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Record W4386248540 · doi:10.1017/9781009303897.006

Zeros and Minima

2023· book-chapter· en· W4386248540 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

VenueCambridge University Press eBooks · 2023
Typebook-chapter
Languageen
FieldMathematics
TopicAdvanced Optimization Algorithms Research
Canadian institutionsUniversity of Guelph
Fundersnot available
KeywordsMaxima and minimaSection (typography)Action (physics)Nonlinear systemMathematicsApplied mathematicsStatement (logic)MinificationVariable (mathematics)Calculus (dental)Mathematical optimizationMathematical analysisComputer sciencePhysics

Abstract

fetched live from OpenAlex

Chapter 5 starts out with a physics motivation, as well as a mathematical statement of the problems that will be tackled in later sections. Several methods are introduced to solve a single nonlinear equation in one variable: fixed-point iteration, the bisection method, Newton’s method, the secant method, and Ridders’ method. After providing some advice about advantages and disadvantages of each approach, the text then studies how to find zeros of polynomials, employing two different techniques. The sophistication is then increased, by tackling systems of nonlinear equations and examining the corresponding challenges; in addition to Newton’s method, the text derives the equations behind Broyden’s method. A related subject is then broached, minimization in one or several dimensions; this includes the gradient-descent method, as well as detailed analysis of critical points; the second edition includes extensive new material on derivative-free optimization (golden-section search and Powell’s method).The chapter is rounded out by a physics project, the extremization of the action in classical mechanics, and a problem set. The physics project shows Hamilton’s principle in... action, translated into a multidimensional minimization problem.

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)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.955
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
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 science0.0000.001
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 head0.078
GPT teacher head0.281
Teacher spread0.203 · 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