Mathematics and its Applications in New Computer Systems: MANCS-2021 (Lecture Notes in Networks and Systems, 424)

✍ Scribed by Andrei Tchernykh (editor), Anatoly Alikhanov (editor), Mikhail Babenko (editor), Irina Samoylenko (editor)

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 571
• Category: Library

✦ Synopsis

This book is based on the best papers accepted for presentation during the International Conference on Mathematics and its Applications in New Computer Systems (MANCS-2021), Russia.
The book includes research materials on modern mathematical problems, solutions in the field of cryptography, data analysis and modular computing, as well as scientific 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 mathematical solutions to cryptography issues are devoted to secret sharing schemes, public key systems, private key systems, n-degree comparisons, modular arithmetic of simple, addition of points of an elliptic curve, Hasse theorem, homomorphic encryption and learning with error, and modifications of the RSA system. Furthermore, issues in data analysis and modular computing include contributions in the field of mathematical statistics, machine learning methods, deep learning, and neural networks. Finally, the book gives insights into the fundamental problems in mathematics education. The book intends for readership specializing in the field of cryptography, information security, parallel computing, computer technology, and mathematical education.

✦ Table of Contents

Preface
Contents
Comparison of Approaches to the Circuits Design for DWT with CDF 9/7 Wavelet
1 Introduction
2 Materials and Methods
2.1 Theoretical Analysis of Generations Discrete Wavelet Transform
2.2 Comparison of Direct Implementations and Lifting Scheme Using the Unit-Gate Model
3 Results and Discussion
4 Conclusion
References
Hamming Neural Network in Discrete Form
1 Introduction
2 Background on Hamming Neural Network
3 Hamming Neural Network in Discrete Form
4 Conclusion
References
Improving Extreme Search with Natural Gradient Descent Using Dirichlet Distribution
1 Introduction
2 Preliminaries
2.1 Gradient Descent with Step-Size Adaptation
2.2 Adam Algorithm
2.3 Natural Gradient Descent and KL-divergence
3 Natural Gradient Descent with Dirichlet Distribution
4 Experimental Results
5 Discussion
References
CRTf-Based Reverse Converter for RNS with Low-Cost Modules {2n,2n-1,2n+1-1}
1 Introduction
2 Preliminaries
2.1 Background on Residue Number System
2.2 RNS to BNS Conversion Using CRTf
2.3 A Measure of RNS Balance with 3 Modules
3 CRTf Method for RNS with Balanced Modules {2n,2n-1,2n+1-1}
4 Reverse Converter for RNS with a Set of Modules {2n,2n-1,2n+1-1}
5 Hardware Modeling of Reverse Converter for RNS {2n,2n-1,2n+1-1}
6 Conclusions
References
Neural Network Classification of Dermatoscopic Images of Pigmented Skin Lesions
1 Introduction
2 Classification System Proposed for Dermatoscopic Images
3 Modeling of Dermatoscopic Images Processing
4 Conclusion
References
Decentralized Role-Based Secure Management in Wireless Sensor Networks
1 Introduction
2 Materials and Methods
3 Results
4 Discussion and Conclusion
References
Numerical Study of Longitudinal-Transverse Vibrations of Objects with a Moving Boundary
1 Introduction
2 Formulation of the problem
3 Description of the Numerical Method
4 Longitudinal-Transverse Vibrations of a String Taking into Account Geometric Nonlinearity
5 Conclusion
References
On the Algorithmic Complexity of Digital Image Processing Filters with Winograd Calculations
1 Introduction
2 Organization of Computations in Digital Image Processing Filters by the Winograd Method
3 Analysis of Algorithmic Complexity of Digital Image Processing Filters
4 Conclusions
References
Non-classical Methods of Determination Critical Forces of Compressed Rods
1 Introduction
2 Constant Cross-section Bar
2.1 Bar of Variable Cross-section
3 Conclusions
References
Numerical Simulation of the Control System of the Propulsion-Steering System of Tele-Controlled Uninhabited Vehicles
1 Introduction
2 Materials and Methods
3 Results
4 Discussion
5 Conclusion
References
Numerical Method for Correcting Command Signals for Combined Control of a Multiengined Complex
1 Introduction
2 Materials and Methods
3 Results
4 Discussion
5 Conclusion
