Mathematical modelling Books

Book SynopsisQuantitative Methods for Finance and Investments ensures that readers come away from reading it with a reasonable degree of comfort and proficiency in applying elementary mathematics to several types of financial analysis.Trade Review"This excellent text patiently guides the reader through a wide array of mathematics, ranging from elementary matrix algebra to differential and integral calculus. The quantitative methods are illustrated with a rich and captivating assortment of applications to the analysis of portfolios, derivatives, exchange, fixed income instruments, and equities. Undergraduate and MBA-level students who have read this book will feel comfortable with the mathematics in their finance courses and their professors can focus on teaching finance as it should be taught." Kose John, Stern School of Business, New York University <1--end--> "This volume provides a comprehensive review of mathematics which will prove invaluable for students of finance. It is a reference book for the nonmathematician and a clear and concise text that will help fill the gaps in students' knowledge. Although the topic is quantitative methods, the organization, emphasis, applications, and numerous examples are all geared to the student of finance. Having Teall and Hasan on your bookshelf provides an essential safety net for students, teachers, and practitioners." Paul Wachtel, Stern School of Business, New York UniversityTable of ContentsPreface Acknowledgments 1 Introduction and Overview 1 1.1 The importance of mathematics in finance 1 1.2 Mathematical and computer modeling in finance 2 1.3 Money, securities, and markets 3 1.4 Time value, risk, arbitrage, and pricing 5 1.5 The organization of this book 6 2 A Review of Elementary Mathematics: Functions and Operations 7 2.1 Introduction 7 2.2 Variables, equations, and inequalities 7 2.3 Exponents 8 Application 2.1: Interest and future value 9 2.4 The order of arithmetic operations and the rules of algebra 10 Application 2.2: Initial deposit amounts 11 2.5 The number e 11 2.6 Logarithms 12 Application 2.3: The time needed to double your money 13 2.7 Subscripts 14 2.8 Summations 14 Application 2.4: Mean values 15 2.9 Double summations 16 2.10 Products 17 Application 2.5: Geometric means 17 Application 2.6: The term structure of interest rates 18 2.11 Factorial products 19 Application 2.7: Deriving the number e 19 2.12 Permutations and combinations 20 Exercises 21 Appendix 2.A An introduction to the Excel™ spreadsheet 23 3 A Review of Elementary Mathematics: Algebra and Solving Equations 25 3.1 Algebraic manipulations 25 Application 3.1: Purchase power parity 27 Application 3.2: Finding break-even production levels 28 Application 3.3: Solving for spot and forward interest rates 29 3.2 The quadratic formula 29 Application 3.4: Finding break-even production levels 30 Application 3.5: Finding the perfectly hedged portfolio 31 3.3 Solving systems of equations that contain multiple variables 32 Application 3.6: Pricing factors 35 Application 3.7: External financing needs 35 3.4 Geometric expansions 38 Application 3.8: Money multipliers 40 3.5 Functions and graphs 41 Application 3.9: Utility of wealth 43 Exercises 44 Appendix 3.A Solving systems of equations on a spreadsheet 48 4 The Time Value of Money 51 4.1 Introduction and future value 51 4.2 Simple interest 51 4.3 Compound interest 52 4.4 Fractional period compounding of interest 53 Application 4.1: APY and bank account comparisons 55 4.5 Continuous compounding of interest 56 4.6 Annuity future values 57 Application 4.2: Planning for retirement 59 4.7 Discounting and present value 60 4.8 The present value of a series of cash flows 61 4.9 Annuity present values 62 Application 4.3: Planning for Retirement, Part Ii 64 Application 4.4: Valuing a bond 64 4.10 Amortization 65 Application 4.5: Determining the mortgage payment 66 4.11 Perpetuity models 67 4.12 Single-stage growth models 68 Application 4.6: Stock valuation models 70 4.13 Multiple-stage growth models 72 Exercises 73 Appendix 4.A Time value spreadsheet applications 77 5 Return, Risk, and Co-movement 79 5.1 Return on investment 79 Application 5.1: Fund performance 81 5.2 Geometric mean return on investment 82 Application 5.2: Fund Performance, Part Ii 83 5.3 Internal rate of return 84 5.4 Bond yields 87 5.5 An introduction to risk 88 5.6 Expected return 88 5.7 Variance and standard deviation 89 5.8 Historical variance and standard deviation 91 5.9 Covariance 93 5.10 The coefficient of correlation and the coefficient of determination 94 Exercises 95 Appendix 5.A Return and risk spreadsheet applications 99 6 Elementary Portfolio Mathematics 103 6.1 An introduction to portfolio analysis 103 6.2 Portfolio return 103 6.3 Portfolio variance 104 6.4 Diversification and efficiency 106 6.5 The market portfolio and beta 110 6.6 Deriving the portfolio variance expression 111 Exercises 113 7 Elements of Matrix Mathematics 115 7.1 An introduction to matrices 115 Application 7.1: Portfolio mathematics 116 7.2 Matrix arithmetic 117 Application 7.2: Portfolio Mathematics, Part Ii 120 Application 7.3: Put–call parity 121 7.3 Inverting matrices 123 7.4 Solving systems of equations 125 Application 7.4: External funding requirements 126 Application 7.5: Coupon bonds and deriving yield curves 127 Application 7.6: Arbitrage with riskless bonds 130 Application 7.7: Fixed income portfolio dedication 131 Application 7.8: Binomial option pricing 132 7.5 Spanning the state space 133 Application 7.9: Using options to span the state space 136 Exercises 137 Appendix 7.A Matrix mathematics on a spreadsheet 142 8 Differential Calculus 145 8.1 Functions and limits 145 Application 8.1: The natural log 146 8.2 Slopes, derivatives, maxima, and minima 147 8.3 Derivatives of polynomials 149 Application 8.2: Marginal utility 151 Application 8.3: Duration and immunization 153 Application 8.4: Portfolio risk and diversification 156 8.4 Partial and total derivatives 157 8.5 The chain rule, product rule, and quotient rule 158 Application 8.5: Plotting the Capital Market Line 159 8.6 Logarithmic and exponential functions 165 8.7 Taylor series expansions 166 Application 8.6: Convexity and immunization 167 Exercises 172 Appendix 8.A Derivatives of polynomials 176 Appendix 8.B A table of rules for finding derivatives 177 Appendix 8.C Portfolio risk minimization on a spreadsheet 178 9 Integral Calculus 180 9.1 Antidifferentiation and the indefinite integral 180 9.2 Riemann sums 181 9.3 Definite integrals and areas 185 Application 9.1: Cumulative densities 186 Application 9.2: Expected value and variance 188 Application 9.3: Valuing continuous dividend payments 189 Application 9.4: Expected option values 191 9.4 Differential equations 191 Application 9.5: Security returns in continuous time 193 Application 9.6: Annuities and growing annuities 194 Exercises 195 Appendix 9.A Rules for finding integrals 198 Appendix 9.B Riemann sums on a spreadsheet 199 10 Elements of Options Mathematics 203 10.1 An introduction to stock options 203 10.2 Binomial option pricing: one time period 205 10.3 Binomial option pricing: multiple time periods 207 10.4 The Black–Scholes option pricing model 210 10.5 Puts and valuation 212 10.6 Black–Scholes model sensitivities 213 10.7 Estimating implied volatilities 215 Exercises 219 References 222 Appendix A Solutions to Exercises 224 Appendix B The z-Table 266 Appendix C Notation 267 Appendix D Glossary 270 Index 274

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Book Synopsisaeo provides all the specialist knowledge, understanding and confidence needed to use models aeo focuses on life--cycle modelling, from the commissioning of a building through to demolition aeo offers practitioners an insight through detailed case studies to use of models.Table of ContentsPreface. Chapter 1 Heat Transfer in Building Elements. 1.1 Heat and mass transfer processes in buildings. 1.2 Heat transfer through external walls and roofs. 1.3 Analytical methods for solving the one-dimensional transient heat conduction equation. 1.4 Lumped capacitance methods. 1.5 Heat transfer through glazing. Chapter 2 Modelling Heat Transfer in Building Envelopes. 2.1 Finite Difference Method – A Numerical Method for Solving the Heat Conduction Equation. 2.2 Heat Transfer in Building Spaces. 2.3 Synthesis of Heat Transfer Methods. 2.4 Latent Loads and Room Moisture Content Balance. Chapter 3 Mass Transfer, Air Movement and Ventilation. Chapter 4 Steady-State Plant Modelling. 4.1 Model Formulations for Plant. 4.2 Mathematical Models of Air-conditioning Equipment using Equation-fitting. 4.3 A Detailed Steady-state Cooling and Dehumidifying Coil Model. 4.4 Modelling Distribution Networks. 4.5 Modelling Air-conditioning Systems. Chapter 5 Modelling Control Systems. 5.1 Distributed System Modelling. 5.2 Modelling Control Elements. 5.3 Modelling Control Algorithms. 5.4 Solution Schemes. Chapter 6 Modeling in Practice I. 6.1 Developments in General. 6.2 Internal Ventilation Problems6.3 Wind Flow Around Buildings. 6.4 Applications to Plant. 6.5 Applications to Control and Fault Detection. Chapter 7 Modeling in Practice II. 7.1 Interrelationships Between Methodologies. 7.2 Tools and Their Integration. 7.3 Validation and Verification. References. Appendix A. Appendix B. Index

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Book SynopsisServes as a how-to guide for developing mathematical models in biology. Starting at an elementary level of mathematical modeling, this title gradually builds from classic models in ecology and evolution to more intricate class-structured and probabilistic models. It provides primers with instructive exercises.Trade ReviewHonorable Mention for the 2007 Best Professional/Scholarly Book in Biological Sciences, Association of American Publishers "A gentle but thorough introduction to the mathematical techniques employed in ecological and evolutionary theory. Readers who ... finish this well-written book will be prepared to read and understand a sizeable fraction of the current literature."--Donald L. DeAngelis, Quarterly Review of Biology "At long last, Sally Otto and Troy Day have provided relief for biologists and epidemiologists in search of an easily read, practical, and thorough starting point from which to learn mathematical modeling... We would recommend this book over shorter texts that are labeled as 'introductory'... The depth and detail that Otto and Day have included in this text arc appealing rather than intimidating, and the structure of the text is empowering rather than didactic or formulaic."--Sanjay Basu and Alison P. Galvani, Siam Review "[T]he great value of the Otto/Day book is that it attempts pedagogical soundness, and so is useful for teaching. Besides being perfectly readable, it engages and impresses the reader quickly not only with the subject matter, but also with the quality of printing and layout which have to be seen to be believed. These praises may sound lavish by many a reader of these columns but first see the book or better still buy the volume and you will see our passion and rage for going all out in praise of this volume."--Current Engineering Practice "I highly recommend this book for every university biology department because it provides both a unique, and often uplifting, introduction and a comprehensive reference of techniques for building and analysing mathematical models."--Volker Grimm, Basic and Applied Ecology "I cannot help but think that future textbook authors will want to have Otto and Day front and center on the work desk, for this is a valuable source of material... This book stands out, and its contribution is quite apparent. In sum, this book is a valuable contribution to the literature, and one to which I expect to refer regularly in connection with my teaching and writing duties."--Steven G. Krantz, UMAP Journal "[A] great textbook... [M]asterful use of figures and illustrations and exercises ... provide the reader with valuable practice in constructing models and implementing related mathematical techniques. I certainly recommend this text and can attest to its usefulness for budding researchers in the biological sciences."--Jason M. Graham, MAA ReviewsTable of ContentsPreface ix Chapter 1: Mathematical Modeling in Biology 1 1.1 Introduction 1 1.2 HIV 2 1.3 Models of HIV/AIDS 5 1.4 Concluding Message 14 Chapter 2: How to Construct a Model 17 2.1 Introduction 17 2.2 Formulate the Question 19 2.3 Determine the Basic Ingredients 19 2.4 Qualitatively Describe the Biological System 26 2.5 Quantitatively Describe the Biological System 33 2.6 Analyze the Equations 39 2.7 Checks and Balances 47 2.8 Relate the Results Back to the Question 50 2.9 Concluding Message 51 Chapter 3: Deriving Classic Models in Ecology and Evolutionary Biology 54 3.1 Introduction 54 3.2 Exponential and Logistic Models of Population Growth 54 3.3 Haploid and Diploid Models of Natural Selection 62 3.4 Models of Interactions among Species 72 3.5 Epidemiological Models of Disease Spread 77 3.6 Working Backward--Interpreting Equations in Terms of the Biology 79 3.7 Concluding Message 82 Primer 1: Functions and Approximations 89 P1.1 Functions and Their Forms 89 P1.2 Linear Approximations 96 P1.3 The Taylor Series 100 Chapter 4: Numerical and Graphical Techniques--Developing a Feeling for Your Model 110 4.1 Introduction 110 4.2 Plots of Variables Over Time 111 4.3 Plots of Variables as a Function of the Variables Themselves 124 4.4 Multiple Variables and Phase-Plane Diagrams 133 4.5 Concluding Message 145 Chapter 5: Equilibria and Stability Analyses--One-Variable Models 151 5.1 Introduction 151 5.2 Finding an Equilibrium 152 5.3 Determining Stability 163 5.4 Approximations 176 5.5 Concluding Message 184 Chapter 6: General Solutions and Transformations--One-Variable Models 191 6.1 Introduction 191 6.2 Transformations 192 6.3 Linear Models in Discrete Time 193 6.4 Nonlinear Models in Discrete Time 195 6.5 Linear Models in Continuous Time 198 6.6 Nonlinear Models in Continuous Time 202 6.7 Concluding Message 207 Primer 2: Linear Algebra 214 P2.1 An Introduction to Vectors and Matrices 214 P2.2 Vector and Matrix Addition 219 P2.3 Multiplication by a Scalar 222 P2.4 Multiplication of Vectors and Matrices 224 P2.5 The Trace and Determinant of a Square Matrix 228 P2.6 The Inverse 233 P2.7 Solving Systems of Equations 235 P2.8 The Eigenvalues of a Matrix 237 P2.9 The Eigenvectors of a Matrix 243 Chapter 7: Equilibria and Stability Analyses--Linear Models with Multiple Variables 254 7.1 Introduction 254 7.2 Models with More than One Dynamic Variable 255 7.3 Linear Multivariable Models 260 7.4 Equilibria and Stability for Linear Discrete-Time Models 279 7.5 Concluding Message 289 Chapter 8: Equilibria and Stability Analyses--Nonlinear Models with Multiple Variables 294 8.1 Introduction 294 8.2 Nonlinear Multiple-Variable Models 294 8.3 Equilibria and Stability for Nonlinear Discrete-Time Models 316 8.4 Perturbation Techniques for Approximating Eigenvalues 330 8.5 Concluding Message 337 Chapter 9: General Solutions and Tranformations--Models with Multiple Variables 347 9.1 Introduction 347 9.2 Linear Models Involving Multiple Variables 347 9.3 Nonlinear Models Involving Multiple Variables 365 9.4 Concluding Message 381 Chapter 10: Dynamics of Class-Structured Populations 386 10.1 Introduction 386 10.2 Constructing Class-Structured Models 388 10.3 Analyzing Class-Structured Models 393 10.4 Reproductive Value and Left Eigenvectors 398 10.5 The Effect of Parameters on the Long-Term Growth Rate 400 10.6 Age-Structured Models--The Leslie Matrix 403 10.7 Concluding Message 418 Chapter 11: Techniques for Analyzing Models with Periodic Behavior 423 11.1 Introduction 423 11.2 What Are Periodic Dynamics? 423 11.3 Composite Mappings 425 11.4 Hopf Bifurcations 428 11.5 Constants of Motion 436 11.6 Concluding Message 449 Chapter 12: Evolutionary Invasion Analysis 454 12.1 Introduction 454 12.2 Two Introductory Examples 455 12.3 The General Technique of Evolutionary Invasion Analysis 465 12.4 Determining How the ESS Changes as a Function of Parameters 478 12.5 Evolutionary Invasion Analyses in Class-Structured Populations 485 12.6 Concluding Message 502 Primer 3: Probability Theory 513 P3.1 An Introduction to Probability 513 P3.2 Conditional Probabilities and Bayes' Theorem 518 P3.3 Discrete Probability Distributions 521 P3.4 Continuous Probability Distributions 536 P3.5 The (Insert Your Name Here) Distribution 553 Chapter 13: Probabilistic Models 567 13.1 Introduction 567 13.2 Models of Population Growth 568 13.3 Birth-Death Models 573 13.4 Wright-Fisher Model of Allele Frequency Change 576 13.5 Moran Model of Allele Frequency Change 581 13.6 Cancer Development 584 13.7 Cellular Automata--A Model of Extinction and Recolonization 591 13.8 Looking Backward in Time--Coalescent Theory 594 13.9 Concluding Message 602 Chapter 14: Analyzing Discrete Stochastic Models 608 14.1 Introduction 608 14.2 Two-State Markov Models 608 14.3 Multistate Markov Models 614 14.4 Birth-Death Models 631 14.5 Branching Processes 639 14.6 Concluding Message 644 Chapter 15: Analyzing Continuous Stochastic Models--Diffusion in Time and Space 649 15.1 Introduction 649 15.2 Constructing Diffusion Models 649 15.3 Analyzing the Diffusion Equation with Drift 664 15.4 Modeling Populations in Space Using the Diffusion Equation 684 15.5 Concluding Message 687 Epilogue: The Art of Mathematical Modeling in Biology 692 Appendix 1: Commonly Used Mathematical Rules 695 A1.1 Rules for Algebraic Functions 695 A1.2 Rules for Logarithmic and Exponential Functions 695 A1.3 Some Important Sums 696 A1.4 Some Important Products 696 A1.5 Inequalities 697 Appendix 2: Some Important Rules from Calculus 699 A2.1 Concepts 699 A2.2 Derivatives 701 A2.3 Integrals 703 A2.4 Limits 704 Appendix 3: The Perron-Frobenius Theorem 709 A3.1: Definitions 709 A3.2: The Perron-Frobenius Theorem 710 Appendix 4: Finding Maxima and Minima of Functions 713 A4.1 Functions with One Variable 713 A4.2 Functions with Multiple Variables 714 Appendix 5: Moment-Generating Functions 717 Index of Definitions, Recipes, and Rules 725 General Index 727

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Book SynopsisWritten for students, researchers, consultants, professionals, and scholars, Logic Modeling Methods in Program Evaluation provides a step-by-step explanation of logic modeling and its importance in connecting theory with implementation and outcomes in program evaluation in the social sciences.Trade Review"The book is definitely worth buying. Both program developers and evaluators will find the text useful." (Journal of Multidisciplinary Evaluation, March 2008)Table of ContentsList of Figures. Preface. 1. Evaluation and Logic Models. 2. The Uses of Logic Models. 3. The Components of a Logic Model. 4. The Connections in a Logic Model. 5. Developing Logic Models to Support Evaluation. 6. Developing Logic Models of Differing Complexity. 7. Using a Logic Model to Identify Evaluation Questions. 8. Using a Logic Model to Support Explanatory Evaluation. 9. Challenges in Developing Logic Models. 10. Developing Logic Models for Complex Projects. 11. Using Logic Models to Evaluate a Family of Projects. 12. Using the Logic Model to Provide Technical Assistance. Appendix: The Phases of an Evaluation. About the Author. Glossary. References.

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Book SynopsisThere have been many wonderful developments in the theory of minimal surfaces and geometric measure theory. This book covers variational geometry. It focuses on Plateau's Problem, which is concerned with surfaces that model the behavior of soap films.Table of ContentsThe phenomena of least area problems Integration of differential forms over rectifiable sets Varifolds Variational problems involving varifolds References Additional references Index.

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Book SynopsisWritten by leading researchers from the USA, Canada and Europe, this is an essential reference tool for researchers and advanced students in animal nutrition. Farm livestock have evolved digestive systems that are capable of digesting fibrous materials and by-products unsuited for man. Throughout the world, production from farm livestock is concerned with providing food and clothing of animal origin for man. Animal production science underpins this goal and provides the scientific basis for livestock management practices. Feed evaluation concerns the use of methods to describe animal feedstuffs with respect to their ability to sustain different types and levels of animal performance. The main themes of the book are methods of feed evaluation, current feeding systems, and mechanistic mathematical modelling. No other title brings together methods, systems and models under one cover.Table of Contents1: Feed Evaluation for Animal Production, J France, MK Theodorou, RS Lowman and DE Beever 2: Feed Characterisation, A Chesson 3: Intake, Passage and Digestibility, DP Poppi, J France and SR McLennan 4: In Vitro and In Situ Methods for Estimating Digestibility with Reference to Protein Degradability, GA Broderick and RC Cochran 5: Measurement of Energy Metabolism, C K Reynolds 6: Feeding Systems for Dairy Cows, S Tamminga and G Hof 7: Feeding Systems for Beef Cattle, JG Buchanan-Smith and DG Fox 8: Feeding Systems for Sheep, LA Sinclair and RG Wilkinson 9: Feeding Systems for Pigs, LI Chiba 10: Feeding Systems for Poultry, S Leeson and JD Summers 11: Feeding Systems for Horses, D Cuddeford 12: Prediction of Response to Nutrients by Ruminants Through Mathematical Modelling and Improved Feed Characterization, DE Beever, J France and G Alderman 13: Analyses of Modelling Whole Rumen Function, J Dijkstra and A Bannink 14: Modelling the Lactating Dairy Cow, RL Baldwin and KC Donovan 15: Modelling Growth and Wool Production in Ruminants, WJ Gerrits and J Dijkstra 16: Modelling Growth and Lactation in Pigs, JL Black 17: Modelling the Utilization of Dietary Energy and Amino Acids by Poultry, MG MacLeod 18: Modelling Growth in Fish, Y Cui and S Xie 19: The Nutrition of Companion Animals, AC Longland, MK Theodorou and IH Burger 20: Index

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Book SynopsisMathematical modeling - the ability to apply mathematical concepts and techniques to real-life systemsâhas expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters.

