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pro vyhledávání: '"Otter, Nina"'
Persistent homology (PH) is a method for generating topology-inspired representations of data. Empirical studies that investigate the properties of PH, such as its sensitivity to perturbations or ability to detect a feature of interest, commonly rely
Externí odkaz:
http://arxiv.org/abs/2310.07073
Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known for which cl
Externí odkaz:
http://arxiv.org/abs/2206.10551
Magnitude is an isometric invariant for metric spaces that was introduced by Leinster around 2010, and is currently the object of intense research, since it has been shown to encode many known invariants of metric spaces. In recent work, Govc and Hep
Externí odkaz:
http://arxiv.org/abs/2205.09521
Publikováno v:
In Journal of Pure and Applied Algebra December 2024 228(12)
The use of persistent homology in applications is justified by the validity of certain stability results. At the core of such results is a notion of distance between the invariants that one associates with data sets. Here we introduce a general frame
Externí odkaz:
http://arxiv.org/abs/2107.09036
Autor:
Bodnar, Cristian, Frasca, Fabrizio, Otter, Nina, Wang, Yu Guang, Liò, Pietro, Montúfar, Guido, Bronstein, Michael
Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the computational gr
Externí odkaz:
http://arxiv.org/abs/2106.12575
It has long been suggested that the mid-latitude atmospheric circulation possesses what has come to be known as `weather regimes', loosely categorised as regions of phase space with above-average density and/or extended persistence. Their existence a
Externí odkaz:
http://arxiv.org/abs/2104.03196
Autor:
Bodnar, Cristian, Frasca, Fabrizio, Wang, Yu Guang, Otter, Nina, Montúfar, Guido, Liò, Pietro, Bronstein, Michael
The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive power of
Externí odkaz:
http://arxiv.org/abs/2103.03212
Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data, and persis
Externí odkaz:
http://arxiv.org/abs/2011.14688
Autor:
Otter, Nina, Porter, Mason A.
A key concern in network analysis is the study of social positions and roles of actors in a network. The notion of "position" refers to an equivalence class of nodes that have similar ties to other nodes, whereas a "role" is an equivalence class of c
Externí odkaz:
http://arxiv.org/abs/2006.10733