Necessary conditions for discontinuities of multidimensional persistent Betti numbers (Articolo in rivista)

Type
Label
  • Necessary conditions for discontinuities of multidimensional persistent Betti numbers (Articolo in rivista) (literal)
Anno
  • 2015-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1002/mma.3093 (literal)
Alternative label
  • Cerri, Andrea; Frosini, Patrizio (2015)
    Necessary conditions for discontinuities of multidimensional persistent Betti numbers
    in Mathematical methods in the applied sciences
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Cerri, Andrea; Frosini, Patrizio (literal)
Pagina inizio
  • 617 (literal)
Pagina fine
  • 629 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://www.scopus.com/record/display.url?eid=2-s2.0-84921857309&origin=inward (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 38 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 4 (literal)
Note
  • Scopu (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Consiglio Nazionale delle Ricerche; Alma Mater Studiorum Universita di Bologna (literal)
Titolo
  • Necessary conditions for discontinuities of multidimensional persistent Betti numbers (literal)
Abstract
  • Topological persistence has proven to be a promising framework for dealing with problems concerning the analysis of data. In this context, itwas originally introduced by taking into account 1-dimensional properties of data, modeled by real-valued functions. More recently, topological persistence has been generalized to consider multidimensional properties of data, coded by vector-valued functions. This extension enables the study of multidimensional persistent Betti numbers, which provide a representation of data based on the properties under examination. In this contribution, we establish a new link between multidimensional topological persistence and Pareto optimality, proving that discontinuities of multidimensional persistent Betti numbers are necessarily pseudocritical or special values of the considered functions. (literal)
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