COLLECTIVE BEHAVIOR OF BIOLOGICAL AGGREGATIONS IN TWO DIMENSIONS: A NONLOCAL KINETIC MODEL
Bibliographic record
Abstract
We construct and investigate a new nonlocal kinetic model for the formation and movement of animal groups in two dimensions. The model generalizes to two dimensions, the one-dimensional hyperbolic model from (R. Eftimie, G. de Vries, M. A. Lewis and F. Lutscher, Modeling group formation and activity patterns in self-organizing collectives of individuals, Bull. Math. Biol.69 (2007) 1537–1566). The main modeling aspect in the present approach concerns the assumptions we make on the turning rates, to include, in a nonlocal fashion, the three types of social interactions that act among individuals of a group: attraction, repulsion and alignment. We show that solutions to the new mathematical model are bounded, along with their gradients. We also present numerical results to illustrate three types of group formations that we obtained with the new model, starting from random initial conditions: (i) swarms (aggregation into a group, with no preferred direction of motion), (ii) parallel/translational motion (uniform spatial density, movement in a certain preferred direction) and (iii) parallel groups (aggregation into a group, with movement in a preferred direction).
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".