj7zzzrhdKiwUALo7a2gvVkVbiZxPIkxapp3CUFgsAHOzl/DwL/iyXEkdJKhUsHnPBbhEiIiJqsZpVywUREZE1amkDOplcEBERKayljblgtwgRERFJxZYLIiIihan+98/SGE0FkwsiIiKFsVuEiIiIyAJsuSAiIlJYS2u5YHJBRESkMJVKBZXFN9FqOtkFu0WIiIhIKrZcEBERKYzdIkRERCRVS7tDJ7tFiIiISCq2XBARESlMrVJZ/FRUS/dvSGy5ICIiUljVmAtLl/qIj4+Hr68vtFotAgICcPjw4Trtt3nzZqhUKkyaNMnsYzK5ICIiaqa2bNmC6OhoxMTE4NixY/Dz80NwcDCuXLlS437nz5/HM888gxEjRtTruEwuiIiIlKb6a1BnfZf6PFpk9erViIyMxKxZs9CnTx8kJCTAwcEBiYmJJveprKzEjBkzsHTpUnTp0qVep8vkgoiISGFqqKQsAJCfn2+wlJaWGj1mWVkZjh49iqCgoL/qoVYjKCgIBw8eNFnXF154AW5ubpg9e3a9z7dZDei0VatgK2EicIVOSKjNDTqJsQBAa28jLZbMusm8ZrLflGornRwu9b3h3VdeLAC4ekFerOI8ebH+yJYWKq+yUlosANj+nyJpsXoP8JEW62+93KTFcrCV9/sHACqFnM9AUaG8a98UeHt7G7yOiYlBbGxstXI5OTmorKyEu7u7wXp3d3ecPn3aaOz9+/djw4YNSE1NtaiOzSq5ICIiskYy73Nx8eJFODk56ddrNBrLAv9PQUEBHn74YbzzzjtwcXGxKBaTCyIiIoXJvEOnk5OTQXJhiouLC2xsbJCdbdjil52dDQ8Pj2rl09PTcf78eYSGhurX6XQ6AICtrS3OnDmDrl271q2udSpFRERETYq9vT38/f2RnJysX6fT6ZCcnIzAwMBq5Xv16oVffvkFqamp+mXChAkYPXo0UlNTq3XH1IQtF0RERAprrJtoRUdHIyIiAoMHD8aQIUOwZs0aFBUVYdasWQCA8PBwdOjQAXFxcdBqtejXr5/B/m3btgWAautrw+SCiIhIYY31bJFp06bh6tWrWLJkCbKysjBw4EDs2LFDP8gzMzMTarX8TgwmF0RERM1YVFQUoqKijG5LSUmpcd+kpKR6HZPJBRERkcLUkNAtUp+7aDUSJhdEREQK4yPXiYiIiCzAlgsiIiKFqWH5X/NNqTWAyQUREZHCVCoVVBb2a1i6f0NqSokQERERNQFsuSAiIlJYPZ+YXi1GU8HkgoiISGGNdYfOxmJ2t8i+ffsQGhoKLy8vqFQqbNu2Tb+tvLwcCxYsQP/+/dG6dWt4eXkhPDwcv//+e40xY2Nj9f1RVUuvXr3MPhkiIiJqfGYnF0VFRfDz80N8fHy1bcXFxTh27BgWL16MY8eO4dNPP8WZM2cwYcKEWuP27dsXly9f1i/79+83t2pERERWS2Xh0pSY3S0SEhKCkJAQo9ucnZ2xc+dOg3Vr167FkCFDkJmZiU6dOpmuiK2t0UfAEhERNXW8iZZkeXl5UKlU+iermXL27Fl4eXmhS5cumDFjBjIzM5WuGhERESlA0QGdJSUlWLBgAcLCwuDk5GSyXEBAAJKSktCzZ09cvnwZS5cuxYgRI3DixAk4OjpWK19aWorS0lL96/z8fACAWq2CWm15aifzougkZ5oVlTppsWQODpJw2RVjtddM4kXr1NN0q2B9ZNrYyAv2R7bEWDWP3zJL4TV5sQBUuPhIi3XmxEVpsSorhbRYf5ZVSosFAH4dKqTEKSkqkBJHSS3tPheKJRfl5eV44IEHIITAunXraix7czfLgAEDEBAQAB8fH3zyySeYPXt2tfJxcXFYunSp9DoTEREpoaXdoVORulYlFhcuXMDOnTtrbLUwpm3btujRowfS0tKMbl+4cCHy8vL0y8WL8rJ8IiIisoz05KIqsTh79ix27dqF2267zewYhYWFSE9Ph6enp9HtGo0GTk5OBgsREZG1uvV2C/Vdmgqzk4vCwkKkpqYiNTUVAJCRkYHU1FRkZmaivLwc999/P44cOYKPPvoIlZWVyMrKQlZWFsrKyvQxxowZg7Vr1+pfP/PMM9i7dy/Onz+PAwcOYPLkybCxsUFYWJjlZ0hERNTILJ2G2tSmo5o95uLIkSMYPXq0/nV0dDQAICIiArGxsfjiiy8AAAMHDjTYb8+ePRg1ahQAID09HTk5Ofptly5dQlhYGK5duwZXV1cMHz4chw4dgqurq7nVIyIiokZmdnIxatQoCGF69HFN26qcP3/e4PXmzZvNrQYREVGTwdkiREREJBVnixARERFZgC0XRERECmO3CBEREUklY7ZH00kt2C1CREREkrHlgoiISGEt7amoTC6IiIgUpoYKags7NizdvyGxW4SIiIikYssFERGRwtgtQkRERFKp/vfP0hhNBbtFiIiISCq2XBARESmM3SIkla2N3MahikqdtFhlFfJiVehqf2BdXbXRSn5byjtNqeeprsND/urK29tZWiwAyLteKC9WZaW0WCi8Ji9Weam8WABQkFN7mToqkxYJ+C2zlbRY3Tu1lRYLAC7myvkZlBbLvGLKUEmYLcJuESIiImqx2HJBRESkMHaLEBERkVQtLblgtwgRERFJxZYLIiIihbW0+1wwuSAiIlKYWnVjsTRGU8FuESIiIpKKLRdEREQKa2ndImy5ICIiIqnYckFERKSwljYVlckFERGRwlSwvFujCeUW7BYhIiIiudhyQUREpLCWNhWVyQUREZHCOFuEiIiIyAJsuSAiIlIYZ4sQERGRVCpYPtujCeUW7BYhIiIiudhyQUREpDA1VFBb2K+hbkJtF0wujKjQCWmx7CXPHbL0zXkzWxtpoaCWeJ46idcfkPvzlEnmz7Kfd1tpsQDAxVErLdb2/xRJi1Xh4iMtFgpy5MUCgMLr8mKVyrtmedIiAd//aCcxGuDdqZ2UOBUl8q6XUtgtQkRERGQBtlwQEREprYU1XTC5ICIiUhhvokVERERkAbOTi3379iE0NBReXl5QqVTYtm2bwfaZM2dCpVIZLOPGjas1bnx8PHx9faHVahEQEIDDhw+bWzUiIiLrpPrrRlr1XZpQw4X5yUVRURH8/PwQHx9vssy4ceNw+fJl/fLxxx/XGHPLli2Ijo5GTEwMjh07Bj8/PwQHB+PKlSvmVo+IiMjqqCQtTYXZYy5CQkIQEhJSYxmNRgMPD486x1y9ejUiIyMxa9YsAEBCQgK2b9+OxMREPPfcc+ZWkYiIiBqRImMuUlJS4Obmhp49e2LOnDm4du2aybJlZWU4evQogoKC/qqUWo2goCAcPHhQieoRERE1rBbWdCF9tsi4ceNw3333oXPnzkhPT8eiRYsQEhKCgwcPwsam+l2bcnJyUFlZCXd3d4P17u7uOH36tNFjlJaWorS0VP86Pz9f7kkQERFJ1NJmi0hPLqZPn67/f//+/TFgwAB07doVKSkpGDNmjJRjxMXFYenSpVJiERERkVyKT0Xt0qULXFxckJaWZnS7i4sLbGxskJ2dbbA+Ozvb5LiNhQsXIi8vT79cvHhRer2JiIhksXSmiIxHtjckxZOLS5cu4dq1a/D09DS63d7eHv7+/khOTtav0+l0SE5ORmBgoNF9NBoNnJycDBYiIiJr1cKGXJifXBQWFiI1NRWpqakAgIyMDKSmpiIzMxOFhYV49tlncejQIZw/fx7JycmYOHEiunXrhuDgYH2MMWPGYO3atfrX0dHReOedd/Dee+/h1KlTmDNnDoqKivSzR4iIiKjpMHvMxZEjRzB69Gj96+joaABAREQE1q1bh59//hnvvfcecnNz4eXlhbFjx2LZsmXQaDT6fdLT05GT89cTCadNm4arV69iyZIlyMrKwsCBA7Fjx45qgzyJiIiaJD5bpGajRo2CEKYfYf3NN9/UGuP8+fPV1kVFRSEqKsrc6hAREVm9xpwtEh8fjxUrViArKwt+fn548803MWTIEKNl33nnHbz//vs4ceIEAMDf3x8vv/yyyfKm8NkiREREzZS5d8BOSUlBWFgY9uzZg4MHD8Lb2xtjx47Fb7/9ZtZxmVwQEREprLFmi9x8B+w+ffogISEBDg4OSExMNFr+o48+wty5czFw4ED06tUL7777rn6ShTmYXBARESlM5myR/Px8g+Xmm0reTMYdsIuLi1FeXo727dubdb7Sb6LVHKglDpqpqNTJCyaZWuKkaZnXTFfDmJ76sJVYOZl1U0usV2/3VtJiAYDWVt7fHb0H+EiLdeaEvHvalEmL9D+lRfJilRv/sqiX65ekhcqpvYhZSopLpMTRlRVLidNUeHt7G7yOiYlBbGxstXL1uQP2rRYsWAAvLy+DBKUumFwQEREpTeJskYsXLxrc3+nm2ZgyvfLKK9i8eTNSUlKg1WrN2pfJBRERkcJkzhap680j63MH7CorV67EK6+8gl27dmHAgAFm15VjLoiIiJqh+twBGwBeffVVLFu2DDt27MDgwYPrdWy2XBARESlMxrNB6rN/dHQ0IiIiMHjwYAwZMgRr1qwxuAN2eHg4OnTogLi4OADA8uXLsWTJEmzatAm+vr7IysoCALRp0wZt2rSp83GZXBARESmssW7QWdsdsDMzM6FW/9WJsW7dOpSVleH+++83iGNq0KgpTC6IiIiasZrugJ2SkmLw2tgdtOuDyQUREZHS+GwRIiIikqkxny3SGDhbhIiIiKRiywUREZHCGmu2SGNhckFERKSwFjbkgt0iREREJBdbLoiIiJTWwpoumFwQEREpjLNFiIiIiCzAlgsiIiKFcbYIERERSdXChlywW4SIiIjkYsuFEeqm1PZkJdRqiddMJy8UAFTohLRYOomx1Cp5sfq2d5YW64Y8aZH+1stNWqzKSnnX7LfMVtJiATKvGIDrl+TFKi2WFyvngrxYAAolxRHlJZIiKaiFNV0wuSAiIlIYZ4sQERERWYAtF0REREqTMFukCTVcMLkgIiJSWgsbcsFuESIiIpKLLRdERERKa2FNF0wuiIiIFMbZIkREREQWYMsFERGRwvhsESIiIpKqhQ25YLcIERERycWWCyIiIqW1sKYLJhdEREQK42wRIiIiIguYnVzs27cPoaGh8PLygkqlwrZt2wy2q1Qqo8uKFStMxoyNja1WvlevXmafDBERkTVS4a8ZI/VeGvskzGB2clFUVAQ/Pz/Ex8cb3X758mWDJTExESqVClOmTKkxbt++fQ32279/v7lVIyIiskoqSUtTYfaYi5CQEISEhJjc7uHhYfD6888/x+jRo9GlS5eaK2JrW21fIiIianoUHXORnZ2N7du3Y/bs2bWWPXv2LLy8vNClSxfMmDEDmZmZSlaNiIiowVjcJSLjke0NSNHZIu+99x4cHR1x33331VguICAASUlJ6NmzJy5fvoylS5dixIgROHHiBBwdHauVLy0tRWlpqf51fn6+1Hqr1fJ+ghWVOmmxAMDWRl4+qNMJabHKKuSdp72t3JxXJ7FuOiHvmsnUvo291Hg9RfXPXX052NpIi/VnWaW0WN07tZUWCwC+/9FOWqwcaZEA5FyQF6u8tPYy5ijOkxOnokROHEW1rLmoiiYXiYmJmDFjBrRabY3lbu5mGTBgAAICAuDj44NPPvnEaKtHXFwcli5dKr2+REREZDnFukW+++47nDlzBo8++qjZ+7Zt2xY9evRAWlqa0e0LFy5EXl6efrl48aKl1SUiIlJMS+sWUSy52LBhA/z9/eHn52f2voWFhUhPT4enp6fR7RqNBk5OTgYLERGRtWpps0XMTi4KCwuRmpqK1NRUAEBGRgZSU1MNBmDm5+dj69atJlstxowZg7Vr1+pfP/PMM9i7dy/Onz+PAwcOYPLkybCxsUFYWJi51SMiIqJGZvaYiyNHjmD06NH619HR0QCAiIgIJCUlAQA2b94MIYTJ5CA9PR05OX8NWbp06RLCwsJw7do1uLq6Yvjw4Th06BBcXV3NrR4REZHV4SPXazFq1CiIWkbMP/bYY3jsscdMbj9//rzB682bN5tbDSIioiaDzxYhIiIisgCfikpERKS0lnWbCyYXRERESmthuQW7RYiIiEgutlwQEREpjLNFiIiISCrOFiEiIiKyAFsuiIiIlNbCRnQyuSAiIlJYC8st2C1CREREcrHlgoiISGGcLUJERESSWT5bpCl1jLBbhIiIiKRiy4XCbG2sN3+r0NX8dFtzqK04oba1kVe5ikppoaTyaquVGs/B3kZarMpanqJsDr8OFdJiXcwtlRYLALw7tZMWq6S4RFqsQmmRABTnyYwG5GXLiVNZJieOglpat4j1fvMRERFRk8TkgoiIiKRitwgREZHCWlq3CJMLIiIihfHZIkREREQWYMsFERGRwtgtQkRERFLx2SJEREREFmDLBRERkdJaWNMFkwsiIiKFcbYIERERkQXYckFERKQwzhYhIiIiqVrYkAt2ixAREZFcTC6IiIiUppK01EN8fDx8fX2h1WoREBCAw4cP11h+69at6NWrF7RaLfr374+vv/7a7GMyuSAiIlKYStI/c23ZsgXR0dGIiYnBsWPH4Ofnh+DgYFy5csVo+QMHDiAsLAyzZ8/G8ePHMWnSJEyaNAknTpww67hMLoiIiJqp1atXIzIyErNmzUKfPn2QkJAABwcHJCYmGi3/+uuvY9y4cXj22WfRu3dvLFu2DIMGDcLatWvNOm6zGNAphAAAFOTnN3JNmpayCp20WGqJI41sbeTmvBWV8s6zolJIi2VvK+88Zf4sAaDgz3JpsYoKi6TFKikqkBartLhMWiwAqCiRd566smJpsUR5ibRYqJAYCwAq5fwMxP/iVH0XWKOCgnyLZ3sUFNz4jsu/5btOo9FAo9FUK19WVoajR49i4cKF+nVqtRpBQUE4ePCg0WMcPHgQ0dHRBuuCg4Oxbds2s+raLJKLgoIbv3C6dfZu5JoQEVFjKSgogLOzc2NXw4C9vT08PDzQXdL3U5s2beDtbRgrJiYGsbGx1crm5OSgsrIS7u7uBuvd3d1x+vRpo/GzsrKMls/KyjKrns0iufDy8sLFixfh6OgIVQ2pYX5+Pry9vXHx4kU4OTk1YA3lYP0bV1OvP9D0z4H1b1zWWn8hBAoKCuDl5dXYValGq9UiIyMDZWWSWmmEqPY9Z6zVorE1i+RCrVajY8eOdS7v5ORkVR8Mc7H+jaup1x9o+ufA+jcua6y/tbVY3Eyr1UKr1Tb4cV1cXGBjY4Ps7GyD9dnZ2fDw8DC6j4eHh1nlTeGATiIiombI3t4e/v7+SE5O1q/T6XRITk5GYGCg0X0CAwMNygPAzp07TZY3pVm0XBAREVF10dHRiIiIwODBgzFkyBCsWbMGRUVFmDVrFgAgPDwcHTp0QFxcHADgqaeewsiRI7Fq1SqMHz8emzdvxpEjR7B+/XqzjtuikguNRoOYmBir7J+qC9a/cTX1+gNN/xxY/8bV1OvfEk2bNg1Xr17FkiVLkJWVhYEDB2LHjh36QZuZmZlQq//qxBg6dCg2bdqE559/HosWLUL37t2xbds29OvXz6zjqoQ1z90hIiKiJodjLoiIiEgqJhdEREQkFZMLIiIikorJBREREUnV7JKLxni0rAxxcXH429/+BkdHR7i5uWHSpEk4c+ZMjfskJSVBpVIZLI1xoxYAiI2NrVaXXr161biPtVz7Kr6+vtXOQaVSYd68eUbLN/b137dvH0JDQ+Hl5QWVSlXt3v9CCCxZsgSenp5o1aoVgoKCcPbs2VrjmvsZUqL+5eXlWLBgAfr374/WrVvDy8sL4eHh+P3332uMWZ/3oRL1B4CZM2dWq8u4ceNqjWsN1x+A0c+CSqXCihUrTMZsyOtP1q1ZJReN9WhZGfbu3Yt58+bh0KFD2LlzJ8rLyzF27FgUFdX8MCQnJydcvnxZv1y4cKGBalxd3759Deqyf/9+k2Wt6dpX+fHHHw3qv3PnTgDA1KlTTe7TmNe/qKgIfn5+iI+PN7r91VdfxRtvvIGEhAT88MMPaN26NYKDg1FSYvrhU+Z+hpSqf3FxMY4dO4bFixfj2LFj+PTTT3HmzBlMmDCh1rjmvA8tUdv1B4Bx48YZ1OXjjz+uMaa1XH8ABvW+fPkyEhMToVKpMGXKlBrjNtT1JysnmpEhQ4aIefPm6V9XVlYKLy8vERcXZ7T8Aw88IMaPH2+wLiAgQDz++OOK1rMurly5IgCIvXv3miyzceNG4ezs3HCVqkFMTIzw8/Orc3lrvvZVnnrqKdG1a1eh0+mMbrem6w9AfPbZZ/rXOp1OeHh4iBUrVujX5ebmCo1GIz7++GOTccz9DMlya/2NOXz4sAAgLly4YLKMue9DWYzVPyIiQkycONGsONZ8/SdOnCjuuuuuGss01vUn69NsWi6qHi0bFBSkX1eXR8veXB648WhZU+UbUl5eHgCgffv2NZYrLCyEj48PvL29MXHiRJw8ebIhqmfU2bNn4eXlhS5dumDGjBnIzMw0Wdaarz1w4/304Ycf4pFHHqnxYXjWdP1vlpGRgaysLINr7OzsjICAAJPXuD6foYaUl5cHlUqFtm3b1ljOnPeh0lJSUuDm5oaePXtizpw5uHbtmsmy1nz9s7OzsX37dsyePbvWstZ0/anxNJvkoqZHy5p6VKysR8vKptPpMH/+fAwbNqzGu6L17NkTiYmJ+Pzzz/Hhhx9Cp9Nh6NChuHTpUgPW9oaAgAAkJSVhx44dWLduHTIyMjBixAgUFBQYLW+t177Ktm3bkJubi5kzZ5osY03X/1ZV19Gca1yfz1BDKSkpwYIFCxAWFlbjA7PMfR8qady4cXj//feRnJyM5cuXY+/evQgJCUFlZaXR8tZ8/d977z04Ojrivvvuq7GcNV1/alwt6vbfTcW8efNw4sSJWvsqAwMDDR4mM3ToUPTu3Rtvv/02li1bpnQ1DYSEhOj/P2DAAAQEBMDHxweffPJJnf7asTYbNmxASEhIjY9wtqbr35yVl5fjgQcegBAC69atq7GsNb0Pp0+frv9///79MWDAAHTt2hUpKSkYM2ZMg9bFUomJiZgxY0atA5at6fpT42o2LReN+WhZmaKiovDVV19hz549Zj1GHgDs7Oxw++23Iy0tTaHa1V3btm3Ro0cPk3Wxxmtf5cKFC9i1axceffRRs/azputfdR3Nucb1+QwprSqxuHDhAnbu3Gn2Y75rex82pC5dusDFxcVkXazx+gPAd999hzNnzpj9eQCs6/pTw2o2yUVjPlpWBiEEoqKi8Nlnn2H37t3o3Lmz2TEqKyvxyy+/wNPTU4EamqewsBDp6ekm62JN1/5WGzduhJubG8aPH2/WftZ0/Tt37gwPDw+Da5yfn48ffvjB5DWuz2dISVWJxdmzZ7Fr1y7cdtttZseo7X3YkC5duoRr166ZrIu1Xf8qGzZsgL+/P/z8/Mze15quPzWwxh5RKtPmzZuFRqMRSUlJ4tdffxWPPfaYaNu2rcjKyhJCCPHwww+L5557Tl/++++/F7a2tmLlypXi1KlTIiYmRtjZ2Ylffvmlwes+Z84c4ezsLFJSUsTly5f1S3Fxsb7MrfVfunSp+Oabb0R6ero4evSomD59utBqteLkyZMNXv9//OMfIiUlRWRkZIjvv/9eBAUFCRcXF3HlyhWjdbema3+zyspK0alTJ7FgwYJq26zt+hcUFIjjx4+L48ePCwBi9erV4vjx4/rZFK+88opo27at+Pzzz8XPP/8sJk6cKDp37iz+/PNPfYy77rpLvPnmm/rXtX2GGqr+ZWVlYsKECaJjx44iNTXV4DNRWlpqsv61vQ8bqv4FBQXimWeeEQcPHhQZGRli165dYtCgQaJ79+6ipKTEZP2t5fpXycvLEw4ODmLdunVGYzTm9Sfr1qySCyGEePPNN0WnTp2Evb29GDJkiDh06JB+28iRI0VERIRB+U8++UT06NFD2Nvbi759+4rt27c3cI1vAGB02bhxo77MrfWfP3++/lzd3d3FPffcI44dO9bwlRdCTJs2TXh6egp7e3vRoUMHMW3aNJGWlqbfbs3X/mbffPONACDOnDlTbZu1Xf89e/YYfc9U1VGn04nFixcLd3d3odFoxJgxY6qdl4+Pj4iJiTFYV9NnqKHqn5GRYfIzsWfPHpP1r+192FD1Ly4uFmPHjhWurq7Czs5O+Pj4iMjIyGpJgrVe/ypvv/22aNWqlcjNzTUaozGvP1k3PnKdiIiIpGo2Yy6IiIjIOjC5ICIiIqmYXBAREZFUTC6IiIhIKiYXREREJBWTCyIiIpKKyQURERFJxeSCiIiIpGJyQURERFIxuSAiIiKpmFwQERGRVEwuiIiISKr/B1HhdJGirrDAAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(matrix_train_sirius),\n", + " interpolation='nearest', origin='upper', cmap='Blues')\n", + "axs.set_title(\"Quantum Kernel Matrix (IQM Sirius)\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "f7d3c714-e5fa-42ed-a3fc-f740f4c30b40", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Kernel matrix shape: (20, 20)\n", + "First few rows:\n", + " [[1. 0.98 0.9 0.81 0.63 0.58 0.34 0.3 0.09 0.06 0.05 0.03 0.01 0.\n", + " 0. 0. 0. 0. 0. 0. ]\n", + " [0.98 1. 0.94 0.87 0.83 0.52 0.53 0.42 0.25 0.19 0.01 0.01 0.03 0.01\n", + " 0.01 0.03 0.02 0.01 0. 0. ]\n", + " [0.9 0.94 1. 0.97 0.89 0.83 0.68 0.51 0.31 0.3 0.02 0.02 0.04 0.02\n", + " 0. 0. 0.02 0.01 0.02 0. ]\n", + " [0.81 0.87 0.97 1. 0.98 0.93 0.76 0.63 0.45 0.49 0.02 0.03 0. 0.02\n", + " 0.02 0.01 0.02 0.01 0. 0. ]\n", + " [0.63 0.83 0.89 0.98 1. 0.96 0.92 0.76 0.82 0.53 0.02 0. 0.01 0.01\n", + " 0.04 0.02 0.01 0.01 0.01 0.03]]\n", + "Diagonal:\n", + " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n", + "Mean value: 0.36254999999999993\n" + ] + } + ], + "source": [ + "print(\"Kernel matrix shape:\", matrix_train_sirius.shape)\n", + "print(\"First few rows:\\n\", matrix_train_sirius[:5])\n", + "print(\"Diagonal:\\n\", np.diag(matrix_train_sirius))\n", + "print(\"Mean value:\", np.mean(matrix_train_sirius))" + ] + }, + { + "cell_type": "markdown", + "id": "4b29e3d6-4da9-48c6-b0b3-071a3c7bbe70", + "metadata": {}, + "source": [ + "## SVR Prediction Using IQM Sirius Quantum Kernel\n", + "\n", + "This section trains a Support Vector Regression (SVR) model using the quantum kernel matrix computed from the IQM Sirius backend. The target values are log-odds of transition probabilities, and predictions are transformed back to probabilities for interpretability.\n", + "\n", + "The plot shows actual vs predicted transition probabilities across age groups, separated by gender." