Emerson G. Escolar

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20152020

most citedPersistent Homology and Many-Body Atomic Structure for Medium-Range Order in the Glass

1 citations · 1 across the 2 of their papers we have counts for

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math.RT2020

The Whole in the Parts: Putting $n$ D Persistence Modules Inside Indecomposable $(n + 1)$ 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…

math.RT2020

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,…

math.RT2019

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 $2$ D persistence modules by using their restrictions onto lines, giving a family of $1$ D persistence modules. We giv…

The Whole in the Parts: Putting nD Persistence Modules Inside Indecomposable (n+1)D Ones

Interleavings and Matchings as Representations

Every 1D Persistence Module is a Restriction of Some Indecomposable 2D Persistence Module

The Whole in the Parts: Putting $n$ D Persistence Modules Inside Indecomposable $(n + 1)$ D Ones