Mathematics Books

Book SynopsisMatrices and kernels with positivity structures, and the question of entrywise functions preserving them, have been studied throughout the 20th century, attracting recent interest in connection to high-dimensional covariance estimation. This is the first book to systematically develop the theoretical foundations of the entrywise calculus, focusing on entrywise operations - or transforms - of matrices and kernels with additional structure, which preserve positive semidefiniteness. Designed as an introduction for students, it presents an in-depth and comprehensive view of the subject, from early results to recent progress. Topics include: structural results about, and classifying the preservers of positive semidefiniteness and other Loewner properties (monotonicity, convexity, super-additivity); historical connections to metric geometry; classical connections to moment problems; and recent connections to combinatorics and Schur polynomials. Based on the author''s course, the book is struTrade Review'Positive definite matrices, kernels, sequences and functions, and operations on them that preserve their positivity, have been studied intensely for over a century. The techniques involved in their analysis and the variety of their applications both continue to grow. This book is an admirably comprehensive and lucid account of the topic. It includes some very recent developments in which the author has played a major role. This will be a valuable resource for researchers and an excellent text for a graduate course.' Rajendra Bhatia, Ashoka University'The opening notes of this symphony of ideas were written by Schur in 1911. Schoenberg, Loewner, Rudin, Herz, Hiai, FitzGerald, Jain, Guillot, Rajaratnam, Belton, Putinar, and others composed new themes and variations. Now, Khare has orchestrated a masterwork that includes his own harmonies in an elegant synthesis. This is a work of impressive scholarship.' Roger Horn, University of Utah, RetiredTable of ContentsPart I. Preliminaries, Entrywise Powers Preserving Positivity in Fixed Dimension: 1. The cone of positive semidefinite matrices; 2. The Schur product theorem and nonzero lower bounds; 3. Totally positive (TP) and totally non-negative (TN) matrices; 4. TP matrices – generalized Vandermonde and Hankel moment matrices; 5. Entrywise powers preserving positivity in fixed dimension; 6. Mid-convex implies continuous, and 2 x 2 preservers; 7. Entrywise preservers of positivity on matrices with zero patterns; 8. Entrywise powers preserving positivity, monotonicity, superadditivity; 9. Loewner convexity and single matrix encoders of preservers; 10. Exercises; Part II. Entrywise Functions Preserving Positivity in All Dimensions: 11. History – Shoenberg, Rudin, Vasudeva, and metric geometry; 12. Loewner's determinant calculation in Horn's thesis; 13. The stronger Horn–Loewner theorem, via mollifiers; 14. Stronger Vasudeva and Schoenberg theorems, via Bernstein's theorem; 15. Proof of stronger Schoenberg Theorem (Part I) – positivity certificates; 16. Proof of stronger Schoenberg Theorem (Part II) – real analyticity; 17. Proof of stronger Schoenberg Theorem (Part III) – complex analysis; 18. Preservers of Loewner positivity on kernels; 19. Preservers of Loewner monotonicity and convexity on kernels; 20. Functions acting outside forbidden diagonal blocks; 21. The Boas–Widder theorem on functions with positive differences; 22. Menger's results and Euclidean distance geometry; 23. Exercises; Part III. Entrywise Polynomials Preserving Positivity in Fixed Dimension: 24. Entrywise polynomial preservers and Horn–Loewner type conditions; 25. Polynomial preservers for rank-one matrices, via Schur polynomials; 26. First-order approximation and leading term of Schur polynomials; 27. Exact quantitative bound – monotonicity of Schur ratios; 28. Polynomial preservers on matrices with real or complex entries; 29. Cauchy and Littlewood's definitions of Schur polynomials; 30. Exercises.

