Khmelnitskiy, Ukraine
Khmelnitskiy, Ukraine

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In finite noncooperative game, a method for finding approximate Nash equilibrium situations is developed. The method is prior-based on sampling fundamental simplexes being the sets of players’ mixed strategies. Whereas the sampling is exercised, the sets of players’ mixed strategies are mapped into finite lattices. Sampling steps are envisaged dissimilar. Thus, each player within every dimension of its simplex selects and controls one’s sampling individually. For preventing approximation low quality, however, sampling steps are restricted. According to the restricted sampling steps, a player acting singly with minimal spacing over its lattice cannot change payoff of any player more than by some predetermined magnitude, being specific for each player. The finite lattice is explicitly built by the represented routine, where the player’s mixed strategies are calculated and arranged. The product of all the players’ finite lattices approximates the product of continuous fundamental simplexes. This re-defines the finite noncooperative game in its finite mixed extension on the finite lattices’ product. In such a finite-mixed-extension-defined game, the set of Nash equilibrium situations may be empty. Therefore, approximate Nash equilibrium situations are defined by the introduced possible payoff concessions. A routine for finding approximate equilibrium situations is represented. Approximate strong Nash equilibria with possible concessions are defined, and a routine for finding them is represented as well. Acceleration of finding approximate equilibria is argued also. Finally, the developed method is discussed to be a basis in stating a universal approach for the finite noncooperative game solution approximation implying unification of the game solvability, applicability, realizability, and adaptability. © 2016, University of Zagreb. All rights reserved.


Romanuke V.,Khmelnitskiy National University
Journal of Information and Organizational Sciences | Year: 2015

A method of constructing boosting ensembles of heavy two-layer perceptrons is stated. The benchmark classification problem is recognition of shifted-tumed-scaled flat images of a medium format with binary features. The boosting gain is suggested in two aspects. The earliest one is the ratio of minimal recognition error percentage among the ensemble perceptrons to the recognition error percentage performed by the ensemble. The second gain type is the ratio of minimal variance of perceptrons’ recognition error percentages over 26 classes to variance of the ensemble’s recognition error percentages over 26 classes. Both ratios increase as the number of perceptron classifiers in the ensemble increase. The ensemble of 36 classifiers performs with increased accuracy, where recognition error percentage is decreased for 33 %, and the variance is decreased for more than 50 %. Further increment of classifiers into ensemble cannot increase accuracy much as there is the saturation effect of the boosting gain. And the gain itself depends on the range of noise modeling object’s distortions. Thus, the heavier perceptron classifier the less gain is expected. © 2014, University of Zagreb. All rights reserved.


Boiko Yu.M.,Khmelnitskiy National University | Boryachok R.O.,Khmelnitskiy National University
CriMiCo 2013 - 2013 23rd International Crimean Conference Microwave and Telecommunication Technology, Conference Proceedings | Year: 2013

The digital data transmission system scheme with external and internal turbo-encoder has been developed. The recommendation for cascade encoder components type and structure has been issued. The analytical relationships and research results for describing bit error rate of the cascade turbo-encoder components have been represented. © 2013 CriMiCo'2013 Organising Committee, CrSTC.


Romanuke V.V.,Khmelnitskiy National University
Journal of Automation and Information Sciences | Year: 2013

A procedure of practical implementation of the optimality principle in matrix games with empty set of saddle points in pure strategies, where finite number of plays is in advance known, is under consideration. Convergence of this procedure is proved, and estimate of average win or loss of player, participating in it, is shown. © 2013 by Begell House Inc.


There is suggested a method of approximating unit-hypercubic infinite antagonistic game with the matrix game and the corresponding solution in finite strategies. The method is based on dimension-dependent irregular samplings over the game kernel. Numbers of the sampling points and their coordinates are chosen due to the stated conditions. If the sampled kernel is not the flat matrix then the multidimensional payoff matrix is reshaped into the flat one wherewith to solve the matrix game. The reshaping is a reversible matrix map. The concluding step of the approximation is in checking the finite solution consistency. Consistency can be weakened, and consistency can be checked at some rank corresponding to a natural number. The higher rank of the finite solution consistency is, the wider neighborhood of the sampling numbers at which the solution properties are monotonic-like. © 2014, University of Zagreb. All rights reserved.


