=Paper=
{{Paper
|id=Vol-2744/paper79
|storemode=property
|title=Intelligent Data Analysis for Forecasting Threats in Complex Distributed Systems
|pdfUrl=https://ceur-ws.org/Vol-2744/paper79.pdf
|volume=Vol-2744
|authors=Evgeny Palchevsky,Olga Khristodulo,Sergey Pavlov,Artur Kalimgulov
}}
==Intelligent Data Analysis for Forecasting Threats in Complex Distributed Systems==
https://ceur-ws.org/Vol-2744/paper79.pdf
Intelligent Data Analysis for Forecasting Threats in
Complex Distributed Systems*
Evgeny Palchevsky[0000−0001−9033−5741], Olga Khristodulo[0000−0002−3987−6582],
Sergey Pavlov[0000−0001−9672−7623] and Artur Kalimgulov[0000−0002−9969−0712]
Ufa State Aviation Technical University, Ufa 450008, Russia
teelxp@inbox.ru, o-hristodulo@mail.ru, psvgis@mail.ru,
kalimgulovartur@gmail.com
Abstract. A threat prediction method based on the intellectual analysis of his-
torical data in complex distributed systems (CDS) is proposed. The relevance of
the chosen research topic in terms of considering the flood as a physical process
of raising the water level, which is measured at stationary and automatic hydro-
logical posts, is substantiated. Based on this, a mathematical formulation of the
problem is formulated, within the framework of which an artificial neural net-
work based on the freely distributed TensorFlow software library is implement-
ed. The analysis of the effectiveness of the implemented artificial neural net-
work was carried out, according to which the average deviation of the predicted
water level when forecasting for one day at a stationary hydrological post was
3.323%. For further research on forecasting water levels, an algorithm is pro-
posed for evaluating historical data at automatic posts, which will allow using
these data to predict water levels according to the proposed method and at au-
tomatic posts. Thus, the neural network allows predicting the flood situation
with acceptable accuracy, which allows special services to take measures to
counter this threat.
Keywords: Complex Distributed Systems, Threat Prediction, Data Mining,
Neural Networks, Flood Situation, Water Level Prediction
1 Introduction
The ever-more rapid development of digital technologies allows us to take a fresh
look at the interaction of various components of the real world: physical, biological,
social, etc. Moreover, digital technologies themselves become the most important
component of this world, and these technologies allow people to influence the interac-
tion of all components among themselves and especially to people. This complex
interconnected set of objects of various complexity and physical nature can be con-
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons Li-
cense Attribution 4.0 International (CC BY 4.0).
* The reported study was funded by RFBR, project number 20-08-00301.
2 E. Palchevsky, O. Khristodulo, S. Pavlov, et al.
sidered as a complex distributed system (CDS), which is characterized by a signifi-
cant remoteness of the component components from each other and a quick change in
their characteristics over time.
The components of such CDS themselves are complex distributed systems and
have (or potentially can have), including negative impact on each other, that is, they
constitute or pose a threat to each other. For example, such a biological (natural)
component of the CDS as a river network when a natural (spring or rain flood) or
artificial (dam destruction) high water rise occurs on it can have a negative impact on
such technical components of the CDS as power lines, piping systems, etc., or on the
social components of the CDS – places of residence and recreation of people. Today,
one of the urgent tasks is the development of various, as a rule, highly computerized,
means and methods of countering various threats based on forecasting the develop-
ment of processes that form the basis of these threats.
This article discusses the task of countering one of the types of threats - flood,
based on the physical process of raising the water level in water bodies, and capable
of causing significant material damage to individual components of the CDS in the
territory of the subject of the Russian Federation (for example, the Republic of Bash-
kortostan). To counter this threat, complex technical systems with an increasingly
significant digital component are created and intensively developed, which allow
monitoring and predicting water levels in water bodies. These systems are based on
the integration of modern technical means of obtaining the information necessary for
monitoring (measuring the level and temperature of water and air, water flow rate,
etc.) and modern information technologies for processing this information for fore-
casting (analysis of large, including poorly structured data; distributed databases data;
the Internet of things (or the Internet of everything); artificial intelligence, etc.) and
can be classified as cyberphysical systems.
