## Volume №2(34) / 2024

#### Articles in journal

The difference between political geography as part of the hermeneutical meta-theory of understanding and geopolitics as an intertheory of explaining the specifics of spatially distributed activity, activities with or without taking into account the feature of the geohistorical environment, is proved on the basis of a critical mathematical approach with the procedures of knowledge stratification (fibration). The role and place of mathematics in the system of humanities and in solving problems of statistical data analysis and modeling of political processes and phenomena are discussed. The complementarity of methodological, mathematical and empirical research methods is substantiated. Schemes of the structure and organization of tangent layers (fibers) of activities and equations of quantitative analysis and modeling of political phenomena are proposed. Their application is demonstrated by the example of the interpretation of the popular election results.

The paper considers a class of fast neural networks with a pyramidal structure. Methods of topological construction of one-dimensional and two-dimensional pyramidal networks are given. Networks of the class under consideration are representable by linear operators, have a self-similar structure, and are a special case of the fast Fourier transform algorithm. Topological models of pyramidal neural networks of direct and reverse orientation are proposed. The paper shows the use of pyramidal neural networks of fast learning for the implementation of correlative digital signal and image processing, combinational logic and memory elements. Examples of the construction of an encoder and a decoder of binary codes are considered. It is noted that the pyramidal memory network provides storage and accurate recovery of images similar to storing data in random access computer memory. It is proved that a fast pyramid network is a deep learning neural network, and a self-similar structure allows the network to be trained to new data without the need for a complete retraining of the network. This work is the third part of the generalizing article "Fast transformations and self-similar neural networks of deep learning". In the first part, stratified models of self-similar neural networks are considered, in the second part, algorithms for training fast neural networks and generalized spectral transformations are considered.

The spatial distribution of GC-content values of chloroplast and mitochondrial genome fragments is considered. Spatial distribution refers to the distribution of points corresponding to genome regions in the frequency space of triplets. It was found that the values of the GC-content of fragments for most genomes are distributed not chaotically, but in an orderly manner. Two main types of distribution were found: gradient and centrally symmetric. In chloroplast genomes, only a gradient distribution occurs. In mitochondria genomes, both types of distribution occur. The type of distribution for mitochondria genomes depends on the type of organism. The spatial distribution of the GC-content is stable with respect to changes in the reading window length.

In this paper, a variant of the compartmental spiking neuron model hardware implementation on operational amplifiers is proposed. The relevance of the work is due to the growing need for both hardware implementations of neural network solutions in general and the need to develop adaptive abilities of networks, primarily to changing environmental conditions. One of the promising directions is the implementation of spike neural networks, in which the main functional element is not a neuron, but a compartment of the neuron membrane. The hardware implementation of such neuron models on a discrete element base should make it possible to facilitate experimental research in this area. The proposed solution is based on the CSNM neuron model. The paper considers the existing approaches to the hardware implementation of neuron models and selects the implementation approach on operational amplifiers. Schematics of each compartment of the implemented neuron model have been developed. Test experiments and comparison with a mathematical model were carried out, the results of which allowed us to state that the implementation reproduces the required time characteristics of signal conversion processes in a neuron quite accurately. The proposed implementation makes it possible to flexibly change the structure of the dendritic and synaptic apparatus of a neuron, and it is convenient to interpret signals for comparison with a mathematical model. The disadvantage of the proposed solution is low energy efficiency, however, for research purposes, this aspect is not critical at this stage.

Spike neural networks are a class of neural networks based on plausible neuron models. The spiking nature of such networks, in the presence of specialized accelerators, makes it possible to achieve energy efficiency values that are orders of magnitude higher than those of classical neural networks, which is especially important for integrating neural networks into autonomous systems. However, now such computers are not publicly available, so FPGAs are a good alternative. One of the classes of spike neuron models are segmental models. Segmental models, unlike point ones, allow one to consider the structure of a neuron, which in turn allows one to reproduce more complex dynamics of neural structures. Existing neuromorphic computers allow the implementation of only a limited set of spike models, which is also a reason for using FPGAs. Today, there is no work on hardware implementation of segmented neuron models, so this work is relevant. During the work, the approximation and hardware implementation of CSNM model (Compartmental spiking neuron model) on an FPGA was performed. To evaluate the performance of the resulting implementation, an IRIS data classifier was built. Based on the results, it was concluded that the resulting model has competitive indicators in terms of the amount of FPGA resources used, and the calculation speed is three orders of magnitude higher than on a computer. The accuracy of the resulting implementation is inferior to other works due to the use of a small number of neurons and rough approximation. Further research into approximation methods and incremental learning algorithms will improve accuracy. It is also planned to use RAM for scaling models and optimizing calculations. Another area of future work is implementing on-chip learning, both to speed up model testing and for reinforcement learning research.

