Convergence of discrete exterior calculus
Bibliographic record
Abstract
Discrete exterior calculus" (DEC) est une thorie assez rcente obtenue par le developpment d'oprateurs discrets permettant un calcul simplicial analogue au calcul diffrentiel et intgral des formes diffrentielles.DEC est fond sur la gometrie algbrique des complexes simplicials et exploite la reciprocit entre une triangulation et sa construction duale de faon reproduire les proprites geomtriques cls des formes differentielles utiles pour le calcul scientifique.Dans la littrature, la thorie fut dej utilise pour affronter des problmes varis appartenant des domaines tels que l'homologie, la geomtrie riemannienne, la dynamique des fluides, la mchanique discrte, incluant le calcul des variations en vision par ordinateur et en animation.Jusqu' prsent, tablir la convergence des methodes produites par DEC reste un problme non-resolu.Dans cette thse, nous partagerons de rcentes dcouvertes qui largissent notre comprhension de cette question dans le cas des probmes d'quations diffrentielles avec conditions limites pour des formes de degr zero (fonctions valeurs reles).Nous discuterons galement des difficults encontres lorsqu'on tente d'tendre ces rsultats des ordres suprieurs.
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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 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.003 | 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 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".