Recent Advances in Mathematics and Technology: Proceedings of the First International Conference on Technology, Engineering, and Mathematics, Kenitra, ... (Applied and Numerical Harmonic Analysis)

The chapters in this volume are based on talks given at the inaugural Technology, Engineering and Mathematics Conference (TEM18), held from March 26 to 27, 2018 in Kenitra, Morocco. Advances in mathematical modeling, optimization, numerical analysis, signal processing, and computer science are presented by leading experts in these fields. There is a particular emphasis on stochastic analysis, machine learning algorithms, and deep learning models, which are highly relevant to the state-of-the-art in augmented, virtual, and mixed realities. Topics include: Harmonic analysis Big data analytics and applications Biomathematics Computer engineering and applications Economics and financial engineering Medical imaging and non-destructive testing This volume is ideal for engineers and researchers working in technological fields that need to be modeled and simulated using the tools of modern mathematics. ANHA Series Preface 7 Preface 10 Contents 12 Contributors 16 Acronyms 18 Part I Mathematical Modeling 21 1 The Two-Sided Gabor Quaternionic Fourier Transformand Uncertainty Principles 22 1.1 Introduction 22 1.2 Definition and Properties of Quaternion H 23 1.3 The Two-Sided Gabor Quaternionic Fourier Transform(GQFT) 24 1.3.1 Examples of the GQFT 25 1.4 Properties of GQFT 28 1.5 Uncertainty Principles For the GQFT 31 1.5.1 Heisenberg Uncertainty Principle 31 1.5.2 Logarithmic Inequality 34 References 37 2 Reflected Backward SDEs in a Convex Polyhedron 39 2.1 Introduction 39 2.2 Statement of the Problem 40 2.2.1 Notations 40 2.2.2 Main Definition 41 2.3 Existence and Uniqueness 42 References 49 3 On the Energy Decay of a Nonhomogeneous Hybrid Systemof Elasticity 50 3.1 Introduction 50 3.2 Well-Posedness and Asymptotic Stability 51 3.3 Asymptotic Expressions of Eigenfrequencies 55 3.4 Riesz Basis Property 64 References 67 Part II Advanced Mathematics for Imaging 69 4 Advanced Ground Truth Multimodal Imaging Using Time Reversal (TR) Based Nonlinear Elastic Wave Spectroscopy (NEWS): Medical Imaging Trends Versus Non-destructive Testing Applications 70 4.1 Introduction to Non-invasive and Non-destructive (NDT)Testing 71 4.2 Memory Effects, Aging, and Nonlinear Viscoelastic Multiscale Behavior 76 4.3 Multiscale Analysis and Hierarchical Structure 78 4.3.1 TR-NEWS Signal Processing 80 4.4 Lie Groups and Symmetries for Nonlinear Systems 81 4.4.1 Symmetries for Nonlinear TR Discrete Processes 84 4.4.2 Universality of Nonlinear Systems and the Associated Signal Processing 85 4.5 The Systemic Gold Proportion of a Complex System: Determinism Versus Stochasticity Evaluation 86 4.5.1 Multiscale Analysis and Stochastic Aspects inNDT 4.0 86 4.5.2 Dynamic of Nonlinear Systems: The Elementary Stochastic Cell of the Complexity 87 4.5.3 Multiscality of Complex Systems: The Elementary Determinism Pattern of the Complexity 88 4.6 Determinism Versus Stochasticity: A Pragmatic Approach for Engineering Organization's Strategies 89 4.6.1 Excitation and Responses of Hierarchically Multiscale Complex Systems 91 4.6.2 Mutability, Tunability, Optimality, Evolvability Coming from the Nano-scale Science 95 4.6.3 Vulnerability of Stochastic Data and Cascade of Uncertainty 95 4.6.4 Multilevel Approach in Social and Epidemiological Sciences 96 4.7 Conclusion 97 References 98 5 A Geometrically Constrained Manifold Embedding for an Extrinsic Gaussian Process 103 5.1 Introduction 103 5.2 Notations and Background 106 5.2.1 Curve Representation and Shape Space 106 5.2.2 Geodesics in Shape Space, Exponential Map, and Parallel Transport 107 5.3 The Geometric Constraints on the Embedded Manifold 108 5.3.1 Local Solutions as Eigenfunctions of the Covariance Operator 109 5.3.2 Global Solution as a Random Field 111 5.3.3 Numerical Solution 112 5.4 Numerical Examples 113 References 116 6 Numerical Study of SIF for a Crack in P265GH Steel by XFEM 118 6.1 Introduction 119 6.2 FEM Methodology 120 6.2.1 Local Approach: Stress Intensity Factor 121 