Zobrazeno 1 - 10
of 180
pro vyhledávání: '"Blumberg, Andrew J."'
We introduce ORC-ManL, a new algorithm to prune spurious edges from nearest neighbor graphs using a criterion based on Ollivier-Ricci curvature and estimated metric distortion. Our motivation comes from manifold learning: we show that when the data g
Externí odkaz:
http://arxiv.org/abs/2410.01149
We introduce algorithms for robustly computing intrinsic coordinates on point clouds. Our approach relies on generating many candidate coordinates by subsampling the data and varying hyperparameters of the embedding algorithm (e.g., manifold learning
Externí odkaz:
http://arxiv.org/abs/2408.01379
We construct a stable infinity category with objects flow categories and morphisms flow bimodules; our construction has many flavors, related to a choice of bordism theory, and we discuss in particular framed bordism and the bordism theory of complex
Externí odkaz:
http://arxiv.org/abs/2404.03193
Autor:
van Delft, Anne, Blumberg, Andrew J.
A classical question about a metric space is whether Borel measures on the space are determined by their values on balls. We show that for any given measure this property is stable under Gromov-Wasserstein convergence of metric measure spaces. We the
Externí odkaz:
http://arxiv.org/abs/2401.11125
We describe a structure on a commutative ring (pre)cyclotomic spectrum $R$ that gives rise to a (pre)cyclotomic structure on topological Hochschild homology ($THH$) relative to its underlying commutative ring spectrum. This lets us construct $TC$ rel
Externí odkaz:
http://arxiv.org/abs/2310.02348
Autor:
Hickok, Abigail, Blumberg, Andrew J.
We introduce an intrinsic estimator for the scalar curvature of a data set presented as a finite metric space. Our estimator depends only on the metric structure of the data and not on an embedding in $\mathbb{R}^n$. We show that the estimator is con
Externí odkaz:
http://arxiv.org/abs/2308.02615
A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions
Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\
Externí odkaz:
http://arxiv.org/abs/2306.11170
Autor:
van Delft, Anne, Blumberg, Andrew J.
We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric space-valued stoch
Externí odkaz:
http://arxiv.org/abs/2304.01984
We propose a construction of an analogue of the Hill-Hopkins-Ravenel relative norm $N_{H}^{G}$ in the context of a positive dimensional compact Lie group $G$ and closed subgroup $H$. We explore expected properties of the construction. We show that in
Externí odkaz:
http://arxiv.org/abs/2212.11404
In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when
Externí odkaz:
http://arxiv.org/abs/2206.02026