Application of regression in algorithm of nonlinear stochastic adaptation of unstable multidimensional objects

The results of a study of applicability of kernel estimation in the synergetic control systems for the objects unstable in an open-loop state (without a stabilizing control) have been presented. The effectiveness of kernel estimates has been shown for four nonlinear objects with unstable limiting states. The estimate the effectiveness of embedding the kernel predictive estimate of the state variables of a nonlinear object, subjected to disturbances of an unknown nature, into the system of synergetic control is demonstrated.

Cluster analysis for multidimensional objects in fuzzy data conditions

This article presents many different areas of practical applications of multivariate cluster analysis under conditions of fuzzy initial data that are described in the literature. New algorithms and formula expressions are proposed for combining various multi-dimensional objects, the parameters of which are given by fuzzy-sets, into clusters along with calculating the coordinates of the centroids of their membership functions. Various types of clustering criteria are formulated in the form of minimizing the weighted average and the sum of distances between the centroids of objects and clusters presented in different metrics, as well as maximizing the distances between the centroids of different clusters. The formulations and mathematical models of three different NP-hard problems of multidimensional clustering in fuzzy-data conditions are proposed; while solving them any of the considered optimality criteria can be used. Heuristic algorithms for the approximate solution of two formulated problems have been developed. The algorithm for solving the 1st problem is illustrated with a numerical example. The obtained results can serve as a direction for further research and have wide practical applications.

Development of a model for choosing strategies for investing in information security

This paper has proposed a model of the computational core for the decision support system (DSS) when investing in the projects of information security (IS) of the objects of informatization (OBI). Including those OBI that can be categorized as critically important. Unlike existing solutions, the proposed model deals with decision-making issues in the ongoing process of investing in the projects to ensure the OBI IS by a group of investors. The calculations were based on the bilinear differential quality games with several terminal surfaces. Finding a solution to these games is a big challenge. It is due to the fact that the Cauchy formula for bilinear systems with arbitrary strategies of players, including immeasurable functions, cannot be applied in such games. This gives grounds to continue research on finding solutions in the event of a conflict of multidimensional objects. The result was an analytical solution based on a new class of bilinear differential games. The solution describes the interaction of objects investing in OBI IS in multidimensional spaces. The modular software product "Cybersecurity Invest decision support system " (Ukraine) for the Windows platform is described. Applied aspects of visualization of the results of calculations obtained with the help of DSS have been also considered. The Plotly library for the Python algorithmic language was used to visualize the results. It has been shown that the model reported in this work can be transferred to other tasks related to the development of DSS in the process of investing in high-risk projects, such as information technology, cybersecurity, banking, etc.

Evaluation of the level of social development of poviats in Małopolskie Voivodship with the use of a dynamic synthetic measure

The level of social development of territorial units in Poland is an important topic in the context of the pursued policy to equalise the differences in regional development. Nowadays, spatial disproportions in development are considered one of the main social problems also in Małopolskie Voivodship. The purpose of the study described in the article involves the comparison of changes in the level of social development in the poviats of Małopolskie Voivodship in the period of 2010–2019 by means of a dynamic synthetic measure. The situation of these poviats was evaluated based on data provided by the Local Data Bank of Statistics Poland, describing 10 selected diagnostic features relating to the following areas: the demographic situation, the labour market, education, standard of living and health protection of the inhabitants. The method of linear ordering of multidimensional objects in a dynamic approach was applied. The volume of changes in the level of development of the poviats was determined on the basis of a dynamic synthetic measure. The results of the study indicate that in all of the poviats, a significant decline was observed in the value of the synthetic measure describing the demographic situation and education. On the other hand, the positive aspect is that in all of the poviats the value of the synthetic measure relating to the labour market, living conditions and health protection of the population increased significantly. Consequently, the disproportions between the poviats in the analysed period deepened in terms of the demographic situation and education, whereas the differences in the level of development decreased in the case of the labour market, living conditions and health protection of the population.

Use of Mechanisms Marking Centers of Simplexes in Their 2-Dimensional Projections as Axonographs of Multidimensional Spaces

