Nataliya Kalashnykova - Academia.edu (original) (raw)

Papers by Nataliya Kalashnykova

IOS Press eBooks, Aug 15, 2023

In this chapter, we explore the application of the derivative of disproportion functions in devel... more In this chapter, we explore the application of the derivative of disproportion functions in developing a cryptographic system and a pattern recognition technique. Firstly, we present an algorithm that utilizes focal functions, known as functions of disproportion, in a cryptographic system. The transmitted symbols are encrypted using the weighted sum of at least two of these functions with randomly generated coefficients. Numerical experiments demonstrate the robustness and reliability of the proposed procedure. Furthermore, we demonstrate how the derivative of disproportion functions can govern a dynamic process, serving as a tool to identify the form of a real-valued function. This process enables us to determine the class to which the function belongs, independently of its unknown parameter values.

Journal of Combinatorics, Information & System Sciences

We study a mixed oligopoly model, including a nonprivate firm that maximizes the convex combinati... more We study a mixed oligopoly model, including a nonprivate firm that maximizes the convex combination of domestic social surplus and net profit, under the concepts of consistent conjectural variations (CCVE), Cournot–Nash, and perfect competition equilibria and analyze the behavior of these equilibria. We compare the results to develop an optimality criterion for a parameter, decided by the nonprivate firm, known as socialization level. To work with the CCVE, we need to define the concept of consistency; hence, we also consider a classic oligopoly, which only includes private firms that maximize net profit, and reformulated it as a non-cooperative game, named meta-game, where the players (the private firms) select a conjecture as their strategies; then, we prove that the Nash equilibrium for the meta-game implies the CCVE. After that, due to its similarities with the meta-game, we study the Tolls Optimization Problem (TOP). Taking advantage of the sensitivity analysis for convex quadr...

In many practical situations, we only know a few first moments of a random variable, and out of a... more In many practical situations, we only know a few first moments of a random variable, and out of all probability distributions which are consistent with this information, we need to select one. When we know the first two moments, we can use the Maximum Entropy approach and get normal distribution. However, when we know the first three moments, the Maximum Entropy approach doe snot work. In such situations, a very efficient selection is a so-called skew normal distribution. However, it is not clear why this particular distribution should be selected. In this paper, we provide an explanation for this selection.

International Journal of Combinatorial Optimization Problems and Informatics, Nov 14, 2016

One of the main problems of optimization algorithms is that they often end up in a local optimum.... more One of the main problems of optimization algorithms is that they often end up in a local optimum. It is, therefore, necessary to make sure that the algorithm gets out of the local optimum and eventually reaches the global optimum. One of the promising ways guiding one from the local optimum is prompted by the filled function method. It turns out that empirically, the best smoothing functions to use in this method are the Gaussian and Cauchy functions. In this paper, we provide a possible theoretical explanation of this empirical effect.

In this paper, a model of partially mixed oligopoly with conjectured variations equilibrium (CVE)... more In this paper, a model of partially mixed oligopoly with conjectured variations equilibrium (CVE) is studied. The agents make conjectures concerning the price variations depending upon their production output's fluctuations. Existence and uniqueness results for the conjectured variations equilibrium (called an exterior equilibrium) is established for any collection of feasible conjectures. To deal with the concept of an interior (i.e., consistent) equilibrium, a consistency criterion for the influence coefficients is introduced and the existence theorem for the interior equilibrium (understood as a CVE with consistent conjectures) is established. As a base for the extension of the above-mentioned results to the case of non-differentiable demand functions, the behavior of the consistent conjectures as a function of a parameter representing the demand function's derivative with respect to the market price is investigated.

International Journal of Combinatorial Optimization Problems and Informatics, 2017

This paper proposes an algorithm for designing a cryptosystem, in which the derivative disproport... more This paper proposes an algorithm for designing a cryptosystem, in which the derivative disproportion functions are used. The symbols to be transmitted are encoded with the sum of at least two of these functions combined with random coefficients. A new algorithm is proposed for decoding the received messages by making use of important properties of the derivative disproportion functions. Numerical experiments are reported as demonstrating the algorithm's reliability and robustness.

BENTHAM SCIENCE PUBLISHERS eBooks, Mar 13, 2018

International Journal of Innovative Computing Information and Control, Aug 1, 2010

Studies in Systems, Decision and Control, 2017

In this paper, we investigate the properties of consistent conjectural variations equilibrium (CC... more In this paper, we investigate the properties of consistent conjectural variations equilibrium (CCVE) developed for a single-commodity oligopoly. Although, in general, the consistent conjectures are distinct from those of Cournot-Nash, we establish the following remarkable fact. Define a meta-game as such where the players are the same agents as in the original oligopoly but now using the conjectures as their strategies. Then the consistent conjectures of the original oligopoly game provide for the Cournot-Nash optimal strategies for the meta-game.

