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

What we can learn from Bohemian Matrices?

2021· article· en· W3201469789 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.
venuePublished in a venue whose home country is Canada.

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.

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: Other design · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.976
Threshold uncertainty score0.430

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 communication0.0000.001
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 head0.015
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