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Record W3034157606 · doi:10.1017/jpr.2021.34

Intersections of random sets

2022· preprint· en· W3034157606 on OpenAlex
Jacob Richey, Amites Sarkar

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueJournal of Applied Probability · 2022
Typepreprint
Languageen
FieldMathematics
TopicPoint processes and geometric inequalities
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsIntersection (aeronautics)Boolean modelPoisson point processPoint processLimit (mathematics)MathematicsCombinatoricsBall (mathematics)Unit sphereClass (philosophy)Point (geometry)Poisson distributionUnit (ring theory)Discrete mathematicsComputer scienceGeometryMathematical analysisStatisticsGeographyArtificial intelligenceCartography

Abstract

fetched live from OpenAlex

Abstract We consider a variant of a classical coverage process, the Boolean model in $\mathbb{R}^d$ . Previous efforts have focused on convergence of the unoccupied region containing the origin to a well-studied limit C . We study the intersection of sets centered at points of a Poisson point process confined to the unit ball. Using a coupling between the intersection model and the original Boolean model, we show that the scaled intersection converges weakly to the same limit C . Along the way, we present some tools for studying statistics of a class of intersection models.

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.

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)0.004
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.276
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0040.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0010.000

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 head0.080
GPT teacher head0.338
Teacher spread0.258 · 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