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Record W306917649 · doi:10.13001/1081-3810.3010

Sparse spectrally arbitrary patterns

2015· article· en· W306917649 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

VenueElectronic Journal of Linear Algebra · 2015
Typearticle
Languageen
FieldComputer Science
TopicMatrix Theory and Algorithms
Canadian institutionsRedeemer University
Fundersnot available
KeywordsMathematicsJacobian matrix and determinantMonic polynomialMatrix (chemical analysis)Order (exchange)Nilpotent matrixCompanion matrixZero (linguistics)Pure mathematicsEigenvalues and eigenvectorsPolynomialCombinatoricsMathematical analysisPolynomial matrixMatrix polynomialApplied mathematicsSymmetric matrixMatrix functionPhysics

Abstract

fetched live from OpenAlex

We explore combinatorial matrix patterns of order n for which some matrix entries are necessarily nonzero, some entries are zero, and some are arbitrary. In particular, we are interested in when the pattern allows any monic characteristic polynomial with real coefficients, that is, when the pattern is spectrally arbitrary. We describe some order n patterns that are spectrally arbitrary. We show that each superpattern of a sparse companion matrix pattern is spectrally arbitrary. We determine all the minimal spectrally arbitrary patterns of order 2 and 3. Finally, we demonstrate that there exist spectrally arbitrary patterns for which the nilpotent-Jacobian method fails.

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: none
Teacher disagreement score0.679
Threshold uncertainty score0.496

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 communication0.0000.001
Open science0.0010.000
Research integrity0.0000.001
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 head0.016
GPT teacher head0.244
Teacher spread0.229 · 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