# «INFORMATICS AND APPLICATIONS» Scientific journal Volume 9, Issue 3, 2015

## Abstract and Keywords.

##### ANALYSIS OF SURVEY DATA CONTAINING ROUNDED CENSORING INTERVALS.
• Yu. K. Belyaev  Department of Mathematics and Mathematical Statistics, Ume a University, Ume a SE-901 87, Sweden, yuri.belyaev@umu.se
• B. Kristrom  Center for Environmental and Resource Economics (CERE), Swedish University of Agricultural Sciences, Ume a SE-901 83, Sweden, bengt.kristrom@umu.se

Abstract: This paper makes a contribution towards the statistical analysis of data sets containing intervals, that naturally arises in survey contexts. The suggested approach is sufficiently general to cover most cases where interval data are used. Interval data appear in many contexts, such as in reliability studies and survival analysis, in medicine and economics, in opinion elicit surveys, etc. There are several reasons for the extensive use of interval data, perhaps, the most common being one of necessity; exact values of the underlying observations are censored. The nature of the intervals analyzed here is somewhat unusual. The self-selected intervals (SeSeI) are (freely) chosen by the subjects. A generalization of the influential approach has been suggested to the statistical analysis of general censoring introduced by B. W Turnbull. A key independence assumption in Turnbull's analysis has been explained and generalized. A sampling stopping rule based on the coverage probability has been suggested and the properties of a two-step estimator, based on the idea of asking two questions, where the second involves a way of fine-graining the information, has been discussed. This paper provides several informatics methods for SeSeI, targeting the problem of partial nonparametric identification. The properties of the suggested statistical models are stated, including a recursion for easy numerical calculations. An extensive simulation study, displaying, inter alia, the usefulness of the proposed resampling methods for the situation under study, completes the paper.

Keywords: elicitation surveys; random sampling; rounding; anchoring; coverage probability; likelihood; recursion; maximization; resampling

##### ANALYTICAL MODELING IN STOCHASTIC SYSTEMS ON MANIFOLDS BASED ON ORTHOGONAL EXPANSIONS.
• I. N. Sinitsyn Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: Problems of accuracy and sensitivity of one-dimensional distributions by parametrical analytical modeling algorithms on the basis of the orthogonal expansion method (OEM) and the quasi-moment method (QMM) in stochastic systems on manifolds (MStS) are considered. Stochastic system on manifolds is described by Ito linear, linear with multiplicative noises and nonlinear equations with Wiener and Poisson noises. The OEM and QMM equations are derived by generalized Ito formula. Methodological results are the basis of the original symbolic software tools for MATLAB-MAPLE. The problems of reduction of number of OEM and QMM equations are discussed, reliability and security algorithms are presented. Scalar nonlinear MStS with multiplicative white noise is investigated. Some possible generalizations are formulated.

Keywords:  analytical modeling method (AMM); generalized Ito formula; Hermite polynomials; OEM and QMM accuracy equations; OEM and QMM sensitivity equations; orthogonal expansion method (OEM); quasi-moment method (QMM); stochastic system on manifold (MStS)

##### JOINT STATIONARY DISTRIBUTION OF m QUEUES IN THE N-SERVER QUEUEING SYSTEM WITH REORDERING.
• A. V. Pechinkin  Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
• R. V. Razumchik Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation, Peoples’ Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation

Abstract: The paper considers a continuous-time N-server queueing system with a buffer of infinite capacity and customer reordering. The Poisson flow of customers arrives at the system. Service times of customers at each server are exponentially distributed with the same parameter. Each customer obtains a sequential number upon arrival. The order of customers upon arrival should be preserved upon departure from the system. Customers which violated the order form different queues in the reordering buffer which has infinite capacity. If there are n, n = 1, N, customers in servers, then the latest customer to occupy a server is called the 1st level customer, the last but one - the 2nd level customer, . . . , the first - the nth level customer. Customers in the reordering buffer that arrived between the 1st level and the 2nd level customers, form the queue number one. Customers, which arrived between the 2nd level and the 3rd level customers, form the queue number two, etc. Customers, which arrived between the Nth level and the (N - 1)th level customers, form the queue number (N - l) in the reordering buffer. Mathematical relations in terms of Z-transform, which make it possible to calculate the joint stationary distribution of the number of customers in the buffer, servers, and in the 1st, 2nd, . . . , mth queues (m = 1, N - 1) in the reordering buffer, are obtained.