Traditionally, the water level is measured at stationary hydrological observation
posts (gauging stations) of the regional department of hydrometeorology and envi-
ronmental monitoring (Bashhydromet) and planning of measures to counter the flood
threat is carried out on the basis of the forecast of the water level according to these
data (for these posts). Recently, water bodies have additionally begun to install auto-
matic water level monitoring posts equipped with video cameras for early detection
and recording of a sharp rise in the water level, which is dangerous for the compo-
nents of the CDS. It would be logical to use the values of water levels obtained from
automatic posts as additional data for forecasting water levels in water bodies, how-
ever, there are no historical data needed for forecasting.
There are various approaches to solving the problem of predicting water levels in
water bodies, based on the analysis of hydrogeological and hydrodynamic parameters
of the state of water bodies [1–3], a number of works by domestic and foreign authors
are devoted to various aspects of the development of methods in this area [4–6].
However, in these works, insufficient attention was paid to the problem of predicting
water levels based on the intellectual analysis of retrospective data, including from
automatic posts using artificial neural networks (ANNs).
Intelligent Data Analysis for Forecasting Threats in Complex Distributed Systems 3
2 The use of artificial intelligence technologies to predict
the levels of water rise during the spring flood
One of the main parameters of the possible negative impact of the flood situation on
various components of the emergency control system is h – the water level in water
bodies, measured daily at n stationary hydrological posts by Bashhydromet employ-
ees. We introduce the notation: ℎ𝑗𝑖𝑘 is the value of the water level measured at the k-th
hydrological post on the i-th date of the j-th year. Here 𝑘 = 1, ⃗⃗⃗⃗⃗⃗𝑛, where n is the num-
ber of hydrological posts involved in the calculations, j is the number of the year, i is
the specific measurement date. At the stage of making a short-term forecast of water
levels, the forecasting task is to calculate the value of the level of water rise on the
𝑘
next i+1 day, that is, ℎ𝑗𝑖+1 , for any 𝑘 = ⃗⃗⃗⃗⃗⃗
1, 𝑛 on a specific current i-day of measure-
ment.
To solve this problem, it is proposed to use the results of previous measurements of
the level of water rise ℎ𝑗𝑖𝑘 at all stationary hydrological posts located in the territory
under consideration in the same climatic and hydrological conditions for all previous
years.
In each specific territory (including the Republic of Bashkortostan), various water
bodies can be in different conditions that affect the nature of the development of the
flood situation. For example, in one part of the territory the river flows in the moun-
tains, and in another part – along the plain. Also, on the same territory, different rivers
can belong to different basins with different hydrological and climatic characteristics.
Therefore, to predict the water level at a particular gauging station, it is logical to use
data on water levels at those hydrological posts that are in the same conditions with it
and the number of hydrological posts participating in the forecasting can be less than
n. Determining the uniformity of conditions in which hydrological posts are located is
an independent scientific task, and in this article, for simplicity of presentation of the
forecasting method, but without violating the generality of reasoning, we assume that
data from n hydrological posts are used.
A similar remark must be made with respect to the possible values of the index i
denoting the date of measurement. In fact, the value of the date itself for forecasting is
not significant, since in different years at different posts the rise in the water level and
the return of the water level to the normal value occur on different days. The serial
number of the measurement since the start of the flood is significant. The number of
measurements, which corresponds to the duration of the flood situation, for each fixed
pair of values of the indices k and j is also different, therefore we introduce its nota-
tion 𝑙𝑘𝑗 . In the framework of the comments made, we denote the entire set of previ-
ously measured water level values as
𝐻1 = {ℎ𝑗𝑖𝑘 }, 𝑘 = ⃗⃗⃗⃗⃗⃗ 1, 𝑚; 𝑖 = ⃗⃗⃗⃗⃗⃗⃗⃗⃗
1, 𝑛; 𝑗 = ⃗⃗⃗⃗⃗⃗⃗⃗ 1, 𝑙𝑘𝑗 , (1)
where m is the number of years of observations. But in the current (m+1) th year, by
the time the flood starts and during the flood, measurements are also taken and can be
4 E. Palchevsky, O. Khristodulo, S. Pavlov, et al.
used to predict the values of the water level on each specific day on the next (𝑖0 + 1)
th day, therefore into consideration another set
𝑘
𝐻2 = {ℎ𝑚+1,𝑖 }, 𝑘 = ⃗⃗⃗⃗⃗⃗
1, 𝑛; 𝑖 = ⃗⃗⃗⃗⃗⃗⃗
1, 𝑖0 . (2)
In this case, of course, it is important to choose the day the flood starts, from which
the forecasting starts (that is, to which day i=1 corresponds). This article is not con-
sidered in this article, since it affects the specific values of 𝑙𝑘𝑗 , the number and list of
elements of the sets H1 and H2, which in turn affects the time for calculating forecast
values, but does not affect the method and forecasting algorithm itself.
