Evolution of moments and correlations in nonrenewal escape-time processes
Bibliographic record
Abstract
The theoretical description of nonrenewal stochastic systems is a challenge. Analytical results are often not available or can be obtained only under strong conditions, limiting their applicability. Also, numerical results have mostly been obtained by ad hoc Monte Carlo simulations, which are usually computationally expensive when a high degree of accuracy is needed. To gain quantitative insight into these systems under general conditions, we here introduce a numerical iterated first-passage time approach based on solving the time-dependent Fokker-Planck equation (FPE) to describe the statistics of nonrenewal stochastic systems. We illustrate the approach using spike-triggered neuronal adaptation in the leaky and perfect integrate-and-fire model, respectively. The transition to stationarity of first-passage time moments and their sequential correlations occur on a nontrivial time scale that depends on all system parameters. Surprisingly this is so for both single exponential and scale-free power-law adaptation. The method works beyond the small noise and time-scale separation approximations. It shows excellent agreement with direct Monte Carlo simulations, which allow for the computation of transient and stationary distributions. We compare different methods to compute the evolution of the moments and serial correlation coefficients (SCCs) and discuss the challenge of reliably computing the SCCs, which we find to be very sensitive to numerical inaccuracies for both the leaky and perfect integrate-and-fire models. In conclusion, our methods provide a general picture of nonrenewal dynamics in a wide range of stochastic systems exhibiting short- and long-range correlations.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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) | 0.001 | 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".