Constructing a relativistic heat flow by transport time steps
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Bibliographic record
Abstract
An alternative construction to Andreu et al. (2005) [12] is given for L_{w}^{1}([0,T],\mathrm{BV}(\Omega )) solutions to the relativistic heat equation (1) (see Brenier (2003) [14], Mihalas and Mihalas (1984) [37], Rosenau (1992) [40], Chertock et al. (2003) [20], Caselles (2007) [19]) under the assumption of initial data bounded from below and from above. For that purpose, we introduce a time discretized scheme in the style of Jordan et al. (1998) [30], Otto (1996) [38] involving an optimal transportation problem with a discontinuous hemispherical cost function. The limiting process is based on a monotonicity argument and on a bound of the Fisher information by an entropy balance characteristic of the minimization problem. Résumé Nous présentons ici une construction alternative à celle d'Andreu et al. (2005) [12] de solution L_{w}^{1}([0,T],\mathrm{BV}(\Omega )) de l'équation de la chaleur relativiste (1) (voir Brenier (2003) [14], Mihalas et Mihalas (1984) [37], Rosenau (1992) [40], Chertock et al. (2003) [20], Caselles (2007) [19]) dans le cas de conditions initiales bornées inférieurement et supérieurement. Pour cela, nous introduisons un schéma discret en temps dans le style de Jordan et al. (1998) [30], Otto (1996) [38] basé sur un problème de transport optimal faisant intervenir une fonction de coût hémisphérique et discontinue. Le passage à la limite lorsque le pas de temps tend vers zéro repose sur un argument de monotonie et une borne de l'information de Fisher par la variation de l'entropie, inégalité caractéristique du problème de transport optimal.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it