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Modeling banking systems using a network approach has received growing attention in recent years. One of the notable models is that developed by Iori et al, who proposed a banking system model for analyzing systemic risks in interbank networks. The model is built based on the simple dynamics of several bank balance sheet variables such as deposit, equity, loan, liquid asset, and interbank lending (or borrowing) in the form of difference equations. Each bank faces random shocks in deposits and loans. The balance sheet is updated at the beginning or end of each period. In the model, banks are grouped into either potential lenders or borrowers. The potential borrowers are those that have lack of liquidity and the potential lenders are those which have excess liquids after dividend payment and channeling new investment. The borrowers and the lenders are connected through the interbank market. Those borrowers have some percentage of linkage to random potential lenders for borrowing funds to maintain their safety net of the liquidity. If the demand for borrowing funds can meet the supply of excess liquids, then the borrower bank survives. If not, they are deemed to be in default and will be removed from the banking system. However, in their paper, most part of the interbank borrowing-lending mechanism is described qualitatively rather than by detailed mathematical or computational analysis. Therefore, in this paper, we enhance the mathematical parts of borrowing-lending in the interbank market and present an algorithm for simulating the model. We also perform some simulations to analyze the effects of the model’s parameters on banking stability using the number of surviving banks as the measure. We apply this technique to analyze the effects of a macroprudential policy called loan-to-deposit ratio based reserve requirement for banking stability.

The article describes a simulation agent-based model of intercultural interactions in a country whose population belongs to different cultures. It is believed that the space of cultures can be represented as a Hilbert space, in which certain subspaces correspond to different cultures. In the model, the concept of culture is understood as a structured subspace of the Hilbert space. This makes it possible to describe the state of agents by a vector in a Hilbert space. It is believed that each agent is described by belonging to a certain «culture». The number of agents belonging to certain cultures is determined by demographic processes that correspond to these cultures, the depth and integrity of the educational process, as well as the intensity of intercultural contacts. Interaction between agents occurs within clusters, into which, according to certain criteria, the entire set of agents is divided. When agents interact according to a certain algorithm, the length and angle that characterize the state of the agent change. In the process of imitation, depending on the number of agents belonging to different cultures, the intensity of demographic and educational processes, as well as the intensity of intercultural contacts, aggregates of agents (clusters) are formed, the agents of which belong to different cultures. Such intercultural clusters do not entirely belong to any of the cultures initially considered in the model. Such intercultural clusters create uncertainties in cultural dynamics. The paper presents the results of simulation experiments that illustrate the influence of demographic and educational processes on the dynamics of intercultural clusters. The issues of the development of the proposed approach to the study (discussion) of the transitional states of the development of cultures are discussed.

Expert systems imitate professional experience and thinking process of a specialist to solve problems in various subject areas. An example of the problem that it is expedient to solve with the help of the expert system is the problem of forming a diagnosis that arises in technology, medicine, and other fields. When solving the diagnostic problem, it is necessary to anticipate the occurrence of critical or emergency situations in the future. They are situations, which require timely intervention of specialists to prevent critical aftermath. Fuzzy sets theory provides one of the approaches to solve ill-structured problems, diagnosis-making problems belong to which. The theory of fuzzy sets provides means for the formation of linguistic variables, which are helpful to describe the modeled process. Linguistic variables are elements of fuzzy logical rules that simulate the reasoning of professionals in the subject area. To develop fuzzy rules it is necessary to resort to a survey of experts. Knowledge engineers use experts’ opinion to evaluate correspondence between a typical current situation and the risk of emergency in the future. The result of knowledge extraction is a description of linguistic variables that includes a combination of signs. Experts are involved in the survey to create descriptions of linguistic variables and present a set of simulated situations.When building such systems, the main problem of the survey is laboriousness of the process of interaction of knowledge engineers with experts. The main reason is the multiplicity of questions the expert must answer. The paper represents reasoning of the method, which allows knowledge engineer to reduce the number of questions posed to the expert. The paper describes the experiments carried out to test the applicability of the proposed method. An expert system for predicting risk groups for neonatal pathologies and pregnancy pathologies using the proposed knowledge extraction method confirms the feasibility of the proposed approach.

