Bibliographic record
Abstract
Make everything as simple as possible, but not simpler. – Albert Einstein. Someone told me that each equation I included in the book would halve the sales. – Stephen Hawking. When the author was a graduate student, introductions to texts on nonlinear evolution equations contained a long description of physical applications, numerous references to the works of others, and sparse details of the justification of analytical results. Times have changed, however, and the main interest in the nonlinear evolution equations has moved from modeling to analysis. It is now more typical for applied mathematics texts to start an introduction with the main equations in the first lines, to give no background information on applications, to reduce the list of references to a few relevant mathematical publications, and to focus discussions on technical aspects of analysis. Since this book is aimed at young mathematicians, we should reduce the background information to a minimum and focus on useful analytical techniques in the context of the nonlinear Schrödinger equation with a periodic potential. It is only in this introduction that we recall the old times and review the list of nonlinear evolution equations that we are going to work with in this book. The few references will provide a quick glance at physical applications, without distracting attention from equations.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".