6.2.2 Global Approach G-Theta Method (Gθ) 121 6.2.3 Numerical Calculation of the Stress IntensityFactor (K) 122 6.2.4 Geometry 122 6.2.5 Meshing of the CT Specimen 124 6.3 XFEM Methodology 124 6.3.1 Mathematical Formulation of XFEM 124 6.3.2 Numerical Integration 130 6.3.3 Crack Meshing 131 6.3.4 Enrichment and Level Sets 132 6.4 Results and Discussion 134 6.4.1 Calculation of Stress Intensity Factor (K) 134 6.4.2 Comparison of CPU Times of Numerical Methods 137 6.4.3 Stress Concentration Coefficient Kt 137 6.5 Conclusion and Perspective 139 References 139 Part III Computer Sciences and Smart Technologies 141 7 Hardware Acceleration of SVM Training for Real-Time Embedded Systems: Overview 142 7.1 Introduction 142 7.2 Research Works 144 7.2.1 Accelerating SVM Training with GPU 144 7.2.2 Accelerating SVM Training with FPGA 146 7.3 GPU vs FPGA Performance Comparison 147 7.4 Conclusion and Perspectives 148 References 149 8 Integrating an Intelligent Tutoring System into an Adaptive E-Learning Process 151 8.1 Introduction 151 8.2 Limitations of a Classical E-Learning 152 8.3 Intelligent Tutoring System 152 8.3.1 Definition 152 8.3.2 Architecture 153 8.3.3 Application of ITS 154 8.4 Related Work 155 8.4.1 Implicit Strategies for Intelligent Tutoring Systems 155 8.4.2 Explicit Strategies for Intelligent Tutoring Systems 155 8.5 Model of Smart Tutoring 156 8.5.1 Proposed Approach 156 8.6 Smart Tutoring System: Developed Platform 157 8.6.1 The Context and Proposed Solution 157 8.6.2 Results 158 8.7 Conclusion and Perspectives 159 References 160 9 NDN vs TCP/IP: Which One Is the Best Suitable for Connected Vehicles? 161 9.1 Introduction 161 9.2 Limitations of the Current Internet (TCP/IP) 162 9.3 Presentation of Named Data Networking (NDN) 164 9.3.1 NDN System Architecture 165 9.3.2 Forwarding Process 166 9.4 Comparative Study 166 9.5 Conclusion 168 References 168 10 Predictive Analysis for Diabetes Using Big Data Classification 170 10.1 Introduction 170 10.2 Big Data in Healthcare 171 10.2.1 Existing Technologies 172 10.2.2 Classification Data 173 10.3 Result and Discussion 175 10.4 Conclusion 178 References 178 Index 180 Applied and Numerical Harmonic Analysis (97 volumes) 186 Part I Mathematical Modeling -- The two-sided Gabor Quaternionic Fourier transform and uncertainty principles -- Reflected backward SDEs in a convex polyhedron -- On the energy decay of a nonhomogeneous hybrid system of elasticity -- Part II Advanced Mathematics for Imaging -- Advanced ground truth multimodal imaging using Time Reversal (TR) based Nonlinear Elastic Wave Spectroscopy (NEWS): medical imaging trends versus non-destructive testing applications -- A geometrically constrained manifold embedding for an extrinsic Gaussian process -- Numerical study of SIF for a crack in P265GH steel by XFEM -- Part III Computer Sciences and Smart Technologies -- Hardware acceleration of SVM training for real-time embedded systems: Overview -- Integrating intelligent tutoring system into an adaptive E-Learning process -- NDN VS TCP/IP: Which one is the best suitable for connected vehicles? -- A new optimization method to Enhance QoS in OLSR protocol -- Predictive analysis for diabetes using Big Data classification The chapters in this volume are based on talks given at the inaugural Technology, Engineering and Mathematics Conference (TEM18), held from March 26 to 27, 2018 in Kenitra, Morocco. Advances in mathematical modeling, optimization, numerical analysis, signal processing, and computer science are presented by leading experts in these fields. There is a particular emphasis on stochastic analysis, machine learning algorithms, and deep learning models, which are highly relevant to the state-of-the-art in augmented, virtual, and mixed realities. Topics include: Harmonic analysis Big data analytics and applications Biomathematics Computer engineering and applications Economics and financial engineering Medical imaging and non-destructive testing This volume is ideal for engineers and researchers working in technological fields that need to be modeled and simulated using the tools of modern mathematics.-- Provided by publisher