Mathematical modelling Books

Book Synopsisone-of-a-kind introduction to the theory and application of modeling and simulation techniques in the realm of international studies Modeling and Simulation for Analyzing Global Events provides an orientation to the theory and application of modeling and simulation techniques in social science disciplines.Table of ContentsPreface. I PRINCIPLES OF MODELING AND SIMULATION: ADVANCING GLOBAL STUDIES. 1 Modeling and Simulation: What, When, and Why. Introduction. An Overview of Modeling and Simulation. A Brief History of Modeling and Simulation. Why Use Modeling and Simulation. Conclusions. Key Terms. References. Further Reading. 2 Research Methodologies for Modeling Global Events. Introduction. Global Events and the Social Sciences. Qualitative and Quantitative Research. Modeling and Simulation of Global Events. Mapping Data: A Suggested Methodology. Model Validation. Conclusions. Key Terms. References. II MODELING PARADIGMS. 3 System Dynamics. Introduction. Dynamic System Behavior. Building Blocks of System Dynamics Models. Conclusions. Key Terms. References. 4 Agent-Based Modeling and Social Networks. Introduction. Agent-Based Models: Description and Definition. Social Networks. Building an Agent-Based Model. Conclusions. Key Terms. References. 5 Game Theory. Introduction. Fundamentals of Game Theory. Types of Games. Conclusions. Key Terms. References. III MODELING GLOBAL EVENTS. 6 Case Study: Colombia—A Country Study on Insurgency. Introduction. Developing the Research Question and Methodology. Background: Qualitative Research. Mapping Qualitative to Quantitative. System Dynamics. Responding to the Research Question. Key Terms. References. Case Study Bibliography. 7 Case Study: The Polish Solidarity Movement—Laying the Foundation for the Collapse of Soviet Communism. Introduction. Developing the Research Question and Methodology. Background: Qualitative Research. Measuring Agents and Environments: Stimuli and Actions. Modeling Human Behavior with Agents. Responding to the Research Question. Conclusions. Key Terms. References. Case Study Bibliography. 8 Case Study: Vietnam—Johnson’s War, 1963–1965. Introduction. Developing the Research Question and Methodology. Background: Qualitative Research. Analyzing the Social Network Structures. Social Network Aspects of Human Behavior Modeling. Agent-Based Model Development. Responding to the Research Question. Key Terms. References. Case Study Bibliography. 9 Case Study: Cuban Missile Crisis—A National Security Emergency. Introduction. Developing the Research Question and Methodology. Background: Qualitative Research. Evaluating Behaviors. Game Theory. Responding to the Research Question. Key Terms. References. Case Study Bibliography. Index.

