Igor Malyk | CHNU - Academia.edu (original) (raw)

Papers by Igor Malyk

International Journal of Computing, Dec 30, 2023

The research is devoted to the study of information in complex networks, namely: calculation of s... more The research is devoted to the study of information in complex networks, namely: calculation of statistical characteristics and cluster analysis of data. Special software (crawler) was developed for direct data collection from the web space. In addition, a new structure of information technology has been developed for the collection, processing, and storage of large volumes of data collected from the web space. With the help of this structure, statistical characteristics of different segments of the web space (Ukrainian-edu.ua, Polish-edu.pl and Israeli-ac.il) are studied and their cluster structure is studied. The study of the cluster structure of web space zones was carried out using the spectral clustering algorithm of РІС (Rower iteration clustering). The results of the search for the optimal number of clusters using the "elbow" method and the k-Core decomposition method are presented, graphs illustrating the cluster structure of the investigated subnets are drawn. The paper also proposes a new approach to solving the problem of clustering and finding the optimal number of clusters when clustering objects are given by unstructured data (graphs) based on the spectral analysis of the stochastic matrix of the given graph. On this basis, a new method developed by the authors for determining the optimal number of clusters is proposed. Model examples are given and testing of the new method based on Monte Carlo simulation is performed. The optimal number of clusters was found by four methods: the "elbow" method, the k-core decomposition method, the silhouette method, and a new method developed by the authors. A conclusion is made concerning the accuracy of the developed new method, its advantages and disadvantages.

Theory of Probability and Mathematical Statistics, 2009

Necessary and sufficient conditions are found for the exponential mean square stability of a stoc... more Necessary and sufficient conditions are found for the exponential mean square stability of a stochastic differential-difference linear equation of neutral type in the scalar case.

arXiv (Cornell University), May 19, 2023

This article aims to investigate sufficient conditions for the stability of stochastic differenti... more This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic stability leverages the use of Lyapunov functions, supplemented by additional constraints on the magnitudes of jumps and jump times, as well as the Markov property of the system solutions. The findings are elucidated with an example, demonstrating both stable and unstable conditions of the system.

Основна увага надається оцінці оптимальної кількості кластерів для системи, що задається матрицею... more Основна увага надається оцінці оптимальної кількості кластерів для системи, що задається матрицею суміжності A з N вузлами при N→∞ . Розглянуто асимптотичний розподіл власних значень стохастичної випадкової матриці без умов незалежності елементів, спектр якої можна розкласти на регулярну частину та викиди. На основі припущень про однотипність зв’язків у кластері зроблено висновок про оптимальну кількість кластерів для різних прикладних задач. Проведено моделювання мережі зв’язків, що розподілені за законом Пуассона, та знайдено оптимальну кількість кластерів. Результати моделювання вказують на високу точність визначення оптимальної кількості кластерів. У основній теоремі важливим є припущення про існування моменту вище другого для кожного елементу матриці A. Проте, з урахуванням нормалізації, цю умову можна послабити до існування математичного сподівання матриці. Дане послаблення умов збіжності дає можливість використання доведеного твердження на ширший клас прикладних задач, де наявність скінченної дисперсії не вимагається. Зазначимо, що викиди є дійсними власними значеннями для нормалізованої матриці, що дозволяє швидко локалізувати викиди зі складністю O(N), де N — кількість вузлів системи. Отже, вдалося послабити два важливі припущення щодо розподілу елементів випадкової матриці, а саме припущення про рівність нулю математичних сподівань елементів матриці та про незалежність елементів матриці. Крім того, незалежність елементів можна замінити слабкою незалежністю, яка зберігає збіжність до середнього значення в законі великих чисел.

International Journal of Differential Equations, 2017

In this article the problem of existence and uniqueness of solutions of stochastic differential e... more In this article the problem of existence and uniqueness of solutions of stochastic differential equations with jumps and concentration points are solved. The theoretical results are illustrated by one example.

Cybernetics and Systems Analysis, May 1, 2011

ABSTRACT The Bogoliubov–Mitropolsky small parameter method is used to study the behavior of stoch... more ABSTRACT The Bogoliubov–Mitropolsky small parameter method is used to study the behavior of stochastic differential systems in the analysis of the corresponding properties of solutions of averaged systems.

The Bogoliubov-Mitropolsky small parameter method is used to study the behavior of stochastic dif... more The Bogoliubov-Mitropolsky small parameter method is used to study the behavior of stochastic differential systems in the analysis of the corresponding properties of solutions of averaged systems.

