PIECEWISE NEURAL MODEL BASED ON SPLIT SIGNALS FOR BERNOULLI MEMRISTORS
UDC 519.65; 621.3.01
E.B. Solovyeva, H.A. Harchuk
Actuality of the investigation theme is specified by complexity of mathematical modeling of nonlinear dynamic devices, since the analytical solutions of the nonlinear differential equation systems of high size are not always obtained, and numerical solutions are often accompanied by the problem of poor conditionality. In this situation, behavioral modeling is effective, herewith the object of investigation is represented as a “black or gray box”, and its mathematical model is constructed using the sets of the input and output signals. Behavioral modeling is important in conditions of restricted information of new elements and technologies, as well as under the complexity and variety of models built at the component level. The behavioral modeling of memristive devices actively developed using nanotechnology for energy-saving equipment is represented. A method of behavioral modeling of the transfer characteristics of memristive devices by means of piecewise neural models based on split signals is proposed. To reduce the dimension on approximating nonlinear operators and, therefore, to simplify mathematical models, are applied the following: neural networks, the signal splitting method that enables to adapt the model to the type of the input signals, and a piecewise approximation method for operators of nonlinear dynamic systems. On the basis of the proposed method, a piecewise neural model is constructed. This model includes five three-layer neural networks of simple structure (3x2x1, 100 parameters) and provides a significantly higher accuracy of modeling the transfer characteristic of memristors, the current dynamics of which are described by the Bernoulli differential equation, in comparison with the two-layer piecewise neural and piecewise polynomial models. The described results are of practical value for the behavioral modeling of memristors and various memristive devices, as well as of other nonlinear dynamic systems, since they develop a universal approach for approximating nonlinear operators based on neural networks.
Keywords:nonlinear dynamic system, mathematical modeling, nonlinear operator, nonlinear model, approximation, neural network, memristor.
ALGORITHMIZATION OF MUTUAL INFORMATION CONSENT IN SYSTEMS WITH A DISTRIBUTED REGISTRY, BASED ON A BLOCK CHAIN
The object of research is distributed registry systems based on a chain of blocks. The subject of the research is mathematical and software for distributed data processing in solving the problem of achieving mutual information coordination in distributed registry systems based on a chain of blocks. The purpose of the work is to develop an algorithm for the functioning of a system node with the ability to implement non-standard functions, an algorithm for mutual information matching in a distributed registry system based on a chain of blocks, planning numerical experiments to evaluate the effectiveness of mathematical and software for mutual information matching in distributed registry systems based on a chain of blocks. The study of existing approaches has shown that most studies do not fully take into account the simultaneous implementation of non-standard functions by nodes and changes in the structural and parametric characteristics of the system due to the combination of nodes in groups. As a result, an algorithm for the functioning of the system node is proposed, which takes into account the possibility of implementing non-standard functions: the formation of a branch of the processed data and a temporary blocking attack. A generalized algorithm for the functioning of a distributed registry system based on a chain of blocks when performing an algorithm for mutual information coordination, taking into account the possibility of combining nodes into groups, is presented. The numerical experiment was planned.
Keywords:distributed ledger technology, formalization, algorithm, mutual information agreement, non-standard functions, centralization.
MATHEMATICAL AND SIMULATION MODELING OF A CLOSED DISTRIBUTED REGISTRY WITH A CONTROL NODE
V.A. Evsin, S.N. Shirobokova, S.P. Vorobyov, V.A. Evsina
This article presents mathematical and simulation modeling of a distributed registry with a control node on the example of the raft consensus algorithm. The process of interaction between individual nodes of the distributed registry network is described, special attention is paid to the algorithm for conducting transactions within this network. The key aspect of this article is the development of a mathematical model of a distributed registry network as a Queuing system using queue theory. We consider the conceptual models of both the distributed registry as a whole and the model of the information process for accessing a cluster of notary nodes. Mathematical modeling of the distributed registry network, as well as the information process of obtaining access to the control node of the network. The state space is represented in a distributed registry with a control node. The description of an infinitesimal matrix for estimating the probability of transitions between States in a distributed registry is formed, the transition probabilities and the intensity of these processes are described. The characteristic of the laws of distribution of indicators in the system under consideration is described. Another important aspect of this article is the simulation of the process in order to identify the best combination of parameters to achieve maximum efficiency. A stack of variable indicators of the simulation model is formed. Tests were carried out on the basis of which the most effective set of characteristics was selected empirically. The results of mathematical and simulation modeling of a distributed registry with a control node are presented.
