Abstract: The article explores the technology of hybrid modeling of chaotic systems in the form of synchronization of digital and analog models of the Rossler system, interacting via analog-digital and digital-analog conversion paths. The unidirectional and bidirectional variants of chaotic synchronization are considered, and the synchronization error is estimated for each of the specified cases. For the analog implementation of the Rössler system, a circuit has been developed based on operational amplifiers, multipliers, and precision passive elements. The digital model of the system is based on a semi-implicit hardware-oriented method of numerical integration of the second order of algebraic accuracy. In order to substantiate the choice of the method, graphs of the performance of various solvers of ordinary differential equations are presented when simulating the Rössler system. It is shown that the chosen semi-implicit numerical integration method has the highest computational efficiency among all second-order methods. Experimentally demonstrated the ability to synchronize analog and digital models of a chaotic system. The synchronization of two and three models of the Rossler system in various variants of the connection topology is considered. By analyzing the synchronization error, it is shown that the greatest accuracy is achieved when using a fully coupled topology, which is based on the bi-directional synchronization method of the three models of the Rössler system.

Keywords: semi-implicit method, Rossler system, digital-to-analog conversion, chaotic systems, nonlinear dynamics, hybrid model, chaos, chaotic synchronization, digital model, analog model

Abstract: The subject of the study is adaptive testing with multiple choice questions. This type of testing allows you to implement a machine assessment of the level of knowledge of the participants is simple and accessible, eliminating errors of evaluating the results. However, the adaptive testing model includes a parameter describing the probability of guessing answers to test tasks, which depends on many factors: the difficulty of the task, the level of knowledge of the learner, the presence of a fine for trying to guess, and the degree to which the participant’s answers with a higher level of knowledge influence the opinions of other participants. in the conditions of individual and group testing. The need to explicitly set this parameter complicates the model and introduces uncertainty in the test results. The introduction of a fuzzy cognitive map, which determines the degree of "pure" and "partial" guessing in response to test tasks, reduces the complexity of the testing model as a result of excluding the explicit probabilistic parameter. Unlike the well-known definitions of a cognitive map, the proposed interpretation is based on models of individual and group adaptive testing with multiple choice. The results of computational experiments in real testing confirmed the effectiveness of the introduction of the map. It was found that fuzzy estimates of the responses of participants with a lower level of knowledge to more complex tasks are more consistent than estimates that require explicit assignment of the probability of "pure" guessing. The method of reducing the complexity of a testing model based on a fuzzy cognitive map can be used both in educational software systems and in intelligent systems and decision support systems that provide for testing with multiple choice.

Keywords: Bloom's taxonomy, interval-valued fuzzy set, cognitive modelling, knowledge assessment, pure guessing, partial guessing, collaborative learning, adaptive testing, cognitive map, logistic model

Abstract: The object of the research of the article is the need and the possibility of developing the resources of an academic environment, that is, on a non-commercial basis, specialized graphic editors that provide a visual design environment for instances of applied mathematical tasks of various types. Software available on the market, as well as their extensions, approximately corresponding to the specified task, are considered. It is shown for what reasons these tools turned out to be unsuitable for those applied tasks or those customers with whom the authors had to deal earlier. The research method is based on a comparison of the functionality of the software available on the market and their extensions, as well as the author's reserves, with the applied tasks on which the authors emphasize. The novelty of the study and the conclusions made is the proposal to separate the task of visual design and automatic generation of computational code, as is customary in existing products. It makes sense to transfer the creation of a computing code to an applied mathematician working with a government customer, but at the same time organizing an effective division of labor between the customer and the mathematician. At this angle, the tasks of the graphic editor are simplified. On the other hand, such an editor can be made more flexible.

Keywords: MATLAB, mathematical graph, user interface, visual design, web browser, mathematical calculations, graphical editor, Simulink, JavaScript, JSON

Abstract: The subject of the research is new software releases and subsequent restrictions on the intensity of installing new software releases for modern cloud services, which are complex globally distributed computing systems that require continuous maintenance. The object of the research is the globally distributed cloud computing system of RingCentral (USA). The authors consider in detail the important criteria for business in the transition to a cloud service, including the levels of availability of modern information services for globally distributed computing systems, taking into account the growing number of changes in them. The article proposes a new method of experimental calculation of the maximum intensity of installation and software updates in cloud information systems without degrading the quality of information services. With the increasing degree of functional decomposition of cloud systems and the number of servers, the issue of assessing the intensity of software changes for globally distributed computing systems becomes urgent. The proposed method allowed the authors to efficiently serve RingCentral's global cloud information system without interruption in its operation.

