Topological data analysis (TDA) method could catch the rich geometric and topologic information of big find subtle differences between different signals. TDA opens up a new way for biomedical analysis. In this study, we applied heart sound signals (PCG) classification. First, sliding window was used to build point cloud. Then, persistent barcode is extracted from cloud by using topology technol...

We consider three monads on Top, the category of topological spaces, which formalize aspects probability and possibility in categorical terms. The first one is Hoare hyperspace monad H, assigns to every space its closed subsets equipped with lower Vietoris topology. second V continuous valuations, also known as extended probabilistic powerdomain. construct both a unified way terms double dualiz...

Upper bounds on the topological Betti numbers of Vietoris-Rips complexes are established, and examples of such complexes with high Betti

The famous “algebraic Mayer–Vietoris theorem” is usually stated for complexes over an Abelian category. In the present paper, this theorem generalized a preabelian proofs are based on technique and results of relative homological algebra developed by author earlier.

We approach the problem of the computation of persistent homology for large datasets by a divide-and-conquer strategy. Dividing the total space into separate but overlapping components, we are able to limit the total memory residency for any part of the computation, while not degrading the overall complexity much. Locally computed persistence information is then merged from the components and t...

Examples of twisted forms of finite étale extensions and separable polynomials are calculated using Mayer-Vietoris sequences for non-abelian cohomology. 2000 Mathematics Subject Classification. 13B05, 13B25, 13B40.

Let X be a h-homogeneous zero-dimensional compact Hausdorff space, i.e. X is a Stone dual of a homogeneous Boolean algebra. Using the dual Ramsey theorem and a detailed combinatorial analysis of what we call stable collections of subsets of a finite set, we obtain a complete list of the minimal sub-systems of the compact dynamical system (Exp(Exp(X)), Homeo(X)), where Exp(X) stands for the hype...