Bibliographic record
Abstract
Nous étudions une équation de chaleur stochastique ā une dimension spatiale non linéaire dirigée par le bruit gaussien : ∂u∂t=∂2u∂x2+σ(u)W˙, où W˙ est blanc dans le temps et fractionnaire dans le espace avec le paramètre Hurst H∈(14,12). Dans un article récent (Ann. Probab. 45 (2017) 4561–616) par Hu, Huang, Lê, Nualart et Tindel une condition technique et inhabituelle σ(0)=0 a été supposée, ce qui est critique dans leur approche. Le principal effort de ce document est de supprimer cette condition. L’idée est de travailler sur un espace pondéré Zλ,Tp pour un certain poids de décroissance polynomiale λ(x)=cH(1+|x|2)H−1. Lorsque σ(u)=1 nous obtenons les asympotiques exactes de la solution uadd(t,x) quand t et x tendent vers l’infini. En particulier, nous trouvons la croissance exacte de sup|x|≤L|uadd(t,x)| et la croissance exacte des coefficients de Hölder, c’est-à-dire, sup|x|≤L|uadd(t,x+h)−uadd(t,x)| |h|β et sup|x|≤L|uadd(t+τ,x)−uadd(t,x)| τα.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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.
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 teacher head, 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".