Turing Pattern Formation from the Cooperation of Competition and Cross-Diffusion
Why this work is in the frame
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Bibliographic record
Abstract
This paper investigates the pattern formation in a reaction–diffusion (R-D) system where two interacting species form coupled positive and negative feedback loops. It is found that the cooperation of competition and cross-diffusion can lead to the Turing pattern formation for which an adequate set of conditions are analytically derived. Such a mechanism of generating Turing patterns is different from the case that self-diffusion is sufficient to generate Turing patterns in a paradigm model (proverbially called as the Turing model) where two interacting species constitute a single negative feedback loop. Therefore, this work not only provides another model paradigm for studying the pattern formation but also would be helpful for understanding the formation of, for example, diversiform skin patterns in the mammalian world where coupled positive and negative feedback loops are ubiquitous.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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