Applied mathematics Books

Book SynopsisAs we evolve from unquantified ignorance to an imperfect but everpresent state of measured awareness, Henshaw gives us a critical perspective from which we can measure upthe measurements that have come to affect our lives so greatly.Trade ReviewAcademic but accessible to the general reader. Scitech Book News 2006 Well written, entertaining, and informative. -- Luiz Henrique de Figueiredo MAA Reviews 2006 Henshaw has a remarkable ability to explain complex mathematics in a manner accessible to general readers. -- Judy Randle Tulsa World 2006 Clear and well written. -- Terry Ishihara Science Books and Films 2006 The book is fun to read... Recommended. Choice 2007 Best of 2006. Library Journal 2007 It is easy to read, and Henshaw has a pleasant style of throwing himself into the action. PsycCRITIQUES 2007Table of ContentsPrefaceAcknowledgments1. Of Love and Luminescene: What, Why, and How Things Get Measured2. Doing the Math: Scales, Standards, and Some Beautiful Measurements3. The Ratings Game: ''Overall'' Measurements and Rankings4. Measurement in Business: What Gets Measured Gets Done5. Games of Inches: Sports and Measurement6. Measuring the Mind: Intelligence, Biology, and Education7. Man: The Measure of All Things8. It's Not Just the Heat, it's the Humidity: Global Warming and Environmental Measurement9. Garbage In, Garbage Out: The Computer and Measurement10. How Funny Is That? Knowledge Without Measurement?11. Faith, Hope, and Love: The Future of Measuremen—and of KnowledgetReferencesIndex

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Book SynopsisThe book features end-of-chapter practice problems, an appendix of worked problems, a glossary of terms, and an annotated bibliography.Trade ReviewMere Thermodynamics is a good learning tool for students, and it's an interesting and thought-provoking book for educators and professionals. American Journal of Physics This book is a little gem. Lemons has a lightness of touch that belies the weight of thought he has given to this subject and how to present it in a non trivial way to a beginner. No awkward corner is avoided or ignored, and the whole piece is touched by enthusiasm, clarity, a central awareness of its relevance to the real world. -- Peter Sammut Physics Education Lucidly written and enjoyable to read... An interesting and informative supplement to other textbooks. Times Higher Education SupplementTable of ContentsPreface1. Definitions1.1. Thermodynamics1.2. System1.3. Boundary, Environment, and Interactions1.4. States and State Variables1.5. Equations of State1.6. Work1.7. HeatProblems2. Equilibrium2.1. Equilibrium2.2. Zeroth Law of Thermodynamics2.3. Empirical Temperature2.4. Traditional Temperature Scales2.5. Equilibrium ProcessesProblems3. Heat3.1. Quantifying Heat3.2. Calorimetry3.3. What is Heat?Problems4. The First Law4.1. Count Rumford4.2. Joule's Experiments4.3. The First Law of Thermodynamics4.4. Thermodynamic Cycles4.5. Cycle AdjustmentProblems5. The Second Law5.1. Sadi Carnot5.2. Statements of the Second Law5.3. Equivalence and Inequivalence5.4. Reversible Heat Engines5.5. Refrigerators and Heat PumpsProblems6. The First and Second Laws6.1. Rudolph Clausius6.2. Thermodynamic Temperature6.3. Clausius's TheoremProblems7. Entropy7.1. The Meaning of Reversibility7.2. Entropy7.3. Entropy Generation in Irreversible Processes7.4. The Entropy Generator7.5. Entropy Corollaries7.6. Thermodynamic Arrow of TimeProblems8. Fluid Variables8.1. What Is a Fluid?8.2. Reversible Work8.3. Fundamental Constraint8.4. Enthalpy8.5. Helmholtz and Gibbs Free Energies8.6. Partial Derivative Rules8.4. Thermodynamic Coeffi cients8.8. Heat CapacitiesProblems9. Simple Fluid Systems9.1. The Ideal Gas9.2. Room-Temperature Elastic Solid9.3. Cavity RadiationProblems10. Nonfluid Systems10.1. Nonfluid Variables10.2. The Theoretician's Rubber Band10.3. Paramagnetism10.4. Surfaces10.5. Chemical Potential10.6. Multivariate SystemsProblems11. Equilibrium and Stability11.1. Mechanical and Thermal Systems11.2. Principle of Maximum Entropy11.3. Other Stability Criteria11.4. Intrinsic Stability of a FluidProblems12. Two-Phase Systems12.1. Phase Diagrams12.2. Van der Waals Equation of State12.3. Two-Phase Transition12.4. Maxwell Construction12.5. Clausius-Clapeyron Equation12.6. Critical PointProblems13. The Third Law13.1. The Principle of Thomsen and Berthelot13.2. Entropy Change13.3. Unattainability13.4. Absolute EntropyProblemsAppendixesA. Physical Constants and Standard DefinitionsB. Catalog of 21 Simple CyclesC. Glossary of TermsD. Selected Worked ProblemsE. Answers to ProblemsAnnotated BibliographyIndex

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Book SynopsisWith more than 150 exercises, Regression Estimators is a valuable resource for graduate students and professional statisticians.Trade Review"A comprehensive treatment... valuable to statisticians who would like to know more about the analytical properties of ridge-type estimators." - Journal of the American Statistical Association "Highly recommended to anyone working on advanced applications or research in estimation in linear models." - Technometrics"Table of ContentsPrefacePart I: Introduction and Mathematical Preliminaries1. Introduction1.1. The Purpose of This Book1.2. Least Square Estimators and the Need for Alternatives1.3. Historical Survey1.4. The Structure of the Book2. Mathematical and Statistical Preliminaries2.0. Introduction2.1. Matrix Theory Results2.2. The Bayes Estimator (BE)2.3. Admissible Estimators2.4. The Minimax Estimator2.5. Criterion for Comparing Estimators: Theobald's 1974 Result2.6. Some Useful Inequalities: Some Miscellaneous Useful Matrix Results2.7. SummaryPart II: The Estimators, Their Derivations, and Their Relationships3. The Estimators3.0. The Least Square Estimator and Its Properties3.1. The Generalized Ridge Regression Estimator3.2. The Mixed Estimators3.3. The Linear Minimax Estimator3.4. The Bayes Estimator3.6. Summary4. How the Different Estimators Are Related4.0. Introduction4.1. Alternative Forms of the Bayes Estimator Full-Rank Case4.2. Alternative Forms of the Bayes Estimator Non-Full-Rank Case Estimable Parametric Functions4.3. Equivalence of the Generalized Ridge Estimator and the BayesEstimator4.4. Equivalence of the Mixed Estimator and the Bayes Estimator4.5. Ridge Estimators in the Literature as Special Cases of the BE, Minimax Estimators, or Mixed Estimators4.6. An Extension of the Gauss-Markov Theorem4.7. Generalities4.8. SummaryPart III: Comparing the Efficiency of the Estimators5. Measures of Efficiency of the Estimators5.0. Introduction5.1. The Different Kinds of Mean Square Error5.2. Zellner's Balanced Loss Function5.3. The LINEX Loss Function5.4. Linear Admissibility5.5. Summary6. The Average Mean Square Error6.0. Introduction6.1. The Forms of the MSE for the Minimax, Bayes, and Mixed Estimators6.2. The Relationship between the Average Variance and the MSE6.3. The Average MSE of the Bayes Estimator6.4. Alternative Forms of the MSE of the Mixed Estimator6.5. Comparison of the MSE of Different BEs6.6. Comparison of the MSE of the Ridge and Contraction Estimators6.7. Comparison of the Average MSE of the Two-Parameter Liu Estimator and the Ordinary Ridge Regression Estimator6.8. Summary7. The MSE Neglecting the Prior Assumptions7.0. Introduction7.1. The MSE of the BE7.2. The MSE of the Mixed Estimators Neglecting PriorAssumptions7.3. Comparison of the Conditional MSE of the Bayes and Least Square Estimators and Comparison of the Conditional and Average MSE7.4. Comparison of the MSE of a Mixed Estimator with That of the LS Estimators7.5. Comparison of the MSE of Two Bayes Estimators7.6. Summary8. The MSE for Incorrect Prior Assumptions8.0. Introduction8.1. The Bayes Estimator and Its MSE8.2. The Minimax Estimator8.3. The Mixed Estimator8.4. Contaminated Priors8.5. Contaminated (Mixed) Bayes Estimators8.6. SummaryPart IV: Applications9. The Kalman Filter9.0. Introduction9.1. The Kalman Filter as a Bayes Estimator9.2. The Kalman Filter as a Recursive Least Square Estimator,and the Connection with the Mixed Estimator9.3. The Minimax Estimator9.4. The Generalized Ridge Estimator9.5. The Average Mean Square Error9.6. The MSE for Incorrect Initial Prior Assumptions9.7. Applications9.8. Recursive Ridge Regression9.9. Summary10. Experimental Design Models10.0. Introduction10.1. The One-Way ANOVA Model10.2. The Bayes and Empirical Bayes Estimators10.3. The Two- Way Classification10.4. The Bayes and Empirical Bayes Estimators10.5. SummaryAppendix to Section 10.2. Calculation of the MSE of Section 10.211. How Penalized Splines and Ridge- Type EstimatorsAre Related11.0. Introduction11.1. Splines as a Special Kind of Regression Model11.2. Penalized Splines11.3. The Best Linear Unbiased Predictor (BLUP)11.4. Two Examples11.5. SummaryPart V: Alternative Measures of Efficiency12. Estimation Using Zellner's Balanced Loss Function12.0. Introduction12.1. Zellner's Balanced Loss Function12.2. The Estimators from Different Points of View12.3. The Average Mean Square Error12.4. The Risk without Averaging over a Prior Distribution12.5. Some Optimal Ridge Estimators12.6. Summary13. The LINEX and Other Asymmetric Loss Functions13.0. Introduction13.1. The LINEX Loss Function13.2. The Bayes Risk for a Regression Estimator13.3. The Frequentist Risk13.4. Summary14. Distances between Ridge-Type Estimators, andInformation Geometry14.0. Introduction14.1. The Relevant Differential Geometry14.2. The Distance between Two Linear Bayes Estimators, Based on the Prior Distributions14.3. The Distance between Distributions of Ridge-Type Estimators from a Non-Bayesian Point of View14.4. Distances between the Mixed Estimators14.5. An Example Using the Kalman Filter14.6. SummaryReferencesAuthor IndexSubject Index

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Book SynopsisThose new to bioscience research as well as experienced practitioners will find that Mouton's explanations are the perfect companion for stereology courses and workshops.Trade Review"An excellent textbook for practical applications of the theoretically rigorous methods of state-of-art unbiased stereology." (Arun M. Gokhale, Georgia Institute of Technology)"Table of ContentsPreface1. Elias Coins A Word2. Solid 3D Objects3. Regional Volume Estimation4. Area Estimation by Point Counting5. Probe Object Intersections6. Volume by Cavalieri Point Counting7. Accuracy and Precision8. From 2D to 3D9. Surface Area and Length10. Total Object Number11. Rare Events12. Local Size Estimators13. Do More, Less Well14. Uncertainty15. Computerized Stereology Systems16. A Survey of Tissue17. Peer Review ConsiderationsAppendix: Conceptual Framework for Organic StereologyGlossaryBibliographyIndex

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Book SynopsisPresents an introduction to differential geometry through differential forms, emphasizing their applications in various areas of mathematics and physics. This work focuses on Stokes' theorem, the classical integral formulas and their applications to harmonic functions and topology.Table of ContentsElements of multilinear algebra Differential forms in ${\mathbb{R}}^n$ Vector analysis on manifolds Pfaffian systems Curves and surfaces in Euclidean 3-space Lie groups and homogeneous spaces Symplectic geometry and mechanics Elements of statistical mechanics and thermodynamics Elements of electrodynamics Bibliography Symbols Index.

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Book SynopsisQuantum mechanics is arguably the most successful physical theory. It provides the structure underlying all of our electronic technology, and much of our mastery over materials. Suitable for undergraduates with minimal mathematical preparation, this title presents a logical path to understanding what quantum mechanics is about.Table of ContentsThe failure of classical theory Consequences of a mistrust of theory Properties of electrons, photons; The De Broglie relations An analysis of electron diffraction Heisenberg's principle of indeterminancy Interpretations of the Heisenberg principle Dynamical properties of microsystems Determinism and state; Statistical determinism Probability amplitudes; The superposition principle Summary and comment Index.

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Book SynopsisPresents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open. The hypotheses range from geometry and topology to combinatorics to algebra and number theory.Table of Contents Introduction The statistics of topology and algebra Combinatorial complexity and randomness Random permutations of Young diagrams of their cycles The geometry of Frobenius numbers for additive semigroups Bibliography

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Book SynopsisForest mensuration provides data on aspects of length, mass and time of areas of forest, individual trees or parcels of felled timber. Such quantitative information is vital to sellers, buyers, planners, managers and researchers within forestry. This book is a revision of a successful text originally published in 1983 but written for students in Africa. The new edition is international in scope, and has also been changed and updated to reflect recent advances, particularly with respect to biomass and fodder measurement, sampling with unequal probabilities and growth modelling. The book covers both the theory and practice of forest mensuration and includes a number of worked examples of calculations. It is a basic textbook for students of forestry and will also be of value to practising foresters.Table of Contents1: Measurements 2: Measuring single trees 3: Measuring tree crops 4: Forest inventory 5: Statistical principles in forest inventory 6: Site assessment 7: Forest growth models

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Book SynopsisMany situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.

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Book SynopsisProvides the reader with a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems. It also addresses specialized topics such as image reconstruction, parameter identification, total variation methods, nonnegativity constraints, and regularization parameter selection methods.

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Book SynopsisA novel approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This method is unique in also yielding novel integral representations for linear PDEs. Several new developments are addressed in the book, including a new transform method for linear evolution equations on the half-line and on the finite interval; analytical inversion of certain integrals such as the attenuated Radon transform and the Dirichlet-to-Neumann map for a moving boundary; integral representations for linear boundary value problems; analytical and numerical methods for elliptic PDEs in a convex polygon; and integrable nonlinear PDEs. An epilogue provides a list of problems on which the author's new approach has been used, offers open problems, and gives a glimpse into how the method might be applied to problems in three dimensions.

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Book SynopsisThe purpose of this book is to promote understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms. Sensitivity and stability are analyzed as mathematical properties, without reference to finite precision arithmetic. The material is presented at a basic level, emphasizing ideas and intuition, but in a mathematically rigorous fashion. The derivations are simple and elegant, and the results are easy to understand and interpret. The book is self-contained. It was written for students in all areas of mathematics, engineering, and the computational sciences, but can easily be used for self-study. This text differs from other numerical linear algebra texts by offering the following: a systematic development of numerical conditioning; a simplified concept of numerical stability in exact arithmetic; simple derivations; a high-level view of algorithms; and results for complex matrices.

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Book SynopsisA First Course on Numerical Methods is designed for students and researchers who seek practical knowledge of modern techniques in scientific computing. Avoiding encyclopaedic and heavily theoretical exposition, the book provides an in-depth treatment of fundamental issues and methods, the reasons behind the success and failure of numerical software, and fresh and easy-to-follow approaches and techniques. The authors focus on current methods, issues and software while providing a comprehensive theoretical foundation, enabling those who need to apply the techniques to successfully design solutions to nonstandard problems. The book also illustrates algorithms using the programming environment of MATLAB , with the expectation that the reader will gradually become proficient in it while learning the material covered in the book. The book takes an algorithmic approach, focusing on techniques that have a high level of applicability to engineering, computer science and industrial mathematics.

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Book SynopsisThe Bulletin of Mathematical Biology, the official journal of the Society for Mathematical Biology, disseminates original research findings and other information relevant to the interface of biology and the mathematical sciences. Contributions should have relevance to both fields. In order to accommodate the broad scope of new developments, the journal accepts a variety of contributions, including: Original research articles focused on new biological insights gained with the help of tools from the mathematical sciences or new mathematical tools and methods with demonstrated applicability to biological investigations Research in mathematical biology education Reviews Commentaries Perspectives, and contributions that discuss issues important to the profession All contributions are peer-reviewed. 

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Book SynopsisLearn how quantitative models can help fight client problems head-on Before financial problems can be solved, they need to be fully understood. Since in-depth quantitative modeling techniques are a powerful tool to understanding the drivers associated with financial problems, one would need a solid grasp of these techniques before being able to unlock their full potential of the methods used. In The Mathematics of Financial Models, the author presents real world solutions to the everyday problems facing financial professionals. With interactive tools such as spreadsheets for valuation, pricing, and modeling, this resource combines highly mathematical quantitative analysis with useful, practical methodologies to create an essential guide for investment and risk-management professionals facing modeling issues in insurance, derivatives valuation, and pension benefits, among others. In addition to this, this resource also provides the relevant tools like matrices, calculuTable of ContentsPreface ix Acknowledgments xi Chapter 1 Setting the Stage 1 Why is This Book Different? 2 Road Map of the Book 3 References 5 Chapter 2 Building Zero Curves 7 Market Instruments 8 Linear Interpolation 16 Cubic Splining 25 Appendix: Finding Swap Rates Using a Floating Coupon Bond Approach 41 References 43 Chapter 3 Valuing Vanilla Options 45 Black-Scholes Formulae 47 Adaptations of the Black-Scholes Formulae 53 Limitations of the Black-Scholes Formulae 70 Application in Currency Risk Management 74 Appendix 78 References 80 Chapter 4 Simulations 81 Uniform Number Generation 82 Non-Uniform Number Generation 86 Applications of Simulations 93 Variance Reduction Techniques 100 References 104 Chapter 5 Valuing Exotic Options 107 Valuing Path-Independent, European-Style Options on a Single Variable 108 Valuing Path-Dependent, European-Style Options on a Single Variable 114 Valuing Path-Independent, European-Style Options on Two Variables 135 Valuing Path-Dependent, European-Style Options on Multiple Variables 152 References 157 Chapter 6 Estimating Model Parameters 159 Calibration of Parameters in the Black-Scholes Model 161 Using Implied Black-Scholes Volatility Surface and Zero Rate Term Structure to Value Options 169 Using Volatility Surface 178 Calibration of Interest Rate Option Model Parameters 190 Statistical Estimation 196 References 203 Chapter 7 The Effectiveness of Hedging Strategies 205 Delta Hedging 206 Assumptions Underlying Delta Hedging 216 Beyond Delta Hedging 223 Testing Hedging Strategies 230 Analysis Associated with the Hedging of a European-Style Vanilla Put Option 235 References 244 Chapter 8 Valuing Variable Annuity Guarantees 245 Basic GMDB 246 Death Benefit Riders 261 Other Details Associated with GMDB Products 269 Improving Modeling Assumptions 273 Living Benefit Riders 276 References 279 Chapter 9 Real Options 281 Surrendering a GMAB Rider 282 Adding Servers in a Queue 300 References 314 Chapter 10 Parting Thoughts 315 About the Author 317 About the Website 319 Index 321

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Book SynopsisCOVERS THE FUNDAMENTAL TOPICS IN MATHEMATICS, STATISTICS, AND FINANCIAL MANAGEMENT THAT ARE REQUIRED FOR A THOROUGH STUDY OF FINANCIAL MARKETS This comprehensive yet accessible book introduces students to financial markets and delves into more advanced material at a steady pace while providing motivating examples, poignant remarks, counterexamples, ideological clashes, and intuitive traps throughout. Tempered by real-life cases and actual market structures, An Introduction to Financial Markets: A Quantitative Approach accentuates theory through quantitative modeling whenever and wherever necessary. It focuses on the lessons learned from timely subject matter such as the impact of the recent subprime mortgage storm, the collapse of LTCM, and the harsh criticism on risk management and innovative finance. The book also provides the necessary foundations in stochastic calculus and optimization, alongside financial modeling concepts that are illustrated with relevantTable of ContentsPreface xv About the Companion Website xix Part I Overview 1 Financial Markets: Functions, Institutions, and Traded Assets 1 1.1 What is the purpose of finance? 2 1.2 Traded assets 12 1.2.1 The balance sheet 15 1.2.2 Assets vs. securities 20 1.2.3 Equity 22 1.2.4 Fixed income 24 1.2.5 FOREX markets 27 1.2.6 Derivatives 29 1.3 Market participants and their roles 46 1.3.1 Commercial vs. investment banks 48 1.3.2 Investment funds and insurance companies 49 1.3.3 Dealers and brokers 51 1.3.4 Hedgers, speculators, and arbitrageurs 51 1.4 Market structure and trading strategies 53 1.4.1 Primary and secondary markets 53 1.4.2 Over-the-counter vs. exchange-traded derivatives 53 1.4.3 Auction mechanisms and the limit order book 53 1.4.4 Buying on margin and leverage 55 1.4.5 Short-selling 58 1.5 Market indexes 60 Problems 63 Further reading 65 Bibliography 65 2 Basic Problems in Quantitative Finance 67 2.1 Portfolio optimization 68 2.1.1 Static portfolio optimization: Mean–variance efficiency 70 2.1.2 Dynamic decision-making under uncertainty: A stylized consumption–saving model 75 2.2 Risk measurement and management 80 2.2.1 Sensitivity of asset prices to underlying risk factors 81 2.2.2 Risk measures in a non-normal world: Value-atrisk 84 2.2.3 Risk management: Introductory hedging examples 93 2.2.4 Financial vs. nonfinancial risk factors 100 2.3 The no-arbitrage principle in asset pricing 102 2.3.1 Why do we need asset pricing models? 103 2.3.2 Arbitrage strategies 104 2.3.3 Pricing by no-arbitrage 108 2.3.4 Option pricing in a binomial model 112 2.3.5 The limitations of the no-arbitrage principle 116 2.4 The mathematics of arbitrage 117 2.4.1 Linearity of the pricing functional and law of one price 119 2.4.2 Dominant strategies 120 2.4.3 No-arbitrage principle and risk-neutral measures 125 S2.1 Multiobjective optimization 129 S2.2 Summary of LP duality 133 Problems 137 Further reading 139 Bibliography 139 Part II Fixed income assets 3 Elementary Theory of Interest Rates 143 3.1 The time value of money: Shifting money forward in time 146 3.1.1 Simple vs. compounded rates 147 3.1.2 Quoted vs. effective rates: Compounding frequencies 150 3.2 The time value of money: Shifting money backward in time 153 3.2.1 Discount factors and pricing a zero-coupon bond 154 3.2.2 Discount factors vs. interest rates 158 3.3 Nominal vs. real interest rates 161 3.4 The term structure of interest rates 163 3.5 Elementary bond pricing 165 3.5.1 Pricing coupon-bearing bonds 165 3.5.2 From bond prices to term structures, and vice versa 168 3.5.3 What is a risk-free rate, anyway? 171 3.5.4 Yield-to-maturity 174 3.5.5 Interest rate risk 180 3.5.6 Pricing floating rate bonds 188 3.6 A digression: Elementary investment analysis 190 3.6.1 Net present value 191 3.6.2 Internal rate of return 192 3.6.3 Real options 193 3.7 Spot vs. forward interest rates 193 3.7.1 The forward and the spot rate curves 197 3.7.2 Discretely compounded forward rates 197 3.7.3 Forward discount factors 198 3.7.4 The expectation hypothesis 199 3.7.5 A word of caution: Model risk and hidden assumptions 202 S3.1 Proof of Equation (3.42) 203 Problems 203 Further reading 205 Bibliography 205 4 Forward Rate Agreements, Interest Rate Futures, and Vanilla Swaps 207 4.1 LIBOR and EURIBOR rates 208 4.2 Forward rate agreements 209 4.2.1 A hedging view of forward rates 210 4.2.2 FRAs as bond trades 214 4.2.3 A numerical example 215 4.3 Eurodollar futures 216 4.4 Vanilla interest rate swaps 220 4.4.1 Swap valuation: Approach 1 221 4.4.2 Swap valuation: Approach 2 223 4.4.3 The swap curve and the term structure 225 Problems 226 Further reading 226 Bibliography 226 5 Fixed-Income Markets 229 5.1 Day count conventions 230 5.2 Bond markets 231 5.2.1 Bond credit ratings 233 5.2.2 Quoting bond prices 233 5.2.3 Bonds with embedded options 235 5.3 Interest rate derivatives 237 5.3.1 Swap markets 237 5.3.2 Bond futures and options 238 5.4 The repo market and other money market instruments 239 5.5 Securitization 240 Problems 244 Further reading 244 Bibliography 244 6 Interest Rate Risk Management 247 6.1 Duration as a first-order sensitivity measure 248 6.1.1 Duration of fixed-coupon bonds 250 6.1.2 Duration of a floater 254 6.1.3 Dollar duration and interest rate swaps 255 6.2 Further interpretations of duration 257 6.2.1 Duration and investment horizons 258 6.2.2 Duration and yield volatility 260 6.2.3 Duration and quantile-based risk measures 260 6.3 Classical duration-based immunization 261 6.3.1 Cash flow matching 262 6.3.2 Duration matching 263 6.4 Immunization by interest rate derivatives 265 6.4.1 Using interest rate swaps in asset–liability management 266 6.5 A second-order refinement: Convexity 266 6.6 Multifactor models in interest rate risk management 269 Problems 271 Further reading 272 Bibliography 273 Part III Equity portfolios 7 Decision-Making under Uncertainty: The Static Case 277 7.1 Introductory examples 278 7.2 Should we just consider expected values of returns and monetary outcomes? 282 7.2.1 Formalizing static decision-making under uncertainty 283 7.2.2 The flaw of averages 284 7.3 A conceptual tool: The utility function 288 7.3.1 A few standard utility functions 293 7.3.2 Limitations of utility functions 297 7.4 Mean–risk models 299 7.4.1 Coherent risk measures 300 7.4.2 Standard deviation and variance as risk measures 302 7.4.3 Quantile-based risk measures: V@R and CV@R 303 7.4.4 Formulation of mean–risk models 309 7.5 Stochastic dominance 310 S7.1 Theorem proofs 314 S7.1.1 Proof of Theorem 7.2 314 S7.1.2 Proof of Theorem 7.4 315 Problems 315 Further reading 317 Bibliography 317 8 Mean–Variance Efficient Portfolios 319 8.1 Risk aversion and capital allocation to risky assets 320 8.1.1 The role of risk aversion 324 8.2 The mean–variance efficient frontier with risky assets 325 8.2.1 Diversification and portfolio risk 325 8.2.2 The efficient frontier in the case of two risky assets 326 8.2.3 The efficient frontier in the case of n risky assets 329 8.3 Mean–variance efficiency with a risk-free asset: The separation property 332 8.4 Maximizing the Sharpe ratio 337 8.4.1 Technical issues in Sharpe ratio maximization 340 8.5 Mean–variance efficiency vs. expected utility 341 8.6 Instability in mean–variance portfolio optimization 343 S8.1 The attainable set for two risky assets is a hyperbola 345 S8.2 Explicit solution of mean–variance optimization in matrix form 346 Problems 348 Further reading 349 Bibliography 349 9 Factor Models 351 9.1 Statistical issues in mean–variance portfolio optimization 352 9.2 The single-index model 353 9.2.1 Estimating a factor model 354 9.2.2 Portfolio optimization within the single-index model 356 9.3 The Treynor–Black model 358 9.3.1 A top-down/bottom-up optimization procedure 362 9.4 Multifactor models 365 9.5 Factor models in practice 367 S9.1 Proof of Equation (9.17) 368 Problems 369 Further reading 371 Bibliography 371 10 Equilibrium Models: CAPM and APT 373 10.1 What is an equilibrium model? 374 10.2 The capital asset pricing model 375 10.2.1 Proof of the CAPM formula 377 10.2.2 Interpreting CAPM 378 10.2.3 CAPM as a pricing formula and its practical relevance 380 10.3 The Black–Litterman portfolio optimization model 381 10.3.1 Black–Litterman model: The role of CAPM and Bayesian Statistics 382 10.3.2 Black-Litterman model: A numerical example 386 10.4 Arbitrage pricing theory 388 10.4.1 The intuition 389 10.4.2 A not-so-rigorous proof of APT 391 10.4.3 APT for Well-Diversified Portfolios 392 10.4.4 APT for Individual Assets 393 10.4.5 Interpreting and using APT 394 10.5 The behavioral critique 398 10.5.1 The efficient market hypothesis 400 10.5.2 The psychology of choice by agents with limited rationality 400 10.5.3 Prospect theory: The aversion to sure loss 401 S10.1Bayesian statistics 404 S10.1.1 Bayesian estimation 405 S10.1.2 Bayesian learning in coin flipping 407 S10.1.3 The expected value of a normal distribution 408 Problems 411 Further reading 413 Bibliography 413 Part IV Derivatives 11 Modeling Dynamic Uncertainty 417 11.1 Stochastic processes 420 11.1.1 Introductory examples 422 11.1.2 Marginals do not tell the whole story 428 11.1.3 Modeling information: Filtration generated by a stochastic process 430 11.1.4 Markov processes 433 11.1.5 Martingales 436 11.2 Stochastic processes in continuous time 438 11.2.1 A fundamental building block: Standard Wiener process 438 11.2.2 A generalization: Lévy processes 440 11.3 Stochastic differential equations 441 11.3.1 A deterministic differential equation: The bank account process 442 11.3.2 The generalized Wiener process 443 11.3.3 Geometric Brownian motion and Itô processes 445 11.4 Stochastic integration and Itô’s lemma 447 11.4.1 A digression: Riemann and Riemann–Stieltjes integrals 447 11.4.2 Stochastic integral in the sense of Itô 448 11.4.3 Itô’s lemma 453 11.5 Stochastic processes in financial modeling 457 11.5.1 Geometric Brownian motion 457 11.5.2 Generalizations 460 11.6 Sample path generation 462 11.6.1 Monte Carlo sampling 463 11.6.2 Scenario trees 465 S11.1Probability spaces, measurability, and information 468 Problems 476 Further reading 478 Bibliography 478 12 Forward and Futures Contracts 481 12.1 Pricing forward contracts on equity and foreign currencies 482 12.1.1 The spot–forward parity theorem 482 12.1.2 The spot–forward parity theorem with dividend income 485 12.1.3 Forward contracts on currencies 487 12.1.4 Forward contracts on commodities or energy: Contango and backwardation 489 12.2 Forward vs. futures contracts 490 12.3 Hedging with linear contracts 493 12.3.1 Quantity-based hedging 493 12.3.2 Basis risk and minimum variance hedging 494 12.3.3 Hedging with index futures 496 12.3.4 Tailing the hedge 499 Problems 501 Further reading 502 Bibliography 502 13 Option Pricing: Complete Markets 505 13.1 Option terminology 506 13.1.1 Vanilla options 507 13.1.2 Exotic options 508 13.2 Model-free price restrictions 510 13.2.1 Bounds on call option prices 511 13.2.2 Bounds on put option prices: Early exercise and continuation regions 514 13.2.3 Parity relationships 517 13.3 Binomial option pricing 519 13.3.1 A hedging argument 520 13.3.2 Lattice calibration 523 13.3.3 Generalization to multiple steps 524 13.3.4 Binomial pricing of American-style options 527 13.4 A continuous-time model: The Black–Scholes–Merton pricing formula 530 13.4.1 The delta-hedging view 532 13.4.2 The risk-neutral view: Feynman–Ka¡c representation theorem 539 13.4.3 Interpreting the factors in the BSM formula 543 13.5 Option price sensitivities: The Greeks 545 13.5.1 Delta and gamma 546 13.5.2 Theta 550 13.5.3 Relationship between delta, gamma, and theta 551 13.5.4 Vega 552 13.6 The role of volatility 553 13.6.1 The implied volatility surface 553 13.6.2 The impact of volatility on barrier options 555 13.7 Options on assets providing income 556 13.7.1 Index options 557 13.7.2 Currency options 558 13.7.3 Futures options 559 13.7.4 The mechanics of futures options 559 13.7.5 A binomial view of futures options 560 13.7.6 A risk-neutral view of futures options 562 13.8 Portfolio strategies based on options 562 13.8.1 Portfolio insurance and the Black Monday of 1987 563 13.8.2 Volatility trading 564 13.8.3 Dynamic vs. Static hedging 566 13.9 Option pricing by numerical methods 569 Problems 570 Further reading 575 Bibliography 576 14 Option Pricing: Incomplete Markets 579 14.1 A PDE approach to incomplete markets 581 14.1.1 Pricing a zero-coupon bond in a driftless world 584 14.2 Pricing by short-rate models 588 14.2.1 The Vasicek short-rate model 589 14.2.2 The Cox–Ingersoll–Ross short-rate model 594 14.3 A martingale approach to incomplete markets 595 14.3.1 An informal approach to martingale equivalent measures 598 14.3.2 Choice of numeraire: The bank account 600 14.3.3 Choice of numeraire: The zero-coupon bond 601 14.3.4 Pricing options with stochastic interest rates: Black’s model 602 14.3.5 Extensions 603 14.4 Issues in model calibration 603 14.4.1 Bias–variance tradeoff and regularized least-squares 604 14.4.2 Financial model calibration 609 Further reading 612 Bibliography 612 Part V Advanced optimization models 15 Optimization Model Building 617 15.1 Classification of optimization models 618 15.2 Linear programming 625 15.2.1 Cash flow matching 627 15.3 Quadratic programming 628 15.3.1 Maximizing the Sharpe ratio 629 15.3.2 Quadratically constrained quadratic programming 631 15.4 Integer programming 632 15.4.1 A MIQP model to minimize TEV under a cardinality constraint 634 15.4.2 Good MILP model building: The role of tight model formulations 636 15.5 Conic optimization 642 15.5.1 Convex cones 644 15.5.2 Second-order cone programming 650 15.5.3 Semidefinite programming 653 15.6 Stochastic optimization 655 15.6.1 Chance-constrained LP models 656 15.6.2 Two-stage stochastic linear programming with recourse 657 15.6.3 Multistage stochastic linear programming with recourse 663 15.6.4 Scenario generation and stability in stochastic programming 670 15.7 Stochastic dynamic programming 675 15.7.1 The dynamic programming principle 676 15.7.2 Solving Bellman’s equation: The three curses of dimensionality 679 15.7.3 Application to pricing options with early exercise features 680 15.8 Decision rules for multistage SLPs 682 15.9 Worst-case robust models 686 15.9.1 Uncertain LPs: Polyhedral uncertainty 689 15.9.2 Uncertain LPs: Ellipsoidal uncertainty 690 15.10Nonlinear programming models in finance 691 15.10.1 Fixed-mix asset allocation 692 Problems 693 Further reading 695 Bibliography 696 16 Optimization Model Solving 699 16.1 Local methods for nonlinear programming 700 16.1.1 Unconstrained nonlinear programming 700 16.1.2 Penalty function methods 703 16.1.3 Lagrange multipliers and constraint qualification conditions 707 16.1.4 Duality theory 713 16.2 Global methods for nonlinear programming 715 16.2.1 Genetic algorithms 716 16.2.2 Particle swarm optimization 717 16.3 Linear programming 719 16.3.1 The simplex method 720 16.3.2 Duality in linear programming 723 16.3.3 Interior-point methods: Primal-dual barrier method for LP 726 16.4 Conic duality and interior-point methods 728 16.4.1 Conic duality 728 16.4.2 Interior-point methods for SOCP and SDP 731 16.5 Branch-and-bound methods for integer programming 732 16.5.1 A matheuristic approach: Fix-and-relax 735 16.6 Optimization software 736 16.6.1 Solvers 737 16.6.2 Interfacing through imperative programming languages 738 16.6.3 Interfacing through non-imperative algebraic languages 738 16.6.4 Additional interfaces 739 Problems 739 Further reading 740 Bibliography 741 Index 743

