Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Riihimäki, Henri"'
Generalised persistence module theory is the study of tame functors $M \colon \mathcal{P} \rightarrow \mathcal{A}$ from an arbitrary poset $\mathcal{P}$, or more generally an arbitrary small category, to some abelian target category $\mathcal{A}$. In
Externí odkaz:
http://arxiv.org/abs/2307.02444
Autor:
Caputi, Luigi, Riihimäki, Henri
Publikováno v:
Theory and Applications of Categories, Vol. 41, 2024, No. 12, pp 426-448
For a finite quiver $Q$, we study the reachability category $\mathbf{Reach}_Q$. We investigate the properties of $\mathbf{Reach}_Q$ from both a categorical and a topological viewpoint. In particular, we compare $\mathbf{Reach}_Q$ with $\mathbf{Path}_
Externí odkaz:
http://arxiv.org/abs/2306.15388
Autor:
Caputi, Luigi, Riihimäki, Henri
Publikováno v:
Journal of Applied and Computational Topology (2023)
We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree $i\geq 2$. To extend them to higher degrees, we introduce the notion of connectivity digrap
Externí odkaz:
http://arxiv.org/abs/2204.00462
Autor:
Riihimäki, Henri
Directed graphs are ubiquitous models for networks, and topological spaces they generate, such as the directed flag complex, have become useful objects in applied topology. The simplices are formed from directed cliques. We extend Atkin's theory of $
Externí odkaz:
http://arxiv.org/abs/2202.07307
Autor:
Conceição, Pedro, Govc, Dejan, Lazovskis, Jānis, Levi, Ran, Riihimäki, Henri, Smith, Jason P.
A binary state on a graph means an assignment of binary values to its vertices. For example, if one encodes a network of spiking neurons as a directed graph, then the spikes produced by the neurons at an instant of time is a binary state on the encod
Externí odkaz:
http://arxiv.org/abs/2104.06519
Autor:
Riihimäki, Henri, Licón-Saláiz, José
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can stabilize invaria
Externí odkaz:
http://arxiv.org/abs/1906.04436
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 topology. When appl
Externí odkaz:
http://arxiv.org/abs/1904.02971
Autor:
Chachólski, Wojciech, Riihimäki, Henri
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between persistent vec
Externí odkaz:
http://arxiv.org/abs/1904.02905
Autor:
Riihimäki, Henri, Chacholski, Wojciech
We believe three ingredients are needed for further progress in persistence and its use: invariants not relying on decomposition theorems to go beyond 1-dimension, outcomes suitable for statistical analysis and a setup adopted for supervised and mach
Externí odkaz:
http://arxiv.org/abs/1807.01217
Autor:
Caputi, Luigi, Riihimäki, Henri
Publikováno v:
Journal of Applied & Computational Topology; Oct2024, Vol. 8 Issue 5, p1121-1170, 50p