References
Hardware Implementation of the Kalman Filter for Video Signal Processing
1 Introduction
2 Materials and Methods
2.1 Theoretical Analysis of Kalman Filter
3 Results and Discussion
4 Conclusion
References
Solving the Euler Problem for a Flexible Support Rod Base on the Finite Difference Method
1 Introduction
2 Mathematical Model
3 Constant Cross-Section Rod
4 Variable Cross-Section Rod
5 Conclusions
References
Multiscale Model Reduction for the Poroelasticity Problems Using Embedded Fracture Model
1 Introduction
2 Mathematical Model and Fine Grid Approximation
3 Coarse Grid Approximation Using GMsFEM
4 Numerical Results
4.1 Two-Dimensional Problems
4.2 Three-Dimensional Problems
5 Conclusion
References
Error Correction Method in Modular Redundant Codes
1 Introduction
2 Materials and Methods
2.1 Modular Redundancy Codes
2.2 Corrective Abilities of RNS
2.3 Development of a Method for Error Correction in Modular Redundancy Code
2.4 Error Correction with One Control Base
2.5 Correction of Errors with Two Control Bases
3 Results
4 Discussion
5 Conclusion
References
Comparative Analysis of the Mathematical Literacy Level in First-Year Students of the North-Caucasus Federal University, Based on the International PISA Studies
1 Introduction
2 Materials and Methods
3 Results
4 Discussion and Conclusion
References
Implementation of the Learning Procedure with Equalized Errors on the Receiving Side of the Information Transmission System
1 Introduction
2 Materials and Methods
3 Results
4 Conclusion
References
A Feature Fusion Based Deep Learning Model for Deepfake Video Detection
1 Introduction
2 Proposed Model
2.1 Generation of Cropped Faces from Video Frames
2.2 Deep Feature Fusion Based Classification
3 Results and Discussion
3.1 Dataset Preparation
3.2 Experimental Setups
3.3 Experimental Results
3.4 Comparison with Past Methods
4 Conclusion
References
Search for an Object with a Recognition Error by a Desktop Grid
1 Introduction
2 The Mathematical Model
3 Solution of the Optimisation Problem
4 Numerical Experiments
5 Conclusion
References
Numerical Methods for Solving the Robin Boundary Value Problem for a Generalized Diffusion Equation with a Non-smooth Solution
1 Introduction
2 Approximation of the Generalized Caputo Derivative by L1 Formula and a Difference Scheme
2.1 Derivation of Formula
2.2 Difference Scheme
3 Stability and Convergence
4 Numerical Results
5 Conclusion
References
Asymptotic of Calculation of Hydro-Mechanical Fields of a Marine Mobile Object by the Finite Volume Method
1 Introduction
2 Materials and Methods
2.1 A Subsection Sample
2.2 Calculations on Bernstein Polygonal Grids
3 Results
4 Discussion and Conclusion
References
A Deep Feature Selection Method for Tumor Classification in Breast Ultrasound Images
1 Introduction
2 Materials and Methods
2.1 Dataset Description
2.2 Spearman Rank Correlation Coefficient
2.3 Methodology
3 Experimental Results
3.1 Performance Metrics
3.2 Results
4 Result Analysis and Discussion
5 Conclusion
References
Reference Points Based RNS Reverse Conversion for General Moduli Sets
1 Introduction
2 Materials and Methods
2.1 Pure Look-up-Table Implementation
2.2 Reference Points Implementation
2.3 Hierarchical Reference Points Implementation
3 Results
4 Conclusion
References
Group Method of Data Separation in Wireless Sensor Networks
1 Introduction
2 Materials and Methods
3 Results
4 Conclusion
References
Data Processing in Problem-Solving of Energy System Vulnerability Based on In-memory Data Grid
1 Introduction
2 Materials and Methods
2.1 Data Processing Scenarios
2.2 Apache Ignite
2.3 Workflow-Based Scientific Application for Solving the Problem of Energy System Vulnerability
3 Experimental Analysis
3.1 Computing Environment
3.2 Analysis of Computation Scaling
3.3 SQL Queries Processing
4 Discussion and Conclusions
References
Wind Speed Recovering from Lidar Sensing Data by Solving of Inverse Problem
1 Introduction
2 Materials and Methods
3 Results
4 Discussion and Conclusion
References
A Simulation Device Model for Managing Access to Confidential Information Stored in a Cloud
1 Introduction
2 Materials and Methods
3 Results
4 Discussion
5 Conclusion
References
Implementation of an Integro-Differential Model of a Singularly Loaded Rod by the Finite Element Method
