Advanced Computing in Industrial Mathematics: 13th Annual Meeting of the Bulgarian Section of SIAM, December 18-20, 2018, Sofia, Bulgaria, Revised ...

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This book gathers the peer-reviewed proceedings of the 13th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM'18, held in Sofia, Bulgaria. The general theme of BGSIAM'18 was industrial and applied mathematics with particular focus on: mathematical physics, numerical analysis, high performance computing, optimization and control, mathematical biology, stochastic modeling, machine learning, digitization and imaging, advanced computing in environmental, biomedical and engineering applications. Preface Contents Design of a Multi-objective Optimization Model for Wireless Sensor Networks 1 Introduction 2 Related Works 3 WSN Modeling 3.1 A Mathematical Model of WSN with Resource Restrictions 3.2 Results from the Simulation Experiment 4 Conclusions References Cross-Validated Sequentially Constructed Multiple Regression with Centered Predictors 1 Introduction 2 Centered Cross-Validated Sequentially Constructed Multiple Regression 3 Summary References Non-local Nonlinear Perturbation Analysis for a Nonlinear Matrix Equation Arising in Tree-Like Stochastic Processes 1 Introduction 2 Statement of the Problem 3 Main Results 4 Numerical Example 5 Conclusion References One Parameter Family of Elliptic Curves and the Equation x4+y4+kx2y2=z2 1 Introduction 2 Basic Theorems 2.1 The Structure of Mordell-Weil Group 2.2 Theorems for Torsions 2.3 Theorems for the Rank 3 Results 3.1 The Main Idea and Results 3.2 Conclusion References An Inner Product Free Solution Method for an Equation of Motion with Indefinite Matrices 1 Introduction 2 The PRESB Preconditioning Method 2.1 Implementation 2.2 Eigenvalue Bounds of B-1A 3 The Familiar Chebyshev Iteration Method 3.1 Advantages 3.2 Numerical Tests 4 A Modification of the Chebyshev Iteration Method for Polynomially Preconditioned Matrices and an Application 4.1 An Equation of Motion 4.2 Modifications of the Chebyshev Iteration Method to Handle Outlier Eigenvalues 5 Concluding Remarks References Simulation Model for Investigation of the Behaviour of an Artificial Immune Algorithm for Generation of S-Boxes with Good Cryptographic Properties 1 Introduction 2 The Simulation Model 3 Some Basic Definitions About S-Boxes 4 Description of the Simulated AIA for Generation of S-Boxes with Good Cryptographic Properties 5 Results from the Simulation 6 New S-Boxes References Self-consistent Monte Carlo Solution of Wigner and Poisson Equations Using an Efficient Multigrid Approach 1 Introduction 2 Wigner Monte Carlo Solver 3 Poisson Equation Solver (Multigrid Approach) 4 Boundary Conditions 5 Results 6 Conclusion References Modelled Versus Satellite Retrieved Estimation of the Direct Normal Irradiance and the Sunshine Duration over Bulgaria 1 Introduction 2 DISC Model and Reference Dataset 2.1 DISC Model Basics 2.2 Reference Dataset Description 3 Calculations and Comparisons 3.1 DNI Estimation 3.2 SDU Estimation 4 Conclusion References Numerical Identification of the Time Dependent Vertical Diffusion Coefficient in a Model of Air Pollution 1 Introduction 2 Mathematical Model and the Inverse Problem 3 Solution of the Semi-discrete Inverse Problem 4 The One-Dimensional Problem 4.1 Solution of the Direct Problem 4.2 Solution of the Fully Discrete Inverse Problem 5 Numerical Results 5.1 Direct Problem Test Examples 5.2 Inverse Problem Test Examples 5.3 Direct and Inverse Problem with Delta-Function Source References Generalized Net Model for Flying Ant Colony Optimization 1 Introduction 2 Short Remarks on Generalized Nets 3 Flaying Ant Colony Optimization 4 Modelling FACO by GNs 5 Conclusion References Numerical Determination of Time-Dependent Implied Volatility by a Point Observation 1 Introduction 2 The Inverse Problem 3 Solution of the Semi-discrete Inverse Problem 4 Solution of the Difference Direct Problem 5 Solution of the Difference Inverse Problem 5.1 Algorithm 6 Computational Results 6.1 Direct Problem 6.2 Inverse Problem 7 Conclusions References Homotopy Analysis Method to Solve Volterra-Fredholm Fuzzy Integral Equations 1 Introduction 2 Basic Concepts 3 Bases of HAM 4 HAM for Solving 2D-NVFFIE 5 Convergence Analysis 6 Numerical Experiment References Spectral