System research and information technologies

New approach to finding eigenvectors for repeated eigenvalues of a matrix

2025-02-09T00:28:25+02:00

An efficient method of calculating eigenvectors for multiple eigenvalues of a matrix is proposed. This method is based on a formalized transformation of the problem of solving degenerate systems of equations into a regular problem by “repairing” their matrices and correspondingly correcting the right-hand sides of the equations, as well as “exclusion” during calculations from the spectrum eigenvalues of the matrix of one of the multiple values. In the case of non-defective multiples of the matrix, orthogonal eigenvectors are formed in contrast to the results obtained using the Mathematica program.

Classical special functions of matrix arguments

2025-02-09T01:28:03+02:00

This article focuses on a few of the most commonly used special functions and their key properties and defines an analytical approach to building their matrix-variate counterparts. To achieve this, we refrain from using any numerical approximation algorithms and instead rely on properties of matrices, the matrix exponential, and the Jordan normal form for matrix representation. We focus on the following functions: the Gamma function as an example of a univariate function with a large number of properties and applications; the Beta function to highlight the similarities and differences from adding a second variable to a matrix-variate function; and the Jacobi Theta function. We construct explicit function views and prove a few key properties for these functions. In the comparison section, we highlight and contrast other approaches that have been used in the past to tackle this problem.

An advanced method of interpolation of short-focus electron beams boundary trajectories using higher-order root-polynomial functions and its comparative study

2025-02-09T02:33:54+02:00

The comparison of three advanced novel methods for estimating the boundary trajectory of electron beams propagated in ionized gas, including lower-order interpolation, self-connected interpolation, and extrapolation, as well as higher-order interpolation, is considered and discussed in the article. All estimations of the corresponding errors have been provided relative to numerically solving the set of algebra-differential equations that describe the boundary trajectory of the electron beam. By providing analysis, it is shown and proven that lower-order interpolation usually gives the minimal value of average error, using the method of self-connected interpolation and extrapolation gives the minimal error for estimation of focal beam parameters, and higher-order interpolation is suitable to obtain a uniform error value over the entire interpolation interval. All results of error estimation were obtained using original computer software written in Python.

On the evolution of recurrent neural systems

2025-02-08T21:21:45+02:00

The evolution of neural network architectures, first of the recurrent type and then with the use of attention technology, is considered. It shows how the approaches changed and how the developers’ experience was enriched. It is important that the neural networks themselves learn to understand the developers’ intentions and actually correct errors and flaws in technologies and architectures. Using new active elements instead of neurons expanded the scope of connectionist networks. It led to the emergence of new structures — Kolmogorov–Arnold Networks (KANs), which may become serious competitors to networks with artificial neurons.

Detecting unsafe behavior in neural network imitation policies for caregiving robotics

2025-02-08T22:01:36+02:00

This paper explores the application of imitation learning in caregiving robotics, aiming at addressing the increasing demand for automated assistance in caring for the elderly and disabled. While leveraging advancements in deep learning and control algorithms, the study focuses on training neural network policies using offline demonstrations. A key challenge addressed is the “Policy Stopping” problem, which is crucial for enhancing safety in imitation learning-based policies, particularly diffusion policies. Novel solutions proposed include ensemble predictors and adaptations of the normalizing flow-based algorithm for early anomaly detection. Comparative evaluations against anomaly detection methods like VAE and Tran-AD demonstrate superior performance on assistive robotics benchmarks. The paper concludes by discussing further research in integrating safety models into policy training, which is crucial for the reliable deployment of neural network policies in caregiving robotics.

Application of neural network technology for public opinion analysis

2024-01-04T12:14:51+02:00

The research is devoted to studying and using neural network technologies, in particular algorithms and methods of natural language processing, to increase the efficiency of studying and analyzing public opinion of Ukraine’s partner countries regarding the war in Ukraine. The research involved analyzing and processing databases consisting of messages about the war in Ukraine on the social network Twitter. The resulting datasets were used to train several neural network models. The best classification results were obtained with the GPT-3.5-turbo model. For a deeper understanding of the results of the public opinion analysis, we created their visualization. The results of the study have shown the high efficiency of the selected solutions. They may be of great practical importance for improving methods of analyzing public opinion and making informed decisions based on a deep understanding of global feedback.

