Development of a Mathematical Model for Tracking Movement of a Human Limb in Three-Dimensional Space Using MEMS Sensors

This article discusses the development of a mathematical model for a device capable of tracking the movements of a human limb based on the readings of microelectromechanical sensors. For developing and selecting the most suitable model, experiments were conducted based on publicly available components. The result obtained is of practical importance since it can be used to create a device.

Ordered Partial Correlation Networks in Psychological Research

Network modeling, which has emerged in recent years, can be successfully applied to the consideration of relationships between measurable psychological variables. In this context, psychological variables are understood as directly affecting each other, and not as a consequence of a latent construct. The article describes regularization methods that can be used to effectively assess the sparse and interpretable network structure based on partial correlations of psychological indicators. An overview of the glasso regularization procedure using EBIC model selection for evaluating an ordered sparse network of partial correlations is presented. The issues of performing this analysis in R in the presence of normal and non-normal data distribution are considered, taking into account the influence of the hyperparameter, which is manually set by the researcher. The considered approach is also interesting as a way to visualize possible causal connections between variables. This review bridges the gap related to the lack of an accessible description in Russian of this approach, which is still uncommon in Russia and at the same time promising.

Interdisciplinary Connections in the General Course of Higher Mathematics

The article discusses the methods of teaching higher mathematics, arising at the modern level of education in our country. The author relies on his experience working at the Faculty of Information Technologies of the Moscow State Psychological and Pedagogical University.

New Psychological Testing Tools

The article provides a detailed description of the diagnostic game system PLines, which was previously described in the journal, discusses the features of conducting research in individual and pair modes, objective indicators of player activity, the use of which, together with the recording of a number of indicators of universal learning activities (ECD): the ability to plan, analyze and reflect, allows you to study more deeply the structure of game behavior and its relationship with personal qualities that are inaccessible to direct observation. The functional components of the system are described, and the methods of storing, extracting, and analyzing the results of experiments are described.

Developing Software of Global Optimization Method Based on Grey Wolf Optimizer

This article discusses the development of software that allows to simulate the algorithm of the “Grey Wolf Optimizer” method. This algorithm belongs to the class of metaheuristic algorithms that allow finding a global extremum on a set of admissible solutions. This algorithm is being the most efficiently used in a situation where the cost function is specified in the form of a black box. The algorithm belongs to both bioinspired algorithms and to the class of algorithms of Particle Swarm Optimization. To analyze the efficiency of the algorithm, software was created that allows to vary the parameters of the method. The article contains examples of the program’s work on various test functions. The purpose of the program is to collect and analyze statistical results, making possible to evaluate the final result. The program provides to build graphs that make it possible to make a more thorough assessment of the results obtained. The program has a step-by-step function that allows one to analyze the specifics and features of the algorithm. Analysis of statistical data provides more detailed selection of the parameters of the algorithm.

Modification of Algorithm of Directed Graph Paths Decomposition with Schedule

This study aims to refinement of the oriented graph paths decomposition algorithm. An additional constraint on the balance parameter is considered to take into account the locomotive departure schedule. Also new rule to compute Ns parameters is given. An example of the operation of the oriented graph paths decomposition algorithm with the schedule is given. The scientific and practical novelty of the work lies in a significant reduction in the dimension of the original problem, which is especially important in the conditions of transport networks of complex topology.

Application of the Digital Adaptive Platform for Learning Programming with the Teamwork Skills Forming Function

Research is carried out on approaches for the digital adaptive platform for learning programming with the teamwork skills forming function application. The work environment interface and key components that make the platform adaptable are demonstrated. The platform services responsible for information security functions are detailed. An example of the presented task is given.

The Relevance of the Problem of Developing Mathematical Models for Solving the Problems of Education Export in Russian Federation

The article is devoted to the current situation in the implementation of domestic and international projects with the participation of Russian universities in the field of education export. Based on the rich personal experience of the authors, a description of typical problems arising in this area is carried out. A combination of organizational and mathematical approaches is proposed as the way that it is advisable to move to achieve practically significant results in the area under consideration. The article does not consider the practical aspects of projects that are currently underway with the participation of Russian and foreign universities and industrial partners. The results of these projects and the obtained practical results will be reported separately. In this article, only the statement of the problem is carried out.

Principles of Developing a Software and Hardware Complex for Crew Intelligent Support and Training Level Assessment

Presented is a new approach to aircraft crew intelligent support, which is based on comparing flight fragments (maneuvers) under study with the relevant patterns contained in the database and representing the system “empirical intelligence”. Principal components of this approach are four new metrics for comparing flight fragments, viz.: the Euclidean metric in the space of wavelet coefficients; the likelihood metric of eigenvalue trajectories for transformations of activity parameters; the Kohonen metric in the space of wavelet coefficients; the likelihood metric for comparing gaze trajectories. Features of the presented approach are: the presence of an “intelligent component” that is contained in empirical data and can be flexibly changed as they accumulate; the use of integral comparisons of the flight fragments under study and video oculography data with relevant patterns of various types and performance quality from a specialized database, with transferring characteristics of the nearest pattern from this specialized database to the fragment under study; applying a complex combination of the methods for stochastic processes analysis and multivariate statistical techniques.

The Concept of an Adaptive Trainer and Assessing Its Effectiveness in a Mathematical Application

Presented is a mathematical model of the self-learning adaptive trainer intended for adaptive learning and providing task selection. The approach in question is an alternative to the adaptive technologies based on the Item Response Theory. Possibility to take into account temporal dynamics of solution ability as well as smaller number of tasks that must be performed by a subject to provide the given results are among the features of the methods in use. To assess the effectiveness of the adaptive trainer concept under consideration, its web-implementation intended for training school students to solve mathematical tasks covered by the school curriculum was employed. The analysis performed revealed both high efficiency of the adaptive trainer (the mean test rating has increased 1.54 times owing to its use) and proven statistically significant influences of the adaptive training factor on the observed mathematical test results.