1 citations · 2 across the 9 of their papers we have counts for
10 papers
Borsuk-Ulam type theorem for the orthogonal group and orthogonal four-partitions
Oleg R. Musin
Makeev [2] stated that every finite Borel measure in assigning zero mass to hyperplanes can be cut by mutually orthogonal hyperplanes so that every pair divides t…
Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions
Oleg R. Musin
We prove a Borsuk--Ulam-type zero theorem for the Stiefel manifold with the free action of the hyperoctahedral group . The theorem gives…
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…
A Second Homotopy Group for Digital Images
Gregory Lupton, Oleg Musin, Nicholas A. Scoville +2
We define a second (higher) homotopy group for digital images. Namely, we construct a functor from digital images to abelian groups, which closely resembles the ordinary second hom…
Homotopy groups and quantitative Sperner-type lemma
Oleg R. Musin
Sperner's lemma guarantees a fully labeled simplex under a boundary labeling rule. We ask how many fully labeled simplices are forced by the homotopy class of the boundary map. For…