Zobrazeno 1 - 10
of 217
pro vyhledávání: '"Multiparameter persistence"'
The $\gamma$-linear projected barcode was recently introduced as an alternative to the well-known fibered barcode for multiparameter persistence, in which restrictions of the modules to lines are replaced by pushforwards of the modules along linear f
Externí odkaz:
http://arxiv.org/abs/2408.01065
Multiparameter persistence modules can be uniquely decomposed into indecomposable summands. Among these indecomposables, intervals stand out for their simplicity, making them preferable for their ease of interpretation in practical applications and t
Externí odkaz:
http://arxiv.org/abs/2403.11939
Autor:
Grady, Ryan1 (AUTHOR), Schenfisch, Anna2 (AUTHOR)
Publikováno v:
Proceedings of the American Mathematical Society, Series B. 3/5/2024, Vol. 11, p63-74. 12p.
Local conditions for the direct summands of a persistence module to belong to a certain class of indecomposables have been proposed in the 2-parameter setting, notably for the class of indecomposables called block modules, which plays a prominent rol
Externí odkaz:
http://arxiv.org/abs/2402.16624
Autor:
Bjerkevik, Håvard Bakke
While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is well known to be unstable in a certain precise sense. Until now, it has not been c
Externí odkaz:
http://arxiv.org/abs/2305.15550
Autor:
Frankland, Martin, Stanley, Donald
A persistence module with $m$ discrete parameters is a diagram of vector spaces indexed by the poset $\mathbb{N}^m$. If we are only interested in the large scale behavior of such a diagram, then we can consider two diagrams equivalent if they agree o
Externí odkaz:
http://arxiv.org/abs/2211.05981
Autor:
Botnan, Magnus Bakke, Lesnick, Michael
In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately capture the s
Externí odkaz:
http://arxiv.org/abs/2203.14289
Motivated both by theoretical and practical considerations in topological data analysis, we generalize the $p$-Wasserstein distance on barcodes to multiparameter persistence modules. For each $p\in [1,\infty]$, we in fact introduce two such generaliz
Externí odkaz:
http://arxiv.org/abs/2106.13589
Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preventing the full development of this promising theory. In this paper we
Externí odkaz:
http://arxiv.org/abs/2008.11532
Autor:
Vipond, Oliver
An ideal invariant for multiparameter persistence would be discriminative, computable and stable. In this work we analyse the discriminative power of a stable, computable invariant of multiparameter persistence modules: the fibered bar code. The fibe
Externí odkaz:
http://arxiv.org/abs/2004.11926