Merging-emerging systems can describe spatio-temporal patterning in a chemotaxis model
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Bibliographic record
Abstract
In a recent study (K.J. Painter and T. Hillen, Spatio-temporal chaos in a chemotaxismodel, Physica D, 240 (4), 363-375, 2011) a model for chemotaxis incorporatinglogistic growth was investigated for its pattern formation properties. In particular,a variety of complex spatio-temporal patterning was found, including stationary,periodic and chaotic. Complicated dynamics appear to arise through asequence of ``merging and emerging'' events: the merging of two neighbouringaggregates or the emergence of a new aggregate in an open space. In thispaper we focus on a time-discrete dynamical system motivated by thesedynamics, which we call the merging-emerging system (MES). We introduce this newclass of set-valued dynamical systems and analyse its capacity to generate similar``pattern formation'' dynamics. The MES shows remarkably close correspondencewith patterning in the logistic chemotaxis model, strengthening our assertionthat the characteristic length scales of merging and emerging are responsiblefor the observed dynamics. Furthermore, the MES describes a novel class ofpattern-forming discrete dynamical systems worthy of study in its own right.
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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 | 0.000 |
| 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) | 0.000 | 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