1 citations · 2 across the 9 of their papers we have counts for
6 papers · 1 filter
On essential simplicial maps
Mikhail V. Bludov, Sergei Vad. Fomin, Oleg R. Musin
A fiber-uniform bound on the complexity of an essential simplicial map is proven, and the tightness of the bound is investigated. It follows that the triangula…
Computing the Hopf invariant
Oleg R. Musin, Timur Shamazov
We consider Whitehead's integral formula and propose an algorithm for computing the Hopf invariant for simplicial mappings.
Algorithms for orthogonal partitioning into four parts
Alexey Fakhrutdinov, Oleg R. Musin
The famous pancake theorem states that for every finite set in the plane, there exist two orthogonal lines that divide into four equal parts. We propose an algorithm whose…
Minimal simplicial spherical mappings with a given degree
Ksenia Apolonskaya, Oleg R. Musin
This paper studies the minimal number of vertices required in a triangulation of the -sphere to admit a simplicial map to the boundary of a -simplex with a given…
Topology-Aware Activation Functions in Neural Networks
Pavel Snopov, Oleg R. Musin
This study explores novel activation functions that enhance the ability of neural networks to manipulate data topology during training. Building on the limitations of traditional a…
On Scarf's theorem for Generalized Cooperative Games
Mikhail V. Bludov, Oleg R. Musin
In this paper, we study a generalization of cooperative games with non-transferable utility. In our model, coalitions are replaced by firms: each firm is assigned a resource vector…