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18Plenary session
tic model for big population N. Practically useful confidential interval �three sigma� for the time interval from
the 1th of June 2020 to the 21th of June 2020 is about 110 % (as to the statistical average) and involves the
corresponding experimental estimates. The influence on the prognosis of introduction the delay, i. e. the incubation
period corresponding to Poisson model, was also investigated.
This work was carried out under state contract with ICMMG SB RAS (0251-2021-0002).
References
1. I. Sazonov, D. Grebennikov, M. Kelbert, G. Bocharov, Modelling Stochastic and Deterministic Behaviours in Virus
Infection Dynamics // Math. Model. Nat. Phenom., V. 12, No. 5, 2017, pp. 63-77.
2. N. V. Pertsev, K. K. Loginov, V. A. Topchii, �Analysis of a stage-dependent epidemic model based on a non-Markov
random process�, Sib. Zh. Ind. Mat., 23:3 (2020), 105�122; J. Appl. Industr. Math., 14:3 (2020), 566�580.
3. O. I. Krivorotko, S. I. Kabanikhin, N. Yu. Zyatkov, A. Yu. Prikhodko, N. M. Prokhoshin, M. A. Shishlenin,
�Mathematical modeling and forecasting of COVID-19 in Moscow and Novosibirsk region�, Sib. Zh. Vychisl. Mat., 23:4
(2020), 395�414.
Challenges of the development of a hardware and software platform for environmental monitoring
and environmental modeling
M. A. Marchenko
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Novosibirsk State University
E-mail: marchenko@sscc.ru
DOI 10.24412/cl-35065-2021-1-03-09
The concept of creating an integrating platform (IP) for collecting and analyzing environmental monitoring
data based on the development of domestic scientific and educational organizations and high-tech companies
is proposed. The software and hardware components of such a platform, which exist at the Institute of Computational
Mathematics and Mathematical Geophysics of the SB RAS (ICMMG), are described.
The world practice of environmental monitoring consists in creating networks for monitoring the environmental
situation using inexpensive sensors based on the Internet of Things (IoT) technology and using artificial
intelligence methods. Objects of monitoring and forecasting of such networks: the layer of the atmosphere
above the land, sea and coastal zones, aquatic environment (sea and coastal zones, rivers and lakes,
reservoirs).
IP composition:
� a network of sensors and environmental monitoring devices with precise reference to the terrain thanks
to the GIS system,
� software package for assimilation of monitoring data and forecasting based on artificial intelligence
methods.
� supercomputer center (SCC) for data collection and analysis.
Application of IP:
� collection of environmental information,
� forecasting and modeling situations necessary for decision-making,
� assessment of the risks of negative impact of hazardous natural and man-made impacts on the ecosystem,
infrastructure and population.
PLenary session
At ICMMG, numerical methods and programs for environmental modeling and forecasting have been developed
(V. V. Penenko, A. V. Penenko, 2021 and earlier). In particular, methods have been developed for
identifying pollution sources based on sensitivity operators based on measurement data. Their purpose is to
compensate for the lack of information about the studied processes based on the joint use of mathematical
models and observational data. Specialized experimental versions have been developed for use: in systems for
monitoring and forecasting the quality (pollution) of the atmosphere in cities and industrial areas; in systems
for processing experimental data to study the processes of development of living systems.
At ICMMG, methods have been developed for the optimal placement of elements of an environmental
monitoring network with an assessment of the reliability of such a network and its throughput (A. S. Rodionov,
G. I. Toktoshov, 2020).
One of the IP components is a specialized GIS shell for visualization and modeling of geospatial data ITRIS
(Integrated Tsunami Research and Information System), developed at ICMMG (I. V. Marinin, 2021 and earlier).
The ITRIS system was used to simulate the propagation of tsunami waves in the sea and on reservoirs, to estimate
the tsunami risk (V. K. Gusyakov, 2020): see http://tsun.sscc.ru/IMP_wld_proj.htm
The Center for Collective Use of the Siberian Supercomputer Center of the Siberian Branch of the Russian
Academy of Sciences operates at ICMMG, the activities of which are characterized by the following indicators:
. total performance of computing clusters . 200 Teraflops,
. more than 200 users from 24 organizations,
. users carry out more than 100 research projects per year for a total amount of more than 700 million
rubles.
The stages of development and implementation of IP include:
. creation of an instrumental monitoring network,
. development on its basis of an information and expert system for monitoring and forecasting the ecological
situation,
. preparation and launch of a training program for scientific and engineering personnel,
. creating an opportunity to expand the functionality of the IP for new objects of monitoring and forecasting.
One class of relativistic invariant systems of equations of first order
N. G. Marchuk
Steklov Mathematical Institute RAS, Moscow
Email: nmarchuk@mi-ras.ru
DOI 10.24412/cl-35065-2021-1-00-38
We consider a new class of partial differential equations of first order (we call them "covariantly equipped
systems of equations"), which are invariant with respect to pseudo-orthogonal changes of Cartesian coordinates
of pseudo-Euclidian space. We describe a procedure to reduce a Cauchy problem for a system of equation
to a Cauchy problem for covariantly equipped system of equations. We prove that such procedure can be
apply to the Cauchy problem for Maxwell equations. Covariantly equipped systems of equations give us new
point of view on field theory equations.
