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Persistence module

A persistence module is a mathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological features of an object across a range of scale parameters. A persistence module often consists of a collection of homology groups (or vector spaces if using field coefficients) corresponding to a…

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Persistence module

Nodes43
Edges42
Triples38
Avg. degree1.95
Density0.046512
Components1

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Persistence module

Top relations

related to Single Parameter Persistence Modules · 7
Persistence module → Common, Let, One, The, Then, To, Vec
related to Structure Theorem · 7
Persistence module → Botnan, Crawley-Boevey, For, One, The, This, Webb
related to Homology Modules · 6
Persistence module → Homology, The, Therefore, Top, Vec, When
related to Multiparameter Persistence Modules · 5
Persistence module → In, Let, Then, This, Vec
related to Interval Modules · 3
Persistence module → In, Let, Then
is a · 2
Persistence module → mathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological features of an object across a range of scale p…, pair
related to Finite Type Conditions · 2
Persistence module → Each, There
related to Free Modules · 2
Persistence module → Let, Then

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Important terminology

persistence displaystyle module modules homology interval mathbb structure spaces finite multiparameter field indexed vector one called leq maps definition free

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Persistence moduleis amathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological features of an object across a range of scale p…0.90text
Persistence moduleis apair0.90text
the integers can be represented intuitively as a diagram of spacesinstance ofA single-parameter persistence module indexed by a discrete poset0.80text
commutative algebrainstance ofimported from well-developed areas of mathematics0.80text
representation theory.Interval ModulesA primary concern in the study of persistence modules is whether modules can be decomposed intoinstance ofimported from well-developed areas of mathematics0.80text
representation theoryinstance ofimported from well-developed areas of mathematics0.80text
Persistence modulerelated to Finite Type ConditionsEach0.60section
Persistence modulerelated to Finite Type ConditionsThere0.60section
Persistence modulerelated to Free ModulesLet0.60section
Persistence modulerelated to Free ModulesThen0.60section
Persistence modulerelated to Homology ModulesWhen0.60section
Persistence modulerelated to Homology ModulesTherefore0.60section

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