Mathematical modelling Books

Book SynopsisNew advanced modeling methods for simulating the electromagnetic properties of complex three-dimensional electronic systems Based on the author''s extensive research, this book sets forth tested and proven electromagnetic modeling and simulation methods for analyzing signal and power integrity as well as electromagnetic interference in large complex electronic interconnects, multilayered package structures, integrated circuits, and printed circuit boards. Readers will discover the state of the technology in electronic package integration and printed circuit board simulation and modeling. In addition to popular full-wave electromagnetic computational methods, the book presents new, more sophisticated modeling methods, offering readers the most advanced tools for analyzing and designing large complex electronic structures. Electrical Modeling and Design for 3D System Integration begins with a comprehensive review of current modeling and simulation methods fTable of ContentsForeword xi Preface xiii 1. Introduction 1 1.1 Introduction of Electronic Package Integration 1 1.2 Review of Modeling Technologies 6 1.3 Organization of the Book 10 References 11 2. Macromodeling of Complex Interconnects in 3D Integration 16 2.1 Introduction 16 2.1.1 Scope of macromodeling 18 2.1.2 Macromodeling in the picture of electrical modeling of interconnects 19 2.2 Network Parameters: Impedance Admittance and Scattering Matrices 19 2.2.1 Impedance matrix 21 2.2.2 Admittance matrix 22 2.2.3 Scattering matrix 23 2.2.4 Conversion between Z Y and S matrices 24 2.3 Rational Function Approximation with Partial Fractions 25 2.3.1 Introduction 25 2.3.2 Iterative weighted linear least-squares estimator 27 2.4 Vector Fitting (VF) Method 29 2.4.1 Two steps in vector fitting method 29 2.4.2 Fitting vectors with common poles 35 2.4.3 Selection of initial poles 37 2.4.4 Enhancement to the original vector fitting method 38 2.5 Macromodel Synthesis 41 2.5.1 Jordan canonical method for macromodel synthesis 42 2.5.2 Equivalent circuits 46 2.6 Stability Causality and Passivity of Macromodel 48 2.6.1 Stability 48 2.6.2 Causality 50 2.6.3 Passivity assessment 54 2.6.4 Passivity enforcement 58 2.6.5 Other issues 78 2.7 Macromodeling Applied to High-Speed Interconnects and Circuits 79 2.7.1 A lumped circuit with nonlinear components 79 2.7.2 Vertically natural capacitors (VNCAPs) 83 2.7.3 Stripline-to-microstrip line transition with vias 87 2.8 Conclusion 91 References 92 3. 2.5D Simulation Method for 3D Integrated Systems 97 3.1 Introduction 97 3.2 Multiple Scattering Method for Electronic Package Modeling with Open Boundary Problems 98 3.2.1 Modal expansion of fields in a parallel-plate waveguide (PPWG) 98 3.2.2 Multiple scattering coefficients among cylindrical PEC and perfect magnetic conductor (PMC) vias 101 3.2.3 Excitation source and network parameter extraction 109 3.2.4 Implementation of effective matrix-vector multiplication (MVM) in linear equations 117 3.2.5 Numerical examples for single-layer power-ground planes 121 3.3 Novel Boundary Modeling Method for Simulation of Finite-Domain Power-Ground Planes 127 3.3.1 Perfect magnetic conductor (PMC) boundary 128 3.3.2 Frequency-dependent cylinder layer (FDCL) 128 3.3.3 Validations of FDCL 131 3.4 Numerical Simulations for Finite Structures 133 3.4.1 Extended scattering matrix method (SMM) algorithm for finite structure simulation 133 3.4.2 Modeling of arbitrarily shaped boundary structures 139 Contents vii 3.5 Modeling of 3D Electronic Package Structure 142 3.5.1 Modal expansions and boundary conditions 143 3.5.2 Mode matching in PPWGs 150 3.5.3 Generalized T-matrix for two-layer problem 158 3.5.4 Formulae summary for two-layer problem 164 3.5.5 Formulae summary for 3D structure problem 169 3.5.6 Numerical simulations for multilayered power-ground planes with multiple vias 176 3.6 Conclusion 182 References 183 4. Hybrid Integral Equation Modeling Methods for 3D Integration 185 4.1 Introduction 185 4.2 2D Integral Equation Equivalent Circuit (IEEC) Method 186 4.2.1 Overview of the algorithm 186 4.2.2 Modal decoupling inside the power distribution network (PDN) 187 4.2.3 2D integral equation solution of parallel plate mode in power-ground planes (PGPs) 189 4.2.4 Combinations of transmission and parallel plate modes 194 4.2.5 Cascade connections of equivalent networks 205 4.2.6 Simulation results 214 4.3 3D Hybrid Integral Equation Method 220 4.3.1 Overview of the algorithm 220 4.3.2 Equivalent electromagnetic currents and dyadic green’s functions 224 4.3.3 Simulation results 231 4.4 Conclusion 238 References 238 5. Systematic Microwave Network Analysis for 3D Integrated Systems 241 5.1 Intrinsic Via Circuit Model for Multiple Vias in an Irregular Plate Pair 242 5.1.1 Introduction 242 5.1.2 Segmentation of vias and a plate pair 245 5.1.3 An intrinsic 3-port via circuit model 248 5.1.4 Determination of the virtual via boundary 263 5.1.5 Complete model for multiple vias in an irregular plate pair 267 5.1.6 Validation and measurements 269 5.1.7 Conclusion 280 5.2 Parallel Plane Pair Model 281 5.2.1 Introduction 281 5.2.2 Overview of two conventional Z pp definitions 283 5.2.3 New Z pp definition using the zero-order parallel plate waves 285 5.2.4 Analytical formula for radial scattering matrix S pp in a circular plate pair 290 5.2.5 BIE method to evaluate S R pp for an irregular plate pair 292 5.2.6 Numerical examples and measurements 296 5.2.7 Conclusion 303 5.3 Cascaded Multiport Network Analysis of Multilayer Structure with Multiple Vias 305 5.3.1 Introduction 305 5.3.2 Multilayer PCB with vias and decoupling capacitors 307 5.3.3 Systematic microwave network method 308 5.3.4 Validations and discussion 316 5.3.5 Conclusion 324 Appendix: Properties of the Auxiliary Function W mn (x y) 326 References 327 6. Modeling of Through-Silicon Vias (TSV) in 3D Integration 331 6.1 Introduction 331 6.1.1 Overview of process and fabrication of TSV 332 6.1.2 Modeling of TSV 335 6.2 Equivalent Circuit Model for TSV 336 6.2.1 Overview 337 6.2.2 Problem statement: Two-TSV configuration 338 6.2.3 Wideband Pi-type equivalent-circuit model 339 6.2.4 Rigorous closed-form formulae for resistance and inductance 341 6.2.5 Scattering parameters of two-TSV system 345 6.2.6 Results and discussion 346 6.3 MOS Capacitance Effect of TSV 351 6.3.1 MOS capacitance effect 351 6.3.2 Bias voltage-dependent MOS capacitance of TSVs 351 6.3.3 Results and analysis 355 6.4 Conclusion 356 References 358 Index 361