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Book SynopsisA modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momeTrade Review “The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.” (Zentralblatt MATH, 2012) Table of ContentsPreface xiii I Nonlinear Continuum Mechanics 1 1 Kinematics of Deformable Bodies 3 1.1 Motion 4 1.2 Strain and Deformation Tensors 7 1.3 Rates of Motion 10 1.4 Rates of Deformation 13 1.5 The Piola Transformation 15 1.6 The Polar Decomposition Theorem 19 1.7 Principal Directions and Invariants of Deformation and Strain 20 1.8 The Reynolds' Transport Theorem 23 2 Mass and Momentum 25 2.1 Local Forms of the Principle of Conservation of Mass 26 2.2 Momentum 28 3 Force and Stress in Deformable Bodies 29 4 The Principles of Balance of Linear and Angular Momentum 35 4.1 Cauchy's Theorem: The Cauchy Stress Tensor 36 4.2 The Equations of Motion (Linear Momentum) 38 4.3 The Equations of Motion Referred to the Reference Configuration: The Piola-Kirchhoff Stress Tensors 40 4.4 Power 42 5 The Principle of Conservation of Energy 45 5.1 Energy and the Conservation of Energy 45 5.2 Local Forms of the Principle of Conservation of Energy 47 6 Thermodynamics of Continua and the Second Law 49 7 Constitutive Equations 53 7.1 Rules and Principles for Constitutive Equations 54 7.2 Principle of Material Frame Indifference 57 7.2.1 Solids 57 7.2.2 Fluids 59 7.3 The Coleman-Noll Method: Consistency with the Second Law of Thermodynamics 60 8 Examples and Applications 63 8.1 The Navier-Stokes Equations for Incompressible Flow 63 8.2 Flow of Gases and Compressible Fluids: The Compressible Navier-Stokes Equations 66 8.3 Heat Conduction 67 8.4 Theory of Elasticity 69 II Electromagnetic Field Theory and Quantum Mechanics 73 9 Electromagnetic Waves 75 9.1 Introduction 75 9.2 Electric Fields 75 9.3 Gauss's Law 79 9.4 Electric Potential Energy 80 9.4.1 Atom Models 80 9.5 Magnetic Fields 81 9.6 Some Properties of Waves 84 9.7 Maxwell's Equations 87 9.8 Electromagnetic Waves 91 10 Introduction to Quantum Mechanics 93 10.1 Introductory Comments 93 10.2 Wave and Particle Mechanics 94 10.3 Heisenberg's Uncertainty Principle 97 10.4 Schrödinger's Equation 99 10.4.1 The Case of a Free Particle 99 10.4.2 Superposition in Rn 101 10.4.3 Hamiltonian Form 102 10.4.4 The Case of Potential Energy 102 10.4.5 Relativistic Quantum Mechanics 102 10.4.6 General Formulations of Schrödinger's Equation 103 10.4.7 The Time-Independent Schrödinger Equation 104 10.5 Elementary Properties of the Wave Equation 104 10.5.1 Review 104 10.5.2 Momentum 106 10.5.3 Wave Packets and Fourier Transforms 109 10.6 The Wave-Momentum Duality 110 10.7 Appendix: A Brief Review of Probability Densities 111 11 Dynamical Variables and Observables in Quantum Mechanics: The Mathematical Formalism 115 11.1 Introductory Remarks 115 11.2 The Hilbert Spaces L2(R) (or L2(Rd)) and H1(R) (or H1(Rd)) 116 11.3 Dynamical Variables and Hermitian Operators 118 11.4 Spectral Theory of Hermitian Operators: The Discrete Spectrum 121 11.5 Observables and Statistical Distributions 125 11.6 The Continuous Spectrum 127 11.7 The Generalized Uncertainty Principle for Dynamical Variables 128 11.7.1 Simultaneous Eigenfunctions 130 12 Applications: The Harmonic Oscillator and the Hydrogen Atom 131 12.1 Introductory Remarks 131 12.2 Ground States and Energy Quanta: The Harmonic Oscillator 131 12.3 The Hydrogen Atom 133 12.3.1 Schrödinger Equation in Spherical Coordinates 135 12.3.2 The Radial Equation 136 12.3.3 The Angular Equation 138 12.3.4 The Orbitals of the Hydrogen Atom 140 12.3.5 Spectroscopic States 140 13 Spin and Pauli's Principle 145 13.1 Angular Momentum and Spin 145 13.2 Extrinsic Angular Momentum 147 13.2.1 The Ladder Property: Raising and Lowering States 149 13.3 Spin 151 13.4 Identical Particles and Pauli's Principle 155 13.5 The Helium Atom 158 13.6 Variational Principle 161 14 Atomic and Molecular Structure 165 14.1 Introduction 165 14.2 Electronic Structure of Atomic Elements 165 14.3 The Periodic Table 169 14.4 Atomic Bonds and Molecules 173 14.5 Examples of Molecular Structures 180 15 Ab Initio Methods: Approximate Methods and Density Functional Theory 189 15.1 Introduction 189 15.2 The Born-Oppenheimer Approximation 190 15.3 The Hartree and the Hartree-Fock Methods 194 15.3.1 The Hartree Method 196 15.3.2 The Hartree-Fock Method 196 15.3.3 The Roothaan Equations 199 15.4 Density Functional Theory 200 15.4.1 Electron Density 200 15.4.2 The Hohenberg-Kohn Theorem 205 15.4.3 The Kohn-Sham Theory 208 III Statistical Mechanics 213 16 Basic Concepts: Ensembles, Distribution Functions, and Averages 215 16.1 Introductory Remarks 215 16.2 Hamiltonian Mechanics 216 16.2.1 The Hamiltonian and the Equations of Motion 218 16.3 Phase Functions and Time Averages 219 16.4 Ensembles, Ensemble Averages, and Ergodic Systems 220 16.5 Statistical Mechanics of Isolated Systems 224 16.6 The Microcanonical Ensemble 228 16.6.1 Composite Systems 230 16.7 The Canonical Ensemble 234 16.8 The Grand Canonical Ensemble 239 16.9 Appendix: A Brief Account of Molecular Dynamics 240 16.9.1 Newtonian's Equations of Motion 241 16.9.2 Potential Functions 242 16.9.3 Numerical Solution of the Dynamical System 245 17 Statistical Mechanics Basis of Classical Thermodynamics 249 17.1 Introductory Remarks 249 17.2 Energy and the First Law of Thermodynamics 250 17.3 Statistical Mechanics Interpretation of the Rate of Work in Quasi-Static Processes 251 17.4 Statistical Mechanics Interpretation of the First Law of Thermodynamics 254 17.4.1 Statistical Interpretation of Q 256 17.5 Entropy and the Partition Function 257 17.6 Conjugate Hamiltonians 259 17.7 The Gibbs Relations 261 17.8 Monte Carlo and Metropolis Methods 262 17.8.1 The Partition Function for a Canonical Ensemble 263 17.8.2 The Metropolis Method 264 17.9 Kinetic Theory: Boltzmann's Equation of Nonequilibrium Statistical Mechanics 265 17.9.1 Boltzmann's Equation 265 17.9.2 Collision Invariants 268 17.9.3 The Continuum Mechanics of Compressible Fluids and Gases: The Macroscopic Balance Laws 269 Exercises 273 Bibliography 317 Index 325

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Book SynopsisA powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, it also enables them to apply these models to any macroscopic physical system. Mathematical Modeling in Science and Engineering focuses on models in which the processes to be modeled are expressed as systems of partial differential equations. It begins with an introductory discussion of the axiomatic formulation of basic models, setting the foundation for further topics such as:Table of ContentsPreface xiii 1 AXIOMATIC FORMULATION OF THE BASIC MODELS 1 1.1 Models 1 1.2 Microscopic and macroscopic physics 2 1.3 Kinematics of continuous systems 3 1.3.1 Intensive properties 6 1.3.2 Extensive properties 8 1.4 Balance equations of extensive and intensive properties 9 1.4.1 Global balance equations 9 1.4.2 The local balance equations 10 1.4.3 The role of balance conditions in the modeling of continuous systems 13 1.4.4 Formulation of motion restrictions by means of balance equations 14 1.5 Summary 16 2 MECHANICS OF CLASSICAL CONTINUOUS SYSTEMS 23 2.1 One-phase systems 23 2.2 The basic mathematical model of one-phase systems 24 2.3 The extensive/intensive properties of classical mechanics 25 2.4 Mass conservation 26 2.5 Linear momentum balance 27 2.6 Angular momentum balance 29 2.7 Energy concepts 32 2.8 The balance of kinetic energy 33 2.9 The balance of internal energy 34 2.10 Heat equivalent of mechanical work 35 2.11 Summary of basic equations for solid and fluid mechanics 35 2.12 Some basic concepts of thermodynamics 36 2.12.1 Heat transport 36 2.13 Summary 38 3 MECHANICS OF NON-CLASSICAL CONTINUOUS SYSTEMS 45 3.1 Multiphase systems 45 3.2 The basic mathematical model of multiphase systems 46 3.3 Solute transport in a free fluid 47 3.4 Transport by fluids in porous media 49 3.5 Flow of fluids through porous media 51 3.6 Petroleum reservoirs: the black-oil model 52 3.6.1 Assumptions of the black-oil model 53 3.6.2 Notation 53 3.6.3 Family of extensive properties 54 3.6.4 Differential equations and jump conditions 55 3.7 Summary 57 4 SOLUTE TRANSPORT BY A FREE FLUID 63 4.1 The general equation of solute transport by a free fluid 64 4.2 Transport processes 65 4.2.1 Advection 65 4.2.2 Diffusion processes 65 4.3 Mass generation processes 66 4.4 Differential equations of diffusive transport 67 4.5 Well-posed problems for diffusive transport 69 4.5.1 Time-dependent problems 70 4.5.2 Steady state 71 4.6 First-order irreversible processes 71 4.7 Differential equations of non-diffusive transport 73 4.8 Well-posed problems for non-diffusive transport 73 4.8.1 Well-posed problems in one spatial dimension 74 4.8.2 Well-posed problems in several spatial dimensions 79 4.8.3 Well-posed problems for steady-state models 80 4.9 Summary 80 5 FLOW OF A FLUID IN A POROUS MEDIUM 85 5.1 Basic assumptions of the flow model 85 5.2 The basic model for the flow of a fluid through a porous medium 86 5.3 Modeling the elasticity and compressibility 87 5.3.1 Fluid compressibility 87 5.3.2 Pore compressibility 88 5.3.3 The storage coefficient 90 5.4 Darcy's law 90 5.5 Piezometric level 92 5.6 General equation governing flow through a porous medium 94 5.6.1 Special forms of the governing differential equation 95 5.7 Applications of the jump conditions 96 5.8 Well-posed problems 96 5.8.1 Steady-state models 97 5.8.2 Time-dependent problems 99 5.9 Models with a reduced number of spatial dimensions 99 5.9.1 Theoretical derivation of a 2-D model for a confined aquifer 100 5.9.2 Leaky aquitard method 102 5.9.3 The integrodifferential equations approach 104 5.9.4 Other 2-D aquifer models 108 5.10 Summary 111 6 SOLUTE TRANSPORT IN A POROUS MEDIUM 117 6.1 Transport processes 118 6.1.1 Advection 118 6.2 Non-conservative processes 118 6.2.1 First-order irreversible processes 119 6.2.2 Adsorption 119 6.3 Dispersion-diffusion 121 6.4 The equations for transport of solutes in porous media 123 6.5 Well-posed problems 125 6.6 Summary 125 7 MULTIPHASE SYSTEMS 129 7.1 Basic model for the flow of multiple-species transport in a multiple-fluid- phase porous medium 129 7.2 Modeling the transport of species i in phase a 130 7.3 The saturated flow case 133 7.4 The air-water system 137 7.5 The immobile air unsaturated flow model 142 7.6 Boundary conditions 143 7.7 Summary 145 8 ENHANCED OIL RECOVERY 149 8.1 Background on oil production and reservoir modeling 149 8.2 Processes to be modeled 151 8.3 Unified formulation of EOR models 151 8.4 The black-oil model 152 8.5 The Compositional Model 156 8.6 Summary 160 9 LINEAR ELASTICITY 165 9.1 Introduction 165 9.2 Elastic Solids 166 9.3 The Linear Elastic Solid 167 9.4 More on the Displacement Field Decomposition 170 9.5 Strain Analysis 171 9.6 Stress Analysis 173 9.7 Isotropic materials 175 9.8 Stress-strain relations for isotropic materials 177 9.9 The governing differential equations 179 9.9.1 Elastodynamics 180 9.9.2 Elastostatics 180 9.10 Well-posed problems 181 9.10.1 Elastostatics 181 9.10.2 Elastodynamics 181 9.11 Representation of solutions for isotropic elastic solids 182 9.12 Summary 183 10 FLUID MECHANICS 189 10.1 Introduction 189 10.2 Newtonian fluids: Stokes' constitutive equations 190 10.3 Navier-Stokes equations 192 10.4 Complementary constitutive equations 193 10.5 The concepts of incompressible and inviscid fluids 193 10.6 Incompressible fluids 194 10.7 Initial and boundary conditions 195 10.8 Viscous incompressible fluids: steady states 196 10.9 Linearized theory of incompressible fluids 196 10.10 Ideal fluids 197 10.11 Irrotational flows 198 10.12 Extension of Bernoulli's relations to compressible fluids 199 10.13 Shallow-water theory 200 10.14 Inviscid compressible fluids 202 10.14.1 Small perturbations in a compressible fluid: the theory of sound 203 10.14.2 Initiation of motion 204 10.14.3 Discontinuous models and shock conditions 206 10.15 Summary 208 A: PARTIAL DIFFERENTIAL EQUATIONS 211 A. 1 Classification 211 A.2 Canonical forms 213 A.3 Well-posed problems 213 A.3.1 Boundary-value problems: the elliptic case 214 A.3.2 Initial-boundary-value problems 214 B: SOME RESULTS FROM THE CALCULUS 217 B.l Notation 217 B.2 Generalized Gauss Theorem 218 C: PROOF OF THEOREM 221 D: THE BOUNDARY LAYER INCOMPRESSIBILITY APPROXIMATION 225 E: INDICIAL NOTATION 229 E.l General 229 E.2 Matrix algebra 230 E.3 Applications to differential calculus 232 Index 235

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Book SynopsisIn recent years, there has been a growing debate, particularly in the UK and Europe, over the merits of using discrete-event simulation (DES) and system dynamics (SD); there are now instances where both methodologies were employed on the same problem.Table of ContentsPreface xv List of contributors xvii 1 Introduction 1Sally Brailsford, Leonid Churilov and Brian Dangerfield 1.1 How this book came about 1 1.2 The editors 2 1.3 Navigating the book 3 References 9 2 Discrete-event simulation: A primer 10 Stewart Robinson 2.1 Introduction 10 2.2 An example of a discrete-event simulation: Modelling a hospital theatres process 11 2.3 The technical perspective: How DES works 12 2.3.1 Time handling in DES 14 2.3.2 Random sampling in DES 15 2.4 The philosophical perspective: The DES worldview 21 2.5 Software for DES 23 2.6 Conclusion 24 References 24 3 Systems thinking and system dynamics: A primer 26 Brian Dangerfield 3.1 Introduction 26 3.2 Systems thinking 28 3.2.1 ‘Behaviour over time’ graphs 28 3.2.2 Archetypes 29 3.2.3 Principles of influence (or causal loop) diagrams 30 3.2.4 From diagrams to behaviour 32 3.3 System dynamics 34 3.3.1 Principles of stock–flow diagramming 34 3.3.2 Model purpose and model conceptualisation 35 3.3.3 Adding auxiliaries, parameters and information links to the spinal stock–flow structure 36 3.3.4 Equation writing and dimensional checking 37 3.4 Some further important issues in SD modelling 40 3.4.1 Use of soft variables 40 3.4.2 Co-flows 42 3.4.3 Delays and smoothing functions 43 3.4.4 Model validation 46 3.4.5 Optimisation of SD models 48 3.4.6 The role of data in SD models 49 3.5 Further reading 49 References 50 4 Combining problem structuring methods with simulation: The philosophical and practical challenges 52 Kathy Kotiadis and John Mingers 4.1 Introduction 52 4.2 What are problem structuring methods? 53 4.3 Multiparadigm multimethodology in management science 54 4.3.1 Paradigm incommensurability 55 4.3.2 Cultural difficulties 57 4.3.3 Cognitive difficulties 58 4.3.4 Practical problems 59 4.4 Relevant projects and case studies 60 4.5 The case study: Evaluating intermediate care 62 4.5.1 The problem situation 62 4.5.2 Soft systems methodology 64 4.5.3 Discrete-event simulation modelling 66 4.5.4 Multimethodology 67 4.6 Discussion 68 4.6.1 The multiparadigm multimethodology position and strategy 68 4.6.2 The cultural difficulties 70 4.6.3 The cognitive difficulties 70 4.7 Conclusions 72 Acknowledgements 72 References 72 5 Philosophical positioning of discrete-event simulation and system dynamics as management science tools for process systems: A critical realist perspective 76 Kristian Rotaru, Leonid Churilov and Andrew Flitman 5.1 Introduction 76 5.2 Ontological and epistemological assumptions of CR 80 5.2.1 The stratified CR ontology 80 5.2.2 The abductive mode of reasoning 81 5.3 Process system modelling with SD and DES through the prism of CR scientific positioning 82 5.3.1 Lifecycle perspective on SD and DES methods 84 5.4 Process system modelling with SD and DES: Trends in and implications for MS 90 5.5 Summary and conclusions 97 References 99 6 Theoretical comparison of discrete-event simulation and system dynamics 105 Sally Brailsford 6.1 Introduction 105 6.2 System dynamics 106 6.3 Discrete-event simulation 108 6.4 Summary: The basic differences 110 6.5 Example: Modelling emergency care in Nottingham 112 6.5.1 Background 112 6.5.2 The ECOD project 113 6.5.3 Choice of modelling approach 114 6.5.4 Quantitative phase 114 6.5.5 Model validation 116 6.5.6 Scenario testing and model results 116 6.5.7 The ED model 118 6.5.8 Discussion 119 6.6 The $64 000 question: Which to choose? 120 6.7 Conclusion 123 References 123 7 Models as interfaces 125 Steffen Bayer, Tim Bolt, Sally Brailsford and Maria Kapsali 7.1 Introduction: Models at the interfaces or models as interfaces 125 7.2 The social roles of simulation 126 7.3 The modelling process 129 7.4 The modelling approach 131 7.5 Two case studies of modelling projects 134 7.6 Summary and conclusions 137 References 138 8 An empirical study comparing model development in discrete-event simulation and system dynamics 140 Antuela Tako and Stewart Robinson 8.1 Introduction 140 8.2 Existing work comparing DES and SD modelling 142 8.2.1 DES and SD model development process 143 8.2.2 Summary 146 8.3 The study 146 8.3.1 The case study 146 8.3.2 Verbal protocol analysis 147 8.3.3 The VPA sessions 149 8.3.4 The subjects 149 8.3.5 The coding process 150 8.4 Study results 151 8.4.1 Attention paid to modelling topics 152 8.4.2 The sequence of modelling stages 154 8.4.3 Pattern of iterations among topics 155 8.5 Observations from the DES and SD expert modellers’ behaviour 158 8.6 Conclusions 160 Acknowledgements 162 References 162 9 Explaining puzzling dynamics: A comparison of system dynamics and discrete-event simulation 165 John Morecroft and Stewart Robinson 9.1 Introduction 165 9.2 Existing comparisons of SD and DES 166 9.3 Research focus 169 9.4 Erratic fisheries – chance, destiny and limited foresight 170 9.5 Structure and behaviour in fisheries: A comparison of SD and DES models 173 9.5.1 Alternative models of a natural fishery 174 9.5.2 Alternative models of a simple harvested fishery 178 9.5.3 Alternative models of a harvested fishery with endogenous ship purchasing 184 9.6 Summary of findings 192 9.7 Limitations of the study 193 9.8 SD or DES? 194 Acknowledgements 196 References 196 10 DES view on simulation modelling: SIMUL8 199 Mark Elder 10.1 Introduction 199 10.2 How software fits into the project 200 10.3 Building a DES 202 10.4 Getting the right results from a DES 208 10.4.1 Verification and validation 210 10.4.2 Replications 211 10.5 What happens after the results? 212 10.6 What else does DES software do and why? 212 10.7 What next for DES software? 213 References 214 11 Vensim and the development of system dynamics 215 Lee Jones 11.1 Introduction 215 11.2 Coping with complexity: The need for system dynamics 216 11.3 Complexity arms race 219 11.4 The move to user-led innovation 221 11.5 Software support 222 11.5.1 Apples and oranges (basic model testing) 223 11.5.2 Confidence 224 11.5.3 Helping the practitioner do more 237 11.6 The future for SD software 245 11.6.1 Innovation 245 11.6.2 Communication 245 References 247 12 Multi-method modeling: AnyLogic 248 Andrei Borshchev 12.1 Architectures 249 12.1.1 The choice of model architecture and methods 251 12.2 Technical aspect of combining modeling methods 252 12.2.1 System dynamics ® discrete elements 252 12.2.2 Discrete elements ® system dynamics 253 12.2.3 Agent based « discrete event 255 12.3 Example: Consumer market and supply chain 257 12.3.1 The supply chain model 257 12.3.2 The market model 258 12.3.3 Linking the DE and the SD parts 259 12.3.4 The inventory policy 260 12.4 Example: Epidemic and clinic 262 12.4.1 The epidemic model 262 12.4.2 The clinic model and the integration of methods 264 12.5 Example: Product portfolio and investment policy 267 12.5.1 Assumptions 268 12.5.2 The model architecture 270 12.5.3 The agent product and agent population portfolio 271 12.5.4 The investment policy 274 12.5.5 Closing the loop and implementing launch of new products 275 12.5.6 Completing the investment policy 277 12.6 Discussion 278 References 279 13 Multiscale modelling for public health management: A practical guide 280 Rosemarie Sadsad and Geoff McDonnell 13.1 Introduction 280 13.2 Background 281 13.3 Multilevel system theories and methodologies 281 13.4 Multiscale simulation modelling and management 283 13.5 Discussion 289 13.6 Conclusion 290 References 290 14 Hybrid modelling case studies 295 Rosemarie Sadsad, Geoff McDonnell, Joe Viana, Shivam M. Desai, Paul Harper and Sally Brailsford 14.1 Introduction 295 14.2 A multilevel model of MRSA endemicity and its control in hospitals 296 14.2.1 Introduction 296 14.2.2 Method 296 14.2.3 Results 297 14.2.4 Conclusion 302 14.3 Chlamydia composite model 302 14.3.1 Introduction 302 14.3.2 Chlamydia 302 14.3.3 DES model of a GUM department 303 14.3.4 SD model of chlamydia 304 14.3.5 Why combine the models 304 14.3.6 How the models were combined 305 14.3.7 Experiments with the composite model 305 14.3.8 Conclusions 307 14.4 A hybrid model for social care services operations 308 14.4.1 Introduction 308 14.4.2 Population model 308 14.4.3 Model construction 309 14.4.4 Contact centre model 310 14.4.5 Hybrid model 311 14.4.6 Conclusions and lessons learnt 313 References 316 15 The ways forward: A personal view of system dynamics and discrete-event simulation 318 Michael Pidd 15.1 Genesis 318 15.2 Computer simulation in management science 319 15.3 The effect of developments in computing 320 15.4 The importance of process 324 15.5 My own comparison of the simulation approaches 324 15.5.1 Time handling 324 15.5.2 Stochastic and deterministic elements 326 15.5.3 Discrete entities versus continuous variables 327 15.6 Linking system dynamics and discrete-event simulation 328 15.7 The importance of intended model use 329 15.7.1 Decision automation 330 15.7.2 Routine decision support 331 15.7.3 System investigation and improvement 331 15.7.4 Providing insights for debate 332 15.8 The future? 333 15.8.1 Use of both methods will continue to grow 333 15.8.2 Developments in computing will continue to have an effect 334 15.8.3 Process really matters 335 References 335 Index 337

