Current Problems in Applied Mathematics and Computer Science and Systems

Description

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. Preface Contents About the Authors Numerical Methods in Scientific Computing Modeling of the Potential Dependence on the Permittivity at the Metal – Dielectric Medium Interface 1 Introduction 2 Materials and Methods 3 Results 4 Discussion 5 Conclusion References Difference Method for Solving the Dirichlet Problem for a Multidimensional Integro-Differential Equation of Convection-Diffusion 1 Introduction 2 Materials and Methods 2.1 Statement of the Boundary Value Problem and a Priori Estimate in Differential Form 3 Constructing a Difference Scheme 4 Stability and Convergence of the Difference Scheme 5 Algorithm for the Numerical Solution of the Problem 6 Results 7 Numerical Results 8 Conclusion References The Problem of Restoring the Unit of Approximation in the Model for Studying Functional Dependence from Approximate Data 1 Introduction 2 Materials and Methods 3 Results 4 Discussion 5 Conclusion References RNS Reverse Conversion Algorithm and Parity Detection for the Wide Arbitrary Moduli Set 1 Introduction 2 Residue Number System 2.1 Rank Calculation Using Redundant Modulo 2.2 Approximate Rank Calculation 3 Proposed Method 3.1 Selection of Parameters s, di and 3.2 Base Extension and Parity Detection 4 Results 5 Conclusion References Anomalous Solute Transport in an Inhomogeneous Porous Medium Taking into Account Mass Transfer 1 Introduction 2 Mathematical Model 3 Numerical Solution 4 Numerical Calculations 5 Conclusion References Determination of Relaxation and Flow Coefficients During Filtration of a Homogeneous Liquid in Fractured-Porous Media 1 Introduction 2 Statement of the Inverse Problem 3 Solution of the Inverse Problem 4 Difference Problems 5 Results of Numerical Calculations 6 Conclusion References Solution of the Anomalous Filtration Problem in Two-Dimensional Porous Media 1 Introduction 2 Statement and Numerical Solution of the Problem 3 Results and Discussion 4 Conclusion References On Calculating the Hyperbolic Parameter of a Two-Dimensional Lattice of Linear Comparison Solutions 1 Introduction 2 Formulas for the Hyperbolic Parameter 3 Relations for the Hyperbolic Parameter 4 Conclusion References Inverse Problem of Contaminant Transport in Porous Media 1 Introduction 2 Statement of the Inverse Problem 3 Algorithm for Solving the Inverse Problem 3.1 Difference Problems 4 Numerical Results 5 Conclusion References Numerical Solution of Anomalous Solute Transport in a Two-Zone Fractal Porous Medium 1 Introduction 2 Statement and Numerical Solution of the Problem 3 Results and Discussion 4 Conclusion References Initial-Boundary Value Problems for the Loaded Hallaire Equation with Gerasimov–Caputo Fractional Derivatives of Different Orders 1 Introduction 2 Materials and Methods 2.1 Problem Statement 2.2 A Priori Estimate in Differential Form 2.3 Stability and Convergence of the Difference Scheme 2.4 Statement of the Boundary Value Problem with a Condition of the Third Kind and a Priori Estimate in Differential Form 2.5 Stability and Convergence of the Difference Scheme 3 Results 4 Conclusion References Grid Method for Solving Local and Nonlocal Boundary Value Problems for a Loaded Moisture Transfer Equation with Two Fractional Differentiation Operators 1 Introduction 2 Materials and Methods 2.1 Problem Statement 2.2 A Priori Estimate in Differential Form 2.3 Stability and Convergence of the Difference Scheme 2.4 Statement of the Non-local Boundary Value Problem and a Priori Estimate in Differential Form 2.5 Stability and Convergence of the