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Book SynopsisThe decision to implement environmental protection options is a political one. These, and other political and social decisions affect the balance of the ecosystem and how the point of equilibrium desired is to be reached. This book develops a stochastic, temporal model of how political processes influence and are influenced by ecosystem processes and looks at how to find the most politically feasible plan for managing an at-risk ecosystem. Finding such a plan is accomplished by first fitting a mechanistic political and ecological model to a data set composed of observations on both political actions that impact an ecosystem and variables that describe the ecosystem. The parameters of this fitted model are perturbed just enough to cause human behaviour to change so that desired ecosystem states occur. This perturbed model gives the ecosystem management plan needed to reach desired ecosystem states. To construct such a set of interacting models, topics from political science, ecology, prTrade Review"This said, I acknowledge that the goal that stands behind this book was very challenging and that the EMT model can represent a good starting point." (Journal of Artificial Societies and Social Simulation, 2011) Table of ContentsPreface. List of Figures. List of Tables. Nomenclature. Part I Managing a Political-Ecological System. 1 Introduction. 1.1 The Problem to be Addressed. 1.2 The Book's Running Example: East African Cheetah. 1.3 The EMT's Simulator. 1.4 How to Use the EMT to Manage an Ecosystem. 1.5 Chapter Topics and Order. 1.6 The Book's Accompanying Web Resources. 2 Simulator Architecture, Operation, and Example Output. 2.1 Introduction. 2.2 Theory for Agent-Based Simulation. 2.3 Action Messages and IntIDs Model Operation. 2.4 A Plot for Displaying an Actions History. 2.5 Conclusions. 2.6 Exercises. 3 Blue Whale Population Management. 3.1 Introduction. 3.2 Current Status of Blue Whales. 3.3 Groups that Affect Blue Whale Populations. 3.4 Blue Whale Ecosystem ID. 3.5 Interactions Between IDs. 3.6 Data Sets for the Blue Whale EMT. 3.7 Main Points of this Chapter's Example. 3.8 Exercises. 4 Finding the Most Practical Ecosystem Management Plan. 4.1 Introduction. 4.2 Some Methods for Developing Ecosystem Management Plans. 4.3 Consistency Analysis Parameter Estimator Overview. 4.4 The MPEMP: Definition and Construction. 4.5 The MPEMP for East African Cheetah. 4.6 Conclusions. 4.7 Exercises. 5 An Open, Web-Based Ecosystem Management Tool. 5.1 Introduction. 5.2 Components of a Politically Realistic EMT. 5.3 Id Language and Software System. 5.4 How the EMT Website Would be Used. Part II Model Formulation, Estimation, and Reliability. 6 Influence Diagrams of Political Decision Making. 6.1 Introduction. 6.2 Theories of Political Decision Making. 6.3 Architecture of a Group Decision Making ID. 6.4 Related Modeling Efforts. 6.5 Conclusions. 6.6 Exercises. 7 Group IDs for the East African Cheetah EMT. 7.1 Introduction. 7.2 Country Backgrounds. 7.3 Selection of Groups to Model. 7.4 President IDs. 7.5 EPA IDs. 7.6 Rural Residents IDs. 7.7 Pastoralists IDs. 7.8 Conservation NGOs ID. 7.9 Conclusions. 7.10 Exercises. 8 Modeling Wildlife Population Dynamics with an Influence Diagram. 8.1 Introduction. 8.2 Model of Cheetah and Prey Population Dynamics. 8.3 Solving SDEs within an ID. 8.4 Example of Ecosystem ID Output. 8.5 Conclusions. 8.6 Exercises. 9 Political Action Taxonomies, Collection Protocols, and an Actions History Example. 9.1 Introduction. 9.2 Political Action Taxonomies. 9.3 Adapting the BCOW Taxonomy to Ecosystem Management Actions. 9.4 EMAT Coding Protocol. 9.5 Actions History Data for the East African Cheetah EMT. 9.6 Conclusions. 10 Ecosystem Data. 10.1 Introduction. 10.2 Wildlife Monitoring. 10.3 Wildlife Abundance Estimation Methods. 10.4 East African Cheetah Prey Abundance Data. 10.5 Data on Cheetah Habitat Suitability Nodes. 10.6 Conclusions. 10.7 Exercises. 11 Statistical Fitting of the Political-Ecological System Simulator. 11.1 Introduction. 11.2 Consistency Analysis Applied to an Actions History. 11.3 Consistency Analysis of the East African Cheetah EMT Simulator. 11.4 Conclusions and Another Collection Initialization Algorithm. 11.5 Exercises. 12 Assessing the Simulator's Reliability and Improving Its Construct Validity. 12.1 Introduction. 12.2 Steps for Assessing Simulator Reliability. 12.3 Sensitivity Analysis. 12.4 One-Step-Ahead Prediction Error Rates. 12.5 MC Hypothesis Tests. 12.6 Sensitivity to Hidden Bias Analysis. 12.7 Conclusions. 12.8 Exercises. Part III Assessment. 13 Current Capabilities and Limitations of the Politically Realistic EMT. 13.1 Introduction. 13.2 Current Capabilities of the EMT. 13.3 Current Limitations of the EMT. 13.4 Supporting the EMT in the Real World. 13.5 Consequences of Using a Politically Realistic EMT. Appendices. Appendix A Heuristics Used to Assign Hypothesis Values to Parameters. Appendix B Cluster Computing Version of Hooke and Jeeves Search. References. Index.

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Book Synopsis- It reveals the interrelationships between multiple variables and features of the underlying conditional independence. - It covers conditional independence, several types of independence graphs, Gaussian models, issues in model selection, regression and decomposition. - Many numerical examples and exercises with solutions are included.Table of ContentsIndependence and Interaction. Independence Graphs. Information Divergence. The Inverse Variance. Graphical Gaussian Models. Graphical Log-Linear Models. Model Selection. Methods for Sparse Tables. Regression and Graphical Chain Models. Models for Mixed Variables. Decompositions and Decomposability. Appendices. References. Author Index. Subject Index.

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Book SynopsisDetailing the link between computational models and physical models, Modeling and Simulation in the Medical and Health Sciences encourages a more uniform discussion of simulation within both the engineering and medical domains.Table of ContentsContributors. Foreword. Preface. Part One Fundamentals of Medical and Health Sciences Modeling and Simulation. 1 Introduction to Modeling and Simulation in the Medical and Health Sciences (Catherine M. Banks). 2 The Practice of Modeling and Simulation: Tools of the Trade (John A. Sokolowski). Part Two. Modeling for the Medical and Health Sciences. 3 Mathematical Models of Tumor Growth and Wound Healing (John A. Adam). 4 Physical Modeling (Stacie I. Ringleb). Part Three. Modeling and Simulation Applications. 5 Humans as Models (C. Donald Combs). 6 Modeling the Human System (Mohammed Ferdjallah and Gyu Tae Kim). 7 Robotics (Richard Lee). 8 Training (Paul E. Phrampus). 9 Patient Care (Eugene Santos Jr, Joseph Rosen, Keum Joo Kim, Fei Yu, Dequing Li, Elizabeth Jacob, Lindsay Katona). 10 Future of Modeling and Simulation in the Medical and Health Sciences (Richard M. Satava). Appendix. Index.

