Программирование. Рубрика в журнале - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Constructing of OE-postman path for a planar graph
Статья научная
With automated preparation of the cutting process, the cutting plan can be represented as a flat graph. The purpose of this simulation is to determine the shortest path of the cutting tool, provided that the part cut from the sheet would not require additional cuts. The article deals with the task of building the path of the Chinese postman in a flat graph, which is a model of the cutting plan. An orderly coverage condition is imposed on this path (i.e., the cycle of traversed edges does not encompass those not yet traversed). Such a path will also be called an OE path. This limitation means the absence of additional cuts for parts. The article discusses the recursive algorithm for constructing such chains. It is proved that the algorithm has polynomial complexity. The developed software allows solving the problem for an arbitrary flat graph. The program has been tested for various types of flat graphs.
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Convergence analysis of the finite difference solution for coupled Drinfeld-Sokolov-Wilson system
Статья научная
This paper is devoted to drive the matrix algebraic equation for the coupled Drinfeld-Sokolov-Wilson (DSW) system using the implicit finite difference (IMFD) method. The convergence analysis of the finite difference solution is proved. Numerical experiment is presented with initial conditions describing the generation and evolution. The numerical results were being compared on the basis of calculating the absolute error (ABSE) and the mean square error (MSE). The numerical results proved that the numerical solution was close to the real solution at different values of time.
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Статья научная
The paper considers two simple systems of differential-algebraic equations that appear in the study of chemical kinetics problems with partial equilibria: some of the variables are determined from the condition argmin for some system function state, which depends on all variables of the problem. For such a statement, we can write a differential-algebraic system of equations where the algebraic subproblem expresses the conditions for the minimality of the state function at each moment. It is convenient to use splitting methods in numerical solving, i.e. to solve dynamic and optimization subproblems separately. In this work, we investigate the applicability of differential-algebraic splitting using two simplified systems. The convergence and order of accuracy of the numerical method are determined. Different decomposition options are considered. Calculations show that the numerical solution of the split system of equations has the same order of accuracy as the numerical solution of the joint problem. The constraints are fulfilled with sufficient accuracy if the procedure of the numerical method ends with the solution of the optimization subproblem. The results obtained can be used in the numerical solving of more complex chemical kinetics problems.
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Статья научная
The research work develops a Context aware Data Fusion with Ensemblebased Machine Learning Model (CDF-EMLM) for improving the health data treatment. This research work focuses on developing the improved context aware data fusion and efficient feature selection algorithm for improving the classification process for predicting the health care data. Initially, the data from Internet of Things (IoT) devices are gathered and pre-processed to make it clear for the fusion processing. In this work, dual filtering method is introduced for data pre-processing which attempts to label the unlabeled attributes in the data that are gathered, so that data fusion can be done accurately. And then the Dynamic Bayesain Network (DBN) is a good trade-off for tractability becoming a tool for CADF operations. Here the inference problem is handled using the Hidden Markov Model (HMM) in the DBN model. After that the Principal Component Analysis (PCA) is used for feature extraction as well as dimension reduction. The feature selection process is performed by using Enhanced Recursive Feature Elimination (ERFE) method for eliminating the irrelevant data in dataset. Finally, this data are learnt using the Ensemble based Machine Learning Model (EMLM) for data fusion performance checking.
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Effective practices of using spatial models in document image classification
Статья научная
This paper presents a new approach to modelling the structure of document images for classification tasks. Each of the document images is considered as a realization of a stochastic point process. Estimates of the properties of the point process are used to describe the document structure. The main objective of this paper is to determine the type of a new document using a nonparametric classification method. A method of classification of functional properties of point processes based on the concept of statistical depth is proposed. Practical issues of experimentation are considered. Modeling on real data showed the effectiveness of the proposed approach.
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Evaluation of the docking algorithm based on tensor train global optimization
Статья научная
Effectiveness of modern rational new drugs development is connected with accurate modelling of binding between target-proteins responsible for the disease and small molecules (ligands) candidates to become drugs. The main modeling tools are docking programs for positioning of the ligands in the target proteins. Ligand positioning is realized in the frame of the docking paradigm: the ligand binds to the protein in the pose corresponding to the global energy minimum on the complicated multidimensional energy surface of the protein-ligand system. Docking algorithm on the base of the novel method of tensor train global optimization is presented. The respective novel docking program SOL-T is validated on the set of 30 protein-ligand complexes with known 3D structures. The energy of the protein-ligand system is calculated in the frame of MMFF94 force field. SOL-T performance is compared with the results of exhaustive low energy minima search carried out by parallel FLM docking program on the base of Monte Carlo method using large supercomputer resources. It is shown that SOL-T docking program is about 100 times faster than FLM program, and SOL-T is able to find the global minimum (found by FLM docking program) for 50% of investigated protein-ligand complexes. Dependence of SOL-T performance on the rank of tensor train decomposition is investigated, and it is shown that SOL-T with rank 16 has almost the same performance as SOL-T with rank 64. It is shown that the docking paradigm is true not for all investigated complexes in the frame of MMFF94 force field.
