Variable time-stepping in the pathwise numerical solution of the chemical Langevin equation
Bibliographic record
Abstract
Stochastic modeling is essential for an accurate description of the biochemical network dynamics at the level of a single cell. Biochemically reacting systems often evolve on multiple time-scales, thus their stochastic mathematical models manifest stiffness. Stochastic models which, in addition, are stiff and computationally very challenging, therefore the need for developing effective and accurate numerical methods for approximating their solution. An important stochastic model of well-stirred biochemical systems is the chemical Langevin Equation. The chemical Langevin equation is a system of stochastic differential equation with multidimensional non-commutative noise. This model is valid in the regime of large molecular populations, far from the thermodynamic limit. In this paper, we propose a variable time-stepping strategy for the numerical solution of a general chemical Langevin equation, which applies for any level of randomness in the system. Our variable stepsize method allows arbitrary values of the time-step. Numerical results on several models arising in applications show significant improvement in accuracy and efficiency of the proposed adaptive scheme over the existing methods, the strategies based on halving/doubling of the stepsize and the fixed step-size ones.
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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 | 0.001 | 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 | 0.000 |
| 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".