Keywords:  multiserver queueing system; reordering; separate queues; joint stationary distribution

##### THE APPROXIMATION OF RESPONSE TIME OF A CLOUD COMPUTING SYSTEM.
• A. V. Gorbunova Peoples’ Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
• I. S. Zaryadov Peoples’ Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
• S. I. Matyushenko Peoples’ Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
• K. E. Samouylov Peoples’ Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
• S. Ya. Shorgin Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: Cloud computing is an evolutionary technology that allows a remote user to gain access to resources through Internet services. The article discusses the cloud computing system, which receives complex user queries consisting of several subqueries. The allocation of one unit of the resource is required for processing each subquery. Accurate assessment of effectiveness of cloud computing resources is a prerequisite to ensure the required quality of service. Response time, i. e., the maximum of subqueries service times, is chosen as an indication of effectiveness of a cloud computing system. To analyze the characteristics of response time, a simplified mathematical model of a cloud system was constructed as a queuing system with single Poisson input flow of requests and several subsystems (a buffer and a server). Each request at the instant of arrival is divided into several parts, each of which is served by its queuing subsystem with unlimited storage capacity with exponentially distributed service time. The analytical formulas for approximation of mean response time and its variance are presented. To assess the accuracy of the approximation, a GPSS (General Purpose Simulation System) model was constructed.

Keywords:  cloud computing system; response time; complex queries processing; queueing system; approximation; simulation

##### EXTREMAL INDICES IN A SERIES SCHEME AND THEIR APPLICATIONS.
• A. V. Lebedev Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation

Abstract: The concept of an extremal index of a stationary random sequence is generalized to a series scheme of identically distributed random variables with random series sizes tending to infinity in probability. The new extremal indices are introduced through two definitions generalizing the basic properties of the classical extremal index. Some useful properties of the new extremal indices are proved. The paper shows how the behavior of aggregate activity maxima on random graphs (in information network models) and the behavior of maxima of random particles scores in branching processes (in biological populations models) can be described in terms ofthe new extremal indices. New results on models with copulas and threshold models are obtained. The paper shows that the new indices can take different values for one system and the values greater than one.

Keywords:  extremal index; series scheme; random graph; information network; branching process; copula

##### THE THRESHOLD STRATEGY FOR RESTRICTING ACCESS IN THE M/D/1 QUEUEING SYSTEM WITH PENALTY FUNCTION FOR LATE SERVICE.
• Ya. M. Agalarov Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: The paper considers the problem of optimizing the access control on a set of dynamic threshold strategies in an M/D/1 system. If the number of concurrent requests in a system is more than the threshold, then the system stops accepting requests. If the number of requests is less or equal to this value, then the system resumes accepting requests. As a target function, the average value of the marginal revenue obtained per time unit in the stationary mode is used. It is assumed that the system receives a fixed fee for each accepted request and pays a fixed penalty for each overdue service of a request. The system does not receive a fee and does not pay a penalty for each rejected request. Estimates of the optimal value of the target function and the optimal threshold value are obtained.

Keywords:  queueing system; threshold strategy; optimization

##### FOREST FIRE ON A CONFIGURATION GRAPH WITH RANDOM FIRE PROPAGATION.
• M. M. Leri Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 11 Pushkinskaya Str., Petrozavodsk 185910, Russian Federation

Abstract: The paper considers a random process of fire propagation over links of two types of configuration graphs with random node degrees. Node degrees follow either a power law or the Poisson distribution. The process takes place in a random environment where the probabilities of fire propagation follow the standard uniform distribution.
The optimal values of the node degree distribution parameters that ensure maximum node survival in case of a fire were estimated. The results were obtained for two cases of fire start: targeted start - when a fire starts from the node with the highest degree and random ignition - when a fire starts from an equiprobably chosen node. A comparative analysis of two graph models (power law and Poisson) in terms of the number of nodes remained after the fire was performed.

Keywords:  configuration graphs; power-law distribution; Poisson distribution; robustness; forest fire model

##### HIGHER-ORDER ASYMPTOTIC EXPANSIONS OF UNBIASED ESTIMATORS AND THEIR VARIANCES ON THE ONE-PARAMETER EXPONENTIAL FAMILY MODEL.
• V. V. Chichagov Perm State University, 15 Bukireva Str., Perm 614990, Russian Federation

Abstract: The paper considers a model of duplicate sampling with the fixed size n from a distribution belonging to the natural one-parameter exponential family A limiting behavior of the uniformly minimum variance unbiased estimator (UMVUE) of the given parametric function and the UMVUE variance of this estimator is studied in the case of infinite size of the sample. Higher-order asymptotic expansions are obtained for functions defining unbiased estimators and variances of these estimators. The results are presented for both the canonical parameterization and the mean parameterization.

