Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование @vestnik-susu-mmp
Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Все статьи: 838
Evolution of the Viola - Jones Object Detection Method: a Survey
Статья научная
The Viola and Jones algorithm is one of the most well-known methods of object detection in digital images. Over the past 20 years since the first publication, the method has been extensively studied, and many modifications of the original algorithm and its individual parts have been proposed by researchers and engineers. Some ideas popularized by Paul Viola and Michael Jones became the basis for many other algorithms of object localization in images. This paper presents a description of Viola and Jones algorithm, the history of its development and modifications in the context of various problems of object localization in images, as well as a description of the current state of affairs: the method’s place in the era of convolutional neural networks extensive application
Бесплатно
Exact solutions of beta-fractional Fokas-Lenells equation via sine-cosine method
Статья научная
In nonlinear plasma physics, photonics and optics, the space-time fractional nonlinear Fokas-Lenells equation associated with beta derivative has significiant applications. This equation is used in this study to provide precise solutions using the Sine-Cosine method. Furthermore, using computer software, we plot the 2D-3D figures of the obtained solutions based on the appropriate parameters. The findings indicate that the suggested technique is simple, efficient and capable of producing complete solutions to nonlinear models due to mathematical physics.
Бесплатно
Exact solutions of the (2+1)-dimensional Kundu-Mukherjee-Naskar model via IBSEFM
Статья научная
The aim of this study is to construct the exact solutions of the (2+1)-dimensional Kundu-Mukherjee-Naskar (KMN) equation via Improved Bernoulli Sub-Equation Function Method (IBSEFM). The physics of this model describes optical dromions in (2+1)-dimensional case. It is also studied in fluid dynamics. Applying the proposed method, we obtain new exact solutions of (2+1)-dimensional KMN equation. Moreover, we plot the 2D-3D figures and contour surfaces according to the suitable parameters by the aid of computer software. The results confirm that IBSEFM is powerful, effective and straightforward for solving nonlinear partial differential equations arising in mathematical physics.
Бесплатно
Статья научная
We prove existence of upper and lower solutions in reverse order with respect a part of the variables in a system of nonlinear ordinary differential equations modelling acidogenesis in anaerobic digestion. The corresponding existence theorems are established. The upper and lower solutions are constructed analytically, by defining semi-trivial solutions for each of the variables in the model. We introduce the concept of indicator semi-trivial solutions. Finally, we numerically solve the system supported by the Matlab software and matching the graphs of the numerical solutions with analytical solutions is found.
Бесплатно
Статья научная
We investigate stability of solutions in linear stochastic Sobolev type models with the relatively bounded operator in spaces of smooth differential forms defined on smooth compact oriented Riemannian manifolds without boundary. To this end, in the space of differential forms, we use the pseudo-differential Laplace-Beltrami operator instead of the usual Laplace operator. The Cauchy condition and the Showalter-Sidorov condition are used as the initial conditions. Since "white noise'' of the model is non-differentiable in the usual sense, we use the derivative of stochastic process in the sense of Nelson-Gliklikh. In order to investigate stability of solutions, we establish existence of exponential dichotomies dividing the space of solutions into stable and unstable invariant subspaces. As an example, we use a stochastic version of the Barenblatt-Zheltov-Kochina equation in the space of differential forms defined on a smooth compact oriented Riemannian manifold without boundary.
Бесплатно
Fast x-ray sum calculation algorithm for computed tomography problem
Статья научная
In iterative methods of computed tomography, each iteration requires to calculate a multitude of sums over values for the current reconstruction approximation. Each summable set is an approximation of a straight line in the three-dimensional space. In a cone-beam tomography, the number of sums to be calculated on each iteration has a cubic dependence on the linear size of the reconstructed image. Direct calculation of these sums requires the number of summations in a quartic dependence on the linear image size, which limits the performance of the iterative methods. The novel algorithm proposed in this paper approximates the three-dimensional straight lines using dyadic patterns, and, using the adjustment of precalculation and inference complexity similar to the adjustment employed in the Method of Four Russians, provides the calculation of these sums with a sub-quartic dependence on the linear size of the reconstructed image.
