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“Informatics and Applications” scientific journalVolume 14, Issue 2, 2020Content Abstract and Keywords About Authors ON APPROACHES TO CONSTRUCTING LIMITING REGIMES FOR SOME QUEUING MODELS
Abstract: The authors consider nonstationary queuing models, the number of customers in which is described by finite Markov chains with periodic intensities. For many classes of such models, the methods of obtaining upper bounds on the rate of convergence to the limiting regime were developed in previous papers of the authors. Using these methods, one can find the main limiting characteristics of the system, study their stability with respect to small perturbations of the arrival and service intensities, and receive information on how current characteristics of the system differ from the limiting characteristics at each moment of time. In the present paper, the authors study a different situation, namely, it is assumed that explicit estimates of the rate of convergence to the limiting regime cannot be obtained. The methods for constructing the limiting regimes of such systems and for obtaining information on the rate of convergence to them are considered. As an example, the authors consider a simple model of a nonstationary system with a rather slow rate of convergence to the limiting regime. Keywords: queuing system; finite Markov chains; periodic intensities; limiting characteristics; rate of convergence NUMERICAL SCHEMES OF MARKOV JUMP PROCESS FILTERING GIVEN DISCRETIZED OBSERVATIONS III: MULTIPLICATIVE NOISES CASE
Abstract: The paper presents the final part of investigations initialized in the papers Borisov, A. 2019. Numerical schemes of Markov jump process filtering given discretized observations I: Accuracy characteristics. Inform. Appl. 13(4):68-75 and Borisov, A. 2020. Numerical schemes of Markov jump process filtering given discretized observations II: Multiplicative noises case. Inform. Appl. 14(1):17-23. Relying on the theoretical results, this paper presents a numerical algorithm of the state filtering of homogeneous Markov jump processes (MJP) given indirect noisy continuous time observations discretized by time. The class of observation systems under consideration is restricted by ones with multiplicative noises: any additive payload component is absent in the observable signal, but the observation noise intensity is a function of the MJP state under estimation. To calculate the integrals in the estimate, the author uses the composite midpoint rule of the precision order 3, along with the composite midpoint rule for triangles of the precision order 4. The constructed numerical algorithms of filtering have the final precision of the orders 1 and 2. Keywords: Markov jump process; optimal filtering; additive and multiplicative observation noises; stochastic differential equation; analytical and numerical approximation STOCHASTIC DIFFERENTIAL SYSTEM OUTPUT CONTROL BY THE QUADRATIC CRITERION. V. CASE OF INCOMPLETE STATE INFORMATION
Abstract: A generalization of the optimal control problem for the Ito diffusion process and a linear controlled output with a quadratic quality criterion for the case of indirect observation of the state is considered. The available solution of the problem with full information is used to synthesize control from indirect observations based on the principle of separation. The ability to separate control and state filtering tasks is justified by the properties of the quadratic criterion used. Instead of solving the arising auxiliary problem of optimal filtering described by the general equations of nonlinear filtering based on innovation processes, it is proposed to use the estimate of the conditionally optimal filter of V. S. Pugachev. Thus, the suboptimal solution of the control problem under consideration is obtained as a result of the traditional approach to control synthesis in the problem with incomplete information, consisting in a formal replacement in solving the corresponding problem with complete information of the state variable by its estimate. Finally, a case of numerical implementation of the obtained suboptimal control is proposed. It is based on the method of computer simulation, using a common beam of simulated paths both for calculating the parameters of a conditionally optimal filter and for calculating the parameters in the original control problem. Keywords: stochastic differential equation; stochastic differential system; optimal control; stochastic filtering; conditionally-optimal filtering; computer simulations ASYMPTOTICS OF THE MEAN-SQUARE RISK ESTIMATE IN THE PROBLEM OF INVERTING THE RADON TRANSFORM FROM PROJECTIONS REGISTERED ON A RANDOM GRID
Abstract: When reconstructing tomographic images, it is necessary to use regularization methods, since the problem of inverting the Radon transform, which is the basis of mathematical models of most tomographic experiments, is ill-posed. Regularization methods based on wavelet analysis have become popular due to their adaptation to local image features and computational efficiency. The analysis of errors in tomographic images is an important practical task, since it makes it possible to evaluate the quality of both the methods themselves and the equipment used. Sometimes, it is not possible to register projection data on a uniform grid of samples. If sample points for each coordinate form a variation series based on a sample from a uniform distribution, then the use of the usual threshold processing procedure is adequate. In this paper, the author analyzes the estimate of the mean-square risk in the Radon transform inversion problem and demonstrates that if the image function is uniformly Lipschitz-regular, then this estimate is strongly consistent and asymptotically normal. Keywords: threshold processing; Radon transform; random grid; mean-square risk estimate METHODS OF FINDING THE CAUSES OF INFORMATION TECHNOLOGY FAILURES BY MEANS OF METADATA
