Persistent homologyHamiltonian orbitsMagnetic geometryA method for the automatic classification of the orbits of magnetic field lines into topologically distinct classes using the Vietoris鈥揜ips persistent homology is presented. The input to the method is the Poincare map orbits of field lines and the ...
pythontopologysimplex-algorithmpersistent-homologygudhipersistence-landscapetomato-clusteringbetti-curves UpdatedMay 3, 2025 Python BorgwardtLab/topological-autoencoders Star145 Code Issues Pull requests Code for the paper "Topological Autoencoders" by Michael Moor, Max Horn, Bastian Rieck, and Karsten Borgw...
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such topological features is often a rather formidable task necessitating the ...
123 Stable volumes for persistent homology Algorithm 1 Computing persistence trees by the merge-tree algorithm. procedure Compute- Tree(Xr ) initialize G¯ = {ω∞} for σ∈ X in ( r )-descending order do if σ is an n-simplex then add σ to G¯ as a vertex else if σ is an ...
The basic idea of the algorithm developed in [115] is that one can compute a partial matching of the simplices in a filtered simplicial complex so that (i) pairs occur only between simplices that enter the filtration at the same step, (ii) unpaired simplices determine the homology, and ...
Figure S4. Example cross-session cell footprint alignment using the CellReg cell registration algorithm, related toFigure 2 A. CNMF-E-extracted cell footprints from four recording sessions, same animal as in S2B and S3B. Green-filled footprints are those detected across all recording sessions. ...
Persistent homology for MCI classification: a comparative analysis between graph and Vietoris-Rips filtrationsdoi:10.3389/fnins.2025.1518984DEFAULT mode networkLARGE-scale brain networksMILD cognitive impairmentBRAIN anatomyTIME series analysisIntroduction: Mild cognitive impairment (MCI), o...
Persistence theory applied to anthropometric point clouds together with clustering algorithms show that relevant information about shapes is extracted by persistent homology. In particular, the homologies of human body points have interesting interpretations in terms of human anatomy. In the first place,...
In particular, we identify the geometric and topological properties of both non-homology and homology eigenvectors for molecular struc- tures. We generalize these results to weighted simplicial complexes on top of which the weighted Dirac operator63 is carefully defined. In particular, we analyse ...
ALGORITHMIC CLASSIFICATION OF RESONANT ORBITS USING PERSISTENT HOMOLOGY IN POINCARé SECTIONSWe demonstrate an numerical algorithmic method to identify arbitrary families of periodic and quasiperiodic orbits in nonintegrable dynamical systems, in particular, the circular restricted three-body problem (CR3BP)....