Zobrazeno 1 - 10
of 116
pro vyhledávání: '"Brodzki, Jacek"'
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:
Madeleine, Tristan, Podoliak, Nina, Buchnev, Oleksandr, Solis, Ingrid Membrillo, D'Alessandro, Giampaolo, Brodzki, Jacek, Kaczmarek, Malgosia
Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods, or explicitly designed and built lithographically. Correlated disorder, induced by a minimum inter-nanostructure
Externí odkaz:
http://arxiv.org/abs/2306.13540
Autor:
Solis, Ingrid Membrillo, Orlova, Tetiana, Bednarska, Karolina, Lesiak, Piotr, Woliński, Tomasz R., D'Alessandro, Giampaolo, Brodzki, Jacek, Kaczmarek, Malgosia
We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder transition at
Externí odkaz:
http://arxiv.org/abs/2106.13169
Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preventing the full development of this promising theory. In this paper we
Externí odkaz:
http://arxiv.org/abs/2008.11532
We give a new proof of the Baum--Connes conjecture with coefficients for any second countable, locally compact topological group that acts properly and cocompactly on a finite-dimensional CAT(0)-cubical space with bounded geometry. The proof uses the
Externí odkaz:
http://arxiv.org/abs/1908.10485
Understanding the geometry and topology of configuration or conformational spaces of molecules has relevant applications in chemistry and biology such as the proteins folding problem, drug design and the structure activity relationship problem. Despi
Externí odkaz:
http://arxiv.org/abs/1907.07770
Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of the algori
Externí odkaz:
http://arxiv.org/abs/1906.01507
This paper presents a novel time series clustering method, the self-organising eigenspace map (SOEM), based on a generalisation of the well-known self-organising feature map (SOFM). The SOEM operates on the eigenspaces of the embedded covariance stru
Externí odkaz:
http://arxiv.org/abs/1905.05540
We develop a geometric framework that characterizes the synchronization problem --- the problem of consistently registering or aligning a collection of objects. The theory we formulate characterizes the cohomological nature of synchronization based o
Externí odkaz:
http://arxiv.org/abs/1610.09051
In the 1980's Pierre Julg and Alain Valette, and also Tadeusz Pytlik and Ryszard Szwarc, constructed and studied a certain Fredholm operator associated to a simplicial tree. The operator can be defined in at least two ways: from a combinatorial flow
Externí odkaz:
http://arxiv.org/abs/1610.05069