Abstract: The work is devoted to remote detection and localization of failures in information systems. Information resources for these tasks have been identified and models for the use of these information resources have been investigated. This article describes metadata by firected acyclic graphs (DAG) which are used for business processes and information technology descriptions. The task in question is as follows. In case of a failure or an error, it is necessary to find quickly the block containing the cause of failure, which is not so expensive that it could not be replaced, and it would be replaced. If a unit contains very expensive components, such as a server, replacing it may not be cost-effective for an organization. In terms of software applications, they can be easily reinstalled and the cost of such a replacement is low. Therefore, the cause should be sought in the top-down direction along the levels of hierarchical decomposition of DAG of information technology. A study has been carried out on analysis and detection of failed data in information technology, provided that all blocks of an information system operate correctly. Keywords: models of information technologies; metadata; directed acyclic graphs; causes of information technology failures and errors JOINT ASSESSMENT OF DATA PREDICTABILITY AND QUALITY PREDICTORS
Abstract: The paper proposes and analyzes a new approach to the selection of predictors necessary for predicting future values in data sequences in a specific time period. Our goal is low-cost implemented techniques that ensure the selection of an acceptable predictor for the current prediction session, or the decision about the impossibility of making a reliable forecast if one finds that this section of the sequence does not have the predictability property. For this, the predictability of this sequence is defined as the maximum conditional probability of the correct prediction in the set of available predictors for a given set of observed values. The selection of predictors is performed by both the magnitude of the conditional probability estimation and the degree of difference between a specific predictor and a predictor that is optimal for predicting the next outcome of the Bernoulli trials sequence. Keywords: random sequences prediction; predictors; data analysis APPROXIMATION OF PARTICLE SIZE DISTRIBUTIONS OF LUNAR REGOLITH BASED ON THE RESAMPLING
Abstract: The paper considers the problem of modeling the size distribution of dust particles of lunar regolith based on approximating with finite lognormal mixtures. These models make it possible to take into account the stochastic nature of the intensities of splitting/baking processes during the formation of ensembles of dust of various influences (bombardment by meteorites, radiation). A method for statistical approximation of unknown distributions based on simulation of samples was developed. It is demonstrated that the model distributions fit very well to the real observations of lunar regolith gathered by missions "Apollo 11, 12, 14-17" and "Luna-24" that had been presented in the NASA's grain size catalog (317 samples). Keywords: finite lognormal mixtures; bootstrap; EM algorithm; statistical methods ORDERING THE SET OF NEURAL NETWORK PARAMETERS
Abstract: This paper investigates a method for setting order on a set of the model parameters. It considers linear models and neural networks. The set is ordered by the covariance matrix of the gradients. It is proposed to use a given order to freeze the model parameters during the optimization procedure. It is assumed that, after few iterations of the optimization algorithm, most of the model parameters can be frozen without significant loss of the model quality. It reduces the dimensionality of the optimization problem. This method is analyzed in the computational experiment on the real data. The proposed order is compared with the random order on the set of the model parameters. Keywords: sample approximation; linear model; neural network; model selection; error function STATIONARY CHARACTERISTICS OF M/G/2/infinity QUEUE WITH IDENTICAL SERVERS, LIFO SERVICE, AND RESAMPLING POLICY
Abstract: Consideration is given to the M/G/2/infinity queue with identical servers, LIFO (last in, first out) service discipline and one special case of the generalized probabilistic priority policy called resampling. The latter implies that a customer arriving to the nonidle system assigns independently new remaining service time to each customer currently in service. The new customer itself either enters a free server, if there is any, or occupies a place in the queue. Remaining service times are assumed to be independent identically distributed random variables with the known general absolute continuous distribution. Under the assumption that the stationary regime exists, the main performance characteristics of the system, including the joint stationary distribution of the total number of customers in the system and the remaining service times of customers in service, are derived. Keywords: multiserver system; inverse service order; probabilistic priority; resampling OPTIMIZATION OF THE CAPACITY OF THE MAIN STORAGE IN G/M/1/K QUEUEING SYSTEM WITH AN ADDITIONAL STORAGE DEVICE
Abstract: The problem of optimizing the capacity of the main storage device of a queuing system of the type G/M/l/K with an additional storage device with the cost objective function is formulated taking into account the costs of the system associated with the loss of requests, storage of requests, maintenance of storage devices, and device downtime. A request arriving to the system is accepted into the main storage device if there is a free space; otherwise, according to the given probability distribution, it goes to the additional device if there is a free space.