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "63985ab0-ce07-4b15-bed7-7430a4cbcbde", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SVR model R² score on training data (IQM Sirius): 0.7812\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Train SVR model using IQM Sirius kernel\n", + "f_matrix_train = matrix_train_sirius\n", + "svr_sirius = SVR(kernel='precomputed')\n", + "svr_sirius.fit(f_matrix_train, y, w)\n", + "\n", + "# Evaluate model\n", + "score_sirius = svr_sirius.score(f_matrix_train, y, w)\n", + "print(f\"SVR model R² score on training data (IQM Sirius): {score_sirius:.4f}\")\n", + "\n", + "# Predict and transform back to probabilities\n", + "pred = svr_sirius.predict(f_matrix_train)\n", + "p_hat = 1 / (1 + np.exp(-pred))\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# Sort data by age for smoother plots\n", + "group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", + "group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", + "group_0.sort()\n", + "group_1.sort()\n", + "\n", + "# Plot actual vs predicted transition probabilities\n", + "plt.figure(figsize=(10, 5))\n", + "plt.plot([a for a, _, _ in group_0], [p for _, p, _ in group_0], 'or', label='Group 0 Actual')\n", + "plt.plot([a for a, _, _ in group_0], [p_hat for _, _, p_hat in group_0], 'r', label='Group 0 Predicted')\n", + "plt.plot([a for a, _, _ in group_1], [p for _, p, _ in group_1], 'ob', label='Group 1 Actual')\n", + "plt.plot([a for a, _, _ in group_1], [p_hat for _, _, p_hat in group_1], 'b', label='Group 1 Predicted')\n", + "\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.title(\"SVR Prediction vs Actual by Gender (IQM Sirius Kernel)\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b8cfd0ae-797f-41b2-8425-8ba281d3f57a", + "metadata": {}, + "source": [ + "## Quantum SVR Comparison: IQM Sirius vs Statevector\n", + "\n", + "This section compares the performance of Quantum Support Vector Regression (QSVR) models using two different quantum kernels:\n", + "\n", + "- **IQM Sirius**: Kernel computed using real quantum hardware.\n", + "- **Statevector Simulation**: Kernel computed using idealized simulation.\n", + "\n", + "Both models are trained on log-odds of transition probabilities and evaluated using in-sample R² scores. Predictions are transformed back to probabilities for interpretability." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "5affd9a8-e632-4a63-a514-2423129da834", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.svm import SVR\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "# SVR with IQM Sirius kernel\n", + "f_matrix_sirius = matrix_train_sirius\n", + "svr_sirius = SVR(kernel='precomputed')\n", + "svr_sirius.fit(f_matrix_sirius, y, w)\n", + "score_sirius = svr_sirius.score(f_matrix_sirius, y, w)\n", + "pred_sirius = svr_sirius.predict(f_matrix_sirius)\n", + "p_hat_sirius = 1 / (1 + np.exp(-pred_sirius))\n", + "p_sirius = 1 / (1 + np.exp(-y))\n", + "\n", + "# SVR with Statevector kernel\n", + "f_matrix_statevector = matrix_train_statevector\n", + "svr_statevector = SVR(kernel='precomputed')\n", + "svr_statevector.fit(f_matrix_statevector, y, w)\n", + "score_statevector = svr_statevector.score(f_matrix_statevector, y, w)\n", + "pred_statevector = svr_statevector.predict(f_matrix_statevector)\n", + "p_hat_statevector = 1 / (1 + np.exp(-pred_statevector))\n", + "p_statevector = 1 / (1 + np.exp(-y))\n", + "\n", + "# Group and sort data by gender and age\n", + "def group_and_sort(x, p, p_hat):\n", + " group_0 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 0]\n", + " group_1 = [(a[1], p_val, p_hat_val) for a, p_val, p_hat_val in zip(x, p, p_hat) if a[0] == 1]\n", + " return sorted(group_0), sorted(group_1)\n", + "\n", + "group_sirius_0, group_sirius_1 = group_and_sort(x, p_sirius, p_hat_sirius)\n", + "group_statevector_0, group_statevector_1 = group_and_sort(x, p_statevector, p_hat_statevector)\n", + "\n", + "# Plot both models side-by-side\n", + "plt.figure(figsize=(12, 5))\n", + "\n", + "# IQM Sirius\n", + "plt.subplot(1, 2, 1)\n", + "plt.plot([a for a, _, _ in group_sirius_0], [p for _, p, _ in group_sirius_0], 'or', label='Group 0 Actual')\n", + "plt.plot([a for a, _, _ in group_sirius_0], [p_hat for _, _, p_hat in group_sirius_0], 'r', label='Group 0 Predicted')\n", + "plt.plot([a for a, _, _ in group_sirius_1], [p for _, p, _ in group_sirius_1], 'ob', label='Group 1 Actual')\n", + "plt.plot([a for a, _, _ in group_sirius_1], [p_hat for _, _, p_hat in group_sirius_1], 'b', label='Group 1 Predicted')\n", + "plt.title(f\"IQM Sirius Kernel\\nR² = {score_sirius:.4f}\")\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "\n", + "# Statevector\n", + "plt.subplot(1, 2, 2)\n", + "plt.plot([a for a, _, _ in group_statevector_0], [p