Informatics and Applications scientific journal
Volume 6, Issue 4, 2012
ANALYTICAL MODELING INVARIANT MEASURE DISTRIBUTIONS IN STOCHASTIC SYSTEMS WITH AUTOCORRELATED NOISES.
Abstract: For multidimensional nonlinear normal (Gaussian) differential systems with un- and autocorrelated noises, on the basis of normal approximation, the correlational algorithms for analytical modeling of stochastic regimes with invariant measure are considered. Special software tools in MATLAB are developed. Test examples confirm practical accuracy.
Keywords: analytical modeling; autocorrelated noise; correlational algorithm; distribution with invariant measure; multidimensional nonlinear differential stochastic system; normal approximation method
ON THE ACCURACY OF SOME MATHEMATICAL MODELS OF CATASTROPHICALLY ACCUMULATED EFFECTS IN PREDICTION OF RISKS OF EXTREMAL EVENTS.
Abstract: Estimates are constructed for the accuracy of approximation of the distributions of extrema of special random sums by scale mixtures of half-normal laws. The possibility of the application of these results in prediction of risks of extremal events due to catastrophically accumulated effects is discussed.
Keywords: nonhomogeneous flows of events; doubly stochastic Poisson process; negative binomial distribution; gamma-distribution; convergence rate estimate
ABOUT ADAPTIVE STRATEGIES AND THEIR EXISTENCE CONDITIONS.
Abstract: The optimal control problem is considered under deficiency of a priori information about a controlled object. The solution of the problem is the construction of adaptive strategies on the base of in-control available observations. Some conditions of adaptive controllability are studied. Controlled random sequences are used as mathematical model.
Keywords: ñontrolled random sequences; adaptive strategies; existence conditions
BOUNDS IN NULL ERGODIC CASE FOR SOME QUEUEING SYSTEMS.
Abstract: Markovian queueing models with batch arrivals and group services are considered. The bounds on the rate of convergence in null ergodic situation are obtained. Also, a class of such queueing systems is considered.
Keywords: nonstationary queueing systems with batch arrivals and group services; null ergodicity; bounds
GENERALIZED LAPLACE DISTRIBUTION AS A LIMIT LAW FOR RANDOM SUMS AND STATISTICS CONSTRUCTED FROM SAMPLES WITH RANDOM SIZES.
Abstract: Limit theorems establishing necessary and sufficient conditions of convergence of random sums and statistics constructed from the samples with random sizes to the generalized Laplace distribution are proved.
Keywords: generalized Laplace distribution; symmetric stable distribution; one-sided stable distribution; scale mixture of normal laws; random sum; sample with random size; mixed Poisson distribution
LOWER BOUNDS FOR THE STABILITY OF NORMAL MIXTURE MODELS WITH RESPECT TO PERTURBATIONS OF MIXING DISTRIBUTION.
Abstract: The stability of normal mixture models with respect to perturbations of mixing distribution is investigated. Inequality estimating the distance between two mixing distributions through the closeness of the corresponding mixtures is presented. Existence theorem for stability estimates is proved for subclasses of scale and shift mixtures of normal distributions. For the class of shift mixtures, the estimate is obtained in an explicit form. It is shown that the presented results cannot be radically improved without additional assumptions.
Keywords: normal distribution mixtures; stability problems for stochastic models; Fourier transform; Plancherel theorem; Prokhorov’s theorem; Levy metric; lower bounds
PREPROCESSING OF TEXT RECOGNITION UNDER THE POOR QUALITY IMAGE.
Abstract: The methods of preprocessing of text images including the skew correction and the line segmentation are discussed for the case where the recognizable image is of low quality being obtained with high resolution. Provided that the brightness of the pixel rows of characters differs, even slightly, from the brightness of the background pixels, the procedures for the skew correction and segmentation of the text lines are proposed and analyzed.
Keywords: text recognition; image preprocessing; skew correction; text line segmentation
RANDOM GRAPHS MODEL FOR DESCRIPTION OF INTERACTIONS IN THE NETWORK.