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Book SynopsisGroundwater is a vital source of water throughout the world. As the number of groundwater investigations increase, it is important to understand how to develop comprehensive quantified conceptual models and appreciate the basis of analytical solutions or numerical methods of modelling groundwater flow. Groundwater Hydrology: Conceptual and Computational Models describes advances in both conceptual and numerical modelling. It gives insights into the interpretation of field information, the development of conceptual models, the use of computational models based on analytical and numerical techniques, the assessment of the adequacy of models, and the use of computational models for predictive purposes. It focuses on the study of groundwater flow problems and a thorough analysis of real practical field case studies. It is divided into three parts: * Part I deals with the basic principles, including a summary of mathematical descriptions of groundwater flow, recharge estimTrade Review"...well written and structured...a comprehensive and thorough reference source...highly recommended for anyone in the business..." (Circulation - N'ltr of British Hydrological Soc, Feb 2004) "...delighted to have this book on my shelf and it is already becoming well thumbed...no hesitation in recommending it..." (Geoscientist, May 2004) "The information and techniques presented in this book provide illuminating guidelines and application directions for practicing hydrogeologists, geohydrologists and water resource engineers." (Hydrological Sciences Journal, Feb 2005, Vol 50 (1))Table of ContentsPreface. 1. Introduction. PART I: BASIC PRINCIPLES. 2. Background to Groundwater Flow. 3. Recharge due to Precipitation or Irrigation. 4. Interaction between Surface Water and Groundwater. PART II: RADIAL FLOW. 5. Radial Flow to Pumped Boreholes – Fundamental Issues. 6. Large Diameter Wells. 7. Radial Flow where Vertical Components of Flow are Significant. 8. Practical Issues of Interpretation and Assessing Resources. PART III: REGIONAL GROUNDWATER FLOW. 9. Regional Groundwater Studies in which Transmissivity is Effectively Constant. 10. Regional Groundwater Flow in Multi-Aquifer Systems. 11. Regional Groundwater Flow with Hydraulic Conductivity Varying with Saturated Thickness. 12. Numerical Modelling Insights. Appendix: Computer Program for Two-zone Model. List of Symbols. References. Index.

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Book SynopsisThis book covers engineering principles and state-of-the-art methods involved in the many facets of combat modeling and distributed simulation.Trade Review“Tolk and his coauthors have extensive experience in this area, making this volume a standard reference for researchers engaged in combat modeling. The complexity of the domain, the consequences of error, and the prohibitive cost of direct experimentation are as great in combat modeling as in any other problem area, making this volume a valuable source of examples and techniques for modelers in other areas that are highly complex, consequential, and inaccessible by direct experiment." (Computing Reviews, 1 October 2012) Table of ContentsPreface xi Contributors xiii Biographies xvii Acknowledgments xxvii Abbreviations xxix 1. Challenges of Combat Modeling and Distributed Simulation 1 Andreas Tolk Part I Foundations 2. Applicable Codes of Ethics 25 Andreas Tolk 3. The NATO Code of Best Practice for Command and Control Assessment 33 Andreas Tolk 4. Terms and Application Domains 55 Andreas Tolk 5. Scenario Elements 79 Andreas Tolk Part II Combat Modeling 6. Modeling the Environment 95 Andreas Tolk 7. Modeling Movement 113 Andreas Tolk 8. Modeling Sensing 127 Andreas Tolk 9. Modeling Effects 145 Andreas Tolk 10. Modeling Communications, Command, and Control 171 Andreas Tolk Part III Distributed Simulation 11. Challenges of Distributed Simulation 187 Andreas Tolk 12. Standards for Distributed Simulation 209 Andreas Tolk 13. Modeling and Simulation Development and Preparation Processes 243 Andreas Tolk 14. Verification and Validation 263 Andreas Tolk 15. Integration of M&S Solutions into the Operational Environment 295 Andreas Tolk Part IV Advanced Topics 16. History of Combat Modeling and Distributed Simulation 331 Margaret L. Loper and Charles Turnitsa 17. Serious Games, Virtual Worlds, and Interactive Digital Worlds 357 Roger D. Smith 18. Mathematical Applications for Combat Modeling 385 Patrick T. Hester and Andrew Collins 19. Combat Modeling with the High Level Architecture and Base Object Models 413 Mikel D. Petty and Paul Gustavson 20. The Test and Training Enabling Architecture (TENA) 449 Edward T. Powell and J. Russell Noseworthy 21. Combat Modeling using the DEVS Formalism 479 Tag Gon Kim and Il-Chul Moon 22. GIS Data for Combat Modeling 511 David Lashlee, Joe Bricio, Robert Holcomb, and William T. Richards 23. Modeling Tactical Data Links 537 Joe Sorroche 24. Standards-Based Combat Simulation Initialization using the Military Scenario Definition Language (MSDL) 579 Robert L. Wittman Jr 25. Multi-Resolution Combat Modeling 607 Mikel D. Petty, Robert W. Franceschini, and James Panagos 26. New Challenges: Human, Social, Cultural, and Behavioral Modeling 641 S. K. Numrich and P. M. Picucci 27. Agent Directed Simulation for Combat Modeling and Distributed Simulation 669 Gnana K. Bharathy, Levent Yilmaz, and Andreas Tolk 28. Uncertainty Representation and Reasoning for Combat Models 715 Paulo C. G. Costa, Heber Herencia-Zapana, and Kathryn Laskey 29. Model-Based Data Engineering for Distributed Simulations 747 Saikou Y. Diallo 30. Federated Simulation for System of Systems Engineering 765 Robert H. Kewley and Marc Wood 31. The Role of Architecture Frameworks in Simulation Models: The Human View Approach 811 Holly A. H. Handley 32. Multinational Computer Assisted Exercises 825 Erdal Cayirci Annex 1: M&S Organizations/Associations 841 Salim Chemlal and Tuncer Ören Annex 2: Military Simulation Systems 851 José J. Padilla Index 869