It is also necessary to introduce an additional notation for the predicted value of the
water level – hp, since in the future, to evaluate the effectiveness of forecasting meth-
ods, it will be necessary to use the notation h and hp together.
Based on the introduced notation, predicting the water level in the current m+1
year at a fixed hydrological station 𝑘0 , 1 ≤ 𝑘0 ≤ 𝑛 at some fixed point in time 𝑖0 will
be described one day in advance by a certain function of the set of previously per-
formed measurements:
𝑘
0
ℎ𝑝𝑚+1,𝑖0 +1
= 𝑓(𝐻1, 𝐻2). (3)
There are many approaches and methods for constructing this function, using all or
part of the H1 and H2 data, including various statistical [7–9], hydrological [10] and
intelligent methods [11–13].
Currently, the so-called artificial intelligence methods and, in particular, the meth-
ods of constructing artificial neural networks (ANNs) are widely used to solve various
problems [14, 15]. In this paper, it is proposed to predict the future value of the water
level using an artificial neural network with training without a teacher based on the
integration of the back propagation method of error and the Rosenblatt method, which
are carried out in two stages (Fig. 1).
At the first stage, which is carried out before the development of the flood situa-
tion, the parameters are selected and ANNs are trained based on existing values from
the set H1. The result of the training are the values of the weight coefficients of the
synapses, which are subsequently used for forecasting. At the second stage, the fore-
𝑘
cast values of ℎ𝑝𝑚+1,𝑖 0
are calculated daily for all n observation posts (𝑘 = ⃗⃗⃗⃗⃗⃗
1, 𝑛) using
a trained ANN.
Since ANNs only process data that varies in the range [0,1], it is necessary to con-
vert (normalize or normalize) all measured (archived and current) water levels accord-
ing to the most common ratio:
𝑘
ℎ𝑗𝑖 −ℎ𝑚𝑖𝑛
⃗ 𝑗𝑖𝑘 =
ℎ , (4)
ℎ𝑚𝑎𝑥 −ℎ𝑚𝑖𝑛
⃗⃗⃗⃗⃗⃗𝑛; 𝑗 = ⃗⃗⃗⃗⃗⃗⃗⃗
where ℎmin = min(ℎ𝑗𝑖𝑘 ) and ℎmax = max(ℎ𝑗𝑖𝑘 ), for all 𝑘 = 1, 1, 𝑚; 𝑖 =
𝑘,𝑗,𝑖 𝑘,𝑗,𝑖
⃗⃗⃗⃗⃗⃗⃗⃗⃗
1, 𝑙𝑘𝑗 .
Intelligent Data Analysis for Forecasting Threats in Complex Distributed Systems 5
ANN
1st stage parameters
H1 Norma- H1 ANN Synapse
DB
lization training weights
Synapse
2nd stage weights
Current H2 Norma- H2 Trained hp Denorma- hp Flood control
values lization ANN lization measures
Fig. 1. Scheme of using a neural network for prediction.
Subsequently, normalized values of ℎ ⃗ 𝑗𝑖𝑘 are fed to the input of the ANN both at the
training stage and at the forecasting stage, as a result of which the result (predicted
value) is also normalized. Therefore, before applying the predicted values to counter
the threat of flood, they are denormalized (reduced to the usual values of the water
level) in a ratio that is the opposite (4):
⃗ 𝑗𝑖𝑘 ⋅ (ℎ𝑚𝑎𝑥 − ℎ𝑚𝑖𝑛 ) + ℎ𝑚𝑖𝑛 .
