Synchronized Memory-Dependent Intracellular Oscillations for a Cell-Bulk ODE-PDE Model in \(\boldsymbol {\mathbb {R}^2}\)
Bibliographic record
Abstract
Abstract. For a cell-bulk ODE-PDE model in [Formula: see text], a hybrid asymptotic-numerical theory is developed to provide a new theoretical and computationally efficient approach for studying how oscillatory dynamics associated with spatially segregated dynamically active “units” or “cells” are regulated by a PDE bulk diffusion field that is both produced and absorbed by the entire cell population. The study of oscillator synchronization in a PDE diffusion field was one of the initial aims of Yoshiki Kuramoto’s foundational work. For this cell-bulk model, strong localized perturbation theory, as extended to a time-dependent setting, is used to derive a new integro-differential ODE system that characterizes intracellular dynamics in a memory-dependent bulk diffusion field. For this nonlocal reduced system, a novel fast time-marching scheme, relying in part on the sum-of-exponentials method to numerically treat convolution integrals, is developed to rapidly and accurately compute numerical solutions to the integro-differential system over long time intervals. For a particular choice of two-component reaction kinetics, a wide variety of large-scale oscillatory dynamical behavior including phase synchronization, mixed-mode oscillations, and quorum-sensing are illustrated for various ranges of the influx and efflux permeability parameters, the bulk degradation rate and bulk diffusivity, and the specific spatial configuration of cells. Results from our fast algorithm, obtained in under one minute of CPU time on a laptop, are benchmarked against PDE simulations of the cell-bulk model, which are performed with a commercial PDE solver, that have run-times that are orders of magnitude larger.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".