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Book SynopsisSystem Simulation Techniques with MATLAB and Simulink comprehensively explains how to use MATLAB and Simulink to perform dynamic systems simulation tasks for engineering and non-engineering applications.Table of ContentsForeword xiiiPreface xv1 Introduction to System Simulation Techniques and Applications 11.1 Overview of System Simulation Techniques 11.2 Development of Simulation Software 21.3 Introduction to MATLAB 51.4 Structure of the Book 7Exercises 9References 92 Fundamentals of MATLAB Programming 112.1 MATLAB Environment 112.2 Data Types in MATLAB 132.3 Matrix Computations in MATLAB 162.5 Programming and Tactics of MATLAB Functions 232.6 Two-dimensional Graphics in MATLAB 272.7 Three-dimensional Graphics 332.8 Graphical User Interface Design in MATLAB 362.9 Accelerating MATLAB Functions 52Exercises 60References 633 MATLAB Applications in Scientific Computations 653.1 Analytical and Numerical Solutions 663.2 Solutions to Linear Algebra Problems 673.3 Solutions of Calculus Problems 853.4 Solutions of Ordinary Differential Equations 913.5 Nonlinear Equation Solutions and Optimization 1103.6 Dynamic Programming and its Applications in Path Planning 1203.7 Data Interpolation and Statistical Analysis 124Exercises 136References 1424 Mathematical Modeling and Simulation with Simulink 1454.1 Brief Description of the Simulink Block Library 1464.2 Simulink Modeling 1594.3 Model Manipulation and Simulation Analysis 1644.4 Illustrative Examples of Simulink Modeling 1724.5 Modeling, Simulation and Analysis of Linear Systems 1804.6 Simulation of Continuous Nonlinear Stochastic Systems 184Exercises 188References 1915 Commonly Used Blocks and Intermediate-level Modeling Skills 1935.1 Commonly Used Blocks and Modeling Skills 1935.2 Modeling and Simulation of Multivariable Linear Systems 2025.3 Nonlinear Components with Lookup Table Blocks 2095.4 Block Diagram Based Solutions of Differential Equations 2175.5 Output Block Library 2265.6 Three-dimensional Animation of Simulation Results 2385.7 Subsystems and Block Masking Techniques 245Exercises 260References 2646 Advanced Techniques in Simulink Modeling and Applications 2656.1 Command-line Modeling in Simulink 2656.2 System Simulation and Linearization 2726.3 S-function Programming and Applications 2806.4 Examples of Optimization in Simulation: Optimal Controller Design Applications 296Exercises 303References 3067 Modeling and Simulation of Engineering Systems 3077.1 Physical System Modeling with Simscape 3087.2 Description of SimPowerSystems 3187.3 Modeling and Simulation of Electronic Systems 3227.4 Simulation of Motors and Electric Drive Systems 3367.5 Modeling and Simulation of Mechanical Systems 346Exercises 360References 3628 Modeling and Simulation of Non-Engineering Systems 3638.1 Modeling and Simulation of Pharmacokinetics Systems 3638.2 Video and Image Processing Systems 3768.3 Finite State Machine Simulation and Stateflow Applications 3908.4 Simulation of Discrete Event Systems with SimEvents 408Exercises 416References 4179 Hardware-in-the-loop Simulation and Real-time Control 4199.1 Simulink and Real-Time Workshop 4199.2 Introduction to dSPACE and its Blocks 4299.3 Introduction to Quanser and its Blocks 4309.4 Hardware-in-the-loop Simulation and Real-time Control Examples 4339.5 Low Cost Solutions with NIAT 4399.6 HIL Solutions with Even Lower Costs 4469.6.3 The MESABox 449Exercises 450References 451Appendix: Functions and Models 453Index 459

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Book SynopsisDiscusses the CFD-DEM method of modeling which combines both the Discrete Element Method and Computational Fluid Dynamics to simulate fluid-particle interactions. Deals with both theoretical and practical concepts of CFD-DEM, its numerical implementation accompanied by a hands-on numerical code in FORTRAN Gives examples of industrial applications Table of ContentsAbout the Authors xi Preface xiii 1 Introduction 1 1.1 Multiphase Coupling 2 1.2 Modeling Approaches 2 1.3 Modeling with DEM 5 1.4 CFD‐DEM Modeling 7 1.5 Applications 10 1.6 Scope and Overall Plan 10 1.7 Online Content 12 References 12 Part I DEM 15 2 DEM Formulation 17 2.1 Hard‐Sphere 18 2.1.1 Equation of Motion 19 2.1.2 Collision Model 19 2.1.3 Interparticle Forces 22 2.2 Soft‐Sphere 24 2.2.1 Equations of Motion 25 2.3 Force‐Displacement Laws 27 2.3.1 Linear Viscoelastic Model 29 2.3.2 Nonlinear Viscoelastic Models 36 2.3.3 Comparison of Viscoelastic Force‐Displacement Models 45 2.3.4 Elastic Perfectly Plastic Models 49 2.4 Torque Expressions 56 2.4.1 Model A: Constant Torque Model 56 2.4.2 Model B: Viscous Model 57 2.4.3 Model C: Spring‐Dashpot Model 57 2.5 Boundary and Initial Conditions 58 2.5.1 Boundary Conditions 58 2.5.2 Initial Condition 60 Nomenclature 60 References 64 3 DEM Implementation 68 3.1 Computational View 68 3.2 Program Structure 71 3.3 Contact Search Algorithms 76 3.3.1 Definition of Problem 79 3.3.2 Cell‐Based Algorithms 80 3.3.3 Sort‐Based Algorithms 96 3.3.4 Tree‐Based Broad Search Algorithms 99 3.3.5 Fine Search for Spherical Particles 103 3.4 Integration Methods 103 3.4.1 Single‐Step Methods 106 3.4.2 Multi‐Step Algorithms 110 3.4.3 Predictor‐Corrector Methods 112 3.4.4 Evaluation of Integration Methods 114 3.5 Spring Stiffness 119 3.5.1 Maximum Overlap 122 3.5.2 Collision Time and Maximum Contact Force 123 3.6 Wall Implementation 123 3.6.1 Definition of Wall Elements 125 3.6.2 Contact Detection 128 3.6.3 Moving Wall 136 3.7 Parallelization 138 3.7.1 Distributed Memory Parallelization 138 3.7.2 Shared‐Memory Parallelization 141 Nomenclature 145 References 147 4 Non‐Spherical Particles 152 4.1 Shape Representation 153 4.2 Kinematics and Dynamics of a Rigid Body 156 4.2.1 Euler Angles and Transformation Matrix 157 4.2.2 Equations of Motion 159 4.2.3 Quaternions for Rigid Body Dynamics 163 4.3 Superellipsoids 164 4.3.1 Contact Forces 166 4.3.2 Effective Radius and Curvatures 169 4.3.3 Torque Calculations 173 4.3.4 Contact Detection 174 4.4 Multi‐Sphere Method 178 Nomenclature 184 References 186 5 DEM Applications to Granular Flows 189 5.1 Packing of Particles 189 5.1.1 Confined Packing 189 5.1.2 Pile Formation 192 5.1.3 Rigid and Flexible Fibers 194 5.2 Flow in Hoppers 196 5.2.1 Flow Patterns 197 5.2.2 Segregation 199 5.2.3 Discharge Rate 201 5.3 Solid Mixing 203 5.3.1 Mechanisms of Mixing and Segregation 203 5.3.2 Mixing Index 205 5.3.3 Rotating Drums 209 5.3.4 Tumbling Blenders 220 5.3.5 Shaft Batch Mixers 223 5.3.6 Continuous Mixers 229 5.4 Screw Conveying 234 5.4.1 Simulation of Screw Conveyor 237 5.4.2 Results of the Simulations 238 5.4.3 Literature 239 5.5 Film Coating 241 5.5.1 Phenomenological Models 243 5.5.2 Monte‐Carlo Method 244 Nomenclature 247 References 249 Part II CFD‐DEM 257 6 CFD‐DEM Formulation and Coupling 259 6.1 Multiphase Coupling 260 6.1.1 Coupling Strategies 260 6.1.2 Types of Coupling 262 6.1.3 Interphase Interactions 265 6.2 Momentum Coupling 267 6.2.1 Single Phase Flow of Fluids 267 6.2.2 Fluid Resolution in CFD‐DEM 274 6.2.3 Unresolved Surface CFD‐DEM 275 6.2.4 Surface Force Decomposition 287 6.3 Energy Coupling 303 6.3.1 Governing Equations 304 6.3.2 Rates of Heat Transfer for Particles 308 6.3.3 Rates of Heat Transfer for Fluid 316 6.3.4 Sequence of Calculations 317 6.4 Mass Coupling 319 6.4.1 Governing Equations 319 6.4.2 Rates of Mass Transfer for Particles 324 6.4.3 Rates of Change in Fluid 329 6.4.4 Sequence of Calculations 329 Nomenclature 329 References 335 7 CFD‐DEM Applications to Multiphase Flow 341 7.1 Fluidization 341 7.1.1 Macro‐Scale Phenomena 342 7.1.2 Meso‐Scale Phenomena 344 7.1.3 Micro‐Scale Phenomena 345 7.2 Spouting 347 7.3 Pneumatic Conveying 355 7.3.1 Dilute Phase and Dense Phase Conveying 356 7.3.2 Horizontal Conveying 357 7.3.3 Vertical Conveying 359 7.4 Non‐Isothermal Flows 359 7.5 Reactive Flows 362 7.6 Miscellaneous 364 Nomenclature 365 References 366 8 Interparticle Forces and External Fields 372 8.1 Governing Equations 373 8.1.1 Sequence of Calculations 375 8.2 Interparticle Forces 376 8.2.1 van der Waals Force 376 8.2.2 Liquid Bridge Force 379 8.2.3 Electrostatic Force 386 8.3 External Fields 390 8.3.1 Electric Field 390 8.3.2 Magnetic Field 393 8.3.3 Vibration Field 397 8.3.4 Acoustic Field 398 8.4 Applications 399 Nomenclature 404 References 407 Index 412

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Book SynopsisThis set includes: Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel and Solutions Manual to Accompany Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel. With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel guides readers in the solution of relevant, practical problems by introducing both mathematical and Excel techniques. The book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how a quantity changes from one point in time to the next. Readers are taken through the process, language, and notation required for the construction of such models as well as their implementation in Excel. The book examines single-compartment models in contexts such as population growth, personal financ

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Book SynopsisThe long-awaited, comprehensive guide to practical credit risk modeling Credit Risk Analytics provides a targeted training guide for risk managers looking to efficiently build or validate in-house models for credit risk management. Combining theory with practice, this book walks you through the fundamentals of credit risk management and shows you how to implement these concepts using the SAS credit risk management program, with helpful code provided. Coverage includes data analysis and preprocessing, credit scoring; PD and LGD estimation and forecasting, low default portfolios, correlation modeling and estimation, validation, implementation of prudential regulation, stress testing of existing modeling concepts, and more, to provide a one-stop tutorial and reference for credit risk analytics. The companion website offers examples of both real and simulated credit portfolio data to help you more easily implement the concepts discussed, and the expert author team providesTable of ContentsAcknowledgments xi About the Authors xiii Chapter 1 Introduction to Credit Risk Analytics 1 Chapter 2 Introduction to SAS Software 17 Chapter 3 Exploratory Data Analysis 33 Chapter 4 Data Preprocessing for Credit Risk Modeling 57 Chapter 5 Credit Scoring 93 Chapter 6 Probabilities of Default (PD): Discrete-Time Hazard Models 137 Chapter 7 Probabilities of Default: Continuous-Time Hazard Models 179 Chapter 8 Low Default Portfolios 213 Chapter 9 Default Correlations and Credit Portfolio Risk 237 Chapter 10 Loss Given Default (LGD) and Recovery Rates 271 Chapter 11 Exposure at Default (EAD) and Adverse Selection 315 Chapter 12 Bayesian Methods for Credit Risk Modeling 351 Chapter 13 Model Validation 385 Chapter 14 Stress Testing 445 Chapter 15 Concluding Remarks 475 Index 481

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Book SynopsisThe engineering of materials with advanced features is driving the research towards the design of innovative materials with high performances. New materials often deliver the best solution for structural applications, precisely contributing towards the finest combination of mechanical properties and low weight.Table of ContentsPreface xiii Part 1 Engineering of Materials, Characterizations, and Applications 1 Mechanical Behavior and Resistance of Structural Glass Beams in Lateral–Torsional Buckling (LTB) with Adhesive Joints 3 Chiara Bedon and Jan Belis 1.1 Introduction 4 1.2 Overview on Structural Glass Applications in Buildings 5 1.3 Glass Beams in LTB 5 1.3.1 Susceptibility of Glass Structural Elements to Buckling Phenomena 5 1.3.2 Mechanical and Geometrical Influencing Parameters in Structural Glass Beams 8 1.3.3 Mechanical Joints 9 1.3.4 Adhesive Joints 10 1.4 Theoretical Background for Structural Members in LTB 14 1.4.1 General LTB Method for Laterally Unrestrained (LU) Members 14 1.4.2 LTB Method for Laterally Unrestrained (LU) Glass Beams 17 1.4.2.1 Equivalent Thickness Methods for Laminated Glass Beams 18 1.4.3 Laterally Restrained (LR) Beams in LTB 23 1.4.3.1 Extended Literature Review on LR Beams 23 1.4.3.2 Closed-form Formulation for LR Beams in LTB 24 1.4.3.3 LR Glass Beams Under Positive Bending Moment My 28 1.5 Finite-element Numerical Modeling 31 1.5.1 FE Solving Approach and Parametric Study 32 1.5.1.1 Linear Eigenvalue Buckling Analyses (lba) 32 1.5.1.2 Incremental Nonlinear Analyses (inl) 35 1.6 LTB Design Recommendations 38 1.6.1 LR Beams Under Positive Bending Moment My 38 1.6.2 Further Extension and Developments of the Current Outcomes 39 1.7 Conclusions 42 References 44 2 Room Temperature Mechanosynthesis of Nanocrystalline Metal Carbides and Their Microstructure Characterization 49 S.K. Pradhan and H. Dutta 2.1 Introduction 50 2.1.1 Application 50 2.1.2 Different Methods for Preparation of Metal Carbide 50 2.1.3 Mechanical Alloying 51 2.1.4 Planetary Ball Mill 51 2.1.5 The Merits and Demerits of Planetary Ball Mill 52 2.1.6 Review of Works on Metal Carbides by Other Authors 53 2.1.7 Significance of the Study 54 2.1.8 Objectives of the Study 55 2.2 Experimental 56 2.3 Theoretical Consideration 58 2.3.1 Microstructure Evaluation by X-ray Diffraction 58 2.3.2 General Features of Structure 60 2.4 Results and Discussions 60 2.4.1 XRD Pattern Analysis 60 2.4.2 Variation of Mol Fraction 65 2.4.3 Phase Formation Mechanism 69 2.4.4 Is Ball-milled Prepared Metal Carbide Contains Contamination? 71 2.4.5 Variation of Particle Size 72 2.4.6 Variation of Strain 74 2.4.7 High-Resolution Transmission Electron Microscopy Study 76 2.4.8 Comparison Study between Binary and Ternary Ti-based Metal Carbides 76 2.5 Conclusion 80 Acknowledgment 80 References 80 3 Toward a Novel SMA-reinforced Laminated Glass Panel 87 Chiara Bedon and Filipe Amarante dos Santos 3.1 Introduction 87 3.2 Glass in Buildings 89 3.2.1 Actual Reinforcement Techniques for Structural Glass Applications 92 3.3 Structural Engineering Applications of Shape-Memory Alloys (SMAs) 93 3.4 The Novel SMA-Reinforced Laminated Glass Panel Concept 94 3.4.1 Design Concept 94 3.4.2 Exploratory Finite-Element (FE) Numerical Study 96 3.4.2.1 General FE Model Assembly Approach and Solving Method 96 3.4.2.2 Mechanical Characterization of Materials 98 3.5 Discussion of Parametric FE Results 101 3.5.1 Roof Glass Panel (M1) 101 3.5.1.1 Short-term Loads and Temperature Variations 102 3.5.1.2 First-cracking Configuration 106 3.5.2 Point-supported Façade Panel (M2) 109 3.5.2.1 Short-term Loads and Temperature Variations 111 3.6 Conclusions 114 References 117 4 Sustainable Sugarcane Bagasse Cellulose for Papermaking 121 Noé Aguilar-Rivera 4.1 Pulp and Paper Industry 122 4.2 Sugar Industry 123 4.3 Sugarcane Bagasse 124 4.4 Advantageous Utilizations of SCB 129 4.5 Applications of SCB Wastes 130 4.6 Problematic of Nonwood Fibers in Papermaking 131 4.7 SCB as Raw Material for Pulp and Paper 134 4.8 Digestion 135 4.9 Bleaching 135 4.10 Properties of Bagasse Pulps 136 4.10.1 Pulp Strength 137 4.10.2 Pulp Properties 137 4.10.3 Washing Technology 138 4.10.4 Paper Machine Operation 138 4.11 Objectives 138 4.12 Old Corrugated Container Pulps 139 4.13 Synergistic Delignification SCB–OCC 141 4.14 Elemental Chlorine-Free Bleaching of SCB Pulps 150 4.15 Conclusions 156 References 158 5 Bio-inspired Composites: Using Nature to Tackle Composite Limitations 165 F. Libonati 5.1 Introduction 166 5.2 Bio-inspiration: Bone as Biomimetic Model 169 5.3 Case Studies Using Biomimetic Approach 172 5.3.1 Fiber-reinforced Bone-inspired Composites 172 5.3.2 Fiber-reinforced Bone-inspired Composites with CNTs 176 5.3.3 Bone-inspired Composites via 3D Printing 177 5.4 Methods 179 5.4.1 Composite Lamination 180 5.4.2 Additive Manufacturing 181 5.4.3 Computational Modeling 182 5.5 Conclusions 183 References 185 Part 2 Computational Modeling of Materials 6 On the Electronic Structure and Band Gap of ZnSxSe1–x 193 Ghassan H. E. Al-Shabeeb and A. K. Arof 6.1 Introduction 193 6.2 Computational Method 194 6.3 The k·p Perturbation Theory with the Effect of Spin–Orbit Interaction 197 6.4 Results and Discussion 202 Acknowledgment 205 References 205 7 Application of First Principles Theory to the Design of Advanced Titanium Alloys 207 Y. Song, J. H. Dai, and R. Yang 7.1 Introduction 207 7.2 Basic Concepts of First Principles 208 7.3 Theoretical Models of Alloy Design 211 7.3.1 The Hume-Rothery Theory 211 7.3.2 Discrete Variational Method and d-Orbital Method 216 7.3.2.1 Discrete Variational Method 216 7.3.2.2 d-Electrons Alloy Theory 218 7.4 Applications 219 7.4.1 Phase Stability 219 7.4.1.1 Binary Alloy 219 7.4.1.2 Multicomponent Alloys 222 7.4.2 Elastic Properties 223 7.4.3 Examples 226 7.4.3.1 Gum Metal 226 7.4.3.2 Ti2448 (Ti–24Nb–4Zr–8Sn) 227 7.5 Conclusions 230 Acknowledgment 230 References 230 8 Digital Orchid: Creating Realistic Materials 233 Iftikhar B. Abbasov 8.1 Introduction 234 8.2 Conclusion 243 References 243 9 Transformation Optics-based Computational Materials for Stochastic Electromagnetics 245 Ozlem Ozgun and Mustafa Kuzuoglu 9.1 Introduction 246 9.2 Theory of Transformation Optics 249 9.3 Scattering from Rough Sea Surfaces 252 9.3.1 Numerical Validation and Monte Carlo Simulations 256 9.4 Scattering from Obstacles with Rough Surfaces or Shape Deformations 258 9.4.1 Numerical Validation and Monte Carlo Simulations 263 9.4.2 Combining Perturbation Theory and Transformation Optics for Weakly Perturbed Surfaces 264 9.5 Scattering from Randomly Positioned Array of Obstacles 268 9.5.1 Separate Transformation Media 269 9.5.1.1 Numerical Validation & Monte Carlo Simulations 271 9.5.2 A Single Transformation Medium 273 9.5.2.1 Numerical Validation & Monte Carlo Simulations 275 9.5.3 Recurring Scaling and Translation Transformations 276 9.5.3.1 Numerical Validation & Monte Carlo Simulations 278 9.6 Propagation in a Waveguide with Rough or Randomly Varying Surface 278 9.3.1 Numerical Validation and Monte Carlo Simulations 283 9.7 Conclusion 287 References 288 10 Superluminal Photons Tunneling through Brain Microtubules Modeled as Metamaterials and Quantum Computation 291 Luigi Maxmilian Caligiuri and Takaaki Musha 10.1 Introduction 292 10.2 QED Coherence in Water: A Brief Overview 295 10.3 “Electronic” QED Coherence in Brain Microtubules 301 10.4 Evanescent Field of Coherent Photons and Their Superluminal Tunneling through MTs 305 10.5 Coupling between Nearby MTs and their Superluminal Interaction through the Exchange of Virtual Superradiant Photons 312 10.6 Discussion 316 10.7 Brain Microtubules as “Natural” Metamaterials and the Amplification of Evanescent Tunneling Wave Amplitude 319 10.8 Quantum Computation by Means of Superluminal Photons 325 10.9 Conclusions 329 References 330 11 Advanced Fundamental-solution-based Computational Methods for Thermal Analysis of Heterogeneous Materials 335 Hui Wang and Qing-Hua Qin 11.1 Introduction 336 11.2 Basic Formulation of MFS 338 11.2.1 Standard MFS 338 11.2.2 Modified MFS 340 11.2.2.1 RBF Interpolation for the Particular Solution 341 11.2.2.2 MFS for the Homogeneous Solution 342 11.2.2.3 Complete Solution 343 11.3 Basic Formulation of HFS-FEM 344 11.3.1 Problem Statement 344 11.3.2 Implementation of the HFS-FEM 346 11.3.4 Recovery of Rigid-body Motion 349 11.4 Applications in Functionally Graded Materials 349 11.4.1 Basic Equations in Functionally Graded Materials 349 11.4.2 MFS for Functionally Graded Materials 350 11.4.3 HFS-FEM for Functionally Graded Materials 353 11.5 Applications in Composite Materials 357 11.5.1 Basic Equations of Composite Materials 357 11.5.2 MFS for Composite Materials 360 11.5.2.1 MFS for the Matrix Domain 360 11.5.2.2 MFS for the Fiber Domain 360 11.5.2.3 Complete Linear Equation System 361 11.5.3 HFS-FEM for Composite Materials 362 11.5.3.1 Special Fundamental Solutions 362 11.5.3.2 Special n-Sided Fiber/Matrix Elements 363 11.6 Conclusions 365 Acknowledgments 366 Conflict of Interest 366 References 366 12 Understanding the SET/RESET Characteristics of Forming Free TiOx/TiO2–x Resistive-Switching Bilayer Structures through Experiments and Modeling 373 P. Bousoulas and D. Tsoukalas 12.1 Introduction 374 12.2 Experimental Methodology 376 12.3 Bipolar Switching Model 378 12.3.1 Resistive-Switching Performance 378 12.3.2 Resistive-Switching Model 383 12.4 RESET Simulations 389 12.4.1 I–V Response 389 12.4.2 Influence of TE on the CFs Broken Region 393 12.5 SET Simulations 398 12.6 Simulation of Time-dependent SET/RESET Processes 401 12.7 Conclusions 403 Acknowledgments 404 References 404 13 Advanced Materials and Three-dimensional Computer-aided Surgical Workflow in Cranio-maxillofacial Reconstruction 411 Luis Miguel Gonzalez-Perez, Borja Gonzalez-Perez-Somarriba Gabriel Centeno, Carpóforo Vallellano, and Juan Jose Egea-Guerrero 13.1 Introduction 412 13.2 Methodology 413 13.3 Findings 418 13.4 Discussion 427 References 436 14 Displaced Multiwavelets and Splitting Algorithms 439 Boris M. Shumilov 14.1 An Algorithm with Splitting of Wavelet Transformation of Splines of the First Degree 443 14.1.1 “Lazy” Wavelets 444 14.1.2 Examples of Wavelet Decomposition of a Signal of Length 8 447 14.1.3 “Orthonormal” Wavelets 450 14.1.4 An Example of Function of Harten 454 14.2 An Algorithm for Constructing Orthogonal to Polynomials Multiwavelet Bases 456 14.2.1 Creation of System of Basic Multiwavelets of Any Odd Degree on a Closed Interval 456 14.2.2 Creation of the Block of Filters 459 14.2.3 Example of Orthogonal to Polynomials Multiwavelet Bases 461 14.2.4 The Discussion of Approximation on a Closed Interval 463 14.3 The Tridiagonal Block Matrix Algorithm 464 14.3.1 Inverse of the Block of Filters 464 14.3.2 Example of the Hermite Quintic Spline Function Supported on [−1, 1] 465 14.3.3 Example of the Hermite Septimus Spline Function Supported on [−1, 1] 467 14.3.4 Numerical Example of Approximation of Polynomial Function 470 14.3.5 Numerical Example with Two Ruptures of the First Kind and a Corner 471 14.4 Problem of Optimization of Wavelet Transformation of Hermite Splines of Any Odd Degree 475 14.4.1 An Algorithm with Splitting for Wavelet Transformation of Hermite Splines of Fifth Degree 478 14.4.2 Examples 485 14.5 Application to Data Processing of Laser Scanning of Roads490 14.5.1 Calculation of Derivatives on Samples 490 14.5.2 Example of Wavelet Compression of One Track of Data of Laser Scanning 490 14.5.3 Modeling of Surfaces 490 14.5.4 Functions of a Package of Applied Programs for Modeling of Routes and Surfaces of Highways 492 14.6 Conclusions 494 References 494

