128 citations · 352 across the 30 of their papers we have counts for
36 papers
Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices
Ievgenii Afanasiev, Leonid Berlyand, Mariia Kiyashko
The paper is concerned with deformed Wigner random matrices. These matrices are closely related to Deep Neural Networks (DNNs): weight matrices of trained DNNs could be represented…
Bifurcation of finger-like structures in traveling waves of epithelial tissues spreading
Leonid Berlyand, Antonina Rybalko, Volodymyr Rybalko +1
We consider a continuum active polar fluid model for the spreading of epithelial monolayers introduced by R. Alert, C. Blanch-Mercader, and J. Casademunt, 2019. The corresponding f…
Dynamics and steady state of squirmer motion in liquid crystal
Leonid Berlyand, Hai Chi, Mykhailo Potomkin +1
We analyze a nonlinear PDE system describing the motion of a microswimmer in a nematic liquid crystal environment. For the microswimmer's motility, the squirmer model is used in wh…
A novel multi-scale loss function for classification problems in machine learning
Leonid Berlyand, Robert Creese, Pierre-Emmanuel Jabin
We introduce two-scale loss functions for use in various gradient descent algorithms applied to classification problems via deep neural networks. This new method is generic in the…
Emergence of traveling waves and their stability in a free boundary model of cell motility
Volodymyr Rybalko, Leonid Berlyand
We introduce a two-dimensional Hele-Shaw type free boundary model for motility of eukaryotic cells on substrates. The key ingredients of this model are the Darcy law for overdamped…
Stability of Contraction-Driven Cell Motion
C. Alex Safsten, Volodymyr Rybalko, Leonid Berlyand
We consider motility of keratocyte cells driven by myosin contraction and introduce a 2D free boundary model for such motion. This model generalizes a 1D model from [12] by combini…