Igor Malyk
CHNU, Applied Math, Post-Doc
Research Interests:
Research Interests:
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... 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.
Research Interests:
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.
Research Interests:
Research Interests:
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... 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.
Research Interests:
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... 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.
Research Interests:
Research Interests:
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... 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.
Research Interests:
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... 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.
Research Interests:
Research Interests:
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... 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
Research Interests:
Research Interests:
Встановлено достатні умови існування допустимого керування для лінійних стохастичних систем випадкової структури з марковськими перемиканнями і пуассоновими збуреннями.
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,... 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...
Research Interests:
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... 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...
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... 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 ...
Research Interests:
In this manuscript, the time-fractional diffusion equation in the framework of the Yang–Abdel–Cattani derivative operator is taken into account. A detailed proof for the existence, as well as the uniqueness of the solution of the... more
In this manuscript, the time-fractional diffusion equation in the framework of the Yang–Abdel–Cattani derivative operator is taken into account. A detailed proof for the existence, as well as the uniqueness of the solution of the time-fractional diffusion equation, in the sense of YAC derivative operator, is explained, and, using the method of α-HATM, we find the analytical solution of the time-fractional diffusion equation. Three cases are considered to exhibit the convergence and fidelity of the aforementioned α-HATM. The analytical solutions obtained for the diffusion equation using the Yang–Abdel–Cattani derivative operator are compared with the analytical solutions obtained using the Riemann–Liouville (RL) derivative operator for the fractional order γ=0.99 (nearby 1) and with the exact solution at different values of t to verify the efficiency of the YAC derivative operator.
Research Interests:
Stimulation of human neutrophils with tumor necrosis factor-α (TNF), granulocyte-macrophage colony-stimulating factor (GM-CSF), or granulocyte CSF (G-CSF) resulted in decreased fluorescence intensity of FITC-phalloidin (actin... more
Stimulation of human neutrophils with tumor necrosis factor-α (TNF), granulocyte-macrophage colony-stimulating factor (GM-CSF), or granulocyte CSF (G-CSF) resulted in decreased fluorescence intensity of FITC-phalloidin (actin depolymerization) and morphological changes. Cytokine-induced actin depolymerization was dependent on the concentration of cytokines used as stimuli. The maximal changes were detected at 10 min after stimulation with TNF or GM-CSF and at 20 min after stimulation with G-CSF. Cytokine-induced actin depolymerization was sustained for at least 30 min after stimulation. In contrast, N-formyl-methionyl-leucyl-phenylalanine (FMLP) rapidly (within 45 s) induced an increase in the fluorescence intensity of FITC-phalloidin (actin polymerization) and morphological changes. TNF- and GM-CSF-induced actin depolymerization and morphological changes, but not FMLP-induced responses, were partially inhibited by either PD-98059, an inhibitor of mitogen-activated protein kinase (M...
Research Interests: Physiology, Biology, Enzyme Inhibitors, Polymers, Flavonoids, and 14 moreMedicine, Humans, American, Phosphorylation, Medical Physiology, Neutrophils, Adult, Tumor necrosis factor-alpha, Pyridines, Imidazoles, MAP Kinase, Recombinant Proteins, Biochemistry and cell biology, and Mitogen- Activated Protein Kinases
Research Interests:
In this paper, we consider some properties of stochastic random matrices of large dimensions under conditions of independence of matrix elements or under conditions of independence of rows (columns). The main properties of stochastic... more
In this paper, we consider some properties of stochastic random matrices of large dimensions under conditions of independence of matrix elements or under conditions of independence of rows (columns). The main properties of stochastic random matrices spectrum are analyzed and the result of convergence to 0 is proved of almost all eigenvalues. Also, the application of these results to clustering problems and selection of the optimal number of clusters is considered. Note that the results obtained in this work are consistent with the Marchenko - Pastur theorem on the asymptotic distribution of eigenvalues of random matrices with independent elements. The results proved in this paper can be interpreted as a law of large numbers and will be used in the study of the asymptotic behavior of the maximum.
We propose a new approach for solving the classification problem, which is based on the using \(\epsilon \)-nets theory. It is showed that for separating two sets one can use their \(\epsilon \)-nets, which considerably reduce the... more
We propose a new approach for solving the classification problem, which is based on the using \(\epsilon \)-nets theory. It is showed that for separating two sets one can use their \(\epsilon \)-nets, which considerably reduce the complexity of the separating algorithm for large sets’ sizes. The necessary and sufficient conditions of separable \(\epsilon \)-nets of two sets are proved. The algorithm of building separable \(\epsilon \)-nets is proposed. The \(\epsilon \)-nets, constructed according to this algorithm, have size \(O(1/\varepsilon )\), which does not depended on the size of set. The set of possible values of \(\epsilon \) for \(\epsilon \)-nets of both sets is considered. The properties of this set and the theorem of its convergence are proved. The proposed algorithm of solving the classification problem using the \(\epsilon \)-nets has the same computational complexity as Support Vector Machine \(O(n\ln n)\) and its accuracy is comparable with SVM results.