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Book SynopsisA guide to the validation and risk management of quantitative models used for pricing and hedging Whereas the majority of quantitative finance books focus on mathematics and risk management books focus on regulatory aspects, this book addresses the elements missed by this literature--the risks of the models themselves. This book starts from regulatory issues, but translates them into practical suggestions to reduce the likelihood of model losses, basing model risk and validation on market experience and on a wide range of real-world examples, with a high level of detail and precise operative indications.Table of ContentsPreface xi Acknowledgements xix Part I Theory and Practice of Model Risk Management 1 Understanding Model Risk 3 1.1 What Is Model Risk? 3 1.1.1 The Value Approach 4 1.1.2 The Price Approach 6 1.1.3 A Quant Story of the Crisis 9 1.1.4 A Synthetic View on Model Risk 17 1.2 Foundations of Modelling and the Reality of Markets 22 1.2.1 The Classic Framework 22 1.2.2 Uncertainty and Illiquidity 30 1.3 Accounting for Modellers 38 1.3.1 Fair Value 38 1.3.2 The Liquidity Bubble and the Accountancy Boards 40 1.3.3 Level 1, 2, 3 .go? 41 1.3.4 The Hidden Model Assumptions in ‘vanilla’ Derivatives 42 1.4 What Regulators Said After the Crisis 48 1.4.1 Basel New Principles: The Management Process 49 1.4.2 Basel New Principles: The Model, The Market and The Product 51 1.4.3 Basel New Principles: Operative Recommendations 52 1.5 Model Validation and Risk Management: Practical Steps 53 1.5.1 A Scheme for Model Validation 54 1.5.2 Special Points in Model Risk Management 59 1.5.3 The Importance of Understanding Models 60 2 Model Validation and Model Comparison: Case Studies 63 2.1 The Practical Steps of Model Comparison 63 2.2 First Example: The Models 65 2.2.1 The Credit Default Swap 66 2.2.2 Structural First-Passage Models 67 2.2.3 Reduced-Form Intensity Models 69 2.2.4 Structural vs Intensity: Information 72 2.3 First Example: The Payoff. Gap Risk in a Leveraged Note 74 2.4 The Initial Assessment 77 2.4.1 First Test: Calibration to Liquid Relevant Products 77 2.4.2 Second Test: a Minimum Level of Realism 78 2.5 The Core Risk in the Product 81 2.5.1 Structural Models: Negligible Gap Risk 82 2.5.2 Reduced-Form Models: Maximum Gap Risk 82 2.6 A Deeper Analysis: Market Consensus and Historical Evidence 85 2.6.1 What to Add to the Calibration Set 85 2.6.2 Performing Market Intelligence 86 2.6.3 The Lion and the Turtle. Incompleteness in Practice 86 2.6.4 Reality Check: Historical Evidence and Lack of it 87 2.7 Building a Parametric Family of Models 88 2.7.1 Understanding Model Implications 93 2.8 Managing Model Uncertainty: Reserves, Limits, Revisions 95 2.9 Model Comparison: Examples from Equity and Rates 99 2.9.1 Comparing Local and Stochastic Volatility Models in Pricing Equity Compound and Barrier Options 99 2.9.2 Comparing Short Rate and Market Models in Pricing Interest Rate Bermudan Options 105 3 Stress Testing and the Mistakes of the Crisis 111 3.1 Learning Stress Test from the Crisis 111 3.1.1 The Meaning of Stress Testing 112 3.1.2 Portfolio Stress Testing 113 3.1.3 Model Stress Testing 116 3.2 The Credit Market and the ‘Formula that Killed Wall Street’ 118 3.2.1 The CDO Payoff 118 3.2.2 The Copula 119 3.2.3 Applying the Copula to CDOs 122 3.2.4 The Market Quotation Standard 124 3.3 Portfolio Stress Testing and the Correlation Mistake 125 3.3.1 From Flat Correlation Towards a Realistic Approach 126 3.3.2 A Correlation Parameterization to Stress the Market Skew 131 3.4 Payoff Stress and the Liquidity Mistake 136 3.4.1 Detecting the Problem: Losses Concentrated in Time 137 3.4.2 The Problem in Practice 139 3.4.3 A Solution. From Copulas to Real Models 145 3.4.4 Conclusions 150 3.5 Testing with Historical Scenarios and the Concentration Mistake 151 3.5.1 The Mapping Methods for Bespoke Portfolios 152 3.5.2 The Lehman Test 156 3.5.3 Historical Scenarios to Test Mapping Methods 157 3.5.4 The Limits of Mapping and the Management of Model Risk 164 3.5.5 Conclusions 168 4 Preparing for Model Change. Rates and Funding in the New Era 171 4.1 Explaining the Puzzle in the Interest Rates Market and Models 171 4.1.1 The Death of a Market Model: 9 August 2007 173 4.1.2 Finding the New Market Model 174 4.1.3 The Classic Risk-free Market Model 178 4.1.4 A Market Model with Stable Default Risk 182 4.1.5 A Market with Volatile Credit Risk 192 4.1.6 Conclusions 200 4.2 Rethinking the Value of Money: The Effect of Liquidity in Pricing 201 4.2.1 The Setting 204 4.2.2 Standard DVA: Is Something Missing? 206 4.2.3 Standard DVA plus Liquidity: Is Something Duplicated? 207 4.2.4 Solving the Puzzle 207 4.2.5 Risky Funding for the Borrower 208 4.2.6 Risky Funding for the Lender and the Conditions for Market Agreement 209 4.2.7 Positive Recovery Extension 210 4.2.8 Two Ways of Looking at the Problem: Default Risk or Funding Benefit? The Accountant vs the Salesman 211 4.2.9 Which Direction for Future Pricing? 214 Part II Snakes in the Grass: Where Model Risk Hides 5 Hedging 219 5.1 Model Risk and Hedging 219 5.2 Hedging and Model Validation: What is Explained by P&L Explain? 221 5.2.1 The Sceptical View 222 5.2.2 The Fundamentalist View and Black and Scholes 222 5.2.3 Back to Reality 224 5.2.4 Remarks: Recalibration, Hedges and Model Instability 226 5.2.5 Conclusions: from Black and Scholes to Real Hedging 228 5.3 From Theory to Practice: Real Hedging 229 5.3.1 Stochastic Volatility Models: SABR 231 5.3.2 Test Hedging Behaviour Leaving Nothing Out 232 5.3.3 Real Hedging for Local Volatility Models 238 5.3.4 Conclusions: the Reality of Hedging Strategies 241 6 Approximations 243 6.1 Validate and Monitor the Risk of Approximations 243 6.2 The Swaption Approximation in the Libor Market Model 245 6.2.1 The Three Technical Problems in Interest Rate Modelling 245 6.2.2 The Libor Market Model and the Swaption Market 247 6.2.3 Pricing Swaptions 250 6.2.4 Understanding and Deriving the Approximation 253 6.2.5 Testing the Approximation 257 6.3 Approximations for CMS and the Shape of the Term Structure 264 6.3.1 The CMS Payoff 265 6.3.2 Understanding Convexity Adjustments 266 6.3.3 The Market Approximation for Convexity Adjustments 267 6.3.4 A General LMM Approximation 269 6.3.5 Comparing and Testing the Approximations 271 6.4 Testing Approximations Against Exact. Dupire’s Idea 276 6.4.1 Perfect Positive Correlation 278 6.4.2 Perfect Negative Correlation 280 6.5 Exercises on Risk in Computational Methods 283 6.5.1 Approximation 283 6.5.2 Integration 285 6.5.3 Monte Carlo 285 7 Extrapolations 287 7.1 Using the Market to Complete Information: Asymptotic Smile 288 7.1.1 The Indetermination in the Asymptotic Smile 288 7.1.2 Pricing CMS with a Smile: Extrapolating to Infinity 292 7.1.3 Using CMS Information to Transform Extrapolation into Interpolation and Fix the Indetermination 293 7.2 Using Mathematics to Complete Information: Correlation Skew 295 7.2.1 The Expected Tranched Loss 295 7.2.2 Properties for Interpolation 298 7.2.3 Properties for Turning Extrapolation into Interpolation 298 8 Correlations 303 8.1 The Technical Difficulties in Computing Correlations 303 8.1.1 Correlations in Interest Rate Modelling 305 8.1.2 Cross-currency Correlations 307 8.1.3 Stochastic Volatility Correlations 312 8.2 Fundamental Errors in Modelling Correlations 315 8.2.1 The Zero-correlation Error 316 8.2.2 The 1-Correlation Error 319 9 Calibration 323 9.1 Calibrating to Caps/Swaptions and Pricing Bermudans 324 9.1.1 Calibrating Caplets 325 9.1.2 Understanding the Term Structure of Volatility 326 9.1.3 Different Parameterizations 329 9.1.4 The Evolution of the Term Structure of Volatility 332 9.1.5 The Effect on Early-Exercise Derivatives 334 9.1.6 Reducing Our Indetermination in Pricing Bermudans: Liquid European Swaptions 335 9.2 The Evolution of the Forward Smiles 340 10 When the Payoff is Wrong 347 10.1 The Link Between Model Errors and Payoff Errors 347 10.2 The Right Payoff at Default: The Impact of the Closeout Convention 348 10.2.1 How Much Will be Paid at Closeout, Really? 350 10.2.2 What the Market Says and What the ISDA Says 352 10.2.3 A Quantitative Analysis of the Closeout 353 10.2.4 A Summary of the Findings and Some Conclusions on Payoff Uncertainty 360 10.3 Mathematical Errors in the Payoff of Index Options 362 10.3.1 Too Much Left Out 364 10.3.2 Too Much Left In 365 10.3.3 Empirical Results with the Armageddon Formula 365 10.3.4 Payoff Errors and Armageddon Probability 367 11 Model Arbitrage 371 11.1 Introduction 371 11.2 Capital Structure Arbitrage 373 11.2.1 The Credit Model 373 11.2.2 The Equity Model 375 11.2.3 From Barrier Options to Equity Pricing 377 11.2.4 Capital-structure Arbitrage and Uncertainty 381 11.3 The Cap-Swaption Arbitrage 391 11.4 Conclusion: Can We Use No-Arbitrage Models to Make Arbitrage? 394 12 Appendix 397 12.1 Random Variables 397 12.1.1 Generating Variables from Uniform Draws 397 12.1.2 Copulas 397 12.1.3 Normal and Lognormal 398 12.2 Stochastic Processes 399 12.2.1 The Law of Iterated Expectation 399 12.2.2 Diffusions, Brownian Motions and Martingales 400 12.2.3 Poisson Process 403 12.2.4 Time-dependent Intensity 404 12.3 Useful Results from Quantitative Finance 405 12.3.1 Black and Scholes (1973) and Black (1976) 405 12.3.2 Change of Numeraire 407 Bibliography 409 Index 417

