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Record W4235843859 · doi:10.1002/9781118884003.ch7

Nonlinear equations

2014· other· en· W4235843859 on OpenAlexaff
John C. Nash

Bibliographic record

Venuenot available
Typeother
Languageen
FieldMathematics
TopicAdvanced Optimization Algorithms Research
Canadian institutionsUniversity of Ottawa
Fundersnot available
KeywordsNonlinear systemMaxima and minimaNon-linear least squaresConstraint (computer-aided design)Least-squares function approximationApplied mathematicsFunction (biology)MathematicsMathematical optimizationMinificationExplained sum of squaresMathematical analysisPhysicsStatisticsGeometry

Abstract

fetched live from OpenAlex

This chapter focuses on nonlinear equations (NLEs) in more than one unknown parameter. People sometimes try to use NLEs methods to find extrema of nonlinear functions. For such problems, the author suggests that it is almost always better to use an optimization tool. There are two R packages that are explicitly used for solving NLEs, BB and nleqslv. Nonlinear least squares methods can be used solve NLEs. One further level higher is the application of general function minimization tools to the sum-of-squares function of the equations. The nonlinear least squares approach to NLEs problems is useful as a natural check on solutions and a measure of how “bad” proposed solutions may be. Nonlinear least squares and general optimization offer other approaches to a solution by seeking a minimal sum of squares of the residuals (constraint violations) that is zero.

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: Methods · Consensus signal: none
Teacher disagreement score0.048
Threshold uncertainty score0.162

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.004
Meta-epidemiology (narrow)0.0020.001
Meta-epidemiology (broad)0.0010.002
Bibliometrics0.0010.001
Science and technology studies0.0010.002
Scholarly communication0.0030.003
Open science0.0020.003
Research integrity0.0020.004
Insufficient payload (model declined to judge)0.0480.017

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 head0.067
GPT teacher head0.396
Teacher spread0.329 · 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".

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Citations1
Published2014
Admission routes1
Has abstractyes

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