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Book SynopsisThis introductory guide provides a fresh approach to integrating design and statistics in a hands-on fashion that incorporates the power of SPSS (R) software to solve real-world problems.Trade Review“This is a good book on designing good research studies and using statistical and analytical tools to measure their results accurately.” (Biz India, 22 April 2013) Table of ContentsPreface xvii Acknowledgments xix PART I WHEEL OF SCIENCE: PREMISES OF RESEARCH 1 1 "DUH" SCIENCE VERSUS "HUH" SCIENCE 3 2 THEORIES AND HYPOTHESES 21 3 OBSERVATION AND EMPIRICAL GENERALIZATION 35 4 ETHICS 52 PART II WHEEL OF SCIENCE: PROCEDURES OF RESEARCH 63 5 MEASUREMENT 65 6 USING SPSS IN RESEARCH 83 7 CHI-SQUARE AND CONTINGENCY TABLE ANALYSIS 90 8 LEARNING FROM POPULATIONS: CENSUSES AND SAMPLES 102 9 CORRELATION 127 10 REGRESSION 146 11 CAUSATION 162 PART III WHEEL OF SCIENCE: DESIGNS OF RESEARCH 203 12 SURVEY RESEARCH 205 13 AGGREGATE RESEARCH 234 14 EXPERIMENTS 251 15 STATISTICAL METHODS OF DIFFERENCE: T TEST 270 16 ANALYSIS OF VARIANCE 280 17 FIELD RESEARCH 301 18 CONTENT ANALYSIS 316 PART IV STATISTICS AND DATA MANAGEMENT 327 STATISTICAL PROCEDURES UNIT A: WRITING THE STATISTICAL RESEARCH SUMMARY 329 STATISTICAL PROCEDURES UNIT B: THE NATURE OF INFERENTIAL STATISTICS 333 DATA MANAGEMENT UNIT A: USE AND FUNCTIONS OF SPSS 343 DATA MANAGEMENT UNIT B: USING SPSS TO RECODE FOR T TEST 357 DATA MANAGEMENT UNIT C: DESCRIPTIVE STATISTICS 364 STATISTICAL PROCEDURES UNIT C: Z SCORES 389 Glossary 397 Bibliography 411 Index 416

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Book SynopsisThe mathematical and statistical tools needed in the rapidly growing quantitative finance field With the rapid growth in quantitative finance, practitioners must achieve a high level of proficiency in math and statistics. Mathematical Methods and Statistical Tools for Finance, part of the Frank J.Table of ContentsPreface xi About the Authors xvii CHAPTER 1 Basic Concepts: Sets, Functions, and Variables 1 Introduction 2 Sets and Set Operations 2 Distances and Quantities 6 Functions 10 Variables 10 Key Points 11 CHAPTER 2 Differential Calculus 13 Introduction 14 Limits 15 Continuity 17 Total Variation 19 The Notion of Differentiation 19 Commonly Used Rules for Computing Derivatives 21 Higher-Order Derivatives 26 Taylor Series Expansion 34 Calculus in More Than One Variable 40 Key Points 41 CHAPTER 3 Integral Calculus 43 Introduction 44 Riemann Integrals 44 Lebesgue-Stieltjes Integrals 47 Indefinite and Improper Integrals 48 The Fundamental Theorem of Calculus 51 Integral Transforms 52 Calculus in More Than One Variable 57 Key Points 57 CHAPTER 4 Matrix Algebra 59 Introduction 60 Vectors and Matrices Defined 61 Square Matrices 63 Determinants 66 Systems of Linear Equations 68 Linear Independence and Rank 69 Hankel Matrix 70 Vector and Matrix Operations 72 Finance Application 78 Eigenvalues and Eigenvectors 81 Diagonalization and Similarity 82 Singular Value Decomposition 83 Key Points 83 CHAPTER 5 Probability: Basic Concepts 85 Introduction 86 Representing Uncertainty with Mathematics 87 Probability in a Nutshell 89 Outcomes and Events 91 Probability 92 Measure 93 Random Variables 93 Integrals 94 Distributions and Distribution Functions 96 Random Vectors 97 Stochastic Processes 100 Probabilistic Representation of Financial Markets 102 Information Structures 103 Filtration 104 Key Points 106 CHAPTER 6 Probability: Random Variables and Expectations 107 Introduction 109 Conditional Probability and Conditional Expectation 110 Moments and Correlation 112 Copula Functions 114 Sequences of Random Variables 116 Independent and Identically Distributed Sequences 117 Sum of Variables 118 Gaussian Variables 120 Appproximating the Tails of a Probability Distribution: Cornish-Fisher Expansion and Hermite Polynomials 123 The Regression Function 129 Fat Tails and Stable Laws 131 Key Points 144 CHAPTER 7 Optimization 147 Introduction 148 Maxima and Minima 149 Lagrange Multipliers 151 Numerical Algorithms 156 Calculus of Variations and Optimal Control Theory 161 Stochastic Programming 163 Application to Bond Portfolio: Liability-Funding Strategies 164 Key Points 178 CHAPTER 8 Difference Equations 181 Introduction 182 The Lag Operator L 183 Homogeneous Difference Equations 183 Recursive Calculation of Values of Difference Equations 192 Nonhomogeneous Difference Equations 195 Systems of Linear Difference Equations 201 Systems of Homogeneous Linear Difference Equations 202 Key Points 209 CHAPTER 9 Differential Equations 211 Introduction 212 Differential Equations Defined 213 Ordinary Differential Equations 213 Systems of Ordinary Differential Equations 216 Closed-Form Solutions of Ordinary Differential Equations 218 Numerical Solutions of Ordinary Differential Equations 222 Nonlinear Dynamics and Chaos 228 Partial Differential Equations 231 Key Points 237 CHAPTER 10 Stochastic Integrals 239 Introduction 240 The Intuition behind Stochastic Integrals 243 Brownian Motion Defined 248 Properties of Brownian Motion 254 Stochastic Integrals Defined 255 Some Properties of Itoˆ Stochastic Integrals 259 Martingale Measures and the Girsanov Theorem 260 Key Points 266 CHAPTER 11 Stochastic Differential Equations 267 Introduction 268 The Intuition behind Stochastic Differential Equations 269 Itoˆ Processes 272 Stochastic Differential Equations 273 Generalization to Several Dimensions 276 Solution of Stochastic Differential Equations 278 Derivation of Itoˆ ’s Lemma 282 Derivation of the Black-Scholes Option Pricing Formula 284 Key Points 291 Index 293

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Book SynopsisA comprehensive and accessible introduction to modern quantitative risk management. The business world is rife with risk and uncertainty, and risk management is a vitally important topic for managers. The best way to achieve a clear understanding of risk is to use quantitative tools and probability models.Table of ContentsPreface xiii 1 What is risk management? 1 1.1 Introduction 2 1.2 Identifying and documenting risk 5 1.3 Fallacies and traps in risk management 7 1.4 Why safety is different 9 1.5 The Basel framework 11 1.6 Hold or hedge? 12 1.7 Learning from a disaster 13 Notes 17 References 18 Exercises 19 2 The structure of risk 22 2.1 Introduction to probability and risk 23 2.2 The structure of risk 25 2.3 Portfolios and diversification 30 2.4 The impact of correlation 40 2.5 Using copulas to model multivariate distributions 49 Notes 58 References 59 Exercises 60 3 Measuring risk 63 3.1 How can we measure risk? 64 3.2 Value at risk 67 3.3 Combining and comparing risks 73 3.4 VaR in practice 76 3.5 Criticisms of VaR 79 3.6 Beyond value at risk 82 Notes 88 References 88 Exercises 89 4 Understanding the tails 92 4.1 Heavy-tailed distributions 93 4.2 Limiting distributions for the maximum 100 4.3 Excess distributions 109 4.4 Estimation using extreme value theory 115 Notes 121 References 122 Exercises 123 5 Making decisions under uncertainty 125 5.1 Decisions, states and outcomes 126 5.2 Expected Utility Theory 130 5.3 Stochastic dominance and risk profiles 148 5.4 Risk decisions for managers 156 Notes 160 References 161 Exercises 162 6 Understanding risk behavior 164 6.1 Why decision theory fails 165 6.2 Prospect Theory 172 6.3 Cumulative Prospect Theory 180 6.4 Decisions with ambiguity 189 6.5 How managers treat risk 191 Notes 194 References 194 Exercises 195 7 Stochastic optimization 198 7.1 Introduction to stochastic optimization 199 7.2 Choosing scenarios 212 7.3 Multistage stochastic optimization 218 7.4 Value at risk constraints 224 Notes 228 References 228 Exercises 229 8 Robust optimization 232 8.1 True uncertainty: Beyond probabilities 233 8.2 Avoiding disaster when there is uncertainty 234 8.3 Robust optimization and the minimax approach 250 Notes 261 References 262 Exercises 263 9 Real options 265 9.1 Introduction to real options 266 9.2 Calculating values with real options 267 9.3 Combining real options and net present value 273 9.4 The connection with financial options 278 9.5 Using Monte Carlo simulation to value real options 282 9.6 Some potential problems with the use of real options 285 Notes 287 References 287 Exercises 288 10 Credit risk 291 10.1 Introduction to credit risk 292 10.2 Using credit scores for credit risk 294 10.3 Consumer credit 301 10.4 Logistic regression 308 Notes 317 References 318 Exercises 319 Appendix A Tutorial on probability theory 323 A.1 Random events 323 A.2 Bayes’ rule and independence 326 A.3 Random variables 327 A.4 Means and variances 329 A.5 Combinations of random variables 332 A.6 The normal distribution and the Central Limit Theorem 336 Appendix B Answers to even-numbered exercises 340 Index 361

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Book SynopsisReflecting the fast pace and ever-evolving nature of the financial industry, the Handbook of High-Frequency Trading and Modeling in Finance details how high-frequency analysis presents new systematic approaches to implementing quantitative activities with high-frequency financial data. Introducing new and established mathematical foundations necessary to analyze realistic market models and scenarios, the handbook begins with a presentation of the dynamics and complexity of futures and derivatives markets as well as a portfolio optimization problem using quantum computers. Subsequently, the handbook addresses estimating complex model parameters using high-frequency data. Finally, the handbook focuses on the links between models used in financial markets and models used in other research areas such as geophysics, fossil records, and earthquake studies. The Handbook of High-Frequency Trading and Modeling in Finance also features: Contributions by well-knownTable of ContentsNotes on Contributors xiii Preface xv 1 Trends and Trades 1Michael Carlisle, Olympia Hadjiliadis, and Ioannis Stamos 1.1 Introduction 1 1.2 A trend-based trading strategy 3 1.2.1 Signaling and trends 3 1.2.2 Gain over a subperiod 5 1.3 CUSUM timing 7 1.3.1 Cusum process and stopping time 7 1.3.2 A CUSUM timing scheme 10 1.3.3 US treasury notes, CUSUM timing 11 1.4 Example: Random walk on ticks 12 1.4.1 Random walk expected gain over a subperiod 15 1.4.2 Simple random walk, CUSUM timing 18 1.4.3 Lazy simple random walk, cusum timing 21 1.5 CUSUM strategy Monte Carlo 24 1.6 The effect of the threshold parameter 27 1.7 Conclusions and future work 39 Appendix: Tables 40 References 47 2 Gaussian Inequalities and Tranche Sensitivities 51Claas Becker and Ambar N. Sengupta 2.1 Introduction 51 2.2 The tranche loss function 52 2.3 A sensitivity identity 54 2.4 Correlation sensitivities 55 Acknowledgment 58 References 58 3 A Nonlinear Lead Lag Dependence Analysis of Energy Futures: Oil, Coal, and Natural Gas 61Germán G. Creamer and Bernardo Creamer 3.1 Introduction 61 3.1.1 Causality analysis 62 3.2 Data 64 3.3 Estimation techniques 64 3.4 Results 65 3.5 Discussion 67 3.6 Conclusions 69 Acknowledgments 69 References 70 4 Portfolio Optimization: Applications in Quantum Computing 73Michael Marzec 4.1 Introduction 73 4.2 Background 75 4.2.1 Portfolios and optimization 76 4.2.2 Algorithmic complexity 77 4.2.3 Performance 78 4.2.4 Ising model 79 4.2.5 Adiabatic quantum computing 79 4.3 The models 80 4.3.1 Financial model 81 4.3.2 Graph-theoretic combinatorial optimization models 82 4.3.3 Ising and Qubo models 83 4.3.4 Mixed models 84 4.4 Methods 84 4.4.1 Model implementation 85 4.4.2 Input data 85 4.4.3 Mean-variance calculations 85 4.4.4 Implementing the risk measure 86 4.4.5 Implementation mapping 86 4.5 Results 88 4.5.1 The simple correlation model 88 4.5.2 The restricted minimum-risk model 91 4.5.3 The WMIS minimum-risk, max return model 94 4.6 Discussion 95 4.6.1 Hardware limitations 97 4.6.2 Model limitations 97 4.6.3 Implementation limitations 98 4.6.4 Future research 98 4.7 Conclusion 100 Acknowledgments 100 Appendix 4.A: WMIS Matlab Code 100 References 103 5 Estimation Procedure for Regime Switching Stochastic Volatility Model and Its Applications 107Ionut Florescu and Forrest Levin 5.1 Introduction 107 5.1.1 The original motivation 108 5.1.2 The model and the problem 108 5.1.3 A brief historical note 109 5.2 The methodology 110 5.2.1 Obtaining filtered empirical distributions at t1,…, tT 110 5.2.2 Obtaining the parameters of the Markov chain 112 5.3 Results obtained applying the model to real data 113 5.3.1 Part i: financial applications 113 5.3.2 Part ii: physical data application. temperature data 119 5.3.3 Part iii: analysis of seismometer readings during an earthquake 121 5.3.4 Analysis of the earthquake signal: beginning 123 5.3.5 Analysis: during the earthquake 125 5.3.6 Analysis: end of the earthquake signal, aftershocks 127 5.4 Conclusion 127 5.A Theoretical results and empirical testing 128 5.A.1 How does the particle filter work? 128 5.A.2 Theoretical results about convergence and parameter estimates 129 5.A.3 Markov chain parameter estimates 131 5.A.4 Empirical testing 132 5.A.5 A list of supplementary documents 133 References 133 6 Detecting Jumps in High-Frequency Prices Under Stochastic Volatility: A Review and a Data-Driven Approach 137Ping-Chen Tsai and Mark B. Shackleton 6.1 Introduction 137 6.2 Review on the intraday jump tests 140 6.2.1 Realized volatility measure and the BNS tests 140 6.2.2 The ABD and LM tests 142 6.3 A data-driven testing procedure 146 6.3.1 Spy data and microstructure noise 146 6.3.2 A generalized testing procedure 149 6.4 Simulation study 153 6.4.1 Model specification 153 6.4.2 Simulation results 158 6.5 Empirical results 161 6.5.1 Results on the backward-looking test 162 6.5.2 Results on the interpolated test 165 6.6 Conclusion 165 Acknowledgments 166 Appendix 6.A: Least-square estimation of HAR-MA (2) model for log(BP) of SPY 167 Appendix 6.B: Estimation of ARMA (2, 1) model for log(BP) of SPY 168 Appendix 6.C: Minimized loss function loss(𝜌1, 𝜌2) for SV2FJ_2𝜌 model, SPY 169 Appendix 6.D.1: Calibration of 𝜉 under SV2FJ_2𝜌 model at 2-min frequency, E[Nt] = 0.08 170 Appendix 6.D.2: Calibration of 𝜉 under SV2FJ_2𝜌 model at 2-min frequency, E[Nt] = 0.40 171 Appendix 6.D.3: Calibration of 𝜉 under SV2FJ_2𝜌 model at 5-min frequency, E[Nt] = 0.08 172 Appendix 6.D.4: Calibration of 𝜉 under SV2FJ_2𝜌 Model at 5-min frequency, E[Nt] = 0.40 173 Appendix 6.D.5: Calibration of 𝜉 under SV2FJ_2𝜌 model at 10-min frequency, E[Nt] = 0.08 174 Appendix 6.D.6: Calibration of 𝜉 under SV2FJ_2𝜌 model at 10-min frequency, E[Nt] = 0.40 175 References 175 7 Hawkes Processes and Their Applications to High-Frequency Data Modeling 183Baron Law and Frederi G. Viens 7.1 Introduction 183 7.2 Point processes 184 7.3 Hawkes processes 186 7.3.1 Branching structure representation 188 7.3.2 Stationarity 188 7.3.3 Convergence 189 7.4 Statistical inference of Hawkes processes 191 7.4.1 Simulation 191 7.4.2 Estimation 194 7.4.3 Hypothesis testing 197 7.5 Applications of Hawkes processes 198 7.5.1 Modeling order arrivals 199 7.5.2 Modeling price jumps 200 7.5.3 Modeling jump-diffusion 205 7.5.4 Measuring endogeneity (Reflexivity) 205 Appendix 7.A: Point Processes 207 7.A.1 Definition 207 7.A.2 Moments 208 7.A.3 Marked point processes 209 7.A.4 Stochastic intensity 209 7.A.5 Random time change 211 Appendix 7.B: A Brief History of Hawkes processes 211 References 212 8 Multifractal Random Walk Driven by a Hermite Process 221Alexis Fauth and Ciprian A. Tudor 8.1 Introduction 221 8.2 Preliminaries 224 8.2.1 Fractional brownian motion and hermite processes 224 8.2.2 Wiener integrals with respect to the hermite process 226 8.2.3 Infinitely divisible cascading noise 229 8.3 Multifractal random walk driven by a Hermite process 231 8.3.1 Definition and existence 231 8.3.2 Properties of the hermite multifractal random walk 233 8.4 Financial applications 234 8.4.1 Simulation of the Hmrw 235 8.4.2 Financial statistics 241 8.5 Concluding remarks 243 References 247 9 Interpolating Techniques and Nonparametric Regression Methods Applied to Geophysical and Financial Data Analysis 251K. Basu and Maria C. Mariani 9.1 Introduction 251 9.2 Nonparametric regression models 253 9.2.1 Local polynomial regression 255 9.2.2 Lowess/loess method 257 9.2.3 Numerical applications 259 9.3 Interpolation methods 271 9.3.1 Nearest-neighbor interpolation 271 9.3.2 Bilinear interpolation 272 9.3.3 Bicubic interpolation 276 9.3.4 Biharmonic interpolation 277 9.3.5 Thin plate splines 282 9.3.6 Numerical applications 285 9.4 Conclusion 287 Acknowledgments 292 References 292 10 Study of Volatility Structures in Geophysics and Finance Using Garch Models 295Maria C. Mariani, F. Biney, and I. SenGupta 10.1 Introduction 295 10.2 Short memory models 297 10.2.1 ARMA(p,q) model 297 10.2.2 GARCH(p,q) model 297 10.2.3 IGARCH(1,1) model 298 10.3 Long memory models 298 10.3.1 ARFIMA(p,d,q) model 299 10.3.2 ARFIMA(p,d,q)-GARCH(r,s) 299 10.3.3 Intermediate memory process 300 10.3.4 Figarch model 300 10.4 Detection and estimation of long memory 302 10.4.1 Augmented dickey–fuller test(ADF test) 302 10.4.2 KPSS test 303 10.4.3 Whittle method 304 10.5 Data collection, analysis, and result 306 10.5.1 Analysis on dow Jones index (DJIA) returns 306 10.5.2 Model selection and specification: conditional mean 306 10.5.3 Conditional mean model (returns) 309 10.5.4 Model diagnostics: ARMA(2, 2) 309 10.5.5 Test for ARCH effect 311 10.5.6 Model selection and specification: Conditional variance 313 10.5.7 Standardized residuals test 314 10.5.8 Model diagnostics 314 10.5.9 Returns and variance equation 315 10.5.10 standardized residuals test 317 10.5.11 Model diagnostic of conditional returns with conditional variance 318 10.5.12 One-step ahead prediction of last 10 observations 330 10.5.13 Analysis on high-frequency, earthquake, and explosives series 330 10.6 Discussion and conclusion 335 References 337 11 Scale Invariance and Lévy Models Applied to Earthquakes and Financial High-Frequency Data 341M. P. Beccar-Varela, Ionut Florescu, and I. SenGupta 11.1 Introduction 341 11.2 Governing equations for the deterministic model 342 11.2.1 Application to geophysical (earthquake data) 343 11.2.2 Results 344 11.3 L´evy flights and application to geophysics 345 11.3.1 Truncated L´evy flight distribution 353 11.3.2 Results 356 11.4 Application to the high-frequency market data 360 11.4.1 Methodology 360 11.4.2 Results 361 11.5 Brief program code description 362 11.6 Conclusion 364 11.A Appendix 366 11.A.1 Stable distributions 366 11.A.2 Characterization of stable distributions 367 References 368 12 Analysis of Generic Diversity in the Fossil Record, Earthquake Series, and High-Frequency Financial Data 371M. P. Beccar Varela, F. Biney, Maria C. Mariani, I. SenGupta, M. Shpak, and P. Bezdek 12.1 Introduction 371 12.2 Statistical preliminaries and results 373 12.2.1 Sum of exponential random variables with different parameters 374 12.3 Statistical and numerical analysis 377 12.4 Analysis with Lévy distribution 380 12.4.1 Characterization of Stable Distributions 383 12.4.2 Truncated Lévy flight (TLF) distribution 384 12.4.3 Data analysis with TLF distribution 389 12.4.4 Sum of Lévy random variables with different parameters 390 12.5 Analysis of the Stock Indices, high-frequency (tick) data, and explosive series 394 12.6 Results and discussion 409 Acknowledgments 421 12.A Appendix A—Big ‘O’ notation 421 References 422 Index 425