ℎ𝑗𝑖𝑘 = ℎ (5)
3 Analysis of the effectiveness of the proposed approach
for predicting water levels at stationary hydrological
posts
To predict water levels, the authors developed the software module “Forecaster” [16],
based on the use of the freely distributed library of machine learning programs “Ten-
sorFlow” [17, 18]. The analysis of the effectiveness of applying the proposed ap-
proach for predicting water levels was carried out on retrospective (for the last 20
years) data at stationary gauging stations for the period from January 1, 2000 to May
22, 2019. The total amount of data is 22,341, of which 66% (data long-term observa-
tions of water levels ℎ𝑗𝑖𝑘 from 01.01.2000 to 31.12.2014) are fed to the input sample of
an artificial neural network to create an image of an array of input data for direct
analysis for the purpose of further training, and the remaining 34% (01.01.2015–
22.05.2019) – for training.
Every day, since the beginning of monitoring the development of the flood situa-
tion (in 2020 it was April 18, that is, i=1), using the Forecaster program, the forecast
for the next day was made for 3 hydrological posts (that is, n=3; this value is n taken
to reduce the time of the experiment), that is, it was determined
𝑘
ℎ𝑝𝑚+1,𝑖+1 = 𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑒𝑟(𝐻1, 𝐻2). (6)
6 E. Palchevsky, O. Khristodulo, S. Pavlov, et al.
𝑘
The next day, the actual value of the water levels at the same stations ℎ𝑚+1,𝑖+1 was
measured and the predicted value was compared with the actual value based on the
value of the relative difference, which most often characterizes the forecast accuracy:
2
𝑘 𝑘
(ℎ𝑝𝑚+1,𝑖+1 −ℎ𝑚+1,𝑖+1 )
𝐸𝑖𝑘 = 𝑘 , (7)
ℎ𝑚+1,𝑖+1
for all hydrological posts 𝑘 = ⃗⃗⃗⃗⃗⃗
1, 𝑛. Carrying out forecasting daily until May 17 (that
is, 𝑙𝑘,𝑚+1 = 30), we obtain 30 forecasts for each post and actual values of water lev-
els for each of n posts, which makes it possible to determine the average forecast
accuracy for each k-th post:
1 𝑙
𝑘,𝑚+1 𝑘
𝐸𝑘 = ∑𝑖=1 𝐸𝑖 , (8)
𝑙𝑘,𝑚+1
and for all posts for the entire forecasting period in 2020:
1
𝐸 = ∑𝑛𝑘=1 𝐸 𝑘 . (9)
𝑛
In fig. 2 shows the actually measured and predicted water levels in 2020 at one of the
observation posts. The calculation of the accuracy of the forecast showed the value of
average accuracy for each post E1 = 2.900%; E2 = 3.511%; E3 = 3.560%, and the
average forecast accuracy for the entire flood period of 2020 is E = 3.323, which cor-
responds to the forecasting accuracy by other methods [2].
Fig. 2. An example of the results of forecasting levels of water rise at a stationary gauging
station 76289 (Ufa, Belaya river).
Thus, the use of artificial intelligence technologies in the form of a recurrent neural
network gives a sufficiently accurate result in the framework of forecasting water
levels at stationary hydrological posts, which allows the relevant services to quickly
respond to this threat and take the necessary measures to counter it.
Intelligent Data Analysis for Forecasting Threats in Complex Distributed Systems 7
4 Using data from automatic posts to predict the level of
water rise
In connection with the emergence of new technical capabilities for automatic meas-
urement of the state of the CDS (water level, temperature, wind speed and direction,
etc.), automatic stations for measuring and recording water level in water bodies have
recently been increasingly used [19]. As a rule, they have departmental affiliation
different from Roshydromet divisions: they are part of the structure of local or region-
al executive authorities that deal with the prevention and counteraction of threats. The
main purpose of these stations is the early detection of a threat and informing the
governing bodies and the population about it, at the same time, the data from these
posts can be used to predict a possible threat according to the technique proposed in
the previous paragraphs of this article. To use this technique, there are no archival
measurements at automatic posts (after all, they simply did not exist before), there-
fore, it is proposed to introduce an estimate of the water level at the locations of au-
tomatic hydrological posts in the past (since, despite the fact that there were no auto-
matic posts, the water level in this point was at some point and the regularity of its
(level) change is the same as at stationary hydrological posts) based on archival val-
ues at neighboring stationary gauging stations. This offer can be used only for those
automatic posts that are located between stationary hydrological posts (one upstream
and one lower), and the water level value is interpolated for them. It is necessary to
take into account the fact that at stationary gauging stations one value of the water
level is measured discretely every day at a fixed point in time (usually at 10 a.m. local
time), and at automatic posts the water level is measured continuously. For the correct
application of relations (1)–(6) (that is, for comparability of measurement results at
automatic and stationary hydrological stations), the average of continuously measured
values over 10 minutes is selected as the water level value at the k-th hydrological
station for a specific date ( from 955 to 1005) on this date.
