Informatics and Applications scientific journal
Volume 8, Issue 3, 2014
ON CONDITIONS OF CONVERGENCE OF THE DISTRIBUTIONS OF EXTREMAL ORDER STATISTICS TO THE WEIBULL DISTRIBUTION.
Abstract: Some product representations are obtained for random variables with the Weibull distribution by stable random variables. These results are used to describe the conditions providing convergence of the distributions of linearly transformed minimum order statistics in samples with random sizes to the Weibull distribution. The presented results broaden traditional conceptions concerning conditions of convergence of extremal order statistics to the Weibull distribution and give additional theoretical explanation for high adequacy of the Weibull distribution in lifetime data analysis, in particular, in reliability theory.
Keywords: Weibull distribution; exponential distribution; Rayleigh distribution; strictly stable distribution; sample with random size
ANALYTICAL MODELING OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH COMPLEX NONLINEARITIES.
Abstract: Differential stochastic systems (DStS) with Wiener and Poisson noises and complex finite, differential, and integral nonlinearities and hereditary StS reducible to DStS are considered. Equations and algorithms of analytical modeling based on the normal approximation method (NAM) and the statistical linearization method (SLM) are given. The case of complex continuous and discontinuous nonlinearities of scalar and vector arguments is considered. Special attention is paid to NAM (SLM) typical integrals for finite rational and irrational nonlinear and integral scalar and vector nonlinear functions. The general case of integral nonlinearities reducible to linear is considered. Test examples are given..
Keywords: analytical modeling; complex finite differential and integral nonlinearities; complex irrational non- linerarites differential stochastic system with Wiener and Poisson noises; method of normal approximation; method of statistical linearization; hereditary stochastic systems reducible to differential
ON THE BOUNDS OF THE RATE OF CONVERGENCE AND STABILITY FOR SOME QUEUEING MODELS .
Abstract: A generalization of the famous Erlang loss system has been considered, namely, a class of Markovian queueing systems with possible simultaneous arrivals and group services has been studied. Necessary and sufficient conditions of weak ergodicity have been obtained for the respective queue-length process and explicit bounds on the rate of convergence and stability have been found. The research is based on the general approach developed in the authors' previous studies for nonhomogeneous Markov systems with batch arrival and service requirements. Also, specific models with periodic intensities and different maximum size of number of arrival customers are discussed. The main limiting characteristics of these models have been computed and the effect of the maximum size of the group of arrival customers on the limiting characteristics of the queue has been studied.
Keywords: nonstationary Markovian queue; Erlang model; batch arrivals and group services; ergodicity; stability; bounds
STATIONARY DISTRIBUTION IN A QUEUEING SYSTEM WITH INVERSE SERVICE ORDER AND GENERALIZED PROBABILISTIC PRIORITY .
Abstract: Consideration is given to M|G|1 type queueing system. Inverse service order with generalized probabilistic priority is implemented in the system. It is assumed that at any instant, the remaining service time of each customer residing in the system is known. Upon arrival of a new customer, the system finds out its service time and compares it with the remaining service time of the currently served customer. The result of this comparison leads to one of the cases: one of them enters the server and another occupies the first place in the queue; one of them leaves the system and another enters the server; or both leave the system. In each case when customer remains in the system, its remaining service time may be updated. An analytical method that allows computing stationary performance characteristics related to the number of customers in the system is presented. Numerical examples based on the developed mathematical relations are provided.
Keywords: queueing system; special discipline; LIFO; probabilistic priority; general service time
ANALYSIS OF A QUEUEING SYSTEM WITH AUTOREGRESSIVE ARRIVALS.
Abstract: The paper studies a single server queueing system with infinite capacity and with the Poisson batch arrival process. A feature of the system under study is autoregressive dependence of the arriving batch sizes: the size of the nth batch is equal to the size of the (n - 1)st batch with a fixed probability and is an independent random variable with complementary probability. Service times are supposed to be independent random variables with a specified distribution. The main object of the study is the queue length at an arbitrary moment. The relations derived make it possible to find Laplace transorm in time of the probability generating function of the transient queue length, and also a number of additional characteristics such as the residual service time and the distribution of the size of the last batch that arrived before time t.