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Book SynopsisTable of ContentsForeword by A.G. MALLIARIS, Loyola University, Chicago xi Main Notations xiii Introduction xv PART I THE DETERMINISTIC ENVIRONMENT 1 Prior to the Yield Curve: Spot and Forward Rates 3 2 The Term Structure or Yield Curve 13 3 Spot Instruments 23 4 Equities and Stock Indexes 47 5 Forward Instruments 75 6 Swaps 91 7 Futures 119 PART II THE PROBABILISTIC ENVIRONMENT 8 The Basis of Stochastic Calculus 147 9 Other Financial Models: From ARMA to the GARCH Family 165 10 Option Pricing in General 175 11 Options on Specific Underlyings and Exotic Options 209 12 Volatility and Volatility Derivatives 237 13 Credit Derivatives 257 14 Market Performance and Risk Measures 275 15 Beyond the Gaussian Hypothesis: Potential Troubles with Derivatives Valuation 303 Bibliography 319 Index 323

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Book SynopsisProviding an explanation of the fundamentals, methods, and applications of chemometrics, this title acts as a practical guide to multivariate data analysis techniques. It explains the methods used in Chemometrics and teaches the reader to perform all relevant calculations. It presents the basic chemometric methods as worksheet functions in Excel.Trade Review“The book is for sure very interesting and very well written, and it covers all the major topics of chemometrics.” (Journal of Chemometrics, 14 July 2015) Table of ContentsPreface xvii PART I INTRODUCTION 1 1 What is Chemometrics? 3 1.1 Subject of Chemometrics, 3 1.2 Historical Digression, 5 2 What the Book Is About? 8 2.1 Useful Hints, 8 2.2 Book Syllabus, 9 2.3 Notations, 10 3 Installation of Chemometrics Add-In 11 3.1 Installation, 11 3.2 General Information, 14 4 Further Reading on Chemometrics 15 4.1 Books, 15 4.1.1 The Basics, 15 4.1.2 Chemometrics, 16 4.1.3 Supplements, 16 4.2 The Internet, 17 4.2.1 Tutorials, 17 4.3 Journals, 17 4.3.1 Chemometrics, 17 4.3.2 Analytical, 18 4.3.3 Mathematical, 18 4.4 Software, 18 4.4.1 Specialized Packages, 18 4.4.2 General Statistic Packages, 19 4.4.3 Free Ware, 19 PART II THE BASICS 21 5 Matrices and Vectors 23 5.1 The Basics, 23 5.1.1 Matrix, 23 5.1.2 Simple Matrix Operations, 24 5.1.3 Matrices Multiplication, 25 5.1.4 Square Matrix, 26 5.1.5 Trace and Determinant, 27 5.1.6 Vectors, 28 5.1.7 Simple Vector Operations, 29 5.1.8 Vector Products, 29 5.1.9 Vector Norm, 30 5.1.10 Angle Between Vectors, 30 5.1.11 Vector Representation of a Matrix, 30 5.1.12 Linearly Dependent Vectors, 31 5.1.13 Matrix Rank, 31 5.1.14 Inverse Matrix, 31 5.1.15 Pseudoinverse, 32 5.1.16 Matrix–Vector Product, 33 5.2 Advanced Information, 33 5.2.1 Systems of Linear Equations, 33 5.2.2 Bilinear and Quadratic Forms, 34 5.2.3 Positive Definite Matrix, 34 5.2.4 Cholesky Decomposition, 34 5.2.5 Polar Decomposition, 34 5.2.6 Eigenvalues and Eigenvectors, 35 5.2.7 Eigenvalues, 35 5.2.8 Eigenvectors, 35 5.2.9 Equivalence and Similarity, 36 5.2.10 Diagonalization, 37 5.2.11 Singular Value Decomposition (SVD), 37 5.2.12 Vector Space, 38 5.2.13 Space Basis, 39 5.2.14 Geometric Interpretation, 39 5.2.15 Nonuniqueness of Basis, 39 5.2.16 Subspace, 40 5.2.17 Projection, 40 6 Statistics 42 6.1 The Basics, 42 6.1.1 Probability, 42 6.1.2 Random Value, 43 6.1.3 Distribution Function, 43 6.1.4 Mathematical Expectation, 44 6.1.5 Variance and Standard Deviation, 44 6.1.6 Moments, 44 6.1.7 Quantiles, 45 6.1.8 Multivariate Distributions, 45 6.1.9 Covariance and Correlation, 45 6.1.10 Function, 46 6.1.11 Standardization, 46 6.2 Main Distributions, 46 6.2.1 Binomial Distribution, 46 6.2.2 Uniform Distribution, 47 6.2.3 Normal Distribution, 48 6.2.4 Chi-Squared Distribution, 50 6.2.5 Student’s Distribution, 52 6.2.6 F-Distribution, 53 6.2.7 Multivariate Normal Distribution, 54 6.2.8 Pseudorandom Numbers, 55 6.3 Parameter Estimation, 56 6.3.1 Sample, 56 6.3.2 Outliers and Extremes, 56 6.3.3 Statistical Population, 56 6.3.4 Statistics, 57 6.3.5 Sample Mean and Variance, 57 6.3.6 Sample Covariance and Correlation, 58 6.3.7 Order Statistics, 59 6.3.8 Empirical Distribution and Histogram, 60 6.3.9 Method of Moments, 61 6.3.10 The Maximum Likelihood Method, 62 6.4 Properties of the Estimators, 62 6.4.1 Consistency, 62 6.4.2 Bias, 63 6.4.3 Effectiveness, 63 6.4.4 Robustness, 63 6.4.5 Normal Sample, 64 6.5 Confidence Estimation, 64 6.5.1 Confidence Region, 64 6.5.2 Confidence Interval, 65 6.5.3 Example of a Confidence Interval, 65 6.5.4 Confidence Intervals for the Normal Distribution, 65 6.6 Hypothesis Testing, 66 6.6.1 Hypothesis, 66 6.6.2 Hypothesis Testing, 66 6.6.3 Type I and Type II Errors, 67 6.6.4 Example, 67 6.6.5 Pearson’s Chi-Squared Test, 67 6.6.6 F-Test, 69 6.7 Regression, 70 6.7.1 Simple Regression, 70 6.7.2 The Least Squares Method, 71 6.7.3 Multiple Regression, 72 Conclusion, 73 7 Matrix Calculations in Excel 74 7.1 Basic Information, 74 7.1.1 Region and Language, 74 7.1.2 Workbook, Worksheet, and Cell, 76 7.1.3 Addressing, 77 7.1.4 Range, 78 7.1.5 Simple Calculations, 78 7.1.6 Functions, 78 7.1.7 Important Functions, 81 7.1.8 Errors in Formulas, 85 7.1.9 Formula Dragging, 86 7.1.10 Create a Chart, 87 7.2 Matrix Operations, 88 7.2.1 Array Formulas, 88 7.2.2 Creating and Editing an Array Formula, 90 7.2.3 Simplest Matrix Operations, 91 7.2.4 Access to the Part of a Matrix, 91 7.2.5 Unary Operations, 93 7.2.6 Binary Operations, 95 7.2.7 Regression, 95 7.2.8 Critical Bug in Excel 2003, 99 7.2.9 Virtual Array, 99 7.3 Extension of Excel Possibilities, 100 7.3.1 VBA Programming, 100 7.3.2 Example, 101 7.3.3 Macro Example, 103 7.3.4 User-Defined Function Example, 104 7.3.5 Add-Ins, 105 7.3.6 Add-In Installation, 106 Conclusion, 107 8 Projection Methods in Excel 108 8.1 Projection Methods, 108 8.1.1 Concept and Notation, 108 8.1.2 PCA, 109 8.1.3 PLS, 110 8.1.4 Data Preprocessing, 111 8.1.5 Didactic Example, 112 8.2 Application of Chemometrics Add-In, 113 8.2.1 Installation, 113 8.2.2 General, 113 8.3 PCA, 114 8.3.1 ScoresPCA, 114 8.3.2 LoadingsPCA, 114 8.4 PLS, 116 8.4.1 ScoresPLS, 116 8.4.2 UScoresPLS, 117 8.4.3 LoadingsPLS, 118 8.4.4 WLoadingsPLS, 119 8.4.5 QLoadingsPLS, 120 8.5 PLS2, 121 8.5.1 ScoresPLS2, 121 8.5.2 UScoresPLS2, 122 8.5.3 LoadingsPLS2, 124 8.5.4 WLoadingsPLS2, 125 8.5.5 QLoadingsPLS2, 126 8.6 Additional Functions, 127 8.6.1 MIdent, 127 8.6.2 MIdentD2, 127 8.6.3 MCutRows, 129 8.6.4 MTrace, 129 Conclusion, 130 PART IIICHEMOMETRICS 131 9 Principal Component Analysis (PCA) 133 9.1 The Basics, 133 9.1.1 Data, 133 9.1.2 Intuitive Approach, 134 9.1.3 Dimensionality Reduction, 136 9.2 Principal Component Analysis, 136 9.2.1 Formal Specifications, 136 9.2.2 Algorithm, 137 9.2.3 PCA and SVD, 137 9.2.4 Scores, 138 9.2.5 Loadings, 139 9.2.6 Data of Special Kind, 140 9.2.7 Errors, 140 9.2.8 Validation, 143 9.2.9 Decomposition “Quality”, 143 9.2.10 Number of Principal Components, 144 9.2.11 The Ambiguity of PCA, 145 9.2.12 Data Preprocessing, 146 9.2.13 Leverage and Deviation, 146 9.3 People and Countries, 146 9.3.1 Example, 146 9.3.2 Data, 147 9.3.3 Data Exploration, 147 9.3.4 Data Pretreatment, 148 9.3.5 Scores and Loadings Calculation, 149 9.3.6 Scores Plots, 151 9.3.7 Loadings Plot, 152 9.3.8 Analysis of Residuals, 153 Conclusion, 153 10 Calibration 156 10.1 The Basics, 156 10.1.1 Problem Statement, 156 10.1.2 Linear and Nonlinear Calibration, 157 10.1.3 Calibration and Validation, 158 10.1.4 Calibration “Quality”, 160 10.1.5 Uncertainty, Precision, and Accuracy, 162 10.1.6 Underfitting and Overfitting, 163 10.1.7 Multicollinearity, 164 10.1.8 Data Preprocessing, 166 10.2 Simulated Data, 166 10.2.1 The Principle of Linearity, 166 10.2.2 “Pure” Spectra, 166 10.2.3 “Standard” Samples, 166 10.2.4 X Data Creation, 167 10.2.5 Data Centering, 168 10.2.6 Data Overview, 168 10.3 Classic Calibration, 169 10.3.1 Univariate (Single Channel) Calibration, 169 10.3.2 The Vierordt Method, 172 10.3.3 Indirect Calibration, 174 10.4 Inverse Calibration, 176 10.4.1 Multiple Linear Calibration, 177 10.4.2 Stepwise Calibration, 178 10.5 Latent Variables Calibration, 180 10.5.1 Projection Methods, 180 10.5.2 Latent Variables Regression, 184 10.5.3 Implementation of Latent Variable Calibration, 185 10.5.4 Principal Component Regression (PCR), 186 10.5.5 Projection on the Latent Structures-1 (PLS1), 188 10.5.6 Projection on the Latent Structures-2 (PLS2), 191 10.6 Methods Comparison, 193 Conclusion, 197 11 Classification 198 11.1 The Basics, 198 11.1.1 Problem Statement, 198 11.1.2 Types of Classes, 199 11.1.3 Hypothesis Testing, 199 11.1.4 Errors in Classification, 200 11.1.5 One-Class Classification, 200 11.1.6 Training and Validation, 201 11.1.7 Supervised and Unsupervised Training, 201 11.1.8 The Curse of Dimensionality, 201 11.1.9 Data Preprocessing, 201 11.2 Data, 202 11.2.1 Example, 202 11.2.2 Data Subsets, 203 11.2.3 Workbook Iris.xls, 204 11.2.4 Principal Component Analysis, 205 11.3 Supervised Classification, 205 11.3.1 Linear Discriminant Analysis (LDA), 205 11.3.2 Quadratic Discriminant Analysis (QDA), 210 11.3.3 PLS Discriminant Analysis (PLSDA), 214 11.3.4 SIMCA, 217 11.3.5 k-Nearest Neighbors (kNN), 223 11.4 Unsupervised Classification, 225 11.4.1 PCA Again (Revisited), 225 11.4.2 Clustering by K-Means, 225 Conclusion, 229 12 Multivariate Curve Resolution 230 12.1 The Basics, 230 12.1.1 Problem Statement, 230 12.1.2 Solution Ambiguity, 232 12.1.3 Solvability Conditions, 234 12.1.4 Two Types of Data, 235 12.1.5 Known Spectrum or Profile, 236 12.1.6 Principal Component Analysis (PCA), 236 12.1.7 PCA and MCR, 237 12.2 Simulated Data, 237 12.2.1 Example, 237 12.2.2 Data, 238 12.2.3 PCA, 238 12.2.4 The HELP Plot, 240 12.3 Factor Analysis, 241 12.3.1 Procrustes Analysis, 241 12.3.2 Evolving Factor Analysis (EFA), 244 12.3.3 Windows Factor Analysis (WFA), 246 12.4 Iterative Methods, 249 12.4.1 Iterative Target Transform Factor Analysis (ITTFA), 249 12.4.2 Alternating Least Squares (ALS), 250 Conclusion, 252 PART IV SUPPLEMENTS 255 13 Extension Of Chemometrics Add-In 257 13.1 Using Virtual Arrays, 257 13.1.1 Simulated Data, 257 13.1.2 Virtual Array, 259 13.1.3 Data Preprocessing, 259 13.1.4 Decomposition, 260 13.1.5 Residuals Calculation, 260 13.1.6 Eigenvalues Calculation, 262 13.1.7 Orthogonal Distances Calculation, 263 13.1.8 Leverages Calculation, 264 13.2 Using VBA Programming, 265 13.2.1 VBA Advantages, 265 13.2.2 Virtualization of Real Arrays, 265 13.2.3 Data Preprocessing, 266 13.2.4 Residuals Calculation, 267 13.2.5 Eigenvalues Calculation, 268 13.2.6 Orthogonal Distances Calculation, 269 13.2.7 Leverages Calculation, 270 Conclusion, 271 14 Kinetic Modeling of Spectral Data 272 14.1 The “Grey” Modeling Method, 272 14.1.1 Problem Statement, 272 14.1.2 Example, 274 14.1.3 Data, 274 14.1.4 Soft Method of Alternating Least Squares (Soft-ALS), 275 14.1.5 Hard Method of Alternating Least Squares (Hard-ALS), 277 14.1.6 Using Solver Add-In, 279 Conclusions, 282 15 MATLAB®: Beginner’s Guide 283 15.1 The Basics, 283 15.1.1 Workspace, 283 15.1.2 Basic Calculations, 285 15.1.3 Echo, 285 15.1.4 Workspace Saving: MAT-Files, 286 15.1.5 Diary, 286 15.1.6 Help, 287 15.2 Matrices, 287 15.2.1 Scalars, Vectors, and Matrices, 287 15.2.2 Accessing Matrix Elements, 289 15.2.3 Basic Matrix Operations, 289 15.2.4 Special Matrices, 290 15.2.5 Matrix Calculations, 292 15.3 Integrating Excel and MATLAB®, 294 15.3.1 Configuring Excel, 294 15.3.2 Data Exchange, 294 15.4 Programming, 295 15.4.1 M-Files, 295 15.4.2 Script File, 296 15.4.3 Function File, 297 15.4.4 Plotting, 298 15.4.5 Plot Printing, 300 15.5 Sample Programs, 301 15.5.1 Centering and Scaling, 301 15.5.2 SVD/PCA, 301 15.5.3 PCA/NIPALS, 302 15.5.4 PLS1, 303 15.5.5 PLS2, 304 Conclusion, 306 Afterword. The Fourth Paradigm 307 Index 311

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Book SynopsisWith big data analytics comes big insights into profitability Big data is big business. But having the data and the computational power to process it isn't nearly enough to produce meaningful results.Trade Reviewexplains what it covers very well (ZDNet, September 2014)Table of ContentsForward xiii Preface xv Acknowledgments xix Introduction 1 Big Data Timeline 5 Why This Topic is Relevant Now 8 Is Big Data a Fad? 9 Where Using Big Data Makes a Big Difference 12 Part One The Computing Environment 23 Chapter 1 Hardware 27 Storage (Disk) 27 Central Processing Unit 29 Memory 31 Network 33 Chapter 2 Distributed Systems 35 Database Computing 36 File System Computing 37 Considerations 39 Chapter 3 Analytical Tools 43 Weka 43 Java and JVM Languages 44 R 47 Python 49 SAS 50 Part Two Turning Data into Business Value 53 Chapter 4 Predictive Modeling 55 A Methodology for Building Models 58 sEMMA 61 Binary Classifi cation 64 Multilevel Classifi cation 66 Interval Prediction 66 Assessment of Predictive Models 67 Chapter 5 Common Predictive Modeling Techniques 71 RFM 72 Regression 75 Generalized Linear Models 84 Neural Networks 90 Decision and Regression Trees 101 Support Vector Machines 107 Bayesian Methods Network Classifi cation 113 Ensemble Methods 124 Chapter 6 Segmentation 127 Cluster Analysis 132 Distance Measures (Metrics) 133 Evaluating Clustering 134 Number of Clusters 135 K‐means Algorithm 137 Hierarchical Clustering 138 Profi ling Clusters 138 Chapter 7 Incremental Response Modeling 141 Building the Response Model 142 Measuring the Incremental Response 143 Chapter 8 Time Series Data Mining 149 Reducing Dimensionality 150 Detecting Patterns 151 Time Series Data Mining in Action: Nike+ FuelBand 154 Chapter 9 Recommendation Systems 163 What Are Recommendation Systems? 163 Where Are They Used? 164 How Do They Work? 165 Assessing Recommendation Quality 170 Recommendations in Action: SAS Library 171 Chapter 10 Text Analytics 175 Information Retrieval 176 Content Categorization 177 Text Mining 178 Text Analytics in Action: Let’s Play Jeopardy! 180 Part Three Success Stories of Putting It All Together 193 Chapter 11 Case Study of a Large U.S.‐Based Financial Services Company 197 Traditional Marketing Campaign Process 198 High‐Performance Marketing Solution 202 Value Proposition for Change 203 Chapter 12 Case Study of a Major Health Care Provider 205 CAHPS 207 HEDIS 207 HOS 208 IRE 208 Chapter 13 Case Study of a Technology Manufacturer 215 Finding Defective Devices 215 How They Reduced Cost 216 Chapter 14 Case Study of Online Brand Management 221 Chapter 15 Case Study of Mobile Application Recommendations 225 Chapter 16 Case Study of a High‐Tech Product Manufacturer 229 Handling the Missing Data 230 Application beyond Manufacturing 231 Chapter 17 Looking to the Future 233 Reproducible Research 234 Privacy with Public Data Sets 234 The Internet of Things 236 Software Development in the Future 237 Future Development of Algorithms 238 In Conclusion 241 About the Author 243 Appendix 245 References 247 Index 253

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Book SynopsisPraise for the First Edition This pioneering work, in which Rao provides a comprehensive and up-to-date treatment of small area estimation, will become a classic...I believe that it has the potential to turn small area estimation...into a larger area of importance to both researchers and practitioners.Journal of the American Statistical Association Written by two experts in the field, Small Area Estimation, Second Edition provides a comprehensive and up-to-date account of the methods and theory of small area estimation (SAE), particularly indirect estimation based on explicit small area linking models. The model-based approach to small area estimation offers several advantages including increased precision, the derivation of optimal estimates and associated measures of variability under an assumed model, and the validation of models from the sample data. Emphasizing real data throughout, the Second Edition maintaiTrade Review"The book is an excellent reference for practicing statisticians and survey methodologists as well as practitioners interested in learning SAE methods. The second edition is also an ideal textbook for graduate-level courses in SAE and reliable small area statistics." (Zentralblatt MATH, 2016)Table of ContentsList of Figures xv List of Tables xvii Foreword to the First Edition xix Preface to the Second Edition xxiii Preface to the First Edition xxvii 1 *Introduction 1 1.1 What is a Small Area? 1 1.2 Demand for Small Area Statistics 3 1.3 Traditional Indirect Estimators 4 1.4 Small Area Models 4 1.5 Model-Based Estimation 5 1.6 Some Examples 6 1.6.1 Health 6 1.6.2 Agriculture 7 1.6.3 Income for Small Places 8 1.6.4 Poverty Counts 8 1.6.5 Median Income of Four-Person Families 8 1.6.6 Poverty Mapping 8 2 Direct Domain Estimation 9 2.1 Introduction 9 2.2 Design-Based Approach 10 2.3 Estimation of Totals 11 2.3.1 Design-Unbiased Estimator 11 2.3.2 Generalized Regression Estimator 13 2.4 Domain Estimation 16 2.4.1 Case of No Auxiliary Information 16 2.4.2 GREG Domain Estimation 17 2.4.3 Domain-Specific Auxiliary Information 18 2.5 Modified GREG Estimator 21 2.6 Design Issues 23 2.6.1 Minimization of Clustering 24 2.6.2 Stratification 24 2.6.3 Sample Allocation 24 2.6.4 Integration of Surveys 25 2.6.5 Dual-Frame Surveys 25 2.6.6 Repeated Surveys 26 2.7 *Optimal Sample Allocation for Planned Domains 26 2.7.1 Case (i) 26 2.7.2 Case (ii) 29 2.7.3 Two-Way Stratification: Balanced Sampling 31 2.8 Proofs 32 2.8.1 Proof of ŶGR(𝐱) = 𝐗 32 2.8.2 Derivation of Calibration Weights 𝑤∗j 32 2.8.3 Proof of Y = X^T𝐁^when cj = 𝝂T𝐗j 32 3 Indirect Domain Estimation 35 3.1 Introduction 35 3.2 Synthetic Estimation 36 3.2.1 No Auxiliary Information 36 3.2.2 *Area Level Auxiliary Information 36 3.2.3 *Unit Level Auxiliary Information 37 3.2.4 Regression-Adjusted Synthetic Estimator 42 3.2.5 Estimation of MSE 43 3.2.6 Structure Preserving Estimation 45 3.2.7 *Generalized SPREE 49 3.2.8 *Weight-Sharing Methods 53 3.3 Composite Estimation 57 3.3.1 Optimal Estimator 57 3.3.2 Sample-Size-Dependent Estimators 59 3.4 James–Stein Method 63 3.4.1 Common Weight 63 3.4.2 Equal Variances 𝜓i = 𝜓 64 3.4.3 Estimation of Component MSE 68 3.4.4 Unequal Variances 𝜓i 70 3.4.5 Extensions 71 3.5 Proofs 71 4 Small Area Models 75 4.1 Introduction 75 4.2 Basic Area Level Model 76 4.3 Basic Unit Level Model 78 4.4 Extensions: Area Level Models 81 4.4.1 Multivariate Fay–Herriot Model 81 4.4.2 Model with Correlated Sampling Errors 82 4.4.3 Time Series and Cross-Sectional Models 83 4.4.4 *Spatial Models 86 4.4.5 Two-Fold Subarea Level Models 88 4.5 Extensions: Unit Level Models 88 4.5.1 Multivariate Nested Error Regression Model 88 4.5.2 Two-Fold Nested Error Regression Model 89 4.5.3 Two-Level Model 90 4.5.4 General Linear Mixed Model 91 4.6 Generalized Linear Mixed Models 92 4.6.1 Logistic Mixed Models 92 4.6.2 *Models for Multinomial Counts 93 4.6.3 Models for Mortality and Disease Rates 93 4.6.4 Natural Exponential Family Models 94 4.6.5 *Semi-parametric Mixed Models 95 5 Empirical Best Linear Unbiased Prediction (EBLUP): Theory 97 5.1 Introduction 97 5.2 General Linear Mixed Model 98 5.2.1 BLUP Estimator 98 5.2.2 MSE of BLUP 100 5.2.3 EBLUP Estimator 101 5.2.4 ML and REML Estimators 102 5.2.5 MSE of EBLUP 105 5.2.6 Estimation of MSE of EBLUP 106 5.3 Block Diagonal Covariance Structure 108 5.3.1 EBLUP Estimator 108 5.3.2 Estimation of MSE 109 5.3.3 Extension to Multidimensional Area Parameters 110 5.4 *Model Identification and Checking 111 5.4.1 Variable Selection 111 5.4.2 Model Diagnostics 114 5.5 *Software 118 5.6 Proofs 119 5.6.1 Derivation of BLUP 119 5.6.2 Equivalence of BLUP and Best Predictor E(𝐦T𝐯|𝐀T𝐲) 120 5.6.3 Derivation of MSE Decomposition (5.2.29) 121 6 Empirical Best Linear Unbiased Prediction (EBLUP): Basic Area Level Model 123 6.1 EBLUP Estimation 123 6.1.1 BLUP Estimator 124 6.1.2 Estimation of 𝜎2𝑣 126 6.1.3 Relative Efficiency of Estimators of 𝜎2𝑣 128 6.1.4 *Applications 129 6.2 MSE Estimation 136 6.2.1 Unconditional MSE of EBLUP 136 6.2.2 MSE for Nonsampled Areas 139 6.2.3 *MSE Estimation for Small Area Means 140 6.2.4 *Bootstrap MSE Estimation 141 6.2.5 *MSE of a Weighted Estimator 143 6.2.6 Mean Cross Product Error of Two Estimators 144 6.2.7 *Conditional MSE 144 6.3 *Robust Estimation in the Presence of Outliers 146 6.4 *Practical Issues 148 6.4.1 Unknown Sampling Error Variances 148 6.4.2 Strictly Positive Estimators of 𝜎2𝑣 151 6.4.3 Preliminary Test Estimation 154 6.4.4 Covariates Subject to Sampling Errors 156 6.4.5 Big Data Covariates 159 6.4.6 Benchmarking Methods 159 6.4.7 Misspecified Linking Model 165 6.5 *Software 169 7 Basic Unit Level Model 173 7.1 EBLUP Estimation 173 7.1.1 BLUP Estimator 174 7.1.2 Estimation of 𝜎2𝑣 and 𝜎2e 177 7.1.3 *Nonnegligible Sampling Fractions 178 7.2 MSE Estimation 179 7.2.1 Unconditional MSE of EBLUP 179 7.2.2 Unconditional MSE Estimators 181 7.2.3 *MSE Estimation: Nonnegligible Sampling Fractions 182 7.2.4 *Bootstrap MSE Estimation 183 7.3 *Applications 186 7.4 *Outlier Robust EBLUP Estimation 193 7.4.1 Estimation of Area Means 193 7.4.2 MSE Estimation 198 7.4.3 Simulation Results 199 7.5 *M-Quantile Regression 200 7.6 *Practical Issues 205 7.6.1 Unknown Heteroscedastic Error Variances 205 7.6.2 Pseudo-EBLUP Estimation 206 7.6.3 Informative Sampling 211 7.6.4 Measurement Error in Area-Level Covariate 216 7.6.5 Model Misspecification 218 7.6.6 Semi-parametric Nested Error Model: EBLUP 220 7.6.7 Semi-parametric Nested Error Model: REBLUP 224 7.7 *Software 227 7.8 *Proofs 231 7.8.1 Derivation of (7.6.17) 231 7.8.2 Proof of (7.6.20) 232 8 EBLUP: Extensions 235 8.1 *Multivariate Fay–Herriot Model 235 8.2 Correlated Sampling Errors 237 8.3 Time Series and Cross-Sectional Models 240 8.3.1 *Rao–Yu Model 240 8.3.2 State-Space Models 243 8.4 *Spatial Models 248 8.5 *Two-Fold Subarea Level Models 251 8.6 *Multivariate Nested Error Regression Model 253 8.7 Two-Fold Nested Error Regression Model 254 8.8 *Two-Level Model 259 8.9 *Models for Multinomial Counts 261 8.10 *EBLUP for Vectors of Area Proportions 262 8.11 *Software 264 9 Empirical Bayes (EB) Method 269 9.1 Introduction 269 9.2 Basic Area Level Model 270 9.2.1 EB Estimator 271 9.2.2 MSE Estimation 273 9.2.3 Approximation to Posterior Variance 275 9.2.4 *EB Confidence Intervals 281 9.3 Linear Mixed Models 287 9.3.1 EB Estimation of 𝜇i = 𝐥iT𝜷 + 𝐦Ti 𝐯i 287 9.3.2 MSE Estimation 288 9.3.3 Approximations to the Posterior Variance 288 9.4 *EB Estimation of General Finite Population Parameters 289 9.4.1 BP Estimator Under a Finite Population 290 9.4.2 EB Estimation Under the Basic Unit Level Model 290 9.4.3 FGT Poverty Measures 293 9.4.4 Parametric Bootstrap for MSE Estimation 294 9.4.5 ELL Estimation 295 9.4.6 Simulation Experiments 296 9.5 Binary Data 298 9.5.1 *Case of No Covariates 299 9.5.2 Models with Covariates 304 9.6 Disease Mapping 308 9.6.1 Poisson–Gamma Model 309 9.6.2 Log-Normal Models 310 9.6.3 Extensions 312 9.7 *Design-Weighted EB Estimation: Exponential Family Models 313 9.8 Triple-Goal Estimation 315 9.8.1 Constrained EB 316 9.8.2 Histogram 318 9.8.3 Ranks 318 9.9 Empirical Linear Bayes 319 9.9.1 LB Estimation 319 9.9.2 Posterior Linearity 322 9.10 Constrained LB 324 9.11 *Software 325 9.12 Proofs 330 9.12.1 Proof of (9.2.11) 330 9.12.2 Proof of (9.2.30) 330 9.12.3 Proof of (9.8.6) 331 9.12.4 Proof of (9.9.1) 331 10 Hierarchical Bayes (HB) Method 333 10.1 Introduction 333 10.2 MCMC Methods 335 10.2.1 Markov Chain 335 10.2.2 Gibbs Sampler 336 10.2.3 M–H Within Gibbs 336 10.2.4 Posterior Quantities 337 10.2.5 Practical Issues 339 10.2.6 Model Determination 342 10.3 Basic Area Level Model 347 10.3.1 Known 𝜎2𝑣 347 10.3.2 *Unknown 𝜎2𝑣: Numerical Integration 348 10.3.3 Unknown 𝜎2𝑣: Gibbs Sampling 351 10.3.4 *Unknown Sampling Variances 𝜓i 354 10.3.5 *Spatial Model 355 10.4 *Unmatched Sampling and Linking Area Level Models 356 10.5 Basic Unit Level Model 362 10.5.1 Known 𝜎2𝑣 and 𝜎2e 362 10.5.2 Unknown 𝜎2𝑣 and 𝜎2e: Numerical Integration 363 10.5.3 Unknown 𝜎2𝑣 and 𝜎2e: Gibbs Sampling 364 10.5.4 Pseudo-HB Estimation 365 10.6 General ANOVA Model 368 10.7 *HB Estimation of General Finite Population Parameters 369 10.7.1 HB Estimator under a Finite Population 370 10.7.2 Reparameterized Basic Unit Level Model 370 10.7.3 HB Estimator of a General Area Parameter 372 10.8 Two-Level Models 374 10.9 Time Series and Cross-Sectional Models 377 10.10 Multivariate Models 381 10.10.1 Area Level Model 381 10.10.2 Unit Level Model 382 10.11 Disease Mapping Models 383 10.11.1 Poisson-Gamma Model 383 10.11.2 Log-Normal Model 384 10.11.3 Two-Level Models 386 10.12 *Two-Part Nested Error Model 388 10.13 Binary Data 389 10.13.1 Beta-Binomial Model 389 10.13.2 Logit-Normal Model 390 10.13.3 Logistic Linear Mixed Models 393 10.14 *Missing Binary Data 397 10.15 Natural Exponential Family Models 398 10.16 Constrained HB 399 10.17 *Approximate HB Inference and Data Cloning 400 10.18 Proofs 402 10.18.1 Proof of (10.2.26) 402 10.18.2 Proof of (10.2.32) 402 10.18.3 Proof of (10.3.13)–(10.3.15) 402 References 405 Author Index 431 Subject Index 437