Бесплатно
Finite non-commutative associative algebras as carriers of hidden discrete logarithm problem
Статья научная
The article introduces new finite algebras attractive as carriers of the discrete logarithm problem in a hidden group. In particular new 4-dimensional and 6-dimensional finite non-commutative algebras with associative multiplication operation and their properties are described. It is also proposed a general method for defining finite non-commutative associative algebras of arbitrary even dimension m≥2. Some of the considered algebras contain a global unit, but the other ones include no global unit element. In the last case the elements of the algebra are invertible locally relatively local bi-side units that act in the frame of some subsets of elements of algebra. For algebras of the last type there have been derived formulas describing the sets of the (right-side, left-side, and bi-side) local units. Algebras containing a large set of the global single-side (left-side and right-side) units and no global bi-side unit are also introduced. Since the known form of defining the hidden discrete logarithm problem uses invertibility of the elements of algebra relatively global unit, there are introduced new forms of defining this computationally difficult problem. The results of the article can be applied for designing public-key cryptographic algorithms and protocols, including the post-quantum ones. For the first time it is proposed a digital signature scheme based on the hidden discrete logarithm problem.
Бесплатно
Forecasting stock return volatility using the realized Garch model and an artificial neural network
Статья научная
Volatility forecasting is required for risk management, asset allocation, option pricing, and financial market trading. It can be done by using various time series forecasting techniques and Artificial Neural Networks (ANN). The current research focuses on the modeling and forecasting of stock market indices using high-frequency data. A recent high-frequency volatility model is called the Realized GARCH (RGARCH) model, where the key feature is an equation that relates the realized measure to the conditional variance of returns. This equation incorporates an asymmetric reaction to shocks, providing a highly flexible representation of market dynamics. This paper proposes an hybrid model where ANN and RGARCH are used to forecast stock return volatility. This model was established by entering the predicted Realized Volatility (RV), calculated using RGARCH, into the ANN. The choice of the input variables of the ANN is made using the Granger causality test in order to reduce the noise which would affect the prediction system and which could be generated by an input variable not statistically linked to stock market volatility. The results show that a hybrid model based on a recurrent neural network (RNN) outperforms the RGARCH and HAR-type models in out-of-sample evaluations according to the RMSE and the correlation coefficient.
Бесплатно
Forecasting tariffs for the day-ahead market based on the additive model
Краткое сообщение
The problem of constructing an additive model for forecasting of the market tariff for the day ahead is solved. The trend component is constructed on the basis of the autoregressive model of already known values of the day-ahead market tariff and the external factor of electricity consumption according to the United Energy System (UES) of the Urals Wholesale Electricity and Power Market (OREM) of Russia for 2009-2018. Based on the construction of the autocorrelation function, three seasonal components are identified in the time series of hourly values of the market tariff for the day ahead: annual (8760 values), weekly (168 values), daily (24 values). A harmonic model of each component is constructed. The final additive model is constructed taking into account the specifics of the electricity market and the process of setting the market tariff for the day ahead and a balancing market. The practical significance of the developed additive model is adequate accuracy with the well-known models for forecasting of the market tariff for the day ahead of the UES of the Urals. The proposed model allows the subjects of the electric power industry to avoid penalties from the balancing market by ensuring high accuracy of forecasting.
Бесплатно
Forecasting the return of the loan portfolio on the basis of Markov model
Статья научная
We consider the problem of mathematical modelling of flows of loan portfolio payments. We assume that the change in the quality of each loan is described by a simple Markov chain with a finite number of states. In this case, the flow of loan payments is a random process, which depends on the Markov chain. On the basis of the proposed model and known relations of the stochastic systems theory, we describe the expected flows of payments of the entire loan portfolio and construct a method to forecast the expected return (net present value) of the portfolio. We analyze an accuracy of the obtained model and a sensitivity of net present value of the portfolio to a change in the transition probabilities in the Markov chain.
