Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Wojciech Chachólski"'
Publikováno v:
BMC Bioinformatics, Vol 21, Iss 1, Pp 1-18 (2020)
Abstract Background Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data
Externí odkaz:
https://doaj.org/article/c8919804eef949028b416aaef27e8ed0
Publikováno v:
Frontiers in Applied Mathematics and Statistics, Vol 7 (2021)
Exciting recent developments in Topological Data Analysis have aimed at combining homology-based invariants with Machine Learning. In this article, we use hierarchical stabilization to bridge between persistence and kernel-based methods by introducin
Externí odkaz:
https://doaj.org/article/84a516fddb8b498c89b25eaf7de664dd
In Topological Data Analysis, filtered chain complexes enter the persistence pipeline between the initial filtering of data and the final persistence invariants extraction. It is known that they admit a tame class of indecomposables, called interval
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6bab4c2e19e5eab2785262387a97b57
https://hdl.handle.net/11380/1286365
https://hdl.handle.net/11380/1286365
Publikováno v:
Barbara Giunti
In this work, we provide a model structure on full subcategories of tame objects in functor categories indexed by continuous realizations of posets of dimension 1. We also characterize the indecomposable cofibrant objects when the landing category is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::13d9c277741f238592e3bb467e407d12
Publikováno v:
Homology, Homotopy and Applications. 23:183-213
We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at chain complexes level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes several case
Autor:
Gloria Colombo, Ryan John A. Cubero, Lida Kanari, Alessandro Venturino, Rouven Schulz, Martina Scolamiero, Jens Agerberg, Hansruedi Mathys, Li-Huei Tsai, Wojciech Chachólski, Kathryn Hess, Sandra Siegert
Publikováno v:
Nature neuroscience. 25(10)
Environmental cues influence the highly dynamic morphology of microglia. Strategies to characterize these changes usually involve user-selected morphometric features, which preclude the identification of a spectrum of context-dependent morphological
Autor:
Wojciech Chachólski
Publikováno v:
Emerging Topics in Artificial Intelligence (ETAI) 2021.
In the last decade, there has been an unprecedented development in topological data analysis tools to encode geometrical information. These tools have been successful for extracting new information from brain networks with a range of methods such as
Autor:
Ilaria Carannante, Johanna Frost Nylén, Johannes Hjorth, Alexander Kozlov, Joana Braga Pereira, Martina Scolamiero, Wojciech Chachólski, Arvind Kumar, Lihao Guo, Jeanette Hellgren Kotaleski
The relationship between the structure and network dynamics within the striatum is currently not well understood. We have applied algebraic topology to investigate the local structural connectivity in the striatum, and then used simulations to predic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e49d7a84f49ebf936fe8d2486e1c0ab9
https://doi.org/10.14293/s2199-1006.1.sor-.ppaemim.v1
https://doi.org/10.14293/s2199-1006.1.sor-.ppaemim.v1
Motivated by applications in Topological Data Analysis, we consider decompositions of a simplicial complex induced by a cover of its vertices. We study how the homotopy type of such decompositions approximates the homotopy of the simplicial complex i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::af95b8c6f33b22fea12830b56e7ee9ea
http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-304028
http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-304028
Publikováno v:
Journal of Pure and Applied Algebra. 221:1055-1075
A multifiltration is a functor indexed by $\mathbb{N}^r$ that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural $\mathbb{N}^r$-graded $R[x_1,\ldots, x_r]$-module structure on t