Quantum mechanics approximation approach to investigate molecular behavior in nitrogen binding to enzymes and proteins: Implications for biofuel production

2025-02-08T00:28:16+02:00

This research delves into the essential mechanisms underlying the binding of Nitrogen (N) atoms to enzyme molecules and their implications for protein formation in food crops and biogas production. Nitrogen (N), along with Phosphorus (P) and Potassium (K), plays a pivotal role in soil fertility and crop growth. The study explores the interactions between atoms through various mechanisms, such as catalysts, photosynthesis, and adiabatic reactions, to comprehend their roles in facilitating organic molecule formation. Additionally, the research examines the influence of enzymes on amino acids and their contributions to protein structure. The simulation process employs the Hamiltonian equation to quantify energy intensities and explore the effectiveness of adiabatic reactions in organic transformations. By investigating the molecular interactions in enzyme-catalyzed processes, this research aims to enhance protein formation in crops and optimize biogas production.

Identification of nonlinear systems with periodic external actions (Part II)

2025-02-08T14:25:11+02:00

The article presents the results of the study, which is a continuation of the author’s previous research. This paper considers more complex problems in identifying nonlinear systems with periodic external actions. The article shows that the previously proposed method is applicable when the periods of external actions in the same differential equation may differ. At the same time, the ratio between the values of the periods can be both integer and fractional. The conditions under which this is possible are formulated. These conditions are based on the theorem proved in the previous work. Part of this study is devoted to the problem of identification of a chaotic system with an external non-sinusoidal action. To create such an external action, a function with three harmonic components was used. A numerical experiment confirmed the effectiveness of the algorithm in this case as well.

Systematic studies of cryptocurrency usage tools for financial markets

2025-02-07T00:37:46+02:00

The paper analyzes mining processes when using cryptocurrency on financial exchanges. It considers the cognitive map (CM) of the use of cryptocurrency as a complex system. It reveals all functions of mining processes when interacting with speculative instruments under conditions of uncertainties and risks. Digital modeling of impulse processes in the CM was carried out to study the dynamic properties of the free movement of the tops of the CM under random disturbances.

Short-term forecasting of the main indicators of the COVID-19 epidemic in Ukraine based on the seasonal cycle model

2025-02-07T18:03:24+02:00

The authors of this study propose a method of short-term forecasting of time series of the main indicators of the COVID-19 epidemic, which has a pronounced seasonality. This method, which has no direct analogies, provides the decomposition of a general forecasting task into several simpler tasks, such as the tasks of building a model of the seasonal cycle of a time series, aggregating the original time series, taking into account the duration of the seasonal cycle, forecasting an aggregated time series, developing an aggregated forecast into a forecast in the original time scale, using the seasonal cycle model. The solution for each task allows the usage of relatively simple methods of mathematical statistics. The article provides a formally rigorous description of all procedures of the method and illustrations of their numerical implementation on the example of a real forecasting task. The use of this method for short-term forecasting of the COVID-19 epidemic development in Ukraine has systematically demonstrated its effectiveness.

Crowd navigation monitoring during emergencies

2024-04-26T14:43:11+03:00

The paper considers the task of crowd navigation monitoring, which might be performed using various sensors and technologies, with surveillance cameras being the most commonly employed. These cameras provide a video stream that typically lacks supplementary information. Extracting additional data from these streams could significantly enhance pedestrian behavior modeling and the automation of the monitoring process. A critical parameter in the analysis of pedestrian movement is their speed. The analytical method and the algorithm of pedestrians’ speed estimation based on the surveillance camera video are proposed. The first step of the proposed algorithm is object detection and tracking between frames. The second step is the speed estimation method, which is based on calculating the real-world distances and knowing camera parameters and distances in pixels on the resulting image. Implementation of the algorithm was tested on real videos and showed an error of about 0.04 m/s.

Scientist and organizer of engineering education

2025-02-09T21:39:50+02:00