Abstract: It is unquestioned that the importance of IP network will further increase and that it will serve as a platform for more and more services, requiring different types and degrees of service quality. Modern architectures and protocols are being standardized, which aims at guaranteeing the quality of service delivered to users. In this paper, we investigate the queueing behaviour found in IP output buffers. This queueing increases because multiple streams of packets with different length are being multiplexed together. We develop balance equations for the state of the system, from which we derive packet loss and delay results. To analyze these types of behaviour, we study the discrete-time version of the “classical” queue model M/M/1/k called Geo/Gx/1/k, where Gx denotes a different packet length distribution defined on a range between a minimum and maximum value.

Keywords: delay system, queueing analyses, discrete time queue, IP traffic modelling; packet size distribution.

ACM Classification Keywords: G.3 Probability and statistics: queueing theory, I.6.5 Model development

Link:

STUDY OF QUEUEING BEHAVIOUR IN IP BUFFERS

Seferin Mirtchev

http://www.foibg.com/ijitk/ijitk-vol02/ijitk02-2-p13.pdf

Abstract: A method for prediction of multidimensional heterogeneous time series using logical decision functions is suggested. The method implements simultaneous prediction of several goal variables. It uses deciding function construction algorithm that performs directed search of some variable space partitioning in class of logical deciding functions. To estimate a deciding function quality the realization of informativity criterion for conditional distribution in goal variables' space is offered. As an indicator of extreme states, an occurrence a transition with small probability is suggested.

Keywords: multidimensional heterogeneous time series analysis, data mining, pattern recognition, classification, statistical robustness, deciding functions.

ACM Classification Keywords: G.3 Probability and Statistics: Time series analysis; H.2.8 Database Applications: Data mining; I.5.1 Pattern Recognition: Statistical Models

Link:

EXTREME SITUATIONS PREDICTION BY MULTIDIMENSIONAL HETEROGENEOUS TIME SERIES USING LOGICAL DECISION FUNCTIONS1

Svetlana Nedel’ko

http://www.foibg.com/ijita/vol13/ijita13-3-p14.pdf

Abstract: An approach to solving the problem of heterogeneous multivariate time series analysis with respect to the sample size is considered in this paper. The criterion of prediction multivariate heterogeneous variable is used in this approach. For the fixed complexities of probability distribution and logical decision function class the properties of this criterion are presented.

Keywords: the prediction of multivariate heterogeneous variable, multivariate time series, the complexity of distribution.

ACM Classification Keywords: G.3 Probability and Statistics: Time series analysis

Link:

APPLICATION OF THE MULTIVARIATE PREDICTION METHOD TO TIME SERIES 1

Tatyana Stupina, Gennady Lbov

http://www.foibg.com/ijita/vol13/ijita13-3-p12.pdf

Abstract. An application of the heterogeneous variables system prediction method to solving the time series analysis problem with respect to the sample size is considered in this work. It is created a logical-and-probabilistic correlation from the logical decision function class. Two ways is considered. When the information about event is kept safe in the process, and when it is kept safe in depending process.

Keywords: the prediction of heterogeneous variables system, the adaptive method, multidimensional time series, logical decision function.

ACM Classification Keywords: G.3 Probability and statistics

Link:

DETECTION OF LOGICAL-AND-PROBABILISTIC CORRELATION IN TIME SERIES1

Tatyana Stupina

http://www.foibg.com/ijita/vol15/ijita15-3-p11.pdf

Abstract: The problem of sequent two-block decomposition of a Boolean function is regarded in case when a good solution does exist. The problem consists mainly in finding an appropriate weak partition on the set of arguments of the considered Boolean function, which should be decomposable at that partition. A new fast heuristic combinatorial algorithm is offered for solving this task. At first the randomized search for traces of such a partition is fulfilled. The recognized traces are represented by some "triads" - the simplest weak partitions corresponding to non-trivial decompositions. After that the whole sought-for partition is restored from the discovered trace by building a track initialized by the trace and leading to the solution. The results of computer experiments testify the high practical efficiency of the algorithm.

Keywords: Boolean function, non-disjunctive decomposition, appropriate partition, combinatorial search, recognition, randomization, computer experiment.

ACM Classification Keywords: G.2.1 Combinatorics – combinatorial problems, combinatorial search, G.3 Probability and Statistics – randomization.