Difference Scheme 3 Results 4 Conclusion References Determining Frequencies of Free Longitudinal Vibrations of Rods by Analytical and Numerical Methods 1 Introduction 2 Problem Statement 3 Analytical Solution Method 4 Numerical Solution Method 5 Conclusion References Forced Longitudinal Oscillations of a Rod with a Mass at the End 1 Introduction 2 Mathematical model of the problem 3 Analytical Solution Method 4 Numerical Solution Method 5 Conclusion References On the Unassociated Matrices Number of the n Order and a Given Determinant 1 Introduction 2 Lemmas About Integer Matrices of the n Order 3 Main Results on the Number of Nonassociated Primitive Matrices of the n Order 4 An Estimate for the Number of Unassociated Matrices of the n Order 5 Conclusion References Fast Calculation of Parameters of Parallelepipedal Nets for Integration and Interpolation 1 Introduction 2 Algorithms for Constructing the Bykovsky Set and Calculating the H-function 2.1 Construction of the Bykovsky Set 2.2 Calculation of the Hyperbolic Parameter 2.3 Calculation of the Bykovsky Sums 2.4 H-function Calculation 3 Increasing Sequence of Hyperbolic Parameters 4 Decreasing Sequence of Bykovsky Sums 5 Decreasing Sequence of H Functions 6 Construction of Sequences by the Form of a Continued Fraction 7 Conclusion References Modeling of the Adjustable DC Voltage Source for Industrial Greenhouse Lighting Systems 1 Introduction 2 Materials and Methods 2.1 Mathematical Model of an Adjustable DC Source for High-Pressure Discharge Lamps 2.2 Modeling of the rectifier unit in NI Multisim 10.1 3 Results 4 Conclusion References Modeling of Temperature Contribution to the Interphase Energy of the Faces of Cadmium Crystals at the Boundary with Organic Liquids 1 Introduction 2 Materials and Methods 3 Results 4 Discussion 5 Conclusion References Information and Computation Systems for Distributed Environments Mathematical Concept of a Model for Processing Metadata of Employee’s Psycho-States for Identifying Him as an Internal Violator (Insider) 1 Introduction 2 Materials and Methods 3 Results and Discussion 4 Conclusion References Analysis of Influence of Byzantine Robots with Random Behaviour Strategy on Collective Desicion-Making in Swarms 1 Introduction 2 Materials and Methods 3 Results 3.1 Influence of BR with RBS on Effectiveness of SRS with an Increase in the Number of Signs of the External Environment 3.2 Influence of BR with RBS on SRS Efficiency When Changing the External Environment 3.3 How to Change the Effect of BR with RBS on the Effectiveness of SRS When Changing the Stability of Random Opinion 4 Discussion 5 Conclusion References Beamforming for Dense Networks-Trends and Techniques 1 Introduction 2 Background 3 Femtocells 3.1 Femtocells Deployment Modes 3.2 Femtocell Access Modes 3.3 Femtocell Interference Scenario 4 Beamforing 4.1 Classification of Beamformers 5 Review of Some Recent Works 5.1 Zero-Forcing Beamforming (ZFBF) 5.2 Minimum Variance Distortionless Response Beamformer (MVDR) 5.3 Linear Constrained Minimum Variance Beamformer (LCMV) 6 Practical Challenges in Implementation of a Beamformer 7 Conclusion References Modified CLNet: A Neural Network Based CSI Feedback Compression Model for Massive MIMO System 1 Introduction 2 Massive MIMO System Model 3 Neural Network Model Description 3.1 Forged Complex Valued Input Layer 3.2 Attention Mechanism 3.3 Modified CLNet/CLNet+ 4 Results and Discussion 4.1 Dataset Consideration 4.2 Training Scheme 5 Conclusion References Facemask Wearing Correctness Detection Using Deep Learning Approaches 1 Introduction 2 Block Diagram of Proposed Model 2.1 About the Facemask Datasets 2.2 