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Book SynopsisAn accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductorTable of ContentsPreface xiii Part I Overview and Motivation 1 Introduction to Monte Carlo Methods 3 1.1 Historical origin of Monte Carlo simulation 4 1.2 Monte Carlo Simulation vs. Monte Carlo Sampling 7 1.3 System dynamics and the mechanics of Monte Carlo simulation 10 1.4 Simulation and optimization 21 1.5 Pitfalls in Monte Carlo simulation 30 1.6 Software tools for Monte Carlo simulation 35 1.7 Prerequisites 37 For further reading 38 Chapter References 38 2 Numerical Integration Methods 41 2.1 Classical quadrature formulae 43 2.2 Gaussian quadrature 48 2.3 Extension to higher dimensions: Product rules 53 2.4 Alternative approaches for high-dimensional integration 55 2.5 Relationship with moment matching 67 2.6 Numerical integration in R 69 For further reading 71 Chapter References 71 Part II Input Analysis: Modeling and Estimation 3 Stochastic Modeling in Finance and Economics 75 3.1 Introductory examples 77 3.2 Some common probability distributions 86 3.3 Multivariate distributions: Covariance and correlation 111 3.4 Modeling dependence with copulae 127 3.5 Linear regression models: a probabilistic view 136 3.6 Time series models 137 3.7 Stochastic differential equations 158 3.8 Dimensionality reduction 177 S3.1 Risk-neutral derivative pricing 190 S3.1.1 Option pricing in the binomial model 192 S3.1.2 A continuous-time model for option pricing: The Black–Scholes–Merton formula 194 S3.1.3 Option pricing in incomplete markets 199 For further reading 202 Chapter References 203 4 Estimation and Fitting 205 4.1 Basic inferential statistics in R 207 4.2 Parameter estimation 215 4.3 Checking the fit of hypothetical distributions 224 4.4 Estimation of linear regression models by ordinary least squares 229 4.5 Fitting time series models 232 4.6 Subjective probability: the Bayesian view 235 For further reading 244 Chapter References 245 Part III Sampling and Path Generation 5 Random Variate Generation 249 5.1 The structure of a Monte Carlo simulation 250 5.2 Generating pseudo-random numbers 252 5.3 The inverse transform method 263 5.4 The acceptance–rejection method 265 5.5 Generating normal variates 269 5.6 Other ad hoc methods 274 5.7 Sampling from copulae 276 For further reading 277 Chapter References 279 6 Sample Path Generation for Continuous-Time Models 281 6.1 Issues in path generation 282 6.2 Simulating geometric Brownian motion 287 6.3 Sample paths of short-term interest rates 298 6.4 Dealing with stochastic volatility 306 6.5 Dealing with jumps 308 For further reading 310 Chapter References 311 Part IV Output Analysis and Efficiency Improvement 7 Output Analysis 315 7.1 Pitfalls in output analysis 317 7.2 Setting the number of replications 323 7.3 A world beyond averages 325 7.4 Good and bad news 327 For further reading 327 Chapter References 328 8 Variance Reduction Methods 329 8.1 Antithetic sampling 330 8.2 Common random numbers 336 8.3 Control variates 337 8.4 Conditional Monte Carlo 341 8.5 Stratified sampling 344 8.6 Importance sampling 350 For further reading 363 Chapter References 363 9 Low-Discrepancy Sequences 365 9.1 Low-discrepancy sequences 366 9.2 Halton sequences 367 9.3 Sobol low-discrepancy sequences 374 9.4 Randomized and scrambled low-discrepancy sequences 379 9.5 Sample path generation with low-discrepancy sequences 381 For further reading 385 Chapter References 385 Part V Miscellaneous Applications 10 Optimization 389 10.1 Classification of optimization problems 390 10.2 Optimization model building 405 10.3 Monte Carlo methods for global optimization 412 10.4 Direct search and simulation-based optimization methods 416 10.5 Stochastic programming models 420 10.6 Scenario generation and Monte Carlo methods for stochastic programming 428 10.7 Stochastic dynamic programming 433 10.8 Numerical dynamic programming 440 10.9 Approximate dynamic programming 451 For further reading 453 Chapter References 453 11 Option Pricing 455 11.1 European-style multidimensional options in the BSM world 456 11.2 European-style path-dependent options in the BSM world 462 11.3 Pricing options with early exercise features 475 11.4 A look outside the BSM world 487 11.5 Pricing interest-rate derivatives 490 For further reading 497 Chapter References 498 12 Sensitivity Estimation 501 12.1 Estimating option greeks by finite differences 503 12.2 Estimating option greeks by pathwise derivatives 509 12.3 Estimating option greeks by the likelihood ratio method 513 For further reading 517 Chapter References 518 13 Risk Measurement and Management 519 13.1 What is a risk measure? 520 13.2 Quantile-based risk measures: value at risk 522 13.3 Monte Carlo methods for V@R 533 13.4 Mean-risk models in stochastic programming 537 13.5 Simulating delta-hedging strategies 540 13.6 The interplay of financial and nonfinancial risks 546 For further reading 548 Chapter References 548 14 Markov Chain Monte Carlo and Bayesian Statistics 551 14.1 An introduction to Markov chains 552 14.2 The Metropolis–Hastings algorithm 555 14.3 A re-examination of simulated annealing 558 For further reading 560 Chapter References 561 Index 563

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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 SynopsisThis 1971 classic on linear models features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.Table of ContentsGeneralized Inverse Matrices. Distributions and Quadratic Forms. Regression, or the Full Rank Model. Introducing Linear Models: Regression on Dummy Variables. Models Not of Full Rank. Two Elementary Models. The 2-Way Crossed Classification. Some Other Analyses. Introduction to Variance Components. Methods of Estimating Variance Components from UnbalancedData. Variance Component Estimation from Unbalanced Data: Formulae. Literature Cited. Statistical Tables. 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 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 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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