Keywords: queueing system; optimization; storage device; storage capacity STATISTICAL PROPERTIES OF BINARY NONAUTONOMOUS SHIFT REGISTERS WITH INTERNAL XOR
Abstract: The statistical and algebraic properties of binary nonautonomous shift registers and shift registers with internal XOR are compared, during which the state vector is summed with its one-step shift. The isomorphism of transition graphs of these automata is proved. It is shown that, with a Bernoulli random input, the stationary distribution of the register states with internal XOR is uniform. The form of the probability function of these registers is obtained. It is shown that, under certain conditions on the output function, registers with internal XOR are not Cesaro-hereditary. The authors show input sequences that possess the property of stability of the relative frequencies of arbitrary multigrams, while output sequences do not have this property Keywords: random input automata; shift register; de Bruijn graph SEQUENTIAL ANALYSIS OF SERIAL MEASUREMENTS BASED ON MULTIVARIATE REFERENCE REGIONS
Abstract: Sequential data series analysis procedures are considered. An approach is developed when a set of multivariate features of a certain object, which varies in time, is presented as a single vector of observed values. By increasing the dimensionality of the data, it is possible to obtain a single picture of the description of objects, to take into account the objectively existing dependence of individual observations, and to simulate changes over time. The basis for solving classification problems is the use of multivariate reference regions. Three options for data processing procedures are proposed, their properties are investigated, and recommendations for practical application are developed. To demonstrate the capabilities of these procedures, the task of early diagnosis of cancer using the PSA (prostate-specific antigen) biomarker is considered. Features of the application of sequential methods for analyzing data series are indicated, recommendations for their effective use are formed, and the advantages of the consolidating approach in data analysis are identified. Keywords: serial measurements; consolidation approach; sequential procedures; analysis of prostate-specific antigen (PSA) MULTIFACTOR FULLY CONNECTED LINEAR REGRESSION MODELS WITHOUT CONSTRAINTS TO THE RATIOS OF VARIABLES ERRORS VARIANCES
Abstract: The article is devoted to the problem of constructing errors-in-variables regression models. Currently, such models are not widely used because they are not suitable for forecasting and interpretation, they are difficult to estimate, and the variables errors variances are unknown. To eliminate these shortcomings, the author developed and investigated two-factor fully connected linear regression models. Such models are easily estimated, they can be used for forecasting, and they lack the effect of multicollinearity. In this paper, for the first time, multifactor fully connected linear regression models are considered. It is proved that in the case of removing the restrictions, on the ratio of variables errors variances, there are the one estimates of a fully connected regression, in which the approximation qualities of its secondary equation and the classical multiple linear regression model, estimated using the ordinary least squares, coincide. Keywords: errors-in-variables models; fully connected regression; Deming regression; ordinary least squares SOLUTION OF THE UNCONDITIONAL EXTREMAL PROBLEM FOR A LINEAR-FRACTIONAL INTEGRAL FUNCTIONAL DEPENDENT ON THE PARAMETER
Abstract: The paper is devoted to the study of the unconditional extremal problem for a fractional linear integral functional defined on a set of probability distributions. In contrast to results proved earlier, the integrands of the integral expressions in the numerator and the denominator in the problem under consideration depend on a real optimization parameter vector. Thus, the optimization problem is studied on the Cartesian product of a set of probability distributions and a set of admissible values of a real parameter vector. Three statements on the extremum of a fractional linear integral functional are proved. It is established that, in all the variants, the solution of the original problem is completely determined by the extremal properties of the test function of the linear-fractional integral functional; this function is the ratio of the integrands of the numerator and the denominator. Possible applications of the results obtained to problems of optimal control of stochastic systems are described. Keywords: linear-fractional integral functional; unconditional extremal problem for a fractional linear integral functional; test function; optimal control problems for Markov and semi-Markov random processes INTEGRATION PLATFORM FOR MULTISCALE MODELING OF NEUROMORPHIC SYSTEMS
