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Record W3201469789 · doi:10.5206/mt.v1i1.14039

What we can learn from Bohemian Matrices?

2021· article· en· W3201469789 on OpenAlexaffvenue
Robert M. Corless

Bibliographic record

VenueMaple Transactions · 2021
Typearticle
Languageen
FieldComputer Science
TopicPolynomial and algebraic computation
Canadian institutionsWestern University
FundersEngineering and Physical Sciences Research Council
KeywordsWorkbookReading (process)Computer sciencePoint (geometry)Linear algebraMapleCode (set theory)Algebra over a fieldEigenvalues and eigenvectorsMathematics educationProgramming languageMathematicsLinguisticsPure mathematicsPhilosophyLaw

Abstract

fetched live from OpenAlex

This Maple Workbook explores a new topic in linear algebra, which is called "Bohemian Matrices". The topic is accessible to people who have had even just one linear algebra course, or have arrived at the point in their course where they have touched "eigenvalues". We use only the concepts of characteristic polynomial and eigenvalue. Even so, we will see some open questions, things that no-one knows for sure; even better, this is quite an exciting new area and we haven't even finished asking the easy questions yet! So it is possible that the reader will have found something new by the time they have finished going through this workbook. Reading this workbook is not like reading a paper: you will want to execute the code, and change things, and try alternatives. You will want to read the code, as well. I have tried to make it self-explanatory. We will begin with some pictures, and then proceed to show how to make such pictures using Maple (or, indeed, many other computational tools). Then we start asking questions about the pictures, and about other things.

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)0.010
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: none
Teacher disagreement score0.035
Threshold uncertainty score0.117

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.010
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.001
Science and technology studies0.0020.004
Scholarly communication0.0040.017
Open science0.0010.003
Research integrity0.0020.005
Insufficient payload (model declined to judge)0.0350.014

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 head0.015
GPT teacher head0.227
Teacher spread0.212 · 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

Citations0
Published2021
Admission routes2
Has abstractyes

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