Keywords: queueing theory; transient behavior; batch arrivals
MODELS FOR COMPARATIVE ANALYSIS OF CLASSIFICATION METHODS IN DISTRIBUTED OBJECT RECOGNITION SYSTEMS .
Abstract: The paper considers recognition systems where classes are defined by appropriate patterns located in distributed data base. Recognition criterion is full coincidence of the presented sample with at least one of the patterns. Parallel and sequential classification methods are compared in terms of mean response time to recognition request and performance requirements. The results of numerical experiments which were carried out for multibiometric recognition systems using analytical and simulation models of queueing networks are presented.
Keywords: distributed recognition system; parallel and sequential classification methods; resource allocation; queueing network
MONITORING REMOTE SERVER ACCESSIBILITY: THE OPTIMAL FILTERING APPROACH .
Abstract: The online monitoring problem of a remote server, accessible via the http protocol, is formulated in the terms of optimal filtering. The unobservable server state is treated as a finite-dimensional Markov jump process, meanwhile the observation is supposed to be a multivariate point process with a finite set of possible values. The key point of the investigated observation system is that the random intensity of observations is a linear function of the unobservable Markov state. It is proved that the optimal filtering estimate is a solution to some closed finite system of recursive formulae and ordinary linear differential equations with a random right-hand side. The applicability of the obtained theoretical results is illustrated by an example of monitoring accessibility of the queueing system "communication channel - database server." The unobservable state of this system consists of three possible values (no connection, low workload, high workload), meanwhile the possible observations belong to the set of two possible values (answer to the query, error message). The conclusion of the paper contains possible prospectives for the further research.
Keywords: Markov models; optimal filtering; stochastic jump processes; conditional probability distribution; queueing theory
COMPARATIVE ANALYSIS OF REGRESSION ANALYSIS PROCEDURES .
Abstract: The article considers the problem of forecasting the values of one variable from the values of another variable using regression analysis techniques. The list of compared regression analysis procedures included the following parameter estimation methods: ordinary least squares, least squares based on the sign statistics, and zero correlation based on rank statistics. To implement the method of least squares on the basis of sign statistics, it is necessary to construct efficient data processing procedures. An efficient variant of the corresponding algorithm was realized for a difficult situation, when the goal function is piecewise constant. The comparative analysis of regression analysis procedures in real conditions, when data are not normally distributed, showed that nonparametric techniques are advantageous. In this case, taking into account algorithmic aspects, the preference should be given to procedures based on rank, not on signs. Advantages of nonparametric methods can improve the accuracy of measuring chromogranin A, widely used as an immunohistochemical marker of neuroendocrine differentiation.
Keywords: regression analysis; rank and sign-based procedures; prediction quality; adjustment of measurement results
MATHEMATICAL STATISTICS METHODS AS A TOOL OF TWO-PARAMETRIC MAGNETIC-RESONANCE IMAGE ANALYSIS.
Abstract: The paper considers the methods of the magnetic-resonance image analysis, based on the solution of the so-called two-parametric task. The elaborated methods provide joint calculation of both statistical parameters - the mathematical expectation of the random value being analyzed and its dispersion, i. e., simultaneous estimation of both the useful signal and the noise. The considered variants of the task solution employ the methods of mathematical statistics: the maximum likelihood method and variants of the method of moments. A significant advantage of the elaborated two-parametric approach consists in the fact that it provides an efficient solution of nonlinear tasks including the tasks of noise suppression in the systems of magnetic-resonance visualization. Estimation of the sought-for parameters is based upon measured samples' data only and is not limited by any a priori suppositions. The paper provides the comparative analysis of the considered methodology's variants and presents the results of the computer simulation providing the statistical characteristics of the estimated parameters' shift and scatter while solving the task by various methods. The presented methods of the Rician signal's two-parametric analysis can be used within new information technologies at the stage of the stochastic values' processing.
Keywords: Rice distribution; maximum likelihood method; method of moments; two-parametric analysis; signal-to-noise ratio
APPLICATION OF GRAY-SCALE PRESENTATIONS IN THE CASE OF TREND ANALYSIS OF COLOR IMAGES.