for _, p, _ in group_statevector_0], 'or', label='Group 0 Actual')\n", + "plt.plot([a for a, _, _ in group_statevector_0], [p_hat for _, _, p_hat in group_statevector_0], 'r', label='Group 0 Predicted')\n", + "plt.plot([a for a, _, _ in group_statevector_1], [p for _, p, _ in group_statevector_1], 'ob', label='Group 1 Actual')\n", + "plt.plot([a for a, _, _ in group_statevector_1], [p_hat for _, _, p_hat in group_statevector_1], 'b', label='Group 1 Predicted')\n", + "plt.title(f\"Statevector Kernel\\nR² = {score_statevector:.4f}\")\n", + "plt.xlabel(\"Normalized Age\")\n", + "plt.ylabel(\"Transition Probability\")\n", + "plt.legend()\n", + "plt.grid(True)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8bd22be7-48bd-419c-9f4f-1240422e8523", + "metadata": {}, + "source": [ + "### 📊 Model Performance Summary\n", + "\n", + "| Model | R² Score | Interpretation |\n", + "|-------|----------|----------------|\n", + "| **Quantum SVR (IQM Sirius)** | **0.7812** | Good fit despite hardware noise. Captures most of the structure. |\n", + "| **Quantum SVR (Statevector)** | **0.9009** | Higher score due to ideal simulation. Represents best-case scenario. |\n", + "\n", + "### 🧠 Interpretation\n", + "\n", + "- The **IQM Sirius kernel** performs well, showing that quantum hardware can produce useful kernels for regression tasks.\n", + "- The **statevector kernel** performs slightly better, as expected, due to perfect simulation conditions.\n", + "- Both models successfully learn the relationship between age, gender, and transition probability.\n", + "- This comparison is valuable for teaching the difference between **ideal quantum simulation** and **real quantum execution**.\n", + "\n", + "Further evaluation (e.g., cross-validation, residual analysis) can help assess generalization and robustness." + ] + }, + { + "cell_type": "markdown", + "id": "3835ce0c-47a0-4a16-b337-44dd347a343a", + "metadata": {}, + "source": [ + "## Kernel Matrix Error Comparison\n", + "\n", + "To assess the fidelity of the quantum kernel computed on real hardware (IQM Sirius), we compare it to the ideal kernel computed via statevector simulation.\n", + "\n", + "We calculate the **absolute error matrix** between the two kernel matrices and visualize it using a heatmap. This helps identify where the quantum hardware deviates most from the ideal simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "b27c8d3d-d94f-4f1d-a982-3add9b91d42f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Compute absolute error matrix\n", + "error_matrix = np.abs(matrix_train_sirius - matrix_train_statevector)\n", + "\n", + "# Visualize the error matrix\n", + "fig, ax = plt.subplots(figsize=(10, 5))\n", + "cax = ax.imshow(error_matrix, interpolation='nearest', origin='upper', cmap='Reds')\n", + "ax.set_title(\"Absolute Error Between IQM Sirius and Statevector Kernel Matrices\")\n", + "fig.colorbar(cax, ax=ax)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "39b3171b-9870-4fde-9b86-d96e590b3a70", + "metadata": {}, + "source": [ + "## Kernel Fidelity Analysis: IQM Sirius vs Statevector\n", + "\n", + "This heatmap shows the **absolute error** between two quantum kernel matrices:\n", + "\n", + "- **IQM Sirius Kernel**: Computed using real quantum hardware.\n", + "- **Statevector Kernel**: Computed using ideal simulation.\n", + "\n", + "### 🔍 How to Interpret the Heatmap\n", + "- **Color Scale**: Darker red indicates larger discrepancies; white means near-zero error.\n", + "- **Diagonal**: Should be close to zero because both kernels have perfect self-similarity (value = 1).\n", + "- **Bright Spots**: These represent pairs of samples where hardware noise or imperfections caused the largest deviations from the ideal kernel.\n", + "- **Overall Pattern**: Most cells are light pink, meaning the kernels are fairly similar. The maximum error here is about **0.16**, which is moderate and expected for real quantum hardware.\n", + "\n", + "### 🧠 Why This Matters\n", + "- Quantum kernels are sensitive to noise and calibration errors.\n", + "- Comparing hardware kernels to ideal kernels helps us understand **fidelity** and **robustness**.\n", + "- This analysis is crucial for teaching the difference between **ideal quantum simulation** and **real quantum execution**.