I will interpret the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer as the Möbius inversion of the rank function. I will then show how to generalize the persistence diagram to the setting of constructible persistence modules valued in any small symmetric monoidal category.Non UBCUnreviewedAuthor affiliation: Colorado State UniversityFacult
Persistence theory discussed in this paper is an application of algebraic topology (Morse Theory [29...
We study persistence modules defined on commutative ladders. This class of persis-tence modules freq...
2021 Summer.Includes bibliographical references.Persistent homology typically starts with a filtered...
Starting with a persistence module - a functor M from a finite poset to the category of finite dimen...
We give a self-contained treatment of the theory of persistence modules indexed over the real line. ...
We introduce a refinement of the persistence diagram, the graded persistence diagram. It is the Mobi...
26 pages, 4 figuresThe notion of rank decomposition of a multi-parameter persistence module was intr...
Persistence modules have a natural home in the setting of stratified spaces and constructible coshea...
Multidimensional persistent modules do not admit a concise representation analogous to that provided...
In a context where huge amounts of data are available, extracting meaningful and non trivial informa...
Chazal F, Crawley-Boevey WW, de Silva V. THE OBSERVABLE STRUCTURE OF PERSISTENCE MODULES. HOMOLOGY H...
In persistent topology, q-tame modules appear as a natural and large class of persistence modules in...
Abstract. Topological persistence is, by now, an established paradigm for constructing robust topo-l...
International audienceTopological persistence has proven to be a key concept for the study of real-v...
Multidimensional persistence modules do not admit a concise representation analogous to that provide...
Persistence theory discussed in this paper is an application of algebraic topology (Morse Theory [29...
We study persistence modules defined on commutative ladders. This class of persis-tence modules freq...
2021 Summer.Includes bibliographical references.Persistent homology typically starts with a filtered...
Starting with a persistence module - a functor M from a finite poset to the category of finite dimen...
We give a self-contained treatment of the theory of persistence modules indexed over the real line. ...
We introduce a refinement of the persistence diagram, the graded persistence diagram. It is the Mobi...
26 pages, 4 figuresThe notion of rank decomposition of a multi-parameter persistence module was intr...
Persistence modules have a natural home in the setting of stratified spaces and constructible coshea...
Multidimensional persistent modules do not admit a concise representation analogous to that provided...
In a context where huge amounts of data are available, extracting meaningful and non trivial informa...
Chazal F, Crawley-Boevey WW, de Silva V. THE OBSERVABLE STRUCTURE OF PERSISTENCE MODULES. HOMOLOGY H...
In persistent topology, q-tame modules appear as a natural and large class of persistence modules in...
Abstract. Topological persistence is, by now, an established paradigm for constructing robust topo-l...
International audienceTopological persistence has proven to be a key concept for the study of real-v...
Multidimensional persistence modules do not admit a concise representation analogous to that provide...
Persistence theory discussed in this paper is an application of algebraic topology (Morse Theory [29...
We study persistence modules defined on commutative ladders. This class of persis-tence modules freq...
2021 Summer.Includes bibliographical references.Persistent homology typically starts with a filtered...