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Record W2057591991 · doi:10.4171/owr/2008/27

Nonlinear Evolution Equations

2009· article· en· W2057591991 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.

aboutThe title or abstract carries a Canadian signal from the geographic lexicon.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueOberwolfach Reports · 2009
Typearticle
Languageen
FieldMathematics
TopicMathematical Biology Tumor Growth
Canadian institutionsnot available
Fundersnot available
KeywordsNonlinear systemMathematicsApplied mathematicsPhysics

Abstract

fetched live from OpenAlex

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.

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)0.001
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.406
Threshold uncertainty score0.594

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.003
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)0.0000.000

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 head0.041
GPT teacher head0.314
Teacher spread0.273 · 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