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Record W267502919 · doi:10.13001/1081-3810.1676

Refined inertias of tree sign-patterns

2013· article· en· W267502919 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.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueElectronic Journal of Linear Algebra · 2013
Typearticle
Languageen
FieldMathematics
TopicGraph theory and applications
Canadian institutionsUniversity of Victoria
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematicsDigraphSign (mathematics)CombinatoricsDiagonalEigenvalues and eigenvectorsStar (game theory)Zero (linguistics)Tree (set theory)Order (exchange)Path (computing)Diagonal matrixDiscrete mathematicsMathematical analysisGeometryPhysicsComputer science

Abstract

fetched live from OpenAlex

The refined inertia (n + , n -, nz, 2np) of a real matrix is the ordered 4-tuple that subdivides the number n 0 of eigenvalues with zero real part in the inertia (n + , n -, n 0 ) into those that are exactly zero (nz) and those that are nonzero (2np). For n 2, the set of refined inertias Hn = {(0, n, 0, 0), (0, n -2, 0, 2), (2, n -2, 0, 0)} is important for the onset of Hopf bifurcation in dynamical systems. Tree sign patterns of order n that require or allow the refined inertias Hn are considered. For n = 4, necessary and sufficient conditions are proved for a tree sign pattern (necessarily a path or a star) to require H 4 . For n 3, a family of n n star sign patterns that allows Hn is given, and it is proved that if a star sign pattern requires Hn, then it must have exactly one zero diagonal entry associated with a leaf in its digraph.

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)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation 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 score0.007
Threshold uncertainty score0.539

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
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 head0.018
GPT teacher head0.278
Teacher spread0.260 · 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