Cybernetics and Systems Analysis, May 1, 2015

The generating equation and equations for amplitude and phase fluctuations of the parametric tube... more The generating equation and equations for amplitude and phase fluctuations of the parametric tube oscillator with delayed feedback are analyzed in the paper. The steady-state oscillation modes and the influence of fluctuations in the natural frequency of the oscillator on the operation of the self-oscillator and parametric “pumping” in the presence of interference are investigated. The domains for the parameters of the original equation corresponding to unstable nodes, stable nodes, and focal points are identified.

Bukovinsʹkij matematičnij žurnal, 2022

Lyapunov’s second method is used to study the problem of stability of controlled stochastic dynam... more Lyapunov’s second method is used to study the problem of stability of controlled stochastic dynamical systems of random structure with Markov and Poisson perturbations. Markov switches reﬂect random eﬀects on the system at ﬁxed points in time. Poisson perturbations describe random eﬀects on the system at random times. In both cases there may be breaks in the phase trajectory of the ﬁrst kind. The conditions for the coeﬃcients of the system are written, which guarantee the existence and uniqueness of the solution of the stochastic system of a random structure, which is under the action of Markov switches and Poisson perturbations. The diﬀerences between these systems and systems that do not contain internal perturbations in the equation, which cause a change in the structure of the system, and external perturbations, which cause breaks in the phase trajectory at ﬁxed points in time, are discussed. The upper bound of the solution for the norm is obtained. The deﬁnition of the discrete Lyapunov operator based on the system and the Lyapunov function for the above-mentioned systems is given. Suﬃcient conditions of asymptotic stochastic stability in general, stability in l.i.m. and asymptotic stability in the l.i.m. for controlled stochastic dynamic systems of random structure with Markov switches and Poisson perturbations are obtained. A model example that reﬂects the features of the stability of the solution of a system with perturbations is considered: the conditions of asymptotic stability in the root mean square as a whole are established; the conditions of exponential stability and exponential instability are discussed. For linear systems, the necessary and suﬃcient stability conditions are determined in the example, based on the generalized Lyapunov exponent.

Cybernetics and Systems Analysis, Jul 1, 2016

We propose a new method to solve the classification problem based on separation of two sets in sp... more We propose a new method to solve the classification problem based on separation of two sets in space R d by constructing and separating their e-nets in a range space with respect to hyperplanes. The concept of separation domain is introduced as the set of possible values of e for which the sets can be separated. The paper contains examples of separation domain for random variables with different distributions and proves the theorem about its convergence. The concept of the set of all possible e-nets of some set is introduced and its properties are proved. The weak convergence of the normalized difference of empirical and theoretical separation curves to the normal distribution is proved. It makes it possible to check the hypothesis about the place of theoretical separation curve at a specific point.

Cybernetics and Systems Analysis, Nov 1, 2015

This paper introduces the concept of -separability. Necessary and sufficient conditions of ε-sepa... more This paper introduces the concept of -separability. Necessary and sufficient conditions of ε-separability are proved. It is proved that the problem of ε-separability of two sets can be reduced to the trivial problem of separability of their disjoint ε-nets.

AIMS Mathematics

This article aims to investigate sufficient conditions for the stability of the trivial solution ... more This article aims to investigate sufficient conditions for the stability of the trivial solution of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic stability leverages the use of Lyapunov functions, supplemented by additional constraints on the magnitudes of jumps and jump times, as well as the Markov property of the system solutions. The findings are elucidated with an example, demonstrating both stable and unstable conditions of the system. The novelty of this work is in the consideration of jump concentration points, which are not considered in classical works. The assumption of the existence of concentration points leads to additional constraints on jumps, jump times and relations between them.

Cybernetics and Systems Analysis, Nov 1, 2016

The authors propose a new method to solve classification problem based on separation of two sets ... more The authors propose a new method to solve classification problem based on separation of two sets in space R d. The necessary and sufficient conditions of e-separability are proved. The algorithm of constructing two separable e-nets of size [ / ] 2d e is proposed. The paper contains an example of applying this algorithm to two sets generated from normally distributed sets. The classification results for the proposed method and for support vector machines are compared.

