LIST OF CONTRIBUTORS xiii
PREFACE xv
SECTION 1 INTRODUCTION 1
1 Universality of Mathematical Models in Understanding Nature, Society, and Man-Made World 3
Roderick 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 19
Israel 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 59
David 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 92
Mel 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 101
Julien 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 121
Eili 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 137
Dimitrios 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 192
Bernd 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 222
Nicolae 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 254
Ronald 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 275
Steven 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 299
Godfried 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