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Book SynopsisThe second edition of Statistics for the Social Sciences prepares students from a wide range of disciplines to interpret and learn the statistical methods critical to their field of study. By using the General Linear Model (GLM), the author builds a foundation that enables students to see how statistical methods are interrelated enabling them to build on the basic skills. The author makes statistics relevant to students'' varying majors by using fascinating real-life examples from the social sciences. Students who use this edition will benefit from clear explanations, warnings against common erroneous beliefs about statistics, and the latest developments in the philosophy, reporting, and practice of statistics in the social sciences. The textbook is packed with helpful pedagogical features including learning goals, guided practice, and reflection questions.Trade Review'Dr Warne's gift for teaching statistics is apparent in his writing of this book. Indeed, I wish I had this book when I was a student. His use of the General Linear Model as a schema for understanding how statistical methods are interrelated sets the book apart from others.' Leena J. Landmark, Associate Professor of Special Education, Sam Houston State University, USATable of Contents1. Statistics and Models; 2. Levels of Data; 3. Models of Central Tendency and Variability; 4. Visual Models; 5. Linear Transformations and z-Scores; 6. Probability and the Central Limit Theorem; 7. Null Hypothesis Statistical Significance Testing and z-Tests; 8. One-Sample t-Tests; 9. Paired-Samples t-Tests; 10. Unpaired Two-Sample t-Tests; 11. Analysis of Variance; 12. Correlation; 13. Regression; 14. Chi-Squared Test; 15 Applying Statistics to Research, and Advanced Statistical Methods.

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Book SynopsisBased on the author''s forty years of teaching experience, this unique textbook covers both basic and advanced concepts of optimization theory and methods for process systems engineers. Topics covered include continuous, discrete and logic optimization (linear, nonlinear, mixed-integer and generalized disjunctive programming), optimization under uncertainty (stochastic programming and flexibility analysis), and decomposition techniques (Lagrangean and Benders decomposition). Assuming only a basic background in calculus and linear algebra, it enables easy understanding of mathematical reasoning, and numerous examples throughout illustrate key concepts and algorithms. End-of-chapter exercises involving theoretical derivations and small numerical problems, as well as in modeling systems like GAMS, enhance understanding and help put knowledge into practice. Accompanied by two appendices containing web links to modeling systems and models related to applications in PSE, this is an essentialTrade Review'Authored by Ignacio Grossmann, the creator and key developer of the field of mixed integer nonlinear programming, this outstanding textbook provides a thorough and comprehensive treatment of fundamental concepts, optimization models and effective solution strategies for discrete and continuous optimization. It is an essential, 'must-have' reference for all students, researchers and practitioners in process systems engineering.' Lorenz Biegler, Carnegie Mellon University'From the globally recognized leading authority in the field of process systems engineering, this long-awaited book will definitely become the standard reference for anyone interested in optimization. It is very well thought and written, with excellent presentation of the material. The theory is described in a very effective, rigorous, and clear way, with appropriate explanations and examples used throughout, covering traditional topics such as linear and nonlinear optimization concepts and mixed-integer linear programming, along with more advanced topics, such as disjunctive programming, global optimization, and stochastic programming. A real gem and a must read!' Stratos Pistikopoulos, Texas A & M University'Excellent coverage of the basic concepts and approaches developed in the area of process systems engineering in the last forty years. A unique book that can be easily adapted to advanced undergraduate and graduate-level classes to provide overall guidance to different tools that can be used to model and optimize complex engineering problems. I am certainly looking forward to using it in my class on mathematical modeling and optimization principles.' Marianthi Ierapetritou, University of DelawareTable of ContentsPreface; 1. Optimization in process systems engineering; 2. Solving nonlinear equations; 3. Basic theoretical concepts in optimization; 4. Nonlinear programming algorithms; 5. Linear programming; 6. Mixed-integer programming models; 7. Systematic modeling of constraints with logic; 8. Mixed-integer linear programming; 9 Mixed-integer nonlinear programming; 10. Generalized disjunctive programming; 11. Constraint programming; 12. Nonconvex optimization; 13. Lagrangean decomposition; 14. Stochastic programming; 15. Flexibility analysis; Appendix A. Modeling systems and optimization software; Appendix B. Optimization models for process systems engineering; References; Index.

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Book SynopsisThis is the first book in English on BruhatTits theory, an important topic in number theory, representation theory, and algebraic geometry. A comprehensive account of the theory, it can serve both as a reference for researchers in the field and as a thorough introduction for graduate students and early career mathematicians.Table of ContentsIntroduction; Part I. Background and Review: 1. Affine root systems and abstract buildings; 2. Algebraic groups; Part II. Bruhat–Tits theory: 3. Examples: Quasi-split groups of rank 1; 4. Overview and summary of Bruhat–Tits theory; 5. Bruhat, Cartan, and Iwasawa decompositions; 6. The apartment; 7. The Bruhat–Tits building for a valuation of the root datum; 8. Integral models; 9. Unramified descent; Part III. Additional Developments: 10. Residue field f of dimension ≤ 1; 11. The buildings of classical groups via lattice chains; 12. Component groups of integral models; 13. Finite group actions and tamely ramified descent; 14. Moy–Prasad filtrations; 15. Functorial properties; Part IV. Applications: 16. Classification of maximal unramified tori (d'après DeBacker); 17. Classification of tamely ramified maximal tori; 18. The volume formula; Part V. Appendices: A. Operations on integral models; B. Integral models of tori; C. Integral models of root subgroups; References; Index.

