Survivability of bouncing robots
Bibliographic record
Abstract
Bouncing robots are mobile agents with limited sensing capabilities adjusting their movements upon collisions either with other robots or obstacles in the environment. They behave like elastic particles sliding on a cycle or a segment. When two of them collide, they instantaneously update their velocities according to the laws of classical mechanics for elastic collisions. They have no control on their movements which are determined only by their masses, velocities, and upcoming sequence of collisions. We suppose that a robot arriving for the second time to its initial position dies instantaneously. We study the survivability of collections of swarms of bouncing robots. More exactly, we are looking for subsets of swarms such that after some initial bounces which may result in some robots dying, the surviving subset of the swarm continues its bouncing movement, with no robot reaching its initial position. For the case of robots of equal masses and speeds we prove that all robots bouncing in the segment must always die while there are configurations of robots on the cycle with surviving subsets. We show the smallest such configuration containing four robots with two survivors. We show that any collection of less than four robots must always die. On the other hand, we show that [Formula: see text] robots always die where [Formula: see text] (and [Formula: see text]) is the number of robots starting their movements in clockwise (respectively, counterclockwise) direction in swarm [Formula: see text]. When robots bouncing on a cycle or a segment have arbitrary masses we show that at least one robot must always die. Further, we show that in either environment it is possible to construct swarms with [Formula: see text] survivors. We prove, however, that the survivors in the segment must remain static indefinitely while in the case of the cycle it is possible to have surviving collections with strictly positive kinetic energy.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".