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Record W2007648947 · doi:10.1137/050632427

A Classification of Spikes and Plateaus

2007· article· en· W2007648947 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

VenueSIAM Review · 2007
Typearticle
Languageen
FieldMathematics
TopicMathematical Biology Tumor Growth
Canadian institutionsUniversity of Alberta
Fundersnot available
KeywordsMathematicsScalar (mathematics)Mathematical and theoretical biologyReaction–diffusion systemPattern formationDimension (graph theory)Statistical physicsMathematical analysisPure mathematicsMathematical physicsPhysicsApplied mathematicsGeometry

Abstract

fetched live from OpenAlex

In this paper we classify local maxima into spikes and plateaus. We give analytic definitions for spikes and plateaus in terms of a nonlocal gradient and a fourth order derivative. In higher dimensions the Hesse matrix of $\Delta f(x)$ is of relevance. This classification is applied to pattern formation models in mathematical physics and mathematical biology, including Cahn–Hilliard equations, chemotaxis equations, reaction‐diffusion equations, Gierer–Meinhardt models, and Gray–Scott models. We show for some of these examples that the stability of spatial patterns depends on the spike versus plateau type of the solution. We prove, for example, that scalar reaction‐diffusion equations in any spatial dimension cannot have stable spike steady states.

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)0.001
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 score0.437
Threshold uncertainty score0.228

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
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 head0.084
GPT teacher head0.381
Teacher spread0.297 · 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