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Book SynopsisUsing a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student''s understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor''s resources are available.Trade Review'A broad coverage of more advanced topics, rich set of exercises, and thorough index make this stylish book an excellent choice for a second course in linear algebra.' Nick Higham, University of Manchester'This textbook thoroughly covers all the material you'd expect in a Linear Algebra course plus modern methods and applications. These include topics like the Fourier transform, eigenvalue adjustments, stochastic matrices, interlacing, power method and more. With 20 chapters of such material, this text would be great for a multi-part course and a reference book that all mathematicians should have.' Deanna Needell, University of California, Los Angeles'The original edition of Garcia and Horn's Second Course in Linear Algebra was well-written, well-organized, and contained several interesting topics that students should see - but rarely do in first-semester linear algebra - such as the singular value decomposition, Gershgorin circles, Cauchy's interlacing theorem, and Sylvester's inertia theorem. This new edition also has all of this, together with useful new material on matrix norms. Any student with the opportunity to take a second course on linear algebra would be lucky to have this book.' Craig Larson, Virginia Commonwealth University'An extremely versatile Linear Algebra textbook that allows numerous combinations of topics for a traditional course or a more modern and applications-oriented class. Each chapter contains the exact amount of information, presented in a very easy-to-read style, and a plethora of interesting exercises to help the students deepen their knowledge and understanding of the material.' Maria Isabel Bueno Cachadina, University of California, Santa Barbara'This is an excellent textbook. The topics flow nicely from one chapter to the next and the explanations are very clearly presented. The material can be used for a good second course in Linear Algebra by appropriately choosing the chapters to use. Several options are possible. The breadth of subjects presented makes this book a valuable resource.' Daniel B. Szyld, Temple University and President of the International Linear Algebra Society'With a careful selection of topics and a deft balance between theory and applications, the authors have created a perfect textbook for a second course on Linear Algebra. The exposition is clear and lively. Rigorous proofs are supplemented by a rich variety of examples, figures, and problems.' Rajendra Bhatia, Ashoka University'The authors have provided a contemporary, methodical, and clear approach to a broad and comprehensive collection of core topics in matrix theory. They include a wealth of illustrative examples and accompanying exercises to re-enforce the concepts in each chapter. One unique aspect of this book is the inclusion of a large number of concepts that arise in many interesting applications that do not typically appear in other books. I expect this text will be a compelling reference for active researchers and instructors in this subject area.' Shaun Fallat, University of Regina'It starts from scratch, but manages to cover an amazing variety of topics, of which quite a few cannot be found in standard textbooks. All matrices in the book are over complex numbers, and the connections to physics, statistics, and engineering are regularly highlighted. Compared with the first edition, two new chapters and 300 new problems have been added, as well as many new conceptual examples. Altogether, this is a truly impressive book.' Claus Scheiderer, University of KonstanzTable of ContentsContents; Preface; Notation; 1. Vector Spaces; 2. Bases and Similarity; 3. Block Matrices; 4. Rank, Triangular Factorizations, and Row Equivalence; 5. Inner Products and Norms; 6. Orthonormal Vectors; 7. Unitary Matrices; 8. Orthogonal Complements and Orthogonal Projections; 9. Eigenvalues, Eigenvectors, and Geometric Multiplicity; 10. The Characteristic Polynomial and Algebraic Multiplicity; 11. Unitary Triangularization and Block Diagonalization; 12. The Jordan Form: Existence and Uniqueness; 13. The Jordan Form: Applications; 14. Normal Matrices and the Spectral Theorem; 15. Positive Semidefinite Matrices; 16. The Singular Value and Polar Decompositions; 17. Singular Values and the Spectral Norm; 18. Interlacing and Inertia; 19. Norms and Matrix Norms; 20. Positive and Nonnegative Matrices; References; Index.