Fractional Laplacian with Inhomogeneous Dirichlet Data: Questions, Problems, Solutions 1 Introduction 1.1 Riesz Formulation 1.2 Spectral Formulation 2 Homogeneous Dirichlet Conditions 2.1 Analysis of Solution (11) 3 Inhomogeneous Spectral Fractional Laplacian 4 Numerical Tests 5 Concluding Remarks References Spike Timing Neural Model of Eye Movement Motor Response with Reinforcement Learning 1 Introduction 2 Model Structure 2.1 Sensory Information Processing Layers 2.2 Basal Ganglia 2.3 Superior Colliculus 3 Simulation Results and Discussion 4 Conclusions References Programming Techniques for Energy-Efficient Software Abstract 1 Programming Techniques for Energy-Efficient Software Approach 2 The Case Study MSP430™ Advanced Power Optimizations 3 TI EnergyTrace Technology™ 3.1 Energy Measurement Method 3.2 Energy Capture Modes 3.3 Limitations 4 The Case Study Verification 4.1 The Case Study 4.2 Feedback from ULP Advisor™ 4.3 Create a Reference Profile Using EnergyTrace Technology™ 4.4 Goals of Improvement and Compartment of Profiles 4.4.1 Pay Special Attention to Low-Power Mode Use 4.4.2 Analyse Code in ULP Advice Window 4.4.3 Compare the Profiles 4.5 Goals of Improvement and Compartment of Profiles 4.5.1 Analyse Code in ULP Advice Window 4.5.2 Analyse the States Window 4.6 Compare All Profiles 4.7 Absolute Power Consumption 5 Summary of MSP430™ Advanced Power Optimizations 6 Conclusions About X86 Low-Power Programming Techniques References Modelling Human Biometeorological Conditions Using Meteorological Data from Reanalysis and Objective Analysis—Preliminary Results 1 Biometeorological Indices 2 Used Data and Performed Calculations 3 Results and Discussion 4 Conclusion References The Braided Group of a Square-Free Solution of the Yang-Baxter Equation and Its Group Algebra 1 Introduction 2 Preliminaries on Braided Groups 3 The Symmetric Group G(X,r) of a Finite Square-Free Symmetric Set (X,r) and Its Group Algebra K[G] 3.1 Square-Free Solutions and Their Algebraic Objects 3.2 The Braided Group G=G(X,r) 3.3 The Group Algebra k[G] over a Field k References Exploring Applicability of the InterCriteria Analysis to Evaluate the Performance of MOE and GOLD Scoring Functions 1 Introduction 2 Materials and Methods 2.1 Target Proteins 2.2 Dataset Preparation 2.3 Molecular Docking 2.4 MOE Software 2.5 GOLD Software 2.6 InterCriteria Analysis 2.7 ICrAData Software Package 3 Results and Discussion 4 Conclusions References Multiobjective Approach for Solving Engineering Robust Design Problems Abstract 1 Introduction 2 Multiobjective Decision Making Problem 3 An Application of Multiobjective Approach in Ship Design Optimization 4 Conclusion Acknowledgments References Iterative Implicit Schemes for Compaction-Driven Darcy Flow of Magma 1 Introduction 2 Model Formulation 3 Numerical Schemes 4 Computational Results 5 Conclusions References Finite Time Blow up of the Solutions to Double Dispersive Equations with Linear Restoring Force and High Energy 1 Introduction 2 Preliminaries 3 Proof of the Main Results 4 Discussions and Comments 4.1 Sign of the Nehari Functional I(0) 4.2 Comparison with Known Sufficient Condition 5 Conclusion References Coupled Thermo-Hydro-Mechanical Finite Element Simulation of Loess Slope Under Atmospheric Boundary Conditions 1 Introduction 2 Description of the Numerical Model 2.1 Atmospheric Boundary Conditions (ATM) 2.2 Initial and Boundary Conditions 2.3 Material Parameters 3 Results 3.1 Sensitivity to the Components of the ATM Boundary Conditions 3.2 Comparison between TH and THM Analyses 3.3 Plastic Strain Analysis and Development of the Failure Zone 4 Conclusion References Molecular Dynamics Simulations of His6-FLAG-hIFN Fusion Glycoproteins 1 Introduction 2 Materials and Methods 2.1 Fusion His6-FLAG-hIFN Protein Model 2.2 Glycan Models 2.3 MD Simulation Protocol 3 Results and Discussion 3.1 Dependence on Glycosylation Sites 3.2 Influence of Glycan Chain Length 4 Conclusions References Several Results Concerning the Barnes G-function, a Cosecant Integral, and Some Other Special Functions 1 Introduction 2 Correction of Some Formulas Given by Choi, Srivastava and Adamchik 3 Identities Involving the Inverse Tangent Integral Ti2 and Legendre's Chi-Function 2 References Influence of the Temperature on Simulated Annealing Method for Metal Nanoparticle Structures