Bibliographic record
Abstract
The response of nonlinear systems with slow variation of a parameter through a bifurcation may be critically affected by very-low-level noise. Examples to be discussed include passage through resonance of a periodically pumped laser, a transcritical bifurcation associated with a coupled pitch/roll model of ship motion, and a period-doubling cascade of a discrete map. In each case the original form of the response persists as the control parameter varies through the bifurcation, even though this original form is now unstable. Noise is required to trigger the bifurcated form; then there is a rapid transition with exponential growth from one form of response to another. Sinusoidal parameter variation through the bifurcation at sufficiently high frequency may effectively stabilize the original form by preventing an appreciable growth of the bifurcated form; noise is destabilizing. The two competing effects are analyzed using matched-asymptotic-expansions. The innermost of a nested set of three expansions describes how noise causes the growth of the bifurcating form from the original unstable form. Previous results for period-doubling [H. G. Davies and K. Rangavajhula, Proc R. Soc. London, Ser. A 457, 2965–2982 (2001)] are modified for the other types of bifurcation, and are extended to a higher order period-doubling cascade using renormalization.
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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 | 0.000 |
| 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".