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Book SynopsisA comprehensive, thoroughly modern approach to environmental quality assessment The only textbook to combine engineering transport fundamentals and equilibrium aquatic chemistry, Environmental Modeling brings a uniquely contemporary perspective to the assessment of environmental quality. Addressing key questions about fate, transport, and long-term effects of chemical pollutants in the environment, this inherently practical text gives readers the important tools they need to develop and solve their own mathematical models. Contains detailed examples from a wide range of crucial water quality areas-conventional pollutants in rivers, eutrophication of lakes, and toxic organic chemicals and heavy metals in both surface and groundwaters Examines current global issues, including atmospheric deposition, hazardous wastes, soil pollution, global change, and more Features over 200 high-quality illustrations, plus skill-building problems in every chapter <Table of ContentsTransport Phenomena. Chemical Reaction Kinetics. Equilibrium Chemical Modeling. Eutrophication of Lakes. Conventional Pollutants in Rivers. Toxic Organic Chemicals. Modeling Trace Metals. Groundwater Contamination. Atmospheric Deposition and Biogeochemistry. Global Change and Global Cycles. Appendices. Index.

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Book SynopsisUnderstanding how to properly manage urban stormwater is a critical concern to civil and environmental engineers the world over. Mismanagement of stormwater and urban runoff results in flooding, erosion, and water quality problems.Table of ContentsURBAN STORMWATER MANAGEMENT. Urban Drainage Systems: Evolution of Problems. Urban Runoff Quantity and Quality Control Strategies. Urban Stormwater Management Modeling. DATA ANALYSIS. Meteorological Data Analysis. Runoff Quality Data Analysis. DRAINAGE SYSTEM PERFORMANCE ANALYSIS. Elements of Derived Probability Distribution Theory. Model of Urban Drainage System. Quantity Control Analysis of Urban Drainage Systems. Advanced Quantity Control Analysis. Multiple Reservoir Systems. Quality Control Analysis of Urban Drainage Systems. Urban Drainage Systems Analysis: Optimization and SensitivityAnalysis. Appendices. Glossary. Notation. Index.

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Book SynopsisBased around a conference on financial modeling held in Milan in December 1999, this book brings together the leading names in quantitative finance to discuss the modeling techniques in a variety of areas of financial engineering.Table of ContentsPreface The Quantitative Finance Timeline (Paul Wilmott) Part I. New Directions in Equity Modelling Introduction Asymptotic analysis of stochastic volatility models (Henrik Rasmussen and Paul Wilmott) Passport options, a review (Antony Penaud) Equity Dividend Models (David Bakstein and Paul Wilmott) Isoperimetry, log-concavity and elasticity of option prices (Christer Borell) Part II. New Directions in Interest Rate Modelling Introduction Dynamic, deterministic and static optimal portfolio strategies in a mean-variance framework under stochastic interest rates (Isabelle Bajeux-Besnainou and Roland Portrait) Pricing bond options in a worst-case scenario (David Epstein and Paul Wilmott) Part III. New Directions in Risk Management Introduction Implementing VaR by Historical Simulation (Aldo Nassigh, Andrea Piazzetta and Ferdinando Samaria) CrashMetrics (Philip Hua and Paul Wilmott) Herding in financial markets: a role for psychology in explaining investor behaviour? (Henriëtte Prast) Further Reading Author Biographies Index

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Book SynopsisA state-of-the-art approach to urban travel demand modeling Currently used travel forecasting methodology was developed almostthree decades ago, primarily to assess the impacts of large-scalecapital improvement projects, and was not designed to deal withcontemporary urban transportation problems. To be effective today,travel demand models must explicitly represent traveler behavior,must be policy-sensitive, and must be operationally reliable. Urban Travel Demand Modeling: From Individual Choices to GeneralEquilibrium presents an integrated system of models which overhaulthe four traditional phases of travel generation, modal split, tripdistribution, and network assignment. This book shows, for thefirst time, how generalized network equilibrium may be rigorouslyforecast from the optimal travel choices of trip consumerswithout the need to resort to heuristic procedures such asfeedbacks. In addition, models for optimal transportation supplydecisions are integrated with tTable of ContentsModeling Travelers' Decisions as Discrete Choices. Route Choice on Uncongested Networks. Combined Travel Demand Modeling Under Uncongested Conditions. Route Choice Modeling Under Congested Conditions. Combined Travel Demand Modeling Under Congested Conditions. Model Parameter Estimation. Joint Equilibrium Modeling of Activity and Travel Systems. Optimal Transportation Supply. Appendices. Bibliography. Indexes.

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Book SynopsisBioremediation and Natural Attenuation: Process Fundamentals and Mathematical Models provides, under one cover, the current methodology needed by groundwater scientists and engineers in their efforts to evaluate contamination problems, to estimate risk to human health and ecosystems, and to design and formulate remediation strategies.Trade Review"…does a very good job of bringing together material form disparate sources…readers new to the field will be well served by it." (Ground Water, March-April 2007) "The topic is important; both theory and state-of-the-art are well discussed…this is an excellent book." (Journal of Hazardous Materials, September 1, 2006) “… a reference book for practitioners, regulators, and researchers dealing with contaminant hydrogeology and correction action.” (Environmental Geology, December 2006)Table of ContentsPreface. 1. Introduction to Bioremediation. 2. Geochemical Attenuation Mechanisms. 3. Biodegradation Principles. 4. Fundamentals of Ground Water Flow and Contaminant Transport Processes. 5. Fate and Transport Equations and Analytical Models for Natural Attenuation. 6. Numerical Modeling of Contaminant Transport, Transformation, and Degradation Processes. 7. Field and Laboratory Techniques to Determine Site-Specific Parameters for Modeling the Fate and Transport of Groundwater Pollutants. 8. Bioremediation Technologies. 9. Performance Assessment and Demonstration of Bioremediation and Natural Attenuation. Appendix A: Chemical Properties of Various Compounds. Appendix B: Free Energy and Thermodynamic Feasibility of Chemical and Biochemical Reactions. Appendix C: Commonly Used Numerical Groundwater Flow and Solute Transport Codes (Modified after Wiedemeier et al., 1999). Appendix D: Nonparametric Statistical Tests for Determining the Effectiveness of Natural Attenuation (after Wisconsin Department of Natural Resources). Appendix E: Critical Values of the Student t-Distribution. Glossary. Index.

