Adaptive time-stepping in the numerical solution of the reaction-diffusion master equation
Bibliographic record
Abstract
Stochastic modeling and simulation are essential tools for studying cellular processes. The dynamics of spatially heterogeneous biochemical systems with species in low amounts is governed by a discrete, stochastic model, the Reaction-Diffusion Master Equation (RDME). The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is an exact numerical method for the RDME, but is prohibitively slow as it simulates every chemical reaction and diffusion event. To overcome this difficulty, an approximate strategy, the tau-leaping scheme, was developed that steps over multiple reactions and diffusion events. Mathematical models of biochemical systems are often prone to stiffness, thus computationally challenging. In this thesis, we propose an adaptive time-stepping scheme for the tau-leaping method for the RDME. This strategy is compared to the ISSA, for several models of interest. The numerical results show that the proposed adaptive technique significantly speeds-up the simulation, while maintaining excellent accuracy of the numerical solution.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".