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Chachólski, Wojciech
Publications (2 of 2) Show all publications
Manouchehrinia, A., Chachólski, W., Hillert, J. & Ramanujam, R. (2018). Topological data analysis to identify subgroups of multiple sclerosis patients with faster disease progression. Paper presented at 34th Congress of the European-Committee-for-Treatment-and-Research-in-Multiple-Sclerosis (ECTRIMS), OCT 10-12, 2018, Berlin, GERMANY. Multiple Sclerosis, 24, 342-343
Open this publication in new window or tab >>Topological data analysis to identify subgroups of multiple sclerosis patients with faster disease progression
2018 (English)In: Multiple Sclerosis, ISSN 1352-4585, E-ISSN 1477-0970, Vol. 24, p. 342-343Article in journal, Meeting abstract (Other academic) Published
Place, publisher, year, edition, pages
Sage Publications, 2018
National Category
Neurosciences
Identifiers
urn:nbn:se:kth:diva-239108 (URN)000446861401025 ()
Conference
34th Congress of the European-Committee-for-Treatment-and-Research-in-Multiple-Sclerosis (ECTRIMS), OCT 10-12, 2018, Berlin, GERMANY
Note

QC 20181121

Available from: 2018-11-21 Created: 2018-11-21 Last updated: 2018-11-21Bibliographically approved
Scolamiero, M., Chachólski, W., Lundman, A., Ramanujam, R. & Öberg, S. (2017). Multidimensional Persistence and Noise. Foundations of Computational Mathematics, 17(6), 1367-1406
Open this publication in new window or tab >>Multidimensional Persistence and Noise
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2017 (English)In: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, Vol. 17, no 6, p. 1367-1406Article in journal (Refereed) Published
Abstract [en]

In this paper, we study multidimensional persistence modules (Carlsson and Zomorodian in Discrete Comput Geom 42(1):71–93, 2009; Lesnick in Found Comput Math 15(3):613–650, 2015) via what we call tame functors and noise systems. A noise system leads to a pseudometric topology on the category of tame functors. We show how this pseudometric can be used to identify persistent features of compact multidimensional persistence modules. To count such features, we introduce the feature counting invariant and prove that assigning this invariant to compact tame functors is a 1-Lipschitz operation. For one-dimensional persistence, we explain how, by choosing an appropriate noise system, the feature counting invariant identifies the same persistent features as the classical barcode construction.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2017
Keywords
Multidimensional persistence, Noise systems, Persistence modules, Stable invariants, Computational methods, Mathematical techniques, Functors, Persistent feature, Pseudo-metrices, Algebra
National Category
Algebra and Logic
Identifiers
urn:nbn:se:kth:diva-197199 (URN)10.1007/s10208-016-9323-y (DOI)000415739500001 ()2-s2.0-84976493395 (Scopus ID)
Note

QC 20161212

Available from: 2016-12-12 Created: 2016-11-30 Last updated: 2017-12-08Bibliographically approved
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