2023 | Buch

# Current Problems in Applied Mathematics and Computer Science and Systems

herausgegeben von: Anatoly Alikhanov, Pavel Lyakhov, Irina Samoylenko

Verlag: Springer Nature Switzerland

Buchreihe : Lecture Notes in Networks and Systems

2023 | Buch

herausgegeben von: Anatoly Alikhanov, Pavel Lyakhov, Irina Samoylenko

Verlag: Springer Nature Switzerland

Buchreihe : Lecture Notes in Networks and Systems

This book is based on the best papers accepted for presentation during the International Conference on Actual Problems of Applied Mathematics and Computer Systems (APAMCS-2022), Russia. The book includes research materials on modern mathematical problems, solutions in the field of scientific computing, data analysis and modular computing. The scope of numerical methods in scientific computing presents original research, including mathematical models and software implementations, related to the following topics: numerical methods in scientific computing; solving optimization problems; methods for approximating functions, etc. The studies in data analysis and modular computing include contributions in the field of deep learning, neural networks, mathematical statistics, machine learning methods, residue number system and artificial intelligence. Finally, the book gives insights into the fundamental problems in mathematics education. The book intends for readership specializing in the field of scientific computing, parallel computing, computer technology, machine learning, information security and mathematical education.

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The processes occurring at the interface of metal with organic dielectric media have a wide practical application in various devices. The features of the metal-organic interface make it possible to create materials with practically useful properties used in catalysis, energy storage, electronics, gas storage and separation, magnetism, nonlinear optics, etc. Knowing the course of the potential at the phase interface, it is possible to obtain interphase characteristics, including interphase energy. In this paper, the dependence of the potential on the permittivity is modeled in the framework of a modified version of the Frenkel–Gambosch-Zadumkin electron-statistical theory at the metal–dielectric medium boundary. The course of the dimensionless potential at the interface is obtained and it is shown that the greater the dielectric constant of the medium, the more the dimensionless potential drops at the physical interface. The coordinate of the Gibbs interface for the metal–dielectric medium system is obtained, which can be found from the condition of electroneutrality at this boundary. It is shown that with an increase in the value of the permittivity, the Gibbs coordinate increases, that is, it shifts towards the dielectric medium. The dependence of the interfacial energies of faces with different structures on the dielectric permittivity is shown.

The work is devoted to a numerical method for solving the Dirichlet problem for a multidimensional integro-differential convection-diffusion equation with variable coefficients. Using the method of energy inequalities for solving the first initial-boundary value problem, a priori estimates are obtained in differential and difference interpretations. The obtained estimates imply the uniqueness and stability of the solution of the original differential problem with respect to the right-hand side and initial data, as well as the convergence of the solution of the difference problem to the solution of the original differential problem at a rate of $$O(|h|+\tau )$$ O ( | h | + τ ) . For an approximate solution of the differential problem, an algorithm for the numerical solution was constructed, and numerical calculations of test examples were carried out, illustrating the theoretical calculations obtained.

In this paper, we demonstrate the application of the analytical apparatus of representing functions by their singular integrals for developing numerical methods by interpreting approximate data in the problem of correctly restoring the studied functional dependencies. Such approach significantly extends the substantive basis of the apparatus for approximating functions in problems, where it is necessary to build a model of the functional dependence, which depends on approximate data. The main goal of this article is to provide the restoring of the real-valued functions $$f=\left\{f\left({x}_{0}\right),f\left({x}_{1}\right),\text{...},f\left({x}_{m}\right)\right\}$$ f = f x 0 , f x 1 , ... , f x m , associated with discrete sequence of points $${\left\{{x}_{k}\right\}}_{k=0}^{m}$$ x k k = 0 m on $$\left[a,b\right]$$ a , b , using generalized kernel $$\left({K}_{n}f\right)\left(x\right)$$ K n f x . We will demonstrate the theoretical calculations of restoring of the unit approximation, which is able to increase the accuracy of approximations. In the end of our research, the application of proposed approximation is used for solving optimization problem, where rising of the accuracy with minimal time computations plays an important role.

Due to absence of long carry propagation logic in its modular adders and multipliers Residue Number System (RNS) provides advantages for performing arithmetic computations in the hardware accelerators targeting multiplications and additions only. However, a conversion from RNS to Binary Number System (BNS) is a well-known complex operation requiring larger hardware area and consuming more power than modular multipliers which significantly limits applicability of RNS. Many non-modular operation (e.g. comparison, division) implementations are also based on reverse conversion. In this article we demonstrate a variation of Chinese Reminder Theorem (CRT) based algorithm for RNS to BNS reverse conversion for an arbitrary moduli set. We propose an approximate method to overcome the heaviest $$mod\;M$$ m o d M operation via the rank of number calculation and demonstrate its correctness on the covered number range. We show that algorithm parameters selection has no restrictions on moduli set and needed parameters can always be found assuming that covered maximum value is less than $$M - 1$$ M - 1 . Hardware implementation of the new RNS reverse conversion algorithm based on CRT is more than 30% faster and consumes up to 80% less power than implementations of CRT based reverse conversion algorithms using other known ways to compute the final reduction operation.

