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Minimum Area Venn Diagrams Whose Curves Are Polyominoes

2007· article· en· W2963073772 on OpenAlexaff
Stirling Chow, Frank Ruskey

Bibliographic record

VenueMathematics Magazine · 2007
Typearticle
Languageen
FieldMathematics
TopicMathematics and Applications
Canadian institutionsUniversity of Victoria
Fundersnot available
KeywordsPolyominoVenn diagramMathematicsDiagramCombinatoricsGeometryStatisticsMathematics education

Abstract

fetched live from OpenAlex

While working at the Berlin Academy, the renowned Swiss mathematician Leonard Euler was asked to tutor Frederick the Great's niece, the of Anhalt-Dessau, in all matters of natural science and philosophy [17]. Euler's tutelage of the princess continued from 1760 to 1762 and culminated in the publishing of the popular and widely-translated Letters to a German Princess [9]. In the letters, Euler eloquently wrote about diverse topics ranging from why the sky was blue to free will and deter minism. In his lesson on categorical propositions and syllogisms, Euler used diagrams com prised of overlapping circles; these diagrams became known as Eulerian circles, or simply Euler diagrams. In an Euler diagram, a proposition's classes are represented as circles whose overlap depends on the relationship established by the proposition. For example, the propositions

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)0.004
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 score0.016
Threshold uncertainty score0.052

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.004
Meta-epidemiology (narrow)0.0000.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0030.002
Science and technology studies0.0020.002
Scholarly communication0.0030.007
Open science0.0010.002
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0160.002

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 head0.062
GPT teacher head0.322
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

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

Citations4
Published2007
Admission routes1
Has abstractyes

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