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Book SynopsisIntroduction to Statistical Analysis of Laboratory Data presents a detailed discussion of important statistical concepts and methods of data presentation and analysis Provides detailed discussions on statistical applications including a comprehensive package of statistical tools that are specific to the laboratory experiment process Introduces terminology used in many applications such as the interpretation of assay design and validation as well as fit for purpose procedures including real world examples Includes a rigorous review of statistical quality control procedures in laboratory methodologies and influences on capabilities Presents methodologies used in the areas such as method comparison procedures, limit and bias detection, outlier analysis and detecting sources of variation Analysis of robustness and ruggedness including multivariate influences on response are introduced to account for controllable/uncontrollable laboraTrade Review"The book presents a detailed discussion of important statistical concepts and methods of data presentation and analysis. -Provides detailed discussions on statistical applications including a comprehensive package of statistical tools that are specific to the laboratory experiment process. - Introduces terminology used in many applications such as the interpretation of assay design and validation as well as fit for purpose" procedures including real world examples." (Zentralblatt MATH 2016)Table of ContentsPreface xi Acknowledgments xv 1 Descriptive Statistics 1 1.1 Measures of Central Tendency 1 1.2 Measures of Variation 4 1.3 Laboratory Example 7 1.4 Putting it All Together 8 1.5 Summary 10 References 10 2 Distributions and Hypothesis Testing in Formal Statistical Laboratory Procedures 11 2.1 Introduction 11 2.2 Confidence Intervals (CT) 19 2.2.1 Confidence Interval (CI) for the Population Mean – The t-Distribution 20 2.2.2 Confidence Interval for the Variance and Standard Deviation 21 2.3 Inferential Statistics – Hypothesis Testing 23 2.3.1 t-Test for Means 25 2.3.2 Test for Variation: Coefficient of Variation (CV) 28 2.3.3 Two-Sample Test of the Population Means 29 2.3.4 One-Way Analysis of Variance (ANOVA) 34 2.3.5 Nonparametric Tests for Skewed Data 40 References 41 3 Method Validation 43 3.1 Introduction 43 3.2 Accuracy 45 3.2.1 Method 1 45 3.2.2 Method 2 56 3.3 Brief Introduction to Bioassay 59 3.3.1 Direct Assay 59 3.3.2 Indirect Assay 61 3.4 Sensitivity, Specificity (Selectivity) 69 3.5 Method Validation and Method Agreement – Bland-Altman 73 References 76 4 Methodologies in Outlier Analysis 79 4.1 Introduction 79 4.2 Some Outlier Determination Techniques 80 4.2.1 Grubb Statistic 82 4.2.2 Other Forms of the Grubb Statistic 84 4.2.3 Studentized Range Statistic 85 4.2.4 Sequential Test of Many Outliers 86 4.2.5 Mahalanobis Distance Measure 88 4.2.6 Dixon Q-Test for a Single Outlier 91 4.2.7 The Box Plot 94 4.2.8 Median Absolute Deviation 95 4.3 Combined Method Comparison Outlier Analysis 96 4.3.1 Further Outlier Considerations 96 4.3.2 Combined Method Comparison Outlier Analysis – Refined Method Comparisons Using Bland – Altman 98 4.4 Some Consequences of Outlier Removal 103 4.5 Considering Outlier Variance 104 4.5.1 The Cochran C test 104 4.5.2 Cochran G Test 107 References 110 5 Statistical Process Control 113 5.1 Introduction 113 5.2 Control Charts 115 5.2.1 Means (X-bar) Control Charts 117 5.2.2 Range Control Charts 122 5.2.3 The S-Chart 124 5.2.4 The Median Chart 126 5.2.5 Mean (X-bar) and S-Charts Based on the Median Absolute Deviation (MAD) 128 5.3 Capability Analysis 131 5.4 Capability Analysis – An Alternative Consideration 137 References 139 6 Limits of Calibration 141 6.1 Calibration: Limit Strategies for Laboratory Assay Data 141 6.1.1 Definition – Calibration 141 6.2 Limit Strategies 142 6.2.1 Example – Estimation of LoB and LoD for Drug Assay 142 6.2.2 LoQ Results 144 6.2.3 A Comparison of Empirical and Statistical Approaches to the LoD and LoQ 145 6.2.4 Example – LoD/LoQ, GC – MS Approach 145 6.2.5 LoD/LoQ, GC – MS Approach 146 6.2.6 Explanation of the Difficulty of the Statistical Methodology for the LoD and LoQ 147 6.2.7 Another LoQ Method 151 6.3 Method Detection Limits (EPA) 151 6.3.1 Method Detection Limits 151 6.3.2 Example – Atrazine by Gas Chromatography (GC) 152 6.3.3 LoD and LoQ Summary 153 6.4 Data Near the Detection Limits 154 6.4.1 Biased Estimators 154 6.4.2 Computing Some Statistics with the LoD in the Data 154 6.5 More on Statistical Management of Nondetects 156 6.5.1 Model-Based Examples of Measuring Nondetects 157 6.5.2 An Alternative Regression Approach with Improvements (Refer to the Box Cox Transformation in Chapter 5) 160 6.5.3 Extension of the ROS Method for Multiple NDs in Various Positions 163 6.5.4 Cohen’s Adjustment 165 6.6 The Kaplan – Meier Method (Nonparametric Approach) for Analysis of Laboratory Data with Nondetects 170 References 174 7 Calibration Bias 177 7.1 Error 177 7.1.1 Types of Error 179 7.2 Uncertainty 180 7.3 Sources of Uncertainty 180 7.4 Estimation Methods of Uncertainty 181 7.4.1 Statistical Estimation Methods of Type A Uncertainty 181 7.4.2 Estimation Methods of Type B Uncertainty 183 7.4.3 Estimation Methods of Combined and Expanded Uncertainties (Normal Data) 187 7.4.4 Estimation Methods of Combined and Expanded Uncertainties (Nonnormal Data) 190 7.4.5 Another Method of Estimating Uncertainties for Nonnormal Data (Nonparametric) 192 7.5 Calibration Bias 194 7.5.1 Gas Chromatographic/Mass Spectrometric (GC – MS) Calibration Bias 197 7.5.2 Discussion 205 7.6 Multiple Instruments 205 7.7 Crude Versus Precise Methodologies 208 References 210 8 Robustness and Ruggedness 213 8.1 Introduction 213 8.2 Robustness 214 8.3 Ruggedness 216 8.4 An Alternative Procedure for Ruggedness Determination 224 8.5 Ruggedness and System Suitability Tests 227 8.5.1 Determining the SST Limits from Replicated Experimentation 228 8.5.2 Determining the SST Limits from Statistical Prediction 231 References 233 Index 235

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Book SynopsisDemonstrates techniques which will allow rewiring rates of over 95%, enabling adoption of deep sub-micron chips for industrial applications Logic synthesis is an essential part of the modern digital IC design process in semi-conductor industry. This book discusses a logic synthesis technique called rewiring and its latest technical advancement in term of rewirability. Rewiring technique has surfaced in academic research since 1993 and there is currently no book available on the market which systematically and comprehensively discusses this rewiring technology. The authors cover logic transformation techniques with concentration on rewiring. For many decades, the effect of wiring on logic structures has been ignored due to an ideal view of wires and their negligible role in the circuit performance. However in today's semiconductor technology wiring is the major player in circuit performance degeneration and logic synthesis engines can be improved to deal with thiTable of ContentsList of Figures ix List of Tables xiii Preface xv Introduction xvii 1 Preliminaries 1 1.1 Boolean Circuits 1 1.2 Redundancy and Stuck-at Faults 4 1.3 Automatic Test Pattern Generation (ATPG) 6 1.4 Dominators 6 1.5 Mandatory Assignments and Recursive Learning 7 1.6 Graph Theory and Boolean Circuits 8 References 10 2 Concept of Logic Rewiring 11 2.1 What is Rewiring? 11 2.2 ATPG-based Rewiring Techniques 12 2.2.1 Add-First 12 2.2.2 Delete-First 18 2.3 Non-ATPG-based Rewiring Techniques 24 2.3.1 Graph-based Alternate Wiring (GBAW) 24 2.3.2 SPFD 25 2.4 Why are Rewiring Techniques Important? 31 References 33 3 Add-First and Non-ATPG-Based Rewiring Techniques 37 3.1 Redundancy Addition and Removal (RAR) 37 3.1.1 RAMBO 37 3.1.2 REWIRE 38 3.1.3 RAMFIRE 41 3.1.4 Comparison Between RAR-Based Rewiring Techniques 43 3.2 Node-Based Network Addition and Removal (NAR) 43 3.2.1 Node Merging 43 3.2.2 Node Addition and Removal 48 3.3 Other Rewiring Techniques 51 3.3.1 SPFD-Based Rewiring 51 References 65 4 Delete-First Rewiring Techniques 67 4.1 IRRA 69 4.1.1 Destination of Alternative Wires 71 4.1.2 Source of Alternative Wires 72 4.2 ECR 76 4.2.1 Destination of Alternative Wires 80 4.2.2 Source of Alternative Wires 85 4.2.3 Overview of the Approach of Error-Cancellation-Based Rewiring 86 4.2.4 Complexity Analysis of ECR 87 4.2.5 Comparison Between ECR and Other Resynthesis Techniques 90 4.2.6 Experimental Result 92 4.3 FECR 96 4.3.1 Error Flow Graph Construction 97 4.3.2 Destination Node Identification 98 4.3.3 Source Node Identification 102 4.3.4 ECR is a Special Case of FECR 104 4.3.5 Complexity Analysis of FECR 105 4.3.6 Experimental Result 105 4.4 Cut-Based Error Cancellation Rewiring 107 4.4.1 Preliminaries 107 4.4.2 Error Frontier 109 4.4.3 Cut-Based Error Cancellation Rewiring 117 4.4.4 Verification of Alternative Wires 121 4.4.5 Complexity Analysis of CECR 122 4.4.6 Relationship Between ECR, FECR, and CECR 122 4.4.7 Extending CECR for n-to-m Rewiring 123 4.4.8 Speedup for CECR 124 4.4.9 Experimental Results 125 References 129 5 Applications 133 5.1 Area Reduction 133 5.1.1 Preliminaries 134 5.1.2 Our Methodology (“Long tail” vs “Bump tail” Curves) 135 5.1.3 Details of our Approach 140 5.1.4 Experimental Results 143 5.2 Postplacement Optimization 145 5.2.1 Wire-Length-Driven Rewiring-Based Postplacement Optimization 145 5.2.2 Timing-Driven Rewiring-Based Postplacement Optimization 151 5.3 ECO Timing Optimization 158 5.3.1 Preliminaries 160 5.3.2 Nego-Rout Operation 161 5.3.3 Path-Restructuring Operation 164 5.3.4 Experimental Results 166 5.4 Area Reduction in FPGA Technology Mapping 167 5.4.1 Incremental Logic Resynthesis (ILR): Depth-Oriented Mode 170 5.4.2 Incremental Logic Resynthesis (ILR): Area-Oriented Mode 171 5.4.3 Experimental Results 173 5.4.4 Conclusion 183 5.5 FPGA Postlayout Routing Optimization 184 5.5.1 Optimization by Alternative Functions 185 5.5.2 Optimization with Mapping-to-Routing Logic Rewirings 187 5.5.3 Optimization by SPFD-Based Rewiring 198 5.6 Logic Synthesis for Low Power Using Clock Gating and Rewiring 199 5.6.1 Mechanism of Clock Gating 199 5.6.2 Rewiring-Based Optimization 203 References 207 6 Summary 211 Index 213

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Book SynopsisFree Mathematica 10 Update Included! Now available from www.wiley.com/go/magrab Updated material includes:- Creating regions and volumes of arbitrary shape and determining their properties: arc length, area, centroid, and area moment of inertia- Performing integrations, solving equations, and determining the maximum and minimum values over regions of arbitrary shape- Solving numerically a class of linear second order partial differential equations in regions of arbitrary shape using finite elements An Engineer''s Guide to Mathematica enables the reader to attain the skills to create Mathematica 9 programs that solve a wide range of engineering problems and that display the results with annotated graphics. This book can be used to learn Mathematica, as a companion to engineering texts, and also as a reference for obtaining numerical and symbolic solutions to a wide range of engineTable of ContentsPreface xiii Table of Engineering Applications xvii Part 1 Introduction 1 Mathematica Environment and Basic Syntax 3 1.1 Introduction 3 1.2 Selecting Notebook Characteristics 4 1.3 Notebook Cells 8 1.4 Delimiters 12 1.5 Basic Syntax 12 1.5.1 Introduction 12 1.5.2 Templates: Greek Symbols and Mathematical Notation 15 1.5.3 Variable Names and Global Variables 18 1.6 Mathematical Constants 19 1.7 Complex Numbers 21 1.8 Elementary, Trigonometric, Hyperbolic, and a Few Special Functions 22 1.9 Strings 25 1.9.1 String Creation: StringJoin[] and ToString[] 25 1.9.2 Labeled Output: Print[], NumberForm[], EngineeringForm[], and TraditionalForm[] 26 1.10 Conversions, Relational Operators, and Transformation Rule 28 1.11 Engineering Units and Unit Conversions: Quantity[] and UnitConvert[] 30 1.12 Creation of CDF Documents and Documents in Other Formats 33 1.13 Functions Introduced in Chapter 1 34 Exercises 35 2 List Creation and Manipulation: Vectors and Matrices 39 2.1 Introduction 39 2.2 Creating Lists and Vectors 39 2.2.1 Introduction 39 2.2.2 Creating a List with Table[] 45 2.2.3 Summing Elements of a List: Total[] 46 2.2.4 Selecting Elements of a List 47 2.2.5 Identifying List Elements Matching a Pattern: Position[] 49 2.3 Creating Matrices 51 2.3.1 Introduction 51 2.3.2 Matrix Generation Using Table[] 54 2.3.3 Accessing Elements of Arrays 55 2.4 Matrix Operations on Vectors and Arrays 56 2.4.1 Introduction 56 2.4.2 Matrix Inverse and Determinant: Inverse[] and Det[] 57 2.5 Solution of a Linear System of Equations: LinearSolve[] 58 2.6 Eigenvalues and Eigenvectors: EigenSystem[] 59 2.7 Functions Introduced in Chapter 2 61 References 61 Exercises 61 3 User-Created Functions, Repetitive Operations, and Conditionals 69 3.1 Introduction 69 3.2 Expressions and Procedures as Functions 69 3.2.1 Introduction 69 3.2.2 Pure Function: Function[] 74 3.2.3 Module[] 78 3.3 Find Elements of a List that Meet a Criterion: Select[] 80 3.4 Conditionals 82 3.4.1 If[] 82 3.4.2 Which[] 83 3.5 Repetitive Operations 83 3.5.1 Do[] 83 3.5.2 While[] 83 3.5.3 Nest[] 84 3.5.4 Map[] 84 3.6 Examples of Repetitive Operations and Conditionals 85 3.7 Functions Introduced in Chapter 3 92 Exercises 92 4 Symbolic Operations 95 4.1 Introduction 95 4.2 Assumption Options 101 4.3 Solutions of Equations: Solve[] 101 4.4 Limits: Limit[] 105 4.5 Power Series: Series[], Coefficient[], and CoefficientList[] 108 4.6 Optimization: Maximize[]/Minimize[] 112 4.7 Differentiation: D[] 114 4.8 Integration: Integrate[] 120 4.9 Solutions of Ordinary Differential Equations: DSolve[] 126 4.10 Solutions of Partial Differential Equations: DSolve[] 136 4.11 Laplace Transform: LaplaceTransform[] and InverseLaplaceTransform[] 138 4.12 Functions Introduced in Chapter 4 145 References 145 Exercises 146 5 Numerical Evaluations of Equations 151 5.1 Introduction 151 5.2 Numerical Integration: NIntegrate[] 151 5.3 Numerical Solutions of Differential Equations: NDSolveValue[] and ParametricNDSolveValue[] 154 5.4 Numerical Solutions of Equations: NSolve[] 178 5.5 Roots of Transcendental Equations: FindRoot[] 180 5.6 Minimum and Maximum: FindMinimum[] and FindMaximum[] 182 5.7 Fitting of Data: Interpolation[] and FindFit[] 186 5.8 Discrete Fourier Transforms and Correlation: Fourier[], InverseFourier[], and ListCorrelate[] 189 5.9 Functions Introduced in Chapter 5 194 References 195 Exercises 196 6 Graphics 209 6.1 Introduction 209 6.2 2D Graphics 209 6.2.1 Basic Plotting 209 6.2.2 Basic Graph Enhancements 213 6.2.3 Common 2D Shapes: Graphics[] 217 6.2.4 Additional Graph Enhancements 222 6.2.5 Combining Figures: Show[] and GraphicsGrid[] 238 6.2.6 Tooltip[] 241 6.2.7 Exporting Graphics 244 6.3 3D Graphics 244 6.4 Summary of Functions Introduced in Chapter 6 253 References 254 Exercises 254 7 Interactive Graphics 263 7.1 Interactive Graphics: Manipulate[] 263 References 287 Exercises 287 Part 2 Engineering Applications 8 Vibrations of Spring–Mass Systems and Thin Beams 293 8.1 Introduction 293 8.2 Single Degree-of-Freedom Systems 294 8.2.1 Periodic Force on a Single Degree-of-Freedom System 294 8.2.2 Squeeze Film Damping and Viscous Fluid Damping 298 8.2.3 Electrostatic Attraction 302 8.2.4 Single Degree-of-Freedom System Energy Harvester 304 8.3 Two Degrees-of-Freedom Systems 307 8.3.1 Governing Equations 307 8.3.2 Response to Harmonic Excitation: Amplitude Response Functions 307 8.3.3 Enhanced Energy Harvester 310 8.4 Thin Beams 315 8.4.1 Natural Frequencies and Mode Shapes of a Cantilever Beam with In-Span Attachments 315 8.4.2 Effects of Electrostatic Force on the Natural Frequency and Stability of a Beam 318 8.4.3 Response of a Cantilever Beam with an In-Span Attachment to an Impulse Force 323 References 326 9 Statistics 327 9.1 Descriptive Statistics 327 9.1.1 Introduction 327 9.1.2 Location Statistics: Mean[], StandardDeviation[], and Quartile[] 327 9.1.3 Continuous Distribution Functions: PDF[] and CDF[] 329 9.1.4 Histograms and Probability Plots: Histogram[] and ProbabilityScalePlot [] 331 9.1.5 Whisker Plot: BoxWhiskerChart[] 332 9.1.6 Creating Data with Specified Distributions: RandomVariate[] 334 9.2 Probability of Continuous Random Variables 334 9.2.1 Probability for Different Distributions: NProbability[] 334 9.2.2 Inverse Cumulative Distribution Function: InverseCDF[] 337 9.2.3 Distribution Parameter Estimation: EstimatedDistribution[] and FindDistributionParameters[] 337 9.2.4 Confidence Intervals: ⋯CI[] 340 9.2.5 Hypothesis Testing: LocationTest[] and VarianceTest[] 342 9.3 Regression Analysis: LinearModelFit[] 343 9.3.1 Simple Linear Regression 343 9.3.2 Multiple Linear Regression 347 9.4 Nonlinear Regression Analysis: NonLinearModelFit[] 351 9.5 Analysis of Variance (ANOVA) and Factorial Designs: ANOVA[] 354 9.6 Functions Introduced in Chapter 9 358 10 Control Systems and Signal Processing 359 10.1 Introduction 359 10.2 Model Generation: State-Space and Transfer Function Representation 359 10.2.1 Introduction 359 10.2.2 State-Space Models: StateSpaceModel[] 360 10.2.3 Transfer Function Models: TransferFunctionModel[] 362 10.3 Model Connections – Closed-Loop Systems and System Response: SystemsModelFeedbackConnect[] and SystemsModelSeriesConnect[] 363 10.4 Design Methods 369 10.4.1 Root Locus: RootLocusPlot[] 369 10.4.2 Bode Plot: BodePlot[] 371 10.4.3 Nichols Plot: NicholsPlot[] 372 10.5 Signal Processing 374 10.5.1 Filter Models: ButterworthFilterModel[], EllipticFilterModel[], ... 374 10.5.2 Windows: HammingWindow[], HannWindow[], ... 381 10.5.3 Spectrum Averaging 385 10.6 Aliasing 388 10.7 Functions Introduced in Chapter 10 390 Reference 391 11 Heat Transfer and Fluid Mechanics 393 11.1 Introduction 393 11.2 Conduction Heat Transfer 394 11.2.1 One-Dimensional Transient Heat Diffusion in Solids 394 11.2.2 Heat Transfer in Concentric Spheres: Ablation of a Tumor 398 11.2.3 Heat Flow Through Fins 401 11.3 Natural Convection Along Heated Plates 405 11.4 View Factor Between Two Parallel Rectangular Surfaces 408 11.5 Internal Viscous Flow 411 11.5.1 Laminar Flow in Horizontal Cylindrical Pipes 411 11.5.2 Flow in Three Reservoirs 412 11.6 External Flow 416 11.6.1 Pressure Coefficient of a Joukowski Airfoil 416 11.6.2 Surface Profile in Nonuniform Flow in Open Channels 419 References 423 Index 425