Features Identification and Extraction from Optical Facemask Image Transfer Learning 2.3 Model Selection and Implementation 3 Experimental Results 4 Conclusion References An Approach to the Implementation of Nonparametric Algorithms for Controlling Multidimensional Processes in a Production Problem 1 Introduction 2 Modeling Multidimensional Systems 3 The Task of Managing Multidimensional Processes 4 Implementation 5 Conclusion References Analysis of Neural Networks for Image Classification 1 Introduction 2 Materials and Methods 2.1 The Wave Model of Feedforward ANN 2.2 Wave Model of Convolutional ANN 3 Results References Factors of a Mathematical Model for Detection an Internal Attacker of the Company 1 Introduction 2 Materials and Methods 3 Results and Discussion 4 Conclusion References Comparative Analysis of Methods and Algorithms for Building a Digital Twin of a Smart City 1 Introduction 2 The Digital Twin of a Smart City 3 Methods 4 Comparative Analysis 5 Conclusion References Modification of the Projection Method to Correct Errors in RNS 1 Introduction 2 Materials and Methods 2.1 Projection Method 2.2 Converting Numbers from RNS to WNS Based on CRT 2.3 Modified CRT Method 2.4 Core Function Method 2.5 Core Diagonal Function Method 2.6 Core Diagonal Function Method 2.7 Nullivisation Method for Determining Error in RNS 3 Results 4 Conclusion References An Overview of Modern Fully Homomorphic Encryption Schemes 1 Introduction 2 Materials and Methods 2.1 First Homomorphic Ciphers and Semi Homomorphic Encryption 2.2 Fully Homomorphic Encryption 3 Results 3.1 DGHV 3.2 BFV 3.3 HEAAN/CKKS 4 Discussion 5 Conclusion References Model of Error Correction Device in RNS-FRNN 1 Introduction 2 Materials and Methods 2.1 RNS and Error Detection 2.2 RNS and Error Correction 2.3 Finite Ring Neural Network 3 Results 4 Discussion 5 Conclusion References Review of Modern Technologies of Computer Vision 1 Introduction 2 Materials and Methods 3 Results 4 Discussion 5 Conclusion References Data Analysis and Modular Computing Discrete Neural Network of Bidirectional Associative Memory 1 Introduction 2 Discrete Mathematical Model of a Bidirectional Associative Memory 3 Experimental Modeling of a Discrete Neural Network of Bidirectional Associative Memory 4 Conclusion References Modulo 2k + 1 Truncated Multiply-Accumulate Unit 1 Introduction 2 Preliminaries 2.1 Background on Residue Number System 2.2 Coding in Diminished-One for Modulo 2k + 1 Representation 2.3 State of the Art Truncated Multiply-Accumulate Units 2.4 Proposed Modulo 2k + 1 TMAC Architecture 3 Hardware Implementation and Results 4 Conclusion References Neural Network Skin Cancer Recognition with a Modified Cross-Entropy Loss Function 1 Introduction 2 Materials and Methods 2.1 Modification of the Cross-Entropy Loss Function Using Weighting Coefficients 2.2 Convolutional Neural Network System for Recognition of Pigmented Skin Lesions 3 Results 4 Discussion 5 Conclusion References Application of the SIFT Algorithm in the Architecture of a Convolutional Neural Network for Human Face Recognition 1 Introduction 2 Materials and Methods 2.1 Background CNN 3 Results and Discussion 4 Conclusion References High-Speed Wavelet Image Processing Using the Winograd Method 1 Introduction 2 Wavelet Image Processing Using the Direct Implementation and the Winograd Method 3 Acceleration of Wavelet Image Processing Using the Winograd Method 4 Conclusion References Improving the Parallelism and Balance of RNS with Low-Cost and 2k + 1 Modules 1 Introduction 2 Measuring the Balance of RNS with Low-Cost Modules and Modules of the Form 2k + 1 3 Analysis of the Parallelism and