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Book SynopsisUsing a pedagogical, unified approach, this book presents both the analytic and combinatorial aspects of convexity and its applications in optimization. On the structural side, this is done via an exposition of classical convex analysis and geometry, along with polyhedral theory and geometry of numbers. On the algorithmic/optimization side, this is done by the first ever exposition of the theory of general mixed-integer convex optimization in a textbook setting. Classical continuous convex optimization and pure integer convex optimization are presented as special cases, without compromising on the depth of either of these areas. For this purpose, several new developments from the past decade are presented for the first time outside technical research articles: discrete Helly numbers, new insights into sublinear functions, and best known bounds on the information and algorithmic complexity of mixed-integer convex optimization. Pedagogical explanations and more than 300 exercises make this book ideal for students and researchers.

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Book SynopsisAs a result of the COVID-19 pandemic, medical statistics and public health data have become staples of newsfeeds worldwide, with infection rates, deaths, case fatality and the mysterious R figure featuring regularly. However, we don''t all have the statistical background needed to translate this information into knowledge. In this lively account, Stephen Senn explains these statistical phenomena and demonstrates how statistics is essential to making rational decisions about medical care. The second edition has been thoroughly updated to cover developments of the last two decades and includes a new chapter on medical statistical challenges of COVID-19, along with additional material on infectious disease modelling and representation of women in clinical trials. Senn entertains with anecdotes, puzzles and paradoxes, while tackling big themes including: clinical trials and the development of medicines, life tables, vaccines and their risks or lack of them, smoking and lung cancer, and even the power of prayer.Trade Review'The COVID pandemic has shown the power of statistics to save millions of lives by revealing 'what works'. Yet statistical methods have a deeply controversial history, and provoke sometimes bitter debate to this day. Professor Stephen Senn is renowned for his brilliant insights on the subject, and in Dicing with Death he offers us a series of fascinating journeys through its vast and varied landscape.' Robert Matthews, Visiting Professor Aston University and author of Chancing It: The Laws of Chance and How They Can Work for YouTable of Contents1. Circling the square; 2. The diceman cometh; 3. Trials of life; 4. Of dice and men; 5. Sex and the single patient; 6. A hale view of pills (and other matters); 7. Time's tables; 8. A dip in the pool; 9. The things that bug us; 10. The law is a ass; 11. The empire of the sum; 12. Going viral; Notes; Index.

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Book SynopsisIntroduces number operators with a focus on the relationship between quantum mechanics and social science Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum toolsthe number operator in particularcan be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results. The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features Table of ContentsPREFACE xi ACKNOWLEDGMENTS xv 1 WHY A QUANTUM TOOL IN CLASSICAL CONTEXTS? 1 1.1 A First View of (Anti-)Commutation Rules 2 1.2 Our Point of View 4 1.3 Do Not Worry About Heisenberg! 6 1.4 Other Appearances of Quantum Mechanics in Classical Problems 7 1.5 Organization of the Book 8 2 SOME PRELIMINARIES 11 2.1 The Bosonic Number Operator 11 2.2 The Fermionic Number Operator 15 2.3 Dynamics for a Quantum System 16 2.3.1 Schr¨odinger Representation 17 2.3.2 Heisenberg Representation 20 2.3.3 Interaction Representation 21 2.4 Heisenberg Uncertainty Principle 26 2.5 Some Perturbation Schemes in Quantum Mechanics 27 2.5.1 A Time-Dependent Point of View 28 2.5.2 Feynman Graphs 31 2.5.3 Dyson’s Perturbation Theory 33 2.5.4 The Stochastic Limit 35 2.6 Few Words on States 38 2.7 Getting an Exponential Law from a Hamiltonian 39 2.7.1 Non-Self-Adjoint Hamiltonians for Damping 42 2.8 Green’s Function 44 I SYSTEMS