1 citations · 1 across the 2 of their papers we have counts for
5 papers
The Whole in the Parts: Putting D Persistence Modules Inside Indecomposable D Ones
Mickaël Buchet, Emerson G. Escolar
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 algebra…
Interleavings and Matchings as Representations
Emerson G. Escolar, Killian Meehan, Michio Yoshiwaki
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,…
Every 1D Persistence Module is a Restriction of Some Indecomposable 2D Persistence Module
Mickaël Buchet, Emerson G. Escolar
A recent work by Lesnick and Wright proposed a visualisation of D persistence modules by using their restrictions onto lines, giving a family of D persistence modules. We giv…
Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension
Mickaël Buchet, Emerson G. Escolar
While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is th…
Persistent Homology and Many-Body Atomic Structure for Medium-Range Order in the Glass
Takenobu Nakamura, Yasuaki Hiraoka, Akihiko Hirata +2
Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarch…