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Record W4399726610 · doi:10.32920/26052676

Evacuating the ℓp Disc

2024· preprint· en· W4399726610 on OpenAlexaff
Sean Leizerovich

Bibliographic record

Venuenot available
Typepreprint
Languageen
FieldComputer Science
TopicPolynomial and algebraic computation
Canadian institutionsToronto Metropolitan University
Fundersnot available
KeywordsBusiness

Abstract

fetched live from OpenAlex

Evacuation is a search-type problem where collaborating agents seek a hidden exit on some continuous domain (for example, lines, rays, graphs, polygons.) We generalize the problem of evacuating two agents in the wireless model from the Euclidean disk to any lp metric space where p ∈ [1,∞). The original problem has seen an extensive line of variations, and our study is the first to embed this evacuation in more general metric spaces. Solving an evacuation is an optimization problem that seeks to minimize the worst-case evacuation time. We show that our family of algorithms, Wireless-Searchp(φ), is optimal for p ∈ [1,2] if φ = 0, and for p ∈ [2,∞) if φ = π/4. Our proof of optimality reduces to a novel observation in convex geometry on the relationship between chord and arc lengths on lp disks.

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 distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.960
Threshold uncertainty score0.658

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0010.000
Open science0.0010.005
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.021
GPT teacher head0.269
Teacher spread0.248 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations0
Published2024
Admission routes1
Has abstractyes

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Same topicPolynomial and algebraic computationFrench-language works237,207