Bibliographic record
Abstract
In this thesis, we study the space of immersions from the circle to the plane Imm(S 1 , R 2 ), modulo the group of diffeomorphisms on S 1 .We discuss various Riemannian metrics and find surprisingly that the L 2 -metric fails to separate points.We show two methods of strengthening this metric, one to obtain a non-vanishing metric, and the other to stabilize the minimizing energy flow.We give the formulas for geodesics, energy and give an example of computed geodesics in the case of concentric circles.We then carry our results over to the larger spaces of immersions from a compact manifold M to a Riemannian manifold (N, g), modulo the group of diffeomorphisms on M .iv ABR ÉG É Dans cette thése, nous étudierons l'espace d'immersions d'un cercle au plan Imm(S 1 , R 2 ), modulo le groupe de difféomorphisme sur S 1 .Nous discuterons de divers mtriques riemanniennes et monterons la surprenante impossibilité de séparer des points dans la métrique L 2 .Nous prsenterons deux méthodes de renforcer cette métrique, une pour obtenir une métrique non-nulle, et une autre pour stabiliser le flot d'énergie.Nous donnerons les formules pour les géodésiques et l'énergie, et donnerons un exemple de calcul de géodésiques dans le cas des cercles concentriques.Nous étendrons alors nos résultats sur la plus grande espace d'immersion d'une variété M compacte à une variété riemannienne (N, g), modulo le groupe de diffomorphisme sur M .
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.032 | 0.007 |
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".