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Book SynopsisGraphical models----a subset of log--linear models----reveal the interrelationships between multiple variables and features of the underlying conditional independence.Table of ContentsIndependence and Interaction. Independence Graphs. Information Divergence. The Inverse Variance. Graphical Gaussian Models. Graphical Log-Linear Models. Model Selection. Methods for Sparse Tables. Regression and Graphical Chain Models. Models for Mixed Variables. Decompositions and Decomposability. Appendices. References. Author Index. Subject Index.

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Book SynopsisThe first book to provide a comprehensive treatment integrating finite-time thermodynamics and optimal control, giving an overview of important breakthroughs in the last 20 years. It presents a survey of the optimization technique, including the basics of optimal control theory, and the principal thermodynamic concepts and equations.Table of ContentsMathematical Modeling of Thermodynamic Systems. Optimization Methods. Optimal Control Methods. Limiting Possibilities of Heat-Mechanical Systems with One Reservoir. Heat-Exchange Processes with Minimal Dissipation. Optimization and Estimates of the Limiting Possibilities of Heat-Mechanical Systems with a Number of Reservoirs. Limiting Possibilities of Complex Systems with a Number of Heat-Mechanical Systems. Mass Transfer Processes with Minimal Irreversibility. Thermodynamic Analysis of Separation Processes and Chemical Reactions. Commodity Exchange in Economic Systems. Bibliography. Index.

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Book SynopsisThis text focuses on the issue of non-linear modelling of high frequency financial data. Non-linearity refers to situations in which there is a high degree of apparent randomness to the way in which a particular financial measure, price, interest rate, or exchange rate moves with time.Table of ContentsHIGH FREQUENCY MODELS IN FINANCE: MOTIVATIONS AND THEORETICAL ISSUES. Modelling with High Frequency Data: A Growing Interest for Financial Economists and Fund Managers (M. Gavridis). High Frequency Foreign Exchange Rates: Price Behavior Analysis and 'True Price' Models (J. Moody & L. Wu). DETECTING NONLINEARITIES IN HIGH FREQUENCY DATA: EMPIRICAL TESTS AND MODELLING IMPLICATIONS. Testing Linearity with Information-Theoretic Statistics and the Bootstrap (F. Acosta). Testing for Linearity: A Frequency Domain Approach (J. Drunat, et al.). Stochastic or Chaotic Dynamics in High Frequency Financial Data (D. Guégan & L. Mercier). F-consistency, De-volatization and Normalization of High Frequency Financial Data (B. Zhou). PARAMETRIC MODELS FOR NONLINEAR FINANCIAL TIME SERIES. High Frequency Financial Time Series Data: Some Stylized Facts and Models of Stochastic Volatility (E. Ghysels, et al.). Modelling Short-term Volatility with GARCH and HARCH Models (M. Dacorogna, et al.). High Frequency Switching Regimes: A Continuous-time Threshold Process (R. Dacco' & S. Satchell). Modelling Burst Phenomena: Bilinear and Autoregressive Exponential Models (J. Drunat, et al.). NON-PARAMETRIC MODELS FOR NONLINEAR FINANCIAL TIME SERIES. Application of Neural Networks to Forecast High Frequency Data: Foreign Exchange (P. Bolland, et al.). An Application of Genetic Algorithms to High Frequency Trading Models: A Case Study (C. Dunis, et al.). High Frequency Exchange Rate Forecasting by the Nearest Neighbours Method (H. Alexandre, et al.). Index.

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Book SynopsisThis general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics.Trade Review'… It gives an excellent general introduction to epidemic modelling, starting with an interesting historical account and then describing the most important and useful models which can be used.' Robert MacMillan, Mathematical Gazette'The book will be accessible … and its study highly rewarding, to anyone with an interest in epidemic models…' V. S. Isham, Short Book Reviews'Daley and Gani's monograph is a concise and useful presentation of a variety of epidemiological models.' Daniel Haydon, Trends in Ecology and Evolution'… gives an excellent general introduction to epidemic modelling … should certainly be available to undergraduates.' Robert MacMillan, The Mathematical Gazette'This book had us hooked … [it] remains an important reference in our library and is frequently consulted for advice on how to think about modelling in related contexts.' Darfiana Nur and Kerrie L. Mengersen, The Australian and New Zealand Journal of Statistics'… the book is clear and well written … could serve as course literature for graduate, or possibly last year undergraduate, course in epidemic modelling.' Statistics in Medicine'I found the book very clear, concise and useful … I recommend the book very strongly as a teaching tool and as a research tool to academics and scientists who are interested in epidemic modeling. I also strongly recommend the book to applied mathematicians who are intetrested in stochastic models in general.' Mathematics TodayTable of ContentsPreface; 1. Some history; 2. Deterministic models; 3. Stochastic models in continuous time; 4. Stochastic models in discrete time; 5. Rumours: modelling spread and its cessation; 6. Fitting epidemic data; 7. The control of epidemics; References and author index; Subject index.

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Book SynopsisUnderstanding wind stress (drag) over the ocean is central to many facets of air-sea interaction, which in turn is vital for models of weather prediction and climate modelling. Wind Stress over the Ocean, first published in 2001, brings together thirty of the world's leading experts in air-sea interaction, under the auspices of the Scientific Committee on Oceanic Research. Wind Stress over the Ocean provides a thorough re-examination of the physical processes that transfer momentum between the atmosphere and the ocean. As well as describing the established fundamentals, the book also explores active areas of research and controversy. The book will form a comprehensive guide and reference for researchers and graduate students in physical oceanography, meteorology, fluid dynamics and coastal engineering.Trade ReviewReview of the hardback: '… helpful and handy for people who want timely, authoritative information about the different processes that affect the wind stress over the sea.' EOSReview of the hardback: '… a very useful book … It will be much referenced.' Grant Bigg, WeatherReview of the hardback: ' … this publication is an essential reference text owing to the rapidly changing nature of scientific progress. It will be a general guide and reference document for researchers and graduates in physical oceanography, meteorology, fluid dynamics and coastal engineering. Many who read this book will be inspired to carry out research in those areas which still have many specific problems to be solved.' BulletinTable of ContentsPreface; 1. Overview; Part I: 2. Historical drag expression; 3. Atmospheric and oceanic boundary layer physics; 4. Ocean wave spectra and integral properties; 5. Drag generation mechanisms; 6. Coupling mechanisms; 7. The measurement of surface stress; Part II: 8. The influence of swell on the drag; 9. The influence of unsteadiness; 10. The dependence on wave age; 11. The influence on mesoscale atmospheric processes; 12. Wind, stress and wave directions; 13. The influence of surface tension; 14. The influence of spatial inhomogeneity; 15. Basin boundaries; References; Index.

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Book SynopsisThis book is an introduction to the study of mathematical models of electrically active cells, which play an essential role in, for example, nerve conduction and cardiac functions. This is an important and vigorously researched field. In the book, Dr Cronin synthesizes and reviews this material and provides a detailed discussion of the Hodgkin-Huxley model for nerve conduction, which forms the cornerstone of this body of work. Her treatment includes a derivation of the Hodgkin-Huxley model, which is a system of four nonlinear differential equations; a discussion of the validity of this model; and a summary of some of the mathematical analysis carried out on this model. Special emphasis is placed on singular perturbation theory, and arguments, both mathematical and physiological, for using the perturbation viewpoint are presented.Table of Contents1. Introduction; 2. Nerve conduction: the work of Hodgkin and Huxley; 3. Nerve conduction: other mathematical models; 4. Models of other electrically excitable cells; 5. Mathematical theory; 6. Mathematical analysis of physiological models; Appendix; References.