Link:

DECOMPOSITION OF BOOLEAN FUNCTIONS – RECOGNIZING A GOOD SOLUTION BY TRACES

Arkadij Zakrevskij

http://www.foibg.com/ijita/vol14/ijita14-4-p10.pdf

Abstract: Any set system can be represented as an n -cube vertices set. Restricted sets of n -cube weighted subsets are considered. The problem considered is in simple description of all set of partitioning characteristic vectors. A smaller generating sets are known as “boundary” and ”steepest” sets and finally we prove that the intersection of these two sets is also generating for the partitioning characteristic vectors.

ACM Classification Keywords: G.2.1 Discrete mathematics: Combinatorics

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DESCRIPTION REDUCTION FOR RESTRICTED SETS OF (0,1) MATRICES 1

Hasmik Sahakyan

http://www.foibg.com/ijita/vol14/ijita14-4-p02.pdf

Abstract: The specific class of all monotone Boolean functions with characteristic vectors of partitioning of sets of all true-vertices to be minimal is investigated. These characteristic vectors correspond to the column-sum vectors of special (0,1)-matrices – constructed by the interval bisection method.

Keywords: monotone Boolean functions, (0,1)-matrices.

ACM Classification Keywords: G.2.1 Discrete mathematics: Combinatorics

Link:

THE BOUNDARY DESCRIPTORS OF THE n-DIMENSIONAL UNIT CUBE SUBSET PARTITIONING1

Hasmik Sahakyan, Levon Aslanyan

http://www.foibg.com/ijita/vol13/ijita13-3-p02.pdf

Abstract: A new method for solving some hard combinatorial optimization problems is suggested, admitting a certain reformulation. Considering such a problem, several different similar problems are prepared which have the same set of solutions. They are solved on computer in parallel until one of them will be solved, and that solution is accepted. Notwithstanding the evident overhead, the whole run-time could be significantly reduced due to dispersion of velocities of combinatorial search in regarded cases. The efficiency of this approach is investigated on the concrete problem of finding short solutions of non-deterministic system of linear logical equations.

Keywords: combinatorial problems, combinatorial search, parallel computations, randomization, run-time, acceleration.

ACM Classification Keywords: G.2.1 Combinatorics – combinatorial problems, combinatorial search, G.3 Probability and Statistics – randomization, G.4 Mathematical software – efficiency, parallel and vector implementations.

Link:

RANDOMIZED PARALLELIZATION – A NEW METHOD FOR SOLVING HARD COMBINATORIAL PROBLEMS

Arkadij Zakrevskij

http://www.foibg.com/ijita/vol13/ijita13-3-p01.pdf

Abstract: ATM network optimization problems defined as combinatorial optimization problems are considered. Several approximate algorithms for solving such problems are developed. Results of their comparison by experiments on a set of problems with random input data are presented.

Keywords: network, ATM, optimization, combinatorial optimization, local search, simulated annealing, genetic algorithm

ACM Classification Keywords: G.2.1 Combinatorics: Combinatorial algorithms

Link:

OPTIMIZATION OF ATM TELECOMMUNICATION NETWORKS

Leonid Hulianytskyi, Andrii Baklan

http://www.foibg.com/ijita/vol12/ijita12-4-p05.pdf

Abstract: The paper considers vector discrete optimization problem with linear fractional functions of criteria on a feasible set that has combinatorial properties of combinations. Structural properties of a feasible solution domain and of Pareto–optimal (efficient), weakly efficient, strictly efficient solution sets are examined. A relation between vector optimization problems on a combinatorial set of combinations and on a continuous feasible set is determined. One possible approach is proposed in order to solve a multicriteria combinatorial problem with linearfractional functions of criteria on a set of combinations.

Keywords: vector optimization, discrete optimization, linear fractional functions, set of combinations.

ACM Classification Keywords: G 2.1 Combinatorics (F2.2), G 1.6 Optimization

Link:

VECTOR COMBINATORIAL PROBLEMS IN A SPACE OF COMBINATIONS WITH LINEAR FRACTIONAL FUNCTIONS OF CRITERIA

Natalia Semenova, Lyudmyla Kolechkina, Alla Nagirna

http://www.foibg.com/ijita/vol15/ijita15-3-p07.pdf

Abstract: Reproducing Kernel Hilbert Space (RKHS) and Reproducing Transformation Methods for Series Summation that allow analytically obtaining alternative representations for series in the finite form are developed.

Keywords: The reproducing transformation method, Hilbert space, reproducing kernel, RKHS, Series Summation Method.

