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Record W4235843859 · doi:10.1002/9781118884003.ch7

Nonlinear equations

2014· other· en· W4235843859 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

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.

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)0.000
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: Not applicable
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.048
Threshold uncertainty score0.998

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.001
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)0.0470.003

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