The paper describes the creation and evaluation of the performance of a neural network model of the probability distribution density function of a random variable, given by a set of measurements of a random variable in the absence of the identification stage of the distribution law. The need to solve this problem is caused by limitations introduced into the accuracy of calculating the probability distribution density function of a random variable both by the tabular-histogram method and in the case of applying approaches to the identification of the distribution law. The problem was solved in Python using the TensorFlow neural network library by creating a neural network model based on the Sequential class with fully connected Dense layers, trained on data from numerical differentiation of the random variable distribution function. The accuracy of the forecast was estimated using the Kullback-Leibler distance measure for various ratios of the volume of experimental data and the number of interpolation intervals on synthetic test data generated for 5 laws of distribution - Rayleigh, Weibull, gamma, exponential and normal (Gaussian). To assess the predictive ability of the approach when testing the interpolator, random variable samples shifted relative to those used in training were used. The proposed solution showed a significantly higher accuracy in calculating the values of the distribution density of a random variable compared to the histogram method. The developed approach will be implemented in the modeling part of the digital twin of a business process based on the mathematical apparatus of stochastic GERT networks.

Abstract. Building knowledge bases in the form of rules, ontologies, or knowledge graphs continues to be a rather time-consuming task in the development of various domain-specific intelligent systems. This article discusses an approach and software for automating the creation of knowledge bases using the analysis and transformation of conceptual models in the form of state transition diagrams. The approach is based on the identification of structural elements of diagrams and their mapping into constructions of the target knowledge representation language. The main stages of the approach are described, as are the analyzed constructions of the considered format of state transition diagrams, as well as the implementation of the approach in the form of web-oriented software, namely, Knowledge Modeling System (KMS). An illustrative example of converting state transition diagrams to form a failure analysis plan is presented.

The article presents a modified transport problem, which takes into account the transportation of goods from suppliers to consumers over several flights, and all goods must be delivered on time. The authors give preference to linear programming problems due to the existence of various solvers that allow one to find a solution using existing methods. In this regard, a mathematical model of the transport problem was developed as an integer linear programming problem, and a solution to the problem was proposed in the Python programming environment using the PuLP library. For clarity, a simple example is considered.

An algorithm for optimizing the path length on a triangulated surface has been proposed and implemented in Wolfram Mathematica. The first two steps are “lightweight” and involve varying the path along the edges only within the triangles adjacent to them. Subsequent steps allow arriving at a shortest path in the mathematical sense in a few iterations. The convergence of the algorithm has not been rigorously proven, but has been ensured in a large number of examples considered.

The problem of energy supply to areas remote from the power grid remains relevant and is solved mainly in the modernization of diesel power plants and the construction of hybrid energy complexes with renewable energy sources. The life cycle of hybrid energy complexes is several decades, so the design must take into account all the main goals - economic and technical efficiency, minimizing environmental impacts, reliability. The multi-criteria nature of the problem requires the involvement of a decision maker to express preferences regarding the importance of performance indicators of various options for the energy complex. The stochastic nature of renewable generation and the variety of operating restrictions lead to the need to use special software for simulating operating conditions with hourly resolution. The article discusses an approach to multi-criteria selection of a hybrid energy complex from a variety of alternatives generated in the HOMER PRO program, using three methods: TOPSIS and PROMETHEE I, II. The methods have differences in the procedures for evaluating alternatives and thereby increase the validity of the choice. A numerical example is considered for the Ust-Soboleka. Hybrid energy complexes are formed using diesel generation technologies, wind power plants, photovoltaic converters, micro-hydroelectric power plants and energy storage devices. The study examines three scenarios for the development of the region, which entails differences in assessments of the importance of the criteria.