Abstract: The current multilevel resistive memory elements allow increasing the integration density of nonvolatile memory as well as designing and creating systems with a parallel computing mechanism. Such devices are based on memristor elements necessary for developing the foundations of analog neuromorphic networks that are used to solve data mining problems. However, the use of memristors as a part of neuromorphic devices encounters a number of problems such as the scatter of the switching parameters (voltage and memory window) from cell to cell, asymmetry and nonlinear effects, and others. Such problems dictate the need to create original simulation models and new software tools that will allow one to evaluate the influence of disturbing factors on the predictive accuracy and network learning process. In this paper, to solve the problem of multiscale modeling of neuromorphic systems, the authors use the original information technology for constructing multiscale models. For its practical implementation, an integration platform has been built that allows one to evaluate the influence of disturbing factors on the predictive accuracy and learning process of a neuromorphic network and in the future, it will be able to provide information for a reasonable choice of materials, configuration, and topology of memory cells of new-generation computers. Keywords: multi-scale modeling; multilevel memory elements; neuromorphic networks; predictive modeling; memristor; integration platform; software package SELECTION OF OPTIMAL COMPLEXITY MODELS BY METHODS OF NONPARAMETRIC STATISTICS (ON THE EXAMPLE OF PRODUCTION FUNCTION MODELS OF THE REGIONS OF THE RUSSIAN FEDERATION)
Abstract: The article describes an approach to comparing alternative variants of linear regression models on time series and determining the appropriateness of complicating them (by adding new variables) using several variants of Monte-Carlo methods. The proposed research methods using pseudosampling generation allow taking into account both the effects associated with possible differences of distributions in empirical data from the Gauss distribution and the effects associated with possible nonstationarity of the time series under study. For this purpose, pseudosampling generation is used - time series, which are Gaussian white noise, random walk generation, as well as the permutation test and the bootstrap method. Reliability of the obtained results is estimated using resampling. Applicability of the considered methods is demonstrated by the example of models of investment production functions of regions of the Russian Federation, calculated on the basis of data from the Federal State Statistics Service. Keywords: Monte-Carlo methods; permutation tests; spurious regression; production functions; model selection; meso level of the economy REDUCING THE SPECTRUM OF TRANSLATION MODELS IN SUPRACORPORA DATABASES
Abstract: The paper describes an approach aimed at reducing the spectrum of translation models that are registered in supracorpora databases (SDB). This approach may be applied to both professional (made by the human) and machine translation. As of today, one can use the information resources of the SDB to research the problems of interest to computing, computer linguistics and linguistic theory. Here, the focus is on examining if and how the SDB can be used in translation practice - for reducing the spectrum of translation models. Very often while translating, a translator finds himself/herself in a multiple-choice situation: due to the synonymic potential, characteristic of natural languages, in translation instead of the only possible solution, there is a set of relatively interchangeable equivalents, i.e., "fan of alternatives." Choosing from a (sometimes wide) range of variants, a translator, in order to narrow the choice, relies on some specific characteristics of the source text. Hence, the goal of the paper is to describe the approach that would allow one to use the SDB for narrowing the choice set of relevant translation models. Keywords: parallel texts; translation; translation models; supracorpora database; multiple choice
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