Zobrazeno 1 - 10
of 12
pro vyhledávání: '"16G20, 55N99"'
Autor:
Buchet, Mickaël, Escolar, Emerson G.
Multidimensional persistence has been proposed to study the persistence of topological features in data indexed by multiple parameters. In this work, we further explore its algebraic complications from the point of view of higher dimensional indecomp
Externí odkaz:
http://arxiv.org/abs/2012.02467
In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular, we provide a representation-theoretic framework for interleavings, sh
Externí odkaz:
http://arxiv.org/abs/2004.03840
In this introductory paper we study nearly Frobenius algebras which are generalizations of the concept of a Frobenius algebra which appear naturally in topology: nearly Frobenius algebras have no traces (co-units). We survey the most basic foundation
Externí odkaz:
http://arxiv.org/abs/1907.05470
Autor:
Buchet, Mickaël, Escolar, Emerson G.
A recent work by Lesnick and Wright proposed a visualisation of $2$D persistence modules by using their restrictions onto lines, giving a family of $1$D persistence modules. We give a constructive proof that any $1$D persistence module with finite su
Externí odkaz:
http://arxiv.org/abs/1902.07405
In the persistent homology of filtrations, the indecomposable decompositions provide the persistence diagrams. However, in almost all cases of multidimensional persistence, the classification of all indecomposable modules is known to be a wild proble
Externí odkaz:
http://arxiv.org/abs/1812.05261
Publikováno v:
Asashiba, H., Escolar, E.G., Hiraoka, Y., Takeuchi, H. "Matrix Method for Persistence Modules on Commutative Ladders of Finite Type" Japan J. Indust. Appl. Math. (2018). https://doi.org/10.1007/s13160-018-0331-y
The theory of persistence modules on the commutative ladders $CL_n(\tau)$ provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence diagrams is still lacking. In this work, we view a persiste
Externí odkaz:
http://arxiv.org/abs/1706.10027
Autor:
Emerson G. Escolar, Mickaël Buchet
Publikováno v:
Journal of Applied and Computational Topology. 4:387-424
A recent work by Lesnick and Wright proposed a visualisation of $2$D persistence modules by using their restrictions onto lines, giving a family of $1$D persistence modules. We give a constructive proof that any $1$D persistence module with finite su
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6f0d5e152bb9949229f19d98d41a8640
https://doi.org/10.1007/s41468-020-00053-z
https://doi.org/10.1007/s41468-020-00053-z
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing.
In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular, we provide a representation-theoretic framework for interleavings, sh
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::80141f88761a08c038349a556af3c4a1
https://doi.org/10.1007/s00200-021-00530-7
https://doi.org/10.1007/s00200-021-00530-7
Publikováno v:
Computational Geometry. :101879
In the persistent homology of filtrations, the indecomposable decompositions provide the persistence diagrams. However, in almost all cases of multidimensional persistence, the classification of all indecomposable modules is known to be a wild proble
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e59e7cdad9ed4f7c3461c20b077bbbc8
https://doi.org/10.1016/j.comgeo.2022.101879
https://doi.org/10.1016/j.comgeo.2022.101879
Publikováno v:
Japan Journal of Industrial and Applied Mathematics. 36:97-130
The theory of persistence modules on the commutative ladders $CL_n(\tau)$ provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence diagrams is still lacking. In this work, we view a persiste
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf2186514a09517555a80fb30978915b
https://doi.org/10.1007/s13160-018-0331-y
https://doi.org/10.1007/s13160-018-0331-y