The object detection by autonomous apparatus as a solution of the Buffon needle problem
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Bibliographic record
Abstract
The problem of object detection by autonomous apparatus is considered.The probabilistic formulation of the problem is proposed by means of a reduction to the classical Buffon problem.The latter naturally arises when the problem is formulated in the coordinate system associated with the apparatus.The problem of detection is considered for devices moving in the open space along a circle around one body, for vehicles patrolling along the linear boundary protecting the bodies, and for devices protecting the system of bodies.The problem of object detection was shown to admit an analysis in the presence of an asymptotic parameter determined by the ratio of the local size of the apparatus scanning area to the global size of the problem under consideration.For all problems, the minimum number of apparatuses that could detect a penetrating object with probability one was calculated.Communicated by Francesco dell'Isola.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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