Программирование. Рубрика в журнале - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Статья научная
Prediction of a new object state at a lack of the known characteristics and estimates of quality indicators of a number of studied objects (a set of reference data) often leads to the problem of multicollinearity of basic data. We propose the following three ways to overcome this problem relating to the sphere of data mining: use a ridge regression, train with the teacher a two-layer neural network, consecutive adapt a single-layer neural network. Also, we compare characteristics of the proposed ways. In the ridge regression method, the introduction of a regularizing term into the LMS equation gives an approximate solution with a sufficient degree of accuracy. A disadvantage of use of the two-layer neural network "feed-forward backprop" and the procedure of training with the teacher "train" is that adjusted weights of the neural network take chaotic (and even negative) values that contradicts a common practice of examination. The following features are revealed: considerable dispersion of weights and shifts of a neural network, ambiguity of the solution due to the choice of random initial conditions, strong dependence on a training algorithm. In order to overcome this shortcoming, we propose a transition to consecutive adaptation of a single-layer neural network with fixing shifts of neurons at zero level.
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Recovering of the heat transfer coefficient from the temperature measurements
Статья научная
An inverse analysis is used to recover the heat transfer coefficient in heat conduction problems from boundary measurement of the temperature. The numerical scheme is based on the finite element method in the space variables, the method of finite differences in time, and a special iteration scheme to determine the heat transfer coefficients on each time step. The heat transfer coefficients is sought in the form of a finite segment of a series with unknown Fourier coefficients depending on time. The algorithm for solving the problem relies on theoretical results stating that this problem is well-posed and can be reduced to an operator equation with a contraction. The results of numerical experiments confirm theoretical arguments that this problem is indeed well-posed. The obtained results reveal the accuracy, efficiency, and robustness of the proposed algorithm. It is stable under random perturbations of the data.
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Статья научная
We propose an approach to simulation of information protection processes at informatization objects in the dynamics of realizing threats of its leakage through technical channels using the apparatus of composite Petri–Markov nets. We investigate the interrelationships of the processes of transferring information at the object of informatization, its interception by a violator from outside this object through technical channels and protection against interception. Analytical expressions are obtained for calculating the probabilistic-temporal characteristics of simulated processes in order to assess the possibility of a violator implementing threats of information leakage at objects of informatization; protection of this information through the use of preventive measures aimed at blocking or anticipating the actions of the violator to implement these threats
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Статья научная
It is shown that multistage concurrent games, or relay-races, are widely used in practice. It is proposed to model relay-races in the state space, in which discrete co-ordinates are the mathematical analogue of stages, which participants pass in the current time, and basic principle of modelling of residence of participant in space states is the M-parallel semi-Markov process. With use of the proposed formalisms formulae for evaluation of stochastic and time characteristics of relay-races evolution are obtained. For arbitrary realization of switching trajectory the recurrent procedure of evolution with evaluation of stochastic and time characteristics of realization under investigation is worked out. Conception of distributed forfeit, which depends on difference of stages of participants compete in pairs is introduced. Dependence for evaluation of total forfeit for every participant is obtained.
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SkifCh: эффективный коммуникационный интерфейс
Статья научная
В работе описывается SkifCh - низкоуровневый интерфейс передачи сообщений. Данный интерфейс эффективно поддерживается на уровне сетевого оборудования, которое, в свою очередь, может быть реализовано в ПЛИС (как сделано в суперкомпьютере СКИФ-Аврора) или в специализированных микросхемах. Интерфейс SkifCh может быть использован для высокоэффективных сетевых обменов непосредственно из прикладных программ, а также для реализации коммуникационных библиотек более высокого уровня. На данный момент поверх интерфейса SkifCh реализованы системы MPI, SHMEM, GASNet и ARMCI. В работе также приведено сравнение эффективности использования SkifCh и MPI на суперкомпьютере СКИФ-Аврора.
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Software set of intellectual support and security of LMS MAI Class.Net
Статья научная
The article discusses integration of mathematical methods and security components in a learning management system (LMS). The discussed methods provide a statistical analysis of user data in process of online training in mathematical disciplines and adapting the content of the system for different users. The software package allows automatic calculation of questions complexity and user ratings by using statistical data. This helps the system administrator to detect users which use illegal hints or help from others. A procedure is designed for content selection for a variety of tests and control activities, with restrictions and without a time limit for the test. Two probabilistic models were used during development of mathematical methods: the Rasch model to describe the probability of users' answer correctness and Van der Linden model to describe the time it took for a user to respond to the question. The software package contains special optimization procedures that estimate the parameters of these models based on the accumulated statistics across all users. Apart from discussing efficiency of LMS usage with the above mentioned methods, the article also discusses general security architecture of the LMS, a set of technologies used for developing system security with specific implementation examples.
