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Record W2038424818 · doi:10.1017/s0963548303005765

Canonical Vertex Partitions

2003· article· en· W2038424818 on OpenAlexaff
N. Sauer

Bibliographic record

VenueCombinatorics Probability Computing · 2003
Typearticle
Languageen
FieldComputer Science
TopicAdvanced Algebra and Logic
Canadian institutionsUniversity of Calgary
Fundersnot available
KeywordsArityCountable setMathematicsVertex (graph theory)Partition (number theory)Signature (topology)Binary numberDiscrete mathematicsFinite setCombinatoricsGraphArithmeticGeometryMathematical analysis

Abstract

fetched live from OpenAlex

Let σ be a finite relational signature, let be a set of finite complete relational structures of signature σ, and let be the countable homogeneous relational structure of signature σ which does not embed any of the structures in . When σ consists of at most binary relations and is finite, the vertex partition behaviour of is completely analysed, in the sense that it is shown that a canonical partition exists and the size of this partition in terms of the structures in is determined. If is infinite some results are obtained, but a complete analysis is still missing. Some general results are presented which are intended to be used in further investigations when σ contains relational symbols of arity larger than two or when the set of bounds is infinite.

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)0.001
metaresearch head score (Gemma)0.007
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 score0.015
Threshold uncertainty score0.049

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.007
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0020.001
Science and technology studies0.0020.003
Scholarly communication0.0050.005
Open science0.0010.003
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0150.002

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 head0.024
GPT teacher head0.249
Teacher spread0.225 · 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

Citations24
Published2003
Admission routes1
Has abstractyes

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