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Том 43, № 3 (2019)
- Год: 2019
- Статей: 9
- URL: https://journals.rcsi.science/0278-6419/issue/view/10813
Article
Algorithm of the Method of Generalized Potentials for Problems of the Optimum Synthesis of Communication Networks with Undefined Factors
Аннотация
The optimum allocation of resources for a Gale problem of supply and demand with uncertain factors is considered. The Dantzig-Wolfe decomposition and the generalized potential method developed earlier by the author for a deterministic version of the problem are used to construct and validate the algorithm for a numerical solution.
138-142
Central Limit Theorem for a Wavelet Estimator of a Probability Density with a Given Weight
Аннотация
The problem of estimating a probability density with a given weight is considered. Probability densities of this type arise in different cases, e.g., analyzing order statistics and studying random-size samples in problems of reliability theory, insurance, and other areas. When constructing an estimator, expansion is used with respect to a wavelet basis based on wavelet functions with bounded spectrum. It is proved that the considered estimator is asymptotically normal when the number of terms of the expansion is fixed and growing.
143-147
Asymptotically Optimum Arrangements for a Special Class of Normed Spaces
Аннотация
A nonclassical queuing-theory problem with calls arising in a space is considered. Stations must be placed to minimize the service time for arising calls. The service time is an increasing function that depends on the distance between a call and a station. The time spent to overcome the same distance frequently depends on the direction of motion. In this case, a metric that considers the nonequivalence of coordinates of the space in order must be chosen to construct an adequate mathematical model. Optimum arrangements of stations can be found for problems of this kind only in exceptional situations. However, an asymptotical solution to the problem can be found that is acceptable from a practical viewpoint. An algorithm is given for constructing asymptotically optimum arrangements.
89-94
Square Roots of Hermitian Matrices and a Rational Algorithm for Checking Their Congruence
Аннотация
A finite computational process using only arithmetical operations is called a rational algorithm. Presently, there is no known rational algorithm for checking congruence between arbitrary complex matrices A and B. The situation may be different if A and B belong to a special matrix class. For instance, there exist rational algorithms for the cases where both matrices are Hermitian, unitary, or accretive. In this publication, we propose a rational algorithm for checking congruence between matrices A and B that are square roots of Hermitian matrices.
95-100
Outlier Detection in Complex Structured Event Streams
Аннотация
Outlier detection methods are now used extensively, particularly in systems for detecting internal intrusions, in medicine, and in systems for detecting extremism in public political discussions on forums and social media. The aim of this work is to consider a fuzzy method of detecting outliers, based on elliptic clustering in the higher-dimensional space of attributes and using the Mahalanobis metrics for calculating the distances between objects and the center of a cluster. A procedure developed by the authors is used to find the optimum values of metaparameters of this algorithm. The classification of both individual events and complete sessions of user activity is considered, using an algorithm based on Welch’s t-statistics. The proposed procedures display a high quality of operation in solving two important problems of the stream analysis of complex data structures: the authentication of users by keystroke dynamics, and detecting extremist information in web text messages.
101-111
Tests Concerning Certain Types of Faults at the Scheme Inputs
Аннотация
Estimates are obtained for the Shannon function of the length of a diagnostic test with respect to cyclic shifts of scheme inputs, and for the Shannon function of fault detection and length of a diagnostic test with respect to a single stuck-at fault and a cyclic shift of scheme inputs.
112-117
Equational Closure and Closure with Respect to Enumeration on a Set of Partial Multivalued Logic Functions
Аннотация
It is proven that for any k ⩾ 2, operators of equational closure and closure with respect to enumeration (Π-operator) generate one and the same classification on set Pk* of partial k-valued logic functions. Thirteen II-precomplete classes are identified in class P3*.
118-125
Eliminating Inequalities in Register Machines with Counters
Аннотация
It is proved that in programs of register machines with counters, only the equal-to/not-equal-to relations between registers and counters are essential without loss of computational capabilities.
126-132
Stabilized Hard Thresholding of Wavelet-Vaguelette Decomposition Coefficients in Reconstructing Tomographic Images Using Projections with Correlated Noise
Аннотация
A way of reconstructing tomographic images based on wavelet-vaguelette decomposition is considered for a model with correlated additive noise. The asymptotic properties of an unbiased estimator are studied for the mean-square risk with stabilized hard thresholding of the coefficients of decomposition. It is shown that under certain conditions, this estimator is strongly consistent and asymptotically normal.
133-137