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Solitary wave effects of Woods-Saxon potential in Schrodinger equation with 3D cubic nonlinearity
Статья научная
In this research article, we apply the generalized projective Riccati equation method to construct traveling wave solutions of the d cubic focusing nonlinear Schrödinger equation with Woods-Saxon potential. The generalized projective Riccati equation method is a powerful and effective mathematical tool for obtaining exact solutions of nonlinear partial differential equations, and it allows us to derive a variety of traveling wave solutions of the 3d cubic focusing nonlinear Schrödinger equation with Woods-Saxon potential. These solutions contain periodic wave solutions, bright and dark soliton solutions. The study of many physical systems, such as Bose-Einstein condensates and nonlinear optics, that give rise to the nonlinear Schrödinger equation. We provide a detailed description of the generalized projective Riccati equation method in the paper, and demonstrate its usefulness in solving the nonlinear Schrödinger equation with Woods-Saxon potential. We present various graphical representations of the obtained solutions using MATLAB software, and analyze their characteristics. Our results provide new insights into the behavior of the d cubic focusing nonlinear Schrödinger equation with Woods-Saxon potential, and have potential applications in numerous fields of physics, as well as nonlinear optics and condensed matter physics.
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Статья научная
A new method for solving the Cauchy problem for an ordinary differential equation is proposed and implemented using the collocation and least squares method of increased accuracy. It is based on the derivation of an approximate nonlinear equation by a multipoint approximation of the problem under consideration. An approximate solution of the problem in the form of the Pade approximation is reduced to an iterative solution of the linear least squares problem with respect to the coefficients of the desired rational function. In the case of nonlinear differential equations, their preliminary linearization is applied. A significant superiority in accuracy of the method proposed in the paper for solving the problem over the accuracy of the NDSolve procedure in the Mathematica system is shown. The solution of a specific example shows the superiority in accuracy of the proposed method over the fourth-order Runge-Kutta method. Examples of solving the Cauchy problem for linear and non-linear equations with an accuracy close to the value of rounding errors during operations on a computer with numbers in the double format are given. It is shown that the accuracy of solving the problem essentially depends on the complexity of the behavior of the values of the right-hand side of the equation on a given interval. An example of constructing a spline from pieces of Pade approximants on partial segments into which a given segment is divided is given in the case when it is necessary to improve the accuracy of the solution.
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Solving of a minimal realization problem in Maple
Статья научная
In the computer algebra system Maple, we have created a package MinimalRealization to solve the minimal realization problem for a discrete-time linear time-invariant system. The package enables to construct the minimal realization of a system starting with either a finite sequence of Markov parameters of a system, or a transfer function, or any non-minimal realization. It is designed as a user library and consists of 11 procedures: ApproxEssPoly, ApproxSpace, Approxrank, ExactEssPoly, FractionalFactorizationG, FractionalFactorizationMP, MarkovParameters, MinimalityTest, MinimalRealizationG, MinimalRealizationMP, Realization2MinimalRealization. The realization algorithm is based on solving of sequential problems: (1) determination of indices and essential polynimials (procedures ExactEssPoly, ApproxEssPoly), (2) construction of a right fractional factorization of the transfer function (FractionalFactorizationG, FractionalFactorizationMP), (3) construction of the minimal realization by the given fractional factorization (MinimalRealizationG, MinimalRealizationMP, Realization2MinimalRealization). We can solve the problem both in the case of exact calculations (in rational arithmetic) and in the presence of rounding errors, or for input data which are disturbed by noise. In the latter case the problem is ill-posed because it requires finding the rank and the space of a matrix. We use the singular value decomposition as the most accurate method for calculation of the numerical rank (Approxrank) and the numerical space (ApproxSpace). Numerical experiments with the package MinimalRealization demonstrate good agreement between the exact and approximate solutions of the problem.
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Статья научная
This paper investigates the possibility of effective implementation of calculations in low-precision neural network models on the Elbrus platform with the VLIW architecture. Such models are widely used in practice to increase the computational efficiency of recognition and well suit computers with the x86 and ARM architectures. In this paper, we consider an 8-bit neural network model, in which matrix multiplication is the most resource-intensive part of the implementation. This paper presents an effective implementation of matrix multiplication that takes into account the features of the Elbrus architecture: the presence of several computational channels with various arithmetic and logic devices, an array prefetch buffer, and its own SIMD extension. We carry out theoretical and experimental comparisons of the computational efficiency of low-precision and classical neural network models, which show that Elbrus processors have much more capabilities for performing fast floating point calculations and require the development of new approaches to increase the computational efficiency of neural network models.