Бесплатно
Статья научная
This study aims to apply a novel technique devised by the authors to process the results of thermal physics experiments. The paper describes a two-stage technique for identifying coefficients of mathematical models from observed experimental data. The technique is based on the maximum likelihood method and is informed by the errors of all sensors used to obtain parameter measurements. Stage 1 of the technique minimizes the maximum relative error over all measured parameters, which allows gross measurement errors to be identified in qualitative terms and reduces the maximum relative error down to acceptable values. At Stage 2, we propose to use the method of weighted least absolute values to minimize the sum of absolute values of relative errors of all measured parameters. The technique was applied to process the results of thermal physics experiments aimed at generalizing the size of vapor bubbles of various types during unsteady heating of a vertical steel cylindrical heater surrounded by an upward flow of water subcooled to the saturation temperature. The numerical simulations reported in this study attest to the high quality of the proposed two-stage technique for identifying coefficients of mathematical models. The study also presents a comparative analysis of the results obtained by the classical least squares method and the novel two-stage technique.
Бесплатно
Краткое сообщение
We study the possibility of influence on the saving of allocated funds for the elimination of consequences of natural disasters. At that, we take into account statistical data on the emergence of such phenomena and the degree of actual damage. The article describes the problem of determining the optimal share of funds that either replenish or spend the principal amount according to the distribution. We prove that, under certain conditions of the distribution and a positive mathematical expectation, it is possible to choose a share that ensures the maximum possible growth of the original deposit account. At the same time, the choice of the share allows not to lose the full provision of damage recovery. This process is presented as a serial multi-stage process based on a Markov chain that takes into account only the distribution based on the statistical data of this year to plan the size of the deposit share for the next year. For simplicity, we assume that the process is established and has a constant distribution for some time. The distribution table can be changed in the case of a major change in stochastic data. We consider a serial multi-stage process of changing the monetary amount that is purposefully deposited for the renewal, replacement and restoration of security and alarm systems at burned-out facilities. The optimal stochastic control of the change in the share of the money deposit providing this restoration is carried out based on the generalized Kelly formula. An example of model validity is shown. On the basis of statistical data, the analysis of the possibility to use this model is carried out.
Бесплатно
Global Schumpeterian dynamics with structural variations
Статья научная
In this paper, we present the investigations developing the schumpeterian theory of endogenous evolution of economic systems. The proposed approach allows to simulate the emergence and propagation of new technologies. We develop a mathematical model of dynamics of sector capital distribution over efficiency levels on the base of the system of nonlinear differential equations. In order to take into account the boundedness of the economic growth conditioned by the boundedness of the markets, the resource base and other factors, we introduce the notion of economical niche volume. The scenario of the emergence of the new highest efficiency level is proposed. In order to simulate the process of the emergence of the new highest efficiency level, the notion of intellectual capital is proposed. According to the proposed scenario, the new level emerges when the intellectual capital achieves the threshold value. Herewith, the dimension of the dynamic system is varied. The necessary condition for the functioning of the new level is formulated. The invariant set of the dynamic system is defined. The local stability of the equilibria is investigated. The global stability of the dynamic system is established on the base of a geometrical method. The proposed models allow to evaluate and predict the dynamics of the technological levels of the economic sector firms development.