Optimization Abstract 1 Introduction 2 Available Approaches 3 The Simulated Annealing Method 4 Numerical Experiments 5 Conclusion and Future Work Acknowledgments References Blood Flow Instabilities Related to Elasticity and Asymmetry of an Abdominal Aorta Aneurysm 1 Introduction 2 Model of Asymmetric Abdominal Aortic Aneurysm (AAAA) and Assumptions 3 Results and Discussions 3.1 Combined Effects of the Asymmetry and Elasticity of the Wall at Laminar Flow 3.2 Instabilities of the Flow Regimes at Lower Elastic Modulus in the Range of 400–477kPa 3.3 Flow in a Straight Tube 3.4 Return to Stability at an Increase of the Elastic Modulus 3.5 Symmetric AAA Form 4 Conclusion References Rank Data Clustering Based on Lee Distance 1 Introduction 2 ``K-Means'' Clustering for Rank Data 2.1 Distances on SN 2.2 Measure of ``Tightness'' 3 Properties of Lee Distance 4 Illustrative Example References Analysis of Swing Oscillatory Motion 1 Introduction 2 Lagrangian Form 3 Hamiltonian Form 4 Integrable Cases 4.1 First Integrable Case 4.2 Second Integrable Case 5 Concluding Remarks References Non-linear Waves of Interacting Populations with Density-Dependent Diffusion 1 Introduction 2 Mathematical Formulation of the Basic Model 3 Analytical Solution for the Nonlinear Evolution Equation: Application of the Modified Method of Simplest Equation 4 Numerical Findings and Discussions 5 Conclusions References Performance Analysis of Hierarchical Semi-separable Compression Solver for Fractional Diffusion Problems 1 Introduction 2 Fractional Diffusion Problem Modeled with Fractional Laplacian Operator 2.1 Finite Element Settings 3 Hierarchical Semi-separable Compression Based Solver 3.1 HSS Representation 3.2 ULV-Like Factorization and Solution 4 Numerical Results 4.1 Square Domain Experiments 4.2 Circle Domain Experiments 5 Concluding Remarks Appendix References On the Spectral Properties of Lax Operators Related to BD.I Symmetric Spaces 1 Introduction 2 Preliminaries 2.1 Lax Representations 2.2 The Direct and the Inverse Scattering Problem for L 3 The FAS and the Riemann-Hilbert Problem 3.1 The Dressing Zakharov-Shabat Method and the Soliton Solutions 3.2 Effects of the Dressing on the Jost Solutions and the Scattering Matrix 3.3 The Dressed FAS 4 The Resolvent of L 4.1 The Resolvent of Generic Lax Operators 4.2 The Resolvent of Lax Operators with Degenerate J 4.3 The Completeness Relation of FAS of L 5 Discussion and Conclusion References Mechanical Properties Assessments for Materials of High Porosity and Light Alloys with Predominant Embedded Phases 1 Introduction 2 Modelling 2.1 Composite A - Elastic Properties Assessment 2.2 Composite B - Elastic Properties Assessment 2.3 Composite A - Initial Plastic State Condition 2.4 Composite B - Initial Plastic State Condition 3 Numerical Simulations and Results 3.1 Mechanical Properties of AZ Mg Alloys Modified by TiC Particles 3.2 Mechanical Properties of Highly Porous Materials 3.3 Conclusions References Symmetries and Conservation Laws of a System of Timoshenko Beam Type Equations 1 Introduction 2 Basic Equations and Variational Statement 3 Symmetry Groups 4 Conservation Laws 5 Concluding Remarks References InterCriteria Analysis of the Human Factor Assessment in a Mobile Company 1 Introduction 2 Short Remarks on the Intercriteria Analysis Method 2.1 Short Notes on Intuitionistic Fuzzy Pairs 2.2 Short Remarks on the Index Matrices 2.3 Short Remarks on Intercriteria Analysis Method 3 Application of ICrA to the Assessment Criteria of the Employees of a Mobile Company 4 Comparison of the Results Obtained from ICrA, Pearson's, Spearman's and Kendall's Rank Correlation Analyzes 5 Conclusion References Using DLT in Software Lifecycle Management 1 Introduction 2 Software Lifecycle Management 3 DLT-based System for Managing Complex SLM Processes 4 Conclusion References Study of a Flow of Reacting Substances in a Channel of Network 1 Introduction 2 Mathematical Formulation of the Model 3 Case of Constant Values of the Parameters and Stationary State of Functioning of the Channel 4 Concluding Remarks References A Symplectic Numerical Method for the Sixth Order Boussinesq Equation 1 Introduction 2 Preliminaries 3 A Symplectic Finite Difference Scheme 4 A Conservative Finite Difference Scheme 5 Analisys of the FDSs 6 Numerical Results 7 Conclusion References Author Index