The purpose of the research presented in this article was to develop digital models for determining the melting modes of ice on the overhead wires of DC railways. The models were implemented in the Fazonord software package, version 5.3.4.9 –2024. The calculation algorithm included the following stages: determination of a series of modes determined by the train schedule, based on an approach using phase coordinates; calculations of the dependences of currents flowing through wires on time; calculation of their heating temperatures over time intervals; calculation of indicators of the process of melting ice-covered grooves; taking into account the evaporation of the water film remaining after the ice sleeve falls off; modeling of heating of wires free from ice, taking into account a possible increase in heat transfer due to drizzle or rain. The initial data necessary for the calculations are described. They include the following groups of parameters: geometric, thermal and electrical. Computer models are presented that take into account the main factors of the processes of heating and removing icing deposits on overhead wires of DC traction networks. The simulated traction power supply system included the following elements: three 110 kV supply power lines; three traction substations; two sections of 3 kV traction network with a length of 20 km. It has been shown that ice is removed from support cables in 17 minutes, and from contact wires in 22 minutes. The heating temperatures of current-carrying parts during melting do not exceed permissible values. The temperatures of the hottest points of traction transformers were determined. It has been shown that melting does not cause unacceptable overheating of transformers. The technique is universal and can be used for traction networks of any design.

This paper presents the technique of decision making support in territory management based on the method of integral estimation of the life quality. A model of management recommendations production based on the analysis of the current state of life quality is proposed. The Internet platform for municipalities monitoring and rating assessment of the life quality of territories in the context of the national projects is presented. The results of a study of rating assessment of the life quality of Krasnoyarsk region territories are presented.

In the paper, an approach for project an optimal wireless sensor network indoors for the technology of the Internet of Things is proposed. To improve the energy efficiency of the network is used a hybrid network structure based on Wi-Fi and ZigBee standards. The advantage of the approach is that the network is designed on a three-dimensional model of the building, given the attenuation of the signal not only in the walls, but also in the floors. The combination of radio-wave (Motley-Keenan model) and optimization (genetic algorithm) methods for optimal arrangement of connecting and sensory nodes is used.

This article describes the process of creating an application system for the KSC SB RAS using the following technologies and tools: vue, express, node, sequelize, redis and primevue. The article discusses in detail the architecture of the application “Application accounting system for IT departments of the KSC SB RAS”, including the client and server parts, data caching system and user interface. The creation of such a system ensures high performance and ease of use for users.

Results related to the developed earlier Boolean constraint method for studying the dynamics and parametric synthesis of control systems, namely, Boolean networks, in a microservice infrastructure using knowledge base tools, are presented. The computational model of the subject area acts as a knowledge base, which is understood as a set of information about the subject area objects and the relationships between them. Each functional relationship is implemented by a computational microservice created based on a software module that calculates the values of the output parameters from the given values of the input parameters. A set of computational microservices constitutes the functional software of an applied microservices package. The system software consists of services for setting the task, planning and monitoring calculations, data management, and processing results. Agents of the applied microservices package, depending on the problem statement and the knowledge base organization, carry out computing management (decentralized, centralized or hierarchical). In connection with the studying of new classes of Boolean networks (controlled, singular, implicit, asynchronous, bipartite, and others), we are extending the earlier created applied microservices package based on the above approach and intended for solving the problems of qualitative analysis of autonomous Boolean networks. The aim of the study is to develop a new toolkit for the HPCSOMAS-MSC microservice intelligent computational platform for creating, configuring and accessing computational microservices, which allows interacting with package microservices directly through a web interface. A web interface for the subject area description is implemented in addition to the existing one based on the JSON language. The new toolkit allows both to speed up the development and debugging of microservices, and to make further interaction more convenient for the subject area specialist.

The authors study the process of text translation, particularly the method of optimizing pre-editing as a way to improve the quality of machine translation into English for Russian-language highly specialized texts. The paper considers the mathematical model of translation process and machine translation task formulation, proposes a new theory for probabilistic estimation of translation task complexity, provides the formulation and solution of optimizing pre-editing task, describes data preparation methodology for training automatic optimizing pre-editing model. As the research result the software package for optimizing pre-editing of Russian-language texts is developed. The software package has been developed using resources of the Center for Scientific Equipment Collective Use "Center for Processing and Storage of Scientific Data of the Far Eastern Branch of the Russian Academy of Sciences". Data for models training and validation are provided by Translation Agency FIAS-Amur Co., Ltd. Software package testing has proved the effectiveness of the proposed methods for improving the quality of machine translation of highly specialized Russian-language texts into English.