ACM Classification Keywords: G.1.10 Mathematics of Computing: Applications

Link:

RKHS-METHODS AT SERIES SUMMATION FOR SOFTWARE IMPLEMENTATION

Svetlana Chumachenko, Ludmila Kirichenko

http://www.foibg.com/ijita/vol13/ijita13-3-p05.pdf

Abstract: The task of revealing the relationship between a search algorithm and a class of functions those it solves is considered. Particularly, there was found a class of functions solvable by some adaptive search algorithm for a discrete space of low cardinality. To find an optimal algorithm exhaustive search was used. Algorithm quality criterion based on equivalence classes was also introduced.

Keywords: search algorithm, adaptive search, optimization, global extreme, no free launch theorem.

ACM Classification Keywords: G.1.6. Numerical analysis: Optimization; G.2.m. Discrete mathematics: miscellaneous.

Link:

FINDING THE RELATIONSHIP BETWEEN A SEARCH ALGORITHM AND A CLASS OF FUNCTIONS ON DISCRETE SPACE BY EXHAUSTIVE SEARCH1

Victor Nedel’ko, Svetlana Nedel’ko

http://www.foibg.com/ijita/vol14/ijita14-4-p06.pdf

Abstract: The general discussion of the data flow algorithmic models, and the linear programming problem with the variating by data flow criterion function coefficients are presented. The general problem is widely known in different names - data streams, incremental and online algorithms, etc. The more studied algorithmic models include mathematical statistics and clustering, histograms and wavelets, sorting, set cover, and others. Linear programming model is an addition to this list. Large theoretical knowledge exists in this as the simplex algorithm and as interior point methods but the flow analysis requires another interpretation of optimal plans and plan transition with variate coefficients. An approximate model is devised which predicts the boundary stability point for the current optimal plan. This is valuable preparatory information of applications, moreover when a parallel computational facility is supposed.

Keywords: data flow algorithm, linear programming, approximation

ACM Classification Keywords: G.1.6 Numerical analysis: Optimization

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DATA FLOW ANALYSIS AND THE LINEAR PROGRAMMING MODEL1

Levon Aslanyan

http://www.foibg.com/ijita/vol13/ijita13-1-p08.pdf

Abstract: Representation of neural networks by dynamical systems is considered. The method of training of neural networks with the help of the theory of optimal control is offered.

Keywords: neural nets, dynamical systems, training.

ACM Classification Keywords: G.1.6 Optimization, G.1.2 Approximation, I.2 Artificial Intelligence

Link:

REPRESENTATION OF NEURAL NETWORKS BY DYNAMICAL SYSTEMS

Volodymyr Donchenko, Denys Serbaev

http://www.foibg.com/ijita/vol12/ijita12-4-p09.pdf

Abstract: The fractional Fourier transform (FrFT) is used for the solution of the diffraction integral in optics. A scanning approach is proposed for finding the optimal FrFT order. In this way, the process of diffraction computing is speeded up. The basic algorithm and the intermediate results at each stage are demonstrated.

Key words: Fresnel diffraction, fractional Fourier-transform

ACM Classification Keywords: G.1.2 Fast Fourier transforms (FFT)

Link:

AN ALGORITHM FOR FRESNEL DIFFRACTION COMPUTING BASED ON FRACTIONAL FOURIER TRANSFORM

Georgi Stoilov

http://www.foibg.com/ijitk/ijitk-vol01/ijitk01-2-p14.pdf

Abstract: The task of approximation-forecasting for a function, represented by empirical data was investigated. Certain class of the functions as forecasting tools: so called RFT-transformers, – was proposed. Least Square Method and superposition are the principal composing means for the function generating. Besides, the special classes of beam dynamics with delay were introduced and investigated to get classical results regarding gradients. These results were applied to optimize the RFT-transformers. The effectiveness of the forecast was demonstrated on the empirical data from the Forex market.

Keywords: empirical functions, learning samples, beam dynamics with delay, recursive nonlinear regressive transformer, Generalized Inverse, Least Square Method.

ACM Classification Keywords: G.1.2 Approximation, G.1.3 Numerical Linear Algebra, G.1.6 Optimization

Link:

DYNAMICAL SYSTEMS IN DESCRIPTION OF NONLINEAR RECURSIVE REGRESSION TRANSFORMERS

Mykola Kirichenko, Volodymyr Donchenko, Denys Serbaev

http://www.foibg.com/ijita/vol13/ijita13-1-p07.pdf

Abstract. The present article discusses units of measure and their base units, work environments built in the Units package of the computer algebra system Maple. An analysis is drawn of the tools of the application in connection with the use of physical quantities and their features. Maple’s main commands are arranged in groups depending on the function. Some applied mathematical problems are given as examples making use of derivative, integral and differential equations.

