Zobrazeno 1 - 9
of 9
pro vyhledávání: '"Elchesen, Alex"'
Autor:
Bubenik, Peter, Elchesen, Alex
We develop a theory of optimal transport relative to a distinguished subset, which acts as a reservoir of mass, allowing us to compare measures of different total variation. This relative transportation problem has an optimal solution and we obtain r
Externí odkaz:
http://arxiv.org/abs/2411.05678
Autor:
Elchesen, Alex, Patel, Amit
We develop a cohomological approach to M\"obius inversion using derived functors in the enriched categorical setting. For a poset $P$ and a closed symmetric monoidal abelian category $\mathcal{C}$, we define M\"obius cohomology as the derived functor
Externí odkaz:
http://arxiv.org/abs/2411.04362
Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures supported on the birth-death plane and endowed with an optimal transp
Externí odkaz:
http://arxiv.org/abs/2212.08295
Publikováno v:
Front. Artif. Intell. 4:668395 (2021)
We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of complex behavior which may be applied to high-throughput data. Our metho
Externí odkaz:
http://arxiv.org/abs/2102.09380
Autor:
Bubenik, Peter, Elchesen, Alex
Publikováno v:
Journal of Applied and Computational Topology (2022)
Persistence diagrams, an important summary in topological data analysis, consist of a set of ordered pairs, each with positive multiplicity. Persistence diagrams are obtained via Mobius inversion and may be compared using a one-parameter family of me
Externí odkaz:
http://arxiv.org/abs/2012.10514
Autor:
Bubenik, Peter, Elchesen, Alex
Publikováno v:
Computational Geometry, Volumes 105-106, August-October 2022, 101882
We prove that persistence diagrams with the p-Wasserstein distance form the universal p-subadditive commutative monoid on an underlying metric space with a distinguished subset. This result applies to persistence diagrams, barcodes, and to multiparam
Externí odkaz:
http://arxiv.org/abs/1912.02563
Autor:
Elchesen, Alex
We use the reflection functors introduced by Bernstein, Gelfand, and Ponomarev to define a metric on the space of all zigzag modules of a given length, which we call the reflection distance. We show that the reflection distance between two given zigz
Autor:
Bubenik, Peter, Elchesen, Alex
Publikováno v:
In Computational Geometry: Theory and Applications August-October 2022 105-106
Autor:
Bubenik, Peter, Elchesen, Alex
Publikováno v:
Journal of Applied & Computational Topology; Dec2022, Vol. 6 Issue 4, p429-474, 46p