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Book SynopsisCovers both holonomic and non-holonomic constraints in a study of the mechanics of the constrained rigid body.Table of ContentsPreface xi 1 Elements of Mathematical Calculation 1 1.1 Vectors: Vector Operations 1 1.2 Real Rectangular Matrix 4 1.3 Square Matrix 6 1.4 Skew Matrix of Third Order 10 Further Reading 12 2 Kinematics of the Rigid Solid 15 2.1 Finite Displacements of the Points of Rigid Solid 15 2.2 Matrix of Rotation: Properties 16 2.2.1 General Properties 16 2.2.2 Successive Displacements 17 2.2.3 Eigenvalues: Eigenvectors 18 2.2.4 The Expression of the Matrix of Rotation with the Aid of the Unitary Eigenvector and the Angle of Rotation 20 2.2.5 Symmetries: Decomposition of the Rotation into Two Symmetries 24 2.2.6 Rotations About the Axes of Coordinates 25 2.3 Minimum Displacements: The Chasles Theorem 27 2.4 Small Displacements 33 2.5 Velocities of the Points of Rigid Solid 34 2.6 The Angular Velocity Matrix: Properties 37 2.6.1 The Matrices of Rotation About the Axes of Coordinates 37 2.6.2 The Angular Velocity Matrix: The Angular Velocity Vector 38 2.6.3 The Matrix of the Partial Derivatives of the Angular Velocity 39 2.7 Composition of the Angular Velocities 41 2.8 Accelerations of the Points of Rigid Solid 42 Further Reading 43 3 General Theorems in the Dynamics of the Rigid Solid 45 3.1 Moments of Inertia 45 3.1.1 Definitions: Relations Between the Moments of Inertia 45 3.1.2 Moments of Inertia for Homogeneous Rigid Solid Bodies 47 3.1.3 Centers of Weight 47 3.1.4 Variation of the Moments of Inertia Relative to Parallel Axes 49 3.1.5 Variation of the Moments of Inertia Relative to Concurrent Axes 50 3.1.6 Principal Axes of Inertia: Principal Moments of Inertia 52 3.2 Momentum: The Theorem of Momentum 54 3.3 Moment of Momentum: The Theorem of Moment of Momentum 56 3.4 The Kinetic Energy of the Rigid Solid 57 Further Reading 58 4 Matrix Differential Equations of the Motion of Rigid Solid 61 4.1 The Differential Equations Obtained from the General Theorems 61 4.1.1 General Aspects 61 4.1.2 The Differential Equations 62 4.2 The Lagrange Equations in the Case of the Holonomic Constraints 63 4.3 The Equivalence between the Differential Equations Obtained from the General Theorems and the Lagrange Equations 65 4.3.1 The Equivalence for the First Component 65 4.3.2 The Equivalence for the Second Component 66 4.4 The Matrix Differential Equations for the Motion of the Constrained Rigid Solid 71 4.4.1 The Matrix of Constraints 71 4.4.2 The Lagrange Equations for Mechanical Systems with Constraints 73 4.4.3 The Mathematical Model of the Motion of Rigid Solid with Constraints 75 4.4.4 General Algorithm of Calculation 76 4.4.5 The Calculation of the Forces of Constraints 78 4.4.6 The Elimination of the Matrix of the Lagrange multipliers 80 Further Reading 85 5 Generalized Forces: The Equilibrium of the Rigid Solid 89 5.1 The Generalized Forces in the Case of a Mechanical System 89 5.2 The General Expressions of the Generalized Forces in the Case of Rigid Solid 90 5.2.1 The Case When at a Point Acts a Given Force 90 5.2.2 The Case When the Rigid Solid is Acted by a Torque of Given Moment 93 5.3 Conservative Forces 94 5.3.1 General Aspects 94 5.3.2 The Weight 96 5.3.3 The Elastic Force of a Spring 97 5.4 The Equilibrium of the Constrained Rigid Solid 98 5.4.1 The Equations of Equilibrium: Numerical Solution 98 5.4.2 The Case When the Functions of Constraints Introduce Auxiliary Coordinates (Pseudo-Coordinates) 100 5.5 The Equilibrium of the Heavy Rigid Solid Hanged by Springs 104 5.5.1 The Matrix Equation of Equilibrium 104 5.5.2 Numerical Solution 106 5.5.3 The Case When the Fixed Reference System Coincides to the Local Reference System at the Equilibrium Position 108 Further Reading 109 6 The Motion of the Rigid Solid with Constraints at Given Proper Points 113 6.1 General Aspects: Classification 113 6.2 Mathematical Aspects: Notations 114 6.2.1 The Case of the Motion Depending on Only the Generalized Coordinates XO, YO, ZO, ψ, θ, φ 114 6.2.2 The Case of the Constraints Depending on the Pseudo-Coordinates Too 115 6.2.3 Relations of Calculation Necessary for the Numerical Algorithm 115 6.3 The Study of the Rigid Solid with a Fixed Point 116 6.4 The Rigid Solid with Two Fixed Points (the Rotational Motion of the Rigid Solid) 118 6.5 The Rigid Solid with a Given Point Situated on a Fixed Surface 121 6.5.1 The Case When the Surface is Defined by an Implicit Equation F X,Y,Z = 0 121 6.5.2 The Case When the Surface is Defined by Parametric Equations 123 6.6 The Rigid Solid with Several Points Situated on Fixed Surfaces (Curves) 125 6.6.1 The Case When the Surfaces are Defined by Implicit Equations 125 6.6.2 The Case When the Surfaces are Defined by Parametric Equations 126 6.7 The Rigid Solid with a Fixed Point and with Another Point Situated on a Fixed Surface 127 6.7.1 The Case When the Fixed Surface is Defined by an Implicit Equation 127 6.7.2 The Case When the Fixed Surface is Defined by Parametric Equations 129 6.8 The Rigid Solid with Two Given Points Situated on a Fixed Curve 130 6.8.1 The Case When the Curve is Defined by Two Implicit Equations 130 6.8.2 The Case When the Curve is Defined by Parametric Equations 131 6.8.3 The Helical Motion of the Rigid Solid 132 Further Reading 133 7 The Motion of the Rigid Solid with Constraints on Given Proper Curves 135 7.1 General Aspects: Classification 135 7.2 The Rigid Solid Supported at Fixed Points on Given Proper Curves 136 7.2.1 Notations 136 7.2.2 The Matrix of Constraints 137 7.3 The Rigid Solid at Which Given Proper Curves Support with Sliding on Fixed Curves 138 7.3.1 Notations 138 7.3.2 The Simple Contact between the Curves 139 7.3.3 The Tangency Contact between Spatial Curves 143 7.3.4 Contact with Sliding between Planar Curves (Rolling with Sliding on the Plan) 144 7.4 Rolling without Sliding of a Curve on a Fixed Curve 147 7.4.1 The General Case for Spatial Curves 147 7.4.2 The Rolling Without Sliding of a Curve on a Fixed Curve in the Plan 148 7.5 The Motion of the Rigid Solid at Which the Curves Jointed to It Support with Sliding on Fixed Surfaces 151 7.5.1 The Case of a Single Curve 151 7.5.2 The Case of the Supporting with Sliding by Curves on Surface 154 7.6 The Rolling without Sliding of a Disk Bounded by a Spatial Curve on a Fixed Surface 157 7.6.1 The Matrix Differential Equation of Motion 157 7.6.2 The Forces at the Contact Point 159 7.7 The Rolling without Sliding of a Planar Circle Disk on a Horizontal Plan 160 7.8 The Rolling without Sliding of a Planar Elliptic Disk on a Horizontal Plan 168 7.9 The Rolling without Sliding of a Hyperboidic Curve on a Horizontal Plan 175 7.9.1 Hyperboidic Curves 175 7.9.2 The Matrix Differential Equation of Motion 176 7.10 The Rolling without Sliding of a Planar Circle Disk on a Cylindrical Surface with Horizontal Generatrices 184 7.11 The Rolling without Sliding of Two Curves of a Rigid Solid on a Fixed Surface 192 7.11.1 General Aspects 192 7.11.2 The Differential Equations of Motion 195 7.11.3 The Algorithm of Numerical Calculation 196 7.12 The Rolling without Sliding of an Axle with Wheels (Disks) with Angular Deviations on a Horizontal Plan 197 7.13 The Rolling without Sliding of an Axle with Disks on a Hyperbolic Paraboloid 204 7.13.1 General Aspects 204 7.13.2 The Initial Position 206 7.13.3 The Differential Equations 207 Further Reading 214 8 The Motion of the Rigid Solid with Constraints on the Bounding Surface 217 8.1 General Aspects: Classification 217 8.2 The Rigid Solid Supported at Fixed Points 218 8.2.1 The Matrix of Constraints 218 8.2.2 The Matrix Differential Equation of Motion 220 8.2.3 The Algorithm of Calculation 221 8.3 The Rigid Solid Supported with Sliding on Fixed Curves 236 8.3.1 The Matrix of Constraints 236 8.3.2 The Matrix Differential Equation of Motion 239 8.3.3 The Reactions 239 8.3.4 The Algorithm of Calculation 240 8.4 The Rolling without Sliding of the Rigid Solid on Two Fixed Curves 244 8.4.1 General Considerations 244 8.4.2 The Differential Equations of Motion 246 8.4.3 The Algorithm for the Numerical Calculation 248 8.5 The Rolling without Sliding of a Rigid Solid on a Fixed Surface 254 8.5.1 The Matrix of Constraints 254 8.5.2 The Matrix Differential Equation of Motion 256 8.6 The Rolling without Sliding of a Toroidal Wheel on a Horizontal Plan 257 8.6.1 The Equations of Torus 257 8.6.2 The Tangency Conditions 258 8.6.3 The Initial Conditions 258 8.6.4 The Differential Equations of Motion 260 8.7 The Rolling without Sliding of a Rigid Solid Supported on Two Fixed Surfaces 265 8.7.1 General Aspects 265 8.7.2 The Differential Equations of Motion 267 8.7.3 The Determination of the Forces of Constraints 269 8.7.4 The Rolling without Sliding of an Ellipsoid Acted only by its Own Weight on Two Plans 270 8.8 The Rolling without Sliding of a Rigid Solid Supported at Two Points on a Fixed Surface 291 8.8.1 General Aspects 291 8.8.2 The Differential Equations of Motion: The Calculation of the Forces of Constraints 293 Further Reading 294 Appendix 297 Index 315

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Book SynopsisAn edited volume for an upcoming conference on Total Survey Error (TSE), this book provides an overview of the TSE framework and current TSE research as related to survey design, data collection, estimation and analysis.Table of ContentsNotes on Contributors xix Preface xxv Section 1 The Concept of TSE and the TSE Paradigm 1 1 The Roots and Evolution of the Total Survey Error Concept 3Lars E. Lyberg and Diana Maria Stukel 1.1 Introduction and Historical Backdrop 3 1.2 Specific Error Sources and Their Control or Evaluation 5 1.3 Survey Models and Total Survey Design 10 1.4 The Advent of More Systematic Approaches Toward Survey Quality 12 1.5 What the Future Will Bring 16 References 18 2 Total Twitter Error: Decomposing Public Opinion Measurement on Twitter from a Total Survey Error Perspective 23Yuli Patrick Hsieh and Joe Murphy 2.1 Introduction 23 2.2 Social Media: An Evolving Online Public Sphere 25 2.3 Components of Twitter Error 27 2.4 Studying Public Opinion on the Twittersphere and the Potential Error Sources of Twitter Data: Two Case Studies 31 2.5 Discussion 40 2.6 Conclusion 42 References 43 3 Big Data: A Survey Research Perspective 47Reg Baker 3.1 Introduction 47 3.2 Definitions 48 3.3 The Analytic Challenge: From Database Marketing to Big Data and Data Science 56 3.4 Assessing Data Quality 58 3.5 Applications in Market, Opinion, and Social Research 59 3.6 The Ethics of Research Using Big Data 62 3.7 The Future of Surveys in a Data-Rich Environment 62 References 65 4 The Role of Statistical Disclosure Limitation in Total Survey Error 71Alan F. Karr 4.1 Introduction 71 4.2 Primer on SDL 72 4.3 TSE-Aware SDL 75 4.4 Edit-Respecting SDL 79 4.5 SDL-Aware TSE 83 4.6 Full Unification of Edit, Imputation, and SDL 84 4.7 “Big Data” Issues 87 4.8 Conclusion 89 Acknowledgments 91 References 92 Section 2 Implications for Survey Design 95 5 The Undercoverage–Nonresponse Tradeoff 97Stephanie Eckman and Frauke Kreuter 5.1 Introduction 97 5.2 Examples of the Tradeoff 98 5.3 Simple Demonstration of the Tradeoff 99 5.4 Coverage and Response Propensities and Bias 100 5.5 Simulation Study of Rates and Bias 102 5.6 Costs 110 5.7 Lessons for Survey Practice 111 References 112 6 Mixing Modes: Tradeoffs Among Coverage, Nonresponse, and Measurement Error 115Roger Tourangeau 6.1 Introduction 115 6.2 The Effect of Offering a Choice of Modes 118 6.3 Getting People to Respond Online 119 6.4 Sequencing Different Modes of Data Collection 120 6.5 Separating the Effects of Mode on Selection and Reporting 122 6.6 Maximizing Comparability Versus Minimizing Error 127 6.7 Conclusions 129 References 130 7 Mobile Web Surveys: A Total Survey Error Perspective 133Mick P. Couper, Christopher Antoun, and Aigul Mavletova 7.1 Introduction 133 7.2 Coverage 135 7.3 Nonresponse 137 7.4 Measurement Error 142 7.5 Links Between Different Error Sources 148 7.6 The Future of Mobile Web Surveys 149 References 150 8 The Effects of a Mid-Data Collection Change in Financial Incentives on Total Survey Error in the National Survey of Family Growth: Results from a Randomized Experiment 155James Wagner, Brady T. West, Heidi Guyer, Paul Burton, Jennifer Kelley, Mick P. Couper, and William D. Mosher 8.1 Introduction 155 8.2 Literature Review: Incentives in Face-to-Face Surveys 156 8.3 Data and Methods 159 8.4 Results 163 8.5 Conclusion 173 References 175 9 A Total Survey Error Perspective on Surveys in Multinational, Multiregional, and Multicultural Contexts 179Beth-Ellen Pennell, Kristen Cibelli Hibben, Lars E. Lyberg, Peter Ph. Mohler, and Gelaye Worku 9.1 Introduction 179 9.2 TSE in Multinational, Multiregional, and Multicultural Surveys 180 9.3 Challenges Related to Representation and Measurement Error Components in Comparative Surveys 184 9.4 QA and QC in 3MC Surveys 192 References 196 10 Smartphone Participation in Web Surveys: Choosing Between the Potential for Coverage, Nonresponse, and Measurement Error 203Gregg Peterson, Jamie Griffin, John LaFrance, and JiaoJiao Li 10.1 Introduction 203 10.2 Prevalence of Smartphone Participation in Web Surveys 206 10.3 Smartphone Participation Choices 209 10.4 Instrument Design Choices 212 10.5 Device and Design Treatment Choices 216 10.6 Conclusion 218 10.7 Future Challenges and Research Needs 219 Appendix 10.A: Data Sources 220 Appendix 10.B: Smartphone Prevalence in Web Surveys 221 Appendix 10.C: Screen Captures from Peterson et al. (2013) Experiment 225 Appendix 10.D: Survey Questions Used in the Analysis of the Peterson et al. (2013) Experiment 229 References 231 11 Survey Research and the Quality of Survey Data Among Ethnic Minorities 235Joost Kappelhof 11.1 Introduction 235 11.2 On the Use of the Terms Ethnicity and Ethnic Minorities 236 11.3 On the Representation of Ethnic Minorities in Surveys 237 Ethnic Minorities 241 11.4 Measurement Issues 242 11.5 Comparability, Timeliness, and Cost Concerns 244 11.6 Conclusion 247 References 248 Section 3 Data Collection and Data Processing Applications 253 12 Measurement Error in Survey Operations Management: Detection, Quantification, Visualization, and Reduction 255Brad Edwards, Aaron Maitland, and Sue Connor 12.1 TSE Background on Survey Operations 256 12.2 Better and Better: Using Behavior Coding (CARIcode) and Paradata to Evaluate and Improve Question (Specification) Error and Interviewer Error 257 12.3 Field-Centered Design: Mobile App for Rapid Reporting and Management 261 12.4 Faster and Cheaper: Detecting Falsification With GIS Tools 265 12.5 Putting It All Together: Field Supervisor Dashboards 268 12.6 Discussion 273 References 275 13 Total Survey Error for Longitudinal Surveys 279Peter Lynn and Peter J. Lugtig 13.1 Introduction 279 13.2 Distinctive Aspects of Longitudinal Surveys 280 13.3 TSE Components in Longitudinal Surveys 281 13.4 Design of Longitudinal Surveys from a TSE Perspective 285 13.5 Examples of Tradeoffs in Three Longitudinal Surveys 290 13.6 Discussion 294 References 295 14 Text Interviews on Mobile Devices 299Frederick G. Conrad, Michael F. Schober, Christopher Antoun, Andrew L. Hupp, and H. Yanna Yan 14.1 Texting as a Way of Interacting 300 14.2 Contacting and Inviting Potential Respondents through Text 303 14.3 Texting as an Interview Mode 303 14.4 Costs and Efficiency of Text Interviewing 312 14.5 Discussion 314 References 315 15 Quantifying Measurement Errors in Partially Edited Business Survey Data 319Thomas Laitila, Karin Lindgren, Anders Norberg, and Can Tongur 15.1 Introduction 319 15.2 Selective Editing 320 15.3 Effects of Errors Remaining After SE 325 15.4 Case Study: Foreign Trade in Goods Within the European Union 328 15.5 Editing Big Data 334 15.6 Conclusions 335 References 335 Section 4 Evaluation and Improvement 339 16 Estimating Error Rates in an Administrative Register and Survey Questions Using a Latent Class Model 341Daniel L. Oberski 16.1 Introduction 341 16.2 Administrative and Survey Measures of Neighborhood 342 16.3 A Latent Class Model for Neighborhood of Residence 345 16.4 Results 348 Appendix 16.A: Program Input and Data 355 Acknowledgments 357 References 357 17 ASPIRE: An Approach for Evaluating and Reducing the Total Error in Statistical Products with Application to Registers and the National Accounts 359Paul P. Biemer, Dennis Trewin, Heather Bergdahl, and Yingfu Xie 17.1 Introduction and Background 359 17.2 Overview of ASPIRE 360 17.3 The ASPIRE Model 362 17.4 Evaluation of Registers 367 17.5 National Accounts 371 17.6 A Sensitivity Analysis of GDP Error Sources 376 17.7 Concluding Remarks 379 Appendix 17.A: Accuracy Dimension Checklist 381 References 384 18 Classification Error in Crime Victimization Surveys: A Markov Latent Class Analysis 387Marcus E. Berzofsky and Paul P. Biemer 18.1 Introduction 387 18.2 Background 389 18.3 Analytic Approach 392 18.4 Model Selection 396 18.5 Results 399 18.6 Discussion and Summary of Findings 404 18.7 Conclusions 407 Appendix 18.A: Derivation of the Composite False-Negative Rate 407 Appendix 18.B: Derivation of the Lower Bound for False-Negative Rates from a Composite Measure 408 Appendix 18.C: Examples of Latent GOLD Syntax 408 References 410 19 Using Doorstep Concerns Data to Evaluate and Correct for Nonresponse Error in a Longitudinal Survey 413Ting Yan 19.1 Introduction 413 19.2 Data and Methods 416 19.3 Results 418 19.4 Discussion 428 Acknowledgment 430 References 430 20 Total Survey Error Assessment for Sociodemographic Subgroups in the 2012 U.S. National Immunization Survey 433Kirk M. Wolter, Vicki J. Pineau, Benjamin Skalland, Wei Zeng, James A. Singleton, Meena Khare, Zhen Zhao, David Yankey, and Philip J. Smith 20.1 Introduction 433 20.2 TSE Model Framework 434 20.3 Overview of the National Immunization Survey 437 20.4 National Immunization Survey: Inputs for TSE Model 440 20.5 National Immunization Survey TSE Analysis 445 20.6 Summary 452 References 453 21 Establishing Infrastructure for the Use of Big Data to Understand Total Survey Error: Examples from Four Survey Research Organizations Overview 457Brady T. West Part 1 Big Data Infrastructure at the Institute for Employment Research (IAB) 458Antje Kirchner, Daniela Hochfellner, Stefan Bender Acknowledgments 464 References 464 Part 2 Using Administrative Records Data at the U.S. Census Bureau: Lessons Learned from Two Research Projects Evaluating Survey Data 467Elizabeth M. Nichols, Mary H. Mulry, and Jennifer Hunter Childs Acknowledgments and Disclaimers 472 References 472 Part 3 Statistics New Zealand’s Approach to Making Use of Alternative Data Sources in a New Era of Integrated Data 474Anders Holmberg and Christine Bycroft References 478 Part 4 Big Data Serving Survey Research: Experiences at the University of Michigan Survey Research Center 478Grant Benson and Frost Hubbard Acknowledgments and Disclaimers 484 References 484 Section 5 Estimation and Analysis 487 22 Analytic Error as an Important Component of Total Survey Error: Results from a Meta-Analysis 489Brady T. West, Joseph W. Sakshaug, and Yumi Kim 22.1 Overview 489 22.2 Analytic Error as a Component of TSE 490 22.3 Appropriate Analytic Methods for Survey Data 492 22.4 Methods 495 22.5 Results 497 22.6 Discussion 505 Acknowledgments 508 References 508 23 Mixed-Mode Research: Issues in Design and Analysis 511Joop Hox, Edith de Leeuw, and Thomas Klausch 23.1 Introduction 511 23.2 Designing Mixed-Mode Surveys 512 23.3 Literature Overview 514 23.4 Diagnosing Sources of Error in Mixed-Mode Surveys 516 23.5 Adjusting for Mode Measurement Effects 523 23.6 Conclusion 527 References 528 24 The Effect of Nonresponse and Measurement Error on Wage Regression across Survey Modes: A Validation Study 531Antje Kirchner and Barbara Felderer 24.1 Introduction 531 24.2 Nonresponse and Response Bias in Survey Statistics 532 24.3 Data and Methods 534 24.4 Results 541 24.5 Summary and Conclusion 546 Acknowledgments 547 Appendix 24.A 548 Appendix 24.B 549 References 554 25 Errors in Linking Survey and Administrative Data 557Joseph W. Sakshaug and Manfred Antoni 25.1 Introduction 557 25.2 Conceptual Framework of Linkage and Error Sources 559 25.3 Errors Due to Linkage Consent 561 25.4 Erroneous Linkage with Unique Identifiers 565 25.5 Erroneous Linkage with Nonunique Identifiers 567 25.6 Applications and Practical Guidance 568 25.7 Conclusions and Take-Home Points 571 References 571 Index 575

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Book SynopsisPresenting a rigorous introduction to the modelling and characterization of random phenomena, this book stands out from the existing texts in this field by characterizing random processes in signal theory.Trade Review"This is a useful textbook for upper-undergraduate and graduate-level courses in applied mathematics as well as electrical and communications engineering departments. The book is also an excellent reference for research engineers and scientists who need to characterize random phenomena in their research." (Zentralblatt MATH, 2016)Table of ContentsPreface xiii 1 A Signal Theoretic Introduction to Random Processes 1 1.1 Introduction 1 1.2 Motivation 2 1.3 Book Overview 8 2 Background: Mathematics 11 2.1 Introduction 11 2.2 Set Theory 11 2.3 Function Theory 13 2.4 Measure Theory 18 2.5 Measurable Functions 24 2.6 Lebesgue Integration 28 2.7 Convergence 37 2.8 Lebesgue–Stieltjes Measure 39 2.9 Lebesgue–Stieltjes Integration 50 2.10 Miscellaneous Results 61 2.11 Problems 62 3 Background: Signal Theory 71 3.1 Introduction 71 3.2 Signal Orthogonality 71 3.3 Theory for Dirichlet Points 75 3.4 Dirac Delta 78 3.5 Fourier Theory 79 3.6 Signal Power 82 3.7 The Power Spectral Density 84 3.8 The Autocorrelation Function 91 3.9 Power Spectral Density–Autocorrelation Function 95 3.10 Results for the Infinite Interval 96 3.11 Convergence of Fourier Coefficients 103 3.12 Cramer’s Representation and Transform 106 3.13 Problems 125 4 Background: Probability and Random Variable Theory 153 4.1 Introduction 153 4.2 Basic Concepts: Experiments-Probability Theory 153 4.3 The Random Variable 160 4.4 Discrete and Continuous Random Variables 162 4.5 Standard Random Variables 165 4.6 Functions of a Random Variable 165 4.7 Expectation 166 4.8 Generation of Data Consistent with Defined PDF 172 4.9 Vector Random Variables 173 4.10 Pairs of Random Variables 175 4.11 Covariance and Correlation 186 4.12 Sums of Random Variables 191 4.13 Jointly Gaussian Random Variables 193 4.14 Stirling’s Formula and Approximations to Binomial 194 4.15 Problems 199 5 Introduction to Random Processes 219 5.1 Random Processes 219 5.2 Definition of a Random Process 219 5.3 Examples of Random Processes 221 5.4 Experiments and Experimental Outcomes 225 5.5 Prototypical Experiments 228 5.6 Random Variables Defined by a Random Process 232 5.7 Classification of Random Processes 233 5.8 Classification: One-Dimensional RPs 236 5.9 Sums of Random Processes 239 5.10 Problems 239 6 Prototypical Random Processes 243 6.1 Introduction 243 6.2 Bernoulli Random Processes 243 6.3 Poisson Random Processes 246 6.4 Clustered Random Processes 255 6.5 Signalling Random Processes 257 6.6 Jitter 262 6.7 White Noise 265 6.8 1/f Noise 272 6.9 Birth–Death Random Processes 275 6.10 Orthogonal Increment Random Processes 278 6.11 Linear Filtering of Random Processes 282 6.12 Summary of Random Processes 283 6.13 Problems 285 7 Characterizing Random Processes 289 7.1 Introduction 289 7.2 Time Evolution of PMF or PDF 291 7.3 First-, Second-, and Higher-Order Characterization 292 7.4 Autocorrelation and Power Spectral Density 297 7.5 Correlation 308 7.6 Notes on Average Power and Average Energy 310 7.7 Classification: Stationarity vs Non-Stationarity 316 7.8 Cramer’s Representation 323 7.9 State Space Characterization of Random Processes 335 7.10 Time Series Characterization 347 7.11 Problems 347 8 PMF and PDF Evolution 369 8.1 Introduction 369 8.2 Probability Mass/Density Function Estimation 370 8.3 Non/Semi-parametric PDF Estimation 372 8.4 PMF/PDF Evolution: Signal Plus Noise 378 8.5 PMF Evolution of a Random Walk 381 8.6 PDF Evolution: Brownian Motion 384 8.7 PDF Evolution: Signalling Random Process 388 8.8 PDF Evolution: Generalized Shot Noise 390 8.9 PDF Evolution: Switching in a CMOS Inverter 396 8.10 PDF Evolution: General Case 400 8.11 Problems 405 9 The Autocorrelation Function 417 9.1 Introduction 417 9.2 Notation and Definitions 417 9.3 Basic Results and Independence Information 419 9.4 Sinusoid with Random Amplitude and Phase 421 9.5 Random Telegraph Signal 423 9.6 Generalized Shot Noise 424 9.7 Signalling Random Process-Fixed Pulse Case 434 9.8 Generalized Signalling Random Process 441 9.9 Autocorrelation: Jittered Random Processes 453 9.10 Random Walk 456 9.11 Problems 457 10 Power Spectral Density Theory 481 10.1 Introduction 481 10.2 Power Spectral Density Theory 481 10.3 Power Spectral Density of a Periodic Pulse Train 485 10.4 PSD of a Signalling Random Process 487 10.5 Digital to Analogue Conversion 501 10.6 PSD of Shot Noise Random Processes 505 10.7 White Noise 509 10.8 1/f Noise 510 10.9 PSD of a Jittered Binary Random Process 513 10.10 PSD of a Jittered Pulse Train 517 10.11 Problems 525 11 Order Statistics 553 11.1 Introduction 553 11.2 Ordered Random Variable Theory 557 11.3 Identical RVs With Uniform Distribution 574 11.4 Uniform Distribution and Infinite Interval 584 11.5 Problems 590 12 Poisson Point Random Processes 621 12.1 Introduction 621 12.2 Characterizing Poisson Random Processes 623 12.3 PMF: Number of Points in a Subset of an Interval 625 12.4 Results From Order Statistics 630 12.5 Alternative Characterization for Infinite Interval 634 12.6 Modelling with Unordered or Ordered Times 636 12.7 Zero Crossing Times of Random Telegraph Signal 638 12.8 Point Processes: The General Case 639 12.9 Problems 639 13 Birth–Death Random Processes 649 13.1 Introduction 649 13.2 Defining and Characterizing Birth–Death Processes 649 13.3 Constant Birth Rate, Zero Death Rate Process 656 13.4 State Dependent Birth Rate - Zero Death Rate 662 13.5 Constant Death Rate, Zero Birth Rate, Process 665 13.6 Constant Birth and Constant Death Rate Process 667 13.7 Problems 669 14 The First Passage Time 677 14.1 Introduction 677 14.2 First Passage Time 677 14.3 Approaches: Establishing the First Passage Time 681 14.4 Maximum Level and the First Passage Time 685 14.5 Solutions for the First Passage Time PDF 690 14.6 Problems 695 Reference Material 709 References 717 Index 721