Key words: conversion, dimension, Maple, unit, systems of quantities, systems of units, Units package.

ACM Classification Keywords: G. Mathematics of Computing, I. Computing Methodologies

Link:

USING PHYSICAL QUANTITIES IN APPLIED MATHEMATICAL PROBLEMS WITH MAPLE

Tsvetanka Kovacheva

http://www.foibg.com/ijitk/ijitk-vol02/ijitk02-5-p08.pdf

Abstract: Trillas et al. introduced in 7 and 8 the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Later, in 1 and 2 the necessity of determine not only the contradiction, but also the degree in that this property occurs, was considered. This paper takes up again these subjects, and firstly we study if there exists some connection between the two first notions. After that, taking into account that selfcontradiction of a fuzzy set could be understood as the contradiction with itself, and starting from the degrees of contradiction between two fuzzy sets proposed in 5, we obtain degrees of self-contradiction. Finally, preservation of some intuitive properties both in the use of connectives and in the obtaining of new knowledge throughout compositional rule of inference, are tested.

Keywords: fuzzy sets, t-norm, t-conorm, strong fuzzy negations, contradiction, measures of contradiction, fuzzy relation, compositional rule of inference.

ACM Classification Keywords: F.4.1 Mathematical Logic and Formal Languages: Mathematical Logic (Model theory, Set theory); I.2.3 Artificial Intelligence: Deduction and Theorem Proving (Uncertainty, “fuzzy” and probabilistic reasoning); I.2.4 Artificial Intelligence: Knowledge Representation Formalisms and Methods (Predicate logic, Representation languages).

Link:

CONTRADICTION VERSUS SELFCONTRADICTION IN FUZZY LOGIC*

Carmen Torres, Susana Cubillo, Elena Castineira

http://www.foibg.com/ijita/vol14/ijita14-4-p05.pdf

Abstract: For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in 5 and 6. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in 1 and 2, suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in 0,12. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.

Keywords: fuzzy sets, t-norm, t-conorm, fuzzy strong negations, contradiction, measures of contradiction.

ACM Classification Keywords: F.4.1 Mathematical Logic and Formal Languages: Mathematical Logic (Model theory, Set theory); I.2.3 Artificial Intelligence: Deduction and Theorem Proving (Uncertainty, “fuzzy” and probabilistic reasoning); I.2.4 Artificial Intelligence: Knowledge Representation Formalisms and Methods (Predicate logic, Representation languages).

Link:

A GEOMETRICAL INTERPRETATION TO DEFINE CONTRADICTION DEGREES BETWEEN TWO FUZZY SETS

Carmen Torres, Elena Castiñeira, Susana Cubillo, Victoria Zarzosa

http://www.foibg.com/ijita/vol12/ijita12-2-p04.pdf

Abstract: Non-preemptive two-machine flow-shop scheduling problem with uncertain processing times of n jobs is studied. In an uncertain version of a scheduling problem, there may not exist a unique schedule that remains optimal for all possible realizations of the job processing times. We find necessary and sufficient conditions (Theorem 1) when there exists a dominant permutation that is optimal for all possible realizations of the job processing times. Our computational studies show the percentage of the problems solvable under these conditions for the cases of randomly generated instances with n ≤100 . We also show how to use additional information about the processing times of the completed jobs during optimal realization of a schedule (Theorems 2 – 4). Computational studies for randomly generated instances with n ≤ 50 show the percentage of the twomachine flow-shop scheduling problems solvable under the sufficient conditions given in Theorems 2 – 4.

Keywords: Scheduling, flow-shop, makespan, uncertainty.

