Linear and Nonlinear Speed Selection for Mono-Stable Wave Propagations
Why this work is in the frame
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Bibliographic record
Abstract
In this paper, we study the selection mechanism of the minimal wave speed for traveling waves to an abstract monotone semiflow. A necessary and sufficient condition for the nonlinear selection of the minimal wave speed is established. Based on this result, we then derive conditions under which the linear or nonlinear selection is realized by way of a comparison principle. Our results on nonlinear selection are new and novel, and they can be viewed as breakthroughs in this topic; and for the linear selection, we successfully improve previous conventional results that always require that the monotone semiflow is dominated by its linear map. The applications to various biological models are also successful. We establish a series of new results to reaction-diffusion models with delay interactions, a lattice system, a scalar integro-difference equation, and a cooperative system, which completely solve some open problems and conjectures in the related references.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.003 | 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 it