Industrial robots have made it possible for robotics to become a worldwide discipline both in economy and in science. However, their capabilities are limited, especially regarding contact tasks where it is required to regulate or at least limit contact forces. At one point, it was noticed that elasticity in the joint transmission, which was treated as a drawback previously, is actually helpful in this regard. This observation led to the introduction of elastic joint robots that are well-suited to contact tasks and cooperative behavior in particular, so they become more and more widespread nowadays. Many researchers try to implement such devices not with trivial series elastic actuators (SEA) but with more sophisticated variable stiffness actuators (VSA) that can regulate their own mechanical stiffness. All elastic actuators demonstrate shock robustness and safe interaction with external objects to some extent, but when stiffness may be varied, it provides additional benefits, e. g., in terms of energy efficiency and task adaptability. Here, we present a novel variable stiffness actuator with a magnetic coupler as an elastic element. Magnetic transmission is contactless and thus advantageous in terms of robustness to misalignment. In addition, the friction model of the transmission becomes less complex. It also has milder stiffness characteristic than typical mechanical nonlinear springs, moreover, the stiffness curve has a maximum after which it descends. Therefore, when this maximum torque is achieved, the coupler slips, and a new pair of poles defines the equilibrium position. As a result, the risk of damage is smaller for this design solution. The design of the joint is thoroughly described, along with its mathematical model. Finally, the control system is also proposed, and simulation tests confirm the design ideas.

The problem of optimal control of traffic flow in an urban road network is considered. The control is carried out by varying the duration of the working phases of traffic lights at controlled intersections. A description of the control system developed is given. The control system enables the use of three types of control: open-loop, feedback and manual. In feedback control, road infrastructure detectors, video cameras, inductive loop and radar detectors are used to determine the quantitative characteristics of current traffic flow state. The quantitative characteristics of the traffic flows are fed into a mathematical model of the traffic flow, implemented in the computer environment of an automatic traffic flow control system, in order to determine the moments for switching the working phases of the traffic lights. The model is a system of finite-difference recurrent equations and describes the change in traffic flow on each road section at each time step, based on retrived data on traffic flow characteristics in the network, capacity of maneuvers and flow distribution through alternative maneuvers at intersections. The model has scaling and aggregation properties. The structure of the model depends on the structure of the graph of the controlled road network. The number of nodes in the graph is equal to the number of road sections in the considered network. The simulation of traffic flow changes in real time makes it possible to optimally determine the duration of traffic light operating phases and to provide traffic flow control with feedback based on its current state. The system of automatic collection and processing of input data for the model is presented. In order to model the states of traffic flow in the network and to solve the problem of optimal traffic flow control, the CTraf software package has been developed, a brief description of which is given in the paper. An example of the solution of the optimal control problem of traffic flows on the basis of real data in the road network of Moscow is given.

Self-organization of molecules on a solid surface is one of the promising directions for materials generation with unique magnetic, electrical, and optical properties. They can be widely used in fields such as electronics, optoelectronics, catalysis, and biology. However, the structure and physicochemical properties of adsorbed molecules are influenced by many parameters that must be taken into account when studying the self-organization of molecules. Therefore, the experimental study of such materials is expensive, and quite often it is difficult for various reasons. In such situations, it is advisable to use the mathematical modeling. One of the parameters in the considered adsorption systems is the multiparticle interaction, which is often not taken into account in simulations due to the complexity of the calculations. In this paper, we evaluated the influence of multiparticle interactions on the total energy of the system using the transfer-matrix method and the Materials Studio software package. The model of monocentric adsorption with nearest interactions on a triangular lattice was taken as the basis. Phase diagrams in the ground state were constructed and a number of thermodynamic characteristics (coverage $\theta$, entropy $S$, susceptibility $\xi$) were calculated at nonzero temperatures. The formation of all four ordered structures (lattice gas with $\theta=0$, $(\sqrt{3} \times \sqrt{3}) R30^{\circ}$ with $\theta = \frac{1}{3}$, $(\sqrt{3} \times \sqrt{3})R^{*}30^{\circ}$ with $\theta = \frac{2}{3}$ and densest phase with $\theta = 1$) in a system with only pairwise interactions, and the absence of the phase  $(\sqrt{3}\times \sqrt{3}) R30^\circ$ when only three-body interactions are taken into account, were found. Using the example of an atomistic model of the trimesic acid adsorption layer by quantum mechanical methods we determined that in such a system the contribution of multiparticle interactions is 11.44% of the pair interactions energy. There are only quantitative differences at such values. The transition region from the  $(\sqrt{3} \times \sqrt{3}) R^{*}30^\circ$ to the densest phase shifts to the right by 38.25% at $\frac{\varepsilon}{RT} = 4$ and to the left by 23.46% at $\frac{\varepsilon}{RT} = −2$.

