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Record W4404280629 · doi:10.4171/aihpd/202

Lineup polytopes of products of simplices

2024· article· en· W4404280629 on OpenAlexafffund
Federico Castillo, Jean‐Philippe Labbé

Bibliographic record

VenueAnnales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions · 2024
Typearticle
Languageen
FieldChemistry
TopicHistory and advancements in chemistry
Canadian institutionsÉcole de Technologie SupérieureUniversité du Québec à Montréal
FundersNatural Sciences and Engineering Research Council of CanadaAlliance de recherche numérique du Canada
KeywordsPolytopeCombinatoricsComputer scienceBusinessArtMathematics

Abstract

fetched live from OpenAlex

Consider a real point configuration \bm{A} of size n and an integer r \leq n . The vertices of the r -lineup polytope of \bm{A} correspond to the possible orderings of the top r points of the configuration obtained by maximizing a linear functional. The motivation behind the study of lineup polytopes comes from the representability problem in quantum chemistry. In that context, the relevant point configurations are the vertices of hypersimplices and the integer points contained in an inflated regular simplex. The central problem consists in providing an inequality representation of lineup polytopes as efficiently as possible. In this article, we adapt the developed techniques to the quantum information theory setup. The appropriate point configurations become the vertices of products of simplices. A particular case is that of lineup polytopes of cubes, which form a type B analog of hypersimplices, where the symmetric group of type A naturally acts. To obtain the inequalities, we center our attention on the combinatorics and the symmetry of products of simplices to obtain an algorithmic solution. Along the way, we establish relationships between lineup polytopes of products of simplices with the Gale order, standard Young tableaux, and the resonance arrangement.

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 machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.001
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
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 score0.012
Threshold uncertainty score0.040

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0000.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0010.001
Scholarly communication0.0020.002
Open science0.0010.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0120.001

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 head0.018
GPT teacher head0.270
Teacher spread0.251 · 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 source (direct Gemma or distilled Codex), 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

Citations2
Published2024
Admission routes2
Has abstractyes

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Same venueAnnales de l’Institut Henri Poincaré D Combinatorics Physics and their InteractionsSame topicHistory and advancements in chemistryFrench-language works237,207