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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.
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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.
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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
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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.
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Implementation of surface-related multiple prediction problem on reconfigurable computer systems
Статья научная
The traditional methodology of computer-aided synthesis of parallel-pipeline programs for reconfigurable computer systems based on field programmable gate arrays (FPGAs) is aimed at the highest possible computer system performance, achieved on available hardware resource. Application of such an approach to real-time problems can lead to inefficient use of system hardware resource. Frequently, this fact leads to idle stand of occupied equipment and to higher requirements to power consumption, size and cost of the end product. We suggest a new methodology to synthesize of parallel-pipeline programs for solution of real-time computationally intensive problems. The methodology provides data processing having a specified rate which depends on a specified time interval. With the help of the developed methodology, it is possible to synthesize a problem computing structure, which requires the minimum hardware resource for the specified system performance. In order to illustrate the suggested methodology, we give the solution of the real-time surface-related multiple prediction problem. We evaluate various configurations of reconfigurable computer systems based on Xilinx Kintex UltraScale FPGAs.
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Статья научная
Preparation of the target-protein, particularly the protein protonation method can affect considerably the spatial arrangement of the attached hydrogen atoms and the charge state of individual molecular groups in amino acid residues. This means that the calculated protein-ligand binding energies can vary significantly depending on the method of the protein preparation, and it also can lead to the different docked positions of the ligand in the case of docking (positioning of the ligand in the protein active site). This work investigates the effect of the hydrogen atoms arrangement method in the target-protein on the protein-ligand binding energy. All hydrogen atoms of target-protein are fixed or movable. The comparison of the protein-ligand binding energies obtained for the test set of target-proteins prepared using six different programs is performed and it is shown that the protein-ligand binding energy depends significantly on the method of hydrogen atoms incorporation, and differences can reach 100 kcal/mol. It is also shown that taking into account solvent in the frame of one of the two continuum implicit models smooths out these differences, but they are still about 10-20 kcal/mol. Moreover, we carried out the docking of the crystallized (native) ligands from the protein-ligand complexes using the SOL program and showed that the different methods of the hydrogen atoms addition to the protein can give significantly different results both for the positioning of the native ligand and for its protein-ligand binding energy.
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Influence to new formulas gradient for removing impulse noise images
Статья научная
In conjugate gradient techniques, the conjugate formula is often the primary point of concentration. The conjugate gradient technique is used to solve problems that arise during the process of picture restoration. By using the quadratic model, a brand-new coefficient conjugate will be produced for the operation. The algorithms demonstrate both local and global convergence and descent. The numerical testing revealed that the newly developed method is much superior to the one that came before it. The recently created conjugate gradient strategy has better performance than the FR conjugate gradient technique, which is the industry standard.
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Intellectual mathematical support software and inner architecture of LMS MAI Class.Net
Статья научная
Distance education prove to be effective in improving the learning and teaching environment. One of the main advantages of distance learning is that web-based courses can be taken anytime and anywhere. The implementation of an e-learning management system (LMS) requires not only good and fast hardware, but also the use of modern software technologies and architectural solutions. This article outlines the main ways of forming the LMS architecture based on a microservice approach, which allows the achievement of high performance and fault tolerance. A distinctive feature of the CLASS.NET system is the presence of a special mathematical software package that allows the optimization of educational processes and tasks (such as students tests generation, students progress analysis, knowledge level assessment, task difficulty analysis, personal learning curve planning). The process of interaction between the LMS system and mathematical software package, as well as the main ways of forming such software as completely independent applications for their further integration into other learning management systems, are thoroughly described. The efficiency of the microservice architecture in terms of scaling, performance and general behavior in case of critical errors in comparison with other systems based on classical architectural approaches is shown. The algorithm of predicting the time a student spends to answer the tasks, which is included in the mathematical software package, is considered.
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Статья научная
The paper is devoted to dosimetric modelling of the human red bone marrow (RBM) internal exposure due to beta-emitting 90Sr incorporated in spongiosa bone. The dose factor calculation (absorbed dose rate due to unit specific activity of 90Sr) is based on the modelling of radiation transport in segments of the skeleton bones with active hematopoiesis. Segmentation considerably simplifies the modelling, but can lead to an underestimation due to electron emission from the neighboring parts of the bone adjacent to the studied segment. The objective of the study is to determine this cross-fire effect on the absorbed dose in RBM. For this purpose, we analyze the results of the numerical experiment on modelling of dose absorption within the bone segments of various shape and size that were parts of the computational phantoms of skeletons of people of different sex and age. We analyze dose factor dependencies on the area of the spongiosa bone surface and the ratio of weights of bone and RBM. It is found that if the area of the spongiosa surface (SS) > 6 cm2, then the effect of neighboring bone parts exposure is negligible. For a smaller SS the extension of the linear dimensions of the spongiosa bone by 2 mean electron path lengths results in dose factor increase proportional to the ratio of the extended spongiosa bone surface area to the original one to the power of 0,28. For human computational phantoms, these values are in the range 1,03-1,21 and are used as adjustment coefficients for the dose factors. Relative standard uncertainty of the adjustment coefficient is 5%.