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Book SynopsisApplied Engineering Analysis Tai-Ran Hsu, San Jose State University, USA A resource book applying mathematics to solve engineering problems Applied Engineering Analysis is a concise textbookwhich demonstrates how toapply mathematics to solve engineering problems.Table of ContentsPreface xvii Suggestions to instructors xxi About the companion website xxv 1 Overview of Engineering Analysis 1 Chapter Learning Objectives 1 1.1 Introduction 1 1.2 Engineering Analysis and Engineering Practices 2 1.2.1 Creation 2 1.2.2 Problem Solving 2 1.2.3 Decision Making 3 1.3 “Toolbox” for Engineering Analysis 5 1.4 The Four Stages in Engineering Analysis 8 1.5 Examples of the Application of Engineering Analysis in Design 10 1.6 The “Safety Factor” in Engineering Analysis of Structures 17 1.7 Problems 19 2 Mathematical Modeling 21 Chapter Learning Objectives 21 2.1 Introduction 21 2.2 MathematicalModeling Terminology 26 2.2.1 The Numbers 26 2.2.1.1 Real Numbers 26 2.2.1.2 Imaginary Numbers 26 2.2.1.3 Absolute Values 26 2.2.1.4 Constants 26 2.2.1.5 Parameters 26 2.2.2 Variables 26 2.2.3 Functions 27 2.2.3.1 Form 1. Functions with Discrete Values 27 2.2.3.2 Form 2. Continuous Functions 27 2.2.3.3 Form 3. Piecewise Continuous Functions 28 2.2.4 Curve Fitting Technique in Engineering Analysis 30 2.2.4.1 Curve Fitting Using Polynomial Functions 30 2.2.5 Derivative 31 2.2.5.1 The Physical Meaning of Derivatives 32 2.2.5.2 Mathematical Expression of Derivatives 33 2.2.5.3 Orders of Derivatives 35 2.2.5.4 Higher-order Derivatives in Engineering Analyses 35 2.2.5.5 The Partial Derivatives 36 2.2.6 Integration 36 2.2.6.1 The Concept of Integration 36 2.2.6.2 Mathematical Expression of Integrals 37 2.3 Applications of Integrals 38 2.3.1 Plane Area by Integration 38 2.3.1.1 Plane Area Bounded by Two Curves 41 2.3.2 Volumes of Solids of Revolution 42 2.3.3 Centroids of Plane Areas 47 2.3.3.1 Centroid of a Solid of Plane Geometry with Straight Edges 49 2.3.3.2 Centroid of a Solid with Plane Geometry Defined by Multiple Functions 50 2.3.4 Average Value of Continuous Functions 52 2.4 Special Functions for MathematicalModeling 54 2.4.1 Special Functions in Solutions in MathematicalModeling 55 2.4.1.1 The Error Function and Complementary Error Function 55 2.4.1.2 The Gamma Function 56 2.4.1.3 Bessel Functions 56 2.4.2 Special Functions for Particular Physical Phenomena 58 2.4.2.1 Step Functions 58 2.4.2.2 Impulsive Functions 60 2.5 Differential Equations 62 2.5.1 The Laws of Physics for Derivation of Differential Equations 62 2.6 Problems 65 3 Vectors and Vector Calculus 73 Chapter Learning Objectives 73 3.1 Vector and Scalar Quantities 73 3.2 Vectors in Rectangular and Cylindrical Coordinate Systems 75 3.2.1 Position Vectors 75 3.3 Vectors in 2D Planes and 3D Spaces 78 3.4 Vector Algebra 79 3.4.1 Addition of Vectors 79 3.4.2 Subtraction of Vectors 79 3.4.3 Addition and Subtraction of Vectors Using Unit Vectors in Rectangular Coordinate Systems 80 3.4.4 Multiplication of Vectors 81 3.4.4.1 Scalar Multiplier 81 3.4.4.2 Dot Product 82 3.4.4.3 Cross Product 84 3.4.4.4 Cross Product of Vectors for Plane Areas 86 3.4.4.5 Triple product 86 3.4.4.6 Additional Laws of Vector Algebra 87 3.4.4.7 Use of Triple Product of Vectors for Solid Volume 87 3.5 Vector Calculus 88 3.5.1 Vector Functions 88 3.5.2 Derivatives of Vector Functions 89 3.5.3 Gradient, Divergence, and Curl 91 3.5.3.1 Gradient 91 3.5.3.2 Divergence 91 3.5.3.3 Curl 91 3.6 Applications of Vector Calculus in Engineering Analysis 92 3.6.1 In Heat Transfer 93 3.6.2 In Fluid Mechanics 93 3.6.3 In Electromagnetism with Maxwell’s Equations 94 3.7 Application of Vector Calculus in Rigid Body Dynamics 95 3.7.1 Rigid Body in RectilinearMotion 95 3.7.2 Plane CurvilinearMotion in Rectangular Coordinates 97 3.7.3 Application of Vector Calculus in the Kinematics of Projectiles 100 3.7.4 Plane CurvilinearMotion in Cylindrical Coordinates 103 3.7.5 Plane CurvilinearMotion with Normal and Tangential Components 109 3.8 Problems 114 4 Linear Algebra and Matrices 119 Chapter Learning Objectives 119 4.1 Introduction to Linear Algebra and Matrices 119 4.2 Determinants and Matrices 121 4.2.1 Evaluation of Determinants 121 4.2.2 Matrices in Engineering Analysis 123 4.3 Different Forms of Matrices 123 4.3.1 Rectangular Matrices 123 4.3.2 Square Matrices 124 4.3.3 Row Matrices 124 4.3.4 Column Matrices 124 4.3.5 Upper Triangular Matrices 124 4.3.6 Lower Triangular Matrices 125 4.3.7 Diagonal Matrices 125 4.3.8 Unit Matrices 125 4.4 Transposition of Matrices 125 4.5 Matrix Algebra 126 4.5.1 Addition and Subtraction of Matrices 126 4.5.2 Multiplication of a Matrix by a Scalar Quantity ;; 127 4.5.3 Multiplication of Two Matrices 127 4.5.4 Matrix Representation of Simultaneous Linear Equations 128 4.5.5 Additional Rules for Multiplication of Matrices 129 4.6 Matrix Inversion, [A]−1 129 4.7 Solution of Simultaneous Linear Equations 131 4.7.1 The Need for Solving Large Numbers of Simultaneous Linear Equations 131 4.7.2 Solution of Large Numbers of Simultaneous Linear Equations Using the Inverse Matrix Technique 133 4.7.3 Solution of Simultaneous Equations Using the Gaussian Elimination Method 135 4.8 Eigenvalues and Eigenfunctions 141 4.8.1 Eigenvalues and Eigenvectors of Matrices 142 4.8.2 Mathematical Expressions of Eigenvalues and Eigenvectors of Square Matrices 142 4.8.3 Application of Eigenvalues and Eigenfunctions in Engineering Analysis 146 4.9 Problems 148 5 Overview of Fourier Series 151 Chapter Learning Objectives 151 5.1 Introduction 151 5.2 Representing Periodic Functions by Fourier Series 152 5.3 Mathematical Expression of Fourier Series 154 5.4 Convergence of Fourier Series 161 5.5 Convergence of Fourier Series at Discontinuities 164 5.6 Problems 169 6 Introduction to the Laplace Transform and Applications 171 Chapter Learning Objectives 171 6.1 Introduction 171 6.2 Mathematical Operator of Laplace Transform 172 6.3 Properties of the Laplace Transform 174 6.3.1 Linear Operator Property 174 6.3.2 Shifting Property 175 6.3.3 Change of Scale Property 175 6.4 Inverse Laplace Transform 176 6.4.1 Using the Laplace Transform Tables in Reverse 176 6.4.2 The Partial Fraction Method 176 6.4.3 The Convolution Theorem 178 6.5 Laplace Transform of Derivatives 180 6.5.1 Laplace Transform of Ordinary Derivatives 180 6.5.2 Laplace Transform of Partial Derivatives 181 6.6 Solution of Ordinary Differential Equations Using Laplace Transforms 184 6.6.1 Laplace Transform for Solving Nonhomogeneous Differential Equations 184 6.6.2 Differential Equation for the Bending of Beams 186 6.7 Solution of Partial Differential Equations Using Laplace Transforms 192 6.8 Problems 195 7 Application of First-order Differential Equations in Engineering Analysis 199 Chapter Learning Objectives 199 7.1 Introduction 199 7.2 Solution Methods for First-order Ordinary Differential Equations 200 7.2.1 Solution Methods for Separable Differential Equations 200 7.2.2 Solution of Linear, Homogeneous Equations 201 7.2.3 Solution of Linear, Nonhomogeneous Equations 202 7.3 Application of First-order Differential Equations in Fluid Mechanics Analysis 204 7.3.1 Fundamental Concepts 204 7.3.2 The Bernoulli Equation 205 7.3.3 The Continuity Equation 206 7.4 Liquid Flow in Reservoirs, Tanks, and Funnels 206 7.4.1 Derivation of Differential Equations 207 7.4.2 Solution of Differential Equations 208 7.4.3 Drainage of Tapered Funnels 209 7.5 Application of First-order Differential Equations in Heat Transfer Analysis 217 7.5.1 Fourier’s Law of Heat Conduction in Solids 217 7.5.2 Mathematical Expression of Fourier’s Law 218 7.5.3 Heat Flux in a Three-dimensional Space 221 7.5.4 Newton’s Cooling Law for Heat Convection 227 7.5.5 Heat Transfer between Solids and Fluids 227 7.6 Rigid Body Dynamics under the Influence of Gravitation 233 7.7 Problems 237 8 Application of Second-order Ordinary Differential Equations in Mechanical Vibration Analysis 243 Chapter Learning Objectives 243 8.1 Introduction 243 8.2 Solution Method for Typical Homogeneous, Second-order Linear Differential Equations with Constant Coefficients 243 8.3 Applications in Mechanical Vibration Analyses 246 8.3.1 What Is Mechanical Vibration? 246 8.3.2 Common Sources for Vibration 247 8.3.3 Common Types of Vibration 247 8.3.4 Classification of Mechanical Vibration Analyses 247 8.3.4.1 Free Vibration 247 8.3.4.2 Damped Vibration 248 8.3.4.3 Forced Vibration 249 8.4 Mathematical Modeling of Free Mechanical Vibration: Simple Mass–Spring Systems 249 8.4.1 Solution of the Differential Equation 251 8.5 Modeling of Damped FreeMechanical Vibration: Simple Mass–Spring Systems 254 8.5.1 The Physical Model 254 8.5.2 The Differential Equation 255 8.5.3 Solution of the Differential Equation 256 8.6 Solution of Nonhomogeneous, Second-order Linear Differential Equations with Constant Coefficients 258 8.6.1 Typical Equation and Solutions 258 8.6.2 The Complementary and Particular Solutions 258 8.6.3 The Particular Solutions 259 8.6.4 Special Case for Solution of Nonhomogeneous Second-order Differential Equations 263 8.7 Application in Forced Vibration Analysis 264 8.7.1 Derivation of the Differential Equation 264 8.7.2 Resonant Vibration 266 8.8 Near Resonant Vibration 273 8.9 Natural Frequencies of Structures and Modal Analysis 277 8.10 Problems 280 9 Applications of Partial Differential Equations in Mechanical Engineering Analysis 285 Chapter Learning Objectives 285 9.1 Introduction 285 9.2 Partial Derivatives 285 9.3 Solution Methods for Partial Differential Equations 287 9.3.1 The Separation of VariablesMethod 287 9.3.2 Laplace Transform Method for Solution of Partial Differential Equations 288 9.3.3 Fourier Transform Method for Solution of Partial Differential Equations 288 9.4 Partial Differential Equations for Heat Conduction in Solids 291 9.4.1 Heat Conduction in Engineering Analysis 291 9.4.2 Derivation of Partial Differential Equations for Heat Conduction Analysis 291 9.4.3 Heat Conduction Equation in Rectangular Coordinate Systems 292 9.4.4 Heat Conduction Equation in a Cylindrical Polar Coordinate System 293 9.4.5 General Heat Conduction Equation 293 9.4.6 Initial and Boundary Conditions 293 9.5 Solution of Partial Differential Equations for Transient Heat Conduction Analysis 298 9.5.1 Transient Heat Conduction Analysis in Rectangular Coordinate System 298 9.5.2 Transient Heat Conduction Analysis in the Cylindrical Polar Coordinate System 303 9.6 Solution of Partial Differential Equations for Steady-state Heat Conduction Analysis 308 9.6.1 Steady-state Heat Conduction Analysis in the Rectangular Coordinate System 308 9.6.2 Steady-state Heat Conduction Analysis in the Cylindrical Polar Coordinate System 311 9.7 Partial Differential Equations for Transverse Vibration of Cable Structures 314 9.7.1 Derivation of Partial Differential Equations for Free Vibration of Cable Structures 314 9.7.2 Solution of Partial Differential Equation for Free Vibration of Cable Structures 318 9.7.3 Convergence of Series Solutions 322 9.7.4 Modes of Vibration of Cable Structures 323 9.8 Partial Differential Equations for Transverse Vibration of Membranes 328 9.8.1 Derivation of the Partial Differential Equation 328 9.8.2 Solution of the Partial Differential Equation for Plate Vibration 331 9.8.3 Numerical Solution of the Partial Differential Equation for Plate Vibration 334 9.9 Problems 336 10 Numerical Solution Methods for Engineering Analysis 339 Chapter Learning Objectives 339 10.1 Introduction 339 10.2 Engineering Analysis with Numerical Solutions 340 10.3 Solution of Nonlinear Equations 341 10.3.1 Solution Using Microsoft Excel Software 341 10.3.2 The Newton–RaphsonMethod 342 10.4 Numerical Integration Methods 347 10.4.1 The Trapezoidal Rule for Numerical Integration 348 10.4.2 Numerical Integration by Simpson’s One-third Rule 352 10.4.3 Numerical Integration by Gaussian Quadrature 356 10.5 Numerical Methods for Solving Differential Equations 361 10.5.1 The Principle of Finite Difference 362 10.5.2 TheThree Basic Finite-difference Schemes 363 10.5.3 Finite-difference Formulation for Partial Derivatives 366 10.5.4 Numerical Solution of Differential Equations 367 10.5.4.1 The Second-order Runge–Kutta Method 367 10.5.4.2 The Fourth-order Runge–Kutta Method 369 10.5.4.3 Runge–Kutta Method for Higher-order Differential Equations 370 10.6 Introduction to Numerical Analysis Software Packages 375 10.6.1 Introduction to Mathematica 375 10.6.2 Introduction to MATLAB 376 10.7 Problems 377 11 Introduction to Finite-element Analysis 381 Chapter Learning Objectives 381 11.1 Introduction 381 11.2 The Principle of Finite-element Analysis 383 11.3 Steps in Finite-element Analysis 383 11.3.1 Derivation of Interpolation Function for Simplex Elements with Scalar Quantities at Nodes 388 11.3.2 Derivation of Interpolation Function for Simplex Elements with Vector Quantities at Nodes 390 11.4 Output of Finite-element Analysis 401 11.5 Elastic Stress Analysis of Solid Structures by the Finite-elementMethod 403 11.5.1 Stresses 404 11.5.2 Displacements 406 11.5.3 Strains 406 11.5.4 Fundamental Relationships 407 11.5.4.1 Strain–Displacement Relations 407 11.5.4.2 Stress–Strain Relations 408 11.5.4.3 Strain Energy in Deformed Elastic Solids 409 11.5.5 Finite-element Formulation 409 11.5.6 Finite-element Formulation for One-dimensional Solid Structures 413 11.6 General-purpose Finite-element Analysis Codes 417 11.6.1 Common Features in General-purpose Finite-element Codes 419 11.6.2 Simulation using general-purpose finite-element codes 420 11.7 Problems 422 12 Statistics for Engineering Analysis 425 Chapter Learning Objectives 425 12.1 Introduction 425 12.2 Statistics in Engineering Practice 427 12.3 The Scope of Statistics 428 12.4 Common Concepts and Terminology in Statistical Analysis 430 12.4.1 The Mode of a Dataset 430 12.4.2 The Histogram of a Statistical Dataset 430 12.4.3 The Mean 431 12.4.4 The Median 433 12.4.5 Variation and Deviation 433 12.5 Standard Deviation (;;) and Variance (;;2) 434 12.5.1 The Standard Deviation 434 12.5.2 The Variance 434 12.6 The Normal Distribution Curve and Normal Distribution Function 435 12.7 Weibull Distribution Function for Probabilistic Engineering Design 437 12.7.1 Statistical Approach to the Design of Structures Made of Ceramic and Brittle Materials 438 12.7.2 TheWeibull Distribution Function 439 12.7.3 Estimation ofWeibull Parameters 441 12.7.4 Probabilistic Design of Structures with Random Fracture Strength of Materials 443 12.8 Statistical Quality Control 447 12.9 Statistical Process Control 448 12.9.1 Quality Issues in Industrial Automation and Mass Production 448 12.9.2 The Statistical Process Control Method 449 12.10 The “Control Charts” 450 12.10.1 Three-Sigma Control Charts 451 12.10.2 Control Charts for Sample Ranges (the R-Chart) 453 12.11 Problems 456 Bibliography 459 A Table for the Laplace Transform 463 B Recommended Units for Engineering Analysis 465 C Conversion of Units 467 D Application of MATLAB Software for Numerical Solutions in Engineering Analysis 469 Index 483

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Book SynopsisThe only how-to guide offering a unified, systemic approach to acquiring, cleaning, and managing data in R Every experienced practitioner knows that preparing data for modeling is a painstaking, time-consuming process. Adding to the difficulty is that most modelers learn the steps involved in cleaning and managing data piecemeal, often on the fly, or they develop their own ad hoc methods. This book helps simplify their task by providing a unified, systematic approach to acquiring, modeling, manipulating, cleaning, and maintaining data in R. Starting with the very basics, data scientists Samuel E. Buttrey and Lyn R. Whitaker walk readers through the entire process. From what data looks like and what it should look like, they progress through all the steps involved in getting data ready for modeling. They describe best practices for acquiring data from numerous sources; explore key issues in data handling, including text/regular expressions, big data, paralTable of ContentsAbout the Authors xv Preface xvii Acknowledgments xix About the CompanionWebsite xxi 1 R 1 1.1 Introduction 1 1.1.1 What Is R? 1 1.1.2 Who Uses R and Why? 2 1.1.3 Acquiring and Installing R 2 1.1.4 Starting and Quitting R 3 1.2 Data 3 1.2.1 Acquiring Data 3 1.2.2 Cleaning Data 4 1.2.3 The Goal of Data Cleaning 4 1.2.4 Making YourWork Reproducible 5 1.3 The Very Basics of R 5 1.3.1 Top Ten Quick Facts You Need to Know about R 5 1.3.2 Vocabulary 8 1.3.3 Calculating and Printing in R 11 1.4 Running an R Session 12 1.4.1 Where Your Data Is Stored 13 1.4.2 Options 13 1.4.3 Scripts 14 1.4.4 R Packages 14 1.4.5 RStudio and Other GUIs 15 1.4.6 Locales and Character Sets 15 1.5 Getting Help 16 1.5.1 At the Command Line 16 1.5.2 The Online Manuals 16 1.5.3 On the Internet 17 1.5.4 Further Reading 17 1.6 How to Use This Book 17 1.6.1 Syntax and Conventions inThis Book 17 1.6.2 The Chapters 18 2 RData,Part1:Vectors 21 2.1 Vectors 21 2.1.1 Creating Vectors 21 2.1.2 Sequences 22 2.1.3 Logical Vectors 23 2.1.4 Vector Operations 24 2.1.5 Names 27 2.2 Data Types 27 2.2.1 Some Less-Common Data Types 28 2.2.2 What Type of Vector IsThis? 28 2.2.3 Converting from One Type to Another 29 2.3 Subsets of Vectors 31 2.3.1 Extracting 31 2.3.2 Vectors of Length 0 34 2.3.3 Assigning or Replacing Elements of a Vector 35 2.4 Missing Data (NA) and Other Special Values 36 2.4.1 The Effect of NAs in Expressions 37 2.4.2 Identifying and Removing or Replacing NAs 37 2.4.3 Indexing with NAs 39 2.4.4 NaN and Inf Values 40 2.4.5 NULL Values 40 2.5 The table() Function 40 2.5.1 Two- and Higher-Way Tables 42 2.5.2 Operating on Elements of a Table 42 2.6 Other Actions on Vectors 45 2.6.1 Rounding 45 2.6.2 Sorting and Ordering 45 2.6.3 Vectors as Sets 46 2.6.4 Identifying Duplicates and Matching 47 2.6.5 Finding Runs of Duplicate Values 49 2.7 Long Vectors and Big Data 50 2.8 Chapter Summary and Critical Data Handling Tools 50 3 R Data, Part 2:More Complicated Structures 53 3.1 Introduction 53 3.2 Matrices 53 3.2.1 Extracting and Assigning 54 3.2.2 Row and Column Names 56 3.2.3 Applying a Function to Rows or Columns 57 3.2.4 Missing Values in Matrices 59 3.2.5 Using a Matrix Subscript 60 3.2.6 Sparse Matrices 61 3.2.7 Three- and Higher-Way Arrays 62 3.3 Lists 62 3.3.1 Extracting and Assigning 64 3.3.2 Lists in Practice 65 3.4 Data Frames 67 3.4.1 Missing Values in Data Frames 69 3.4.2 Extracting and Assigning in Data Frames 69 3.4.3 ExtractingThings That Aren’tThere 72 3.5 Operating on Lists and Data Frames 74 3.5.1 Split, Apply, Combine 75 3.5.2 All-Numeric Data Frames 77 3.5.3 Convenience Functions 78 3.5.4 Re-Ordering, De-Duplicating, and Sampling from Data Frames 79 3.6 Date and Time Objects 80 3.6.1 Formatting Dates 80 3.6.2 Common Operations on Date Objects 82 3.6.3 Differences between Dates 83 3.6.4 Dates and Times 83 3.6.5 Creating POSIXt Objects 85 3.6.6 Mathematical Functions for Date and Times 86 3.6.7 Missing Values in Dates 88 3.6.8 Using Apply Functions with Dates and Times 89 3.7 Other Actions on Data Frames 90 3.7.1 Combining by Rows or Columns 90 3.7.2 Merging Data Frames 91 3.7.3 Comparing Two Data Frames 94 3.7.4 Viewing and Editing Data Frames Interactively 94 3.8 Handling Big Data 94 3.9 Chapter Summary and Critical Data Handling Tools 96 4 RData, Part 3: Text and Factors 99 4.1 Character Data 100 4.1.1 The length() and nchar() Functions 100 4.1.2 Tab, New-Line, Quote, and Backslash Characters 100 4.1.3 The Empty String 101 4.1.4 Substrings 102 4.1.5 Changing Case and Other Substitutions 103 4.2 Converting Numbers into Text 103 4.2.2 Scientific Notation 106 4.2.3 Discretizing a Numeric Variable 107 4.3 Constructing Character Strings: Paste in Action 109 4.3.1 Constructing Column Names 109 4.3.2 Tabulating Dates by Year and Month or Quarter Labels 111 4.3.3 Constructing Unique Keys 112 4.3.4 Constructing File and Path Names 112 4.4 Regular Expressions 112 4.4.1 Types of Regular Expressions 113 4.4.2 Tools for Regular Expressions in R 113 4.4.3 Special Characters in Regular Expressions 114 4.4.4 Examples 114 4.4.5 The regexpr() Function and Its Variants 121 4.4.6 Using Regular Expressions in Replacement 123 4.4.7 Splitting Strings at Regular Expressions 124 4.4.8 Regular Expressions versusWildcard Matching 125 4.4.9 Common Data Cleaning Tasks Using Regular Expressions 126 4.4.10 Documenting and Debugging Regular Expressions 127 4.5 UTF-8 and Other Non-ASCII Characters 128 4.5.1 Extended ASCII for Latin Alphabets 128 4.5.2 Non-Latin Alphabets 129 4.5.3 Character and String Encoding in R 130 4.6 Factors 131 4.6.1 What Is a Factor? 131 4.6.2 Factor Levels 132 4.6.3 Converting and Combining Factors 134 4.6.4 Missing Values in Factors 136 4.6.5 Factors in Data Frames 137 4.7 R Object Names and Commands as Text 137 4.7.1 R Object Names as Text 137 4.7.2 R Commands as Text 138 4.8 Chapter Summary and Critical Data Handling Tools 140 5 Writing Functions and Scripts 143 5.1 Functions 143 5.1.1 Function Arguments 144 5.1.2 Global versus Local Variables 148 5.1.3 Return Values 149 5.1.4 Creating and Editing Functions 151 5.2 Scripts and Shell Scripts 153 5.2.1 Line-by-Line Parsing 155 5.3 Error Handling and Debugging 156 5.3.1 Debugging Functions 156 5.3.2 Issuing Error andWarning Messages 158 5.3.3 Catching and Processing Errors 159 5.4 Interacting with the Operating System 161 5.4.1 File and Directory Handling 162 5.4.2 Environment Variables 162 5.5 SpeedingThings Up 163 5.5.1 Profiling 163 5.5.2 Vectorizing Functions 164 5.5.3 Other Techniques to Speed Things Up 165 5.6 Chapter Summary and Critical Data Handling Tools 167 5.6.1 Programming Style 168 5.6.2 Common Bugs 169 5.6.3 Objects, Classes, and Methods 170 6 Getting Data into and out of R 171 6.1 Reading Tabular ASCII Data into Data Frames 171 6.1.1 Files with Delimiters 172 6.1.2 Column Classes 173 6.1.3 Common Pitfalls in Reading Tables 175 6.1.4 An Example of When read.table() Fails 177 6.1.5 Other Uses of the scan() Function 181 6.1.6 Writing Delimited Files 182 6.1.7 Reading andWriting Fixed-Width Files 183 6.1.8 A Note on End-of-Line Characters 183 6.2 Reading Large, Non-Tabular, or Non-ASCII Data 184 6.2.1 Opening and Closing Files 184 6.2.2 Reading andWriting Lines 185 6.2.3 Reading andWriting UTF-8 and Other Encodings 187 6.2.4 The Null Character 187 6.2.5 Binary Data 188 6.2.6 Reading Problem Files in Action 190 6.3 Reading Data From Relational Databases 192 6.3.1 Connecting to the Database Server 193 6.3.2 Introduction to SQL 194 6.4 Handling Large Numbers of Input Files 197 6.5 Other Formats 200 6.5.1 Using the Clipboard 200 6.5.2 Reading Data from Spreadsheets 201 6.5.3 Reading Data from theWeb 203 6.5.4 Reading Data from Other Statistical Packages 208 6.6 Reading andWriting R Data Directly 209 6.7 Chapter Summary and Critical Data Handling Tools 210 7 Data Handling in Practice 213 7.1 Acquiring and Reading Data 213 7.2 Cleaning Data 214 7.3 Combining Data 216 7.3.1 Combining by Row 216 7.3.2 Combining by Column 218 7.3.3 Merging by Key 218 7.4 Transactional Data 219 7.4.1 Example of Transactional Data 219 7.4.2 Combining Tabular and Transactional Data 221 7.5 Preparing Data 225 7.6 Documentation and Reproducibility 226 7.7 The Role of Judgment 228 7.8 Data Cleaning in Action 230 7.8.1 Reading and Cleaning BedBath1.csv 231 7.8.2 Reading and Cleaning BedBath2.csv 236 7.8.3 Combining the BedBath Data Frames 238 7.8.4 Reading and Cleaning EnergyUsage.csv 239 7.8.5 Merging the BedBath and EnergyUsage Data Frames 242 7.9 Chapter Summary and Critical Data Handling Tools 245 8 Extended Exercise 247 8.1 Introduction to the Problem 247 8.1.1 The Goal 248 8.1.2 Modeling Considerations 249 8.1.3 Examples ofThings to Check 249 8.2 The Data 250 8.3 Five Important Fields 252 8.4 Loan and Application Portfolios 252 8.4.1 Layout of the Beachside Lenders Data 253 8.4.2 Layout of theWilson and Sons Data 254 8.4.3 Combining the Two Portfolios 254 8.5 Scores 256 8.5.1 Scores Layout 256 8.6 Co-borrower Scores 257 8.6.1 Co-borrower Score Examples 258 8.7 Updated KScores 259 8.7.1 Updated KScores Layout 259 8.8 Loans to Be Excluded 260 8.8.1 Sample Exclusion File 260 8.9 Response Variable 260 8.10 Assembling the Final Data Sets 262 8.10.1 Final Data Layout 262 8.10.2 Concluding Remarks 263 A Hints and Pseudocode 265 A.1 Loan Portfolios 265 A.1.1 Things to Check 266 A.2 Scores Database 267 A.2.1 Things to Check 268 A.3 Co-borrower Scores 269 A.3.1 Things to Check 270 A.4 Updated KScores 271 A.4.1 Things to Check 272 A.5 Excluder Files 272 A.5.1 Things to Check 272 A.6 Payment Matrix 273 A.6.1 Things to Check 274 A.7 Starting the Modeling Process 275 Bibliography 277 Index 279

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Book SynopsisThe compiled works of the man behind the evolution of quantitative finance Finance, Economics, and Mathematics is the complete Vasicek reference work, including published and unpublished work and interviews with the man himself. The name Oldrich A. Vasicek is synonymous with cutting-edge research in the finance fields, and this book comes straight from the source to bring you the undiluted mother lode of quant wisdom from one of the founders of the field. From his early work in yield curve dynamics, to the mean-reverting short-rate model, to his thoughts on derivatives pricing, to his work on credit risk, to his most recent research on the economics of interest rates, this book represents the life''s work of an industry leader. Going beyond the papers, you''ll also find the more personal side inspirational as Vasicek talks about the academics and professionals who made lasting impressions and collaborated, debated, and ultimately helped spawn some of his greatest thinkTable of ContentsForeword (by Robert C. Merton) ix Preface xi PART ONE Efforts and Opinions 1 CHAPTER 1 Introduction to Part I 3 CHAPTER 2 Lifetime Achievement Award (by Dwight Cass) 7 CHAPTER 3 One-on-One Interview with Oldrich Alfons Vasicek (by Nina Mehta) 13 CHAPTER 4 Credit Superquant (by Robert Hunter) 21 PART TWO Term Structure of Interest Rates 27 CHAPTER 5 Introduction to Part II 29 CHAPTER 6 An Equilibrium Characterization of the Term Structure 33 CHAPTER 7 The Liquidity Premium 45 CHAPTER 8 Term Structure Modeling Using Exponential Splines (with Gifford Fong) 49 CHAPTER 9 The Heath, Jarrow, Morton Model 63 PART THREE General Equilibrium 65 CHAPTER 10 Introduction to Part III 67 CHAPTER 11 The Economics of Interest Rates 71 CHAPTER 12 General Equilibrium with Heterogeneous Participants and Discrete Consumption Times 89 CHAPTER 13 Independence of Production and Technology Risks 107 CHAPTER 14 Risk-Neutral Economy and Zero Price of Risk 111 PART FOUR Credit 125 CHAPTER 15 Introduction to Part IV 127 CHAPTER 16 Credit Valuation 131 CHAPTER 17 Probability of Loss on Loan Portfolio 143 CHAPTER 18 Limiting Loan Loss Probability Distribution 147 CHAPTER 19 Loan Portfolio Value 149 CHAPTER 20 The Empirical Test of the Distribution of Loan Portfolio Losses 161 PART FIVE Markets, Portfolios, and Securities 163 CHAPTER 21 Introduction to Part V 165 CHAPTER 22 The Efficient Market Model (with John A. McQuown) 169 CHAPTER 23 A Risk Minimizing Strategy for Portfolio Immunization (with Gifford Fong) 195 CHAPTER 24 The Tradeoff between Return and Risk in Immunized Portfolios (with Gifford Fong) 203 CHAPTER 25 Bond Performance: Analyzing Sources of Return (with Gifford Fong and Charles J. Pearson) 213 CHAPTER 26 The Best-Return Strategy 223 CHAPTER 27 Volatility: Omission Impossible (with Gifford Fong and Daihyun Yoo) 237 CHAPTER 28 A Multidimensional Framework for Risk Analysis (with Gifford Fong) 247 CHAPTER 29 Plugging into Electricity (with Hélyette Geman) 261 CHAPTER 30 Pricing of Energy Derivatives 277 PART SIX Probability Theory and Statistics 281 CHAPTER 31 Introduction to Part VI 283 CHAPTER 32 A Note on Using Cross-sectional Information in Bayesian Estimation of Security Betas 287 CHAPTER 33 A Series Expansion for the Bivariate Normal Integral 297 CHAPTER 34 A Conditional Law of Large Numbers 305 CHAPTER 35 A Test for Normality Based on Sample Entropy 315 CHAPTER 36 Monotone Measures of Ergodicity for Markov Chains (with Julian Keilson) 325 CHAPTER 37 An Inequality for the Variance of Waiting Time under a General Queueing Discipline 333 About the Author 339 Index 341

