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45 results on '"Shishlenin, Maxim"'

1. Mathematical modeling and prediction of COVID-19 in Moscow city and Novosibirsk region

Author

Krivorotko, Olga, Kabanikhin, Sergey, Zyatkov, Nikolay, Prikhodko, Alexey, Prokhoshin, Nikita, and Shishlenin, Maxim

Subjects
Quantitative Biology - Populations and Evolution, Mathematics - Dynamical Systems, 65K10, 92F05, G.1.6, G.1.7, I.6.0, F.2.1
Abstract

The paper formulates and solves the problem of identification of unknown parameters of mathematical models of the spread of COVID-19 coronavirus infection, based on SEIR type models, based on additional information about the number of detected cases, mortality, self-isolation coefficient and tests performed for the Moscow city and the Novosibirsk Region from 03.23.2020. Within the framework of the models used, the population is divided into seven (SEIR-HCD) and five (SEIR-D) groups with similar characteristics with transition probabilities between groups depending on a specific region. Identifiability analysis of the SEIR-HCD mathematical model was carried out, which revealed the least sensitive unknown parameters to additional measurements. The tasks of refining the parameters are reduced to minimizing the corresponding target functionals, which were solved using stochastic methods (simulating annealing, differential evolution, genetic algorithm, etc.). For a different amount of tested data, a prognostic scenario for the development of the disease in the city of Moscow and the Novosibirsk region was developed, the peak is predicted the development of the epidemic in Moscow with an error of 2 days and 174 detected cases, and an analysis of the applicability of the developed models was carried out., Comment: 23 pages, in Russian, 8 figures

Published
2020

4. Convex Optimization with Inexact Gradients in Hilbert Space and Applications to Elliptic Inverse Problems

Author

Matyukhin, Vladislav, Kabanikhin, Sergey, Shishlenin, Maxim, Novikov, Nikita, Vasin, Artem, Gasnikov, Alexander, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Pardalos, Panos, editor, Khachay, Michael, editor, and Kazakov, Alexander, editor

Published
2021
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5. Convex optimization in Hilbert space with applications to inverse problems

Author

Gasnikov, Alexander, Kabanikhin, Sergey, Mohammed, Ahmed, and Shishlenin, Maxim

Subjects
Mathematics - Optimization and Control
Abstract

In this paper we propose accelerated gradient descent schemes for convex optimization problems in Hilbert space. We consider inexact oracle case., Comment: 20 pages. Submitted to Applied Numerical Mathematics

Published
2017

8. Regularization of backward parabolic equations in Banach spaces by generalized Sobolev equations.

Author

Duc, Nguyen Van, Hào, Dinh Nho, and Shishlenin, Maxim

Subjects
SOBOLEV spaces, BANACH spaces, GENERALIZED spaces, EQUATIONS, PARABOLIC operators
Abstract

Let X be a Banach space with norm ∥ ⋅ ∥ . Let A : D ⁢ (A) ⊂ X → X be an (possibly unbounded) operator that generates a uniformly bounded holomorphic semigroup. Suppose that ε > 0 and T > 0 are two given constants. The backward parabolic equation of finding a function u : [ 0 , T ] → X satisfying u t + A ⁢ u = 0 , 0 < t < T , ∥ u ⁢ (T) - φ ∥ ⩽ ε , for φ in X, is regularized by the generalized Sobolev equation u α ⁢ t + A α ⁢ u α = 0 , 0 < t < T , u α ⁢ (T) = φ , where 0 < α < 1 and A α = A ⁢ (I + α ⁢ A b ) - 1 with b ⩾ 1 . Error estimates of the method with respect to the noise level are proved. [ABSTRACT FROM AUTHOR]

Published
2024
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13. Regularization Methods of the Continuation Problem for the Parabolic Equation

Author

Belonosov, Andrey, Shishlenin, Maxim, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Dimov, Ivan, editor, Faragó, István, editor, and Vulkov, Lubin, editor

Published
2017
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15. Multilevel Parallelization: Grid Methods for Solving Direct and Inverse Problems

Author

Titarenko, Sofya S., Kulikov, Igor M., Chernykh, Igor G., Shishlenin, Maxim A., Krivorot’ko, Olga I., Voronov, Dmitry A., Hildyard, Mark, Diniz Junqueira Barbosa, Simone, Series editor, Chen, Phoebe, Series editor, Du, Xiaoyong, Series editor, Filipe, Joaquim, Series editor, Kara, Orhun, Series editor, Kotenko, Igor, Series editor, Liu, Ting, Series editor, Sivalingam, Krishna M., Series editor, Washio, Takashi, Series editor, Voevodin, Vladimir, editor, and Sobolev, Sergey, editor

Published
2016
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17. Direct Method for Identification of Two Coefficients of Acoustic Equation.

Author

Novikov, Nikita and Shishlenin, Maxim

Subjects
*SPEED of sound, *INTEGRAL equations, *EQUATIONS
Abstract

We consider the coefficient inverse problem for the 2D acoustic equation. The problem is recovering the speed of sound in the medium (which depends only on the depth) and the density (function of both variables). We describe the method, based on the Gelfand–Levitan–Krein approach, which allows us to obtain both functions by solving two sets of integral equations. The main advantage of the proposed approach is that the method does not use the multiple solution of direct problems, and thus has quite low CPU time requirements. We also consider the variation of the method for the 1D case, where the variation of the wave equation is considered. We illustrate the results with numerical experiments in the 1D and 2D case and study the efficiency and stability of the approach. [ABSTRACT FROM AUTHOR]

Published
2023
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33. DIRECT PROBLEM FOR THE HYPERBOLIC FIRST-ORDER SYSTEM OF ACOUSTIC WAVES PROPAGATION

Author

Kabanikhin Sergey, Klyuchinskiy Dmitriy, Kulikov Igor, Novikov Nikita, and Shishlenin Maxim

Subjects
first-order hyperbolic system, direct problem, inverse problem, MUSCL-Hancock method, tomography, acoustics, Godunov method
Abstract

We investigate the mathematical modeling of the 2D acoustic waves propagation in homogenious and heterogenious areas. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximation and MUSCL-Hancock method of the second order of approximation

Published
2019
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37. Determination of the impedance of a multiperforated plate: an inverse problem

Author

Kabanikhin, Sergey, Popie, Vincent, Shishlenin, Maxim, Tordeux, Sébastien, Institute of Numerical Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences (SB RAS), Sobolev Institute of Mathematics, ONERA - The French Aerospace Lab [Toulouse], ONERA, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In the context of time-harmonic wave equation, we solve the inverse problem to find an impedance coefficient thanks to measurement of the velocity.

Published
2013

41. Michael V. Klibanov

Author

Anikonov, Yury E., primary, Bakushinskii, Anatoly B., additional, Goncharsky, Alexander V., additional, Hasanov, Alemdar, additional, Kabanikhin, Sergey I., additional, Lavrentiev, Mikhail M., additional, Romanov, Vladimir G., additional, Shishlenin, Maxim A., additional, Tanana, Vitaly P., additional, Tikhonravov, Alexander V., additional, Vasin, Vladimir V., additional, and Yagola, Anatoly G., additional

Published
2011
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