Melnik, R 　著

内容

目次

LIST OF CONTRIBUTORS xiii PREFACE xv SECTION 1 INTRODUCTION 1 1 Universality of Mathematical Models in Understanding Nature, Society, and Man–Made World 3Roderick Melnik 1.1 Human Knowledge, Models, and Algorithms 3 1.2 Looking into the Future from a Modeling Perspective 7 1.3 What This Book Is About 10 1.4 Concluding Remarks 15 References 16 SECTION 2 ADVANCED MATHEMATICAL AND COMPUTATIONAL MODELS IN PHYSICS AND CHEMISTRY 17 2 Magnetic Vortices, Abrikosov Lattices, and Automorphic Functions 19Israel Michael Sigal 2.1 Introduction 19 2.2 The Ginzburg–Landau Equations 20 2.3 Vortices 25 2.4 Vortex Lattices 30 2.5 Multi–Vortex Dynamics 48 2.6 Conclusions 51 Appendix 2.A Parameterization of the equivalence classes [L] 51 Appendix 2.B Automorphy factors 52 References 54 3 Numerical Challenges in a Cholesky–Decomposed Local Correlation Quantum Chemistry Framework 59David B. Krisiloff, Johannes M. Dieterich, Florian Libisch, and Emily A. Carter 3.1 Introduction 59 3.2 Local MRSDCI 61 3.3 Numerical Importance of Individual Steps 67 3.4 Cholesky Decomposition 68 3.5 Transformation of the Cholesky Vectors 71 3.6 Two–Electron Integral Reassembly 72 3.7 Integral and Execution Buffer 76 3.8 Symmetric Group Graphical Approach 77 3.9 Summary and Outlook 87 References 87 4 Generalized Variational Theorem in Quantum Mechanics 92Mel Levy and Antonios Gonis 4.1 Introduction 92 4.2 First Proof 93 4.3 Second Proof 95 4.4 Conclusions 96 References 97 SECTION 3 MATHEMATICAL AND STATISTICAL MODELS IN LIFE AND CLIMATE SCIENCE APPLICATIONS 99 5 A Model for the Spread of Tuberculosis with Drug–Sensitive and Emerging Multidrug–Resistant and Extensively Drug–Resistant Strains 101Julien Arino and Iman A. Soliman 5.1 Introduction 101 5.2 Discussion 117 References 119 6 The Need for More Integrated Epidemic Modeling with Emphasis on Antibiotic Resistance 121Eili Y. Klein, Julia Chelen, Michael D. Makowsky, and Paul E. Smaldino 6.1 Introduction 121 6.2 Mathematical Modeling of Infectious Diseases 122 6.3 Antibiotic Resistance, Behavior, and Mathematical Modeling 125 6.4 Conclusion 128 References 129 SECTION 4 MATHEMATICAL MODELS AND ANALYSIS FOR SCIENCE AND ENGINEERING 135 7 Data–Driven Methods for Dynamical Systems: Quantifying Predictability and Extracting Spatiotemporal Patterns 137Dimitrios Giannakis and Andrew J. Majda 7.1 Quantifying Long–Range Predictability and Model Error through Data Clustering and Information Theory 138 7.2 NLSA Algorithms for Decomposition of Spatiotemporal Data 163 7.3 Conclusions 184 References 185 8 On Smoothness Concepts in Regularization for Nonlinear Inverse Problems in Banach Spaces 192Bernd Hofmann 8.1 Introduction 192 8.2 Model Assumptions, Existence, and Stability 195 8.3 Convergence of Regularized Solutions 197 8.4 A Powerful Tool for Obtaining Convergence Rates 200 8.5 How to Obtain Variational Inequalities? 206 8.6 Summary 215 References 215 9 Initial and Initial–Boundary Value Problems for First–Order Symmetric Hyperbolic Systems with Constraints 222Nicolae Tarfulea 9.1 Introduction 222 9.2 FOSH Initial Value Problems with Constraints 223 9.3 FOSH Initial–Boundary Value Problems with Constraints 230 9.4 Applications 236 References 250 10 Information Integration, Organization, and Numerical Harmonic Analysis 254Ronald R. Coifman, Ronen Talmon, Matan Gavish, and Ali Haddad 10.1 Introduction 254 10.2 Empirical Intrinsic Geometry 257 10.3 Organization and Harmonic Analysis of Databases/Matrices 263 10.4 Summary 269 References 270 SECTION 5 MATHEMATICAL METHODS IN SOCIAL SCIENCES AND ARTS 273 11 Satisfaction Approval Voting 275Steven J. Brams and D. Marc Kilgour 11.1 Introduction 275 11.2 Satisfaction Approval Voting for Individual Candidates 277 11.3 The Game Theory Society Election 285 11.4 Voting for Multiple Candidates under SAV: A Decision–Theoretic Analysis 287 11.5 Voting for Political Parties 291 11.6 Conclusions 295 11.7 Summary 296 References 297 12 Modeling Musical Rhythm Mutations with Geometric Quantization 299Godfried T. Toussaint 12.1 Introduction 299 12.2 Rhythm Mutations 301 12.3 Similarity–Based Rhythm Mutations 303 12.4 Conclusion 306 References 307 INDEX 309