Бесплатно
Gravitational model of population dynamics
Статья научная
We consider the author's mathematical model of population dynamics of territories, taking into account the migration between the territories. The model is a system of ordinary differential equations with constant coefficients. The main idea of the presented modelling is to take into account the migration interactions of territories in the form of nonlinear terms (they are the pair products of phase variables of the territories population). On the one hand, the approach allows to consider the model as a variant of expanding the gravitational approach in migration studies. On the other hand, this approach allows to apply the approaches of mathematical biology, which are successfully used in econophysics and sociodynamics. In order to verify the model, we use statistical data on population and migration between federal districts of the Russian Federation. The results of the modelling show the significance of the "repulsion" of migrants arriving in the Central and North-Western federal districts, mainly in the nearby regions (Southern, North Caucasian and Volga federal districts). Model evaluations of the migration balance are obtained. The evaluations exceed statistical ones by dozens of times and, to all appearances, describe the "latent" migration of the population, covering both long-term and short-term movements. An analysis of the change in the stationary values of the population for a linear change in the parameters is carried out. It is shown that there are such values of the parameters of migration attractiveness of the Russian Federation federal districts, under which the population increases both in the whole in the Russian Federation and in individual districts. It is established that such changes can occur due to significant differences in the opportunities, which are "provided" by different federal districts for migrants (e.g., living and working conditions, upbringing and education of children, etc.), and intra-Russian migration.
Бесплатно
Статья научная
Предложен, реализован и верифицирован новый hp-вариант метода коллокации и наименьших квадратов (hp-МКНК) численного решения эллиптических задач со старшими производными второго порядка на треугольных сгущающихся сетках, построенных в Gmsh. В работе использованы пространства аппроксимирующих полиномов степеней p = 2, 3, 5, 6, 8, коэффициенты которых определяются из решения переопределенных разреженных систем линейных алгебраических уравнений (СЛАУ) с помощью ортогонального метода, реализованного в библиотеке SuiteSparse, и распараллеливания на CUDA. Разработанный hp-МКНК протестирован на задаче Дирихле для уравнения Пуассона в квадрате и задаче изгиба защемленной кольцевой пластины в рамках теории Рейсснера-Миндлина, включая случаи с большими градиентами и ограниченной гладкостью решения. Проведено сравнение с коллокационным методом при p = 4(основанном на принципах МКНК), в котором СЛАУ имеет квадратную матрицу, а также проанализированы числа обусловленности и точность решения в зависимости от количества уравнений приближенной задачи и показателя сгущения сетки.
Бесплатно
Hierarchical Game under Uncertainty: a Case of Different Social Behavior
Статья научная
In the paper, a two-level hierarchical game with one upper-level player and N lower-level players is considered. The game models the heterogeneous social behavior of the bottom-level players. Unlike classical game-theoretic models, where all agents are strictly selfish, it is assumed that the bottom-level players are divided into two groups: committed altruists acting within the Berge equilibrium (the desire to maximize the payoff of others) and selfish agents adhering to the traditional Nash equilibrium and maximizing their own payoff. Furthermore, the payoff functions of each player are affected by interval uncertainty. The concept of a Pareto-guaranteed hybrid equilibrium is formalized for the proposed game. A linear-quadratic hierarchical game under uncertainty with one top-level player and three bottom-level players, two of whom are altruists and one of whom adheres to a selfish behavior model, is given as a model example. A Pareto-guaranteed hybrid equilibrium is constructed analytically for this game. The approach developed in this article allows for more accurate modeling of real-world socioeconomic processes characterized by information asymmetry and the presence of different behavioral incentives among individuals, for example, in macroeconomic governance systems or in models of state-society interactions.
