Bibliographic record
Abstract
Following the successful pattern of the meeting in 2005, this year's workshop on 'Nonlinear Evolution Problems' focussed on a small number of currently very active areas in this field. By far the dominant theme, however, were geometric evolution equations of parabolic type, followed by the topic of wave equations and water waves/Navier-Stokes equations both in a classical and relativistic framework. Among the geometric evolution equations, curvature flows of hypersurfaces were considered with priority. In several talks, applications of these to isoperimetric problems and to formulation of appropriate local mass concepts were presented. One talk dealt with mean curvature flow in certain degenerate spaces. Several talks looked into harmonic and biharmonic map flow as well as Ricci flow. Among the nonlinear hyperbolic equations, the water wave equation, Einstein's equations, semilinear wave equation and, for the first time, the d-brane equation from string theory were featured. For the latter, an \epsilon -regularization method was used to establish an existence proof. This is another example of a method which has now been applied to different types of nonlinear equations. It had previously been applied to mean curvature flow and to minimal surfaces. The last theme concerned dispersive equations. This was represented only in a talk by Markus Keel, albeit on seminal work on resonant decompositions applicable to a wide class of example. All together, 21 talks were presented by international specialists from Australia, Canada, Germany, Great Britain, Italy, Sweden, Switzerland and the United States. Many of the speakers were only a few years past their Ph.D., some even still working towards their Ph.D.; 6 out of 42 participants and 4 out of 21 speakers were women. As a rule, three lectures were delivered in the morning session; two lectures were given in the late afternoon, which left ample time for individual discussions.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.019 | 0.005 |
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".