The paper considers non-isothermal anomalous solute transport in an inhomogeneous porous medium consisting of two zones with different filtration-capacitive properties and characteristics of the solute transport. In contrast to the approaches that are used in the theory of interpenetrating continuums for the problems of filtration, solute transport, one medium is considered here, the solute transport to another medium in the corresponding equations is taken into account through the source (sink) term in the form of a fractional time derivative of the concentration of the solute. In the study, we investigate replaced bicontinuum medium by multicontinuum medium.

In this paper, we posed and numerically solved the inverse problem of determining the relaxation coefficient and the flow coefficient in a simplified model of relaxation filtration of a homogeneous fluid in fractured-porous media. To solve the problem, a regularizing identification method was used. It has been established that these coefficients, at various initial approximations with unperturbed initial data, are restored in almost ten to twenty iterations. At a more remote initial approximation from the equilibrium point, the iterative procedure converges to the shifted values of the desired parameters. The optimal range of regularization parameter values is determined.

The problem of anomalous filtration and solute transport in a two-dimensional formulation is posed and numerically solved. It is considered that the medium has a fractal structure. The fractional order piezoconductivity equation based on anomalous Darcy's law, porosity and fluid density equations of state and continuity equation are proposed. The initial and boundary value problem for the system of equations consisting of the balance equation expressed in relation to the concentration of solids in suspension, fractional order piezoconductivity equation and Darcy's anomalous law is solved by finite difference method. The effect of the order of fractional derivative in the anomalous Darcy law on the filtration characteristics of the medium is evaluated. The fields of alteration in concentration, pressure and filtration velocity are determined.

The paper is devoted to the issues of efficient calculation of important characteristics of parallelepipedal nets with optimal coefficients. On the class $$E_s^\alpha $$ E s α of periodic functions, the norm of the linear error functional of approximate integration using quadrature formulas with parallelepipedal nets with optimal coefficients is expressed in terms of the hyperbolic zeta function of the corresponding lattice of linear comparison solutions. For the hyperbolic zeta function of lattices of linear comparison solutions, important estimates of N. S. Bakhvalov from above and from below through the hyperbolic lattice parameter are well known. The paper discusses an efficient algorithm for calculating the hyperbolic parameter of a two-dimensional lattice of linear comparison solutions that requires $$O(\ln N)$$ O ( ln N ) arithmetic operations. The basis of the algorithms under consideration are Euler brackets, which L. Euler used back in the XVIII century. The term itself was proposed by K. F. Gauss in his famous “Arithmetic studies”. It was actively used by P. G. Lejeune Dirichlet. Currently, the term continuant is often used. Such use violates historical justice. Currently, in the two-dimensional case, most algorithmic problems have been solved in the optimal coefficients method, although dense sequences of parallepipedal nets with increasing sequences of hyperbolic parameter values and limited values of Sharygin constants have not yet been constructed.

In this paper, we consider the inverse problem of identifying the retardation coefficient of a parabolic differential equation describing the solute transport in a porous medium, taking into account equilibrium adsorption, advection-diffusion, convection and decomposition (decay) of solute transport. Concentration time curves at given three points of the medium are used as initial data. The retardation coefficient is determined by minimizing the quadratic discrepancy functional. On the basis of a quasi-real experiment, it is shown that the discrepancy parameter can be restored with sufficient accuracy.

The process of anomalous solute transport in a porous medium is modeled by differential equations with a fractional derivative. The problem of the solute transport in a two-zone porous medium consisting of macropores and micropores. The profiles of changes in the concentrations of suspended particles in the macropore and micropore were determined. The influence of the order of the derivative with respect to the space and time coordinates is estimated, i.e. fractal dimension of the medium, on the characteristics of the solute transport in both zones.

Boundary-value problems for the loaded Hallaire equation with variable coefficients and Gerasimov-Caputo fractional derivatives of different orders are studied. Using the method of energy inequalities for various relations between $$\alpha $$ α and $$\beta $$ β , a priori estimates in differential and difference interpretations are obtained for the solution of the problem under consideration, from which the uniqueness and stability of the solution with respect to the initial data and the right-hand side, as well as the convergence of the solution of the difference problem to the solution of the differential problem.

This paper is devoted to the study of local and nonlocal boundary value problems for a loaded moisture transfer equation with two fractional Gerasimov-Caputo derivatives of different orders $$\alpha $$ α , $$\beta $$ β . Using the method of energy inequalities for various relations between $$\alpha $$ α and $$\beta $$ β , a priori estimates in differential and difference interpretations are obtained for solving the problems under consideration, which implies the uniqueness and stability of the solution with respect to the initial data and the right-hand side, as well as the convergence of the solution of the difference problem to the solution of the differential problem with the rate $$O(h^2+\tau ^2)$$ O ( h 2 + τ 2 ) for $$\alpha =\beta $$ α = β and $$O(h^2+\tau ^{2-\max \{\alpha ,\beta \}})$$ O ( h 2 + τ 2 - max { α , β } ) for $$\alpha \ne \beta $$ α ≠ β .