Бесплатно
High Accuracy Numerical Solution of Elliptic Equations with Discontinuous Coefficients
Статья научная
We develop an approach to constructing a new high-accuracy hp-version of the leastsquares collocation (LSC) method for the numerical solution of boundary value problems for elliptic equations with a coefficient discontinuity on lines of different shapes in a problem solution domain. In order to approximate the equation and the conditions on the discontinuity of its coefficient, it is proposed to use the external parts and irregular cells (i-cells) of the computational grid which are cut off by the line of discontinuity from regular rectangular cells. The proposed approach allows to obtain solutions with a high order of convergence and high accuracy by grid refining and/or increasing the degree of the approximating polynomials both in the case of the Dirichlet conditions on the boundary of the domain and in the case of the presence of Neumann conditions on a large part of the boundary. Also, we consider the case of the problem with a discontinuity of the second derivatives of the desired solution in addition to the coefficient discontinuity at the corner points of the domain. We simulate the heat transfer process in the domain where particles of the medium move in a plane-parallel manner with a phase transition and heat release at the front of the discontinuity line. An effective combination of the LSC method with various methods of accelerating the iterative process is demonstrated: the acceleration algorithm based on Krylov subspaces; the operation of prolongation along the ascending branch of the V-cycle on a multigrid complex; parallelization. The results are compared with those of other authors on solving the considered problems
Бесплатно
Hoff's model on a geometric graph. Simulations
Статья научная
This article studies numerically the solutions to the Showalter-Sidorov (Cauchy) initial value problem and inverse problems for the generalized Hoff model. Basing on the phase space method and a modified Galerkin method, we develop numerical algorithms to solve initial-boundary value problems and inverse problems for this model and implement them as a software bundle in the symbolic computation package Maple 15.0. Hoff's model describes the dynamics of H-beam construction. Hoff's equation, set up on each edge of a graph, describes the buckling of the H-beam. The inverse problem consists in finding the unknown coefficients using additional measurements, which account for the change of the rate in buckling dynamics at the initial and terminal points of the beam at the initial moment. This investigation rests on the results of the theory of semi-linear Sobolev-type equations, as the initial-boundary value problem for the corresponding system of partial differential equations reduces to the abstract Showalter-Sidorov (Cauchy) problem for the Sobolev-type equation. In each example we calculate the eigenvalues and eigenfunctions of the Sturm-Liouville operator on the graph and find the solution in the form of the Galerkin sum of a few first eigenfunctions. Software enables us to graph the numerical solution and visualize the phase space of the equations of the specified problems. The results may be useful for specialists in the field of mathematical physics and mathematical modelling.
Бесплатно
Статья научная
The motion of a hydrodynamic flow in a chemical reactor described by a one-dimensional one-parameter diffusion model is considered. Within the framework of this model, the task is set to identify the boundary condition at the reactor outlet containing an unknown concentration of the reagent under study leaving the reactor in a stream. In this case, the law of change in the concentration of the reagent over time at the reactor inlet is additionally set. After the introduction of dimensionless variables, a discrete analogue of the transformed inverse problem in the form of a system of linear algebraic equations is constructed by the method of difference approximation. The discrete analogue of the additional condition is written as a functional and the solution of a system of linear algebraic equations is presented as a variational problem with local regularization. A special representation is proposed for the numerical solution of the constructed variational problem. As a result, the system of linear equations for each discrete value of a dimensionless time splits into two independent linear subsystems, each of which is solved independently of each other. As a result of minimizing the functional, an explicit formula was obtained for determining the approximate concentration of the reagent under study in the flow leaving the reactor at each discrete value of the dimensionless time. The proposed computational algorithm has been tested on the data of a model chemical reactor.
Бесплатно
Impact of Vaccination Opinion Dynamics on Influenza Epidemics
Статья научная
The aim of this study is to test the hypothesis that the dynamics of social opinion about vaccination influence the development of the epidemic process, using an influenza epidemic as an example. It is assumed that the opinion dynamics is completed before the start of the seasonal influenza outbreak, by which time everyone has made a decision about vaccination. Such decisions influence the formation of personal immune status for each economic agent as well as the formation of collective immunity in the population as a whole. The epidemic process is studied using two modifications of compartmental models (SIR and SEIRD). The cost-effectiveness of vaccination is also studied. The modeling is accompanied by a simulation of opinion dynamics and the epidemic process, implemented on a network model based on a random graph. A scenario analysis is performed based on statistical data on influenza incidence and annual vaccination campaigns in Russia.
Бесплатно
