14 citations · 109 across the 30 of their papers we have counts for
7 papers · 1 filter
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…
Topology and geometry of data manifold in deep learning
German Magai, Anton Ayzenberg
Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open q…
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…
The second cohomology of regular semisimple Hessenberg varieties from GKM theory
Anton Ayzenberg, Mikiya Masuda, Takashi Sato
We describe the second cohomology of a regular semisimple Hessenberg variety by generators and relations explicitly in terms of GKM theory. The cohomology of a regular semisimple H…
Matroids in toric topology
Anton Ayzenberg, Vladislav Cherepanov
In this paper we study general torus actions on manifolds with isolated fixed points from combinatorial point of view. The main object of study is the poset of face submanifolds of…
Cluster-permutohedra and submanifolds of flag varieties with torus actions
Anton Ayzenberg, Victor Buchstaber
In this paper we describe a relation between the notion of graphicahedron, introduced by Araujo-Pardo, Del R\'ıo-Francos, López-Dudet, Oliveros, and Schulte in 2010, and toric topo…
How is a graph not like a manifold?
Anton Ayzenberg, Mikiya Masuda, Grigory Solomadin
For an equivariantly formal action of a compact torus on a smooth manifold with isolated fixed points we investigate the global homological properties of the graded poset $…