arXiv:2511.03909v3 Announce Type: replace-cross
Abstract: The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for computing th…
arXiv:2603.29072v1 Announce Type: cross
Abstract: Point-cloud persistent homology (PH) — computing alpha or Rips complexes on spin-position point clouds — has been widely applied to detect phase transitions in classical spin models since Donato et a…
arXiv:2510.14710v2 Announce Type: replace-cross
Abstract: Datasets often possess an intrinsic multiscale structure with meaningful descriptions at different levels of coarseness. Such datasets are naturally described as multi-resolution clusterings, i…
arXiv:2603.27903v1 Announce Type: cross
Abstract: We prove that the persistence diagram of the sublevel set filtration of the quadratic form f(x) = x^T M x restricted to the unit sphere S^{n-1} is analytically determined by the eigenvalues of the symm…
arXiv:2603.27395v1 Announce Type: cross
Abstract: We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the …
arXiv:2603.24613v1 Announce Type: cross
Abstract: Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in o…
arXiv:2603.14831v3 Announce Type: replace-cross
Abstract: We construct a cellular sheaf from any feedforward ReLU neural network by placing one vertex for each intermediate quantity in the forward pass and encoding each computational step – affine tra…