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Book SynopsisUse Big Data and technology to uncover real-world insights You don''t need a time machine to predict the future. All it takes is a little knowledge and know-how, and Predictive Analytics For Dummies gets you there fast. With the help of this friendly guide, you''ll discover the core of predictive analytics and get started putting it to use with readily available tools to collect and analyze data. In no time, you''ll learn how to incorporate algorithms through data models, identify similarities and relationships in your data, and predict the future through data classification. Along the way, you''ll develop a roadmap by preparing your data, creating goals, processing your data, and building a predictive model that will get you stakeholder buy-in. Big Data has taken the marketplace by storm, and companies are seeking qualified talent to quickly fill positions to analyze the massive amount of data that are being collected each day. If you want to get in on the action aTable of ContentsINTRODUCTION 1 PART 1: GETTING STARTED WITH PREDICTIVE ANALYTICS 5 CHAPTER 1: Entering the Arena 7 Exploring Predictive Analytics 7 Mining data 8 Highlighting the model 9 Adding Business Value 10 Endless opportunities 11 Empowering your organization 12 Starting a Predictive Analytic Project 13 Business knowledge 14 Data-science team and technology 15 The Data 16 Ongoing Predictive Analytics 17 Forming Your Predictive Analytics Team 18 Hiring experienced practitioners 18 Demonstrating commitment and curiosity 19 Surveying the Marketplace 19 Responding to big data 20 Working with big data 20 CHAPTER 2: Predictive Analytics in the Wild 23 Online Marketing and Retail 25 Recommender systems 25 Personalized shopping on the Internet 26 Implementing a Recommender System 28 Collaborative filtering 28 Content-based filtering 36 Hybrid recommender systems 39 Target Marketing 41 Targeting using predictive modeling 42 Uplift modeling 43 Personalization 46 Online customer experience 46 Retargeting 47 Implementation 47 Optimizing using personalization 48 Similarities of Personalization and Recommendations 48 Content and Text Analytics 50 CHAPTER 3: Exploring Your Data Types and Associated Techniques 51 Recognizing Your Data Types 52 Structured and unstructured data 52 Static and streamed data 56 Identifying Data Categories 58 Attitudinal data 59 Behavioral data 60 Demographic data 61 Generating Predictive Analytics 61 Data-driven analytics 62 User-driven analytics 64 Connecting to Related Disciplines 65 Statistics 65 Data mining 66 Machine learning 67 CHAPTER 4: Complexities of Data 69 Finding Value in Your Data 70 Delving into your data 70 Data validity 70 Data variety 71 Constantly Changing Data 72 Data velocity 72 High volume of data 73 Complexities in Searching Your Data 73 Keyword-based search 74 Semantic-based search 74 Contextual search 76 Differentiating Business Intelligence from Big-Data Analytics 79 Exploration of Raw Data 80 Identifying data attributes 80 Exploring common data visualizations 81 Tabular visualizations 81 Word clouds 82 Flocking birds as a novel data representation 83 Graph charts 85 Common visualizations 87 PART 2: INCORPORATING ALGORITHMS IN YOUR MODELS 89 CHAPTER 5: Applying Models 91 Modeling Data 92 Models and simulation 92 Categorizing models 94 Describing and summarizing data 96 Making better business decisions 97 Healthcare Analytics Case Studies 97 Google Flu Trends 97 Cancer survivability predictors 99 Social and Marketing Analytics Case Studies 101 Target store predicts pregnant women 101 Twitter-based predictors of earthquakes 102 Twitter-based predictors of political campaign outcomes 103 Tweets as predictors for the stock market 105 Predicting variation of stock prices from news articles 106 Analyzing New York City’s bicycle usage 107 Predictions and responses 110 Data compression 111 Prognostics and its Relation to Predictive Analytics 112 The Rise of Open Data 113 CHAPTER 6: Identifying Similarities in Data 115 Explaining Data Clustering 116 Converting Raw Data into a Matrix 120 Creating a matrix of terms in documents 120 Term selection 121 Identifying Groups in Your Data 122 K-means clustering algorithm 122 Clustering by nearest neighbors 126 Density-based algorithms 130 Finding Associations in Data Items 132 Applying Biologically Inspired Clustering Techniques 136 Birds flocking: Flock by Leader algorithm 136 Ant colonies 143 CHAPTER 7: Predicting the Future Using Data Classification 147 Explaining Data Classification 149 Introducing Data Classification to Your Business 152 Exploring the Data-Classification Process 154 Using Data Classification to Predict the Future 156 Decision trees 156 Algorithms for Generating Decision Trees 159 Support vector machine 163 Ensemble Methods to Boost Prediction Accuracy 165 Naïve Bayes classification algorithm 166 The Markov Model 172 Linear regression 177 Neural networks 177 Deep Learning 179 PART 3: DEVELOPING A ROADMAP 185 CHAPTER 8: Convincing Your Management to Adopt Predictive Analytics 187 Making the Business Case 188 Gathering Support from Stakeholders 195 Presenting Your Proposal 206 CHAPTER 9: Preparing Data 209 Listing the Business Objectives 210 Processing Your Data 212 Identifying the data 212 Cleaning the data 213 Generating any derived data 215 Reducing the dimensionality of your data 215 Applying principal component analysis 216 Leveraging singular value decomposition 218 Working with Features 219 Structuring Your Data 224 Extracting, transforming and loading your data 225 Keeping the data up to date 226 Outlining testing and test data 226 CHAPTER 10: Building a Predictive Model 229 Getting Started 230 Defining your business objectives 232 Preparing your data 233 Choosing an algorithm 236 Developing and Testing the Model 237 Going Live with the Model 242 CHAPTER 11: Visualization of Analytical Results 245 Visualization as a Predictive Tool 246 Evaluating Your Visualization 249 Visualizing Your Model’s Analytical Results 251 Visualizing hidden groupings in your data 251 Visualizing data classification results 252 Visualizing outliers in your data 254 Visualization of Decision Trees 254 Visualizing predictions 256 Novel Visualization in Predictive Analytics 258 Big Data Visualization Tools 262 Tableau 263 Google Charts 263 Plotly 263 Infogram 264 PART 4: PROGRAMMING PREDICTIVE ANALYTICS 265 CHAPTER 12: Creating Basic Prediction Examples 267 Installing the Software Packages 268 Installing Python 268 Installing the machine-learning module 270 Installing the dependencies 274 Preparing the Data 278 Making Predictions Using Classification Algorithms 280 Creating a supervised learning model with SVM 281 Creating a supervised learning model with logistic regression 288 Creating a supervised learning model with random forest 295 Comparing the classification models 297 CHAPTER 13: Creating Basic Examples of Unsupervised Predictions 299 Getting the Sample Dataset 300 Using Clustering Algorithms to Make Predictions 301 Comparing clustering models 301 Creating an unsupervised learning model with K-means 302 Creating an unsupervised learning model with DBSCAN 314 Creating an unsupervised learning model with mean shift 318 CHAPTER 14: Predictive Modeling with R 323 Programming in R 325 Installing R 325 Installing RStudio 326 Getting familiar with the environment 327 Learning just a bit of R 328 Making Predictions Using R 334 Predicting using regression 334 Using classification to predict 345 Classification by random forest 354 CHAPTER 15: Avoiding Analysis Traps 359 Data Challenges 360 Outlining the limitations of the data 361 Dealing with extreme cases (outliers) 364 Data smoothing 367 Curve fitting 371 Keeping the assumptions to a minimum 374 Analysis Challenges 375 PART 5: EXECUTING BIG DATA 381 CHAPTER 16: Targeting Big Data 383 Major Technological Trends in Predictive Analytics 384 Exploring predictive analytics as a service 384 Aggregating distributed data for analysis 385 Real-time data-driven analytics 387 Applying Open-Source Tools to Big Data 388 Apache Hadoop 388 Apache Spark 394 CHAPTER 17: Getting Ready for Enterprise Analytics 399 Analytics as a Service 403 Google Analytics 403 IBM Watson 405 Microsoft Revolution R Enterprise 405 Preparing for a Proof-of-Value of Predictive Analytics Prototype 406 Prototyping for predictive analytics 406 Testing your predictive analytics model 409 PART 6: THE PART OF TENS 411 CHAPTER 18: Ten Reasons to Implement Predictive Analytics 413 CHAPTER 19: Ten Steps to Build a Predictive Analytic Model 423 INDEX 433

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Book SynopsisIntroduction to Modeling and Simulation An essential introduction to engineering system modeling and simulation from a well-trusted source in engineering and education This new introductory-level textbook provides thirteen self-contained chapters, each covering an important topic in engineering systems modeling and simulation. The importance of such a topic cannot be overstated; modeling and simulation will only increase in importance in the future as computational resources improve and become more powerful and accessible, and as systems become more complex. This resource is a wonderful mix of practical examples, theoretical concepts, and experimental sessions that ensure a well-rounded education on the topic. The topics covered in Introduction to Modeling and Simulation are timeless fundamentals that provide the necessary background for further and more advanced study of one or more of the topics. The text includes topics such as linear and nonlinear dynamical systems, continuous-time and discrete-time systems, stability theory, numerical methods for solution of ODEs, PDE models, feedback systems, optimization, regression and more. Each chapter provides an introduction to the topic to familiarize students with the core ideas before delving deeper. The numerous tools and examples help ensure students engage in active learning, acquiring a range of tools for analyzing systems and gaining experience in numerical computation and simulation systems, from an author prized for both his writing and his teaching over the course of his over-40-year career. Introduction to Modeling and Simulation readers will also find: Numerous examples, tools, and programming tips to help clarify points made throughout the textbook, with end-of-chapter problems to further emphasize the material As systems become more complex, a chapter devoted to complex networks including small-world and scale-free networks a unique advancement for textbooks within modeling and simulation A complementary website that hosts a complete set of lecture slides, a solution manual for end-of-chapter problems, MATLAB files, and case-study exercises Introduction to Modeling and Simulation is aimed at undergraduate and first-year graduate engineering students studying systems, in diverse avenues within the field: electrical, mechanical, mathematics, aerospace, bioengineering, physics, and civil and environmental engineering. It may also be of interest to those in mathematical modeling courses, as it provides in-depth material on MATLAB simulation and contains appendices with brief reviews of linear algebra, real analysis, and probability theory.Table of ContentsPreface xiii About the Companion Website xvii 1 Introduction 1 1.1 Introduction 1 1.1.1 Systems Engineering 1 1.1.2 The Input/Output Viewpoint 2 1.1.3 Some Examples 2 1.2 Model Classification 5 1.2.1 Static and Dynamic Systems 5 1.2.2 Linear and Nonlinear Systems 5 1.2.3 Distributed-Parameter Systems 6 1.2.4 Hybrid and Discrete-Event Systems 6 1.2.5 Deterministic and Stochastic Systems 7 1.2.6 Large-Scale Systems 7 1.3 Simulation Languages 9 1.4 Outline of the Text 10 Problems 11 2 Second-Order Systems 15 2.1 Introduction 15 2.2 State-Space Representation 19 2.3 Trajectories and Phase Portraits 22 2.4 The Direction Field 27 2.5 Equilibria 30 2.6 Linear Systems 33 2.7 Linearization of Nonlinear Systems 41 2.8 Periodic Trajectories and Limit Cycles 45 2.8.1 Relaxation Oscillators 45 2.8.2 Bendixson’s Theorem 49 2.8.3 Poincaré–Bendixson Theorem 51 2.9 Coupled Second-Order Systems 53 Problems 55 3 System Fundamentals 61 3.1 Introduction 61 3.2 Existence and Uniqueness of Solution 61 3.3 The Matrix Exponential 64 3.4 The Jordan Canonical Form 67 3.5 Linearization 71 3.6 The Hartman–Grobman Theorem 72 3.7 Singular Perturbations 73 Problems 79 4 Compartmental Models 83 4.1 Introduction 83 4.2 Exponential Growth and Decay 84 4.3 The Logistic Equation 87 4.4 Models of Epidemics 88 4.5 Predator–Prey System 95 Problems 97 5 Stability 101 5.1 Introduction 101 5.2 Lyapunov Stability 102 5.3 Basin of Attraction 109 5.4 The Invariance Principle 110 5.5 Linear Systems and Linearization 113 Problems 116 6 Discrete-Time Systems 119 6.1 Introduction 119 6.2 Stability of Discrete-Time Systems 123 6.3 Stability of Discrete-Time Linear Systems 124 6.4 Moving-Average Filter 126 6.5 Cobweb Diagrams 128 6.5.1 Cobweb Diagrams in Economics 130 6.5.2 The Discrete Logistic Equation 131 Problems 134 7 Numerical Methods 137 7.1 Introduction 137 7.2 Numerical Differentiation 138 7.3 Numerical Integration 141 7.4 Numerical Solution of ODEs 147 7.4.1 Euler Predictor–Corrector Method 150 7.4.2 Runge–Kutta Methods 152 7.5 Stiff Systems 155 7.6 Event Detection 160 7.7 Simulink 163 7.8 Summary 168 Problems 169 8 Optimization 173 8.1 Introduction 173 8.2 Unconstrained Optimization 177 8.2.1 Iterative Search 179 8.2.2 Gradient Descent 180 8.2.3 Newton’s Method 184 8.3 Case Study: Numerical Inverse Kinematics 187 8.4 Constrained Optimization 191 8.4.1 Equality Constraints 191 8.4.2 Inequality Constraints 196 8.5 Convex Optimization 200 Problems 204 9 System Identification 209 9.1 Introduction 209 9.2 Least Squares 209 9.3 Regression 212 9.4 Recursive Least Squares 217 9.5 Logistic Regression 220 9.6 Neural Networks 224 Problems 230 10 Stochastic Systems 233 10.1 Markov Chains 233 10.1.1 Regular and Ergodic Markov Chains 240 10.1.2 Absorbing Markov Chains 244 10.2 Monte Carlo Methods 249 10.2.1 Random Number Generation 250 10.2.2 Monte Carlo Integration 253 10.2.3 Monte Carlo Optimization 255 10.2.4 Monte Carlo Simulation 255 Problems 258 11 Feedback Systems 261 11.1 Introduction 261 11.2 Transfer Functions 263 11.3 Feedback Control 269 11.4 State-Space Models 273 11.4.1 Minimal Realizations 274 11.4.2 Pole Placement 280 11.4.3 State Estimation 283 11.4.4 The Separation Principle 285 11.5 Optimal Control 288 11.6 Control of Nonlinear Systems 289 Problems 292 12 Partial Differential Equation Models 297 12.1 Introduction 297 12.1.1 Existence and Uniqueness of Solutions 297 12.1.2 Classification of Linear Second-Order PDEs 298 12.2 The Wave Equation 299 12.2.1 The D’Alembert Solution 300 12.2.2 Initial-Value Problem 300 12.2.3 Separation of Variables 302 12.3 The Heat Equation 310 12.4 Laplace’s Equation 313 12.5 Numerical Solution of PDEs 315 Problems 319 13 Complex Networks 321 13.1 Introduction 321 13.1.1 Examples of Complex Networks 322 13.2 Graph Theory: Basic Concepts 324 13.2.1 Graph Isomorphism 327 13.2.2 Connectivity 327 13.2.3 Trees 331 13.2.4 Bipartite Graphs 332 13.2.5 Planar Graphs 333 13.2.6 Graphs and Matrices 335 13.3 Matlab Graph Functions 341 13.4 Network Metrics 343 13.4.1 Degree Distribution 343 13.4.2 Centrality 347 13.4.3 Clustering 350 13.5 Random Graphs 354 13.5.1 Erdős–Rényi Networks 354 13.5.2 Small-World Networks 358 13.5.3 Scale-Free Networks 360 13.6 Synchronization in Networks 362 Problems 366 Appendix A Linear Algebra 371 A. 1 Vectors 371 A. 2 Matrices 373 A. 3 Eigenvalues and Eigenvectors 375 Appendix B Real Analysis 379 B. 1 Set Theory 379 B. 2 Vector Fields 380 B. 3 Jacobian 381 B. 4 Scalar Functions 381 B. 5 Taylor’s Theorem 382 B. 6 Extreme-Value Theorem 383 Appendix C Probability 385 C.1 Discrete Probability 385 C.2 Conditional Probability 386 C.3 Random Variables 389 C.4 Continuous Probability 391 Appendix D Proofs of Selected Results 395 D. 1 Proof of Theorem 2.2 395 D. 2 Proof of Theorem 5.1 395 D. 3 Proof of Theorem 5.5 396 D. 4 Proof of Theorem 13.3 397 D. 5 Proof of Corollary 13.2 397 D. 6 Proof of Proposition 13.2 398 D. 7 Proof of Proposition 13.3 398 Appendix E Matlab Command Reference 399 References 403 Index 407

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Book SynopsisProvides readers with information necessary to construct spectral NWP models; a self-contained, well-documented, coded spectral NWP model; and theoretical and practical exercises, some of which include solutions.

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Book SynopsisFocusing on high-end modeling and simulation of earth's climate, this book presents observations about the general circulations of the earth and the partial differential equations used to model the dynamics of weather and climate and covers numerical methods for geophysical flows in more detail than many other texts.

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Book SynopsisThis self-contained book addresses the underlying mathematical theory behind the reconstruction and analysis of phylogenies. The theory is grounded in classical concepts from discrete mathematics and probability theory as well as techniques from other branches of mathematics (algebra, topology, differential equations). The biological relevance of the results is highlighted throughout.

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Book SynopsisEngineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements.The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications.Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.Trade ReviewPiecewise affine systems are widely used as modeling and design tools across a number of applications, ranging from robotics to systems biology. These systems require a delicate touch as they can exhibit complex and sometimes surprising features. This impressive book navigates the world of such systems with clarity, technical depth, and elegance.”- Professor Magnus Egerstedt, Georgia Institute of Technology

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Book SynopsisAmong the many branches of applied mathematics, options pricing theory occupies a unique position: it utilizes a wide range of advanced mathematical concepts, making it appealing to mathematicians, and it is regularly applied at financial institutions, making it indispensable to practitioners. The emergence of artificial intelligence in the financial industry has led to further interest in mathematical finance and has increased the demand for literature on this subject that is accessible to a large audience.This book presents a self-contained introduction to options pricing theory and includes a complete discussion of the required concepts in finance and probability theory; an introduction to basic models, emphasizing both critical thinking and practical applications; and over 200 exercises, several Python codes for the analysis and application of the options pricing models, and numerical projects intended to help close the gap between theory and practice. A First Course in Options Pricing Theory is suitable for an advanced undergraduate course on financial mathematics and options pricing theory in engineering, computer science, and applied mathematics programs. The reader is assumed to be familiar with the standard material in calculus and linear algebra. Stochastic calculus is not used in the book.

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Book SynopsisMultilevel Modeling Methods with Introductory and Advanced Applications provides a cogent and comprehensive introduction to the area of multilevel modeling for methodological and applied researchers as well as advanced graduate students. The book is designed to be able to serve as a textbook for a one or two semester course in multilevel modeling. The topics of the seventeen chapters range from basic to advanced, yet each chapter is designed to be able to stand alone as an instructional unit on its respective topic, with an emphasis on application and interpretation.In addition to covering foundational topics on the use of multilevel models for organizational and longitudinal research, the book includes chapters on more advanced extensions and applications, such as cross-classified random effects models, non-linear growth models, mixed effects location scale models, logistic, ordinal, and Poisson models, and multilevel mediation. In addition, the volume includes chapters addressing some of the most important design and analytic issues including missing data, power analyses, causal inference, model fit, and measurement issues. Finally, the volume includes chapters addressing special topics such as using large-scale complex sample datasets, and reporting the results of multilevel designs.Each chapter contains a section called Try This!, which poses a structured data problem for the reader. We have linked our book to a website (http://modeling.uconn.edu) containing data for the Try This! section, creating an opportunity for readers to learn by doing. The inclusion of the Try This! problems, data, and sample code eases the burden for instructors, who must continually search for class examples and homework problems. In addition, each chapter provides recommendations for additional methodological and applied readings.

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Book SynopsisMultilevel Modeling Methods with Introductory and Advanced Applications provides a cogent and comprehensive introduction to the area of multilevel modeling for methodological and applied researchers as well as advanced graduate students. The book is designed to be able to serve as a textbook for a one or two semester course in multilevel modeling. The topics of the seventeen chapters range from basic to advanced, yet each chapter is designed to be able to stand alone as an instructional unit on its respective topic, with an emphasis on application and interpretation.In addition to covering foundational topics on the use of multilevel models for organizational and longitudinal research, the book includes chapters on more advanced extensions and applications, such as cross-classified random effects models, non-linear growth models, mixed effects location scale models, logistic, ordinal, and Poisson models, and multilevel mediation. In addition, the volume includes chapters addressing some of the most important design and analytic issues including missing data, power analyses, causal inference, model fit, and measurement issues. Finally, the volume includes chapters addressing special topics such as using large-scale complex sample datasets, and reporting the results of multilevel designs.Each chapter contains a section called Try This!, which poses a structured data problem for the reader. We have linked our book to a website (http://modeling.uconn.edu) containing data for the Try This! section, creating an opportunity for readers to learn by doing. The inclusion of the Try This! problems, data, and sample code eases the burden for instructors, who must continually search for class examples and homework problems. In addition, each chapter provides recommendations for additional methodological and applied readings.