1 Introduction
2 Materials and Methods
2.1 A Subsection Sample
3 Results.
4 Conclusion
References
Experience and Prospects of Implementing a Model of Mathematics Distance Learning in North-Caucasus Federal University Training e-Environment
1 Introduction
2 Materials and Methods
2.1 A Review of the Development and Introduction Stages for the Modified Distance Learning Model
2.2 Analysis of the Modified Learning Model Implementation and the Course Content Specifics
2.3 Positive Aspects of Using the Available Content When Switching to Distance Learning
3 Results
4 Discussion
5 Conclusion
References
On Numerical Modeling of the Young’s Experiment with Two Sources of Single-Photon Spherical Coordinate Wave Functions
1 Introduction
2 Photon Wave Function in Coordinate Representation
3 Two-Photon Interference of “Spherical Waves” from Two Point Sources in the Scheme of the Young Experiment
4 Conclusion
References
Employing the TIMSS International Study Tools to Evaluate Mathematical Competencies in Future Teachers of Mathematics
1 Introduction
2 Materials and Methods
3 Results
4 Discussion and Conclusion
References
Elements of Fuzzy Logic in Solving Clustering Problems
1 Introduction
2 Materials and Methods
3 Results
4 Discussion
5 Conclusion
References
Difference Methods of Solving Non-local Boundary Value Problems for a Loaded Generalized Diffusion Equation with Bessel Operator
1 Introduction
2 Non-local Boundary Value Problem A
3 The A-Priori Estimate in the Differential Form
4 Stability and Convergence of the Difference Scheme
5 Non-local Boundary Value Problem B and the A-Priori Estimate in the Differential Form
6 Stability and Convergence of the Difference Scheme
References
Discrete Implementation of Korteweg de Vries Equation Based on a Modified “Cabaret” Scheme
1 Introduction
2 Materials and Methods
2.1 Problem Statement
2.2 Difference Scheme “Left Corner” for Korteweg de Vries Equation
2.3 Stability Investigation of the Scheme “Left Corner”
2.4 Difference Schemes “Cabaret” and “Cross” for Korteweg de Vries Equation
2.5 Stability Investigation of the Scheme Obtained from a Linear Combination of “Cabaret” and “Cross” Schemes
2.6 Accuracy Investigation of a Modified Scheme
3 Results
4 Conclusion
References
Revealing Chaos-Based Steganographic Transmission by the Recurrence Quantification Analysis
1 Introduction
2 Materials and Methods
2.1 Chaos-Based Communication System
2.2 Chaotic Transmission Decryption Method
2.3 Recurrence Quantification Analysis
3 Results
4 Conclusion
References
Using Artificial Neural Networks and Wavelet Transform for Image Denoising
1 Introduction
2 Materials and Methods
2.1 Mathematical Model of Image Processing Based on Discrete Wavelet Transform
2.2 Architecture of the Proposed ANN for Image Denoising
3 Results
4 Discussion
5 Conclusion
References
Computational Techniques for Investigating Low-Potential Gupta Clusters of Extremely Large Dimensions
1 Introduction
2 Materials and Methods
2.1 Gupta Model
2.2 Description of Computational Technology
3 Results
4 Conclusion
References
Software Engineering for Optimal Control Problems
1 Introduction
1.1 Russian Software for the OCP
1.2 Foreign Software for the OCP
2 The Statement of the Optimal Control Problem
3 General Approach to the Application Software Development
3.1 The Task of Creating High-Quality Software for Computing Problems
3.2 Fundamentals of Designing Software Systems for Optimal Control Problems
3.3 The Basic Elements of the Computing Technology for the OCP
3.4 Functional Subsystems of Software Technology
3.5 Algorithm Selection Technique
4 Conclusion
References
Numerical Methods for Solving Boundary Value Problems for the Generalized Integro-differential Modified Moisture Transfer Equation with the Bessel Operator
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 Third Boundary Value Problem and a Priori Estimate in Differential Form