The longitudinal vibrations of a steel rod of constant cross-section along the length are considered. The left end of the rod is pinched, a concentrated mass is attached to the right end. The mathematical model consists of a hyperbolic partial differential equation and boundary conditions. The D'Alembert's principle is used. Free oscillations are undamped and harmonic without initial conditions. The purpose of solving the problem is to determine the frequencies of free oscillations. Analytical and numerical-graphical methods of solving the problem are used. In the first case, the oscillation frequency is determined from the transcendental equation. In the second case, the basic equation and boundary conditions are replaced by a system of algebraic equations. The required oscillation frequencies are defined as the eigenvalues of a square matrix. At the final stage of determining the frequencies of free oscillations, a numerical-graphical method is used, implemented in the environment of the Matlab computing complex. A concrete example of the solution is given. Conclusions are drawn.

Forced longitudinal vibrations of a steel rod of constant cross-section along its length are considered. The left end of the rod is pinched, a concentrated mass is attached to the right end. The source of the oscillations is the harmonic force acting along the axis. The mathematical model consists of a hyperbolic partial differential equation and boundary conditions. The D'Alembert's principle is used. Forced oscillations are undamped and harmonic without initial conditions. The amplitudes of forced oscillations are determined, their dependences on the frequency of the driving force are analyzed. Analytical and numerical-graphical methods of solving the problem are used. In the first case, by traditional methods, the problem is reduced to a transcendental equation, from which the amplitude of the oscillations is determined. In the second case, the basic equation and boundary conditions are replaced by a system of algebraic equations. The desired oscillation amplitudes are determined from the matrix-vector equation. At the final stage of determining the amplitudes, a numerical-graphical method is used, implemented in the environment of the Matlab computing complex. Examples are given. Conclusions are drawn.

The main object of the present work is to derive new relations between the number of n-order non-associated matrices and a determinant N, which can subsequently be put into use. In this study we mainly employ the Hermite triangular form of n-order full matrices and the determinant N. The following new results are obtained in the work: 1. formula for $$\sigma _0 \left( n, p_1 \cdot \dots \cdot p_k\right) $$ σ 0 n , p 1 · ⋯ · p k n-order non-associated primitive matrices with non-square determinants values $$N=p_1 \cdot \dots \cdot p_k$$ N = p 1 · ⋯ · p k , where $$p_i$$ p i are primes; 2. formula for $${\sigma }_0 \left( n, p^{\alpha } \right) $$ σ 0 n , p α primitive non-associated n-order matrices $$N=p^{\alpha }$$ N = p α , where p is a prime; 3. the recurrent relations is established for $${\sigma }_0 \left( n, N\right) $$ σ 0 n , N by order of matrices considered; 4. an upper estimate for the number of the considered n order matrices and the determinant is obtained close to the precise value of $$\sigma (n, N)$$ σ ( n , N ) in the case where the canonical expansion of N is not given; 5. the relationship between $$\sigma \left( n, p^{\alpha } \right) $$ σ n , p α as well as $${\sigma }_0 \left( n, p^{\alpha } \right) $$ σ 0 n , p α and the Gaussian coefficients by combinatorics is established.

This work is devoted to the construction and analysis of search algorithms for two-dimensional parallelepipedal nets with the best parameters. The paper presents algorithms for computing the hyperbolic parameter, Bykovskii sums, and the H-function. Sequences of the best lattices are compared for each parameter. The connection between the lattices parameters (N, a) and the value of the hyperbolic parameter is investigated. In particular, the relationship between the value of a hyperbolic parameter and the representation of the number a/N as a continued fraction is shown. For lattices with an increasing hyperbolic parameter, a conjecture is put forward about the structure of the continued fraction representation of the number a/N.

The article considers issues related to the implementation of energy-efficient power supply modes for high-pressure discharge lamps (HID lamps). In comparison with the standard AC power supply mode, the proposed DC power supply approach with a cyclic change in the polarity of the supply voltage allows to increase the light output by up to 20%. The purpose of the article is to develop a mathematical model of a regulated DC source necessary for controlling the light flux during operation. The developed model reflects the dependence of the effective value of the load voltage on the ratio of the load resistance to the internal resistance of the power supply, the conditional frequency and the fill capacity factor when powered from a single-half-period rectifier. The presented model makes it possible to optimize the mode of changing the electrical parameters of the electronic ballast when regulating the light flux of high-pressure discharge lamps. The model was tested by simulation modeling in the Multisim environment, which showed the high efficiency of the obtained dependencies. The use of the developed mathematical tools in the design of electronic ballast devices will make it possible to effectively control the light output. This mode can be used for lighting industrial greenhouse complexes.

Of great interest is the study of the influence of various factors on the surface characteristics of metallic crystals in contact with organic matter. The features of this interface allow you to create materials with practically useful properties used in various devices. A significant contribution to the surface characteristics of metals is made by free electrons, which at room temperature have sufficient energy of thermal motion to leave the atom and move freely in the crystal lattice. Such electrons do not experience collisions with ion cores and do not deviate from rectilinear motion at distances much larger than the constant lattice, since the ions are located in a regular periodic lattice in which electron waves propagate freely. They also rarely scatter on other conduction electrons due to the Pauli principle. A set of non-interacting free electrons in metals form an electronic liquid. In this paper, a modified version of the electron – statistical method for calculating the temperature contribution to the interfacial energy of metals at the boundary with nonpolar organic liquids is developed. The dependence of the temperature contribution to the interphase energy on the dielectric constant of the liquid and the orientation of the metal crystal are obtained.

