Systèmes isomonodromiques et courbes superelliptiques
Bibliographic record
Abstract
Le sujet de ce mémoire concerne les déformations isomonodromiques. Je propose une solution à dimension matricielle arbitraire à un système fuchsien triangulaire supérieur, admettant des déformations isomonodromiques régies par le système de Schlesinger décrites dans [DGS]. Cette solution est issue de calculs réalisés d’abord à un cas quasi-généralisé, puis en dimensions matricielles 3 × 3 à 6 × 6, d’où une conjecture fut ensuite extrapolée. Dans ce mémoire, j’introduis de manière générale les notions de surfaces de Riemann, de courbes hyperelliptiques et superelliptiques, de système fuchsien, de monodromie et de système de Schlesinger. De même, je discute des déformations isomonodromiques et du XXIème problème d’Hilbert. Finalement, je présente des résultats obtenus par Dragovic-Gontsov-Shramchenko, ainsi que les résultats corollaires à ceux-ci que j’ai trouvés au cours de la recherche effectuée à l’Université de Sherbrooke.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.013 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".