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1 | 1 | # Research Agenda |
2 | 2 |
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3 | | -## To what extent is BioModels linear? |
| 3 | +## How well can BioModels be modelled by a system of linear differential equaitons? |
4 | 4 | - [x] Fit first order monomial to all models and calculate $R^2$ for species time courses. |
5 | 5 | - Minimum $R^2$ is model $R^2$ |
6 | 6 | - Individual $R^2$ are for species. |
7 | 7 | - [x] Evaluate the density of coefficients in the Jacobian. |
8 | 8 | - [ ] For the linear models, assess their dimensionality to see if dimension reduction is possible |
9 | 9 | - [ ] Characterize the linear models based on the what is being model and possibly other characteristics. |
10 | | - |
11 | | -## What are the main reasons for nonlinear behavior? |
12 | | -- [ ] Analyze the nonlinear models to determine which species are nonlinear and how/when the Jacobian changes to look at reactions. |
13 | 10 |
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14 | 11 | ## How robust is linearity to perturbations of initial values? |
15 | 12 | - [ ] repeat the linear studies with perturbations of $\pm 5\%$, $\pm 19\%$, $\pm 20\%$, and $\pm 50\%$. |
16 | 13 | - [ ] Can robustness be improved by training the regression on perturbation data? |
17 | 14 |
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| 15 | +## What are the main reasons for nonlinear behavior? |
| 16 | +- [ ] Analyze the nonlinear models to determine which species are nonlinear and how/when the Jacobian changes to look at reactions. |
| 17 | + |
18 | 18 | ## Are some nonlinear models piecewise linear? |
19 | | -- [ ] Use a standard package for partitioning regressions to see if linearity can be achieved in segements of the time course. |
| 19 | +- [ ] Use a standard package for partitioning regressions to see if linearity can be achieved in segements of the time course. |
| 20 | + - [ ] Normalize Jacobians |
| 21 | + - [ ] k-means cluster with cluster distances with minimum cluster size. |
| 22 | + - [ ] SystemDiscovery for each cluster |
| 23 | + - [ ] Prediction using: (a) ${\bf x} (t)$ using SystemDiscover of cluster at $t$ similarly for adjacent time points; (b) apply gaussian kernel on points; (c) denormalize |
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