Keywords: natural exponential family; unbiased estimate; asymptotic expansion

##### REALIZABILITY OF PROBABILISTIC REACTIONS BY FINITE PROBABILISTIC AUTOMATA.
• A. M. Mironov Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: The paper considers the problem of optimizing the access control on a set of dynamic threshold strategies in an M/D/1 system. If the number of concurrent requests in a system is more than the threshold then the system stops accepting requests. If the number of requests is less or equal to this value, then the system resumes accepting requests. As a target function, the average value of the marginal revenue obtained per time unit in the stationary mode is used. It is assumed that the system receives a fixed fee for each accepted request and pays a fixed penalty for each overdue service of a request. The system does not receive a fee and does not pay a penalty for each rejected request. Estimates of the optimal value of the target function and the optimal threshold value are obtained.

Keywords: probabilistic automata; probabilistic reaction; random functions

##### REFERENTIAL INTEGRITY OF DATA IN CORPORATE INFORMATION SYSTEMS.
• V. S. Zykin  Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation, Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: The paper deals with the task of construction of a nonredundant set of referential constraints on data. This set of constraints allows regulating the business rules of using information on the enterprise, which is supported by a database management system and is located in a relation database. The inclusion dependences are the theoretical bases of the restrictions and they have obtained generalization in this paper; so, it is possible to use null values. This generalization is a consequence of their practical significance. The term "acyclic database schemes" is introduced and investigated for correct solution of this problem. Some attention is given to interpretation of acyclic schemas with hypergraphs, the theorem of acyclic hypergraph is proved. It is proposed to construct the set of all referential constraints automatically by using the rule of decomposition of relations. An algorithm of removing redundant referential integrity constraints is presented.

Keywords:  referential integrity; undefined values; acyclic schemes

##### GOAL-ORIENTED PROCESSES OF CROSS-LINGUAL EXPERT KNOWLEDGE CREATION: SEMIOTIC FOUNDATIONS FOR MODELING.
• I. M. Zatsman Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: The results of development of semiotic foundations for modeling goal-oriented processes of cross-lingual expert knowledge creation are described. The technology supporting these processes is outlined. The demand for such technologies is obvious in situations where present systems of expert knowledge do not answer to new socially or technologically significant purposes, corresponding to new or changed requirements of modern society Instead of centering on the well-known artificial intelligence methods and models of information processing for knowledge representation, this paper focuses on development of new models of goal-oriented processes of expert knowledge creation reflecting dynamics of its formation. The suggested approach to modeling these processes and to development of technologies supporting them is focused on those applied areas where expert knowledge is elicited from domain experts. The experts analyze texts or other interpretation objects which can vary over time and enter the results of analysis into supracorpus databases. The distinguishing feature of the semiotic approach to modeling is the explicit description of relations between new expert knowledge and those interpretation objects, from which parts of new knowledge were generated. Other important feature is the explicit description of parts of knowledge corresponding to interpretation objects that may vary over time. Feasibility of the approach is demonstrated on the example of information technology, which supports the processes of creation of cross-lingual expert knowledge based on French translations of Russian verbal constructions. Cross-lingual knowledge is generated in the course of analysis of parallel texts in Russian and French languages.

Keywords: cross-lingual expert knowledge; computer modeling; knowledge creation; interpretation objects; semiotic foundations; models of knowledge creation processes

##### INFLUENCE OF MORPHOLOGICAL OPERATIONS ON RECOGNITION OF A MOVING HUMAN FIGURE FROM A SET OF IMAGES.
• M. O. Abramov National Research Tomsk State University, 36 Lenin Av., Tomsk 634050, Russian Federation
• M. Yu. Kataev Tomsk State University of Control Systems and Radioelectronics, 40 Lenin Av., Tomsk 634050, Russian Federation, Yurga Institute of Technology (Branch) of National Research Tomsk Polytechnic University, 26 Leningradskaya Str., Yurga, Kemerovo Region 652055, Russian Federation

Abstract: The article describes the methodology of moving human figure recognition from set of images with the help of morphological operations. Accuracy of recognition results is determined by the difference between the true and recovering figure squares from binary images. Comparison of the obtained accuracy for different morphological operations for some color spaces (RGB, HSV, and YUV) is investigated. The paper provides recommendations for improvement of human figure recognition from set of images.

Keywords:  morphological operations; one camera; human figure recognition; digital processing; binary images

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