DELAY-INDEPENDENT STABILITY OF GENETIC REGULATORY NETWORKS WITH TIME DELAYS
Bibliographic record
Abstract
In an organism, genes encode proteins, some of which in turn regulate other genes. Such interactions work in highly structured but incredibly complex ways, and make up a genetic regulatory network. Recently, nonlinear delay differential equations have been proposed for describing genetic regulatory networks in the state-space form. In this paper, we study stability properties of genetic regulatory networks with time delays, by the notion of delay-independent stability. We first present necessary and sufficient conditions for delay-independent local stability of genetic regulatory networks with a single time delay, and then extend the main result to genetic regulatory networks with multiple time delays. To illustrate the main theory, we analyze delay-independent stability of three genetic regulatory networks in E. coli or zebra fish. For E. coli, an autoregulatory network and a repressilatory network are analyzed. The results show that these two genetic regulatory networks with parameters in the physiological range are delay-independently robustly stable. For zebra fish, an autoregulatory network for the gene her1 is analyzed. The result shows that delay-independent stability of this network depends on the initial number of protein molecules, which is in agreement with the existing biological knowledge. The theories presented in this paper provide a very useful complement to the previous work and a framework for further studying the stability of more complex genetic regulatory networks.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".