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Book SynopsisA practical introduction to intelligent computer vision theory, design, implementation, and technology The past decade has witnessed epic growth in image processing and intelligent computer vision technology.Table of ContentsPreface xi About the Companion Website xv 1 Introduction 1 1.1 The Scope of the Book 2 1.1.1 Classification 3 1.1.2 Parameter Estimation 4 1.1.3 State Estimation 5 1.1.4 Relations between the Subjects 7 1.2 Engineering 10 1.3 The Organization of the Book 12 1.4 Changes from First Edition 14 1.5 References 15 2 PRTools Introduction 17 2.1 Motivation 17 2.2 Essential Concepts 18 2.3 PRTools Organization Structure and Implementation 22 2.4 Some Details about PRTools 26 2.4.1 Datasets 26 2.4.2 Datafiles 30 2.4.3 Datafiles Help Information 31 2.4.4 Classifiers and Mappings 34 2.4.5 Mappings Help Information 36 2.4.6 How to Write Your Own Mapping 38 2.5 Selected Bibliography 42 3 Detection and Classification 43 3.1 Bayesian Classification 46 3.1.1 Uniform Cost Function and Minimum Error Rate 53 3.1.2 Normal Distributed Measurements; Linear and Quadratic Classifiers 56 3.2 Rejection 62 3.2.1 Minimum Error Rate Classification with Reject Option 63 3.3 Detection: The Two-Class Case 66 3.4 Selected Bibliography 74 Exercises 74 4 Parameter Estimation 77 4.1 Bayesian Estimation 79 4.1.1 MMSE Estimation 86 4.1.2 MAP Estimation 87 4.1.3 The Gaussian Case with Linear Sensors 88 4.1.4 Maximum Likelihood Estimation 89 4.1.5 Unbiased Linear MMSE Estimation 91 4.2 Performance Estimators 94 4.2.1 Bias and Covariance 95 4.2.2 The Error Covariance of the Unbiased Linear MMSE Estimator 99 4.3 Data Fitting 100 4.3.1 Least Squares Fitting 101 4.3.2 Fitting Using a Robust Error Norm 104 4.3.3 Regression 107 4.4 Overview of the Family of Estimators 110 4.5 Selected Bibliography 111 Exercises 112 5 State Estimation 115 5.1 A General Framework for Online Estimation 117 5.1.1 Models 117 5.1.2 Optimal Online Estimation 123 5.2 Infinite Discrete-Time State Variables 125 5.2.1 Optimal Online Estimation in Linear-Gaussian Systems 125 5.2.2 Suboptimal Solutions for Non-linear Systems 133 5.3 Finite Discrete-Time State Variables 147 5.3.1 Hidden Markov Models 148 5.3.2 Online State Estimation 152 5.3.3 Offline State Estimation 156 5.4 Mixed States and the Particle Filter 163 5.4.1 Importance Sampling 164 5.4.2 Resampling by Selection 166 5.4.3 The Condensation Algorithm 167 5.5 Genetic State Estimation 170 5.5.1 The Genetic Algorithm 170 5.5.2 Genetic State Estimation 176 5.5.3 Computational Issues 177 5.6 State Estimation in Practice 183 5.6.1 System Identification 185 5.6.2 Observability, Controllability and Stability 188 5.6.3 Computational Issues 193 5.6.4 Consistency Checks 196 5.7 Selected Bibliography 201 Exercises 204 6 Supervised Learning 207 6.1 Training Sets 208 6.2 Parametric Learning 210 6.2.1 Gaussian Distribution, Mean Unknown 211 6.2.2 Gaussian Distribution, Covariance Matrix Unknown 212 6.2.3 Gaussian Distribution, Mean and Covariance Matrix Both Unknown 213 6.2.4 Estimation of the Prior Probabilities 215 6.2.5 Binary Measurements 216 6.3 Non-parametric Learning 217 6.3.1 Parzen Estimation and Histogramming 218 6.3.2 Nearest Neighbour Classification 223 6.3.3 Linear Discriminant Functions 230 6.3.4 The Support Vector Classifier 237 6.3.5 The Feedforward Neural Network 242 6.4 Adaptive Boosting – Adaboost 245 6.5 Convolutional Neural Networks (CNNs) 249 6.5.1 Convolutional Neural Network Structure 249 6.5.2 Computation and Training of CNNs 251 6.6 Empirical Evaluation 252 6.7 Selected Bibliography 257 Exercises 257 7 Feature Extraction and Selection 259 7.1 Criteria for Selection and Extraction 261 7.1.1 Interclass/Intraclass Distance 262 7.1.2 Chernoff–Bhattacharyya Distance 267 7.1.3 Other Criteria 270 7.2 Feature Selection 272 7.2.1 Branch-and-Bound 273 7.2.2 Suboptimal Search 275 7.2.3 Several New Methods of Feature Selection 278 7.2.4 Implementation Issues 287 7.3 Linear Feature Extraction 288 7.3.1 Feature Extraction Based on the Bhattacharyya Distance with Gaussian Distributions 291 7.3.2 Feature Extraction Based on Inter/Intra Class Distance 296 7.4 References 300 Exercises 300 8 Unsupervised Learning 303 8.1 Feature Reduction 304 8.1.1 Principal Component Analysis 304 8.1.2 Multidimensional Scaling 309 8.1.3 Kernel Principal Component Analysis 315 8.2 Clustering 320 8.2.1 Hierarchical Clustering 323 8.2.2 K-Means Clustering 327 8.2.3 Mixture of Gaussians 329 8.2.4 Mixture of probabilistic PCA 335 8.2.5 Self-Organizing Maps 336 8.2.6 Generative Topographic Mapping 342 8.3 References 345 Exercises 346 9 Worked Out Examples 349 9.1 Example on Image Classification with PRTools 349 9.1.1 Example on Image Classification 349 9.1.2 Example on Face Classification 354 9.1.3 Example on Silhouette Classification 357 9.2 Boston Housing Classification Problem 361 9.2.1 Dataset Description 361 9.2.2 Simple Classification Methods 363 9.2.3 Feature Extraction 365 9.2.4 Feature Selection 367 9.2.5 Complex Classifiers 368 9.2.6 Conclusions 371 9.3 Time-of-Flight Estimation of an Acoustic Tone Burst 372 9.3.1 Models of the Observed Waveform 374 9.3.2 Heuristic Methods for Determining the ToF 376 9.3.3 Curve Fitting 377 9.3.4 Matched Filtering 379 9.3.5 ml Estimation Using Covariance Models for the Reflections 380 9.3.6 Optimization and Evaluation 385 9.4 Online Level Estimation in a Hydraulic System 392 9.4.1 Linearized Kalman Filtering 394 9.4.2 Extended Kalman Filtering 397 9.4.3 Particle Filtering 398 9.4.4 Discussion 403 9.5 References 406 Appendix A: Topics Selected from Functional Analysis 407 Appendix B: Topics Selected from Linear Algebra and Matrix Theory 421 Appendix C: Probability Theory 437 Appendix D: Discrete-Time Dynamic Systems 453 Index 459

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Book SynopsisSolutions Manual to accompany Introduction to Quantitative Methods in Business: With Applications Using Microsoft(R) Office Excel(R).Table of Contents1. The Mathematical Toolbox: A Summary 1 1.2 Linear Functions 1 1.3.1 Solving Two Simultaneous Linear Equations 1 1.4 Summation Notation 2 1.5 Sets 3 1.6 Functions and Graphs 3 1.7 Working with Functions 4 1.8 Differentiation and Integration 5 Solutions to Odd-Numbered Exercises 8 2. Applications of Linear and Nonlinear Functions: A Summary 32 2.2 Linear Demand and Supply Functions 32 2.3 Linear Total Cost and Total Revenue Functions 33 2.4 Market Equilibrium 33 2.6 Applications of Nonlinear Functions 34 2.7 Present Value of an Income Stream 35 2.8 Average Values 35 2.9 Marginal Values 36 2.10 Elasticity 36 Solutions to Odd-Numbered Exercises 37 3. Optimization: A Summary 47 3.2 Unconstrained Optimization 47 3.2.1 Models of Profit and Revenue Maximization 47 3.2.3 Solution Using the Calculus Approach 47 3.2.5 Solution Using the Calculus Approach 47 3.3 Models of Cost Minimization: Inventory Cost Functions and Economic Order Quantity (EOQ) 48 3.3.2 Solution Using the Calculus Approach 49 3.4 Constrained Optimization: Linear Programming 50 3.4.1 Linear Programming: Maximization 50 3.4.2 Linear Programming: Minimization 51 Solutions to Odd-Numbered Exercises 52 4. What Is Business Statistics? 68 4.3 Descriptive Statistics: Tabular and Graphical Techniques 68 4.4 Descriptive Statistics: Numerical Measures of Central Tendency or Location of Data 70 4.4.1 Population Mean 70 4.4.2 Sample Mean 70 4.4.3 Weighted Mean 70 4.4.4 Mean of a Frequency Distribution: Grouped Data 71 4.4.5 Geometric Mean 71 4.4.6 Median 71 4.4.7 Quantiles, Quartiles, Deciles, and Percentiles 71 4.4.8 Mode 72 4.5 Descriptive Statistics: Measures of Dispersion (Variability or Spread) 73 4.5.2 Variance 73 4.5.3 Standard Deviation 74 4.5.4 Coefficient of Variation 74 4.5.5 Some Important Uses of the Standard Deviation 75 1. Standardization of Values 75 2. Chebysheff’s Theorem 75 4.5.6 Empirical Rule 75 4.6 Measuring Skewness 76 Solutions to Odd-Numbered Exercises 76 5. Probability and Applications 96 5.2 Some Useful Definitions 96 5.3 Probability Sources 96 5.3.1 Objective Probability 96 5.4 Some Useful Definitions Involving Sets of Events in the Sample Space 96 5.5 Probability Laws 97 5.5.2 Rule of Complements 97 5.5.3 Conditional Probability 97 5.5.4 General Multiplication Rule (Product Rule) 97 5.5.5 Independent Events 98 5.5.6 Probability Tree Approach 98 5.6 Contingency Table 98 Solutions to Odd-Numbered Exercises 100 6. Random Variables and Probability Distributions 105 6.2 Probability Distribution of a Discrete Random Variable X 105 6.3 Expected Value, Variance, and Standard Deviation of a Discrete Random Variable 106 6.3.1 Some Basic Rules of Expectation 106 6.3.2 Some Useful Properties of the Variance of X 107 6.4 Continuous Random Variables and Their Probability Distributions 107 6.5 A Specific Discrete Probability Distribution: The Binomial Case 108 6.5.1 Binomial Probability Distribution 108 6.5.2 Mean and Standard Deviation of the Binomial Random Variable 109 6.5.3 Cumulative Binomial Probability Distribution 110 Solutions to Odd-Numbered Exercises 110 Index 119

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Book SynopsisSet includes Introduction to Quantitative Methods in Business: With Applications Using Microsoft Office Excel ISBN 978-1-119-22097-8 and the accompanying Solutions Manual ISBN 978-1-119-22102-9 A well-balanced and accessible introduction to the elementary quantitative methods and Microsoft Office Excel applications used to guide business decision making Featuring quantitative techniques essential for modeling modern business situations, Introduction to Quantitative Methods in Business: With Applications Using Microsoft Office Excel provides guidance to assessing real-world data sets using Excel. The book presents a balanced approach to the mathematical tools and techniques with applications used in the areas of business, finance, economics, marketing, and operations. The authors begin by establishing a solid foundation of basic mathematics and statistics before moving on to more advanced concepts. The first part of the book starts by develop

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Book SynopsisA comprehensive introduction to the theory and practice of contemporary data science analysis for railway track engineering Featuring a practical introduction to state-of-the-art data analysis for railway track engineering, Big Data and Differential Privacy: Analysis Strategies for Railway Track Engineering addresses common issues with the implementation of big data applications while exploring the limitations, advantages, and disadvantages of more conventional methods. In addition, the book provides a unifying approach to analyzing large volumes of data in railway track engineering using an array of proven methods and software technologies. Dr. Attoh-Okine considers some of today's most notable applications and implementations and highlights when a particular method or algorithm is most appropriate. Throughout, the book presents numerous real-world examples to illustrate the latest railway engineering big data applications of predictive analytics, such aTable of ContentsPreface xi Acknowledgments xiii 1 Introduction 1 1.1 General 1 1.2 Track Components 2 1.3 Characteristics of Railway Track Data 4 1.4 Railway Track Engineering Problems 6 1.5 Wheel–Rail Interface Data 11 1.6 Geometry Data 15 1.7 Track Geometry DegradationModels 20 1.8 Rail Defect Data 25 1.9 Inspection and Detection Systems 33 1.10 Rail Grinding 37 1.11 Traditional Data Analysis Techniques 40 1.12 Remarks 41 References 42 2 Data Analysis – Basic Overview 49 2.1 Introduction 49 2.2 Exploratory Data Analysis (EDA) 49 2.3 Symbolic Data Analysis 53 2.4 Imputation 54 2.5 Bayesian Methods and Big Data Analysis 56 2.6 Remarks 57 References 57 3 Machine Learning: A Basic Overview 59 3.1 Introduction 59 3.2 Supervised Learning 60 3.3 Unsupervised Learning 61 3.4 Semi-Supervised Learning 61 3.5 Reinforcement Learning 61 3.6 Data Integration 63 3.7 Data Science Ontology 63 3.8 Imbalanced Classification 69 3.9 Model Validation 70 3.10 Ensemble Methods 71 3.11 Big P and Small N (P â N) 74 3.12 Deep Learning 79 3.13 Data Stream Processing 95 3.14 Remarks 105 References 105 4 Basic Foundations of Big Data 113 4.1 Introduction 113 4.2 Query 116 4.3 Taxonomy of Big Data Analytics in Railway Track Engineering 123 4.4 Data Engineering 124 4.5 Remarks 130 References 130 5 Hilbert–Huang Transform, Profile, Signal, and Image Analysis 133 5.1 Hilbert–Huang Transform 133 5.2 Axle Box Acceleration 150 5.3 Analysis 151 5.4 Remarks 153 References 153 6 Tensors – Big Data in Multidimensional Settings 157 6.1 Introduction 157 6.2 Notations and Definitions 158 6.3 Tensor Decomposition Models 161 6.4 Application 164 6.5 Remarks 170 References 171 7 Copula Models 175 7.1 Introduction 175 7.2 Pair Copula: Vines 184 7.3 Computational Example 186 7.4 Remarks 192 References 193 8 Topological Data Analysis 197 8.1 Introduction 197 8.2 Basic Ideas 197 8.3 A Simple Railway Track Engineering Application 203 8.4 Remarks 204 References 204 9 Bayesian Analysis 207 9.1 Introduction 207 9.2 Markov Chain Monte Carlo (MCMC) 210 9.3 Approximate Bayesian Computation 210 9.4 Markov Chain Monte Carlo Application 216 9.5 ABC Application 219 9.6 Remarks 221 References 222 10 Basic Bayesian Nonparametrics 225 10.1 General 225 10.2 Dirichlet Family 226 10.3 Dirichlet Process 227 10.4 Finite Mixture Modeling 231 10.5 Bayesian Nonparametric Railway Track 232 10.6 Remarks 233 References 233 11 Basic Metaheuristics 235 11.1 Introduction 235 11.2 Remarks 237 References 239 12 Differential Privacy 241 12.1 General 241 12.2 Differential Privacy 242 12.3 Remarks 247 References 247 Index 249

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Book SynopsisA GUIDE TO ECONOMICS, STATISTICS AND FINANCE THAT EXPLORES THE MATHEMATICAL FOUNDATIONS UNDERLING ECONOMETRIC METHODS An Introduction to Econometric Theory offers a text to help in the mastery of the mathematics that underlie econometric methods and includes a detailed study of matrix algebra and distribution theory. Designed to be an accessible resource, the text explains in clear language why things are being done, and how previous material informs a current argument. The style is deliberately informal with numbered theorems and lemmas avoided. However, very few technical results are quoted without some form of explanation, demonstration or proof. The authora noted expert in the fieldcovers a wealth of topics including: simple regression, basic matrix algebra, the general linear model, distribution theory, the normal distribution, properties of least squares, unbiasedness and efficiency, eigenvalues, statistical inference in regression, t and F tests, the partitioned regression, sTable of ContentsList of Figures ix Preface xi About the CompanionWebsite xv Part I Fitting 1 1 Elementary Data Analysis 3 1.1 Variables and Observations 3 1.2 Summary Statistics 4 1.3 Correlation 6 1.4 Regression 10 1.5 Computing the Regression Line 12 1.6 Multiple Regression 16 1.7 Exercises 18 2 Matrix Representation 21 2.1 Systems of Equations 21 2.2 Matrix Algebra Basics 23 2.3 Rules of Matrix Algebra 26 2.4 Partitioned Matrices 27 2.5 Exercises 28 3 Solving the Matrix Equation 31 3.1 Matrix Inversion 31 3.2 Determinant and Adjoint 34 3.3 Transposes and Products 37 3.4 Cramer’s Rule 38 3.5 Partitioning and Inversion 39 3.6 A Note on Computation 41 3.7 Exercises 43 4 The Least Squares Solution 47 4.1 Linear Dependence and Rank 47 4.2 The General Linear Regression 50 4.3 Definite Matrices 52 4.4 Matrix Calculus 56 4.5 Goodness of Fit 57 4.6 Exercises 59 Part II Modelling 63 5 Probability Distributions 65 5.1 A Random Experiment 65 5.2 Properties of the Normal Distribution 68 5.3 Expected Values 72 5.4 Discrete Random Variables 75 5.5 Exercises 80 6 More on Distributions 83 6.1 Random Vectors 83 6.2 The Multivariate Normal Distribution 84 6.3 Other Continuous Distributions 87 6.4 Moments 90 6.5 Conditional Distributions 92 6.6 Exercises 94 7 The Classical RegressionModel 97 7.1 The Classical Assumptions 97 7.2 The Model 99 7.3 Properties of Least Squares 101 7.4 The Projection Matrices 103 7.5 The Trace 104 7.6 Exercises 106 8 The Gauss-Markov Theorem 109 8.1 A Simple Example 109 8.2 Efficiency in the General Model 111 8.3 Failure of the Assumptions 113 8.4 Generalized Least Squares 114 8.5 Weighted Least Squares 116 8.6 Exercises 118 Part III Testing 121 9 Eigenvalues and Eigenvectors 123 9.1 The Characteristic Equation 123 9.2 Complex Roots 124 9.3 Eigenvectors 126 9.4 Diagonalization 128 9.5 Other Properties 130 9.6 An Interesting Result 131 9.7 Exercises 133 10 The Gaussian RegressionModel 135 10.1 Testing Hypotheses 135 10.2 Idempotent Quadratic Forms 137 10.3 Confidence Regions 140 10.4 t Statistics 141 10.5 Tests of Linear Restrictions 144 10.6 Constrained Least Squares 146 10.7 Exercises 149 11 Partitioning and Specification 153 11.1 The Partitioned Regression 153 11.2 Frisch-Waugh-Lovell Theorem 155 11.3 Misspecification Analysis 156 11.4 Specification Testing 159 11.5 Stability Analysis 160 11.6 Prediction Tests 162 11.7 Exercises 163 Part IV Extensions 167 12 Random Regressors 169 12.1 Conditional Probability 169 12.2 Conditional Expectations 170 12.3 StatisticalModels Contrasted 174 12.4 The Statistical Assumptions 176 12.5 Properties of OLS 178 12.6 The Gaussian Model 182 12.7 Exercises 183 13 Introduction to Asymptotics 187 13.1 The Lawof Large Numbers 187 13.2 Consistent Estimation 192 13.3 The Central LimitTheorem 195 13.4 Asymptotic Normality 198 13.5 Multiple Regression 201 13.6 Exercises 203 14 Asymptotic Estimation Theory 207 14.1 Large Sample Efficiency 207 14.2 Instrumental Variables 208 14.3 Maximum Likelihood 210 14.4 Gaussian ML 213 14.5 Properties of ML Estimators 214 14.6 Likelihood Inference 216 14.7 Exercises 218 Part V Appendices 221 A The Binomial Coefficients 223 B The Exponential Function 225 C Essential Calculus 227 D The Generalized Inverse 229 Recommended Reading 233 Index 235

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Book SynopsisThis book provides a comprehensive and up to date treatment of theory and practical implementation in Register-based statistics. It begins by defining the area, before explaining how to structure such systems, as well as detailing alternative approaches. It explains how to create statistical registers, how to implement quality assurance, and the use of IT systems for register-based statistics. Further to this, clear details are given about the practicalities of implementing such statistical methods, such as protection of privacy and the coordination and coherence of such an undertaking. This edition offers a full understanding of both the principles and practices of this increasingly popular area of statistics, and can be considered a first step to a more systematic way of working with register-statistical issues. This book addresses the growing global interest in the topic and employs a much broader, more international approach than the 1st edition. New chapters eTable of ContentsPreface xi Chapter 1 Register Surveys – An Introduction 1 1.1 The purpose of the book 1 1.2 The need for a new theory and new methods 3 1.3 Four ways of using administrative registers 5 1.4 Preconditions for register-based statistics 6 1.4.1 Reliable administrative systems 7 1.4.2 Legal base and public approval 8 1.5 Basic concepts and terms 10 1.5.1 What is a statistical survey? 10 1.5.2 What is a register? 11 1.5.3 What is a register survey? 13 1.5.4 The Income and Taxation Register 14 1.5.5 The Quarterly and Annual Pay Registers 16 1.6 Comparing sample surveys and register surveys 20 1.7 Conclusions 23 Chapter 2 The Nature of Administrative Data 25 2.1 Different kinds of administrative data 25 2.2 How are data recorded? 26 2.3 Administrative and statistical information systems 27 2.4 Measurement errors in statistical and administrative data 29 2.5 Why use administrative data for statistics? 30 2.6 Comparing sample survey and administrative data 32 2.6.1 A questionnaire to persons compared with register data 32 2.6.2 An enterprise questionnaire compared with register data 34 2.7 Conclusions 36 Chapter 3 Protection of Privacy and Confidentiality 37 3.1 Internal security 38 3.1.1 No text in output databases! 38 3.1.2 Existence of identity numbers 39 3.2 Disclosure risks – tables 40 3.2.1 Rules for tables with counts, totals and mean values 41 3.2.2 The threshold rule – analyse complete tables! 43 3.2.3 Frequency tables are often misunderstood 44 3.2.4 Combining tables can cause disclosure 45 3.3 Disclosure risks – micro data 45 3.4 Conclusions 46 Chapter 4 The Register System 47 4.1 A register model based on object types and relations 47 4.1.1 The register system and protection of privacy 53 4.1.2 The register system and data warehousing 53 4.2 Organising the work with the system 54 4.3 The populations in the system 56 4.3.1 How to produce consistent register-based statistics 57 4.3.2 Registers and time 58 4.3.3 Populations, variables and time 59 4.4 The variables in the system 60 4.4.1 Standardised variables in the register system 60 4.4.2 Derived variables 62 4.4.3 Variables with different origins 63 4.4.4 Variables with different functions in the system 64 4.5 Using the system for micro integration 65 4.6 Three kinds of registers with different roles 70 4.7 Register systems and register surveys within enterprises 72 4.8 Conclusions 74 Chapter 5 The Base Registers in the System 77 5.1 Characteristics of a base register 77 5.2 Requirements for base registers 78 5.2.1 Defining and deriving statistical units 78 5.2.2 Objects and identities – requirements for a base register 80 5.2.3 Coverage and spanning variables in base registers 81 5.3 The Population Register 83 5.4 The Business Register 88 5.5 The Real Estate Register 93 5.6 The Activity Register 94 5.7 Everyone should support the base registers! 98 5.8 Conclusions 101 Chapter 6 How to Create a Register – Matching and Combining Sources 103 6.1 Preconditions in different countries 103 6.2 Matching methods and problems 105 6.2.1 Deterministic record linkage 105 6.2.2 Probabilistic record linkage 106 6.2.3 Four causes of matching errors 112 6.3 Matching sources with different object types 114 6.4 Conclusions 120 Chapter 7 How to Create a Register – The Population 121 7.1 How should register surveys be structured? 121 7.2 Register survey design 125 7.2.1 Determining the research objectives 125 7.2.2 Making an inventory of different sources 128 7.2.3 Analysing the usability of administrative sources 128 7.3 Defining a register’s object set 131 7.3.1 Defining a population 131 7.3.2 Can you alter data from the National Tax Agency? 134 7.3.3 Defining a population – primary registers 135 7.3.4 Defining a population – integrated registers 136 7.3.5 Defining a calendar year population 137 7.3.6 Defining a population – frame or register population? 138 7.3.7 Base registers should be used when defining populations 141 7.4 Defining the statistical units 142 7.4.1 Units and identities when creating primary registers 143 7.4.2 Using administrative objects instead of statistical units 144 7.5 Creating longitudinal registers – the population 145 7.6 Conclusions 146 Chapter 8 How to Create a Register – The Variables 147 8.1 The variables in the register 147 8.1.1 Variable definitions 148 8.1.2 Variables in statistical science 149 8.1.3 Variables in informatics 150 8.1.4 Creating register variables – check list 151 8.2 Forming derived variables using models 151 8.2.1 Exact calculation of values using a rule 152 8.2.2 Estimating values with a rule 153 8.2.3 Estimating values with a causal model 154 8.2.4 Derived variables and imputed variable values 157 8.2.5 Creating variables by coding 158 8.3 Activity data 159 8.3.1 Activity statistics 160 8.3.2 Activity data aggregated for enterprises and organisations 161 8.3.3 Activity data aggregated for persons – multi-valued variables 161 8.4 Creating longitudinal registers – the variables 165 8.5 Conclusions 169 Chapter 9 How to Create a Register – Editing 171 9.1 Editing register data 171 9.1.1 Editing one administrative register 173 9.1.2 Consistency editing – is the population correct? 175 9.1.3 Consistency editing – are the units correct? 178 9.1.4 Consistency editing – are the variables correct? 180 9.2 Case studies – editing register data 181 9.2.1 Editing work within the Income and Taxation Register 181 9.2.2 Editing work with the Income Statement Register 183 9.2.3 What more can be learned from these examples? 184 9.3 Editing, quality assurance and survey design 185 9.3.1 Survey design in a register-based production system 185 9.3.2 Quality assessment in a register-based production system 186 9.3.3 Total survey error in a register-based production system 191 9.4 Conclusions 192 Chapter 10 Metadata 193 10.1 Primary registers – the need for metadata 193 10.1.1 Documentation of administrative sources 194 10.1.2 Documentation of sources within the system 195 10.1.3 Documentation of a new register 195 10.2 Changes over time – the need for metadata 195 10.3 Integrated registers – the need for metadata 196 10.4 Classification and definitions database 197 10.5 The need for metadata for registers 198 10.6 Conclusions 200 Chapter 11 Estimation Methods – Introduction 201 11.1 Estimation in sample surveys and register surveys 202 11.2 Estimation methods for register surveys that use weights 203 11.3 Calibration of weights in register surveys 204 11.4 Using weights for estimation 207 11.5 Conclusions 208 Chapter 12 Estimation Methods – Missing Values 209 12.1 Make no adjustments, publish ‘value unknown’ 210 12.2 Adjustment for missing values using weights 214 12.3 Adjustment for missing values by imputation 215 12.4 Missing values in a system of registers 218 12.5 Conclusions 220 Chapter 13 Estimation Methods – Coverage Problems 221 13.1 Reducing overcoverage and undercoverage 221 13.1.1 Coverage problems in the Population Register 221 13.1.2 Coverage problems in the Business Register 222 13.2 Estimation methods to correct for overcoverage 224 13.3 Undercoverage in the administrative system 226 13.4 Conclusions 228 Chapter 14 Estimation Methods – Multi-valued Variables 229 14.1 Multi-valued variables 229 14.2 Estimation methods 232 14.2.1 Occupation in the Activity and Occupation Registers 232 14.2.2 Industrial classification in the Business Register 236 14.2.3 Importing many multi-valued variables 238 14.2.4 Consistency between estimates from different registers 242 14.2.5 Multi-valued variables – what is done in practice? 245 14.2.6 Additional estimation methods 247 14.3 Application of the method 251 14.4 Linking of time series using combination objects 254 14.4.1 Linking time series 254 14.4.2 Changed industrial classification in the Business Register 256 14.5 Conclusions 258 Chapter 15 Theory and Quality of Register-based Statistics 259 15.1 Is there a theory for register surveys? 259 15.1.1 Statistical inference at a national statistical office 260 15.1.2 Theory-based methods or ad hoc methods 262 15.1.3 The survey approach and the systems approach 263 15.2 Measuring quality – why and how? 267 15.3 Analysing administrative sources – input data quality 271 15.4 Output data quality 278 15.5 The integration process – integration errors 279 15.5.1 Creating register populations – coverage errors 280 15.5.2 Creating statistical units –errors in units 282 15.5.3 Creating statistical variables – errors in variables 283 15.6 Random variation in register data 288 15.7 The register system and data warehousing 291 15.8 Conclusions 295 Chapter 16 Conclusions 297 References 301 Index 305

