Bibliographic record
Abstract
Electrical propagation in excitable tissue, such as nerve bers and heart muscle, is described by a nonlinear di usion-reaction parabolic partial di erential equation for the transmembrane voltage V (x; t), known as the cable equation. This equation involves a highly nonlinear source term, representing the total ionic current across the membrane, governed by a Hodgkin-Huxley type ionic model, and requires the solution of a system of ordinary di erential equations. Thus, the model consists of a PDE (in 1-, 2or 3-dimensions) coupled to a system of ODEs, and it is very expensive to solve, especially in 2 and 3 dimensions. To solve this problem numerically, we develop and implement an extension of the time-parallel Parareal Algorithm, introduced by Lions-Maday-Turinici in 2001, to e ciently incorporate space-parallelized solvers into the time-parallelization framework of the Parareal algorithm, to achieve time-and-space parallelization. We analyze the speedup, e ciency, and scaling of space-only, time-only, and timeand-space parallel algorithms, and determine conditions under which each is likely to perform well. We present numerical results and comparison of the performance of several serial, space-parallelized and time-and-space-parallelized time-stepping numerical schemes in one-dimension and in two-dimensions on the electrical potential propagation problem. Finally, we conduct extensive numerical experiments of action potential propagation in cardiac tissue in one and two dimensions, to determine the e ect of varying
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 0.003 |
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".