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Record W2131783450 · doi:10.1287/moor.1050.0163

Estimating Tangent and Normal Cones Without Calculus

2005· article· en· W2131783450 on OpenAlexaff
Warren Hare, Adrian S. Lewis

Bibliographic record

VenueMathematics of Operations Research · 2005
Typearticle
Languageen
FieldMathematics
TopicPoint processes and geometric inequalities
Canadian institutionsMcMaster University
Fundersnot available
KeywordsMathematicsTangent coneTangentSimple (philosophy)Base (topology)Boundary (topology)Set (abstract data type)Calculus (dental)Point (geometry)Tangent vectorMathematical analysisApplied mathematicsGeometryComputer science

Abstract

fetched live from OpenAlex

We study simple estimates of the tangent and normal cones to a set with a nonsmooth boundary. We seek estimates that are robust relative to the base point and that depend only on collections of nearby points known to lie inside and outside of the set.

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)0.010
metaresearch head score (Gemma)0.049
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: Methods · Consensus signal: Methods
Teacher disagreement score0.010
Threshold uncertainty score0.051

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0100.049
Meta-epidemiology (narrow)0.0020.001
Meta-epidemiology (broad)0.0030.002
Bibliometrics0.0040.002
Science and technology studies0.0010.005
Scholarly communication0.0040.010
Open science0.0030.005
Research integrity0.0020.004
Insufficient payload (model declined to judge)0.0020.000

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 head0.204
GPT teacher head0.466
Teacher spread0.262 · 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
GenreMethods

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

Citations16
Published2005
Admission routes1
Has abstractyes

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