Biological aggregations from spatial memory and nonlocal advection
Why this work is in the frame
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Bibliographic record
Abstract
We investigate a nonlocal reaction–diffusion–advection model of a population of organisms that integrates spatial memory of previously visited locations and nonlocal detection in space, resulting in a coupled PDE–ODE system reflective of several models found in spatial ecology. Our study advances the mathematical understanding of such models by proving the existence and uniqueness of a global weak solution in one spatial dimension using an iterative approach. This result includes potentially discontinuous detection kernels, explicitly emphasizing the so-called ‘top-hat’ detection function, and does not place any restriction on the rate of advection, thereby addressing some analytical voids in the mathematical discourse on such models. A comprehensive spectral and stability analysis is also performed, providing analytical expressions for bifurcation values contingent on various model parameters, such as species advection rate, diffusion rate, memory uptake and decay rates. Unlike classical reaction–diffusion systems, the point spectrum may now include elements that have an infinite-dimensional kernel. We show the existence of such a point and that it remains negative, ensuring that it does not influence the stability of the constant steady state. Linear stability analysis then provides critical values for destabilizing the constant steady state. We explicitly describe the form of the non-constant steady state near these critical values and classify the nature of the pitchfork bifurcation as forward/backward and stable/unstable. To complement our analytical insights, we explore a targeted case study of three particular instances with the top-hat detection function. Using a pseudo-spectral method, we depict a numerical bifurcation diagram showing cases with sub or supercritical behaviour.
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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 | 0.000 |
| 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