The identification of an internal violator is becoming more and more relevant with the development of information processing technologies, the security of technical and software complexes in information systems is increasing, and the person remains the most vulnerable place. An employee who processes information and has full access to it becomes the target of an attacker, as well as he himself may be an intruder and become a source of leakage of confidential information. The analysis of data about the employee allows us to make assumptions about his emotional state, willingness to honestly do the job. The collected data requires analysis according to their type, and this is what the work is dedicated to. Data from video surveillance cameras is analyzed to identify the time of the employee's appearance and his location during working hours. The metadata obtained is intended to create a model of an internal violator, followed by an assessment of the threat level emanating from the employee.

The development of a decentralized type of management for military use, searching, exploration and monitoring actualizes issues of providing information security in swarm robotics systems. One of the unique and complex problems of information security in swarm robotics is the possibility of negative influence of Byzantine robots on collective decision-making, by voting during consensus for false alternatives. Existing studies are focused on the consideration by the Byzantine robots with the strategy of the behavior “against most” in the tasks with a binary choice. However, practical tasks often have a greater number of alternatives to the choice, and Byzantine robots are a greater diversity of the impact strategies on consensus achievement. This work is devoted to the study of the influence of Byzantine robots with a random strategy of behavior if there are two to five alternatives to the process of collective decision-making in swarm. The purpose of the study is to identify the laws of the influence of Byzantine robots with a random strategy of behavior on the effectiveness of rotary robotic systems. Modeling the operation of the swarm robotics system in the presence of Byzantine robots with random behavior and an assessment was made to reduce the effectiveness of consensus. The practical significance of the study lies in the laws received and information that can be used in the development and justification of the effectiveness of information security systems in swarm robotics systems.

Due to the proliferation of hand-held devices, such as smartphones and other wireless communication devices, spectrum and capacity in the field of wireless communication technology have become more scarce in recent decades. Long Term Evolution (LTE) and Long Term Evolution Advanced (LTE-A), often known as 4G, are the most recent addition to the rapidly expanding wireless technology as a result of the researchers’ continued exploration of these technologies. In order to boost cell capacity, numerous tiny cells (femtocells, picocells) are placed next to larger macrocells in the mobile and associated networks being built around 4G and succeeding next generation technologies. The problem of interference and associated phenomena, which emerges owing to the mass roll out of smaller cells near huge macro cells, is one of the negative elements that stands as a barrier to this technology. One answer to the interference problem in dense networks is beamforming. In an effort to illustrate the interference issue in LTE/LTE-A dense networks, this study attempts to do so. As a response to the interference scenario, several beamforming techniques that help to lessen interference have been highlighted. A discussion of some of these beamforming techniques that have been previously suggested and made available in other works of literature is also included in this study.

The downlink Channel State Information (CSI) is necessary for the precoder design in a massive multiple input multiple output (MIMO) system. This CSI, generally estimated at the user equipment (UE) is feedback to the base station (BS) by frequency division duplexing (FDD) which is a bandwidth consuming technique. In a massive MIMO system, the large antenna array size at BS may cause such feedback overhead to be very overwhelming. It is therefore necessary to utilize appropriate CSI compression with low computational complexity and high accuracy. This paper discusses a neural network based CSI compression method based on intrinsic properties of CSI and with a novel activation function. Named as CLNet+, the simulation results shows that the proposed method outperforms the existing CS-based and some DL-based methods.

The occurrence of widespread fatality, inadequate medical infrastructure and the infectious nature of the COVID-19 virus have necessitated the formulation of appropriate risk minimization methods including extensive use of technology. In the absence of effective antiviral and limited medical resources, among the measures recommended by the World Health Organization (WHO), wearing a mask is considered to be an effective non-pharmaceutical intervention that can be used to prevent the spread of the COVID-19 virus. Hence proper wearing of the mask and its effective monitoring in public placed for reliable enforcing of the community level protocol, adoption of technology becomes crucial. To contribute towards communal health, this paper aims to report the design of an accurate and real-time technique that can efficiently detect non-mask faces in public and thus, suggest ways to formulate measures for enforcing proper wearing of the mask. Among many such technologies, internet of things (IoT) and artificial intelligence (AI) have emerged as viable ones as these combine a host of sensor packs, wireless communication based networking and automated decision making. Further emerging applications involving edge computing, deep learning (DL) and Deep Transfer Learning (DTL) have enabled IoT to take part in a decisive role in the health care sector and help to minimizing damages related to pandemic situations. The presented framework is based on Artificial Neural Network (ANN) tools that use hand–crafted feature samples and DL techniques like Convolutional Neural Network (CNN) and a specialized CNN called YOLO and Support Vector Machine (SVM) classifiers. Here MobileNet has been used as a baseline method which is extended by applying the concept of transfer learning to fuse high-level semantic information in multiple feature maps with samples from Real World Masked Face Dataset. In addition, we also propose a bounding box transformation to improve localization performance during mask detection. It is observed that the proposed technique achieves high accuracy (97.2%) when implemented with MobileNet.