2.5 Stability and Convergence of the Difference Scheme
3 Results
4 Conclusion
References
Modeling Hyperchaotic Datasets for Neural Networks
1 Introduction
2 Materials and Methods
2.1 Related Works
2.2 Hyperchaotic Models
2.3 Lorenz Attractor
2.4 Ressler Attractor
2.5 Saito Attractor
2.6 Liapunov Attractor
3 Results
4 Conclusion
References
Neural Network Analysis for Image Classification
1 Introduction
2 Materials and Methods
2.1 Wave Model of Feed-Forward ANN
2.2 Convolutional ANN Wave Model
3 Conclusion
References
An Overview of the Methods Used to Recognize Garbage
1 Introduction
2 Materials and Methods
2.1 Machine Vision for Recognition
2.2 Hardware Systems for Intelligent Systems of Household Waste Sorting
3 Conclusion
References
Implementation of Spline-Wavelet Robust Bent Code in Code-Division Multiple Access
1 Introduction
2 Robust Codes
3 Spline-Wavelet Bent Robust Codes
4 Implementation of Spline-Wavelet Robust Bent Code in Code Division Multiple Access
5 Conclusion
References
On the Possibility of Increasing the Accuracy of Computations in the Floating-Point Format with Multiple Exponents
1 Introduction
2 Format for the Representation of Floating-Point Numbers with Multiple Exponents
3 Estimating the Quantity of Presentable Numbers with Multiple Exponent
4 Results
4.1 Quantity of Different Floating-Point Numbers
4.2 Rules of Multiplication and Division
4.3 Rules of Addition and Subtraction
4.4 Results of Experimental Research
5 Conclusion
References
Method of Building a Scalable Neural Control System for Underwater Robotic Complexes
1 Introduction
2 Materials and Methods
3 Results
4 Discussion
5 Conclusion
References
Analytical Review of Methods for Detection, Localization and Error Correction in the Residue Number System
1 Introduction
2 Projection Method
3 Syndrome Method
4 Examples of Practical Application of the Syndrome Decoding Method
5 Conclusion
References
A High-Order Difference Scheme for the Diffusion Equation of Multi-term and Distributed Orders
1 Introduction
2 Materials and Methods
2.1 The L2 Type Fractional Numerical Differentiation Formula
2.2 A Difference Scheme for the Multi-term Time-Fractional Diffusion Equation
2.3 Stability and Convergence
2.4 A Difference Scheme for the Time-Fractional Diffusion Equation of Distributed Order
2.5 Stability and Convergence
3 Conclusion
References
A Locally One-Dimensional Difference Scheme for a Multidimensional Integro-Differential Equation of Parabolic Type of General Form
1 Introduction
2 Materials and Methods
2.1 Problem statement
2.2 Locally One-Dimensional Scheme
2.3 Approximation Error for a Locally One-Dimensional Scheme
2.4 Stability of a Locally One-Dimensional Scheme
2.5 Convergence of a Locally One-Dimensional Scheme
3 Results
4 Conclusion
References
Solution for Inverse Boundary Value Problems on the Power of a Concentrated Charge in a Mathematical Model of Subsidence Soils Compaction
1 Introduction
2 Materials and Methods
2.1 Mathematical Modeling for Solving Inverse Problems of Charge Power in Subsidence Soils
2.2 Formulation of Inverse Problems on Charge Power Recovery
2.3 Analytical Solution for Inverse Problems of Subsidence Soils Compaction
3 Results
4 Conclusion
References
Dynamic Model of Inter-Industry Balance, the Problem of Its Digitizing and Simulation of Structural Transient Processes
1 Introduction
2 Materials and Methods
3 Results
4 Conclusion
References
Anthropomorphic Model of States of Subjects of Critical Information Infrastructure Under Destructive Influences
1 Introduction
2 Formulation of the Problem
3 Conditions for Building a Model of States of CII Subjects
4 Classification of Types of Inter-Object Connections on the Subject of CII
5 Modes of Functioning of the Subject of CII
6 Methodology and Discussion
7 Experiment
8 Conclusion
References