Optimization of First Passage Times by Multiple Cooperating Mobile Traps
Bibliographic record
Abstract
We study the mean capture time of an unbiased random walker by multiple absorbing mobile traps in bounded domains of one and two spatial dimensions. In one dimension, we consider multiple traps undergoing prescribed oscillatory motion on an interval with reflecting or absorbing boundary conditions. We develop trap cooperation strategies which optimize the mean capture time. We find that as the frequency of oscillation passes through certain fixed values, the optimal trap strategy alternates between oscillating exactly in phase and exactly out of phase with neighboring traps. We also demonstrate a scenario in which the optimal configuration is neither in phase nor antiphase. In two dimensions, we consider two small traps rotating with the same angular velocity $\omega$ inside a unit disk and characterize the optimal positions (radii of rotation and relative phase) of the two traps as a function of $\omega$ and trap radius $\varepsilon \ll 1$. We identify several distinguished regimes in $\omega$ where the optimal configuration can be distinctly characterized. In particular, in the $\omega \sim \mathcal {O}(1)$ regime, the optimal configuration jumps from one in which two traps rotate antipodal and along the same radius to one where the two traps rotate on the same side of the disk but at different radii. In addition, we demonstrate an algebraic approach to obtaining optimal configurations of $N$ rotating traps as $\omega \to \infty$.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".