\n", + "\n", + "Next steps could include:\n", + "- Computing **mean and max error** for quantitative assessment." + ] + }, + { + "cell_type": "markdown", + "id": "075186d4-ea8c-47d5-919f-71b6abcbedea", + "metadata": {}, + "source": [ + "## 🏋️ Exercise: Try Other IQM Backends\n", + "\n", + "Now that you have seen how to compute quantum kernels and train SVR models using **IQM Sirius**, it's time to explore other available IQM backends:\n", + "\n", + "- **IQM Emerald**\n", + "- **IQM Garnet**\n", + "\n", + "### ✅ Your Task\n", + "1. Replace `backend=iqm_sirius` with `backend=iqm_emerald` or `backend=iqm_garnet` in the kernel computation function.\n", + "2. Compute the kernel matrix for the new backend.\n", + "3. Train an SVR model using the new kernel matrix.\n", + "4. Compare:\n", + " - **R² scores**\n", + " - **Prediction plots**\n", + " - **Kernel error heatmaps** (vs statevector kernel)\n", + "5. Summarize your observations:\n", + " - Which backend produced the most accurate kernel?\n", + " - How does hardware noise affect SVR performance?\n", + "\n", + "### 💡 Hint\n", + "Use the same workflow:\n", + "- `train_kernel_matrix_x1(x1, build_feature_map, backend=iqm_emerald)`\n", + "- Fit SVR with `kernel='precomputed'`\n", + "- Transform predictions back to probabilities\n", + "- Visualize and compare results\n", + "\n", + "Good luck! 🎯" + ] + }, + { + "cell_type": "markdown", + "id": "07250a78-be17-4748-aa4e-891361186208", + "metadata": {}, + "source": [ + "## ✅ Summary of What We Did\n", + "\n", + "- Generated a synthetic dataset simulating disability insurance transitions.\n", + "- Built a **quantum feature map** using Ry rotations.\n", + "- Computed quantum kernel matrices using:\n", + " - **Statevector simulation** (ideal conditions)\n", + " - **IQM Sirius backend** (real hardware)\n", + "- Trained **Support Vector Regression (SVR)** models on quantum kernels.\n", + "- Compared predictions and R² scores for both kernels.\n", + "- Visualized:\n", + " - Actual vs predicted transition probabilities\n", + " - Kernel fidelity using error heatmaps\n", + "- Discussed the impact of hardware noise and kernel normalization.\n", + "\n", + "This notebook demonstrates how quantum machine learning can be applied to actuarial problems and provides a foundation for experimenting with different quantum backends." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5e37214b-1a22-4530-a442-d8d38452d3ab", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7e503ccb-bf2e-4115-9371-3bc7ac122ffd", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5ea146c8-6175-486b-87cd-730eb2acf6cd", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ab9d1602-180f-401f-a14f-4e8e65b86140", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "87795efb-9b76-4a49-b792-0e34909e3128", + "metadata": {}, + "source": [ + "### VTT HELMI results 2023" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fcc71d8f-2023-4e91-bbe8-97733bd24e9d", + "metadata": { + "id": "e09a4a10-61a5-4f02-92a3-2bdd33a5e7ba", + "outputId": "226f709d-e913-4db8-b7c4-eb6c27ac180c" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(K_helmi),\n", + " interpolation='nearest', origin='upper', cmap='Blues')\n", + "axs.set_title(\"kernel matrix from Helmi\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "3ab74e22-d559-46b8-8777-396d0af98e79", + "metadata": { + "id": "3ab74e22-d559-46b8-8777-396d0af98e79" + }, + "source": [ + "**Kernel Matrix Construction**: The script constructs a kernel matrix `K_helmi` using the estimates. The kernel matrix is a symmetric matrix where each element represents a measure of similarity between two data points." + ] + }, + { + "cell_type": "markdown", + "id": "9f7f0f1d-bf79-45fd-9763-2b448c10c884", + "metadata": { + "id": "9f7f0f1d-bf79-45fd-9763-2b448c10c884" + }, + "source": [ + " **Kernel Matrix Visualization**: The kernel matrix is then visualized using matplotlib's `imshow` function. The color map 'Blues' is used, and a color bar is added for reference." