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8The Markov chain based models are formulated to study stochastic aspects prominent at low variable num-
bers. The hybrid simulation algorithm based on direct Gillespie method [3] with automatic switching between
stochastic and deterministic methods when variables exceed a specified threshold is implemented in C++. The
stochastic models are used to predict (1) the probability of target cell infection as function of multiplicity of
infection, (2) the heterogeneous structure in the evolution of the viral progeny number distribution, (3) the
processes having the biggest impact on the total progeny number, (4) the integrated provirus number distribu-
tion in HIV-infected cells [4]. The model extensions to describe the innate IFN-I response and the evasion
mechanisms by which HIV-1 and SARS-CoV-2 antagonize it are discussed.
This work was supported by the Russian Foundation for Basic Research (grants 20-01-00352, 20-04-60157) and the
Russian Science Foundation (grant 18-11-00171).
References
1. Shcherbatova et al. Modeling of the HIV-1 life cycle in productively infected cells to predict novel therapeutic
targets // Pathogens. 2020. V. 9. N. 4. P. 255.
2. Grebennikov et al. Intracellular life cycle kinetics of SARS-CoV-2 predicted using mathematical modelling //
Viruses. 2021. V. 13. N. 9. P. 1735.
3. Sazonov et al. Viral infection dynamics model based on a Markov process with time delay between cell infection
and progeny production // Mathematics. 2020. V. 8. N. 8. P. 1207.
4. Sazonov et al. Markov Chain-Based Stochastic Modelling of HIV-1 Life Cycle in a CD4 T Cell // Mathematics. 2021.
V. 9. No 17. P. 2025.
Solution of stochastic optimal control problems
S. A. Gusev
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Novosibirsk State Technical University
Email: sag@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-77
The report is devoted to solution of the problem of stochastic optimal control of dynamical systems, which
are described by stochastic differential equations (SDE�s) of the Ito type [1]. The coefficients of the SDE of the
problem being solved depend on the random process, which is the control at each time item. In the problem, it is
required to define a control such that optimizes the mathematical expectation of the functional of the controlled
process. The determination of the optimal control is carried out on the basis of the principle of dynamic pro-
gramming and solving the HJB equation. Numerical solution of problems of this type is considered.
This work was supported by the budget project 0315-2019-0002 for ICMMG SB RAS.
References
1. Krylov N. V. Controlled Processes of Diffusion Type. M.: Nauka, 1977.
Numerical simulation of a two-dimensional electron gas transfer in a quantum well heterostructure
E. G. Kablukova1, K. K. Sabelfeld1, D. Yu. Protasov2 and K. S. Zhuravlev2
1Institute of Computational Mathematics and Mathematical Geophysics, SB RAS
2Rzhanov Institute of Semiconductor Physics SB RAS
Email: KablukovaE@sscc.ru
DOI 10.24412/cl-35065-2021-1-00-78
In this work, a question of an influence of quantum well subbands number on a drift velocity of a two-
dimensional electron gas in strong and weak electric fields is investigated by numerical modeling. A semicon-
ductor heterostructure AlGaAs/InGaAs/GaAs used as a sample. Self-consistent numerical solution of Poisson�s
equation for electrostatic potential V(z) and Schrodinger�s equation for energy levels Ei and their correspond-
ing wave functions .i lets us to define zone structure of the semiconductor [2, 3]. The obtained data on the
wave functions and the distribution of the charge carriers across the layered structure are used to solve the
Boltzmann kinetic equation and to determine the electron drift velocity. It describes the transfer of two-
dimensional electron gas in the layered heterostructure [4, 5]. The model of electron gas transfer takes into
account the electron scattering by optical and acoustic phonons, and scattering at the roughness of the het-
erointerface.
This work was supported by the Russian Science Foundation under Grant 19-11-00019.
References
1. Gulyaev D.V., Zhuravlev K.S., et al., Influence of the additional p+ doped layers on the properties of
AlGaAs/InGaAs/AlGaAs heterostructures for high power SHF transistors. 2016. J. Phys. D:Appl. Phys., V. 49, 095108.
2. Abgaryan, K.K., Reviznikov, D.L. Numerical simulation of the distribution of charge carrier in nanosized semiconductor
heterostructures with account for polarization effects. Comput. Math. and Math. Phys. 2016, V. 56, P. 161�172.
3. Harrison P., Valavanis A., Quantum Wells, Wires and Dots. Theoretical and Computational Physics of
Semiconduccter Nanostructures. Wiley, UK. 2016.
4. Fawcett W., Boardman A. D., and Swain S., Monte Carlo determination of electron transport properties in Gallium
Arsenide. 1970. J. Phys. Chem. Solids, Pergamon Press, V. 31, p. 1963-1990.
5. Ivashenko V. M. and Mitin V. V., Simulation of Kinetic Phenomena in Semiconductors. Monte Carlo Method, Kiev:
Naukova Dumka, 1990.
Numerical stochastic models of non-stationary time series of bioclimatic indices in West and East Siberia
N. A. Kargapolova1,2, V. A. Ogorodnikov1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: nkargapolova@gmail.com
DOI 10.24412/cl-35065-2021-1-00-79
The report presents the results of numerical modeling of time series of several bioclimatic indices used to
study the unfavorable weather conditions during the cold season. The considered stochastic models of uncon-
ditional and conditional time series reproduce the diurnal cyclicity of the real bioclimatic processes. For a
number of weather stations located in West and East Siberia the results of comparison of estimates of the oc-
currence probability, duration and other characteristics of adverse meteorological conditions characterized
with extreme behavior of the bioclimatic indicators are presented.
This study was carried out under state contract with ICMMG SB RAS (0251-2021-0002).
Application of kernel regression in nonlinear adaptation algorithms as applied to multidimensional objects
S. I. Kolesnikova
Saint-Petersburg State University of Aerospace Instrumentation
Email: skolesnikova@yandex.ru
DOI 10.24412/cl-35065-2021-1-00-80
The application of the time series smoothing algorithm based on the construction of nuclear regression [1]
in the problems of nonlinear synthesis of control for continuous and discrete multidimensional objects is con-
sidered.