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Book SynopsisDetailed guidance on the mathematics behind equity derivatives Problems and Solutions in Mathematical Finance Volume II is an innovative reference for quantitative practitioners and students, providing guidance through a range of mathematical problems encountered in the finance industry.Table of ContentsPreface ix About the Authors xi 1 Basic Equity Derivatives Theory 1 1.1 Introduction 1 1.2 Problems and Solutions 8 1.2.1 Forward and Futures Contracts 8 1.2.2 Options Theory 15 1.2.3 Hedging Strategies 27 2 European Options 63 2.1 Introduction 63 2.2 Problems and Solutions 74 2.2.1 Basic Properties 74 2.2.2 Black–Scholes Model 89 2.2.3 Tree-Based Methods 190 2.2.4 The Greeks 218 3 American Options 267 3.1 Introduction 267 3.2 Problems and Solutions 271 3.2.1 Basic Properties 271 3.2.2 Time-Independent Options 292 3.2.3 Time-Dependent Options 305 4 Barrier Options 351 4.1 Introduction 351 4.2 Problems and Solutions 357 4.2.1 Probabilistic Approach 357 4.2.2 Reflection Principle Approach 386 4.2.3 Further Barrier-Style Options 408 5 Asian Options 439 5.1 Introduction 439 5.2 Problems and Solutions 443 5.2.1 Discrete Sampling 443 5.2.2 Continuous Sampling 480 6 Exotic Options 531 6.1 Introduction 531 6.2 Problems and Solutions 532 6.2.1 Path-Independent Options 532 6.2.2 Path-Dependent Options 586 7 Volatility Models 647 7.1 Introduction 647 7.2 Problems and Solutions 652 7.2.1 Historical and Implied Volatility 652 7.2.2 Local Volatility 685 7.2.3 Stochastic Volatility 710 7.2.4 Volatility Derivatives 769 A Mathematics Formulae 787 B Probability Theory Formulae 797 C Differential Equations Formulae 813 Bibliography 821 Notation 825 Index 829

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Book SynopsisMathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an abstract level, making it problematic when applying these techniques to practical issues in finance.Table of ContentsPreface ix Prologue xi About the Authors xv 1 General Probability Theory 1 1.1 Introduction 1 1.2 Problems and Solutions 4 1.2.1 Probability Spaces 4 1.2.2 Discrete and Continuous Random Variables 11 1.2.3 Properties of Expectations 41 2 Wiener Process 51 2.1 Introduction 51 2.2 Problems and Solutions 55 2.2.1 Basic Properties 55 2.2.2 Markov Property 68 2.2.3 Martingale Property 71 2.2.4 First Passage Time 76 2.2.5 Reflection Principle 84 2.2.6 Quadratic Variation 89 3 Stochastic Differential Equations 95 3.1 Introduction 95 3.2 Problems and Solutions 102 3.2.1 Itō Calculus 102 3.2.2 One-Dimensional Diffusion Process 123 3.2.3 Multi-Dimensional Diffusion Process 155 4 Change of Measure 185 4.1 Introduction 185 4.2 Problems and Solutions 192 4.2.1 Martingale Representation Theorem 192 4.2.2 Girsanov’s Theorem 194 4.2.3 Risk-Neutral Measure 221 5 Poisson Process 243 5.1 Introduction 243 5.2 Problems and Solutions 251 5.2.1 Properties of Poisson Process 251 5.2.2 Jump Diffusion Process 281 5.2.3 Girsanov’s Theorem for Jump Processes 298 5.2.4 Risk-Neutral Measure for Jump Processes 322 Appendix A Mathematics Formulae 331 Appendix B Probability Theory Formulae 341 Appendix C Differential Equations Formulae 357 Bibliography 365 Notation 369 Index 373

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Book SynopsisMany students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method.Table of ContentsPreface to Fifth Edition xv Acknowledgements xvii 1 Preliminaries: Computer Strategies 1 1.1 Introduction 1 1.2 Hardware 2 1.3 Memory Management 2 1.4 Vector Processors 3 1.5 Multi-core Processors 3 1.6 Co-processors 4 1.7 Parallel Processors 4 1.8 Applications Software 5 1.9 Array Features 9 1.10 Third-party Libraries 17 1.11 Visualisation 18 1.12 Conclusions 23 References 24 2 Spatial Discretisation by Finite Elements 25 2.1 Introduction 25 2.2 Rod Element 25 2.3 The Eigenvalue Equation 28 2.4 Beam Element 29 2.5 Beam with an Axial Force 31 2.6 Beam on an Elastic Foundation 32 2.7 General Remarks on the Discretisation Process 33 2.8 Alternative Derivation of Element Stiffness 33 2.9 Two-dimensional Elements: Plane Stress 35 2.10 Energy Approach and Plane Strain 38 2.11 Plane Element Mass Matrix 40 2.12 Axisymmetric Stress and Strain 40 2.13 Three-dimensional Stress and Strain 42 2.14 Plate Bending Element 44 2.15 Summary of Element Equations for Solids 47 2.16 Flow of Fluids: Navier–Stokes Equations 47 2.17 Simplified Flow Equations 50 2.18 Further Coupled Equations: Biot Consolidation 54 2.19 Conclusions 56 References 56 3 Programming Finite Element Computations 59 3.1 Introduction 59 3.2 Local Coordinates for Quadrilateral Elements 59 3.3 Local Coordinates for Triangular Elements 64 3.4 Multi-Element Assemblies 66 3.5 ‘Element-by-Element’ Techniques 68 3.6 Incorporation of Boundary Conditions 72 3.7 Programming using Building Blocks 75 3.8 Solution of Equilibrium Equations 95 3.9 Evaluation of Eigenvalues and Eigenvectors 96 3.10 Solution of First-Order Time-Dependent Problems 99 3.11 Solution of Coupled Navier–Stokes Problems 103 3.12 Solution of Coupled Transient Problems 104 3.13 Solution of Second-Order Time-Dependent Problems 106 4 Static Equilibrium of Structures 115 4.1 Introduction 115 4.2 Conclusions 157 4.3 Glossary of Variable Names 157 4.4 Exercises 159 References 168 5 Static Equilibrium of Linear Elastic Solids 169 5.1 Introduction 169 5.2 Glossary of Variable Names 221 5.3 Exercises 224 References 232 6 Material Non-linearity 233 6.1 Introduction 233 6.2 Stress–strain Behaviour 235 6.3 Stress Invariants 236 6.4 Failure Criteria 238 6.5 Generation of Body Loads 240 6.6 Viscoplasticity 240 6.7 Initial Stress 242 6.8 Corners on the Failure and Potential Surfaces 243 6.9 Elastoplastic Rate Integration 270 6.10 Tangent Stiffness Approaches 275 6.11 The Geotechnical Processes of Embanking and Excavation 289 6.12 Undrained Analysis 305 6.13 Glossary of Variable Names 322 6.14 Exercises 327 References 331 7 Steady State Flow 333 7.1 Introduction 333 7.2 Glossary of Variable Names 359 7.3 Exercises 361 References 367 8 Transient Problems: First Order (Uncoupled) 369 8.1 Introduction 369 8.2 Comparison of Programs 8.4, 8.5, 8.6 and 8.7 397 8.3 Glossary of Variable Names 416 8.4 Exercises 419 References 422 9 Coupled Problems 423 9.1 Introduction 423 9.2 Glossary of Variable Names 454 9.3 Exercises 459 References 460 10 Eigenvalue Problems 461 10.1 Introduction 461 10.2 Glossary of Variable Names 477 10.3 Exercises 480 References 482 11 Forced Vibrations 483 11.1 Introduction 483 11.2 Glossary of Variable Names 517 11.3 Exercises 521 References 522 12 Parallel Processing of Finite Element Analyses 523 12.1 Introduction 523 12.2 Differences between Parallel and Serial Programs 525 12.3 Graphics Processing Units 589 12.4 Cloud Computing 594 12.5 Conclusions 596 12.6 Glossary of Variable Names 597 References 602 Appendix A Equivalent Nodal Loads 605 Appendix B Shape Functions and Element Node Numbering 611 Appendix C Plastic Stress-Strain Matrices and Plastic Potential Derivatives 619 Appendix D main Library Subprograms 623 Appendix E geom Library Subroutines 635 Appendix F Parallel Library Subroutines 639 Appendix G External Subprograms 645 Author Index 649 Subject Index 653

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Book SynopsisEverything you need to know in order to manage risk effectively within your organization You cannot afford to ignore the explosion in mathematical finance in your quest to remain competitive.Table of ContentsPreface xiii 1 Introduction 1 1.1 Basic Challenges in Risk Management 1 1.2 Value at Risk 3 1.3 Further Challenges in Risk Management 6 2 Applied Linear Algebra for Risk Managers 11 2.1 Vectors and Matrices 11 2.2 Matrix Algebra in Practice 17 2.3 Eigenvectors and Eigenvalues 21 2.4 Positive Definite Matrices 24 3 Probability Theory for Risk Managers 27 3.1 Univariate Theory 27 3.1.1 Random variables 27 3.1.2 Expectation 31 3.1.3 Variance 32 3.2 Multivariate Theory 33 3.2.1 The joint distribution function 33 3.2.2 The joint and marginal density functions 34 3.2.3 The notion of independence 34 3.2.4 The notion of conditional dependence 35 3.2.5 Covariance and correlation 35 3.2.6 The mean vector and covariance matrix 37 3.2.7 Linear combinations of random variables 38 3.3 The Normal Distribution 39 4 Optimization Tools 43 4.1 Background Calculus 43 4.1.1 Single-variable functions 43 4.1.2 Multivariable functions 44 4.2 Optimizing Functions 47 4.2.1 Unconstrained quadratic functions 48 4.2.2 Constrained quadratic functions 50 4.3 Over-determined Linear Systems 52 4.4 Linear Regression 54 5 Portfolio Theory I 63 5.1 Measuring Returns 63 5.1.1 A comparison of the standard and log returns 64 5.2 Setting Up the Optimal Portfolio Problem 67 5.3 Solving the Optimal Portfolio Problem 70 6 Portfolio Theory II 77 6.1 The Two-Fund Investment Service 77 6.2 A Mathematical Investigation of the Optimal Frontier 78 6.2.1 The minimum variance portfolio 78 6.2.2 Covariance of frontier portfolios 78 6.2.3 Correlation with the minimum variance portfolio 79 6.2.4 The zero-covariance portfolio 79 6.3 A Geometrical Investigation of the Optimal Frontier 80 6.3.1 Equation of a tangent to an efficient portfolio 80 6.3.2 Locating the zero-covariance portfolio 82 6.4 A Further Investigation of Covariance 83 6.5 The Optimal Portfolio Problem Revisited 86 7 The Capital Asset Pricing Model (CAPM) 91 7.1 Connecting the Portfolio Frontiers 91 7.2 The Tangent Portfolio 94 7.2.1 The market’s supply of risky assets 94 7.3 The CAPM 95 7.4 Applications of CAPM 96 7.4.1 Decomposing risk 97 8 Risk Factor Modelling 101 8.1 General Factor Modelling 101 8.2 Theoretical Properties of the Factor Model 102 8.3 Models Based on Principal Component Analysis (PCA) 105 8.3.1 PCA in two dimensions 106 8.3.2 PCA in higher dimensions 112 9 The Value at Risk Concept 117 9.1 A Framework for Value at Risk 117 9.1.1 A motivating example 120 9.1.2 Defining value at risk 121 9.2 Investigating Value at Risk 122 9.2.1 The suitability of value at risk to capital allocation 124 9.3 Tail Value at Risk 126 9.4 Spectral Risk Measures 127 10 Value at Risk under a Normal Distribution 131 10.1 Calculation of Value at Risk 131 10.2 Calculation of Marginal Value at Risk 132 10.3 Calculation of Tail Value at Risk 134 10.4 Sub-additivity of Normal Value at Risk 135 11 Advanced Probability Theory for Risk Managers 137 11.1 Moments of a Random Variable 137 11.2 The Characteristic Function 140 11.2.1 Dealing with the sum of several random variables 142 11.2.2 Dealing with a scaling of a random variable 143 11.2.3 Normally distributed random variables 143 11.3 The Central Limit Theorem 145 11.4 The Moment-Generating Function 147 11.5 The Log-normal Distribution 148 12 A Survey of Useful Distribution Functions 151 12.1 The Gamma Distribution 151 12.2 The Chi-Squared Distribution 154 12.3 The Non-central Chi-Squared Distribution 157 12.4 The F-Distribution 161 12.5 The t-Distribution 164 13 A Crash Course on Financial Derivatives 169 13.1 The Black–Scholes Pricing Formula 169 13.1.1 A model for asset returns 170 13.1.2 A second-order approximation 172 13.1.3 The Black–Scholes formula 174 13.2 Risk-Neutral Pricing 176 13.3 A Sensitivity Analysis 179 13.3.1 Asset price sensitivity: The delta and gamma measures 179 13.3.2 Time decay sensitivity: The theta measure 182 13.3.3 The remaining sensitivity measures 183 14 Non-linear Value at Risk 185 14.1 Linear Value at Risk Revisited 185 14.2 Approximations for Non-linear Portfolios 186 14.2.1 Delta approximation for the portfolio 188 14.2.2 Gamma approximation for the portfolio 189 14.3 Value at Risk for Derivative Portfolios 190 14.3.1 Multi-factor delta approximation 190 14.3.2 Single-factor gamma approximation 191 14.3.3 Multi-factor gamma approximation 192 15 Time Series Analysis 197 15.1 Stationary Processes 197 15.1.1 Purely random processes 198 15.1.2 White noise processes 198 15.1.3 Random walk processes 199 15.2 Moving Average Processes 199 15.3 Auto-regressive Processes 201 15.4 Auto-regressive Moving Average Processes 203 16 Maximum Likelihood Estimation 207 16.1 Sample Mean and Variance 209 16.2 On the Accuracy of Statistical Estimators 211 16.2.1 Sample mean example 211 16.2.2 Sample variance example 212 16.3 The Appeal of the Maximum Likelihood Method 215 17 The Delta Method for Statistical Estimates 217 17.1 Theoretical Framework 217 17.2 Sample Variance 219 17.3 Sample Skewness and Kurtosis 221 17.3.1 Analysis of skewness 222 17.3.2 Analysis of kurtosis 223 18 Hypothesis Testing 227 18.1 The Testing Framework 227 18.1.1 The null and alternative hypotheses 227 18.1.2 Hypotheses: simple vs compound 228 18.1.3 The acceptance and rejection regions 228 18.1.4 Potential errors 229 18.1.5 Controlling the testing errors/defining the acceptance region 229 18.2 Testing Simple Hypotheses 230 18.2.1 Testing the mean when the variance is known 231 18.3 The Test Statistic 233 18.3.1 Example: Testing the mean when the variance is unknown 234 18.3.2 The p-value of a test statistic 236 18.4 Testing Compound Hypotheses 237 19 Statistical Properties of Financial Losses 241 19.1 Analysis of Sample Statistics 244 19.2 The Empirical Density and Q–Q Plots 247 19.3 The Auto-correlation Function 247 19.4 The Volatility Plot 252 19.5 The Stylized Facts 253 20 Modelling Volatility 255 20.1 The RiskMetrics Model 256 20.2 ARCH Models 258 20.2.1 The ARCH(1) volatility model 260 20.3 GARCH Models 264 20.3.1 The GARCH(1, 1) volatility model 265 20.3.2 The RiskMetrics model revisited 268 20.3.3 Summary 269 20.4 Exponential GARCH 269 21 Extreme Value Theory 271 21.1 The Mathematics of Extreme Events 271 21.1.1 A naive attempt 273 21.1.2 Example 1: Exponentially distributed losses 273 21.1.3 Example 2: Normally distributed losses 274 21.1.4 Example 3: Pareto distributed losses 275 21.1.5 Example 4: Uniformly distributed losses 275 21.1.6 Example 5: Cauchy distributed losses 276 21.1.7 The extreme value theorem 277 21.2 Domains of Attraction 278 21.2.1 The Fr´echet domain of attraction 280 21.3 Extreme Value at Risk 283 21.4 Practical Issues 286 21.4.1 Parameter estimation 286 21.4.2 The choice of threshold 287 22 Simulation Models 291 22.1 Estimating the Quantile of a Distribution 291 22.1.1 Asymptotic behaviour 293 22.2 Historical Simulation 296 22.3 Monte Carlo Simulation 299 22.3.1 The Choleski algorithm 300 22.3.2 Generating random numbers 302 23 Alternative Approaches to VaR 309 23.1 The t-Distributed Assumption 309 23.2 Corrections to the Normal Assumption 313 24 Backtesting 319 24.1 Quantifying the Performance of VaR 319 24.2 Testing the Proportion of VaR Exceptions 320 24.3 Testing the Independence of VaR Exceptions 323 References 327 Index 331

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Book SynopsisThorough, evenly paced, and intuitive, this friendly introduction to high-level covariant electrodynamics is a handy and helpful addition to any physicist's toolkit.Trade Review"John Charap succeeds well in making electrodynamics manifestly covariant, providing historical background and applications of far-reaching importance. The diligent reader, armed with pen and ample scratch paper for filling in the intermediate steps, will see covariant electrodynamics emerge coherently." (Dwight E. Neuenschwander, author of Emmy Noether's Wonderful Theorem)"Table of ContentsPreface1. Introduction2. Mathematical Preliminaries2.1. A Reminder of Vector Calculus2.2. Special Relativity2.3. Four-Vectors2.4. Covariant and Contravariant Vectors2.5. Tensors2.6. Time Dilation and the Lorentz-FitzGerald Contraction2.7. The Four-Velocity2.8. Energy and Momentum2.9. Plane Waves2.10. Exercises for Chapter 23. Maxwell's Equations3.1. Our Starting Point3.2. The Experimental Background3.2.1. Coulomb's Law3.2.2. Absence of Magnetic Monopoles3.2.3. Ørsted and Ampere3.2.4. The Law of Biot and Savart3.2.5. The Displacement Current3.2.6. Faraday's Law of Induction3.2.7. The Lorentz Force3.3. Capacitors and Solenoids3.3.1. Energy3.4. Electromagnetic Waves3.4.1. Polarization3.4.2. Electromagnetism and Light3.5. Exercises for Chapter 34. Behavior under Lorentz Transformations4.1. The Charge-Current Density Four-Vector4.2. The Lorentz Force4.3. The Potential Four-Vector4.4. Gauge Transformations4.5. The Field-Strength Tensor4.6. The Dual Field-Strength Tensor4.7. Exercises for Chapter 45. Lagrangian and Hamiltonian5.1. Lagrange's Equations5.2. The Lagrangian for a Charged Particle5.3. The Hamiltonian for a Charged Particle5.4. The Lagrangian for the Electromagnetic Field5.5. The Hamiltonian for the Electromagnetic Field5.6. Noether's Theorem5.7. Exercises for Chapter 56. Stress, Energy, and Momentum6.1. The Canonical Stress Tensor6.2. The Symmetrical Stress Tensor6.3. The Conservation Laws with Sources6.4. The Field as an Ensemble of Oscillators6.5. Exercises for Chapter 67. Motion of a Charged Particle7.1. Fields from an Unaccelerated Particle7.2. Motion of a Particle in an External Field7.2.1. Uniform Static Magnetic Field7.2.2. Crossed E and B Fields7.2.3. Nonuniform Static B-Field7.2.4. Curved Magnetic Field Lines7.3. Exercises for Chapter 78. Fields from Sources8.1. Introducing the Green's Function8.2. The Delta Function8.3. The Green's Function8.4. The Covariant Form for the Green's Function8.5. Exercises for Chapter 89. Radiation9.1. Potentials from a Moving Charged Particle9.2. The Lienard-Wiechert Potentials9.2.1. Fields from an Unaccelerated Particle9.2.2. Fields from a Charged Oscillator9.3. The General Case9.4. The Multipole Expansion9.4.1. Electric Dipole Radiation9.4.2. Magnetic Dipole and Higher-Order Terms9.5. Motion in a Circle9.6. Radiation from Linear Accelerators9.7. Radiation from an Antenna9.8. Exercises for Chapter 910. Media10.1. Dispersion10.1.1. Newton on the "Phænomena of Colours"10.2. Refraction10.2.1. The Boundary Conditions at the Interface10.3. Cerenkov Radiation10.4. Exercises for Chapter 1011. Scattering11.1. Scattering from a Small Scatterer11.2. Many Scatterers11.3. Scattering from the Sky11.3.1. The Born Approximation11.3.2. Rayleigh's Explanation for the Blue Sky11.4. Critical Opalescence12. Dispersion12.1. The Oscillator Model12.1.1. The High-Frequency Limit12.1.2. The Drude Model12.2. Dispersion Relations12.3. The Optical TheoremEpilogueIndex

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Book SynopsisThis fascinating narrative history of math in America introduces readers to the diverse and vibrant people behind pivotal moments in the nation's mathematical maturation. Once upon a time in America, few knew or cared about math. In Republic of Numbers, David Lindsay Roberts tells the story of how all that changed, as America transformed into a powerhouse of mathematical thinkers. Covering more than 200 years of American history, Roberts recounts the life stories of twenty-three Americans integral to the evolution of mathematics in this country. Beginning with self-taught Salem mathematician Nathaniel Bowditch's unexpected breakthroughs in ocean navigation and closing with the astounding work Nobel laureate John Nash did on game theory, this book is meant to be read cover to cover. Revealing the marvelous ways in which America became mathematically sophisticated, the book introduces readers to Kelly Miller, the first black man to attend Johns Hopkins, who brilliantly melded mathematiTrade ReviewThis charming collection of 20 "unexpected stories of mathematical Americans through history" focuses not only on the greatest US mathematical minds . . . Abraham Lincoln, self-trained as a surveyor, later studied Euclid — as demonstrated in his Gettysburg Address, "dedicated to the proposition that all men are created equal".—Andrew Robinson, NatureIn Republic of Numbers, author and alum David Lindsay Roberts weaves eclectic and entertaining stories about math and mathematicians across two centuries of U.S. history . . . Pleasure in math links lives across more than two centuries in Roberts' elegant and eye-opening work of intellectual history. Mathematicians and math teachers will find in it an eclectic family history of their fields, with special attention to lesser-known characters, especially ones whose achievements beat the odds set against their race, sex, or background. But readers not excited by higher math will also enjoy these 20 deeply researched and gracefully narrated biographical essays.—Rosemary Hutzler Raun, Johns Hopkins University HUBRoberts is to be congratulated for reminding us that the history of mathematics includes those who teach and practice useful mathematics as well as those who create abstract mathematics.—Scott Guthery, MAA ReviewsThis collection of brief biographies of two dozen Americans who relate to mathematics in various ways does not claim to present a representative cross-section or a selection of the most important figures or even the most colorful figures. Each story, however, reveals a unique tie to the history of the country, resulting in a loosely woven national history as seen through a sample of citizens who also reflect something of the progress of American mathematics . . . The emphasis is more on how people came to mathematics and how, native born or immigrant, their lives are connected to the society of their time and sometimes to each other in some remarkable ways.—Mathematical Reviews[Republic of Numbers] is a work of art, in the sense that it feels new and original, and leaves the reader (at least this one) with a bit of awe . . . For anyone interested in the history of American mathematics, this book is a must read . . . The Republic of Numbers offers readers a fascinating and very human journey through a wide swath of history. I'm amazed at what Dave Roberts has been able to pack into a relatively compact book.—Andrew Perry, Canadian Society for the History and Philosophy of Mathematics (CSHPM)Republic of Numbers should appeal to any reader interested in mathematics in its historical and social context.—Notices of the American Mathematical SocietyAn informative and worthwhile read.—Wallace A. Ferguson, Chatham and Clarendon Grammar School, Ramsgate, Mathematics TodayTable of ContentsIntroductionChapter 1. A Practical Navigator: Nathaniel Bowditch, 1806Chapter 2. Hudson River School: Sylvanus Thayer, 1815Chapter 3. Political Arithmetic: Abraham Lincoln, 1826Chapter 4. Textbook Messages: Catherine Beecher and Joseph Ray, 1832Chapter 5. Learning to Count: J. Willard Gibbs, 1841Chapter 6. Naval Reserve: Charles H. Davis, 1857Chapter 7. General Principles: Daniel Harvey Hill, 1862Chapter 8. Fellow Worker: Christine Ladd-Franklin, 1878Chapter 9. Straddler: Kelly Miller, 1887Chapter 10. Frontiersmen: Herman Hollerith and E. H. Moore, 1893Chapter 11. Poetic Historian: E. T. Bell, 1906Chapter 12. Man of School Mathematics: Charles M. Austin, 1914Chapter 13. Organization Man: E. B. Wilson, 1922Chapter 14. Versed in Math: Lillian R. Lieber and Hugh G. Lieber, 1931Chapter 15. Machine Whisperer: Grace Hopper, 1941Chapter 16. Survivor: Izaak Wirszup, 1956Chapter 17. Carrying Old Virginny Forward: Edgar L. Edwards Jr., 1960Chapter 18. Americano: Joaquin Basilio Diaz, 1974Chapter 19. Math Warrior: Frank B. Allen, 1984Chapter 20. Suspicious Minds: John F. Nash Jr., 1994ConclusionAcknowledgmentsSelected BibliographyIndex

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Book SynopsisExplore the hidden powers of math that shape us, influencing everything from our sense of justice to our perception of beauty. Archaeologists decoding ancient messages. Epidemiologists analyzing the spread of a contagious disease. African Americans seeking full enfranchisement in a society that has worked to exclude them. A family doing puzzles at the kitchen table. These scenarios seem to have little in common. But in fact, each of these groups is faced with a multifaceted challengeand each is using math to solve it. In Supermath, popular author and educator Anna Weltman showcases the incredible power of mathematics when people apply it outside of the world of pure numbers, introducing it into the realms of science, politics, history, education, and art. Her stories share how math has protected us from war and disease, helped us communicate across time and space, and made the world a fairer and more beautiful place. But Weltman also warns us that dangers arise when the transformatTrade ReviewWeltman's book can be read as a call for scholars, educators, and communicators of mathematics to grapple with the power our training and credentialing in mathematics grants us, and to understand that its most basic promise of solving problems is not automatic but one that we must realize.—New Books NetworkThis friendly, generalist book is a fun and easy read for anyone interested in mathematics, whether they have a strong background in the subject or not. More importantly, though, it's a thought-provoking look at the not-so-secret human side of mathematics.—Mathematics Magazine...the essays are worthwhile reads that are thought-provoking.—Mathematics MagazineTable of ContentsPrefaceChapter 1. Is Math the Universal Language? Math and the Problem of Communicating across CulturesChapter 2. Can Math Predict the Next Move? Math and the Problem of Winning (or Not Losing, at Least)Chapter 3. Can Math Eliminate Bias? Math and the Problem of Fairness Chapter 4. Can Math Open Doors? Math and the Problem of OpportunityChapter 5. What Is Genuine Beauty? Math and the Problem of PerceptionReferencesIndex

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Book SynopsisThis second, much enlarged edition by Lehmann and Casella of Lehmann's classic text on point estimation maintains the outlook and general style of the first edition. All of the topics are updated, while an entirely new chapter on Bayesian and hierarchical Bayesian approaches is provided, and there is much new material on simultaneous estimation.Trade Review Table of Contents1. Preparations; 2. Unbiasedness; 3. Equivariance; 4. Average risk optimality; 5. Global risk optimality; 6. Asymptotic efficiency and likelihood

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Book SynopsisMany physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods.Trade ReviewA nice introductory text... Presents the basics of linear integral equations theory in a very comprehensive way... [The] richness of examples and applications makes the book extremely useful for teachers and also researchers. —Applications of Mathematics (Review of the Second Edition) This second edition of this highly useful book continues the emphasis on applications and presents a variety of techniques with extensive examples...The book is ideal as a text for a beginning graduate course. Its excellent treatment of boundary value problems and an up-to-date bibliography make the book equally useful for researchers in many applied fields.—MathSciNet ​(Review of the Second Edition)Table of ContentsIntroduction.- Integral Equations with Separable Kernels.- Method Of Successive Approximations.- Classical Fredholm Theory.- Applications of Ordinary Differential Equations.- Applications of Partial Differential Equations.- Symmetric Kernels.- Singular Integral Equations.- Integral Transformation Methods.- Applications to Mixed Boundary Value Problems.- Integral Equations Perturbation Methods.- Appendix.- Bibliography.- Index.​

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