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Book SynopsisThis book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics. Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fréchet and Hilbert, with new developments on Neumann spaces, but also on extractable spaces. The author presents the main properties of these spaces, which are useful for the construction of Lebesgue and Sobolev distributions with real or vector values and for solving partial differential equations. Differential calculus is also extended to semi-normed spaces. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers without restricting or generalizing the results.Table of ContentsIntroduction xi Familiarization with Semi-normed Spaces xv Notations xvii Chapter 1 Prerequisites 1 1.1 Sets, mappings, orders 1 1.2 Countability 3 1.3 Construction of R 4 1.4 Properties of R 5 Part 1 Semi-normed Spaces 9 Chapter 2 Semi-normed Spaces 11 2.1 Definition of semi-normed spaces 11 2.2 Convergent sequences 15 2.3 Bounded, open and closed sets 17 2.4 Interior, closure, balls and semi-balls 21 2.5 Density, separability 23 2.6 Compact sets 25 2.7 Connected and convex sets 30 Chapter 3 Comparison of Semi-normed Spaces 33 3.1 Equivalent families of semi-norms 33 3.2 Topological equalities and inclusions 34 3.3 Topological subspaces 39 3.4 Filtering families of semi-norms 43 3.5 Sums of sets 46 Chapter 4 Banach, Fréchet and Neumann Spaces 49 4.1 Metrizable spaces 49 4.2 Properties of sets in metrizable spaces 51 4.3 Banach, Fréchet and Neumann spaces 55 4.4 Compacts sets in Fréchet spaces 57 4.5 Properties of R 58 4.6 Convergent sequences 60 4.7 Sequential completion of a semi-normed space 62 Chapter 5 Hilbert Spaces 65 5.1 Hilbert spaces 65 5.2 Projection in a Hilbert space 68 5.3 The space Rd 70 Chapter 6 Product, Intersection, Sum and Quotient of Spaces 73 6.1 Product of semi-normed spaces 73 6.2 Product of a semi-normed space by itself 78 6.3 Intersection of semi-normed spaces 80 6.4 Sum of semi-normed spaces 83 6.5 Direct sum of semi-normed spaces 89 6.6 Quotient space 93 Part 2 Continuous Mappings 95 Chapter 7 Continuous Mappings 97 7.1 Continuous mappings 97 7.2 Continuity and change of topology or restriction 100 7.3 Continuity of composite mappings 102 7.4 Continuous semi-norms 102 7.5 Continuous linear mappings 104 7.6 Continuous multilinear mappings 107 7.7 Some continuous mappings 111 Chapter 8 Images of Sets Under Continuous Mappings 115 8.1 Images of open and closed sets 115 8.2 Images of dense, separable and connected sets 117 8.3 Images of compact sets 119 8.4 Images under continuous linear mappings 121 8.5 Continuous mappings in compact sets 123 8.6 Continuous real mappings 124 8.7 Compacting mappings 125 Chapter 9 Properties of Mappings in Metrizable Spaces 129 9.1 Continuous mappings in metrizable spaces 129 9.2 Banach’s fixed point theorem 133 9.3 Baire’s theorem 134 9.4 Open mapping theorem 136 9.5 Banach–Schauder’s continuity theorem 138 9.6 Closed graph theorem 139 Chapter 10 Extension of Mappings, Equicontinuity 141 10.1 Extension of equalities by continuity 141 10.2 Continuous extension of mappings 142 10.3 Equicontinuous families of mappings 146 10.4 Banach–Steinhaus equicontinuity theorem 148 Chapter 11 Compactness in Mapping Spaces 153 11.1 The spaces F(X; F) and C(X; F)-pt 153 11.2 Zorn’s lemma 154 11.3 Compactness in F(X; F) 157 11.4 An Ascoli compactness theorem in C(X; F)-pt 161 Chapter 12 Spaces of Linear or Multilinear Mappings 163 12.1 The space L(E; F) 163 12.2 Bounded sets in L(E; F) 165 12.3 Sequential completeness of L(E; F) when E is metrizable 167 12.4 Semi-norms and norm on L(E; F) when E isnormed 169 12.5 Continuity of the composition of linear mappings 171 12.6 Inversibility in the neighborhood of an isomorphism 174 12.7 The space Ld(E1 × ··· × Ed; F) 178 12.8 Separation of the variables of a multilinear mapping 181 Part 3 Weak Topologies 187 Chapter 13 Duality 189 13.1 Dual 189 13.2 Dual of a metrizable or normed space 193 13.3 Dual of a Hilbert space 196 13.4 Extraction of ∗ weakly converging subsequences 199 13.5 Continuity of the bilinear form of duality 203 13.6 Dual of a product 205 13.7 Dual of a direct sum 206 Chapter 14 Dual of a Subspace 209 14.1 Hahn–Banach theorem 209 14.2 Corollaries of the Hahn–Banach theorem 211 14.3 Characterization of a dense subspace 212 14.4 Dual of a subspace 213 14.5 Dual of an intersection 215 14.6 Dangerous identifications 216 Chapter 15 Weak Topology 221 15.1 Weak topology 221 15.2 Weak continuity and topological inclusions 224 15.3 Weak topology of a product 225 15.4 Weak topology of an intersection 226 15.5 Norm and semi-norms of a weak limit 228 Chapter 16 Properties of Sets for the Weak Topology 231 16.1 Banach–Mackey theorem (weakly bounded sets) 231 16.2 Gauge of a convex open set 233 16.3 Mazur’s theorem (weakly closed convex sets) 235 16.4 ˘Smulian’s theorem (weakly compact sets) 237 16.5 Semi-weak continuity of a bilinear mapping 240 Chapter 17 Reflexivity 243 17.1 Reflexive spaces 243 17.2 Sequential completion of a semi-reflexive space 247 17.3 Prereflexivity of metrizable spaces 248 17.4 Reflexivity of Hilbert spaces 250 17.5 Reflexivity of uniformly convex Banach spaces 252 17.6 A property of the combinations of linear forms 256 17.7 Characterizations of semi-reflexivity 257 17.8 Reflexivity of a subspace 261 17.9 Reflexivity of the image of a space 261 17.10 Reflexivity of the dual 263 Chapter 18 Extractable Spaces 265 18.1 Extractable spaces 265 18.2 Extractability of Hilbert spaces 266 18.3 Extractability of semi-reflexive spaces 267 18.4 Extractability of a subspace or of the image of a space 269 18.5 Extractability of a product or of a sum of spaces 270 18.6 Extractability of an intersection of spaces 271 18.7 Sequential completion of extractable spaces 271 Part 4 Differential Calculus 273 Chapter 19 Differentiable Mappings 275 19.1 Differentiable mappings 275 19.2 Differentiality, continuity and linearity 277 19.3 Differentiation and change of topology or restriction 279 19.4 Mean value theorem 281 19.5 Bounds on a real differentiable mapping 284 19.6 Differentiation of a composite mapping 286 19.7 Differential of an inverse mapping 289 19.8 Inverse mapping theorem 290 Chapter 20 Differentiation of Multivariable Mappings 295 20.1 Partial differentiation 295 20.2 Differentiation of a multilinear or multi-component mapping 298 20.3 Differentiation of a composite multilinear mapping 300 Chapter 21 Successive Differentiations 303 21.1 Successive differentiations 303 21.2 Schwarz’s symmetry principle 305 21.3 Successive differentiations of a composite mapping 308 Chapter 22 Derivation of Functions of One Real Variable 313 22.1 Derivative of a function of one real variable 313 22.2 Derivative of a real function of one real variable 315 22.3 Leibniz formula 319 22.4 Derivatives of the power, logarithm and exponential functions 320 Bibliography 325 Cited Authors 331 Index 335

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Book SynopsisThis book is the second of a set dedicated to the mathematical tools used in partial differential equations derived from physics. It presents the properties of continuous functions, which are useful for solving partial differential equations, and, more particularly, for constructing distributions valued in a Neumann space. The author examines partial derivatives, the construction of primitives, integration and the weighting of value functions in a Neumann space. Many of them are new generalizations of classical properties for values in a Banach space. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers, without restricting or generalizing the results.Table of ContentsIntroduction ix Familiarization with Semi-normed Spaces xiii Notations xv Chapter 1. Spaces of Continuous Functions 1 1.1. Notions of continuity 1 1.2. Spaces C(Ω;E), Cb(Ω;E), CK(Ω;E), C(Ω;E) and Cb(Ω;E) 3 1.3. Comparison of spaces of continuous functions 6 1.4. Sequential completeness of spaces of continuous functions 10 1.5. Metrizability of spaces of continuous functions 11 1.6. The space K(Ω;E) 14 1.7. Continuous mappings 20 1.8. Continuous extension and restriction 22 1.9. Separation and permutation of variables 23 1.10. Sequential compactness in Cb(Ω;E) 28 Chapter 2. Differentiable Functions 31 2.1. Differentiability 31 2.2. Finite increment theorem 34 2.3. Partial derivatives 37 2.4. Higher order partial derivatives 40 2.5. Spaces Cm(Ω;E), Cmb (Ω;E), CmK(Ω;E), Cmb (Ω;E) and Km(Ω;E) 42 2.6. Comparison and metrizability of spaces of differentiable functions 45 2.7. Filtering properties of spaces of differentiable functions 47 2.8. Sequential completeness of spaces of differentiable functions 49 2.9. The space Cm(Ω;E) and the set Cm(Ω;U) 52 Chapter 3. Differentiating Composite Functions and Others 55 3.1. Image under a linear mapping 55 3.2. Image under a multilinear mapping: Leibniz rule 59 3.3. Dual formula of the Leibniz rule 63 3.4. Continuity of the image under a multilinear mapping 65 3.5. Change of variables in a derivative 69 3.6. Differentiation with respect to a separated variable 72 3.7. Image under a differentiable mapping 73 3.8. Differentiation and translation 77 3.9. Localizing functions 79 Chapter 4. Integrating Uniformly Continuous Functions 83 4.1. Measure of an open subset of ℝd 83 4.2. Integral of a uniformly continuous function 87 4.3. Case where E is not a Neumann space 92 4.4. Properties of the integral 93 4.5. Dependence of the integral on the domain of integration 96 4.6. Additivity with respect to the domain of integration 99 4.7. Continuity of the integral 101 4.8. Differentiating under the integral sign 103 Chapter 5. Properties of the Measure of an Open Set 105 5.1. Additivity of the measure 105 5.2. Negligible sets 107 5.3. Determinant of d vectors 112 5.4. Measure of a parallelepiped 115 Chapter 6. Additional Properties of the Integral 119 6.1. Contribution of a negligible set to the integral 119 6.2. Integration and differentiation in one dimension 120 6.3. Integration of a function of functions 123 6.4. Integrating a function of multiple variables 125 6.5. Integration between graphs 130 6.6. Integration by parts and weak vanishing condition for a function 133 6.7. Change of variables in an integral 135 6.8. Some particular changes of variables in an integral 142 Chapter 7. Weighting and Regularization of Functions 147 7.1. Weighting 147 7.2. Properties of weighting 150 7.3. Weighting of differentiable functions 153 7.4. Local regularization 157 7.5. Global regularization 162 7.6. Partition of unity 166 7.7. Separability of K∞(Ω) 170 Chapter 8. Line Integral of a Vector Field Along a Path 173 8.1. Paths 173 8.2. Line integral of a field along a path 176 8.3. Line integral along a concatenation of paths 181 8.4. Tubular flow and the concentration theorem 183 8.5. Invariance under homotopy of the line integral of a local gradient 186 Chapter 9. Primitives of Continuous Functions 191 9.1. Explicit primitive of a field with line integral zero 191 9.2. Primitive of a field orthogonal to the divergence-free test fields 194 9.3. Gluing of local primitives on a simply connected open set 195 9.4. Explicit primitive on a star-shaped set: Poincaré’s theorem 197 9.5. Explicit primitive under the weak Poincaré condition 199 9.6. Primitives on a simply connected open set 203 9.7. Comparison of the existence conditions for a primitive 205 9.8. Fields with local primitives but no global primitive 208 9.9. Uniqueness of primitives 210 9.10. Continuous primitive mapping 211 Chapter 10. Additional Results: Integration on a Sphere 213 10.1. Surface integration on a sphere 213 10.2. Properties of the integral on a sphere 215 10.3. Radial calculation of integrals 218 10.4. Surface integral as an integral of dimension d − 1 220 10.5. A Stokes formula 224 Appendix 227 Bibliography 239 Index 243

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Book SynopsisEarthquake occurrence modeling is a rapidly developing research area. This book deals with its critical issues, ranging from theoretical advances to practical applications. The introductory chapter outlines state-of-the-art earthquake modeling approaches based on stochastic models. Chapter 2 presents seismogenesis in association with the evolving stress field. Chapters 3 to 5 present earthquake occurrence modeling by means of hidden (semi-)Markov models and discuss associated characteristic measures and relative estimation aspects. Further comparisons, the most important results and our concluding remarks are provided in Chapters 6 and 7.Table of ContentsList of Abbreviations ix List of Symbols xi Preface xv Introduction xix Chapter 1. Fundamentals on Stress Changes 1 1.1. Introduction 1 1.2. Stress interaction 4 1.3. Stress changes calculation 12 1.4. Modeling of Coulomb stress changes for different faulting types 15 1.4.1.ΔCS for strike-slip faulting 15 1.4.2.ΔCS for dip-slip faulting 16 1.5. Seismicity triggered by stress transfer 21 1.5.1. Triggering of strong earthquakes 21 1.5.2. Aftershock triggering 23 1.5.3. Triggering of mining seismicity 28 1.6. Discussion on stress interaction 31 Chapter 2. Hidden Markov Models 35 2.1. Introduction 35 2.2. Hidden Markov framework 37 2.3. Seismotectonic regime and seismicity data 42 2.4. Application to earthquake occurrences 44 2.4.1. Two hidden states and three observation types 45 2.4.2. Three hidden states and three observation types 48 2.4.3. Model selection and simulation 50 2.4.4. Steps number for the first earthquake occurrence 53 2.5. Conclusion 54 Chapter 3. Hidden Markov Renewal Models 57 3.1. Introduction 57 3.2. Semi-Markov framework 58 3.3. Hidden Markov renewal framework 65 3.4. Modeling earthquakes in Greece 66 3.4.1. Hitting times and earthquake occurrence numbers 69 3.5. Conclusion 73 Chapter 4. Hitting Time Intensity 75 4.1. Introduction 75 4.2. DTIHT for semi-Markov chains 76 4.2.1. Statistical estimation of the DTIHT 78 4.3. DTIHT for hidden Markov renewal chains 83 4.3.1. Statistical estimation of the DTIHT 85 4.4. Conclusion 87 Chapter 5. Models Comparison 89 5.1. Introduction 89 5.2. Markov framework 90 5.2.1. HMM case 92 5.2.2. HMRM case 92 5.3. Markov renewal framework 93 5.3.1. HMM case 95 5.3.2. HMRM case 96 5.4. Conclusion 97 Discussion & Concluding Remarks 99 Appendices 105 Appendix 1 107 Appendix 2 113 Appendix 3 117 References 119 Index 137

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Book SynopsisBranching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.Table of Contents1. Branching Processes in Varying Environment. 2. Branching Processes in Random Environment. 3. Large Deviations for BPREs. 4. Properties of Random Walks. 5. Critical BPREs: the Annealed Approach. 6. Critical BPREs: the Quenched Approach. 7. Weakly Subcritical BPREs. 8. Intermediate Subcritical BPREs. 9. Strongly Subcritical BPREs. 10. Multi-type BPREs.

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Book SynopsisThis book presents an introduction to structural equation modeling (SEM) and facilitates the access of students and researchers in various scientific fields to this powerful statistical tool. It offers a didactic initiation to SEM as well as to the open-source software, lavaan, and the rich and comprehensive technical features it offers. Structural Equation Modeling with lavaan thus helps the reader to gain autonomy in the use of SEM to test path models and dyadic models, perform confirmatory factor analyses and estimate more complex models such as general structural models with latent variables and latent growth models. SEM is approached both from the point of view of its process (i.e. the different stages of its use) and from the point of view of its product (i.e. the results it generates and their reading). Table of ContentsPreface ix Introduction xi Chapter 1 Structural Equation Modeling 1 1.1 Basic concepts 2 1.1.1 Covariance and bivariate correlation 2 1.1.2 Partial correlation 5 1.1.3 Linear regression analysis 7 1.1.4 Standard error of the estimate 10 1.1.5 Factor analysis 11 1.1.6 Data distribution normality 18 1.2 Basic principles of SEM 21 1.2.1 Estimation methods (estimators) 27 1.3 Model evaluation of the solution of the estimated model 36 1.3.1 Overall goodness-of-fit indices 36 1.3.2 Local fit indices (parameter estimates) 43 1.3.3 Modification indices 44 1.4 Confirmatory approach in SEM 45 1.5 Basic conventions of SEM 47 1.6 Place and status of variables in a hypothetical model 49 1.7 Conclusion 49 1.8 Further reading 50 Chapter 2 Structural Equation Modeling Software 53 2.1 R environment 54 2.1.1 Installing R software 55 2.1.2 R console 55 2.2 lavaan 58 2.2.1 Installing the lavaan package 58 2.2.2 Launching lavaan 58 2.3 Preparing and importing a dataset 60 2.3.1 Entry and import of raw data 60 2.3.2 What to do in the absence of raw data? 63 2.4 Major operators of lavaan syntax 65 2.5 Main steps in using lavaan 66 2.6 lavaan fitting functions 68 Chapter 3 Steps in Structural Equation Modeling 69 3.1 The theoretical model and its conceptual specification 70 3.2 Model parameters and model identification 71 3.3 Models with observed variables (path models) 73 3.3.1 Identification of a path model 74 3.3.2 Model specification using lavaan (step 2) 76 3.3.3 Direct and indirect effects 78 3.3.4 The statistical significance of indirect effects 80 3.3.5 Model estimation with lavaan (step 3) 81 3.3.6 Model evaluation (step 4) 82 3.3.7 Recursive and non-recursive models 83 3.3.8 Illustration of a path analysis model 85 3.4 Actor-partner interdependence model 90 3.4.1 Specifying and estimating an APIM with lavaan 92 3.4.2 Evaluation of the solution 93 3.4.3 Evaluating the APIM re-specified with equality constraints 94 3.5 Models with latent variables (measurement models and structural models) 95 3.5.1 The measurement model or Confirmatory Factor Analysis 97 3.6 Hybrid models 148 3.7 Measure with a single-item indicator 149 3.8 General structural model including single-item latent variables with a single indicator 151 3.9 Conclusion 152 3.10 Further reading 155 Chapter 4 Advanced Topics: Principles and Applications 157 4.1 Multigroup analysis 157 4.1.1 The steps of MG-CFA 162 4.1.2 Model solutions and model comparison tests 166 4.1.3 Total invariance versus partial invariance 171 4.1.4 Specification of a partial invariance in lavaan syntax 172 4.2 Latent trait-state models 172 4.2.1 The STARTS model 173 4.2.2 The Trait-State-Occasion Model 197 4.2.3 Concluding remarks 211 4.3 Latent growth models 213 4.3.1 General overview 213 4.3.2 Illustration of an univariate linear growth model 223 4.3.3 Illustration of an univariate non-linear (quadratic) latent growth model 228 4.3.4 Conditional latent growth model 232 4.3.5 Second-order latent growth model 240 4.4 Further reading 249 References 251 Index 269

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Book SynopsisNumerical simulation is a technique of major importance in various technical and scientific fields. Whilst engineering curricula now include training courses dedicated to it, numerical simulation is still not well-known in some economic sectors, and even less so among the general public. Simulation involves the mathematical modeling of the real world, coupled with the computing power offered by modern technology. Designed to perform virtual experiments, digital simulation can be considered as an "art of prediction". Embellished with a rich iconography and based on the testimony of researchers and engineers, this book shines a light on this little-known art. It is the second of two volumes and gives examples of the uses of numerical simulation in various scientific and technical fields: agriculture, industry, Earth and universe sciences, meteorology and climate studies, energy, biomechanics and human and social sciences.Table of ContentsForeword ix Introduction xi Chapter 1. Agriculture 1 1.1. Feeding the world 2 1.2. Agriculture is being digitized 7 1.3. Decision-making support 10 1.4. Environmental impact 16 1.5. Plant growth 23 Chapter 2. Air and Maritime Transport 31 2.1. The long march of globalization 32 2.2. Going digital! 35 2.3. Optimum design and production 50 2.3.1. Lightening the structures 50 2.3.2. Mastering processes 53 2.3.3. Producing in the digital age 58 2.4. Improving performance 63 2.4.1. Increasing seaworthiness 63 2.4.2. Limiting noise pollution 68 2.4.3. Protecting from corrosion 76 2.4.4. Reducing energy consumption 78 Chapter 3. The Universe and the Earth 87 3.1. Astrophysics 88 3.1.1. Telling the story of the Universe 90 3.1.2. Observing the formation of celestial bodies 105 3.1.3. Predicting the mass of stars 109 3.2. Geophysics 114 3.2.1. Earthquakes 115 3.2.2. Tsunamis 120 3.2.3. Eruptions 127 Chapter 4. The Atmosphere and the Oceans 133 4.1. Meteorological phenomena, climate change 134 4.2. Atmosphere and meteorology 137 4.2.1. Global and local model 138 4.2.2. Scale descent 142 4.3. Oceans and climate 145 4.3.1. Marine currents 145 4.3.2. Climate 155 Chapter 5. Energies 165 5.1. The technical dream 165 5.2. Combustion 168 5.3. Nuclear energy 173 5.3.1. Dual-use energy 173 5.3.2. At the heart of nuclear fission 176 5.3.3. Developing nuclear fusion 183 5.4. New energies 188 5.4.1. Hydroelectricity 189 5.4.2. Wind energy 193 Chapter 6. The Human Body 199 6.1. A digital medicine 200 6.2. Medical data 206 6.2.1. Medical imaging 206 6.2.2. Genetic information 211 6.3. Mechanical behavior of muscles and organs 215 6.4. Blood circulation 216 6.4.1. Blood microcapsules 218 6.4.2. Angioplasty simulation 219 6.5. Cosmetics 227 6.6. Neurosciences 228 Chapter 7. Individuals and Society 237 7.1. Calculated choices 238 7.2. A question of style 241 7.2.1. Assigning a work to its author 243 7.2.2. Understanding a pictorial technique 245 7.2.3. Discovering a personality type 247 7.3. The shape of a city 253 7.3.1. Transport 254 7.3.2. Sound atmosphere 256 7.3.3. Businesses 260 7.4. A question of choice 263 7.5. What about humans? 272 Conclusion 281 Glossary of Terms 287 References 317 Index 353