A brief historical excursion into the graphics of geometry of multidimensional spaces at the paper beginning clarifies the problem – the necessary to reduce the number of geometric actions performed when depicting multidimensional objects. The problem solution is based on the properties of geometric figures called N- simplexes, whose number of vertices is equal to N + 1, where N expresses their dimensionality. The barycenter (centroid) of the N-simplex is located at the point that divides the straight-line segment connecting the centroid of the (N–1)-simplex contained in it with the opposite vertex by 1: N. This property is preserved in the parallel projection (axonometry) of the simplex on the drawing plane, that allows the solution of the problem of determining the centroid of the simplex in its axonometry to be assigned to a mechanism which is a special Assembly of pantographs (the author's invention) with similarity coefficients 1:1, 1:2, 1:3, 1:4,...1:N. Next, it is established, that the spatial location of a point in N-dimensional space coincides with the centroid of the simplex, whose vertices are located on the point’s N-fold (barycentric) coordinates. In axonometry, the ends of both first pantograph’s links and the ends of only long links of the remaining ones are inserted into points indicating the projections of its barycentric coordinates and the mechanism node, which serves as a determinator, graphically marks the axonometric location of the point defined by its coordinates along the axes х1, х2, х3 … хN.. The translational movement of the support rods independently of each other can approximate or remote the barycentric coordinates of a point relative to the origin of coordinates, thereby assigning the corresponding axonometric places to the simplex barycenter, which changes its shape in accordance with its points’ occupied places in the coordinate axes. This is an axonograph of N-dimensional space, controlled by a numerical program. The last position indicates the possibility for using the equations of multidimensional spaces’ geometric objects given in the corresponding literature for automatic drawing when compiling such programs.

System as a complex category of reflection of national security in theoretical-legal research

The subject of this article is the methodology of reconstruction of national security as a complex social and political-legal phenomenon in modern scientific knowledge. Special attention is given to the provisions of the theory of state and law, political science, as well as official documents – the acts of strategic planning that are of theoretical and applied significance due to the presence of formal definitions in their texts. The article employs formal-legal and doctrinal analysis of scientific sources. Methodological framework is comprised of the category of “system” and systemic approach in various interpretations. Logical analysis is conducted on different variants of definitions of the category “national security system” and “system of ensuring national security”. It is revealed that systemic analysis, which historically is one of the most popular approaches that can reflect the multidimensional objects of research, has long been included into the scientific tradition of studying national security. The author explores several variants of systemic approach: the theory of national security as a system; national security as a system property; and national security as a system. The analysis of interpretation of national security as a system determines the two main categories: national security system and system of ensuring national security. The first category features mostly scientific interpretations, while the second category has received a legal definition, having transformed from the scientific category into an element of the object (social reality), and simultaneously, means of its construction. The author indicates the existence of methodological pluralism in determining the components of national security systems. The article examines successful and unsuccessful examples of application of systemic approach in studying national security, and identifies typical methodological errors. The author concludes on the limited heuristic possibilities of systemic approach in reflecting the dynamics of ensuring national security, as well as underlines the need to use the categories of “mechanism”, “regime"”, or “process”.

A Nonparametric Algorithm for Data Preprocessing and Modeling Multidimensional Objects with Delay

The paper devotes to modeling tasks of multidimensional inertialess objects with delay (MIOD). The description of identification scheme of MIOD is determined. The proposed identification scheme includes not only blocks of a process and a model but also a data preprocessing block to improve modelling accuracy. A new method of data preprocessing which includes outliers detection and sparsity filling is proposed. It allows generating new training samples based on initial data that is obtained by measurement of input and output variables of the process. A software package is developed to conduct computer experiments. The results of the study show that the proposed algorithms are universal and can be applied to simulate various objects that are described with liner, nonlinear algebraic and nonlinear transcendental mathematical equations. Computational experiments have shown satisfactory accuracy of the algorithms. Proposed algorithms can be used in modeling and control tasks for inertialess objects in various areas of industry such as metallurgy, petrochemicals and etc.

New Method for Optimal Feature Set Reduction

A problem of searching a minimum-size feature set to use in distribution of multidimensional objects in classes, for instance with the help of classifying trees, is considered. It has an important value in developing high speed and accuracy classifying systems. A short comparative review of existing approaches is given. Formally, the problem is formulated as finding a minimum-size (minimum weighted sum) covering set of discriminating 0,1-matrix, which is used to represent capabilities of the features to distinguish between each pair of objects belonging to different classes. There is given a way to build a discriminating 0,1-matrix. On the basis of the common solving principle, called the group resolution principle, the following problems are formulated and solved: finding an exact minimum-size feature set; finding a feature set with minimum total weight among all the minimum-size feature sets (the feature weights may be defined by the known methods, e.g. the RELIEF method and its modifications); finding an optimal feature set with respect to fuzzy data and discriminating matrix elements belonging to diapason [0,1]; finding statistically optimal solution especially in the case of big data. Statistically optimal algorithm makes it possible to restrict computational time by a polynomial of the problem sizes and density of units in discriminating matrix and provides a probability of finding an exact solution close to 1. Thus, the paper suggests a common approach to finding a minimum-size feature set with peculiarities in problem formulation, which differs it from the known approaches. The paper contains a lot of illustrations for clarification aims. Some theoretical statements given in the paper are based on the previously published works. In the concluding part, the results of the experiments are presented, as well as the information on dimensionality reduction for the coverage problem for big datasets. Some promising directions of the outlined approach are noted, including working with incomplete and categorical data, integrating the control model into the data classification system.