International journal of biomedical soft computing and human sciences, 2012

Ple develqp a new ctass qf'positionat numerat spstems, namely the binomiat ones, whichform a subc... more Ple develqp a new ctass qf'positionat numerat spstems, namely the binomiat ones, whichform a subclass ofgenerali"7edpositionat numeral systems (GPiVS}. 71he binomiat s)rgtems have wide range oj'applications in the itzlbrmation transmission, proeessing, and storqge due to their error-deteetion ccu)abilities. In this pqper, the hinomial numerat 4},stems are weU-defined their prefix andcompactness pJ'operties are estabtished Aigorithms qfgenerating binomial coding ivorctg (}ion-unij2)rm and untfornij are presented as well as an enhancedprocedure qfconstruction ofconstant weight Bootean combinations based i4)on the non-unij?)rm binomiat coding words. T7ie correctness ofthis procedure is atso estabtished Keywortts Generatifedpositional numeral systems, Binomial numeral systems, Constant weight codes. 1.Introduction Positional numeral systems are widely used in computing. More complicated numeral systems, in which the register's weight need not be equal to the power of the system's base (like, fbr example. in the binary or decimal system). have not been thoroughly studied as yet. Such generalized positional numeral systems (GPNS) may have quite usefu1 properties, like being noise-prooe easy in generating permutations, etc. (see [1]-[3]), These properties aHow one to exploit the GPNS to develop specialized digital devices with high computational speed, reliability, and very Low size and weight parameters. Moreoyer, the GPNS may serve as a base for: (a) generation of codes and construction of coding BiomedicalFuzzy Systems Association Biomedical Sort Computing andIIunianSeiences, Vol.]7, No.2, C2012) efficient way.

Intelligent Systems Reference Library, 2017

One of the most important challenges when creating efficient systems of technical vision is the d... more One of the most important challenges when creating efficient systems of technical vision is the development of efficient methods for enhancing the speed and noise-resistance properties of the digital devices involved in the system. The devices composed of counters and decoders occupy a special niche among the system’s digital tools. One of the most common ways of creating noise-proof devices is providing special coding tricks dealing with their informational redundancy. Various frameworks make that possible, but nowadays, an acute interest is attracted to noise-proof numeral systems, among which the Fibonacci system is the most famous. The latter helps generate the so-called Fibonacci codes, which can be effectively applied to the computer vision systems; in particular when developing counting devices based on Fibonacci counters, as well as the corresponding decoders. However, the Fibonacci counters usually pass from the minimal form of representation of Fibonacci numbers to their maximal form by recurring to the special operations catamorphisms and anamorphisms (or “folds” and “unfolds”). The latter makes the counters quite complicated and time-consuming. In this chapter, we propose a new version of the Fibonacci counter that relies only on the minimal representation form of Fibonacci numerals and thus leads to the counter’s faster calculation speed and a higher level of the noise-resistance. Based on the above-mentioned features, we also present the appropriate fast algorithm implementing the noise-proof computation and the corresponding fractal decoder. The first part of the chapter provides the estimates of the new method’s noise-immunity, as well as that of its components. The second problem studied in the chapter concerns the efficiency of the existing algorithm of Fibonacci representation in the minimal form. Based on this examination, we propose a modernization of the existing algorithm aiming at increasing its calculation speed. The third object of the chapter is the comparative analysis of the Fibonacci decoders and the development of the fractal decoder of the latter.

This book describes recent theoretical findings relevant to bilevel programming in general, and i... more This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.

J. Adv. Comput. Intell. Intell. Informatics, 2020

The study examines the period of the Great Depression and analyzes several measures taken by the ... more The study examines the period of the Great Depression and analyzes several measures taken by the US President Roosevelt’s government that allowed the country to get out of the crisis. An analysis and proof of the correctness of the measures chosen to exit from the crisis was conducted using econometric models and the use of statistics. Techniques for overcoming crises are relevant for all countries. This study adapts an innovative perspective in that it used the sequence of the Cobb–Douglas type function including different types of factors, and applied fuzzy regression methods.

Consider an oligopoly of at least two producers of a homogeneous good with cost functions \(f_i=f... more Consider an oligopoly of at least two producers of a homogeneous good with cost functions \(f_i=f_i(q_i)\), \(i=1,\dots ,n\), \(n\ge 2\), where \(q_i\ge 0\) is the supply by producer i. Consumers’ demand is described by a demand function \(G=G(p)\), whose argument p is the market price established by a cleared market.

Journal of Engineering Sciences, 2020

The primary direction of the increase of reliability of the automated control systems of complex ... more The primary direction of the increase of reliability of the automated control systems of complex electromechanical machines is the application of intelligent information technologies of the analysis of diagnostic information directly in the operating mode. Therefore, the creation of the basics of information synthesis of a functional diagnosis system (FDS) based on machine learning and pattern recognition is a topical task. In this case, the synthesized FDS must be adaptive to arbitrary initial conditions of the technological process and practically invariant to the multidimensionality of the space of diagnostic features, an alphabet of recognition classes, which characterize the possible technical states of the units and devices of the machine. Besides, an essential feature of FDS is the ability to retrain by increasing the power of the alphabet recognition classes. In the article, information synthesis of FDS is performed within the framework of information-extreme intellectual da...

Journal of Optimization Theory and Applications, 2018

The paper presents the extensions of both the antipodal (Borsuk-Ulam) theorem and Browder theorem... more The paper presents the extensions of both the antipodal (Borsuk-Ulam) theorem and Browder theorem to the cases comprising both a star-shaped domain of the considered mapping and a multivalued structure of that mapping. Moreover, an explicit algorithm constructing the desired connected path of the zero points of the mapping is developed.

International Journal of Knowledge Engineering and Soft Data Paradigms, 2014

In the paper, we examine conditions that guarantee the existence of a solution to the parametric ... more In the paper, we examine conditions that guarantee the existence of a solution to the parametric nonlinear complementarity problem with a monotone with respect to x mapping f: R

Springer eBooks, 2011

The paper deals with a problem of reducing dimension of the upper level problem in a bilevel prog... more The paper deals with a problem of reducing dimension of the upper level problem in a bilevel programming model. In order to diminish the number of variables governed by the leader at the upper level, we create the second follower supplied with the objective function coinciding with that of the leader and pass part of the upper level variables to