In paper, consider nonparametric algorithms for the identification and control of multidimensional discrete-continuous processes that are typical for many practical problems. The main feature of the considered multidimensional systems is the presence in them of stochastic dependences of both input and output variables. Under such conditions, the mathematical description of such objects leads to a system of implicit equations. Nonparametric algorithms for modeling and control for multidimensional systems are proposed, as well as the subsequent implementation of software-based on these algorithms in production.Attention should be paid to the fact that the modeling of such processes is reduced to the search for the predicted values of the output variables for the known input. Moreover, for implicit equations, it is only known that one or another input variable can depend on other input and output variables that determine the state of a multidimensional system. The subsequent control of multidimensional systems is considered in conditions of insufficient a priori information about the object of research. The main component in the control problem is the determination of the reference influences, for the search of which a nonparametric algorithm is used. The essence of this algorithm is to find a common area of intersection of the values of the output variables, which will satisfy all components of the output vector. When implementing software, it is necessary to take into account information security issues, especially for three key tasks: process control, archiving (saving history) of technological parameters and working with alarms. This article provides some guidelines for implementing safeguards for archiving and alarms.

The article explores the option of using information theory’s mathematical tools to model artificial neural networks. The two primary network architectures for image recognition, classification, and clustering are the feedforward network and convolutional networks. The study investigates the use of orthogonal transformations to enhance the effectiveness of neural networks and wavelet transforms in convolutional networks. The research proposes practical applications based on the theoretical findings.

For commercial organizations, the issue of tolerance and loyalty of employees is always relevant, since it is closely related to the issue of leakage of trade secrets from those who have access to it. Thus, the identification of an internal violator is becoming increasingly relevant in the development of information processing technologies, when in the information systems of the organization the most vulnerable place remains a person. An employee who processes information and has full access to it, becomes the target of an attacker, and can also be an intruder and become a source of leakage of confidential information. Analysis of metadata about the current psycho-emotional state of the employee with the help of digital technologies allows you to make an assumption about his current and future emotional state, readiness to honestly perform work and predict the likelihood of this employee or violate the law on trade secrets. Thus, the security department of the company, having collected metadata and analyzing them, is able to prevent the threat and get before the leak a certain probability of malicious intent for each employee, and this will increase the security of information.

With the development of next-generation information technologies, especially big data and digital twins, the topic of building smart cities is increasingly dominating discussions about social change and economic performance. The purpose of this article is to analyze methods for building digital twins of a smart city. The paper describes the concepts underlying digital twins. Examples of the implementations of methods for building digital twins are investigated. Advantages of data mining and neural network modeling over other methods in the context of the considered characteristics are revealed. Based on the comparative analysis, it is shown that all methods can be complementary, as they are aimed to optimize processes, as well as predict and analyze problems.

In this paper, we study methods for correcting errors in the system of residual classes. Traditional correction codes have disadvantages, such as Reed-Solomon codes have a large redundancy, others have either the same disadvantages or have greater computational complexity. The residue number system has self-correcting properties that have less redundancy and computational complexity. Thus, error detection methods were considered. Based on the study, it was found that the most effective method for detecting errors is the nullivisation method.

In this paper, research is carried out to ensure the security of cloud storages. The work is devoted to homomorphic encryption. Even though the very concept of homomorphic encryption appeared in the late 70s, a fully homomorphic encryption scheme was obtained only in 2009. Since that time, a variety of fully homomorphic encryption schemes have been developed. In this paper, we analyze the most popular encryption schemes, as well as their software implementations. As a result of the study, it was found that the most promising scheme is CKKS. This scheme can perform homomorphic arithmetic on rational numbers, and already has several software implementations distributed under a free license.

The spread of cloud technologies has made it possible to increase the efficiency and flexibility of computer networks, as well as information storage. However, the decentralized structure and the large geographical distance of data processing centers imposes an additional burden on the infrastructure of such technologies. Both in big data streams and in the processing of information on nodes, an error often occurs, which reduces the reliability of the structure. In this work, we have developed a model of an error correction device in the residue number system using finite ring neural networks. The result of this work is to increase the efficiency of error handling, which in turn increases the reliability of the system.

Today, the use of artificial intelligence technologies is becoming more and more popular. Scientific and technological progress contributes to increasing the power of hardware, as well as obtaining effective methods for implementing methods such as machine learning, neural networks, and deep learning. This created the possibility of creating effective methods for recognizing images and video data, which is what computer vision is. At the time of 2022, a huge number of methods, technologies, and techniques for using computer vision were received, in this paper a study was conducted on the use of computer vision in 2022. Results were obtained on the decrease in the popularity of computer vision in the scientific community, its introduction into industry, medicine, zoology and human social life, the most popular method of computer vision is the ResNet neural network model.