WITH FEW ACTORS 47 3 LOVE AFFAIRS 49 3.1 Introduction and Preliminaries 49 3.2 The First Model 50 3.2.1 Numerical Results for M >1 54 3.3 A Love Triangle 61 3.3.1 Another Generalization 66 3.4 Damped Love Affairs 71 3.4.1 Some Plots 76 3.5 Comparison with Other Strategies 80 4 MIGRATION AND INTERACTION BETWEEN SPECIES 81 4.1 Introduction and Preliminaries 82 4.2 A First Model 84 4.3 A Spatial Model 88 4.3.1 A Simple Case: Equal Coefficients 90 4.3.2 Back to the General Case: Migration 95 4.4 The Role of a Reservoir 100 4.5 Competition Between Populations 103 4.6 Further Comments 105 5 LEVELS OF WELFARE: THE ROLE OF RESERVOIRS 109 5.1 The Model 110 5.2 The Small λ Regime 116 5.2.1 The Sub-Closed System 117 5.2.2 And Now, the Reservoirs! 119 5.3 Back to S 121 5.3.1 What If M = 2? 123 5.4 Final Comments 125 6 AN INTERLUDE: WRITING THE HAMILTONIAN 129 6.1 Closed Systems 129 6.2 Open Systems 133 6.3 Generalizations 136 II SYSTEMS WITH MANY ACTORS 139 7 A FIRST LOOK AT STOCK MARKETS 141 7.1 An Introductory Model 142 8 ALL-IN-ONE MODELS 151 8.1 The Genesis of the Model 151 8.1.1 The Effective Hamiltonian 155 8.2 A Two-Traders Model 162 8.2.1 An Interlude: the Definition of cPˆ 163 8.2.2 Back to the Model 164 8.3 Many Traders 169 8.3.1 The Stochastic Limit of the Model 172 8.3.2 The FPL Approximation 177 9 MODELS WITH AN EXTERNAL FIELD 187 9.1 The Mixed Model 188 9.1.1 Interpretation of the Parameters 194 9.2 A Time-Dependent Point of View 196 9.2.1 First-Order Corrections 200 9.2.2 Second-Order Corrections 203 9.2.3 Feynman Graphs 204 9.3 Final Considerations 206 10 CONCLUSIONS 211 10.1 Other Possible Number Operators 211 10.1.1 Pauli Matrices 212 10.1.2 Pseudobosons 213 10.1.3 Nonlinear Pseudobosons 213 10.1.4 Algebra for an M + 1 Level System 215 10.2 What Else? 217 BIBLIOGRAPHY 219 INDEX 225

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Book SynopsisWhat is national wellbeing and what is progress?Why measure these definitions?Why are measures beyond economic performance needed and how will they be used? How do we measure national wellbeing & turn the definitions into observable quantities? Where are we now and where to next? These questions are asked and answered in this much needed, timely book. The Wellbeing of Nations provides an accessible and comprehensive overview of the measurement of national well-being, examining whether national wellbeing is more than the sum of the wellbeing of everyone in the country, and identifying and reviewing requirements for new measures. It begins with definitions, describes how to operationalize those definitions, and takes a critical look at the uses to which such measures are to be put. The authors examine initiatives from around the world, using the UK measuring national wellbeing programme' as a case study throughout the book, along with case studies drawnTrade Review“Although there are brief discussions of technical topics like measurement theory, the book will be useful to researchers across a range of disciplines and the interested general reader.” (Significance, 15 June 2015)Table of ContentsList of tables and figures viii Preface ix 1 What is national wellbeing and why measure it? 1 1.1 Motivation: Why measure wellbeing? 3 1.2 What is individual wellbeing? 8 1.3 Aspects of individual wellbeing 11 1.4 How to measure individual wellbeing? 16 1.4.1 Basics of measurement 16 1.4.2 What is measured matters 18 1.5 Properties of measurements 21 1.5.1 Validity 21 1.5.2 Reliability 22 1.6 Objective or subjective? 22 1.7 Combining multiple aspects 23 1.8 What is national wellbeing? 26 1.9 And how to measure national wellbeing? 27 1.10 Structure of the book 30 References 31 2 A short history of national wellbeing and its measurement 35 2.1 The good society and philosophies of the role of government, from ancient times 36 2.2 Utilitarianism 39 2.3 The American constitution 41 2.4 Official statistics – statistics about the state and about the state of society 42 2.5 National accounts and GDP 44 2.6 More to life than GDP 51 2.7 Social indicator movement and measuring quality of life 53 2.8 Health and wellbeing 56 2.9 Rise of measurement of psychological wellbeing (life satisfaction, happiness, worthwhile lives) 58 2.10 The Easterlin paradox 61 2.11 Taking note of the change in the quality of the goods and services we use 62 2.12 Capability approach to quality of life (Sen) and the human development index 63 2.13 Social capital and public value 65 2.14 Limits to growth and sustainable development indicators 67 2.14.1 Sustainable development indicators 69 2.14.2 Green growth indicators 72 2.14.3 Natural resource accounting 73 2.15 Commentary 75 References 77 3 Recent developments: Towards economic, social and environmental accounts 83 3.1 Mismeasuring our lives: The report by the Commission on the Measurement of Economic Performance and Social Progress 85 3.2 Replacing the Millennium Development Goals 90 3.3 A new global movement? 