Royzman V.,Khmelnitskiy National University | Goroshko A.,Khmelnitskiy National University
Journal of Vibroengineering | Year: 2012

The problem of providing the required level of quality of products and/or technological processes often becomes difficult due to the fact that there is no general theory for determining optimal sets of values of primary factors, i.e. output parameters of parts and units comprising an object as well as ensuring the equivalence of object parameters to the quality requirements. This is the main reason why the development of complex systems and objects of vital importance takes several years. To create this theory, one has to overcome a number of difficulties and solve the following tasks: creation of reliable and stable mathematical models that indicate the influence of primary factors on output parameters; determination of accurate solutions when mathematical models are poorly stipulated; and creation of a method of assigning nominal values and tolerances for primary factors with regard to economical, technological and other criteria. All of the above-listed tasks are equally important. The present work is an attempt to describe a solution for this problem. The mathematically formalized aspect of the problem of providing the required level of quality has been called the "multiple inverse problem". © Vibroengineering. Journal of vibroengineering.


Tkachuk V.,Khmelnitskiy National University | Bauriene G.,Kaunas University of Technology
21st International Scientific Conference: Mechanika 2016 - Proceedings | Year: 2016

Analysis of experimental studies results allowed specifying that: 1) in passive fluid SBD the fluid tries to place itself on the opposite side of the imbalance both in above resonant, below resonant zone of the rotor rotation and on the resonance itself; 2) self-balancing by the fluid is effective for elastic-deformative rotors where difference in phases between direction of centrifugal force and rotor bending deflection exists.


Romanuke V.V.,Khmelnitskiy National University
Journal of Uncertain Systems | Year: 2015

A problem of classifying diversely distorted objects is considered. These objects are modeled as flat scaled-turnedshifted objects. In order to substitute complicated and slow deep learning architectures, two-layer perceptron is tried to be a classifier. For this, the perceptron classifier is trained by a specific embedding into the training process. The embedding is additional feature distortions regularizing the training so that it makes the perceptron classify diversely distorted objects more accurately. In classifying 60×80 monochrome images of 26 enlarged capital letters, an appropriately trained perceptron is identified which performs with less than 4% of errors at medium intensity of distortions. The perceptron keeps its high-accurate classification capabilities if total number of object features and classes’ number are different from those 4800 and 26, respectively. Furthermore, unlike deep learning classifiers, twolayer perceptron can take just about half a minute to classify 10000 diversely distorted objects. © 2015 World Academic Press, UK. All rights reserved.


Petrashchuk S.,Khmelnitskiy National University | Kovtun I.,Khmelnitskiy National University | Voznyak A.,Khmelnitskiy National University
MATEC Web of Conferences | Year: 2016

Paper represents new approach to physical and mathematical modeling of thermal fields distribution in sealed electronic units on the base of introducing "effective parameters" of the system. Effectiveness of developed mathematical model and its computer implementing are demonstrated on the example of standard unit sealed by compound. © The Authors, published by EDP Sciences, 2016.


A method is suggested for the uniform sampling of fundamental simplexes as the sets of players' mixed strategies in the finite noncooperative game for its approximate solution. This solution is treated in the sense of equilibrium situations with possible concessions as Nash equilibrium situations are not necessarily to be on a finite simplex lattice. The sampling conditions assume that by changing minimally a situation over nodes of the lattice the players' payoff varies no greater than within its constant value. Building a simplex lattice of the player's mixed strategies set is fulfilled by a cyclic descent from the first pure strategy down to the last one. Retrieval of concession-equilibrium situations can be sped up by parallelizing of arrays multiplication when calculating the expected payoffs. © 2015 by Begell House Inc.

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