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Book SynopsisThe book gives a comprehensive and lucid account of the science of the atmospheric boundary layer (ABL). There is an emphasis on the application of the ABL to numerical modelling of the climate. The book comprises nine chapters, several appendices (data tables, information sources, physical constants) and an extensive reference list. Chapter 1 serves as an introduction, with chapters 2 and 3 dealing with the development of mean and turbulence equations, and the many scaling laws and theories that are the cornerstone of any serious ABL treatment. Modelling of the ABL is crucially dependent for its realism on the surface boundary conditions, and chapters 4 and 5 deal with aerodynamic and energy considerations, with attention to both dry and wet land surfaces and sea. The structure of the clear-sky, thermally stratified ABL is treated in chapter 6, including the convective and stable cases over homogeneous land, the marine ABL and the internal boundary layer at the coastline. Chapter 7 thTrade Review'An excellent review of the current state of affairs on boundary-layer meteorology research.' Bulletin of the American Meteorological Society.'I find that it compares favourably to good texts that have appeared recently; I strongly recommend it as a synthesis of present thinking on physical processes in the atmospheric boundary layer.' Waves in Random Media.Table of Contents1. The atmospheric boundary layer; 2. Basic equations for mean and fluctuating quantites; 3. Scaling laws for mean and turbulent quantites; 4. Surface roughness and local advection; 5. Energy fluxes at the land surface; 6. The thermally stratified ABL; 7. The cloud topped boundary layer; 8. ABL modelling and parameterisation schemes; 9. The impact of the ABL on climate.

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Book SynopsisFor many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.Trade Review'The techniques described by Rajeev Motwani and Prabhaker Raghavan are wide-ranging and powerful, so this book is an important one. As far as I have been able to find out this is the only book on the entire subject … this excellent volume does us proud!' American Scientist'This book can serve as an excellent basis for a graduate course. It is highly recommended for students and researchers who wish to deepen their knowledge of the subject. Finally, I believe that the book, with its vast coverage, will be an invaluable source for active researchers in the field.' Y. Aumann, Computing ReviewsTable of ContentsPart I. Tools and Techniques: 1. Introduction; 2. Game-theoretic techniques; 3. Moments and deviations; 4. Tail inequalities; 5. The probabilistic method; 6. Markov chains and random walks; 7. Algebraic techniques; Part II. Applications: 8. Data structures; 9. Geometric algorithms and linear programming; 10. Graph algorithms; 11. Approximate counting; 12. Parallel and distributed algorithms; 13. Online algorithms; 14. Number theory and algebra; Appendix A: notational index; Appendix B: mathematical background; Appendix C: basic probability theory.

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Book SynopsisThis introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.Trade Review'… many institutions, like mine, are looking into ways of adding a mathematical modeling component into the undergraduate curriculum for general biology students. This book will be a great asset to these institutions … a very interesting and challenging book for undergraduate students with a strong interest in biology …'. Mei Zhu, Pacific Lutheran University'I found this book interesting since many institutions, like mine, are looking into ways of adding a mathematical modeling component into the undergraduate curriculum for general biology students. This book will be a great asset to these institutions … Overall, this is a very interesting and challenging book for undergraduate students with a strong interest in biology, but not necessarily with a calculus background. Students with a strong mathematical background will also benefit from this book … This book is also a good reference book for biologists who are interested in learning mathematical modeling or integrating it into teaching their undergraduate biology courses.' Mei Zhu, Pacific Lutheran University'… eminently suitable for their target undergraduate audiences and, indeed, for anyone curious to learn more about this increasingly important and undeniably exciting area of applied mathematics.' The Mathematical Gazette'… an attractive introduction to the modeling of biological processes at a very elementary level.' Zentralblatt MATH'This is an attractive introduction into the modelling of biological processes at a very elementary level. … Many exercises motivate the reader to acquire a deeper understanding of the topics treated. Also a substantial number of MATLAB projects are suggested to give the students hands-on experience.' Monatshefte für MathematikTable of Contents1. Dynamic modeling with different equations; 2. Linear models of structured populations; 3. Non-linear models of interactions; 4. Modeling molecular evolution; 5. Constructing phylogenic trees; 6. Genetics; 7. Infectious disease modeling; 8. Curve fitting and biological modeling; Appendix A. Basic analysis of numerical data; Appendix B. For further reading.

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Book SynopsisThis is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory.Trade Review'… up-to-date … can serve as an introduction to applications of model theory in computer science.' L'Enseignement Mathématique' … a very readable introduction to the subject.' Mathematika'This book contains rich material for a good introductory course in model theory …' European Mathematical Society'I have talked with students who first learned about model theory from this text, and overall it served them well. From his impressive work of 1993, Hodges has distilled an accessible introductory account. In doing so he has provided a valuable resource for a first study of model theory.' Carol Wood, International Journal of Symbolic LogicTable of Contents1. Naming of parts; 2. Classifying structures; 3. Structures that look alike; 4. Interpretations; 5. The first order case: compactness; 6. The countable case; 7. The existential case; 8. Saturation; 9. Structure and categoricity.

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Book SynopsisIn this book, first published in 2006, the authors' main aims are first to present classical results in a way that's accessible to non-specialists. Second, to describe results of Smirnov in conformal invariance. It is essential reading for all working in this exciting area.Trade Review'This book contains a complete account of most of the important results in the fascinating area of percolation. Elegant and straightforward proofs are given with minimal background in probability or graph theory. It is self-contained, accessible to a wide readership and widely illustrated with numerous examples. It will be of considerable interest for both beginners and advanced searchers alike.' Zentralblatt MATHTable of ContentsPreface; 1. Basic concepts; 2. Probabilistic tools; 3. Percolation on Z2 - the Harris-Kesten theorem; 4. Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky; 5. Uniqueness of the infinite open cluster and critical probabilities; 6. Estimating critical probabilities; 7. Conformal invariance - Smirnov's theorem; 8. Continuum percolation; Bibliography; Index; List of notation.

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Book SynopsisWritten to suit a wide audience (including physical sciences), these two volumes will become the reference of choice on the Hilbert transform, whatever the subject background of the reader. The author explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application.Trade Review"The author gives detailed and exhaustive information on almost all properties of the Hilbert transform... the selected topics are presented in an easy-to-use style." Lasha Ephremidze, Mathematical ReviewsTable of ContentsPreface; List of symbols; List of abbreviations; Volume I: 1. Introduction; 2. Review of some background mathematics; 3. Derivation of the Hilbert transform relations; 4. Some basic properties of the Hilbert transform; 5. Relationship between the Hilbert transform and some common transforms; 6. The Hilbert transform of periodic functions; 7. Inequalities for the Hilbert transform; 8. Asymptotic behavior of the Hilbert transform; 9. Hilbert transforms of some special functions; 10. Hilbert transforms involving distributions; 11. The finite Hilbert transform; 12. Some singular integral equations; 13. Discrete Hilbert transforms; 14. Numerical evaluation of Hilbert transforms; References; Subject index; Author index.