Cybernetics and Systems Analysis, 2015

We compare cluster analysis, Wald’s sequential analysis, and the method of coordinate system rota... more We compare cluster analysis, Wald’s sequential analysis, and the method of coordinate system rotation for the classification of patients with acute destructive pancreatitis and patients with acute combined radiation damage for early detection of complications. In the first case, the Wald analysis is efficient. In the second case, k-means cluster analysis and coordinate rotation method are proposed

arXiv (Cornell University), Dec 15, 2022

An optimal control for a dynamical system optimizes a certain objective function. Here we conside... more An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps, which makes the system stable in probability. Sufficient conditions of the stability in probability are obtained, using the second Lyapunov method, in which the construction of the corresponding functions plays an important role. Here we provide a solution to the problem of optimal stabilization in a general case. For a linear system with a quadratic quality function, we give a method of synthesis of optimal control based on the solution of Riccati equations. Finally, in an autonomous case, a system of differential equations was constructed to obtain unknown matrices that are used for the building of an optimal control. The method of a small parameter is justified for the algorithmic search of an optimal control. This approach brings a novel solution to the problem of optimal stabilization for a stochastic dynamical system with a random structure, Markov switches and Poisson perturbations.

Науковий вісник Ужгородського університету. Серія: Математика і інформатика

Встановлено достатні умови існування допустимого керування для лінійних стохастичних систем випад... more Встановлено достатні умови існування допустимого керування для лінійних стохастичних систем випадкової структури з марковськими перемиканнями і пуассоновими збуреннями.

Mathematics

An optimal control for a dynamical system optimizes a certain objective function. Here, we consid... more An optimal control for a dynamical system optimizes a certain objective function. Here, we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps, which makes the system stable in probability. Sufficient conditions of the stability in probability are obtained, using the second Lyapunov method, in which the construction of the corresponding functions plays an important role. Here, we provide a solution to the problem of optimal stabilization in a general case. For a linear system with a quadratic quality function, we give a method of synthesis of optimal control based on the solution of Riccati equations. Finally, in an autonomous case, a system of differential equations was constructed to obtain unknown matrices that are used for the construction of an optimal control. The method using a small parameter is justified for the algorithmic search of an optimal control. This approach brings a novel...

International Journal of Engineering Applied Sciences and Technology, 2020

In almost every college, they provide their bus transportation facility. Under this, updating & m... more In almost every college, they provide their bus transportation facility. Under this, updating & maintaining daily bus records such as bus km, timing, driver and bus details. This every day activity is time consuming & there is chance of manual mistakes /interference. Paper presented here describes a system that intended to overcome the flaws in the existing system & bring out accuracy, safety of records. Proposed system uses GPS & map API for the student, staff to track the bus. Additionally, biometric attendance can be recorded. From the online recorded data on central college server, admin can generate essential report.

Journal of Automation and Information sciences

The main attention is paid to the estimation of the optimal number of clusters for the system giv... more The main attention is paid to the estimation of the optimal number of clusters for the system given by the node adjacency matrix Based on the assumptions about the similarity of connections in the cluster, the conclusion was drawn about optimal number of clusters for different applications. Poisson's network of connections is modeled and the optimal number of clusters is found. The simulation results indicate high accuracy in determining the optimal number of clusters. In the basic theorem, it is important to assume the existence of a moment above the second for each element of the matrix However, taking into account normalization, this condition can be reduced to the existence of a mathematical expectation of the matrix This weakening of the convergence conditions makes it possible to use a proven statement for a wider class of applied problems, where the presence of a finite variance is not required. Note that the emissions are valid eigenvalues for the normalized matrix, whic...

Endocrine Regulations, 2021

Objective. Brain-derived neurotrophic factor (BDNF) is identified as an important growth factor i... more Objective. Brain-derived neurotrophic factor (BDNF) is identified as an important growth factor involved in learning and memory. Patients with Hashimoto’s thyroiditis can suffer from cognitive dysfunction, whereas BDNF is directly regulated by thyroid hormones. It seems reasonable to propose that changes in BDNF expression underlie some of the persistent neurological impairments associated with hypothyroidism. Methods. The study involved a total of 153 patients with various forms of thyroid pathology. BDNF levels in the sera of the patients and healthy individuals were quantified using enzyme-linked immunosorbent assay with highly sensitive Human BDNF ELISA Kit. Genotyping of the BDNF (rs6265) gene polymorphism using TaqMan probes and TaqMan Genotyping Master Mix (4371355) on CFX96™Real-Time PCR Detection System. Polymerase chain reaction (PCR) for TaqMan genotyping was carried out according to the kit instructions. Results. Distribution rs6265 variants in the patients depending on ...