Separable Parameter Estimation Method for Nonlinear Biological Systems
Bibliographic record
Abstract
Models for biological systems derived from the generalized mass action law are typically a group of nonlinear ordinary differential equations. However, parameters in such models can be separated into two groups: one group of parameters linear in the model and another group of parameters nonlinear in the model. This paper introduces a separable parameter estimation method to estimate the parameters in such models. The separable parameter estimation method has three steps: in the first step, parameters linear in a model are estimated by optimizing the objective function using linear least squares method, assuming all parameters nonlinear in the model are known. In the second step, substituting the estimated parameters in the first step into the objective function yields a new objective function which is only of parameters nonlinear in the model. Then parameters nonlinear in the model are estimated by proper nonlinear estimation methods. In the last step, the estimates of parameters linear in the model are calculated using the estimates of parameters in the second step. To investigate its performance, the separable estimation method is applied to a biological system and is compared with the conventional parameter estimation methods. Simulation results show the improvement of the separable estimation method.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".