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Record W2913888525 · doi:10.1017/s0963548306007541

Rayleigh Matroids

2006· article· en· W2913888525 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.

Bibliographic record

VenueCombinatorics Probability Computing · 2006
Typearticle
Languageen
FieldMathematics
TopicMarkov Chains and Monte Carlo Methods
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsMatroidGraphic matroidCombinatoricsBinary numberMatroid partitioningMathematicsClass (philosophy)Property (philosophy)Discrete mathematicsComputer scienceArithmetic

Abstract

fetched live from OpenAlex

Motivated by a property of linear resistive electrical networks, we introduce the class of Rayleigh matroids. These form a subclass of the balanced matroids defined by Feder and Mihail [9] in 1992. We prove a variety of results relating Rayleigh matroids to other well-known classes – in particular, we show that a binary matroid is Rayleigh if and only if it does not contain is the only minor-minimal binary non-balanced matroid, as claimed in [9]. We also give an example of a balanced matroid which is not Rayleigh.

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)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
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 score0.043
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
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 head0.052
GPT teacher head0.318
Teacher spread0.266 · 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