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Book SynopsisThe modeling of cities and territories has progressed greatly in the last 20 years. This is firstly due to geographic information systems, followed by the availability of large amounts of georeferenced data – both on the Internet and through the use of connected objects. In addition, the rise in performance of computational methods for the simulation and exploration of dynamic models has facilitated advancement. Geographical Modeling presents previously unpublished information on the main advances achieved by these new approaches. Each of the six chapters builds a bibliographic review and precisely describes the methods used, highlighting their advantages and discussing their interpretations. They are all illustrated by many examples. The book also explains with clarity the theoretical foundations of geographical analysis, the delicate operations of model selection, and the applications of fractals and scaling laws. These applications include gaining knowledge of the morphology of cities and the organization of urban transport, and finding new methods of building and exploring simulation models and visualizations of data and results.Table of ContentsIntroduction ixDenise PUMAIN Chapter 1. Complexity in Geography 1Denise PUMAIN 1.1. A first bifurcation in the epistemology of geographic modeling 3 1.1.1. “Vertical” explanations for the “science of places, not people” 4 1.1.2. “Horizontal” explanations for the science of the spatiality of societies 5 1.1.3. The discussed status of modeling 7 1.2. Modeled regularities 10 1.2.1. Proximity and distances 11 1.2.2. The scale 15 1.2.3. Concentration and accumulation: geographical inequalities and scaling laws 19 1.2.4. Spatial change and trajectory dependence 21 1.2.5. Territorial drifts, space-time compression, and globalization 25 1.3. Conclusion 29 Chapter 2. Choosing Models to Explain the Dynamics of Cities and Territories 31Lena SANDERS 2.1. Introduction 31 2.2. Explaining by reasons or laws: choosing an epistemological framework 32 2.3. The modeling approach: diversity of models 36 2.4. Explaining through statistical relationships or mechanisms 38 2.5. Choosing the level of abstraction for the phenomenon to be explained: general versus particular 41 2.6. Choosing the level of abstraction for the model: stylized or realistic, KISS or KIDS 44 2.6.1. Modes of representation of space: from a stylized space to a realistic space 45 2.6.2. Formalizing spatial mechanisms: from stylized to realistic 48 2.7. Conclusion 50 Chapter 3. Effects of Distance and Scale Dependence in Geographical Models of Cities and Territories 53Cécile TANNIER 3.1. Three fundamental principles for modeling cities and territories 55 3.1.1. Effects of distance 57 3.1.2. Effects of scale dependence 58 3.2. Role of distance in spatial simulation models 61 3.3. Modeling scale dependence 76 3.3.1. Scale dependence as a result of processes acting at different scales 77 3.3.2. Scale invariance for the description of geographical phenomena 83 3.3.3. Scale dependence as a generative mechanism for simulated spatial configurations 88 3.4. Conclusion 93 Chapter 4. Incremental Territorial Modeling 95Clémentine COTTINEAU, Paul CHAPRON, Marion LE TEXIER and Sébastien REY-COYREHOURCQ 4.1. The map and the territory 96 4.1.1. Modeling as one map: selection and schematization 96 4.1.2. The representation of territory as an input of the model 100 4.1.3. The representation of territory as an output of the model 102 4.2. Generality and specificity: explaining by ways of geographical models 106 4.2.1. Historical contingency and non-ergodicity 106 4.2.2. General/specific/singular 109 4.3. Incremental territorial modeling 110 4.3.1. Identifying the object, scale, configuration, and stylized facts 111 4.3.2. Gathering the different theoretical explanations 112 4.3.3. Hierarchizing the interaction processes between agents 113 4.3.4. Hierarchizing the interaction processes between agents and their environment 114 4.3.5. Implementing mechanisms and their formal alternatives 115 4.3.6. Combining, simulating, and comparing 116 4.4. Challenges and limits of multi-modeling 117 4.4.1. The combinatorial curse 118 4.4.2. Human and technical costs 118 4.4.3. Subjectivity in the choice of building blocks 119 4.4.4. Comparing models of different structures 119 4.4.5. Sharing and accumulation of knowledge 121 4.5. Conclusion 121 Chapter 5. Methods for Exploring Simulation Models 125Juste RAIMBAULT and Denise PUMAIN 5.1. Social sciences and experimentation 126 5.2. Geographical data and computer skills 127 5.3. New generation simulations 130 5.3.1. A virtual laboratory: the OpenMOLE platform 131 5.3.2. The SimpopLocal experiment: simulation of an emergence in geography 134 5.3.3. Implementation of SimpopLocal, from NetLogo to OpenMOLE 137 5.3.4. Calibration and validation 139 5.4. Other examples of OpenMOLE applications: network–territory interaction models 143 5.5. Perspectives 147 5.5.1. Methods 147 5.5.2. Tools 148 5.6. Conclusion 149 Chapter 6. Model Visualization 151Robin CURA 6.1. Introduction 151 6.2. Visualization as modeling 153 6.2.1. Visualization as a tool for interdisciplinarity 155 6.2.2. Visualization and reproducibility 160 6.2.3. Visualizing a model means learning 162 6.3. Visualize to evaluate 163 6.3.1. Visualize before modeling 164 6.3.2. Visualize during the simulation 166 6.3.3. Visualizing after the simulation 169 6.4. Visualizing to compare 172 6.4.1. Which models should be compared? 172 6.4.2. How should visual comparison be done? 174 6.5. Visualizing to communicate 178 6.5.1. Visualizing to disseminate 179 6.6. Some obstacles inherent in model visualization 182 6.6.1. Producing and visualizing massive data 183 6.6.2. Visualization of aggregated data 187 6.7. Conclusion 191 References 193 List of Authors 221 Index 223

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Book SynopsisIsogeometric analysis (IGA) consists of using the same higher-order and smooth spline functions for the representation of geometry in Computer Aided Design as for the approximation of solution fields in Finite Element Analysis. Now, about fifteen years after its creation, substantial works are being reported in IGA, which make it very competitive in scientific computing.This book provides a contemporary vision of IGA by first discussing the current challenges in achieving a true bridge between design and analysis, then proposing original solutions that answer the issues from an analytical point of view, and, eventually, studying the shape optimization of structures, which is one of the greatest applications of IGA. To handle complex structures, a full analysis-to-optimization framework is developed, based on non-invasive coupling, parallel domain decomposition and immersed geometrical modeling. This seems to be very robust, taking on all of the attractive features of IGA (the design–analysis link, numerical efficiency and natural regularization), giving us the opportunity to explore new types of design.Table of ContentsContents Preface ix Chapter 1: Introduction to IGA: Key Ingredients for the Analysis and Optimization of Complex Structures 1 1.1 Brief introduction 1 1.2 Geometric modeling and simulation with splines 2 1.2.1.Parametric representationof geometries 2 1.2.2 B-spline and NURBS technologies 5 1.2.3 Design features and shape parameterization 15 1.2.4 Spline-based finite element analysis: isogeometric principle 21 1.3 Improved CAD-CAE integration for robust optimization 23 1.3.1 Returning to the original motivations behind IGA 23 1.3.2 An ideal framework for parametric shape optimization 25 1.4.The analysis-suitablemodel issue 27 1.4.1.The trimmingconcept 28 1.4.2 Non-conformingmultipatch parameterization 30 1.4.3 Imposingshape variation 33 1.5 Computation of non-conforming interfaces: a brief overview of usual weak coupling methods 35 1.5.1.Governingequations 36 1.5.2.Penalty coupling 38 1.5.3.Mortar coupling 39 1.5.4.Nitsche coupling 41 Chapter 2: Non-invasive Coupling for Flexible Global/Local IGA 45 2.1 Brief introduction 45 2.2 The standard non-invasive strategy 46 2.2.1.Origin 46 2.2.2 Non-invasive resolution of the coupling problem 47 2.3 Interest in the field of IGA 54 2.3.1 Global/local modeling in IGA 55 2.3.2.Challenges 57 2.4 A robust algorithm for non-conforming global/local IGA 59 2.4.1 Reference formulation: non-symmetric Nitsche coupling 59 2.4.2 A Nitsche-based non-invasive algorithm 64 2.4.3.Validation 72 2.5.Summaryand discussion 84 Chapter 3: Domain Decomposition Solvers for Efficient Multipatch IGA 87 3.1 Introduction 87 3.2 Benefiting from the additional Lagrange multiplier field for multipatch analysis 89 3.3 Case of multipatch Kirchhoff–Love shell analysis 91 3.3.1 Kirchhoff–Love shell formulation: basics 92 3.3.2 Formulation of the coupled problem 97 3.3.3 Preliminary results: monolithic resolution 100 3.4 On the construction of dual domain decomposition solvers 103 3.4.1 Formulation of the interface problem 104 3.4.2.Solvingthe interfaceproblem 106 3.4.3 Null space and pseudo-inverse 110 3.4.4.Preconditioning 111 3.5 Numerical investigation of the developed algorithms 115 3.5.1.Standardsolid elasticity 116 3.5.2 Heterogeneous plate bending 121 3.5.3.Scordelis–Loroof 123 3.5.4.Stiffenedpanel 125 3.6.Summaryand discussion 128 Chapter 4: Isogeometric Shape Optimization of Multipatch and Complex Structures 131 4.1 Introduction 131 4.2 Isogeometric shape optimization framework 133 4.2.1.Optimizationflowchart 133 4.2.2 Multilevel design 133 4.2.3.Design variables 135 4.2.4.Formulationandresolution 136 4.3 Unify the DD approach and multipatch optimization: towards ultimate efficiency 145 4.3.1 DD computation of the response functions 145 4.3.2 DD computation of the sensitivities 146 4.3.3.Non-designparts 147 4.3.4.Fast re-analysis 148 4.3.5.Optimizationalgorithm 149 4.4 Innovative design of multipatch structures: focus on aeronautical stiffenedpanels 149 4.4.1 Geometric modeling: embedded entities 150 4.4.2 Analysis: an embedded Kirchhoff–Love shell element 156 4.4.3.Two preliminary examples to illustrate the design capabilities 159 4.5 Application to solid structures and first interests 168 4.5.1.Simple extensionof themethod 169 4.5.2.Atest case in 2D 171 4.6 Advanced numerical optimization examples 175 4.6.1 Global shell optimization: stiffened roof 176 4.6.2.Local shell optimization: curvedwall 179 4.6.3.Designingan aircraftwing-box 185 4.7 Towards the optimal design of structural details within isogeometric patches 192 4.7.1.Asimple but instructive test case 192 4.7.2 Unify the non-invasive global/local approach and the optimizationof local details 193 4.7.3.Preliminaryresults and perspectives 197 4.8.Summaryand discussion 198 References 201 Index 229

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Book SynopsisThis book brings together current research and adopts a pragmatic approach to modeling and using context to solve real-world problems. The editors were instrumental in creating - and continue to be involved in - the interdisciplinary research community, centered around the biennial CONTEXT (International and Interdisciplinary Conference on Modeling and Using Context) conference series, focused on studying context and its implications for artificial intelligence, software applications, psychology, philosophy, linguistics, neuroscience, as well as other fields. The first three chapters lay the foundations, looking at the lessons learned over the past 25 years and arguing for a continued shift toward more pragmatic approaches. The remaining chapters contain contributions to pragmatic context-based research from a wide range of domains, including technological problems - such as subway incident management and autonomous underwater vehicle control - identifying emotions from speech without understanding the words, anonymization in a world where privacy is increasingly threatened, teaching in context and improving management teaching in a business school.Table of ContentsPreface xi Patrick Brézillon and Roy M. Turner Introduction xxi Patrick Brézillon and Roy M. Turner Chapter 1 Pragmatic Research on Context Modeling and Use 1 Patrick Brézillon and Roy M. Turner 1.1 Introduction 1 1.2 Pragmatic research on context 2 1.3 Role of context in AI systems 3 1.3.1 Data, information and knowledge 3 1.3.2 Contextual knowledge 6 1.4 Three examples of pragmatic research on context 8 1.4.1 Introduction 8 1.4.2 Contextual graphs (CxGs) 9 1.4.3 Context-based reasoning (CxBR) 11 1.4.4 Context-mediated behavior (CMB) 12 1.4.5 Conclusions and lessons learned 14 1.5 Conclusion 18 1.6 References 19 Chapter 2. Modeling and Using Context: 25 Years of Lessons Learned 23 Patrick Brézillon 2.1 Introduction 23 2.2 Knowledge in action 25 2.2.1 Operational knowledge and contextual knowledge 25 2.2.2 Operational knowledge and mental models 26 2.2.3 Modeling operational knowledge 27 2.2.4 Indirect modeling from experience reuse 29 2.2.5 Lessons learned 31 2.3 Context in action 32 2.3.1 Conceptual modeling 32 2.3.2 A typology of contexts 33 2.3.3 About contextual elements 34 2.3.4 Implementation of the contextual graphs formalism 39 2.4 Using context in real-world applications 40 2.4.1 Context and focus processing 40 2.4.2 Context and actors 42 2.4.3 Extension of the CxG formalism 43 2.5 Conclusion 46 2.6 References 49 Chapter 3 Toward Pragmatic Context-Based Intelligent Systems 53 Roy M. Turner and Patrick Brézillon 3.1 Introduction 53 3.2 Evolution of AI systems 55 3.2.1 Formal versus pragmatic acontextual approaches 55 3.2.2 Formal consideration of context 56 3.2.3 Pragmatic consideration of context 57 3.3 Pragmatic context-based intelligent systems 62 3.3.1 Explicit context representation 63 3.3.2 Context assessment mechanism 66 3.3.3 Context transitioning mechanism 68 3.3.4 Context-based intelligent assistant systems 68 3.3.5 Context-based intelligent autonomous agents 73 3.4 Conclusion 80 3.5 References 81 Chapter 4 Activating the Context for Learning and Teaching: Findings from the TEEC Project 87 Claire Anjou, Thomas Forissier, Jacqueline Bourdeau, Valéry Psyché, Lamprini Chartofylaka and Alain Stockless 4.1 Introduction 87 4.2 Theoretical framework 89 4.2.1 Internal and external contexts for education 89 4.2.2 Modeling external context 91 4.3 The research focuses 95 4.4 Methodology 98 4.4.1 DBR methodology 98 4.4.2 Data collection and analysis 99 4.4.3 TEEC organization 99 4.5 Results and findings 101 4.5.1 Context effects identification and specification 101 4.5.2 Using the digital technologies 105 4.5.3 Learning as an evolution of mental representations 106 4.5.4 The development of digital tools 107 4.6 Discussion and interpretation 114 4.6.1 Context effect and affective dimension: learning with contexts, contexts effect and cognitive conflict 114 4.6.2 Digital education and context 117 4.6.3 Mazcalc needs to interact with the scripting tool 118 4.7 Conclusion and related work 118 4.8 Acknowledgment and credits 120 4.9 Appendices: description of the TEEC experiment 120 4.9.1 Historical event/social realities 120 4.9.2 Geothermal energy 121 4.9.3 Literature 122 4.9.4 Sustainable development: sugar 122 4.9.5 Sustainable development: fruit 124 4.10 References 125 Chapter 5 Pragmatic Reasoning in Context: Context-Mediated Behavior 131 Roy M. Turner 5.1 Introduction 131 5.2 Context-mediated behavior 133 5.2.1 CMB for autonomous agents: Orca Project 137 5.2.2 Contextual schemas 138 5.2.3 Context assessment 144 5.3 CMB and planning 146 5.4 CMB in multiagent systems 149 5.4.1 Context-appropriate organization and reorganization 149 5.4.2 An ontology for contextual knowledge and contexts 151 5.4.3 Trust in context 154 5.5 (Deep) learning in context 155 5.6 Conclusion 162 5.7 Acknowledgments 162 5.8 References 163 Chapter 6 Using Context to Help Identify the Emotional State of a Human in a Conversation 169 Andreas H. Marpaung and Avelino J. Gonzalez 6.1 Introduction and background 169 6.2 Use case and research hypothesis 170 6.3 Related works 172 6.4 Sentiment analysis as a way to model context 174 6.5 Our approach to the problem 176 6.5.1 Our overall approach to paralinguistic affect recognition 176 6.5.2 A (very) brief description of phase I (context-free classification) 177 6.5.3 Phase II – the context-centered process 178 6.6 Example application: smart phone 189 6.6.1 Phase 1: context-free process 189 6.6.2 Phase 2: context-centered process 190 6.7 Summary and conclusion 191 6.8 References 192 Chapter 7 Context-Driven Behavior: A Proactive Approach to Contextual Reasoning 197 Christian Wilson 7.1 Motivation for a proactive model 197 7.2 Challenges associated with a proactive model 199 7.2.1 Coping with uncertainty 199 7.2.2 A lack of initial knowledge 202 7.3 Context and contextual knowledge 203 7.3.1 Problem-solving contexts 203 7.3.2 Contextual schemas 204 7.4 A framework for context-driven agent 208 7.4.1 Defining a problem-solving scenario 209 7.4.2 Predicting future contexts 210 7.4.3 Identifying context-inappropriate behavior 215 7.4.4 Strategy modification 217 7.5 Conclusion 219 7.6 References 219 Chapter 8. Context-Based Personal Data Discovery for Anonymization 221 Hassane Tahir and Patrick Brézillon 8.1 Introduction 221 8.2 Personal and sensitive data 223 8.3 Procedure of personal data discovery 224 8.3.1 Objective of personal data discovery procedures 224 8.3.2 Role of a DPO in personal data discovery 225 8.3.3 Description of procedure of data discovery 225 8.4 Specifying personal data in the context of an anonymization process 228 8.4.1 Definition of anonymization 228 8.4.2 Motivation for data anonymization 228 8.4.3 Examples of techniques of anonymization 229 8.4.4 Anonymization process 231 8.4.5 Contextual elements in personal data discovery 232 8.5 Related work 235 8.6 Procedure contextualization for data discovery 236 8.6.1 The concept of context 236 8.6.2 Conceptual graph approach 236 8.6.3 A case study 238 8.7 Conclusion 242 8.8 References 243 Chapter 9 Situated Management Learning 245 John Hegarty and Régis Maubrey 9.1 Introduction 245 9.2 Management practices, values and theoretical insights 246 9.2.1 Management practices 247 9.2.2 Management values 251 9.2.3 Management insights 253 9.2.4 Toward a dynamic model of situated management learning 256 9.3 Situated learning – an application in an accounting classroom 257 9.3.1 The rules of the learning game 257 9.3.2 The accounting decision-making situation 258 9.3.3 Learning teams 259 9.3.4 Deliverables by the learning teams 259 9.3.5 Feedback to the learning teams 260 9.4 Results 260 9.5 Discussion, outlook and related research 261 9.6 Acknowledgments 262 9.7 References 263 List of Authors 267 Index 269

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Book SynopsisNumerical Methods for Strong Nonlinearities in Mechanics deals with recent advances in the numerical treatment of contact/friction and damage phenomena. Although physically distinct, these phenomena both lead to a strong nonlinearity in the mechanical problem, therefore limiting the regularity of the problem, which is now non-differentiable. This has two direct consequences: on the one hand, the mathematical characteristics of the problem deviate from wellestablished forms, requiring innovative discretization schemes; on the other hand, the low regularity makes it particularly difficult to solve the corresponding large-scale algebraic systems robustly and efficiently. In addition, neither the uniqueness, nor the existence of solutions, remain assured, resulting in bifurcation points, limit loads and structural instabilities, which are always tricky to overcome numerically.

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Book SynopsisPresenting innovative modelling approaches to the analysis of fiscal policy and government debt, this book moves beyond previous models that have relied upon the assumption that various age-specific rates and policy variables remain unchanged when it comes to generating government expenditures and tax revenues. As a result of population ageing, current policy settings in many countries are projected to lead to unsustainable levels of public debt; Tax Policy and Uncertainty explores models that allow for feedbacks and uncertainty to combat this.Applicable to any country, the models in the book explore the optimal timing and extent of tax changes in the face of anticipated high future debt. Chapters produce stochastic debt projections, including probability distribution of debt ratios at each point in time. It also offers important analysis of fiscal policy trade-offs as well as providing advice on when and by how much tax rates should be increased.Economics scholars focusing on fiscal policy will appreciate the improved models in this book that allow both for uncertainty and feedback effects arising from responses to increased debt. It will also be helpful to economic policy advisors and economists in government departments.Trade Review’This book develops important innovations in addressing two problems in determining short term fiscal policy according to long run fiscal projections. The first problem is the difficulty of modelling the complex interactions of macroeconomic variables that generate feedback effects from policy decisions. Second is the potential sunk costs of making irreversible tax and spending decisions in the face of significant uncertainty about future phenomena such as population ageing and climate change. The authors build their analysis carefully and in a very readable style. It should provide a useful manual for fiscal policy makers around the world.’- Ross Guest, Griffith University, Australia -- ’Anyone seeking to understand tax policy modelling under uncertainty will certainly want to consult this book.’- James R. Hines Jr., University of Michigan, USTable of ContentsContents: 1. Introduction I Deterministic Projection Models 2. Projecting Tax Revenues 3. A Debt Projection Model II Uncertainty in Tax Models 4. Tax Policy under Uncertainty III Debt Projections and Uncertainty 5. Stochastic Projections and Debt 6. Optimal Tax Policy Bibliography Index

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Book SynopsisThis book explores the world of reconfigurable stochastic Petri nets (RSPNs), a powerful method for modeling and verifying complex, dynamic and reconfigurable systems. As modern discrete-event systems become increasingly flexible, requiring structural adaptability at runtime, classical Petri nets are proving insufficient. This book presents innovative extensions to Petri nets, offering enhanced modeling capabilities for reconfigurable systems, while ensuring efficient verification. Through a structured approach, this book introduces reconfigurable generalized stochastic Petri nets (RecGSPNs), an advanced framework that integrates reconfigurability while preserving crucial system properties such as liveness, boundedness and deadlock-freedom. This book systematically explores modeling techniques, including stochastic reward nets and dynamic topology transformations, demonstrating their effectiveness through quantitative and qualitative analyses. By addressing challenges in state-space explosion and computational complexity, this book provides essential methodologies for researchers and practitioners working on reconfigurable systems, and serves as a valuable resource for those working in network security, manufacturing systems and distributed computing, where dynamic reconfigurations are essential.

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Book SynopsisMathematical modelling is increasingly applicable to the practical sciences. Here, mathematical approaches are applied to the study of mechanisms of digestion and metabolism in primary animal species. Farmed animals - ruminants, pigs, poultry and fish are comprehensively covered, as well as sections on companion animals. Common themes between species, such as energy and amino acid metabolism, are explored with a worldwide approach. Leading researchers from around the world have contributed to France and Kebreab's volume to provide an integrated approach to mathematical modelling in animal nutrition.Table of Contents1: Linear Models for Determining Digestibility 2: Nonlinear Functions in Animal Nutrition 3: Interesting Simple Dynamic Growth Models 4: The Dilemma in Models of Intake Regulation: Mechanistic or Empirical 5: Models to Measure and Interpret Exchange of Metabolites Across the Capillary Bed of Intact Organs 6: Modelling Methane Emissions from Farm Livestock 7: Supporting Measurements Required for Evaluation of Greenhouse Gas Emissions 8: Models for Enteric Fermentation and Stored Animal Manure 9: Data Capture: Development of a Mobile Open-Circuit Ventilated Hood System for Measuring Real- time gaseous emissions in cattle 10: Efficiency of Amino Acid Utilization in Simple-Stomached Animals and Humans: A Modelling Approach 11: Compartmental Models of Protein Turnover to Resolve Isotope Dilution Data 12: Assessment of Protein and Amino Acid Requirements in Adult Mammals, with Specific Focus on Cats, Dogs, and Rabbits 13: Mathematical Representation of the Partitioning of Retained Energy in the Growing Pig 14: Aspects of Energy Metabolism and Energy Partitioning in Broiler Chickens 15: Modelling Phosphorus Metabolism 16: Methodological Considerations for Measuring Phosphorus Utilization in Pigs 17: The Prediction of the Consequences of Pathogen Challenges on the Performance of Growing Pigs 18: Factors Regulating Feed Efficiency and Nutrient Utilization in Beef Cattle 19: Models of Nutrient Utilization by Fish and Potential Applications for Fish Culture Operations 20: Integrated Approaches to Evaluate Nutritional Strategies for Dairy Cows 21: Modelling Lactation Potential in an Animal Model 22: The Diary of Molly 23: Modelling Sugarcane Utilization by Dairy Cows in the Tropics 24: Simulation Exercises for Animal Science MSc Students: Rumen Digestion and Pig Growth

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Book Synopsis"If Augustin Cournot had still been alive, he could have won the Nobel Memorial Prize in Economics on at least three different occasions", exclaimed Nobel Laureate Robert Aumann during the 2005 Cournot Centre conference.From his earliest publications, Cournot broke from tradition with his predecessors in applying mathematical modelling to the social sphere. Consequently, he was the first to affirm the mathematization of social phenomena as an essential principle. The fecundity of Cournot's works stems not only from this departure, but also from a richness that irrigated the social sciences of the twentieth century. In this collection, the contributors - including two Nobel laureates in economics - highlight Cournot's profound innovativeness and continued relevance in the areas of industrial economics, mathematical economics, market competition, game theory and epistemology of probability and statistics. Each of the seven authors reminds us of the force and modernity of Cournot's thought as a mathematician, historian of the sciences, philosopher and, not least, as an economist.Combining an epistemological perspective with a theoretical one, this book will be of great interest to researchers and students in the fields of economics, the history of economic thought, and epistemology.Trade Review'. . . readers, especially those with a methodological orientation, will find in this book useful material of a kind not so frequently available in more traditional HET books and journals.' -- Nicola Giocoli, Storia del Pensiero Economico'Augustin Cournot: Modelling Economics is not a biography, but rather a reflection on those ideas of Cournot that persist today and what we can still learn from this great thinker. One cannot help but wonder at the wide range of accomplishments detailed in this book, but the discussion of Cournot's missteps is an unexpected highlight. . . this book should appeal to those who would like to learn more about Cournot as well as the various settings in which his thoughts have been embraced or rejected.' -- Lauren E. Feiler, Journal of Economic Literature'This rich and fascinating collection of essays helps enormously to establish the reputation of Augustin Cournot as a diverse and powerful thinker, whose numerous contributions range far beyond his widely acknowledged model of oligopoly. Cournot is revealed not merely as a mathematician, but one who was engaged in philosophical debates concerning epistemology and the nature of science. Anyone with the preconception that the development of modern economics was confined to the Anglophone world - from Smith through Marshall to the Nobel Laureates of today - will be amazed by the details of Cournot's contribution revealed here.' -- Geoffrey M. Hodgson, University of Hertfordshire, UKTable of ContentsContents: Preface About the Series: Professor Robert Solow The Complete Works of Antoine Augustin Cournot Chronological Biography of Antoine Augustin Cournot Introduction Thierry Martin and Jean-Philippe Touffut 1. Cournot as Economist: 200 Years of Relevance Jean Magnan de Bornier 2. Cournot’s Probabilistic Epistemology Thierry Martin 3. The Functions of Economic Models Bernard Walliser 4. From Cournot’s Principle to Market Efficiency Glenn Shafer 5. War and Peace Robert J. Aumann 6. Cournot and the Social Income Robert M. Solow 7. Comparing the Incomparable: The Sociology of Statistics Alain Desrosières Index