The paper considers bidirectional associative memory, which is one of the known neural network paradigms. To simplify the implementation of the calculation of this paradigm, a discrete mathematical model of its functioning is proposed. Reducing the complexity is achieved by switching to integer calculations because Integer multiplication is several times simpler than real multiplication. The known neural network of bidirectional associative memory neural network was compared with the proposed one. The simulation was carried out in the VHDL language. For comparative evaluation, Spartan3E, Spartan6 and XC9500 chips were used. In the experimental part, it was shown that the hardware costs for the implementation of the neural network of bidirectional associative memory have decreased by more than 3 times compared to the known one. The proposed discrete model of BAM functioning does not narrow the scope of its application in comparison with the known model and can be used to build memory devices and restore distorted or noisy information.

Digital signal processing requires the calculation of large data volume. To increase the speed of data processing, a Residue Number System is used. This number system provides performing calculations in parallel, reducing time costs. In practice, moduli of the Residue Number System of a special form ( $$2^{k} ,2^{k} - 1,2^{k} + 1$$ 2 k , 2 k - 1 , 2 k + 1 ) are most often used. The article proposes a method for calculating modulo $$2^{k} + 1$$ 2 k + 1 using the Diminished-one coding technique and developed the Inverted End-Around Carry Truncated Multiply-Accumulate unit (IEAC-TMAC). This approach increases the number of moduli, affecting a decrease in the capacity of the moduli and the delay. Hardware modeling showes that, compared with the existing varieties of TMAC blocks, the proposed block demonstrates worse results in terms of hardware costs by 27–231%, depending on the block being compared. However, using two blocks of 2 times less bit width of the form $$(2^{k} - 1,2^{k} + 1)$$ ( 2 k - 1 , 2 k + 1 ) provides reducing the occupied area of a device in comparison with the modulo $$(2^{2k} - 1)$$ ( 2 2 k - 1 ) by 24–48% times and decreasing the execution speed by 1.20–1.24 times. A promising direction for further research will be the development of digital signal processing devices with moduli of a special type ( $$2^{k} ,2^{k} - 1,2^{k} + 1$$ 2 k , 2 k - 1 , 2 k + 1 ).

Skin cancer is currently one of the most common types of human cancer. Due to similar morphological manifestations, the diagnosis of malignant neoplasms is difficult even for experienced dermatologists. Artificial intelligence technologies can equal and even surpass the capabilities of an oncologist in terms of the accuracy of visual diagnostics. The available databases of dermoscopic images and statistical data are highly unbalanced about “benign” cases. When training neural network algorithms on unbalanced bases, there is a problem of reducing the accuracy and performance of models due to the prevailing “benign” cases in the samples. One of the possible ways to solve the problem of unbalanced learning is to modify the loss function by introducing different weight coefficients for the recognition classes. The article proposes a neural network system for the recognition of malignant pigmented skin neoplasms, trained using a modified cross-entropy loss function. The accuracy of recognition of malignant neoplasms of the skin in the proposed system was 88.12%. The use of the proposed system by dermatologists-oncologists as an auxiliary diagnostic method will expand the possibilities of early detection of skin cancer and minimize the influence of the human factor.

Solving the problem of pattern recognition is one of the areas of research in the field of digital video signal processing. Recognition of a person’s face in a real-time video data stream requires the use of advanced algorithms. Traditional recognition methods include neural network architectures for pattern recognition. To solve the problem of identifying singular points that characterize a person’s face, this paper proposes a neural network architecture that includes the method of scale-invariant feature transformation. Experimental modeling showed an increase in recognition accuracy and a decrease in the time required for training in comparison with the known neural network architecture. Software simulation showed reliable recognition of a person’s face at various angles of head rotation and overlapping of a person’s face. The results obtained can be effectively applied in various video surveillance, control and other systems that require recognition of a person’s face.

Wavelets are actively used for solving of image processing problems in various fields of science and technology. Modern imaging systems have not kept pace with the rapid growth in the amount of digital visual information that needs to be processed, stored, and transmitted. Many approaches are being developed and used to speed up computations in the implementation of various image processing methods. This paper proposes the Winograd method (WM) to speed up the wavelet image processing methods on modern microelectronic devices. The scheme for wavelet image filtering using WM has been developed. WM application reduced the computational complexity of wavelet filtering asymptotically to 72.9% compared to the direct implementation. An evaluation based on the unit-gate model showed that WM reduces the device delay to 66.9%, 73.6%, and 68.8% for 4-, 6-, and 8-tap wavelets, respectively. Revealed that the larger the processed image fragments size, the less time is spent on wavelet filtering, but the larger the transformation matrices size, the more difficult their compilation and WM design on modern microelectronic devices. The obtained results can be used to improve the performance of wavelet image processing devices for image compression and denoising. WM hardware implementation on a field-programmable gate arrays and an application-specific integrated circuits to accelerate wavelet image processing is a promising direction for further research.