Keywords: software deployment, software release cycle, cloud technologies, high availability, resilience, maintenance, distributed IT systems, change management, outage prevention, continuous deployment

Abstract: The subject of the research is the automatic collision detection mechanism of the manipulator mechanism, with restricted zones used in the knowledge base of intelligent robot control systems. The object of the study is the area of allowed configurations defined in the space of generalized coordinates. The authors consider in detail such aspects as the parametric specification of the area of allowed configurations in the presence of forbidden zones in the working space of the manipulator mechanism. It is proposed to use a sufficient condition for determining the collisions of the manipulator mechanism and the forbidden zones, based on the use of the area of allowed configurations. The research methodology is based on the study of sections defining the shape and position of the region of allowed configurations. All allowed configurations in the space of generalized coordinates are displayed as a geometric object. This geometric object is specified in an analytical way by using several kinematic surfaces that limit it. The simulation results are given, which allowed us to develop a parametric method for specifying a set of sections that define the shape and position of the region of allowed configurations for different positions of the forbidden zones. The main conclusion of the study is to reduce the calculation time of test tasks related to virtual modeling of the movement of the Varan mobile robot arm mechanism using the developed mechanism for collision detection of the mechanism with the environment. A special contribution of the authors to the study of the topic is the development of a parametric method for defining the area of allowed configurations used in the intelligent control of the motion of the manipulator mechanism in a previously known external environment. The novelty of the research lies in the development of a more productive method for analyzing information on the position of the manipulator mechanism and forbidden zones on the basis of the obtained analytical dependencies.

Keywords: mechanism of the manipulator, restricted areas, synthesis of robot movements, virtual modeling, kinematic surfaces, area of allowed configurations, the space of generalized coordinates, vector of the speeds, parameters of a form forming, parameter of locations of forming

Abstract: The subject of research is the intellectual system for controlling the movement of the hand of an android robot in the presence of forbidden zones in the working space. The object of research is the automatic collision detection mechanism of the hand of an android robot, with obstacles at the level of virtual motion simulation. The authors examine in detail such aspects of the topic as determining the conditions of collisions based on the use of the area of allowed configurations and the synthesis of movements excluding the occurrence of dead ends in relation to the movement of the arm of an android robot. Particular attention is paid to the development of an analytical method for specifying the area of allowed configurations in the space of generalized coordinates in the presence of a previously known forbidden zone in the workspace. In this case, the space of generalized coordinates is given by the axes, in the direction of which they lay the angles defining the angular displacements in the rotational kinematic pairs. The research methodology is based on the calculation and analytical task of two-dimensional sections that define the area of allowed configurations. These sections are proposed to be specified using the sets of triangles. A special contribution of the authors to the study of the topic is the development of a generalized method for analytically specifying the area of allowed configurations. The obtained analytical dependences allow you to specify the area of allowed configurations, which is the knowledge base for intelligent control of the movement of the hand mechanism in a previously known external environment. The novelty of the research lies in the use of the area of allowed configurations in the synthesis of the trajectory in the space of generalized coordinates, which allows for the correction of the movement of the android robot arm in order to foresee and eliminate dead ends in the synthesis of movements along the velocity vector.

Keywords: intelligent robots, knowledge base, prohibited zones, the virtual model operation of movements, area of the allowed configurations, space of the generalized coordinates, geometrical analysis, robot traffic control, manipulator mechanism, the generalized coordinates

Abstract: The subject of the research of the article is the actual task of analyzing the state of the documentation support of the management of the organization. In the conditions of modern society, this task becomes particularly acute, since the effectiveness of managing the organization as a whole depends on the proper organization of the DOE system. At the moment there is no uniform methodology for solving this problem, and the existing approaches are subjective. To solve this problem, an automated information system has been developed that allows solving the following tasks: 1) building a knowledge base that captures empirical patterns between the emergence of individual indicators of the state and their probabilistic characteristics; 2) the adaptation of the system to the peculiarities of the current situation and the requirements of the employee performing the analysis; 3) identification of violations in the work with documents and implementation of business processes; 4) identification of indicators of the state of pre-school management and the efficiency of business processes, which may later take on unsatisfactory significance; 5) the provision of recommendations for the elimination of violations. The study used the methods of knowledge engineering, mathematical modeling, graph theory, probability theory, object-oriented programming. As a result of the research, a prototype of an automated information system for analyzing the state of pre-school educational institutions is described in detail, the main functional capabilities of its program modules are described. The procedure of interaction with the system of knowledge engineer and end user is considered. The correctness of the functioning of the AIS prototype is confirmed by successful test tests on the example of the activities of a commercial organization transporting goods both domestically and abroad.