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Book SynopsisThis text gives a self-contained and detailed treatment of presently known results, and new theorems on hyperbolicity, shadowing, complicated motion, and robustness. The book is intended to provide a dependable reference for researchers wishing to apply such results. This book will be of particular interest to researchers and students interested in dynamical systems, particularly in noninvertible maps and infinite dimensional semi-flows or maps and global analysis.Table of ContentsIntroductionHyperbolic operators, projections , diagonalizationSequence spaces and substitution operatorsHyperbolic setsShadowing and persistence of hyperbolic setsTransversal homoclinic orbitsAppendixNotationReferences

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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:. The Importance of Mathematics in Finance. Mathematical and Computer Modeling in Finance. Money, Securities, and Markets. Time Value, Risk, Arbitrage, and Pricing. The Organization of this Book. 2. Review of Elementary Mathematics: Functions and Operations:. Introduction. Variables, Equations, and Inequalities. Exponents. The Order of Arithmetic Operations and the Rules of Algebra. The Number e. Logarithms. Subscripts. Summations. Double Summations. Products. Factorial Products. Permutations and Combinations. Exercises. Appendix: An Introduction to the ExcelT Spreadsheet. 3. A Review of Elementary Mathematics: Algebra and Solving Equations:. Algebraic Manipulations. The Quadratic Formula. Solving Systems of Equations that Contain Multiple Variables. Geometric Expansions. Functions and Graphs. Exercises. Appendix: Solving Systems of Equations on a Spreadsheet. 4. The Time Value of Money:. Introduction and Future Value. Simple Interest. Compound Interest. Fractional Period Compounding of Interest. Continuous Compounding of Interest. Annuity Future Values. Discounting and Present Value. Present Value of a Series of Cash Flows. Annuity Present Values. Amortization. Perpetuity Models. Single-stage Growth Models. Multiple-stage Growth Models. Exercises. Appendix: Time Value Spreadsheet Applications. 5. Return, Risk, and Co-movement:. Return on Investment. Geometric Mean Return on Investment. Internal Rate of Return. Bond Yields. An Introduction to Risk. Expected Return. Variance and Standard Deviation. Historical Variance and Standard Deviation. Covariance. The Coefficient of Correlation and the Coefficient of Determination. Exercises. Appendix: Return and Risk Spreadsheet Applications. 6. Elementary Portfolio Mathematics:. An Introduction to Portfolio Analysis. Portfolio Return. Portfolio Variance. Diversification and Efficiency. The Market Portfolio and Beta. Deriving the Portfolio Variance Expression. Exercises. 7. Elements of Matrix Mathematics:. An Introduction to Matrices. Matrix Arithmetic. Inverting Matrices. Solving Systems of Equations. Spanning the State Space. Exercises. Appendix: Matrix mathematics on a Spreadsheet. 8. Differential Calculus:. Functions and Limits. Slopes, Derivatives, Maxima, and Minima. Derivatives of Polynomials. Partial and Total Derivatives. The Chain Rule, Product Rule, and Quotient Rule. Logarithmic and Exponential Functions. Taylor Series Expansions. The Method of LaGrange Multipliers. Exercises. Appendix: Derivatives of Polynomials. Appendix: A Table of Rules for Finding Derivatives. Appendix: Portfolio Risk Minimization on a Spreadsheet. 9. Integral Calculus:. Antidifferentiation and the Indefinite Integral. Riemann Sums. Definite Integrals and Areas. Differential Equations. Exercises. Appendix: Rules for Finding Integrals. Appendix: Riemann sums on a spreadsheet. 10. Elements of Options Mathematics:. An Introduction to Stock Options. Binomial Option Pricing: One Time Period. Binomial Option Pricing: Multiple Time Periods. The Black–Scholes Option Pricing Model. Puts and Valuation. Black–Scholes Model Sensitivities. Estimating Implied Volatilities. Exercises. References. Appendix A: Solutions to Exercises. Appendix B: The z-Table. Appendix C: Notation. Appendix D: Glossary. Index.

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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 SynopsisDarren Bridger is a consultant to designers and marketers, advising on using and analyzing data that tap into consumers' non-conscious thinking and motivations. He was one of the original pioneers of the Consumer Neuroscience industry, helping to pioneer two of the first companies in the field then joining the world's largest agency, Neurofocus (now part of the Nielsen company). He is currently Head of Insights at NeuroStrata. Trade Review"A super, easy-to-read book demystifying the world of neuro design, addressing the balance between the role of human creativity and that of neuroscience in modern design. If you think neuro design is about creating bland designs by deconstructing beauty, you need to read this book. It's not about that at all. Darren Bridger introduces all the major themes, key methods and tools underlying the science in engaging, manageable chunks. Any book that explains the allure of memes has to get five stars from me." * Jamie Croggon, Design Director, SharkNinja *"With solid science as the starting point, Darren Bridger provides an eminently practical guide to designing for your customer's brain. Neuro Design is packed with actionable strategies and techniques, and is a must-read for every marketer and designer." * Roger Dooley, author of Brainfluence *"A topic which should be of great importance to anyone in the business of retailing, advertising and marketing. Darren Bridger deals with complex topics in an engaging and practical manner, covering all aspects of the interplay between brain function and product design. Such an understanding is crucial for ensuring consumers stop and buy, rather than walking on by." * Dr David Lewis, Chairman of Mindlab International & Author of The Brain Sell *Table of Contents Section - 01: What is Neuro Design?; Section - 02: Neuroaesthetics; Section - 03: Processing Fluency; Section - 04: How First Impressions Work; Section - 05: Multisensory and Emotional Design; Section - 06: Visual Saliency Maps; Section - 07: Visual Persuasion and Behavioural Economics; Section - 08: Designing for Screens; Section - 09: Viral Designs; Section - 10: Designing Presentation Slides; Section - 11: Conducting Neuro Design Research; Section - 12: Conclusion;

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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 SynopsisMathematical Models for Structural Reliability Analysis offers mathematical models for describing load and material properties in solving structural engineering problems. Examples are provided, demonstrating how the models are implemented, and the limitations of the models are clearly stated. Analytical solutions are also discussed, and methods are clearly distinguished from models. The authors explain both theoretical models and practical applications in a clear, concise, and readable fashion.Table of ContentsStochastic Process Models (F. Casciati and M. Di Paola)IntroductionThe Orthogonal-Increment ModelThe Correlation-Stationary Model Time-Invariant Linear Systems Models of Common UseThe Evolutionary Model Time-Invariant Linear SystemsMarkov Processes A Model of Common Use Itô Stochastic Differential Equation Some Examples Approximation of Mechanical Processes: Physical versus Itô EquationsThe Random Pulse Train Model The Delta-Correlated Model Fokker Planck and Moment Equations for Parametric Delta Correlated Input Quasi-Linear Systems Simulation of Delta Correlated Processes and Response Simulation of Normal White Noise Input and Response Orthogonal-Increment Model for Delta Correlated ProcessesMultidegree-of-Freedom Systems Under Parametric Delta Correlated Input Moment Equation Approach for MDOF Systems Simulation of Multivariate Delta Correlated Processes and ResponseConclusions and ReferencesAppendix Characterization of Random Variables Joint Characterization of Random Variables Operation on Stochastic Processes Kronecker Algebra: Some FundamentalsDimension Reduction and Discretization in Stochastic Problems by Regression Method (O. Ditlevsen)IntroductionLinear RegressionNormal DistributionNon-Gaussian Distributions and Linear RegressionMarginally Transformed Gaussian Processes and FieldsDiscretized Fields Defined by Linear Regression on a Finite Set of Field ValuesDiscretization Defined by Linear Regression on a Finite Set of Linear FunctionalsPoisson Load Field ExampleStochastic Finite Element Methods and Reliability CalculationsClassical versus Statistical-Stochastic Interpolation Formulated on the Basis of the Principle of Maximum LikelihoodComputational Practicability of the Statistical-Stochastic Interpolation MethodField Modeling on the Basis of Measured Noisy DataDiscretization Defined by L

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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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