In this paper, extending the set of low-cost modules with modules of $$2^{k} + 1$$ 2 k + 1 form, which are considered next in the complexity of implementation after modules of $$2^{k} - 1$$ 2 k - 1 proposed to consider. An experiment was carried out on the construction of various RNSs for the ranges from 16 to 64 bits and the number of modules from 3 to 8. The results of the experiment showed a significant increase in parallelism and improvement in the balance of RNS with modules of the $$2^{k}$$ 2 k , $$2^{k} - 1$$ 2 k - 1 and $$2^{k} + 1$$ 2 k + 1 forms, compared to using only modules of the $$2^{k}$$ 2 k and $$2^{k} - 1$$ 2 k - 1 forms. In the discussion of the experiment, we raised the questions of more effective measurement of the balance of the RNS, as well as the problem of using the diminished-1 encoding. This problem is a subject to a thorough study both at the theoretical level, for example, using a unit-gate model, and practical tests on modern FPGA and ASIC microelectronic devices.

In this paper, a method for denoising an uncoded video stream in a binary symmetric channel is considered. When a bit of information is damaged, noise similar to impulse noise occurs with a certain probability. This work considers a model for transmitting visual data through a binary symmetric channel, where the noise characteristic corresponds to impulse noise distributed over the image with random values. Both random variables are distributed uniformly, both in brightness and in spatial location. In the proposed method, the distorted pixel is detected by comparing pixels inside the filter mask. Pixels are compared by their brightness value, and the remoteness of pixels within the detector area is also taken into account. The distance between pixels is calculated using the Euclidean metric. The local area of the filter takes into account pixels from the previous and next frames. Video frame recovery is performed using adaptive median filtering. A comparison was made with known methods. Based on the mean square error (MSE) and structural similarity index (SSIM) characteristics, it was shown that the proposed method copes with the task of denoising visual data better than the known methods.

Skin cancer is the most common cancer in humans today and is usually caused by exposure to ultraviolet radiation. There are many diagnostic methods for visual analysis of pigmented neoplasms. However, most of these methods are subjective and largely dependent on the experience of the clinician. To minimize the influence of the human factor, it is proposed to introduce artificial intelligence technologies that have made it possible to reach new heights in terms of the accuracy of classifying medical data, including in the field of dermatology. Artificial intelligence technologies can equal and even surpass the capabilities of an dermatologists in terms of the accuracy of visual diagnostics. The article proposes a web application based on a multimodal neural network system for recognizing pigmented skin lesions as an additional auxiliary tool for oncologist. The system combines and analyzes heterogeneous dermatological data, which are images of pigmented neoplasms and such statistical information about the patient as age, gender, and localization of pigmented skin lesions. The recognition accuracy of the proposed web application was 85.65%. The use of the proposed web application as an auxiliary diagnostic method will expand the possibilities of early detection of skin cancer and minimize the impact of the human factor.

The paper deals with the short-term forecasting problem of the temperature profile based on observational data. The MTP-5 temperature profiler is the observational data source. This remote sensor provides measurement of the temperature profile in the surface layer of the atmosphere with a high spatiotemporal resolution. Measurement data is considered as a multivariate time series. We use a temporal convolutional neural network (TCN) to prediction such a series. A quality analysis of the temperature profiles forecast for several hours using TCN is presented.

Cardiac diseases are one of the most common diseases on the planet. Thousands of people die from this disease every year. For prompt diagnosis, an automated system for processing electrocardiograms is required. The standard model of an automated system consists of signal preprocessing, feature extraction, and classification. In this article, unidirectional and bidirectional network models with long short-term memory were considered for the classification of electrocardiogram signals. The simulation results showed that the use of both methods without preliminary signal processing and feature extraction on them is not advisable. Also, the simulation result showed that models that include the removal of noise from electrocardiograms have more accurate training results for bidirectional networks with a long short-term memory. The simulation was carried out in the MatLab 2020b mathematical environment based on the PhysioNet Computing in Cardiology Challenge 2017 database, taken from an open source. The best result was obtained in the classification of atrial fibrillation.

Cyber-physical systems are widely used. Nevertheless, security issues are quite acute for them. First of all, because the system must work constantly without downtime and failures. The Cyber-Physical System (CPS) must quickly transfer the parameters to the monitoring system, but if the system is not flexible enough, fast and optimal, then collisions and additional loads on the CPS may occur. This study proposes a system for monitoring and detecting anomalies for CPS based on the principles of trust, which allows you to verify the correctness of the system and detect possible anomalies. In our study, we focus on traffic analysis and analysis of the CPU operation, since these parameters are the most critical in the operation of the CPS itself. The technique is based on computationally simple algorithms and allows to analyze the basic parameters that are typical for most CPS. These factors make it highly scalable and applicable to various types of CPS, despite the fragmentation and a large number of architectures. A distributed application architecture was developed for monitoring and analyzing trust in the CPS. The calculation results show the possibility of detecting the consequences of the influences of denial-of-service attacks or CPS. In this case, three basic parameters are sufficient for detection. Thus, one of the features of the system is reflexivity in detecting anomalies, that is, we force devices to independently analyze their behavior and make a decision about the presence of anomalies.

The article has considered approach to ships collision avoidance problem for infinite time horizon in unpredictable navigation environment on the basis of guaranteed safe states in speed space. The possible collisions areas are determined on the basis of the reachable sets of target vessels in the speed space. By avoiding getting into the possible collisions area of each target vessel, the controlled vessel prevents any possible collision, while not having explicit information about the expected trajectories of the target vessels. The safety of navigation is achieved by a combination of reachable sets as functions of time for target vessels, taking into account their dynamic capabilities and the representation of sets in speed space. The control option, which is outside the reachable set of the target vessel in the speed space, is guaranteed to prevent a collision even under conditions of unpredictable motion of the target vessel. On the basis of the target vessels reachable sets in speed space the guaranteed safe states of controlled vessel are defined. Recommendations for practical use have been given. Performed researches contribute to the improvement of the ship’s handling methods.