Keywords: theorem Bahasa, knowledge engineering, software modules, components of AIS, automated information system, analysis of DOU, active focus, prior probability, engineer knowledge, final user

Abstract: With the proliferation of online forms design services for online surveys, the number of researchers using questionnaires in research practice has increased significantly. One of the problems that was present in the traditional form of the survey on paper and was transferred to online surveys is the problem of data reliability. Most researchers using online surveys have higher queries to automate research. They are not ready to make significant efforts to increase the reliability of the data. In this paper, we propose to consider an algorithm for automating the process of analyzing the reliability of questionnaire data. The proposed algorithm is based on the use of a sliding exam procedure for testing individual multidimensional observations obtained during an online survey. The main hypothesis underlying the developed method consists in the fact that the subordination of the questionnaire questions to some general topic leads to some latent connections between answers that are violated by random answers. A multi-dimensional statistical criterion was developed for testing personal data. The method is very simple to use and is available even for not sophisticated researchers.

Keywords: Internet service, nominal features, computer technology, sliding exam, criterion fquality of data, latent connections, multivariate statistical methods, online survey, data quality, questionnaire

Abstract: The subject of the research is methods and approaches for solving a class of key player search tasks (key player problem) applicable for identifying expert users in a certain subject area on social networks; a model for building social graphs from data selected from a social network; methods for constructing weighted oriented random graphs for model experiments and their comparative analysis; methods of cluster analysis of the ranking results of social network users; comparative analysis of various results of the identification of expert users in a given subject area. The research methods used in this work are based on system analysis methods, cluster analysis tools, graph theory, and social network analysis methods. To assess the performance of the proposed method, model experiments were carried out using a computer and experiments on real data. In the process of software implementation of the service, the methods of the theory of algorithms, the theory of data structures, and object-oriented programming were used to demonstrate the operability of the method. A method has been developed for identifying expert users on social networks in a given subject area, taking into account the quantitative data on the activity of these users. Unlike existing methods, users of a social graph can be ranked using two or more effective methods, which allows them to take advantage of these methods, and the method itself provides an opportunity to obtain additional information about users who are influenced by expert leaders, as well as potential hidden leaders public opinion.

Keywords: affinity propagation, Kendall-Wei ranking, Borgatti measure, opinion leader, social network, cluster analysis, directed graph, key players, social graph, user identification

Abstract: The subject of the study is a probabilistic model of hierarchical bit indexes of databases. The object of the study is the output of the model — a three-parameter discrete distribution of the number of indexes for implementing queries to the database, parametrized by the intensity of recording records in the database, the average query length, and the size of a large index. The author considers such aspects of the topic as the choice of a hypothesis from known theoretical distributions, a method for testing a hypothesis, selection of functions for approximating the dependence of the expectation on the third parameter, selection of a function for approximating the dependence of the minimum point of the expectation for the third parameter from the first two. The study of such dependencies is explained by the fact that the optimal choice of the third parameter is the goal of the designer, and the first two are the initial data of the model. The methodology of the research is the methods of mathematical statistics, in particular, the estimation of parameters and the Pearson criterion of testing hypotheses, methods for constructing the best approximations, in particular, the method of least squares, the theory of curves of the third order. The main conclusions of the study: the best approximation for the studied family of distributions is the Polya distribution; The best approximations for the dependence of the expectation on the third parameter are the Bacon-Watts model and the heat capacity model. A special contribution of the author to the study of the topic is the derivation of an empirical formula that has practical significance. It allows the designer on the basis of the first two parameters at once, without using cumbersome calculations on the model, to obtain an approximate optimal value of the third parameter and thus construct an index of the database of the optimal size. The novelty of the research lies in obtaining approximate dependencies for a new type of distribution that cannot be described by a closed formula.

Keywords: power function, output analysis, least square method, heat capacity model, third order curves, Bacon-Watts model, Polia distribution, negative binomial distribution, discrete probability distribution, hierarchical bitmap indexes

Abstract: The relevance of the research topic is due to the fact that the activity of the authorities is to make management decisions in the framework of the implementation of their powers. The introduction of a document management and records management system is one of the priority tasks of the authorities, the successful implementation of which will allow for a transition to a higher quality level of their functioning.The effectiveness of this process is determined by the workflow and workflow system, which is the object of modeling. The purpose of the study is to develop a mathematical model for assessing the effectiveness of the implementation of an electronic document management and workflow system in government to improve performance. The results of the study were obtained on the basis of the use of the theory of system analysis, set theory, graphical models, and the model of system dynamics. The scientific novelty is connected with the development of a model for evaluating the effectiveness of introducing an electronic document management and workflow system in government for simulation modeling and forecasting of their main indicators.The main conclusions of the study are that the authors considered the construction of a mathematical model for evaluating the effectiveness of introducing an electronic document management system and office work in government using the Forrester system dynamics method. The developed model is written in the form of a system of differential equations and presented in the form of a Cauchy problem. According to the results of the study, it was found that the fourth order Runge-Kutta method is appropriate for solving this system, since, despite the increase in the volume of calculations, the fourth order method has an advantage over the first and second order methods, since it provides a small local error, which allows you to increase the step of integration and, consequently, reduce the calculation time.

