«INFORMATICS AND APPLICATIONS»
Volume 6, Issue 4 2012
Content | Bibliography | About Authors
Abstract and Keywords.
ANALYTICAL MODELING INVARIANT MEASURE DISTRIBUTIONS IN STOCHASTIC SYSTEMS
WITH AUTOCORRELATED NOISES.
- I.N. Sinitsyn IPI RAN, email@example.com
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
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.
- I.A. Duchitskii1 Faculty of ComputationalMathematics and Cybernetics, M.V. Lomonosov Moscow State University,
- V.Yu. Korolev M.V. Lomonosov Moscow State University; IPI RAN, firstname.lastname@example.org
- I.A. Sokolov IPI RAN, email@example.com
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.
- M.G. Konovalov IPI RAN, firstname.lastname@example.org
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
Keywords: сontrolled random sequences; adaptive strategies; existence conditions
BOUNDS IN NULL ERGODIC CASE FOR SOME QUEUEING SYSTEMS.
- A. I. Zeifman Vologda State Pedagogical University; IPI RAN; VSCC CEMI RAS, a email@example.com
- A. V. Korotysheva Vologda State Pedagogical University, a firstname.lastname@example.org
- Ya. Satin Vologda State Pedagogical University, email@example.com
- S. Ya. Shorgin IPI RAN, SShorgin@ipiran.ru
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.
- V.Yu. Korolev M. V. Lomonosov Moscow State University; IPI RAN, firstname.lastname@example.org
- V.E. Bening Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics,
M. V. Lomonosov Moscow State University; IPI RAN, email@example.com
- L.M. Zaks Department of Modeling and Mathematical Statistics, Alpha-Bank, firstname.lastname@example.org
- A. I. Zeifman Vologda State Pedagogical University; IPI RAN; VSCC CEMI RAS, email@example.com
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.
- A. Nazarov Department ofMathematical Statistics, Faculty ofComputationalMathematics andCybernetics,M.V. Lomonosov
Moscow State University firstname.lastname@example.org
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.
- M. P. Krivenko IPI RAN, email@example.com
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.
- A. Grusho IPI RAN; Department ofMathematical Statistics, Faculty of Computational Mathematics and Cybernetics,
M.V. Lomonosov Moscow State University, firstname.lastname@example.org
- E. Timonina IPI RAN, email@example.com
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.
- E. V. Djukova Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RAS, firstname.lastname@example.org
- A.V. Sizov Moscow State University, email@example.com
- R.M. Sotnezov Institution of the Russian Academy of Sciences Dorodnicyn Computing Center of RAS, firstname.lastname@example.org
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
- A.A. Tokmakova Moscow Institute of Physics and Technology, email@example.com
- V. V. Strijov Computing Center RAS, firstname.lastname@example.org
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
Keywords: feature selection; regression; coherent Bayesian inference; covariance matrix; model parameters
HOLOGRAPHIC CODING BY WALSH-HADAMARD TRANSFORMATION OF RANDOMIZED AND PERMUTED DATA.
- S. Dolev Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel, email@example.com
- S. Frenkel IPI RAN; Moscow Institute of Radio, Electronics, and Automation (MIREA), firstname.lastname@example.org
- A. Cohen Department of Communication Systems Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel, email@example.com
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
- K. P. Belyaev Shirshov Institute of Oceanology, Russian Academy of Science,Moscow, Russia, firstname.lastname@example.org
- C.A.S. Tanajura Federal University of Bahia, Salvador, Brazil, email@example.com
- N. P. Tuchkova Institution of the Russian Academy of Sciences Dorodnicyn Computing Center of RAS Moscow, Russia, firstname.lastname@example.org
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
COMPLETE CONVERGENCE FOR ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES.
- S.H. Sung Department of Applied Mathematics, Pai Chai University, Taejon, South Korea, email@example.com
- K. Budsaba Center of Excellence in Mathematics, CHE, Bangkok, Thailand; Department of Mathematics and Statistics,
Thammasat University Rangsit Center, Pathumthani, Thailand, firstname.lastname@example.org
- A. Volodin School of Mathematics and Statistics, University of Western Australia, Crawley, Australia; University of Regina,
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