When determining therapeutic absorbed doses in the process of radioiodine therapy, the method of individual dosimetric planning is increasingly used in Russian medicine. However, for the successful implementation of this method, it is necessary to have appropriate software that allows modeling the pharmacokinetics of radioiodine in the patient’s body and calculate the necessary therapeutic activity of a radiopharmaceutical drug to achieve the planned therapeutic absorbed dose in the thyroid gland.

Purpose of the work: development of a software package for pharmacokinetic modeling and calculation of individual absorbed doses in radioiodine therapy based on a five-chamber model of radioiodine kinetics using two mathematical optimization methods. The work is based on the principles and methods of RFLP pharmacokinetics (chamber modeling). To find the minimum of the residual functional in identifying the values of the transport constants of the model, the Hook – Jeeves method and the simulated annealing method were used. Calculation of dosimetric characteristics and administered therapeutic activity is based on the method of calculating absorbed doses using the functions of radioiodine activity in the chambers found during modeling. To identify the parameters of the model, the results of radiometry of the thyroid gland and urine of patients with radioiodine introduced into the body were used.

A software package for modeling the kinetics of radioiodine during its oral intake has been developed. For patients with diffuse toxic goiter, the transport constants of the model were identified and individual pharmacokinetic and dosimetric characteristics (elimination half-lives, maximum thyroid activity and time to reach it, absorbed doses to critical organs and tissues, administered therapeutic activity) were calculated. The activity-time relationships for all cameras in the model are obtained and analyzed. A comparative analysis of the calculated pharmacokinetic and dosimetric characteristics calculated using two mathematical optimization methods was performed. Evaluation completed the stunning-effect and its contribution to the errors in calculating absorbed doses. From a comparative analysis of the pharmacokinetic and dosimetric characteristics calculated in the framework of two optimization methods, it follows that the use of a more complex mathematical method for simulating annealing in a software package does not lead to significant changes in the values of the characteristics compared to the simple Hook – Jeeves method. Errors in calculating absorbed doses in the framework of these mathematical optimization methods do not exceed the spread of absorbed dose values from the stunning-effect.

We have studied properties of non-linear waves in a mathematical model of a predator – prey system with taxis. We demonstrate that, for systems with negative and positive taxis there typically exists a large region in the parameter space, where the waves demonstrate quasi-soliton interaction; colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries. In this paper, we use numerical simulations to demonstrate also a new wave phenomenon — a half-soliton interaction of waves, when of two colliding waves, one annihilates and the other continues to propagate. We show that this effect depends on the «ages» or, equivalently, «widths» of the colliding waves.

This article presents an integrated dynamic model of eco-economic system of the Republic of Armenia (RA). This model is constructed using system dynamics methods, which allow to consider the major feedback related to key characteristics of eco-economic system. Such model is a two-objective optimization problem where as target functions the level of air pollution and gross profit of national economy are considered. The air pollution is minimized due to modernization of stationary and mobile sources of pollution at simultaneous maximization of gross profit of national economy. At the same time considered eco-economic system is characterized by the presence of internal constraints that must be accounted at acceptance of strategic decisions. As a result, we proposed a systematic approach that allows forming sustainable solutions for the development of the production sector of RA while minimizing the impact on the environment. With the proposed approach, in particular, we can form a plan for optimal enterprise modernization and predict long-term dynamics of harmful emissions into the atmosphere.

In the paper the research of the energy and load-stroke parameters of the hemispherical flange forming on the horizontal forging machines has been presented. The Final Element Analysis andUpper Bound Method have been used. On the background of the research the methodic of the load-stroke determination of the hemi-spherical flange upset.