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Статья научная
In the design of iterative learning control (ILC) algorithm for stochastic nonlinear networked systems, the underlying assumption is differentiability of the system dynamics. In many cases, in reality, stochastic nonlinear networked systems have non-differentiable dynamics, but their dynamics functions after discretization by using conventional methods have global Lipschits’ continuous (GLC) condition. In this paper, we apply an ILC algorithm for stochastic nonlinear networked systems that have the GLC condition. We demonstrate that to design the ILC algorithm, differentiability of the system dynamics is not necessary, and the GLC condition is sufficient for designing the ILC algorithm for stochastic nonlinear networked systems with non-differentiable dynamics. We investigate the analysis of convergence and the tracking performance of the proposed update law for stochastic nonlinear networked systems with GLC condition. We show that there exists no limited condition for the stochastic data dropout probabilities in the convergence investigation of the input error. Then, the results are reviewed and confirmed with a numerical example.
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Статья научная
The problem of three-dimensional mathematical modelling of the effect of air flow on an optical-mechanical unit (OMU) located in the unpressurised compartment of the aircraft, is considered. To solve this problem, a mathematical model of gas dynamics based on the solution of a complete system of Navier - Stokes equations that describe the dynamics of a turbulent, spatially unsteady flow of a viscous gas is developed. The software for simulating the process of flow past a WMU model in the aircraft compartment was created. The effect of the air flow on the OMU is described by the torque acting on the OMU from the airflow side. A numerical method for solving the three-dimensional gasdynamic problem is presented. The numerical method is based on the numerical high order Godunov scheme, realized on an irregular grid with arbitrary cells (tetrahedral, prismatic shape). Flows of conservative variables are calculated by solving the Riemann problem with an approximate AUSM method. The system of equations is supplemented by a two-parameter k-model of turbulence, modified for the calculation of high-speed compressible flows. To significantly reduce the cost of computing resources, it is suggested to use stochastic models of the effect of air flow on WMU. A general simulation algorithm is described.
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Mathematical model of a wide class memory oscillators
Статья научная
A mathematical model is proposed for describing a wide class of radiating or memory oscillators. As a basic equation in this model is an integro-differential equation of Voltaire type with difference kernels - memory functions, which were chosen by power functions. This choice is due, on the one hand, to broad applications of power law and fractal properties of processes in nature, and on the other hand it makes it possible to apply the mathematical apparatus of fractional calculus. Next, the model integro-differential equation was written in terms of derivatives of fractional Gerasimov - Caputo orders. Using approximations of operators of fractional orders, a non-local explicit finite-difference scheme was compiled that gives a numerical solution to the proposed model. With the help of lemmas and theorems, the conditions for stability and convergence of the resulting scheme are formulated. Examples of the work of a numerical algorithm for some hereditary oscillators such as Duffing, Airy and others are given, their oscillograms and phase trajectories are constructed.
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Статья научная
Based on the conjugate Darcy-Brinkman-Forchheymer hydrodynamic model and Schumann thermal model with boundary conditions of the second kind, a model with lumped parameters was proposed by means of geometric 2D averaging to identify the integral kinetics of the temperature fields of a porous matrix and a Newtonian coolant without phase transitions. The model was adapted for a heat-stressed surface by means of a porous compact heat exchanger with uniform porosity and permeability, obeying the modified Kozeny-Carman relation, in the form of a Cauchy problem, the solution of which was obtained in the final analytical representation for the average volume temperatures of the coolant and the porous matrix. The possibility of harmonic damped oscillations of the temperature fields and the absence of coolant overheating in the starting condition of the cooling system were shown. For the dimensionless time of establishing the stationary functioning of the porous heat exchanger, an approximate estimate was obtained correlating with the known data of computational and full-scale experiments.
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Статья научная
In this article we construct a mathematical model and examine the characteristics of the injection of carbon dioxide into the natural layer, rich of the methane and its hydrate in its initial state. We consider the case in which due to the injection of carbon dioxide in the layer two areas are formed: in the first (proximal) region the pores of the layer are saturated with carbon dioxide and its hydrate but in the second (distant) region the pores of the layer are saturated with methane and its hydrate. In the numerical experiments it was established when the pressure increasing on the right border of the layer and decreasing the permeability of the layer or of the pressure of the of carbon dioxide injected, the temperature of the layer can rise at the front of the replacement above the equilibrium temperature of gas hydrate decomposition of methane that corresponds to the appearance of the dissociation border of gas hydrate to methane and water.
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