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Statistical analysis module for weight design of aircraft elements
Статья научная
The concept of a statistical analysis module for weight design of aircraft elements (for predicting weight characteristics of one or another aircraft elements) is proposed. Models, methods to construct single-point estimates of the predicted characteristic, quality criteria of constructed models are considered. Two approaches to the confidence estimation of the predicted characteristic are proposed. First approach is based on the assumption that errors at predicting are caused by inaccurate identification of the deterministic part of the predicted characteristic behavior. The second one is based on the assumption that the deterministic part of the predicted characteristic behavior is identified correctly and errors at predicting are caused by inaccuracy in the measurements. The structure, goals of each component of the software package that implements the statistical analysis module is considered in details. Based on the real data the problem of predicting the take-off mass of an empty equipped airliner depending on maximum pay load and the maximum flight distance at maximum pay load is given. By this problem applicability of considered models and methods is demonstrated.
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Statistical analysis of the functional status of the students
Статья научная
The South Ural is one of the most advanced industrial regions in Russia. It has huge industrial potential (metal industry, mechanical engineering, chemical process industry, oil-extracting industry, mineral resource industry) which predetermines negative ecological trends in the region. Levels of air pollution with salts of heavy metals, phenol and CO2 are 2-4 times higher than national air quality standards. Moreover, natural background radiation in the region is increased. Under the stated conditions, low levels of motor activity lead to hypoxia and cumulative disorders of the locomotor system as well as to respiratory, gastric, oncological, allergic and other diseases. Poor environmental background significantly affects demographic rates including the life expectancy which is 72 in average for the region: 60 years for men, and 75 years for women. The paper studies how the main anthropometric and physiological parameters in the local residents who are divided into three groups according to their health status and motor activity (so called health groups) influence the physical fitness. Social-biological and medical aspect of the study - to find out the correlation between parameters in the examined people from different groups - may also be of interest for specialists working on optimization of physical education practice and student's health promotion.
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Structural parametric modelling of an information-analytical system
Статья научная
We develop a method for studying relations between interior and exterior characteristics of an information-analytical system. As interior characteristics, we use the balance estimates accounting for conflict interactions among the elements. We solve the problem on assuming that the interior and exterior characteristics of the system are related. We justify the expediency of using the least squares method to find an explicit functional dependence among the characteristics. We develop a method for calculating the functional dependence in the case of a matrix representation of the values of characteristics basing on pseudoinverse matrices. A numerical example illustrates how the proposed method works in the structure parametric modeling of an information-analytical system in an internal affairs department.
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Supercomputer simulation of oil spills in the Azov Sea
Статья научная
We present the research on microbiological destruction of oil pollution in shallow water. In order to conduct the research, we use a multiprocessor computer system with distributed memory. The research takes into account the oil fractional composition as well as hydrodynamic and chemical-biological features of water. In order to simulate the dynamics of hydrocarbon microbiological degradation in the Azov Sea, we propose the complex of interrelated precision models. For model discretization, we use the space splitting schemes taking into account the partial filling cells of computational domain. Therefore, the computational accuracy significantly increases, while the computational time decreases. On supercomputer, we implement an experimental software for predictive modelling the ecological situation under oil and other pollution conditioned by natural and industrial challenges in shallow water.
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Table recognition technology in tax documents of the Russian Federation
Статья научная
This paper investigates the problem of cell recognition in the image of a table using the example of the Russian tax document (2-NDFL). Despite the simple structure of the tables, the printing method is based on a flexible template. The flexibility of the form is observed in the modifications of textual information and in the table area. The flexibility of tables lies in the modification of the number and size of columns. A structural method was proposed for table detection. The input data are the detected horizontal and vertical segments. Segments were searched by the Smart Document Reader system. Implementing and testing the method were also carried out in the Smart Document Reader system. In addition to detecting the area where tables can be placed, the following objectives were achieved: searching for table cells, naming table cells, and validating the table area. Validation of the table area was performed for separate tables and for table sets. The application of table aggregate descriptions showed the high reliability of linking table sets.
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The Pyt'ev-Chulichkov method for constructing a measurement in the Shestakov-Sviridyuk model
Статья научная
One of the approaches to solution of the problem on restoring a distorted input signal by the recorded output data of the sensor is the problem on optimal dynamic measurement, i.e. the Shestakov-Sviridyuk model. This model is the basis of the theory of optimal dynamic measurements and consists of the problem on minimizing the difference between the values of a virtual observation obtained using a computational model and experimental data, which are usually distorted by some noise. We consider the Shestakov-Sviridyuk model of optimal dynamic measurement in the presence of various types of noises. In the article, the main attention is paid to the preliminary stage of the study of the problem on optimal dynamic measurement. Namely, we consider the Pyt'ev-Chulichkov method of constructing observation data, i.e. transformation of the experimental data to make them free from noise in the form of ``white noise" understood as the Nelson-Gliklikh derivative of the multidimensional Wiener process. In order to use this method, a priori information about the properties of the functions describing the observation is used.
