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Record W4402423510 · doi:10.24908/iqurcp17986

Isoperimetric Control of an Expanding Set

2024· article· en· W4402423510 on OpenAlex

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.
venuePublished in a venue whose home country is Canada.

Bibliographic record

VenueInquiry Queen s Undergraduate Research Conference Proceedings · 2024
Typearticle
Languageen
FieldComputer Science
TopicOptimization and Variational Analysis
Canadian institutionsQueen's University
Fundersnot available
KeywordsIsoperimetric inequalitySet (abstract data type)Control (management)MathematicsComputer scienceCombinatoricsArtificial intelligenceProgramming language

Abstract

fetched live from OpenAlex

Consider a contaminated region in a 2-dimensional plane that is expanding with unit normal speed. Our goal is to apply a control function (e.g. pesticide) along the boundary of this region to reduce the contaminated area to zero in the shortest possible time, while consistently clearing a fixed amount of land per unit time. It has been proven that when the initial contamination forms a convex set, an optimal eradication strategy requires applying pesticide to the boundary segments with the highest curvature at each moment. This is equivalent to adopting a myopic strategy that minimizes the perimeter of the contaminated region at each time step. This result provided insight for developing numerical methods to compute approximations of these optimal strategies for convex sets. Namely, our simulation consists in alternating between computing the isoperimetric (perimeter-minimizing) profile with a convex constraint and then dilating the resulting set by a radius equal to the time mesh. This process is repeated until the shape reaches a circle, which can then be trivially scaled down to a point. The isoperimetric profile is obtained through morphological opening, an erosion-dilation operator commonly used in image processing for noise removal. A major open problem remains: a full characterization of optimal eradication strategies for initial contaminations of general shapes. We have applied the above numerical scheme with non-convex constraints to gain some intuition in this broader context. This may entail replacing the morphological opening operator with a more general algorithm relying on the medial axis of a shape. It turns out that, in some configurations, it is more effective to split the contamination into several components and shrink them separately.

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)0.002
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesScholarly communication
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 score0.978
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0020.004
Science and technology studies0.0000.000
Scholarly communication0.0010.002
Open science0.0010.000
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 head0.105
GPT teacher head0.395
Teacher spread0.290 · 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