Balance of RNS with Low-Cost and 2k + 1 Modules 4 Results and Discussion 5 Conclusion References Uncoded Video Data Stream Denoising in a Binary Symmetric Channel 1 Introduction 2 Binary Symmetric Channel Model 3 Method for Uncoded Video Data Stream Denoising in a Binary Symmetric Channel 4 Modeling of Uncoded Video Data Stream Denoising in a Binary Symmetric Channel 5 Conclusion References Cloud-Based Service for Recognizing Pigmented Skin Lesions Using a Multimodal Neural Network System 1 Introduction 2 Materials and Methods 2.1 The Architecture of a Cloud-Based Web Application Based on a Multimodal Neural Network System for Recognizing Pigmented Skin Lesions 3 Results 4 Conclusion References Temperature Profile Nowcasting Using Temporal Convolutional Network 1 Introduction 2 Temporal Convolution Network 3 Problem Statement 4 Results and Discussion References Application of Bidirectional LSTM Neural Networks and Noise Pre-cleaning for Feature Extraction on an Electrocardiogram 1 Introduction 2 Materials and Methods 2.1 Model Description 2.2 Electrocardiogram Signals 2.3 Signal Preprocessing 2.4 LSTM Network 2.5 Feature Extraction 3 Results 4 Discussion 5 Conclusion References Trust Monitoring in a Cyber-Physical System for Security Analysis Based on Distributed Computing 1 Introduction 2 Materials and Methods 2.1 Basic Concept of a Cyber-Physical System based on State Analysis 2.2 Trust-Based Verification Method of CPS Operation 3 Results 3.1 Software Module for Monitoring and Analyzing Trust in CPS 3.2 Results of Calculating the Probability of Values Going Beyond the Confidence Interval 4 Discussion 5 Conclusion References Guaranteed Safe States in Speed Space for Ships Collision Avoidance Problem 1 Introduction 2 Formulation of the Problem 3 Method for Determining the Sets of Possible Ship Collisions in the Speed Space Based on Reachable Sets 4 Simulation Results 5 Conclusion References An Ensemble of UNet Frameworks for Lung Nodule Segmentation 1 Introduction 2 Materials and Methods 2.1 UNet++ 2.2 BUS-UNet 2.3 Data Pre-processing 2.4 Region of Interest (ROI) 2.5 Proposed Model: BUS-UNet++ 3 Experimental Results 3.1 Dataset Description 3.2 Evaluation Metrics 4 Discussion 5 Conclusion References No-Reference Metrics for Images Quality Estimation in a Face Recognition Task 1 Introduction 2 Materials and Methods 2.1 Dataset 2.2 Image Quality Assessment – IQA 2.3 Statistical Analysis 3 Results 3.1 Regression Models Quality: SSIM vs. PSNR 3.2 Regression Model Quality: No-Reference Metrics vs. Full-Reference Metrics 4 Discussions 5 Conclusion References Using Soft Decisions for Error Correction 1 Introduction 2 Correction of Erasures in Codes with Repetition 3 Combination of Indirect and Code Methods of Error Detection 4 Discussion 5 Conclusion References Actual Problems of Mathematical Education Interactive Methods in the Study of the Discipline “Mathematics” for Non-mathematical Specialties 1 Introduction 2 Materials and Methods 2.1 Methods Used in Classes with Students 2.2 Discussion Methodology 2.3 Case Technology 2.4 Small Group Work 3 Results 4 Discussion 5 Conclusion References Applied Mathematics and Informatics Bachelor's and Master's Educational Programs Continuity During Updating Educational Standards 1 Introduction 2 Applied Mathematics and Informatics Bachelor's and Master's Educational Programs Continuity 3 Updating Educational Standards 4 Discussion 5 Conclusion References Designing Computer Simulators in Support of a Propaedeutic Course on Neural Network Technologies 1 Introduction 2 Problem Statement 3 Development of the Methodology 4 Discussion 5 Conclusion References Author Index