Spectral surface skeletons demonstrator for branched tubular genus-zero shapes
Notice bibliographique
Résumé
The first k eigenvectors u_i (with corresponding decreasing ordered eigenvalues<0) of the mesh-Laplacian L are used to determine a shrinked shape of a closed surface X made of tubular-/ bulb-like sub-structures (2D surface in 3D, genus 0). Approximation of the original surface coordinates X by least-squares may be taken to initialize further skeleton construction, e.g., by means of heuristic algorithms that reduce the mesh to one-dimensional connected filaments (curve skeleton), downstream. Leaving out >k eigenvectors means shrinking their contribution to the surface to zero. In this way, the solution to mesh-Laplacian-flow X(t) = a_0 + sum_i { a_i u_i exp( lambda_i t)} (lambda_i<0) is used for modeling strong volume reduction in tubular sub-structures, taking the fastest modes in terms of high negative eigenvalues as already zero (i.e., assuming their degrees of freedom are already relaxed at t=0). The a_i are the coefficients determined by least squares of the initial surface X, and a_0 is the intercept. It is observed from the reference skeleton shape (k=15) that bulb-like ends and tubes are collapsed stronger to quasi-one-dimensional filaments, than the central connecting/branching regions. The parameter k may be selected from the reverse L-shaped curve of volume v(k) of the skeleton or by visual inspection of the positioning of the skeleton filaments in the middle of tubes. It may be interesting to explore the reverse of the procedure, i.e.. to pump up the shape after the initial fit by scaling up some specific eigenvectors. Furthermore, it may be interesting to characterize components of eigenvectors that are dominating the radial contractions towards skeltal filaments. We hypothesize, that longer tubular structures are more radially contracted than shorter ones due to a yet unspecified low-eigenvalue subspace of eigenvectors u_i, i>k. This may be caused by the triangular mesh structure of tubes, that may be represented as larger blocks with only a few off-block entries (pointing to vertices of the interface to the branching-elements) in the Laplacian (i.e. after renumbering). Therefore, after renumbering, block-structures of L can be used to identifiy and modify tubular sub-structures. Moreover, graph-partitioning (e.g. by George Karypis METIS) would probably do a good job to split the structure into sub-structures of minimal number of interface edges. This could help to identify modular sub-structures of - maybe - piecewise-low-variance mean curvature (p-LVMC) as building blocks of a gluing procedure for the creation of new approximate minimum energy shapes. The R-code and two files for test-surfaces (Wavefront .obj-format) are licensed under CC-BY-4.0. Users should fully cite this work in their references, incl. the ZENODO DOI. The two test-surfaces were computed with the help of scripts for Surface Evolver (K. Brakke, The Surface Evolver, Experimental Mathematics vol. 1 no. 2 (1992), 141-165.), derived from:Frickenhaus, S. (2024). Exploration of extreme vesicle shapes and their modular structure. Zenodo. https://doi.org/10.5281/zenodo.11199344
Récupéré en direct depuis OpenAlex et désinversé. Les résumés ne sont pas conservés dans cette base de données : les index inversés représentent 8,6 Go des 9,3 Go de texte de la base, et le serveur dispose de 13 Go libres.
Comment cette classification a été obtenuedéplier
Prédiction distillée sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,000 | 0,000 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,000 |
| Études des sciences et des technologies | 0,001 | 0,000 |
| Communication savante | 0,000 | 0,000 |
| Science ouverte | 0,001 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,001 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,083 | 0,084 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; les deux têtes enseignantes s’accordent sur ce qui est montré ici.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».