Sensitive dependence on initial conditions in gene networks
Bibliographic record
Abstract
Active regulation in gene networks poses mathematical challenges that have led to conflicting approaches to analysis. Competing regulation that keeps concentrations of some transcription factors at or near threshold values leads to so-called singular dynamics when steeply sigmoidal interactions are approximated by step functions. An extension, due to Artstein and coauthors, of the classical singular perturbation approach was suggested as an appropriate way to handle the complex situation where non-trivial dynamics, such as a limit cycle, of fast variables occur in switching domains. This non-trivial behaviour can occur when a gene regulates multiple other genes at the same threshold. Here, it is shown that it is possible for nonuniqueness to arise in such a system in the case of limiting step-function interactions. This nonuniqueness is reminiscent of but not identical to the nonuniqueness of Filippov solutions. More realistic gene network models have sigmoidal interactions, however, and in the example considered here, it is shown numerically that the corresponding phenomenon in smooth systems is a sensitivity to initial conditions that leads in the limit to densely interwoven basins of attraction of different fixed point attractors.
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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 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".