Bibliographic record
Abstract
Glass networks have been proposed as a model framework for gene regulation, chemical kinetics and neural networks. Their main distinguishing feature is that although the network variables evolve continuously in time, interactions between them depend discontinuously on their sign (i.e. above or below a threshold). While this is a simplification, it has tremendous analytic advantages if the approximation is reasonable in an application. This study explores and classifies bifurcations in Glass networks, and relates them to bifurcations of smooth systems. These bifurcations can often not be studied with traditional bifurcation theory, as the vector fields are discontinuous. However, the theory that has been developed for periodic orbits of Glass networks allows a natural classification for bifurcations of periodic orbits. Some of these are shown to correspond to smooth-system bifurcations, others are shown to fit into the framework of "C-bifurcations" or "border-collision bifurcations" and others are shown to allow truly ambiguous behavior, for which Filippov's theory for discontinuous vector fields is an appropriate tool. Routes to chaos are also explored, and it is demonstrated that period-doubling cascades do not occur. However, sudden transitions to chaos, which are common in Glass networks, can result in a limiting sense from compression to a point of a period-doubling cascade in corresponding networks with sigmoidal interactions as the sigmoid's gain is increased. Other phenomena such as intermittency and multistability are also discussed.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".