Figure 3 shows the location of stationary hydrological posts (34 objects) and auto-
matic posts (38 objects) at the water bodies of the Republic of Bashkortostan [20], an
analysis of their relative position (Fig. 3) showed that 7 automatic posts (during the
flood in 2020) are located between stationary gauging stations (table 1).
8 E. Palchevsky, O. Khristodulo, S. Pavlov, et al.
Fig. 3. Placement of stationary and automatic gauging stations on water bodies of the Republic
of Bashkortostan.
Table 1. Automatic posts located between stationary gauging stations at water bodies of the
Republic of Bashkortostan
# Downstream hydrologi- Automatic post title Upper hydrological post
cal post
1 Krasnaya Gorka village Red key Pavlovskaya hydroelectric
(Ufa river) station, n. pool (r. Ufa)
2 Krasnaya Gorka village Yaman Port Pavlovskaya hydroelectric
(Ufa river) station, n. pool (r. Ufa)
3 Andreevka village (Be- Birsk Birsk city (Belaya river)
laya river)
4 Lyakhovo village Bulgakovo Okhlebinino village (Belaya
(Urshak river) river)
5 Sterlitamak city (Belaya Sterlitamak (st. B. Novofedorovskoe village
river) Khmelnitsky) (Ashkadar river)
6 Sterlitamak city (Belaya Sterlitamak the village of New Otra-
river) (Vodolazhenko St.) dovka (p. Sterlya)
7 Meteli village (Ay river) Bolsheustikinsky Lakly village (Ay river)
Intelligent Data Analysis for Forecasting Threats in Complex Distributed Systems 9
Denote the total number of automatic posts located between two stationary posts by
na. In our case, today na=7, but over time, automatic posts can be closed, moved to
another place or liquidated, so na, generally speaking, is a variable. Since water level
measurements at automatic posts (real and interpolated) were not included in the defi-
nition of the set H1 by relation (1), we denote ℎ𝑎𝑗𝑖𝑘 as the interpolated estimated value
of the water level at the location of the k-th automatic post, 𝑘 = ⃗⃗⃗⃗⃗⃗⃗⃗⃗
1, 𝑛𝑎, in the i-th day
of the j-th year, where𝑗 = 1, 𝑚, 𝑖 = ⃗⃗⃗⃗⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗⃗⃗⃗ 1, 𝑙𝑘𝑗 , as before. Actual measurements at station-
ary posts adjacent to the selected kth automatic post are included in the set H1, but the
order of the numbers of these posts in the set H1 and in table 1 do not coincide, there-
fore, to automate the calculations, we introduce additional notation. We denote by KD
the set of numbers of stationary gauging stations located downstream, and by KU the
set of numbers of stationary gauging stations located upstream of the corresponding
automatic post so that
𝐾𝐷 = (𝑘𝑑1 , 𝑘𝑑2 , . . . , 𝑘𝑑𝑛𝑎 ),
(10)
𝐾𝑈 = (𝑘𝑢1 , 𝑘𝑢2 , . . . , 𝑘𝑢𝑛𝑎 ),
and the automatic post with number k is located between two stationary posts with
numbers kdk and kuk.