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "77e7a3fc-3bd0-4d7f-acb7-17e5fbb2132e", + "metadata": { + "id": "77e7a3fc-3bd0-4d7f-acb7-17e5fbb2132e", + "outputId": "e8f46872-0507-4837-920b-4046bad19bf8" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "score: 0.9001754733534563\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "f_matrix_train = K_helmi\n", + "\n", + "zzpc_svr = SVR(kernel='precomputed')\n", + "zzpc_svr.fit(f_matrix_train, y, w)\n", + "zzpc_score = zzpc_svr.score(f_matrix_train, y, w)\n", + "print(f'score: {zzpc_score}')\n", + "pred = zzpc_svr.predict(f_matrix_train)\n", + "\n", + "p_hat = 1/(1+np.exp(-pred))\n", + "p = 1/(1+np.exp(-y))\n", + "plt.figure()\n", + "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p) if a[0] == 0],'or')\n", + "plt.plot([a[1] for a in x if a[0] == 0], [p for a,p in zip(x,p_hat) if a[0] == 0],'r')\n", + "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p) if a[0] == 1],'ob')\n", + "plt.plot([a[1] for a in x if a[0] == 1], [p for a,p in zip(x,p_hat) if a[0] == 1],'b')\n", + "plt.legend(['Group 0', 'Group 0 model', 'Group 1', 'Group 1 model'])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5e211b3e-7c28-4de0-967d-14bb3c502bd8", + "metadata": { + "id": "5e211b3e-7c28-4de0-967d-14bb3c502bd8" + }, + "source": [ + "**Error Calculation and Visualization**: Finally, the script calculates the absolute errors between `K_helmi` and `matrix_train`, visualizes these errors using `imshow`, and displays this with a color bar for reference." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8a3b538d-9deb-418a-9a3c-4e14590e6074", + "metadata": { + "id": "8a3b538d-9deb-418a-9a3c-4e14590e6074" + }, + "outputs": [], + "source": [ + "# redo the steps for statevector kernel to compare with the Helmi results\n", + "\n", + "zz_kernel = QuantumKernel(feature_map=qc, quantum_instance=Aer.get_backend('statevector_simulator'))\n", + "zz_circuit = zz_kernel.construct_circuit(ParameterVector('x_i', length=2),ParameterVector('x_j', length=2))\n", + "zz_circuit.decompose().draw(output='mpl')\n", + "matrix_train = zz_kernel.evaluate(x_vec=x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "errors = np.abs(K_helmi - matrix_train)\n", + "\n", + "fig, axs = plt.subplots(1, 1, figsize=(10, 5))\n", + "pos = axs.imshow(np.asmatrix(errors),\n", + " interpolation='nearest', origin='upper', cmap='Reds')\n", + "axs.set_title(\"erorrs\")\n", + "fig.colorbar(pos, ax=axs)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "47fa3d94-0b0e-41f9-ba3b-4571be968882", + "metadata": { + "id": "47fa3d94-0b0e-41f9-ba3b-4571be968882" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3ca65f4a-c3b7-43da-b27b-35bf2a7c73d1", + "metadata": { + "id": "3ca65f4a-c3b7-43da-b27b-35bf2a7c73d1" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "nNAylO7d-4iF", + "metadata": { + "id": "nNAylO7d-4iF" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "_mqodsqI-4kK", + "metadata": { + "id": "_mqodsqI-4kK" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "RoP5NvHh-4mp", + "metadata": { + "id": "RoP5NvHh-4mp" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d1960e7f-a57d-4047-b7eb-6054e37ee913", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "d1960e7f-a57d-4047-b7eb-6054e37ee913", + "outputId": "2412fed3-f003-4c32-c3d0-24478e6c35d3" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " ┌──────────┐\n", + "q.0: ┤ Rx(π*x0) ├\n", + " ├──────────┤\n", + "q.1: ┤ Rz(π*x1) ├\n", + " └──────────┘\n" + ] + } + ], + "source": [ + "# solution ex1.1\n", + "\n", + "from qrisp import QuantumVariable, rx, rz\n", + "from sympy import symbols\n", + "import numpy as np\n", + "\n", + "def build_feature_map(sym):\n", + " n = 2\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n))\n", + " rx(np.pi * params[0], q[0])\n", + " rz(np.pi * params[1], q[1])\n", + " return q\n", + "\n", + "feature_map = build_feature_map('x')\n", + "print(feature_map.qs.transpile())\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "__-88RBE-4_g", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "__-88RBE-4_g", + "outputId": "da284955-5d98-42c5-b20f-5f075f7efb18" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " ┌──────────┐┌───┐ \n", + "q.0: ┤ Ry(π*x0) ├┤ H ├──■──\n", + " ├──────────┤└───┘┌─┴─┐\n", + "q.1: ┤ Ry(π*x1) ├─────┤ X ├\n", + " └──────────┘ └───┘\n" + ] + } + ], + "source": [ + "# solution ex1.2\n", + "\n", + "from qrisp import QuantumVariable, ry, h, cx\n", + "\n", + "def build_feature_map(sym):\n", + " n = 2\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n))\n", + " ry(np.pi * params[0], q[0])\n", + " ry(np.pi * params[1], q[1])\n", + " h(q[0])\n", + " cx(q[0], q[1])\n", + " return q\n", + "\n", + "feature_map = build_feature_map('x')\n", + "print(feature_map.qs.transpile())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "eq41tPVY-5B2", + "metadata": { + "id": "eq41tPVY-5B2" + }, + "outputs": [], + "source": [ + "# solution ex1.3\n", + "\n", + "from qrisp import QuantumVariable, ry\n", + "from sympy import symbols\n", + "import numpy as np\n", + "\n", + "def build_feature_map(sym):\n", + " n = 2\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n))\n", + " ry(np.sin(params[0] * np.pi), q[0])\n", + " ry(np.log1p(params[1]) * np.pi, q[1])\n", + " return q\n", + "\n", + "feature_map = build_feature_map('x')\n", + "print(feature_map.qs.transpile())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "kkFik42y_LIc", + "metadata": { + "id": "kkFik42y_LIc" + }, + "outputs": [], + "source": [ + "# solution ex1.4\n", + "\n", + "from qrisp import QuantumVariable, ry\n", + "from sympy import symbols\n", + "import numpy as np\n", + "\n", + "def build_feature_map(sym):\n", + " n = 3\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n))\n", + " for i in range(n):\n", + " ry(np.pi * params[i], q[i])\n", + " return q\n", + "\n", + "feature_map = build_feature_map('x')\n", + "print(feature_map.qs.transpile())\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "whov_4CX-5Di", + "metadata": { + "id": "whov_4CX-5Di" + }, + "outputs": [], + "source": [ + "# solution ex2\n", + "\n", + "# Transform actual values to probabilities\n", + "p = 1 / (1 + np.exp(-y))\n", + "\n", + "# Compute residuals\n", + "residuals_qsvr = p - p_hat_q\n", + "residuals_classical = p - p_hat_c\n", + "\n", + "# Plot histogram of Quantum SVR residuals\n", + "plt.figure(figsize=(12, 5))\n", + "\n", + "plt.subplot(1, 2, 1)\n", + "plt.hist(residuals_qsvr, bins=20, color='skyblue', edgecolor='black')\n", + "plt.xlabel('Residuals (Actual - Predicted)')\n", + "plt.ylabel('Frequency')\n", + "plt.title('Histogram of Residuals - Quantum SVR')\n", + "plt.grid(True)\n", + "\n", + "# Plot histogram of Classical SVR residuals\n", + "plt.subplot(1, 2, 2)\n", + "plt.hist(residuals_classical, bins=20, color='salmon', edgecolor='black')\n", + "plt.xlabel('Residuals (Actual - Predicted)')\n", + "plt.ylabel('Frequency')\n", + "plt.title('Histogram of Residuals - Classical SVR')\n", + "plt.grid(True)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "gyvxsT5A-5Fo", + "metadata": { + "id": "gyvxsT5A-5Fo" + }, + "outputs": [], + "source": [ + "# solution ex3\n", + "\n", + "from qrisp import ry\n", + "\n", + "# Define a simple feature map using Ry rotations\n", + "def build_feature_map(sym):\n", + " n = 2 # Number of qubits\n", + " q = QuantumVariable(n)\n", + " params = symbols(sym + ':' + str(n)) # Create symbolic parameters: x:0, x:1\n", + " ry(np.pi * params[0], q[0]) # Apply Ry rotation to qubit 0\n", + " ry(np.pi * params[1], q[1]) # Apply Ry rotation to qubit 1\n", + " return q\n", + "\n", + "# Build the feature map\n", + "feature_map = build_feature_map('x')\n", + "\n", + "# Inspect the quantum state\n", + "print(feature_map.qs)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7GyO8oYR-5Hn", + "metadata": { + "id": "7GyO8oYR-5Hn" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7555c919-f7b5-426f-8ebc-dfbff645d353", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e2d054ff-7a56-4328-b00e-5ef1bfa2c2b8", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dab61015-f08a-4471-aeef-0ba6cacb433e", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "eaae61c0-9258-4bf7-a929-065ab90d36aa", + "metadata": { + "id": "eaae61c0-9258-4bf7-a929-065ab90d36aa" + }, + "source": [ + "#### TEST CODE" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3397e118-363f-4cb2-b0aa-3166d83ae03f", + "metadata": { + "id": "3397e118-363f-4cb2-b0aa-3166d83ae03f" + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6d2dad5d-6493-460a-a5d6-898448124f31", + "metadata": { + "id": "6d2dad5d-6493-460a-a5d6-898448124f31" + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.14" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}