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Book Synopsis"If Augustin Cournot had still been alive, he could have won the Nobel Memorial Prize in Economics on at least three different occasions", exclaimed Nobel Laureate Robert Aumann during the 2005 Cournot Centre conference.From his earliest publications, Cournot broke from tradition with his predecessors in applying mathematical modelling to the social sphere. Consequently, he was the first to affirm the mathematization of social phenomena as an essential principle. The fecundity of Cournot's works stems not only from this departure, but also from a richness that irrigated the social sciences of the twentieth century. In this collection, the contributors - including two Nobel laureates in economics - highlight Cournot's profound innovativeness and continued relevance in the areas of industrial economics, mathematical economics, market competition, game theory and epistemology of probability and statistics. Each of the seven authors reminds us of the force and modernity of Cournot's thought as a mathematician, historian of the sciences, philosopher and, not least, as an economist.Combining an epistemological perspective with a theoretical one, this book will be of great interest to researchers and students in the fields of economics, the history of economic thought, and epistemology.Trade Review'. . . readers, especially those with a methodological orientation, will find in this book useful material of a kind not so frequently available in more traditional HET books and journals.' -- Nicola Giocoli, Storia del Pensiero Economico'Augustin Cournot: Modelling Economics is not a biography, but rather a reflection on those ideas of Cournot that persist today and what we can still learn from this great thinker. One cannot help but wonder at the wide range of accomplishments detailed in this book, but the discussion of Cournot's missteps is an unexpected highlight. . . this book should appeal to those who would like to learn more about Cournot as well as the various settings in which his thoughts have been embraced or rejected.' -- Lauren E. Feiler, Journal of Economic Literature'This rich and fascinating collection of essays helps enormously to establish the reputation of Augustin Cournot as a diverse and powerful thinker, whose numerous contributions range far beyond his widely acknowledged model of oligopoly. Cournot is revealed not merely as a mathematician, but one who was engaged in philosophical debates concerning epistemology and the nature of science. Anyone with the preconception that the development of modern economics was confined to the Anglophone world - from Smith through Marshall to the Nobel Laureates of today - will be amazed by the details of Cournot's contribution revealed here.' -- Geoffrey M. Hodgson, University of Hertfordshire, UKTable of ContentsContents: Preface About the Series: Professor Robert Solow The Complete Works of Antoine Augustin Cournot Chronological Biography of Antoine Augustin Cournot Introduction Thierry Martin and Jean-Philippe Touffut 1. Cournot as Economist: 200 Years of Relevance Jean Magnan de Bornier 2. Cournot’s Probabilistic Epistemology Thierry Martin 3. The Functions of Economic Models Bernard Walliser 4. From Cournot’s Principle to Market Efficiency Glenn Shafer 5. War and Peace Robert J. Aumann 6. Cournot and the Social Income Robert M. Solow 7. Comparing the Incomparable: The Sociology of Statistics Alain Desrosières Index

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Book SynopsisThis series of five volumes proposes an integrated description of physical processes modeling used by scientific disciplines from meteorology to coastal morphodynamics. Volume 1 describes the physical processes and identifies the main measurement devices used to measure the main parameters that are indispensable to implement all these simulation tools. Volume 2 presents the different theories in an integrated approach: mathematical models as well as conceptual models, used by all disciplines to represent these processes. Volume 3 identifies the main numerical methods used in all these scientific fields to translate mathematical models into numerical tools. Volume 4 is composed of a series of case studies, dedicated to practical applications of these tools in engineering problems. To complete this presentation, volume 5 identifies and describes the modeling software in each discipline.Trade Review"An inventory of ground measurement instruments, which provide necessary input data for the various modeling tools described in the book, is drawn up, and mathematical models describing each field within the overall subject area are detailed by a series of system equations. These are then solved by the use of numerical methods adapted to the particular characteristics of the application in question." (Environmental Expert, 19 April 2011)Table of ContentsIntroduction xix Jean-Michel TANGUY Chapter 1. Reminders on the Mechanical Properties of Fluids 1 Jacques GEORGE 1.1. Laws of conservation, principles and general theorems 1 1.2. Enthalpy, rotation, mixing, saturation 13 1.3. Thermodynamic relations, relations of state and laws of behavior 20 1.4. Turbulent flow 26 1.5. Dynamics of geophysical fluids 30 Chapter 2. 3D Navier-Stokes Equations 35 Véronique DUCROCQ 2.1. The continuity hypothesis 35 2.2. Lagrangian description/Eulerian description 36 2.3. The continuity equation 37 2.4. The movement quantity assessment equation 38 2.5. The energy balance equation 41 2.6. The equation of state 41 2.7. Navier-Stokes equations for a fluid in rotation 41 Chapter 3. Models of the Atmosphere 43 Jean COIFFIER 3.1. Introduction 43 3.2. The various simplifications and corresponding models 44 3.3. The equations with various systems of coordinates 56 3.4. Some typical conformal projections 61 3.5. The operational models 67 3.6. Bibliography 69 Chapter 4. Hydrogeologic Models 71 Dominique THIÉRY 4.1. Equation of fluid mechanics 71 4.2. Continuity equation in porous media 72 4.3. Navier-Stokes’ equations 74 4.4. Darcy’s law 76 4.5. Calculating mass storage from the equations of state 80 4.6. General equation of hydrodynamics in porous media 82 4.7. Flows in unsaturated media 84 4.8. Bibliography 91 Chapter 5. Fluvial and Maritime Currentology Models 93 Jean-Michel TANGUY 5.1. 3D hydrostatic model 99 5.2. 2D horizontal model for shallow water 107 5.3. 1D models of fluvial flows 119 5.4. Putting 1D models into real time 131 5.5. Bibliography 151 Chapter 6. Urban Hydrology Models 155 Bernard CHOCAT 6.1. Global models and detailed models used in surface flows 156 6.2. Rainfall representation and rainfall-flow transformation 161 6.3. Modeling of the losses into the ground 164 6.4. Transfer function 169 6.5. Modeling of the hydraulic operating conditions of the networks 177 6.6. Production and transport of polluting agents 189 6.7. Conclusion 205 6.8. Bibliography 206 Chapter 7. Tidal Model and Tide Streams 213 Bernard SIMON 7.1. Tidal coefficient 214 7.2. Non-harmonic methods 215 7.3. Compatibilities 216 7.4. Tidal coefficient 222 7.5. Modeling 223 7.6. Tidal currents 226 Chapter 8. Wave Generation and Coastal Current Models 235 Jean-Michel TANGUY, Jean-Michel LEFÈVRE and Philippe SERGENT 8.1. Types of swell models 235 8.2. Spectral approach in high waters 242 8.3. Wave generation models 246 8.4. Wave propagation models 260 8.5. Agitating models within the harbors 266 8.6. Non-linear wave model: Boussinesq model 298 8.7. Coastal current models influenced or created by the swell 320 8.8. Bibliography 325 Chapter 9. Solid Transport Models and Evolution of the Seabed 335 Benoît LE GUENNEC and Jean-Michel TANGUY 9.1. Transport due to the overthrust effect 338 9.2. Total load 344 9.3. Bed forms and roughness 344 9.4. Suspension transport 346 9.5. Evolution model of movable beds 357 9.6. Conclusion 364 9.7. Bibliography 364 Chapter 10. Oil Spill Models 371 Pierre DANIEL 10.1. Behavior of hydrocarbons in marine environment 371 10.2. Oil spill drift models 372 10.3. Example: the MOTHY model 375 10.4. Calculation algorithm of the path of polluting particles 378 10.5. Example of a drift prediction map 379 10.6. Bibliography 379 Chapter 11. Conceptual, Empirical and Other Models 381 Christelle ALOT and Florence HABETS 11.1. Evapotranspiration 382 11.2. Bibliography 394 Chapter 12. Reservoir Models in Hydrology 397 Patrick FOURMIGUÉ and Patrick ARNAUD 12.1. Background 397 12.2. Main principles 399 12.3. Mathematical tools 401 12.4. Forecasting 403 12.5. Integration of the spatial information 405 12.6. Modeling limits 406 12.7. Bibliography 406 Chapter 13. Reservoir Models in Hydrogeology 409 Dominique THIÉRY 13.1. Principles and objectives 409 13.2. Catchment basin 410 13.3. Setting the model up 411 13.4. Data and parameters 412 13.5. Application domains 412 Chapter 14. Artificial Neural Network Models 419 Anne JOHANNET 14.1. Neural networks: a rapidly changing domain 420 14.2. Neuron and architecture models 422 14.3. How to take into account the non-linearity 429 14.4. Case study: identification of the rainfall-runoff relation of a karst 434 14.5. Acknowledgments 441 14.6. Bibliography 441 Chapter 15. Model Coupling 445 Rachid ABABOU, Denis DARTUS and Jean-Michel TANGUY 15.1. Model coupling 446 15.2. Bibliography 488 Chapter 16. A Set of Hydrological Models 493 Charles PERRIN, Claude MICHEL and Vasken ANDRÉASSIAN 16.1. Introduction 493 16.2. Description of the annual GR1A rainfall-runoff model 495 16.3. Description of the monthly GR2M rainfall-runoff model 496 16.4. Description of the daily GR4J rainfall-runoff model 500 16.5. Applications of the models 505 16.6. Conclusions and future work 506 16.7. Bibliography 507 List of Authors 511 Index 515 General Index of Authors 517 Summary of the Other Volumes in the Series 519

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Book SynopsisStatistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability, amongst others. Many of these are related to the work of Professor M. Nikulin in statistics over the past 30 years. The authors gather together various contributions with a broad array of techniques and results, divided into three parts - Statistical Models and Methods, Statistical Models and Methods in Survival Analysis, and Reliability and Maintenance. The book is intended for researchers interested in statistical methodology and models useful in survival analysis, system reliability and statistical testing for censored and non-censored data.Table of ContentsPreface xv Biography of Mikhail Stepanovitch Nikouline xvii Vincent COUALLIER, Léo GERVILLE-RÉACHE, Catherine HUBER-CAROL, Nikolaos LIMNIOS and Mounir MESBAH Part 1. Statistical Models and Methods 1 Chapter 1. Unidimensionality, Agreement and Concordance Probability 3 Zhezhen JIN and Mounir MESBAH 1.1. Introduction 3 1.2. From reliability to unidimensionality: CAC and curve 4 1.2.1. Classical unidimensional models for measurement 4 1.2.2. Reliability of an instrument: CAC 6 1.2.3. Unidimensionality of an instrument: BRC 9 1.3. Agreement between binary outcomes: the kappa coefficient 10 1.3.1. The kappa model 10 1.3.2. The kappa coefficient 10 1.3.3. Estimation of the kappa coefficient 10 1.4. Concordance probability 11 1.4.1. Relationship with Kendall’s τ measure 12 1.4.2. Relationship with Somer’s D measure 12 1.4.3. Relationship with ROC curve 13 1.5. Estimation and inference 14 1.6. Measure of agreement 14 1.7. Extension to survival data 15 1.7.1. Harrell’s c-index 15 1.7.2. Measure of discriminatory power 16 1.8. Discussion 17 1.9. Bibliography 18 Chapter 2. A Universal Goodness-of-Fit Test Based on Regression Techniques 21 Florence GEORGE and Sneh GULATI 2.1. Introduction 21 2.2. The Brain and Shapiro procedure for the exponential distribution 22 2.3. Applications of the Brain and Shapiro test 24 2.4. Small sample null distribution of the test statistic for specific distributions 25 2.5. Power studies 28 2.6. Some real examples 28 2.7. Conclusions 31 2.8. Acknowledgment 32 2.9. Bibliography 32 Chapter 3. Entropy-type Goodness-of-Fit Tests for Heavy-Tailed Distributions 33 Andreas MAKRIDES, Alex KARAGRIGORIOU and Filia VONTA 3.1. Introduction 33 3.2. The entropy test for heavy-tailed distributions 35 3.2.1. Development and asymptotic theory 35 3.2.2. Discussion 39 3.3. Simulation study 40 3.4. Conclusions 42 3.5. Bibliography 42 Chapter 4. Penalized Likelihood Methodology and Frailty Models 45 Emmanouil ANDROULAKIS, Christos KOUKOUVINOS and Filia VONTA 4.1. Introduction 45 4.2. Penalized likelihood in frailty models for clustered data 48 4.2.1. Gamma distributed frailty 52 4.2.2. Inverse Gaussian distributed frailty 52 4.2.3. Uniform distributed frailty 54 4.3. Simulation results 55 4.4. Concluding remarks 57 4.5. Bibliography 57 Chapter 5. Interactive Investigation of Statistical Regularities in Testing Composite Hypotheses of Goodness of Fit 61 Boris LEMESHKO, Stanislav LEMESHKO and Andrey ROGOZHNIKOV 5.1. Introduction 61 5.2. Distributions of the test statistics in the case of testing composite hypotheses 63 5.3. Testing composite hypotheses in “real-time” 68 5.4. Conclusions 73 5.5. Acknowledgment 73 5.6. Bibliography 73 Chapter 6. Modeling of Categorical Data 77 Henning LÄUTER 6.1. Introduction 77 6.2. Continuous conditional distributions 78 6.2.1. Conditional normal distribution 78 6.2.1.1. Estimation of parameters 78 6.2.2. More general continuous conditional distributions 81 6.2.2.1. Conditional distribution 82 6.2.2.2. Normal copula 83 6.3. Discrete conditional distributions 84 6.3.1. Parametric conditional distributions 84 6.3.2. Estimation of parameters 86 6.4. Goodness of fit 86 6.4.1. Distribution of ˆX2 87 6.5. Modeling of categorical data 88 6.5.1. Contingency tables 89 6.5.1.1. General tables 89 6.5.1.2. Further examples 93 6.6. Bibliography 93 Chapter 7. Within the Sample Comparison of Prediction Performance of Models and Submodels: Application to Alzheimer’s Disease 95 Catherine HUBER-CAROL, Shulamith T. GROSS and Annick ALPÉROVITCH 7.1. Introduction 95 7.2. Framework 96 7.2.1. General description of the data set and the models to be compared 96 7.2.2. Definition of the performance prediction criteria: IDI and BRI 96 7.3. Estimation of IDI and BRI 97 7.3.1. General estimating equations for IDI and BRI 98 7.3.2. Estimation of IDI and BRI in the logistic case 98 7.3.2.1. Asymptotics of IDI2/1 for logistic predictors 99 7.3.2.2. Asymptotics of BRI2/1 for logistic predictors 100 7.4. Simulation studies 102 7.4.1. First simulation 102 7.4.2. Second simulation: Gu and Pepe’s example 104 7.5. The three city study of Alzheimer’s disease 106 7.6. Conclusion 108 7.7. Bibliography 109 Chapter 8. Durbin–Knott Components and Transformations of the Cramér-von Mises Test 111 Gennady MARTYNOV 8.1. Introduction 111 8.2. Weighted Cramér-von Mises statistic 111 8.3. Examples of the Cramér-von Mises statistics 113 8.3.1. Classical Cramér-von Mises statistic 113 8.3.2. Anderson–Darling statistic 113 8.3.3. Cramér-von Mises statistic with the power weight function 114 8.4. Weighted parametric Cramér-von Mises statistic 114 8.4.1. Covariance functions of weighted parametric empirical process 114 8.4.2. Eigenvalues and eigenfunctions for weighted parametric Cramérvon Mises statistic 116 8.5. Transformations of the Cramér-von Mises statistic 117 8.5.1. Preliminary notes 117 8.5.2. Replacement of eigenvalues 118 8.5.3. Transformed statistics 119 8.6. Bibliography 122 Chapter 9. Conditional Inference in Parametric Models 125 Michel BRONIATOWSKI and Virgile CARON 9.1. Introduction and context 125 9.2. The approximate conditional density of the sample 127 9.2.1. Approximation of conditional densities 127 9.2.2. The proxy of the conditional density of the sample 129 9.2.3. Comments on implementation 131 9.3. Sufficient statistics and approximated conditional density 131 9.3.1. Keeping sufficiency under the proxy density 131 9.3.2. Rao–Blackwellization 132 9.4. Exponential models with nuisance parameters 135 9.4.1. Conditional inference in exponential families 135 9.4.2. Application of conditional sampling to MC tests 137 9.4.2.1. Context 137 9.4.2.2. Bimodal likelihood: testing the mean of a normal distribution in dimension 2 139 9.4.3. Estimation through conditional likelihood 140 9.5. Bibliography 142 Chapter 10. On Testing Stochastic Dominance by Exceedance, Precedence and Other Distribution-Free Tests, with Applications 145 Paul DEHEUVELS 10.1. Introduction 145 10.2. Results 148 10.2.1. The experimental data set 148 10.2.2. An application of the Wilcoxon–Mann–Whitney statistics 149 10.2.3. One-sided Kolmogorov-Smirnov tests 150 10.2.4. Precedence and Exceedance Tests. 152 10.3. Negative binomial limit laws 155 10.4. Conclusion 159 10.5. Bibliography 159 Chapter 11. Asymptotically Parameter-Free Tests for Ergodic Diffusion Processes 161 Yury A. KUTOYANTS and Li ZHOU 11.1. Introduction 161 11.2. Ergodic diffusion process and some limits 165 11.3. Shift parameter 168 11.4. Shift and scale parameters 172 11.5. Bibliography 175 Chapter 12. A Comparison of Homogeneity Tests for Different Alternative Hypotheses 177 Sergey POSTOVALOV and Petr PHILONENKO 12.1. Homogeneity tests 178 12.1.1. Tests for data without censoring 179 12.1.2. Tests for data with censoring 180 12.2. Alternative hypotheses 184 12.3. Power simulation 185 12.3.1. Power of tests without censoring 187 12.3.2. Power of tests with censoring 189 12.3.2.1. How does the distribution of censoring time affect the power of the test? 189 12.3.2.2. How does the censoring rate affect the power of the test? 191 12.4. Statistical inference 191 12.5. Acknowledgment 192 12.6. Bibliography 193 Chapter 13. Some Asymptotic Results for Exchangeably Weighted Bootstraps of the Empirical Estimator of a Semi-Markov Kernel with Applications 195 Salim BOUZEBDA and Nikolaos LIMNIOS 13.1. Introduction 195 13.2. Semi-Markov setting 197 13.3. Main results 201 13.4. Bootstrap for a multidimensional empirical estimator of a continuous-time semi-Markov kernel 205 13.5. Confidence intervals 208 13.6. Bibliography 210 Chapter 14. On Chi-Squared Goodness-of-Fit Test for Normality 213 Mikhail NIKULIN, Léo GERVILLE-RÉACHE and Xuan Quang TRAN 14.1. Chi–squared test for normality 213 14.2. Simulation study 221 14.3. Bibliography 226 Part 2. Statistical Models and Methods in Survival Analysis 229 Chapter 15. Estimation/Imputation Strategies for Missing Data in Survival Analysis 231 Elodie BRUNEL, Fabienne COMTE and Agathe GUILLOUX 15.1. Introduction 231 15.2. Model and strategies 233 15.2.1. Model assumptions 233 15.2.2. Strategy involving knowledge of ζ 234 15.2.3. Strategy involving knowledge of π 235 15.2.4. Estimation of ζ or π: logit or non-parametric regression 236 15.2.5. Computing the hazard estimators 236 15.2.6. Theoretical results 239 15.3. Imputation-based strategy 241 15.4. Numerical comparison 242 15.5. Proofs 244 15.6. Bibliography 251 Chapter 16. Non-Parametric Estimation of Linear Functionals of a Multivariate Distribution Under Multivariate Censoring with Applications 253 Olivier LOPEZ and Philippe SAINT-PIERRE 16.1. Introduction 253 16.2. Non-parametric estimation of the distribution 255 16.3. Asymptotic properties 257 16.4. Statistical applications of functionals 260 16.4.1. Dependence measures 260 16.4.2. Bootstrap 261 16.4.3. Linear regression 262 16.5. Illustration 263 16.6. Conclusion 264 16.7. Acknowledgment 264 16.8. Bibliography 264 Chapter 17. Kernel Estimation of Density from Indirect Observation 267 Valentin SOLEV 17.1. Introduction 267 17.1.1. Random partition 267 17.1.2. Indirect observation 268 17.1.3. Kernel density estimator 269 17.2. Density of random vector Λ(X) 271 17.3. Pseudo-kernel density estimator 273 17.3.1. Pointwise density estimation based on indirect data 273 17.3.2. Bias of the kernel estimator 274 17.3.3. Estimate of variance 276 17.4. Bibliography 279 Chapter 18. A Comparative Analysis of Some Chi-Square Goodness-of-Fit Tests for Censored Data 281 Ekaterina CHIMITOVA and Boris LEMESHKO 18.1. Introduction 281 18.2. Chi-square goodness-of-fit tests for censored data 283 18.2.1. NRR χ2 test 283 18.2.2. GPF χ2 test 284 18.3. The choice of grouping intervals 285 18.3.1. Equifrequent grouping (EFG) 289 18.3.2. Intervals with equal expected numbers of failures (EENFG) 289 18.3.3. Optimal grouping (OptG) 289 18.4. Empirical power study 290 18.5. Conclusions 293 18.6. Acknowledgment 294 18.7. Bibliography 294 Chapter 19. A Non-parametric Test for Comparing Treatments with Missing Data and Dependent Censoring 297 Amel MEZAOUER, Kamal BOUKHETALA and Jean-François DUPUY 19.1. Introduction 297 19.2. The proposed test statistic 299 19.3. Asymptotic distribution of the proposed test statistic 301 19.4. Acknowledgment 305 19.5. Appendix 306 19.6. Bibliography 309 Chapter 20. Group Sequential Tests for Treatment Effect with Covariates Adjustment through Simple Cross-Effect Models 311 Isaac Wu HONG-DAR 20.1. Introduction 311 20.2. Notations and models 313 20.3. Group sequential test 316 20.4. Discussion 318 20.5. Acknowledgment 318 20.6. Bibliography 318 Part 3. Reliability and Maintenance 321 Chapter 21. Optimal Maintenance in Degradation Processes 323 Waltraud KAHLE 21.1. Introduction 323 21.2. The degradation model 324 21.3. Optimal replacement after an inspection 326 21.4. The simulation of degradation processes 327 21.5. Shape of cost functions and optimal δ and a 329 21.6. Incomplete preventive maintenance 330 21.7. Bibliography 333 Chapter 22. Planning Accelerated Destructive Degradation Tests with Competing Risks 335 Ying SHI and William Q. MEEKER 22.1. Introduction 336 22.1.1. Background 336 22.1.2. Motivation: adhesive bond C 336 22.1.3. Related literature 337 22.1.4. Overview 338 22.2. Degradation models with competing risks 338 22.2.1. Accelerated degradation model for the primary response 338 22.2.2. Accelerated degradation model for the competing response 339 22.2.3. Degradation models for adhesive bond C 339 22.2.4. Degradation distribution and quantiles 340 22.3. Failure-time distribution with competing risks 341 22.3.1. Relationship between degradation and failure 341 22.3.2. Failure-time distribution and quantiles 342 22.4. Test planning with competing risks 342 22.4.1. ADDT planning information 342 22.4.2. Criterion for ADDT planning with competing risks 343 22.5. ADDT plans with competing risks 344 22.5.1. Initial optimum ADDT plan with competing risks 344 22.5.2. Constrained optimum ADDT plan with competing risks 348 22.5.3. General equivalence theorem 348 22.5.4. Compromise ADDT plan with competing risks 350 22.6. Monte Carlo simulation to evaluate test plans 352 22.7. Conclusions and extensions 353 22.8. Appendix: technical details 354 22.8.1. The Fisher information matrix for ADDT with competing risks 354 22.8.2. Large-sample approximate variance of ht (tp) and tp 355 22.9. Bibliography 355 Chapter 23. A New Goodness-of-Fit Test for Shape-Scale Families 357 Vilijandas BAGDONAVIČIUS 23.1. Introduction 357 23.2. The test statistic 358 23.3. The asymptotic distribution of the test statistic 359 23.4. The test 364 23.5. Weibull distribution 364 23.6. Loglogistic distribution 365 23.7. Lognormal distribution 366 23.8. Bibliography 367 Chapter 24. Time-to-Failure of Markov-Modulated Gamma Process with Application to Replacement Policies 369 Christian PAROISSIN and Landy RABEHASAINA 24.1. Introduction 369 24.2. Degradation model 370 24.2.1. Covariate process 370 24.2.2. Degradation process 371 24.3. Time-to-failure distribution 371 24.3.1. Case of a non-modulated gamma process 372 24.3.2. Case of a Markov-modulated gamma process 373 24.3.3. Stochastic comparison 374 24.4. Replacement policies 376 24.4.1. Block replacement policy 377 24.4.2. Age replacement policy 379 24.5. Conclusion 381 24.6. Acknowledgment 381 24.7. Bibliography 382 Chapter 25. Calculation of the Redundant Structure Reliability for Agingtype Elements 383 Alexandr ANTONOV, Alexandr PLYASKIN and Khizri TATAEV 25.1. Introduction 383 25.2. The operation process of the renewal and repaired products 384 25.3. The model of the geometric process 386 25.4. Task solution 387 25.5. Conclusion 389 25.6. Bibliography 390 Chapter 26. On Engineering Risks of Complex Hierarchical Systems Analysis 391 Vladimir RYKOV 26.1. Introduction 391 26.2. Risk definition and measurement 392 26.3. Engineering risk 393 26.4. Risk characteristics for general model calculation 395 26.4.1. Lifelength and appropriate loss size CDF 395 26.4.2. Probability of risk event evolution 396 26.4.3. Lifelength and loss moments 397 26.4.4. Mostly dangerous paths of risk event evolution and sensitivity analysis 399 26.5. Risk analysis for short-time risk models 400 26.6. Conclusion 402 26.7. Bibliography 402 List of Authors 405 Index 409

