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Record W2150278829 · doi:10.1142/s0218195903001281

PROPERTIES OF ARRANGEMENT GRAPHS

2003· article· en· W2150278829 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

VenueInternational Journal of Computational Geometry & Applications · 2003
Typearticle
Languageen
FieldComputer Science
TopicComputational Geometry and Mesh Generation
Canadian institutionsUniversity of LethbridgeCarleton University
Fundersnot available
KeywordsCombinatoricsMathematicsGeneral positionHyperplaneHamiltonian pathLine segmentGraphDiscrete mathematicsGeometry

Abstract

fetched live from OpenAlex

An arrangement graph G is the abstract graph obtained from an arrangement of lines L, in general position by associating vertices of G with the intersection points of L, and the edges of G with the line segments joining the intersection points of L. A simple polygon (respectively path) of n sides in general position, induces a set of n lines by extension of the line segments into lines. The main results of this paper are: • Given a graph G, it is NP-Hard to determine if G is the arrangement graph of some set of lines. • There are non-Hamiltonian arrangement graphs for arrangements of six lines and for odd values of n>6 lines. • All arrangements of n lines contain a subarrangement of size [Formula: see text] with an inducing polygon. • All arrangements on n lines contain an inducing path consisting of n line segments. A Java applet implementing the algorithm for determining such a path is also provided. • All arrangements on n hyperplanes in R d contain a simple inducing polygonal cycle of size n.

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: Methods · Consensus signal: none
Teacher disagreement score0.846
Threshold uncertainty score0.612

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0000.000
Scholarly communication0.0000.001
Open science0.0010.000
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 head0.019
GPT teacher head0.265
Teacher spread0.246 · 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