Abstract: In order to cut computing and time expenses during analysis of color images, in practice often the simplified models are used. For example, application of gray-scale presentations of color images in video analysis allows reducing expenses by 2-3 times. At the same time, a part of information about the original image is lost which reduces the analysis accuracy. The error of the result depends essentially on choice of functions used for gray scaling. The algorithm of shared usage of multivariate gray-scale presentations of color images providing increase of accuracy of result is proposed. The regions of practical application are indicated, in which using the proposed algorithm does not result in additional temporary costs on corresponding procedures. Illustrative examples are given.
Keywords: color images; gray-scale presentations; analysis error; video
VOXEL MODELS TEXTURING BASED ON REFERENCE POINTS' COLOR INFORMATION.
Abstract: The article describes a technology for texturing voxel models based on color information contained in reference points. Reference points are special points in three-dimensional space which describe a definite part of an object surface and contain generalized color information about a corresponding area. The color of each voxel located in the area bounded by reference points is defined by each reference point bounding this area. The color components weights of each reference point are proportional to Euclidean distance from each voxel to these reference points. The article presents a method for calculating reference points color components weights based on dependence on the distance from reference points to voxels. This method is used for calculating colors of voxels.
Keywords: three-dimensional reconstruction; texture mapping; voxel
DESIGN OF SELF-TIMED CIRCUITS: STRUCTURAL METHODS IN HIERARCHICAL ANALYSIS .
Abstract: Self-timed circuits have unique properties of the delay-independence and fail-safe. One of the major problems of circuits design, self-timed analysis of large circuits, is considered. In the traditional approach, circuits are analyzed by event methods with elements switches. Computational complexity in this approach increase exponentially with the size and/or other circuit parameters, which does not allow analyzing the most practically important circuits. The solution is proposed in the functional approach, without using switches, and in the hierarchical description of circuits. In the hierarchical analysis along with the analysis of logical functions, the author proposes to use structural methods, i. e., to study the interaction of elements and fragments. This method allows reducing the complexity of calculations dramatically and thus solves one of the major problems of self-timed circuits design - analysis of circuits of any size. Efficiency of the suggested methods is confirmed using the experimental software.
Keywords: self-timed circuits; asynchronous circuits; circuit design; self-timed
INDICATORS OF THEMATIC SCIENCE-TECHNOLOGY LINKAGES: FROM TEXT TO NUMBERS.
Abstract: The article describes the principal stages of calculation of indicators for thematic science-technology linkages. Source data for carrying out calculations are results of processing of full-text descriptions of inventions in natural language. The purpose of processing is extracting information about scientific publications cited in full-text descriptions of inventions. Comparing this information with indexes of the International Patent Classification helps experts to reveal science-technology linkages and to estimate them by means of quantitative indicators. In the article, the technological stages of calculating indicators for linkage assessment on which transition from text processing to numerical calculations is carried out are investigated. The article describes the techniques developed for extracting information about scientific publications from full-text descriptions of inventions and calculating indicator values. These techniques helped to define indicators of science-technology linkages for information technology research fields, which were patented in the Russian Federation in 2000-2012. For the domestic scientific and technical sphere, these indicators were calculated for the first time.
Keywords: science-technology linkages; methodology for calculation of linkage indicators; information technology; text processing; calculation of indicator values
ANALYTICAL ASPECTS OF EVALUATION OF EFFECTIVENESS OF TECHNOLOGICAL SUPPORT OF AN ORGANIZATIONAL SYSTEM.
Abstract: The article discusses the system consisting of normalized and actual indicators, which is used in technological support of activities of an organizational system. The article presents the evaluation criteria that are provided by the classification approach to the choice of scenario for decision for responsible persons for different situations arising in an environment of activities of an organizational system. Classification is performed according to the hierarchy of activities of an organizational system: (a) activities in the divisions of the organizational system; (b) activities in the organizational system; and (c) all activities of the organizational system in general.
Keywords: organizational system; technological support of activities of an organizational system; evaluation of the effectiveness; normalized and actual indicators; information; decision making; monitoring objects
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