ACM Classification Keywords: F.2.2 Non-numerical algorithms and problems: Sequencing and scheduling

Link:

REALIZATION OF AN OPTIMAL SCHEDULE FOR THE TWO-MACHINE FLOW-SHOP WITH INTERVAL JOB PROCESSING TIMES

Natalja Leshchenko, Yuri Sotskov

http://www.foibg.com/ijita/vol14/ijita14-2-p12.pdf

Abstract: Two assembly line balancing problems are addressed. The first problem (called SALBP-1) is to minimize number of linearly ordered stations for processing n partially ordered operations V = {1, 2, ..., n} within the fixed cycle time c. The second problem (called SALBP-2) is to minimize cycle time for processing partially ordered operations V on the fixed set of m linearly ordered stations. The processing time ti of each operation i ∈V is known before solving problems SALBP-1 and SALBP-2. However, during the life cycle of the assembly line the values ti are definitely fixed only for the subset of automated operations V\V~ . Another subset V~ ⊆V includes manual operations, for which it is impossible to fix exact processing times during the whole life cycle of the assembly line. If j ∈V~, then operation times tj can differ for different cycles of the production process. For the optimal line balance b of the assembly line with operation times t1, t2, …, tn, we investigate stability of its optimality with respect to possible variations of the processing times tj of the manual operations j ∈V~.

Keywords: Scheduling, robustness and sensitivity analysis, assembly line.

ACM Classification Keywords: F.2.2 Nonnumerical algorithms and problems: Sequencing and scheduling.

Link:

RECENT RESULTS ON STABILITY ANALYSIS OF AN OPTIMAL ASSEMBLY LINE BALANCE

Yuri Sotskov

http://www.foibg.com/ijita/vol14/ijita14-2-p11.pdf

Abstract: We propose the adaptive algorithm for solving a set of similar scheduling problems using learning technology. It is devised to combine the merits of an exact algorithm based on the mixed graph model and heuristics oriented on the real-world scheduling problems. The former may ensure high quality of the solution by means of an implicit exhausting enumeration of the feasible schedules. The latter may be developed for certain type of problems using their peculiarities. The main idea of the learning technology is to produce effective (in performance measure) and efficient (in computational time) heuristics by adapting local decisions for the scheduling problems under consideration. Adaptation is realized at the stage of learning while solving a set of sample scheduling problems using a branch-and-bound algorithm and structuring knowledge using pattern recognition apparatus.

Keywords: Scheduling, mixed graph, learning, pattern recognition.

ACM Classification Keywords: F.2.2 Nonnumerical algorithms and problems: sequencing and scheduling.

Link:

LEARNING TECHNOLOGY IN SCHEDULING BASED ON THE MIXED GRAPHS

Yuri Sotskov, Nadezhda Sotskova, Leonid Rudoi

http://www.foibg.com/ijita/vol12/ijita12-4-p12.pdf

Abstract: This paper presents an analysis of different techniques that is designed to aid a researcher in determining which of the classification techniques would be most appropriate to choose the ridge, robust and linear regression methods for predicting outcomes for specific quasi-stationary process.

Keywords: classification techniques, neural network, composite classifier

ACM Classification Keywords: F.2.1 Numerical Algorithms and Problems

Link:

SELECTING CLASSIFIERS TECHNIQUES FOR OUTCOME PREDICTION USING NEURAL NETWORKS APPROACH

Tatiana Shatovskaya

http://www.foibg.com/ijita/vol14/ijita14-3-p15.pdf

Abstract: Let V be an array. The range query problem concerns the design of data structures for implementing the following operations. The operation update(j,x) has the effect v v x j j ← + , and the query operation retrieve(i,j) returns the partial sum i j v +K+ v . These tasks are to be performed on-line. We define an algebraic model – based on the use of matrices – for the study of the problem. In this paper we establish as well a lower bound for the sum of the average complexity of both kinds of operations, and demonstrate that this lower bound is near optimal – in terms of asymptotic complexity.

Keywords: zero-one matrices, lower bounds, matrix equations

ACM Classification Keywords: F.2.1 Numerical Algorithms and Problems

Link:

MATRICIAL MODEL FOR THE STUDY OF LOWER BOUNDS

Jose Joaquin Erviti, Adriana Toni

http://www.foibg.com/ijita/vol13/ijita13-1-p09.pdf

Abstract: In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in Evtushenko, 1997 and spatial central finite difference with diagonally implicit Runge-Kutta? method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

Keywords: Distributed control problems, Second order parabolic heat equation, Runge-Kutta? method, CGM.

ACM Classification Keywords: F.2.1 Numerical Algorithms and Problems; G.4 Mathematical Software

Link:

OPTIMAL CONTROL OF A SECOND ORDER PARABOLIC HEAT EQUATION

Mahmoud Farag, Mainouna Al-Manthari?

http://www.foibg.com/ijita/vol13/ijita13-3-p03.pdf