Nataliya Kalashnykova - Profile on 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.

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.

Operations Research and Bilevel Programming

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.

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

Existence of the Nash-Optimal Strategies in the Meta-Game

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.

The Fibonacci Numeral System for Computer Vision

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.

Bilevel Programming Problems: Theory, Algorithms and Applications to Energy Networks

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.

A New Approach to the Classification of Positional Numeral Systems

The Great Depression: Econometric Analysis and Fuzzy Regression

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.

Consistent Conjectural Variations Coincide with the Nash Solution in the Meta-Model

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.

Convergence of a Newton-like algorithm solving the nonlinear complementarity problem

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

Reduction of Dimension of the Upper Level Problem in a Bilevel Programming Model Part 1

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

International Journal of Computing, 2020

The article discusses the technology of forming signals used in mobile, information and telecommu... more The article discusses the technology of forming signals used in mobile, information and telecommunication systems, and also provides an analysis of promising technologies that can be used in wireless communication systems of broadband access. It is shown that the widely used modulation scheme with orthogonal frequency division (OFDM) has a number of drawbacks, which can lead to a decrease in system performance. Alternative technologies for generating signals are presented, in particular, a technology based on windowed signal processing (W-OFDM), a technology based on time division (w-OFDM); UFMC technology and others to eliminate the disadvantages of OFDM technology. New points of view are proposed on the use of multi-carrier transmission technology in the form of multiplexing with orthogonal frequency division (in order to increase the security of modern wireless broadband access communication systems from external and internal threats), a class of non-linear discrete cryptographic...

2022 Joint 12th International Conference on Soft Computing and Intelligent Systems and 23rd International Symposium on Advanced Intelligent Systems (SCIS&ISIS)

In this paper we study a semi-mixed oligopoly model within the framework of conjectural variation... more In this paper we study a semi-mixed oligopoly model within the framework of conjectural variation. The semi-mixed structure refers to the presence of a semipublic producer that maximizes the convex combination of domestic social surplus and its net profit. The parameter of this convex combination is called socialization level. Each producer conjectures the variations of the market-clearing price in response to its own production's variations. We extend the previously studied models to the more general case of oligopoly, considering the case when the consumers' demand function is not necessarily differentiable nor continuous. By introducing the notions of exterior and interior equilibriums, we proved the existence and uniqueness theorems for the conjectural variations equilibrium and the equilibrium state known as consistent. After that, we analyzed the behavior of the market's consistent equilibrium state under the changes in the consumers' demand. Finally, we considered the particular case when the consumers' demand is an affine (linear) function to compare the consistent equilibrium against the Cournot and perfect competition equilibriums. Based on this analysis, we formulated an optimality criterion for the socialization level and provided the necessary conditions for its existence.

Solution of the Portfolio Optimization Model as a Fuzzy Bilevel Programming Problem

Applied Mathematics and Computational Intelligence, 2018

In this chapter, we consider a mixed-integer bilevel linear programming problem with one paramete... more In this chapter, we consider a mixed-integer bilevel linear programming problem with one parameter in the right-hand side of the constraints in the lower level (or, the follower’s) problem. Motivated by an application to the fuzzy portfolio optimization model, we consider a particular case that consists in maximizing the investor’s expected return. The functions are linear at both the upper and lower levels, and the proposed algorithm is based upon an approximation of the optimal value function using the branch-and-bound method. Therefore, at every node of this tree-type structure, we apply a new branch-and-bound procedure to deal with the integrity restriction.