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Record W2059887287 · doi:10.1145/2442829.2442881

Computing minimal nullspace bases

2012· article· en· W2059887287 on OpenAlex

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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

Venuenot available
Typearticle
Languageen
FieldComputer Science
TopicPolynomial and algebraic computation
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsBasis (linear algebra)MathematicsMatrix (chemical analysis)Field (mathematics)Degree (music)UnivariateMatrix multiplicationExponentComputationCombinatoricsDiscrete mathematicsAlgorithmPure mathematicsGeometryStatistics

Abstract

fetched live from OpenAlex

In this paper we present a deterministic algorithm for the computation of a minimal nullspace basis of an m x n input matrix of univariate polynomials over a field K with m ≤ n. This algorithm computes a minimal nullspace basis of a degree d input matrix with a cost of O~ (nω ⌈md/n⌉) field operations in K. Here the soft-O notation is Big-O with log factors removed while ω is the exponent of matrix multiplication. The same algorithm also works in the more general situation on computing a shifted minimal nullspace basis, with a given degree shift [equation] whose entries bound the corresponding column degrees of the input matrix. In this case if ρ is the sum of the m largest entries of s, then a s-minimal right nullspace basis can be computed with a cost of O~(nωρ/m) field operations.

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)0.000
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: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.743
Threshold uncertainty score0.312

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
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 head0.249
Teacher spread0.231 · 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

Quick stats

Citations34
Published2012
Admission routes1
Has abstractyes

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