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Book SynopsisThis book presents basic stochastic processes, stochastic calculus including Lévy processes on one hand, and Markov and Semi Markov models on the other. From the financial point of view, essential concepts such as the Black and Scholes model, VaR indicators, actuarial evaluation, market values, fair pricing play a central role and will be presented. The authors also present basic concepts so that this series is relatively self-contained for the main audience formed by actuaries and particularly with ERM (enterprise risk management) certificates, insurance risk managers, students in Master in mathematics or economics and people involved in Solvency II for insurance companies and in Basel II and III for banks.Table of ContentsINTRODUCTION xi CHAPTER 1. BASIC PROBABILISTIC TOOLS FOR STOCHASTIC MODELING 1 1.1. Probability space and random variables 1 1.2. Expectation and independence 4 1.3. Main distribution probabilities 7 1.3.1. Binomial distribution 7 1.3.2. Negative exponential distribution 8 1.3.3. Normal (or Laplace–Gauss) distribution 8 1.3.4. Poisson distribution 11 1.3.5. Lognormal distribution 11 1.3.6. Gamma distribution 12 1.3.7. Pareto distribution 13 1.3.8. Uniform distribution 16 1.3.9. Gumbel distribution 16 1.3.10. Weibull distribution 16 1.3.11. Multi-dimensional normal distribution 17 1.3.12. Extreme value distribution 19 1.4. The normal power (NP) approximation 28 1.5. Conditioning 31 1.6. Stochastic processes 39 1.7. Martingales 43 CHAPTER 2. HOMOGENEOUS AND NON-HOMOGENEOUS RENEWAL MODELS 47 2.1. Introduction 47 2.2. Continuous time non-homogeneous convolutions 49 2.2.1. Non-homogeneous convolution product 49 2.3. Homogeneous and non-homogeneous renewal processes 53 2.4. Counting processes and renewal functions 56 2.5. Asymptotical results in the homogeneous case 61 2.6. Recurrence times in the homogeneous case 63 2.7. Particular case: the Poisson process 66 2.7.1. Homogeneous case 66 2.7.2. Non-homogeneous case 68 2.8. Homogeneous alternating renewal processes 69 2.9. Solution of non-homogeneous discrete timevevolution equation 71 2.9.1. General method 71 2.9.2. Some particular formulas 73 2.9.3. Relations between discrete time and continuous time renewal equations 74 CHAPTER 3. MARKOV CHAINS 77 3.1. Definitions 77 3.2. Homogeneous case 78 3.2.1. Basic definitions 78 3.2.2. Markov chain state classification 81 3.2.3. Computation of absorption probabilities 87 3.2.4. Asymptotic behavior 88 3.2.5. Example: a management problem in an insurance company 93 3.3. Non-homogeneous Markov chains 95 3.3.1. Definitions 95 3.3.2. Asymptotical results 98 3.4. Markov reward processes 99 3.4.1. Classification and notation 99 3.5. Discrete time Markov reward processes (DTMRWPs) 102 3.5.1. Undiscounted case 102 3.5.2. Discounted case 105 3.6. General algorithms for the DTMRWP 111 3.6.1. Homogeneous MRWP 112 3.6.2. Non-homogeneous MRWP 112 CHAPTER 4. HOMOGENEOUS AND NON-HOMOGENEOUS SEMI-MARKOV MODELS 113 4.1. Continuous time semi-Markov processes 113 4.2. The embedded Markov chain 117 4.3. The counting processes and the associated semi-Markov process 118 4.4. Initial backward recurrence times 120 4.5. Particular cases of MRP 122 4.5.1. Renewal processes and Markov chains 122 4.5.2. MRP of zero-order (PYKE (1962)) 122 4.5.3. Continuous Markov processes 124 4.6. Examples 124 4.7. Discrete time homogeneous and non-homogeneous semi-Markov processes 127 4.8. Semi-Markov backward processes in discrete time 129 4.8.1. Definition in the homogeneous case 129 4.8.2. Semi-Markov backward processes in discrete time for the non-homogeneous case 130 4.8.3. DTSMP numerical solutions 133 4.9. Discrete time reward processes 137 4.9.1. Undiscounted SMRWP 137 4.9.2. Discounted SMRWP 141 4.9.3. General algorithms for DTSMRWP 144 4.10. Markov renewal functions in the homogeneous case 146 4.10.1. Entrance times 146 4.10.2. The Markov renewal equation 150 4.10.3. Asymptotic behavior of an MRP 151 4.10.4. Asymptotic behavior of SMP 153 4.11. Markov renewal equations for the non-homogeneous case 158 4.11.1. Entrance time 158 4.11.2. The Markov renewal equation 162 CHAPTER 5. STOCHASTIC CALCULUS 165 5.1. Brownian motion 165 5.2. General definition of the stochastic integral 167 5.2.1. Problem of stochastic integration 167 5.2.2. Stochastic integration of simple predictable processes and semi-martingales 168 5.2.3. General definition of the stochastic integral 170 5.3. Itô’s formula 177 5.3.1. Quadratic variation of a semi-martingale 177 5.3.2. Itô’s formula 179 5.4. Stochastic integral with standard Brownian motion as an integrator process 180 5.4.1. Case of simple predictable processes 181 5.4.2. Extension to general integrator processes 183 5.5. Stochastic differentiation 184 5.5.1. Stochastic differential 184 5.5.2. Particular cases 184 5.5.3. Other forms of Itô’s formula 185 5.6. Stochastic differential equations 191 5.6.1. Existence and unicity general theorem 191 5.6.2. Solution of stochastic differential equations 195 5.6.3. Diffusion processes 199 5.7. Multidimensional diffusion processes 202 5.7.1. Definition of multidimensional Itô and diffusion processes 203 5.7.2. Properties of multidimensional diffusion processes 203 5.7.3. Kolmogorov equations 205 5.7.4. The Stroock–Varadhan martingale characterization of diffusion processes 208 5.8. Relation between the resolution of PDE and SDE problems. The Feynman–Kac formula 209 5.8.1. Terminal payoff 209 5.8.2. Discounted payoff function 210 5.8.3. Discounted payoff function and payoff rate 210 5.9. Application to option theory 213 5.9.1. Options 213 5.9.2. Black and Scholes model 216 5.9.3. The Black and Scholes partial differential equation (BSPDE) and the BS formula 216 5.9.4. Girsanov theorem 219 5.9.5. The risk-neutral measure and the martingale property 221 5.9.6. The risk-neutral measure and the evaluation of derivative products 224 CHAPTER 6. LÉVY PROCESSES 227 6.1. Notion of characteristic functions 227 6.2. Lévy processes 228 6.3. Lévy–Khintchine formula 230 6.4. Subordinators 234 6.5. Poisson measure for jumps 234 6.5.1. The Poisson random measure 234 6.5.2. The compensated Poisson process 235 6.5.3. Jump measure of a Lévy process 236 6.5.4. The Itô–Lévy decomposition 236 6.6. Markov and martingale properties of Lévy processes 237 6.6.1. Markov property 237 6.6.2. Martingale properties 239 6.6.3. Itô formula 240 6.7. Examples of Lévy processes 240 6.7.1. The lognormal process: Black and Scholes process 240 6.7.2. The Poisson process 241 6.7.3. Compensated Poisson process 242 6.7.4. The compound Poisson process 242 6.8. Variance gamma (VG) process 244 6.8.1. The gamma distribution 244 6.8.2. The VG distribution 245 6.8.3. The VG process 246 6.8.4. The Esscher transformation 247 6.8.5. The Carr–Madan formula for the European call 249 6.9. Hyperbolic Lévy processes 250 6.10. The Esscher transformation 252 6.10.1. Definition 252 6.10.2. Option theory with hyperbolic Lévy processes 253 6.10.3. Value of the European option call 255 6.11. The Brownian–Poisson model with jumps 256 6.11.1. Mixed arithmetic Brownian–Poisson and geometric Brownian–Poisson processes 256 6.11.2. Merton model with jumps 258 6.11.3. Stochastic differential equation (SDE) for mixed arithmetic Brownian–Poisson and geometric Brownian–Poisson processes 261 6.11.4. Value of a European call for the lognormal Merton model 264 6.12. Complete and incomplete markets 264 6.13. Conclusion 265 CHAPTER 7. ACTUARIAL EVALUATION, VAR AND STOCHASTIC INTEREST RATE MODELS 267 7.1. VaR technique 267 7.2. Conditional VaR value 271 7.3. Solvency II 276 7.3.1. The SCR indicator 276 7.3.2. Calculation of MCR 278 7.3.3. ORSA approach 279 7.4. Fair value 280 7.4.1. Definition 280 7.4.2. Market value of financial flows 281 7.4.3. Yield curve 281 7.4.4. Yield to maturity for a financial investment and a bond 283 7.5. Dynamic stochastic time continuous time model for instantaneous interest rate 284 7.5.1. Instantaneous deterministic interest rate 284 7.5.2. Yield curve associated with a deterministic instantaneous interest rate 285 7.5.3. Dynamic stochastic continuous time model for instantaneous interest rate 286 7.5.4. The OUV stochastic model 287 7.5.5. The CIR model 289 7.6. Zero-coupon pricing under the assumption of no arbitrage 292 7.6.1. Stochastic dynamics of zero-coupons 292 7.6.2. The CIR process as rate dynamic 295 7.7. Market evaluation of financial flows 298 BIBLIOGRAPHY 301 INDEX 309

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Book SynopsisThis book provides the mathematical basis for investigating numerically equations from physics, life sciences or engineering. Tools for analysis and algorithms are confronted to a large set of relevant examples that show the difficulties and the limitations of the most naïve approaches. These examples not only provide the opportunity to put into practice mathematical statements, but modeling issues are also addressed in detail, through the mathematical perspective.Table of ContentsPreface ix Chapter 1. Ordinary Differential Equations 1 1.1. Introduction to the theory of ordinary differential equations 1 1.1.1. Existence–uniqueness of first-order ordinary differential equations 1 1.1.2. The concept of maximal solution 11 1.1.3. Linear systems with constant coefficients 16 1.1.4. Higher-order differential equations 20 1.1.5. Inverse function theorem and implicit function theorem 21 1.2. Numerical simulation of ordinary differential equations, Euler schemes, notions of convergence, consistence and stability 27 1.2.1. Introduction 27 1.2.2. Fundamental notions for the analysis of numerical ODE methods 29 1.2.3. Analysis of explicit and implicit Euler schemes 33 1.2.4. Higher-order schemes 50 1.2.5. Leslie’s equation (Perron–Frobenius theorem, power method) 51 1.2.6. Modeling red blood cell agglomeration 78 1.2.7. SEI model 87 1.2.8. A chemotaxis problem 93 1.3. Hamiltonian problems 102 1.3.1. The pendulum problem 106 1.3.2. Symplectic matrices; symplectic schemes 112 1.3.3. Kepler problem 125 1.3.4. Numerical results 129 Chapter 2. Numerical Simulation of Stationary Partial Differential Equations: Elliptic Problems 141 2.1. Introduction 141 2.1.1. The 1D model problem; elements of modeling and analysis 144 2.1.2. A radiative transfer problem 155 2.1.3. Analysis elements for multidimensional problems 163 2.2. Finite difference approximations to elliptic equations 166 2.2.1. Finite difference discretization principles 166 2.2.2. Analysis of the discrete problem 173 2.3. Finite volume approximation of elliptic equations 180 2.3.1. Discretization principles for finite volumes 180 2.3.2. Discontinuous coefficients 187 2.3.3. Multidimensional problems 189 2.4. Finite element approximations of elliptic equations 191 2.4.1. P1 approximation in one dimension 191 2.4.2. P2 approximations in one dimension 197 2.4.3. Finite element methods, extension to higher dimensions 200 2.5. Numerical comparison of FD, FV and FE methods 204 2.6. Spectral methods 205 2.7. Poisson–Boltzmann equation; minimization of a convex function, gradient descent algorithm 217 2.8. Neumann conditions: the optimization perspective 224 2.9. Charge distribution on a cord 228 2.10. Stokes problem 235 Chapter 3. Numerical Simulations of Partial Differential Equations: Time-dependent Problems 267 3.1. Diffusion equations 267 3.1.1. L2 stability (von Neumann analysis) and L∞ stability: convergence 269 3.1.2. Implicit schemes 276 3.1.3. Finite element discretization 281 3.1.4. Numerical illustrations 283 3.2. From transport equations towards conservation laws 291 3.2.1. Introduction 291 3.2.2. Transport equation: method of characteristics 295 3.2.3. Upwinding principles: upwind scheme 299 3.2.4. Linear transport at constant speed; analysis of FD and FV schemes 301 3.2.5. Two-dimensional simulations 326 3.2.6. The dynamics of prion proliferation 329 3.3. Wave equation 345 3.4. Nonlinear problems: conservation laws 354 3.4.1. Scalar conservation laws 354 3.4.2. Systems of conservation laws 387 3.4.3. Kinetic schemes 393 Appendices 407 Appendix 1 409 Appendix 2 417 Appendix 3 427 Appendix 4 433 Appendix 5 443 Bibliography 447 Index 455

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Book SynopsisPetri Nets were defined for the study of discrete events systems and later extended for many purposes including dependability assessment. In our knowledge, no book deals specifically with the use of different type of PN to dependability. We propose in addition to bring a focus on the adequacy of Petri net types to the study of various problems related to dependability such as risk analysis and probabilistic assessment. In the first part, the basic models of PN and some useful extensions are briefly recalled. In the second part, the PN are used as a formal model to describe the evolution process of critical system in the frame of an ontological approach. The third part focuses on the stochastic Petri Nets (SPN) and their use in dependability assessment. Different formal models of SPN are formally presented (semantics, evolution rules…) and their equivalence with the corresponding class of Markov processes to get an analytical assessment of dependability. Simplification methods are proposed in order to reduce the size of analytical model and to make it more calculable. The introduction of some concepts specific to high level PN allows too the consideration of complex systems. Few applications in the field of the instrumentation and control (l&C) systems, safety integrated systems (SIS) emphasize the benefits of SPN for dependability assessment.Table of ContentsIntroduction xi Part 1 Short Review of Petri Net Modeling 1 Introduction to Part 1 3 Chapter 1 Autonomous Petri Nets 5 1.1 Unmarked Petri nets 5 1.1.1 Definitions 5 1.1.2 Drawing 6 1.1.3 Other definitions 7 1.2 Marking of a PN 7 1.2.1 Order relation on markings 8 1.2.2 Enabled transition 9 1.3 Dynamics of autonomous PNs 9 1.3.1 Firing of a transition 9 1.3.2 Transition matrix 11 1.3.3 Firing sequence 11 1.3.4 Reachable marking 12 1.3.5 Fundamental equation 12 1.3.6 Properties of PN 14 1.3.7 Other properties 14 1.3.8 Invariants in a PN 15 1.3.9 Reachability graph 16 Chapter 2 Petri Nets and Event Languages 19 2.1 Labeled PNs 19 2.1.1 Formal definition 19 2.1.2 Generated and marked languages 20 2.2 Example 21 Chapter 3 Comparison Petri Nets – Finite State Automaton 25 3.1 Language expression 26 3.2 Building of the models 27 3.2.1 Synchronization of submodels 28 3.2.2 Resource sharing 29 3.2.3 Construction by refinement 30 3.3 Compactness of the model 32 Chapter 4 Some Extensions of Petri Nets 35 4.1 PN with inhibitor arcs 35 4.2 Timed PN 36 4.2.1 P-timed Petri nets 37 4.2.2 T-timed Petri nets 37 4.3 Synchronized PN 38 4.4 Timed synchronized PN 40 4.5 Interpreted PN 41 4.6 Colored PN 42 4.6.1 Introduction example 42 4.6.2 Formal definition 45 4.6.3 A dedicated software CPN Tools 46 Conclusion to Part 1 51 Part 2 A Formal Approach to Risk Assessment 53 Introduction to Part 2 51 Chapter 5 Ontology-based Accidental Process 61 5.1 Preliminary definitions 61 5.2 Elementary entities: HSE and VTE 63 5.2.1 Hazard supplier entity (HSE) 63 5.2.2 Vulnerable target entity (VTE) 63 5.3 Elementary situations and elementary events 64 5.3.1 State versus situation 64 5.3.2 Initial situation (IS) 64 5.3.3 Initiating event (IEv) 64 5.3.4 Hazard situation (HS) 65 5.3.5 Exposure event (EEv) 65 5.3.6 Exposure situation (ES) 65 5.3.7 Accident situation 65 5.3.8 Hazardous (feared) event (HEv) 65 5.4 Conclusion 66 Chapter 6 Petri Net Modeling of the Accidental Process 67 6.1 Elementary process 68 6.2 Sequence of elementary processes 71 6.3 Modeling the action of a safety barrier 71 6.4 Modeling of a cumulative process 73 6.5 PN as a support for risk assessment 75 6.5.1 Modeling of the damage 75 6.5.2 Modeling of the event frequencies 75 6.5.3 CPN Tools implementation 77 6.5.4 Evaluation rule of the risk 83 6.6 Conclusion 86 Chapter 7 Illustrative Example 87 7.1 Functional description 87 7.2 Building of an accidental process 88 7.2.1 First elementary process 88 7.2.2 Second elementary process 91 7.2.3 Parallel process 92 7.2.4 The whole model 92 7.3 Conclusion 94 Chapter 8 Design and Safety Assessment Cycle 95 8.1 Five essential steps 95 8.2 Ontological interest 98 Conclusion to Part 2 101 Part 3 Stochastic Petri Nets 103 Introduction to Part 3 105 Chapter 9 Basic Concept 107 9.1 Introductory example 107 9.2 Formal definition 108 Chapter 10 Semantics, Properties and Evolution Rules of an SPN 111 10.1 Conservatism properties 112 10.1.1 Conservatism of the mean marking in steady state 112 10.1.2 Conservatism of the flow in steady state 113 10.2 Mean sojourn time in a place of a SPN 113 10.3 Equivalent Markov process 114 10.4 Example of SPN for systems dependability modelling and assessment 116 Chapter 11 Simplification of Complex Models 121 11.1 Introduction 121 11.2 System modeling 122 11.3 Presentation of the quantitative analysis method 124 11.3.1 Steps to obtain an aggregated Markov graph 124 11.3.2 Toward a direct establishment of a reduced Markov graph 137 11.4 Example 137 11.4.1 Failure modeling 138 11.4.2 Study of the different functional and hardware solutions 139 11.4.3 Evaluation of the weighting coefficients from the Petri nets 144 11.4.4 Conclusion 147 Chapter 12 Extensions of SPN 149 12.1 Introduction 149 12.2 Relationship between stochastic Petri nets and stochastic processes 150 12.3 The transition firing policy 151 12.4 Associated stochastic processes 151 12.4.1 Temporal memory based on resampling 152 12.4.2 Temporal memory based on age memory or on enabling memory 153 12.4.3 Stochastic process underlying a stochastic PN 154 12.4.4 Embedded Markov chain of the stochastic process 157 12.4.5 Application to a case study 159 12.5 Synchronization problem in generalized stochastic Petri nets 162 12.5.1 GSPN with internal synchronization 162 12.5.2 SPN with predicates and assertions 164 12.6 Conclusion 168 Part 4 Applications of Stochastic Petri Nets to Assessment Problems in Industrial Systems 169 Introduction to Part 4 171 Chapter 13 Application in Dynamic Reliability 175 13.1 Presentation of the system and hypothesis 175 13.2 System modeling with Petri net 177 13.3 Methodology application 179 13.4 Construction of an aggregated Markov graph 180 13.5 Conclusion 185 Chapter 14 Classical Dependability Assessment 187 14.1 Availability study of a nuclear power plant subsystem 187 14.1.1 CPN modeling 188 14.1.2 Reliability and dependability assessment 192 14.1.3 Conclusion 196 14.2 Common causes failures in nuclear plants (safety oriented) 197 14.2.1 The Atwood model 197 14.2.2 Case study 199 14.2.3 Probabilistic dependability assessment 208 14.2.4 Conclusion 212 Chapter 15 Impact of Failures on System Performances 213 15.1 Reliability evaluation of networked control system 213 15.1.1 Statement of the problem 213 15.1.2 Reliability criteria of an NCS 215 15.1.3 Elements of modeling 216 15.1.4 Simulation and results 225 15.1.5 Evaluation of reliability 230 15.1.6 Conclusion 230 15.2 Railway signaling 231 15.2.1 Introduction 231 15.2.2 Interest 233 15.2.3 Signaling system specifications 234 15.2.4 Elements to be modeled 235 15.2.5 Architecture of the model 236 15.2.6 Example of an elementary model 237 15.2.7 Incident generation 239 15.2.8 Results 239 15.2.9 Conclusion 242 Conclusion 245 Appendix 247 Bibliography 251 Index 261

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