Abstract: A new class of random graphs urged to simulate network functioning in time is considered. It is supposed that observations over a network are carried by means of a “window” method. To detect the anomalies, normal behavior which can be watched in “windows” of a considered model is studied. The asymptotic value of themaximumdegree of vertices in graph which is generated by a “window” of certain size is analyzed.
Keywords: random graphs; simulation of wide area networks; information security; abnormal behavior
ON THE OPTIMAL CORRECT RECODING OF INTEGER DATA IN RECOGNITION.
Abstract: Questions of application of logical procedure of recognition by precedents in the case of float information and highatomicity integer information are investigated. The problem of correct reducing the data atomicity is considered. Genetic algorithms for the search of optimal correct recoding of source information are developed. Developed algorithms are tested on real data.
Keywords: pattern recognition; correct recoding; covering of the Boolean matrix
ESTIMATION OF LINEAR MODEL HYPERPARAMETERS FOR NOISE OR CORRELATED FEATURE SELECTION PROBLEM.
Abstract: The problem of feature selection in linear regression models has been solved. To select the features, the authors estimate the covariance matrix of the model parameters. Dependent variable and model parameters are assumed to be normally distributed vectors. Laplace approximation is used for estimation of the covariance matrix: logarithm of the error function is approximated by the normal distribution function. The problem of noise or correlated features is also examined, since in this case, the covariance matrix of the model parameters becomes singular. An algorithm for feature selection is suggested. The results of the study for a time series are given in the computational experiment.
Keywords: feature selection; regression; coherent Bayesian inference; covariance matrix; model parameters
HOLOGRAPHIC CODING BY WALSH-HADAMARD TRANSFORMATION OF RANDOMIZED AND PERMUTED DATA.
Abstract: Holographic coding has the very appealing property of obtaining partial information on data, from any part of the coded information. Holographic coding schemes are studied based on the Walsh–Hadamard orthogonal codes. It is proposed to randomize the data so that the coefficient of the Walsh–Hadamard code would be approximately uniform in order to ensure, with high probability, a monotonic gain of information. The data are xored with randomly chosen bits from random data that have been stored during a preprocessing stage or pseudorandom data produced by a pseudorandom generator. Statistical properties of the truncated sums of Inverse Walsh–Hadamard Transformation (WHT), taking into account the “white-noise nature” and the mentioned above holographic properties of this encoding method, and the performance of the method is considered based on the theoretic Shannon bound. Using this performancemeasure, an enhancement for the authors’ previousWHT-based holographic coding method is suggested. This enhancement is based on a random permutation.
Keywords: holographic coding; Walsh–Hadamard transformation; Shannon bound
MATHEMATICAL FOUNDATION, APPLICATION, AND COMPARISON OF GENERAL DATA ASSIMILATION METHOD BASED ON DIFFUSION APPROXIMATION WITH OTHER DATA ASSIMILATION SCHEMES.
Abstract: Data assimilation methods commonly used in numerical ocean and atmospheric circulation models for weather and climate prediction produce approximations of state variables in terms of stochastic processes. This approximation consists of random sequences of Markov chains, which converge to a diffusion-type process. The conditions for this convergence are investigated. The optimization problem associated with the search of the best possible approximation of the state variable and the results of a numerical experiment are discussed. It is shown that the data assimilation method can be used in practical applications in meteorology and oceanography. Several applications of the methods as an example of the modern operational data processing system with the ocean circulation model HYCOMand data fromARGO drifters are performed and the results as well as comparisons with other assimilation schemes are presented.
Keywords: sequence of Markov chains; diffusion stochastic process; data assimilation methods; HYCOM; ARGO drifters
COMPLETE CONVERGENCE FOR ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES.
Abstract: A general result establishing complete convergence for the row sums of an array of row-wise negatively dependent random variables is presented. From this result, a number of complete convergence results is obtained for weighted sums of negatively dependent random variables.
Keywords: complete convergence; negatively dependent; weighted sums; arrays
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