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Статья научная
Krasnoyarsk Subsidiary of Kutateladze Institute of Thermophysics SB RAS and the Department of Thermophysics of the Siberian Federal University are developing a freely distributable "SigmaFW" software package for numerical simulation of the hydrodynamics, heat and mass transfer problems. It is assumed that the software package will be used in scientific and educational institutions as well as industrial enterprises in Russian Federation. Mathematical models realized in the software package describe steady and unsteady laminar and turbulent single - and multicomponent flow taking into account the dispersed phase, the conjugate and radiative heat transfer, and homogeneous gas-phase chemical reactions. The "SigmaFW" contains the necessary tools for building numerical domains, carrying out multi-threaded calculation, and visual analysis of the results. The article describes the three main blocks of software package: the grid generator, calculation module and analysis of the results. In additition, a number of test and application tasks are presented to demonstrate the capabilities of the software.
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Статья научная
In this paper, the problem of training the Viola-Jones detector for 3D objects is considered on the example of an inflatable life raft PSN-10. The detector is trained on a fully synthetic training dataset. The paper discusses in detail the methods of modelling an inflatable life raft, water surface, various weather conditions. As a feature space, we use edge Haar-like features, which allow training the detector that is resistant to various lighting conditions. To increase the computational efficiency, the L1 norm is used to calculate the magnitude of the image gradient. The performance of the trained detector is estimated on real data obtained during the rescue operation of the trawler "Dalniy Vostok". The proposed method for training the Viola-Jones detectors can be successfully used as a component of hardware and software "assistants" of the UAV.
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«Эффективность» нитей в многопроцессорных системах с общей памятью
Статья научная
Традиционно предполагается, что вычисление, разбитое на несколько нитей определённым образом, выполняется в системах с общей памятью (SMP или NUMA) быстрее, чем это же вычисление, но разбитое на несколько процессов. В представляемой работе высказана гипотеза о том, что такое предположение может быть неверным для вычислений с большими объёмами данных, главным образом по двум причинам. Во-первых, поддержка единого адресного пространства для нитей может быть существенно более накладной, чем суммарные затраты на переключение контекста выполнения между процессами. Во-вторых, даже если вычисление не требует интенсивного управления памятью, естественное ограничение на объём хранимого в TLB описания рабочего множества страниц, и в случае нитей приводит к необходимости частого обновления этого кэша трансляций. В статье описаны эксперименты и их результаты, которые подтверждают адекватность этой гипотезы.
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Статья научная
В работе рассматривается возможность применения агентно-ориентированной системы имитационного моделирования для решения ряда проблем, возникающих при создании экзафлопсных компьютеров, содержащих десятки и сотни миллионов вычислительных узлов. Предлагается двухуровневая децентрализованная схема управления вычислениями и соответствующая имитационная модель, в которой все вычислительные узлы поделены между областями вычислений, которые контролируются своими локальными управляющими агентами. Головной управляющий агент распределяет между областями поток больших задач и контролирует общие ресурсы. В качестве примера масштабируемого алгоритма рассматривается метод Монте-Карло, перспективный для компьютерного моделирования на экзафлопсных компьютерах. В этом методе существенно то, что чем больше объем выборки из независимых реализаций, тем выше точность оценивания. В работе предлагается генератор базовых псевдослучайных чисел, пригодный для больших расчетов по методу Монте-Карло. При распределении вычислений по узлам допускается возможность реализации различных объемов выборки на различных узлах с использованием статистически оптимального способа осреднения результатов. Объем памяти, доступный каждому вычислительному узлу, и его быстродействие должны быть достаточными для эффективного моделирования реализаций. Данный алгоритм распределенного статистического моделирования асинхронен, и при использовании предлагаемого генератора базовых псевдослучайных чисел масштабируется практически на неограниченное число узлов. Примером масштабируемого приложения распределенного статистического моделирования для современных компьютеров терафлопсного уровня производительности является библиотека PARMONC. Кроме того, в работе рассматривается вариант реализации мультиагентного моделирования для прогнозирования сбоев и отказов вычислительных узлов. Предлагается архитектура динамической системы прогнозирования сбоев, которая состоит из агентов различного назначения, каждый из которых выполняет свою функцию для достижения общей цели.
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