Research Interests:
In this paper we propose a new approach for solving the classification problem, which is based on the using e-nets theory. It is shown that for e-separating of two sets one can use their e-nets in the range space w.r.t. halfspaces, which... more
In this paper we propose a new approach for solving the classification problem, which is based on the using e-nets theory. It is shown that for e-separating of two sets one can use their e-nets in the range space w.r.t. halfspaces, which considerably reduce the complexity of the separating algorithm for large sets’ sizes. The separation space which contains the possible values of e for e-nets of both sets is considered. The separation space is quasi-convex in general case. To check necessary and sufficient conditions of e-separability of two sets one can solve an optimisation problem, using the separation space as constraints. The lower bound of the separation space is convex for the exponential distribution and linear for the uniform distribution. So, we have convex and linear optimisation problems in these cases.
A theoretical basis for the method of polarization-interference mapping of optically thin polycrystalline films of human biological fluids is given. The coordinate distributions of the value of the local contrast of the interference... more
A theoretical basis for the method of polarization-interference mapping of optically thin polycrystalline films of human biological fluids is given. The coordinate distributions of the value of the local contrast of the interference distributions of the polarization-inhomogeneous microscopic images of polycrystalline films of the synovial fluid of the human joint are investigated. In the framework of the statistical (statistical moments of the 1st-4th order) approaches, objective criteria for the distribution of the values of local contrast are established. The possibility of differentiation of weak changes in the optical anisotropy of blood films of healthy and patients with breast cancer patients is determined.
Research Interests:
Vitamin D is known to alter immune regulation. It binds to the vitamin D receptors (VDR) expressed on T lymphocytes and macrophages. In individuals with Hashimoto’s thyroiditis, serum vitamin D levels were found to be lower compared to... more
Vitamin D is known to alter immune regulation. It binds to the vitamin D receptors (VDR) expressed on T lymphocytes and macrophages. In individuals with Hashimoto’s thyroiditis, serum vitamin D levels were found to be lower compared to healthy controls. The study’s objective was to investigate the association between VDR gene polymorphism (rs2228570) with blood serum levels of 25-OH vitamin D in patients with thyroid pathology from western Ukraine. The study involved a total of 153 patients with various forms of thyroid pathology. 25-OH vitamin D levels in the serum of the patients and healthy individuals were quantified with ELISA using the 25-OH vitamin D Total (Vit D-Direct) Test System ELISA Kit (Monobind Inc.®, United States, Product Code: 9425-300) on the EIA Reader Sirio S (Seac, Italy). Genotyping of the VDR (rs2228570) gene polymorphism was performed using TaqMan probes and TaqMan Genotyping Master Mix (4371355) on CFX96™Real-Time PCR Detection System (Bio-Rad Laboratories,...
Research Interests:
In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The... more
In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate function of the new model can be “monotonically asymmetric increasing”, “increasing-constant”, “monotonically asymmetric decreasing” and “upside-down-constant” shaped. We investigate some of mathematical symmetric/asymmetric properties such as the ordinary moments, moment generating function, conditional moment, residual life and reversed residual functions. Bonferroni and Lorenz curves and mean deviations are discussed. The maximum likelihood method is used to estimate the model parameters. Finally, we illustrate the importance of the new model by the study of real data applications to show the flexibility and potentiality of the new model. The kernel density estimation and box plots are used for exploring the symmetry of the used data.
Research Interests:
The problem of synthesis of the optimal control for a stochastic dynamic system of a random structure with Poisson perturbations and Markov switching is solved. To determine the corresponding functions for Bellman functional and optimal... more
The problem of synthesis of the optimal control for a stochastic dynamic system of a random structure with Poisson perturbations and Markov switching is solved. To determine the corresponding functions for Bellman functional and optimal control the system of ordinary differential equation is investigated.
Research Interests:
Research Interests:
Weak convergence of semi-Markov processes in the diffusive approximation scheme is studied in the paper. This problem is not new and it is studied in many papers, using convergence of random processes. Unlike other studies, we used in... more
Weak convergence of semi-Markov processes in the diffusive approximation scheme is studied in the paper. This problem is not new and it is studied in many papers, using convergence of random processes. Unlike other studies, we used in this paper concept of the compensating operator. It enables getting sufficient conditions of weak convergence under the conditions on the local characteristics of output semi-Markov process.
Research Interests:
Research Interests:
The method of building the hyperplane which separates the convex hulls in the Euclidean spaceRnis proposed. The algorithm of prediction of the presence of severity in patients based on this method is developed and applied in practice to... more
The method of building the hyperplane which separates the convex hulls in the Euclidean spaceRnis proposed. The algorithm of prediction of the presence of severity in patients based on this method is developed and applied in practice to predict the presence of severity in patients with acute pancreatitis.
Research Interests:
ABSTRACT We propose an approach to the proof of the weak convergence of a semi-Markov process to a Markov process under certain conditions imposed on local characteristics of the semi-Markov process.
Research Interests:
ABSTRACT Oscillations in quasilinear stochastic hereditary systems and their application to specific problems are investigated. The algorithm of transition to a standard system with the help of the averaging method with small parameter in... more
ABSTRACT Oscillations in quasilinear stochastic hereditary systems and their application to specific problems are investigated. The algorithm of transition to a standard system with the help of the averaging method with small parameter in the presence of fast time is justified.
Research Interests:
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.
Research Interests:
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.