5 papers
A data structure for quotient flag complexes
Konstantin Sorokin, Aleksandr Levin, Maxim Beketov +1
Vietoris-Rips filtrations, which are standard in topological data analysis, are flag complexes, and a simplex tree stores these without any attaching data. In this paper we ask wha…
Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection
Arsenii Onuchin, Konstantin Sorokin, Maxim Beketov +1
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on R…
Global cognitive graph properties dynamics of hippocampal formation
Konstantin Sorokin, Andrey Zaitsew, Aleksandr Levin +3
In the present study we have used a set of methods and metrics to build a graph of relative neural connections in a hippocampus of a rodent. A set of graphs was built on top of tim…
Topology of cognitive maps
Konstantin Sorokin, Anton Ayzenberg, Konstantin Anokhin +4
In present paper we discuss several approaches to reconstructing the topology of the physical space from neural activity data of CA1 fields in mice hippocampus, in particular, havi…
Topological approach to diagonalization algorithms
Anton Ayzenberg, Konstantin Sorokin
In this paper we prove that there exists an asymptotical diagonalization algorithm for a class of sparse Hermitian (or real symmetric) matrices if and only if the matrices become H…