Keywords: Euler method, Cauchy problem, differential equations, system dynamics model, soft modeling models, electronic document flow system, electronic document flow, document flow, modified Euler method, Runge-Kutta method

Abstract: In this paper, the author considers the problem of automatic parallelization of C programs (mainly computational) with the use of Cilk ++ directives, with the help of a limited set of which parallelism in tasks can be clearly expressed. To solve this problem, the concept of recognizing object-event models, potentially capable of parsing and transforming arbitrary texts, is formulated. This concept is a development of the theory of object-event models proposed by the author earlier, which, in the marginal formulation, are equivalent to advanced Turing machines. A general approach of the theory of object-event models is used, which asserts the possibility of describing arbitrary algorithms using these models. The technology of analysis and transformation of both structured and non-structured texts with the use of recognizing object-event models is proposed. A strategy is proposed for automatic parallelization of C programs using Cilk ++ directives based on this technology. Using the example of automatic parallelization of a simple computing program, data on acceleration and efficiency of parallelization are obtained. It is argued that the developed technology can be used as part of a program generating system for parallelizing the generated programs.

Keywords: program generation system, algorithm transformation, algorithm recognition, object-event models, Cilk, C programming language, automatic parallelizing, logical programming, task parallelism, parallel computations

Abstract: The subject of research is the optical transformations of pairs of basic geometric objects on a plane that simulate various sources of radiation. In the general case, when solving problems of geometric optics on a plane, the task of transforming one beam of rays into another, for example, converting rays of a point source into a system of parallel rays, is distinguished. Such tasks require the creation of a relatively simple method based on the laws of geometrical optics and allowing one to obtain reflective lines of a certain geometry corresponding to the given initial data. Obtaining a reflective line for different combinations of central, parallel and scattered direct beam transformations in this work is based on the cyclographic display method. The method is based on the optical properties of a cyclographic model of a spatial curve of a line and makes it possible to obtain reflective curves of various shapes during optical transformations of straight beams. The use of this method in building a source-receiver system makes it possible to select a receiver (or source) from a variety of receivers (sources) with the same reflector line. The study showed that the cyclographic mapping method makes it relatively easy to obtain reflective lines during optical transformations of various beam beams, while the analytical algorithm makes it possible to obtain parametric equations of this line. The results of the work can be used in the design of various optical systems in the antenna, laser and lighting engineering industries.

Keywords: evolvent, reflective lines, cyclographic mapping, pencil of rays, geometrical optics, Optical transformations, evolute, ruled surface, intersection line, spatial visualization

Abstract: The article presents new methods of experimental study of the influence of color on the perception of a movie frame by the viewer and software algorithms for processing the obtained statistical data. The object of scientific research is filmed and edited film material, including individual graphic images of video frames. The subject of the research is graphic models of color solutions, digital color correction methods, digital cinema and video processing algorithms. The specificity of the computational experiment put into practice is that it is conducted online using the Internet resources.The described method is the development of existing methods for the experimental study of human oculomotor activity using I-tracking technology. The proposed methods and algorithms for experimental studies of the influence of color solutions on their perception allow us to objectively measure statistical data and analyze the work of human visual activity according to various criteria. The development of an Internet application has allowed many more subjects to be involved in a computational experiment and to increase the reliability of statistical results.

Keywords: Computing Experiment, Human Visual Perception, Visualization, Digital Color Correction, Graphic Model, Color Scheme, Film Frame, Cinema, Internet Resources, Statistical Data Processing

Abstract: The paper proposes the solution of a number of problems related to the optimization of recognition of information signs by the correlation-extremal contour method based on the evaluation of similarity invariant with respect to affine transformations.A description is given of a speed-efficient algorithm for obtaining regions of a certain color and its parallelization. It is shown that solving this problem allows reducing both the number of objects presented for recognition and the number of standards used, as well as obtaining a better contour description of objects and, therefore, significantly increasing the speed of the recognition algorithm itself. The solution of the problem of optimization of calculations in the recognition algorithm itself is given. It is shown that one of the ways to solve this problem for a particular chosen recognition algorithm is to parallelize the computation of the similarity estimate by the affine transformation parameters. Another presented way of solving the problem of optimization of computations was focused on obtaining estimates of the similarity of the current standard with objects from the local area of the image, which is determined on the basis of the parameters of affine transformation and dimensions of the standard. It is noted that the created algorithmic software allows to solve problems of recognition of information objects in real time.

Keywords: affine transformation, optimization, color segmentation, parallel algorithm, pattern recognition, image processing, computer graphics, standart image, adaptive description, correlation-extreme contour method