Keywords:distributed registry, DLT system, consensus algorithm, mathematical modeling, infinitesimal matrix, Queuing theory, queue theory, simulation modeling.
ALGORITHMS FOR RESEARCH OF MULTIDIMENSIONAL TIME SERIES TAKING INTO ACCOUNT THE EXTENDED INFLUENCE OF FACTORS ON THE BASIS OF MATHEMATICAL MODELING
I.N. Kryuchkova, E.E. Krasnovskiy, E.V. Bolnokina, O.Ja. Kravets
The models and methods of neural network modeling of dynamics based on the analysis of multidimensional time series, taking into account the delayed influence of significant factors, are investigated. In connection with the impossibility of simultaneous determination of the optimal time lag and network training, it is necessary to consider finding a multidimensional lag as a separate optimization problem. The mathematical formulation of the problem of building a neural network for a non-zero delay is described, a description of the optimization characteristics of the latency for one independent variable (input) is given, the information base for modeling and forecasting and neural network data processing algorithms are specified, and the latency vector for significant factors is optimized. The fundamental possibility of using sensitivity analysis to find the optimal multidimensional time lag was confirmed during the computational experiment. The sensitivity analysis was carried out on test data obtained by calculating the values of the sets of functions of several variables with a known delay for some variables. Analysis of learning errors, generalization and forecasting on the original and offset series allowed to conclude that there was a significant decrease in the training error and prediction error on the shifted series with a practically unchanged generalization error, which indicates the effectiveness of the proposed algorithm and the absence of structural effects in changing the quality of the forecast.
Keywords: : mathematical modeling, neural networks, lag, forecast.
ECONOMIC-MATHEMATICAL MODELING OF THE HEALTH LEVEL OF POPULATION IN THE RUSSIAN REGIONS
The article considers the economic and mathematical tools for solving the problem of integrated assessment and raising the level of public health in the region. The main health indicators serve as influencing factors. Linear models of integrated health indicators are constructed on available statistical data of the population of the Russian Federation and the Volgograd region from 2000 to 2014. The dynamic task of increasing the values of the public health integral index in the Volgograd Region was formulated and solved. Basic health indicators are used as phase variables of the dynamic model, taken into account in constructing the integral index. Investments in the fixed capital of the region by main types of economic activity are control variables. The information basis is the data of the social and economic situation of the region for the last 15 years. The presented dynamic model allows to carry out a comprehensive assessment of the health of the population of the region in the current and forecast period. Some scenarios of increasing integral health level of the region under different investment capital restrictions were considered and results were analyzed. The proposed approach can be used to evaluate various options of the region development strategy. In the article, the presented model of the integral indicator of population health support a complex estimation of the level of regional development in the current period and can be considered as a tool of decision-making support at the multivariate scenario analysis of regional development strategies in health.
Keywords: : mathematical modeling, population health, integral indicator of health, dynamic programming, control problem, comprehensive health assessment.
THE PRACTICE OF USE OF +WoundDesk MOBILE APPLICATION FOR EVALUATION OF EXPERIMENTAL WOUND REPAIR DYNAMICS
UDC 617-089.844; 57.087
A.V. Budnevskiy, E.A. Kiseleva, N.V. Boriskin, L.N. Tsvetikova,
A mathematical model of the dynamics of liver mass after its partial anatomical resection in a volume of 67% of the initial mass in a rat experiment using the method of G. Higgins and R. Anderson was proposed, constructed through an approximation to the square root equation by the least squares method. The accuracy of the model is confirmed by low mean approximation errors: 14.6% and 9.6% for simple resection and for resection with intraoperative microtraumatic application to the liver parenchyma, respectively. The proposed model has potential applications as a standard for evaluating liver regeneration after resections in the clinic. A universal evaluation criterion of the intensity of the regenerative process is proposed – the regeneration factor./i>
Keywords: regeneration, liver, resection, mathematical modeling, nonlinear approximation.
ANALYSIS OF THE SCATTERING CHARACTERISTICS OF UWB SIGNALS ON COMPLEX OBJECTS
In this paper we consider problems related to the scattering of UWB signals to the objects of complex shapes. The analysis of the dependence of the impulse responses of the parameters of the problem is carried out.
Keywords: mathematical modeling, UWB signals.