Continuity of Resetting a Pacemaker in an Excitable Medium
Bibliographic record
Abstract
Pacemakers in excitable media generate waves that propagate outward from the pacemaker. Such waves of excitation are well known in biological and chemical systems such as nerves, the heart, and the Belousov–Zhabotinsky reaction. Stimuli delivered at a distant site from the pacemaker can reset the pacemaker, leading to a change in the timing of the pacemaker. The relation between stimulus timing and resultant resetting of the pacemaker is captured by phase resetting curves. The continuity of resetting curves has been investigated in both experiments and numerical models. We present theoretical results discussing conditions for continuity of resetting curves as the amplitude and phase of the stimulus varies. We also use continuation and shooting methods to analyze the continuity of resetting curves in simple mathematical models of cardiac and neural activity. Under continuous changes of stimulus parameters, resetting curves will be continuous unless a stimulus leads to dynamics that fall outside the basin of attraction of the pacemaker-driven excitable medium.
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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 | 0.006 |
| 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 | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".