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Record W2029437181 · doi:10.1093/qjmam/hbq005

Regions of Invalidity of Ray-Centred Coordinates

2010· article· en· W2029437181 on OpenAlexafffund
Len Bos, Michael A. Slawiński

Bibliographic record

VenueThe Quarterly Journal of Mechanics and Applied Mathematics · 2010
Typearticle
Languageen
FieldEarth and Planetary Sciences
TopicSeismic Imaging and Inversion Techniques
Canadian institutionsMemorial University of NewfoundlandUniversity of Calgary
FundersNatural Sciences and Engineering Research Council of CanadaPrinceton University
KeywordsLog-polar coordinatesGeneralityBipolar coordinatesOrthogonal coordinatesSpatial reference systemAction-angle coordinatesGeneralized coordinatesNeighbourhood (mathematics)Computer scienceMathematicsGeometryMathematical analysisComputer visionPsychology

Abstract

fetched live from OpenAlex

Ray-centred coordinates are used in investigating seismic theory and in computing its results. It is commonly stated that they are local in nature. In this paper, we discuss the region of invalidity of such coordinates. Notably, the existence of such regions limits the generality of theoretical conclusions based on a proof that makes use of these coordinates. We discuss several explicit examples; for one of them, the region of invalidity intersects the ray itself, thus showing that, in general, it is not possible to use ray-centred coordinates even in a local neighbourhood of the ray.

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 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: Empirical · Consensus signal: Empirical
Teacher disagreement score0.299
Threshold uncertainty score0.193

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
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 head0.019
GPT teacher head0.210
Teacher spread0.191 · 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 teacher head, 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

Citations2
Published2010
Admission routes2
Has abstractyes

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