Bibliographic record
Abstract
Chapter 6 starts out with a physics motivation, as well as a mathematical statement of the problems that will be tackled in later sections. First, polynomial interpolation is carried out using both the monomial basis and the Lagrange-interpolation formalism, sped up via the barycentric formula. This includes a derivation of the error and an emphasis on using unequally spaced points (Chebyshev nodes). Second, cubic-spline interpolation is introduced. Third, a section is dedicated to trigonometric interpolation, carefully working through the conventions and formalism needed to implement one of the most successful algorithms ever, the fast Fourier transform (FFT). Fourth, the topic of linear least-squares fitting is tackled, including the general formalism of the normal equations. The second edition includes a substantive new section on statistical inference, covering both frequentist and Bayesian approaches to linear regression. Nonlinear least-squares fitting is covered next, including the Gauss-Newton method and artificial neural networks. The chapter is rounded out by a physics project, on the experimental verification of the Stefan-Boltzmann law, and a problem set. In addition to providing a historical background on black-body radiation, the physics project shows an example of nonlinear least-squares fitting.
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 imitationNot 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.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.087 | 0.041 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".