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Asymptotic Methods

2021· preprint· en· W4239693128 on OpenAlexaff
Mohammed Akram Fellah

Bibliographic record

VenuePreprints.org · 2021
Typepreprint
Languageen
FieldMathematics
TopicDifferential Equations and Numerical Methods
Canadian institutionsPerimeter InstituteUniversity of Waterloo
Fundersnot available
KeywordsSingular perturbationAsymptotologySeries (stratigraphy)Asymptotic analysisApplied mathematicsAsymptotic expansionMathematicsDifferential equationPerturbation theory (quantum mechanics)Asymptotic analysisMethod of matched asymptotic expansionsCalculus (dental)Mathematical analysisPhysicsParticle physics

Abstract

fetched live from OpenAlex

In this lecture notes, we will introduce Asymptotics, then we will give a short glimpse on Perturbation theory (regular versus singular), which plays a crucial role especially in theoretical physics. Our goal is to find Asymptotic series that approximates the values of integrals depending on some parameter or the solutions of differential equations. These methods that lead to obtain more effective algorithms of numerical evaluation are called: Asymptotic Methods.

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)0.004
metaresearch head score (Gemma)0.017
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 score0.021
Threshold uncertainty score0.069

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0040.017
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.002
Bibliometrics0.0030.002
Science and technology studies0.0010.002
Scholarly communication0.0030.003
Open science0.0020.004
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0210.010

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 head0.405
GPT teacher head0.514
Teacher spread0.109 · 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

Citations0
Published2021
Admission routes1
Has abstractyes

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Same venuePreprints.orgSame topicDifferential Equations and Numerical MethodsFrench-language works237,207