In the calculations (interpolation) of the ℎ𝑎𝑗𝑖𝑘 value, the distance between the auto-
matic and neighboring stationary gauging stations is involved, therefore we introduce
the variable x, which denotes the distance (distance) of the corresponding post from
the river mouth, and, generally speaking, the water level at any point of the river can
be considered as a function from this distance:
ℎ = ℎ(𝑥). (11)
For each k-th stationary post, this distance is a fixed number xk, 𝑘 = ⃗⃗⃗⃗⃗⃗
1, 𝑛; accordingly,
for automatic posts this distance is denoted by xak, 𝑘 = ⃗⃗⃗⃗⃗⃗⃗⃗⃗
1, 𝑛𝑎. By virtue of the nota-
tion introduced, the location of some automatic post between two stationary hydrolog-
ical posts is described by the relation
𝑥𝑘𝑑𝑘 < 𝑥𝑎𝑘 < 𝑥𝑘𝑢𝑘 ,
⃗⃗⃗⃗⃗⃗𝑛,
ℎ𝑗𝑖𝑘 = ℎ𝑗𝑖𝑘 (𝑥𝑘 ), 𝑘 = 1, (12)
ℎ𝑎𝑗𝑖𝑘 = ℎ𝑗𝑖𝑘 (𝑥𝑎𝑘 ), 𝑘 = ⃗⃗⃗⃗⃗⃗⃗⃗⃗
1, 𝑛𝑎.
In the general case, this dependence has the same nature, defined by relation (11), but
different notations are introduced to explain the interpolation algorithm for stationary
and automatic posts.
Assuming that the change in the water level in the river between two points (the lo-
cations of gauging stations) occurs linearly (which is quite acceptable for small dis-
tances), the interpolated value of ℎ𝑎𝑗𝑖𝑘 is on a straight line connecting the water level
points at neighboring stationary posts and is calculated (in accordance with known
rules Euclidean geometry, see Fig. 4) by the relation
10 E. Palchevsky, O. Khristodulo, S. Pavlov, et al.
𝑘𝑑 𝑘𝑑 𝑘𝑑 𝑥𝑎𝑘 −𝑥𝑘𝑑𝑘
ℎ𝑎𝑗𝑖𝑘 = ℎ𝑗𝑖 𝑘 + (ℎ𝑗𝑖 𝑘 − ℎ𝑗𝑖 𝑘 ) ⋅ . (13)
𝑥𝑘𝑢 −𝑥𝑘𝑑
𝑘 𝑘
h, m
h ku
ji
k
ha kji
h kd
ji
k
x, m
0
xkuk xak xkdk
Fig. 4. Diagram of changes in water level at various (neighboring) gauging stations for a fixed
date depending on their distance from the river mouth.
Fig. 5 shows an example of interpolation of the values of the level of water rise for the
automatic hydrological post “Red Key”, based on data from neighboring stationary
hydrological posts – “p. Krasnaya Gorka (Ufa River)” and “Pavlovskaya Hydroelec-
tric Power Station, n. pool (Ufa River) ". As an example, we use the historical data of
water levels at these hydrological posts from 04.05.2009; water level at the post “s.
Krasnaya Gorka (p. Ufa)” was 197 cm, at the post “Pavlovskaya hydroelectric power
station, n. pool (p. Ufa) ” – 413cm. As a result of the interpolation for the “Red Key”
automatic post, the water level values were obtained – 223 cm, which we will consider
as historical data for this automatic post on 04.05.2009. The water level values thus
obtained as a result of interpolation for each automatic post and for all the remaining
dates will be considered historical data for this automatic post. The amount of these
data is the same as the number of observations at neighboring stationary gauging sta-
tions. Now, the array of the estimated data can be used to predict water levels accord-
ing to the method proposed in paragraph 2 using the ANN for all automatic posts in-
cluded in table 1.
Intelligent Data Analysis for Forecasting Threats in Complex Distributed Systems 11
Fig. 5. The result of the interpolation of data on the levels of water rise for automatic post.
5 Conclusion
Solving complex socially and economically significant tasks for managing the CDS,
which undoubtedly includes parrying such types of threats as floods, requires the inte-
gration of modern breakthrough technologies, such as data mining, distributed data-
bases, the Internet of things and artificial intelligence, which are inextricable parts of a
single process for obtaining and analyzing heterogeneous data on the state of the CDS
and its individual components. The article proposes an approach that allows for the
joint analysis and processing of data on water levels from automatic and stationary
gauging stations to predict flood threats using artificial neural networks. The analysis
of the results of applying the proposed approach for predicting the water level in the
water bodies of the Republic of Bashkortostan during the 2020 flood showed its effec-
tiveness, as it gives a fairly accurate forecast, and thereby allows the relevant services
to quickly respond to this threat and take the necessary measures to counter it.
6 Acknowledgments
The reported study was funded by RFBR, project number 20-08-00301.
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