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Katalog Publikacji

Rok 2024
Rok 2023
Rok 2022
  • A convergence result for mountain pass periodic solutions of perturbed Hamiltonian systems

    In this work, we study second-order Hamiltonian systems under small perturbations. We assume that the main term of the system has a mountain pass structure, but do not suppose any condition on the perturbation. We prove the existence of a periodic solution. Moreover, we show that periodic solutions of perturbed systems converge to periodic solutions of the unperturbed systems if the perturbation tends to zero. The assumption on...

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  • Constructive Controllability for Incompressible Vector Fields
    Publikacja

    - Rok 2022

    We give a constructive proof of a global controllability result for an autonomous system of ODEs guided by bounded locally Lipschitz and divergence free (i.e. incompressible) vector field, when the phase space is the whole Euclidean space and the vector field satisfies so-called vanishing mean drift condition. For the case when the ODE is defined over some smooth compact connected Riemannian manifold, we significantly strengthen...

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  • Limits Theorems for Random Walks on Homeo(S1)
    Publikacja

    - JOURNAL OF STATISTICAL PHYSICS - Rok 2022

    The central limit theorem and law of the iterated logarithm for Markov chains corresponding to random walks on the space Homeo(S1) of circle homeomorphisms for centered Lipschitz functions and every starting point are proved.

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  • On a comparison principle and the uniqueness of spectral flow
    Publikacja

    - MATHEMATISCHE NACHRICHTEN - Rok 2022

    The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about 0 along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance properties of the spectral flow and establish a simple formula which comprises its classical homotopy invariance and yields a comparison theorem for the spectral flow under compact perturbations. We apply...

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  • t-SNE Highlights Phylogenetic and Temporal Patterns of SARS-CoV-2 Spike and Nucleocapsid Protein Evolution
    Publikacja
    • G. Tamazian
    • A. Komissarov
    • D. Kobak
    • D. Polyakov
    • E. Andronov
    • S. Nechaev
    • S. Kryzhevich
    • Y. Porozov
    • E. Stepanov

    - Rok 2022

    We propose applying t-distributed stochastic neighbor embedding to protein sequences of SARS-CoV-2 to construct, visualize and study the evolutionary space of the coronavirus. The basic idea is to explore the COVID-19 evolution space by using modern manifold learning techniques applied to evolutionary distances between variants. Evolutionary distances have been calculated based on the structures of the nucleocapsid and spike proteins.

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Rok 2021