One of the most common types of cancer in the world is lung cancer, which is a cause of increasing mortality. It is most often discovered in the middle and later stages as it does not have obvious symptoms due to which its treatment is often missed. Studies show that most lung cancers are in the form of lung nodules, which can be categorized as benign or malignant. Thus, accurate early identification of malignant lung nodules that might later become cancerous is essential for the prevention of lung cancer. Computed Tomography (CT) images can be useful for identifying and segmenting these nodules. In this paper, we propose an ensemble model, called BUS-UNet++, to segment lung nodules using CT images. We use a combination of the ConvLSTM up-sampling architecture from BUS-UNet and skip connections in aggregation blocks from the UNet++ model to build the BUS-UNet++ ensemble. The dataset for this study is collected from the Lung Image Database Consortium Image Database Resource Initiative (LIDC-IDRI), where we have selected the modality of these images as CT images. These are further preprocessed to obtain nodule masks and nodule images, which constitute the Region of Interest (RoI). The accuracy achieved with the Adam Optimizer is 0.9731, the Intersection over Union (IoU) of about 0.8439, and the dice score coefficient (DSC) of about 0.958 are obtained by the proposed system. This ensemble model outperforms several state-of-the-art models used for the same purpose.

No-reference metrics (BRISQUE, NIQE, PIQE) and full-reference metrics (PSNR, SSIM) for face recognition quality estimation are presented in this paper. Different noise types are considered: gaussian and salt &pepper noise with SNR in range 0...40 dB. Regression models between full-reference and no-reference metrics are considered. The quality of the regression models is estimated via $$R^2$$ R 2 and RMSE.

The article considers a communication channel with erasures, which allows making soft decisions in order to achieve the maximum gain in the fidelity of information reception. A comparative analysis of error correction algorithms using the erasure signal for the most reliable symbols of the same name in a multiple repeated block of information encoded with a redundant code is carried out.

The paper considers some aspects of the use of interactive methods in the study of the discipline “Mathematics” for non-mathematical specialties at the North Caucasus Federal University. The discipline “Mathematics” is included in the block of the mandatory part of the undergraduate curriculum in the natural sciences, and interactive teaching methods are designed to help students in the study of a non-core discipline. The use of interactive technologies contributes to the implementation of the competence-based approach. The paper gives example of the use of interactive methods in the practical classes of training groups of training areas 03.19.01 - Biotechnology and 05.30.01 - Medical Biochemistry, which contribute to mastering the modern mathematical apparatus for further use in solving theoretical and applied tasks in professional activity. A questionnaire was conducted among students of these areas in order to determine the effectiveness of the interactive teaching methods used. The results of the interview were analyzed. It was revealed that the use of interactive methods in the learning process helps to increase motivation and develop independence, stimulates an independent search for new knowledge, improves student performance and makes it possible to apply mathematical knowledge, skills and abilities in practical research.

The education system in the modern world is built from the steps - junior school, high school, college, university (bachelor's, master's, postgraduate). Teachers and psychologists are concerned about the continuity of these levels of education for the education of employed professionals. The paper is devoted to the analysis of the short-term continuity of the educational programs of undergraduate and graduate programs in applied mathematics and computer science in the context of updating the survey. The implementation has been studied of the mechanisms of succession of professional and research components of the training of students of the directions 01.03.02 - “Computational mathematics and mathematical modeling” and 01.04.02 - “Mathematical modeling” in the educational practice of the North Caucasus Federal University. Curricula, the general vectors of training are considered, examples of reporting in areas (final theses and exams, papers in scientific journals) are given. A mechanism is proposed for the formation of a set of professional competencies for bachelor's and master's degree graduates in the specialty “Mathematical Modeling” correlated with the requirements of professional standards. The most productive forms of continuity of the research component of educational programs are identified in the field of applied mathematics and computer science at NCFU.

The article is devoted to the development of computer simulators of artificial neural networks for conducting practical classes and organizing control in the “Neurocomputer technologies” subject for schoolchildren of 8-11th grades, who are studying in the system of additional education. The development and application technology of software modules is described for propaedeutics of mastering the mathematical apparatus, which is necessary for further study of the theory of artificial neural networks in the relevant courses of higher professional education. The program provides an opportunity to study at the level of medium or increased complexity for highly motivated students to study natural science disciplines. In this case, special attention will be paid to the practice of working with mathematical models of artificial neural networks and their implementation on a computer. Further professional education of “highly motivated” gifted children is highly likely to be associated with scientific research, which, regardless of the field of human knowledge, is currently based on the use of artificial neural network, neuromathematics and neuropackages. Since the main tasks solved with the help of neuro-mathematics are related to the search for hidden patterns, classification, forecasting, dimension reduction, the scope of their application covers all scientific areas.

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