93 3.4 Commentary 104 References 110 4 Measuring individual wellbeing 115 4.1 On quantification 119 4.2 Single measures of wellbeing 123 4.3 Combining aspects of wellbeing 125 4.3.1 Causes, effects, and correlates 126 4.3.2 Subjective components of wellbeing 127 4.3.3 Weighted sums 129 4.4 Components of individual wellbeing 132 4.5 The frailty of memory 137 4.6 The devil’s in the details 138 4.7 Conclusion 142 References 143 5 Preparing to measure national wellbeing 146 5.1 Towards a user requirement for measures of national wellbeing and progress 147 5.2 Towards a framework to measure the progress of societies 152 5.3 Constructing measures of progress and national wellbeing: Identifying and meeting user requirements 160 5.4 Commentary 166 References 168 6 How to measure national wellbeing? 171 6.1 Drawing on the national economic accounts 172 6.2 Extending the national accounts 181 6.2.1 Consider income and consumption jointly with wealth 183 6.2.2 Give more prominence to the distribution of income, consumption and wealth 185 6.2.3 Broaden income measures to nonmarket activities 187 6.3 Indicator sets describing social and environmental conditions relating to wellbeing 190 6.3.1 Improve measures of people’s health, education, personal activities and environmental conditions 191 6.3.2 Quality-of-life indicators in all the dimensions covered should assess inequalities in a comprehensive way 193 6.3.3 Surveys should be designed to assess the links between various quality-of-life domains for each person, and this information should be used when designing policies in various fields 193 6.3.4 Statistical offices should provide the information needed to aggregate across quality-of-life dimensions, allowing the construction of different indexes 194 6.3.5 Sustainability assessment requires a well-identified dashboard of indicators 199 6.3.6 The environmental aspects of sustainability deserve a separate follow-up based on a well-chosen set of physical indicators 203 6.4 Survey-based data on subjective wellbeing 204 6.5 Developments in measuring national wellbeing and progress around the world 205 6.6 Important issues in the measurement of national wellbeing 209 References 212 7 Wellbeing policy and measurement in the UK 217 References 233 8 Conclusions 236 8.1 Progress 236 8.2 Measuring wellbeing 241 8.3 New technologies, new data? 244 8.4 Beyond the economy 245 8.5 The future 249 References 250 Appendix: Sources of methods and measures of wellbeing and progress 253 Further reading 269 Index 271

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Book SynopsisA comprehensive introduction to statistical methods for data mining and knowledge discovery.Table of ContentsPreface xiii Part I Background: Introductory Statistical Analytics 1 1 Data analytics and data mining 3 1.1 Knowledge discovery: finding structure in data 3 1.2 Data quality versus data quantity 5 1.3 Statistical modeling versus statistical description 7 2 Basic probability and statistical distributions 10 2.1 Concepts in probability 10 2.1.1 Probability rules 11 2.1.2 Random variables and probability functions 12 2.1.3 Means, variances, and expected values 17 2.1.4 Median, quartiles, and quantiles 18 2.1.5 Bivariate expected values, covariance, and correlation 20 2.2 Multiple random variables∗ 21 2.3 Univariate families of distributions 23 2.3.1 Binomial distribution 23 2.3.2 Poisson distribution 26 2.3.3 Geometric distribution 27 2.3.4 Negative binomial distribution 27 2.3.5 Discrete uniform distribution 28 2.3.6 Continuous uniform distribution 29 2.3.7 Exponential distribution 29 2.3.8 Gamma and chi-square distributions 30 2.3.9 Normal (Gaussian) distribution 32 2.3.10 Distributions derived from normal 37 2.3.11 The exponential family 41 3 Data manipulation 49 3.1 Random sampling 49 3.2 Data types 51 3.3 Data summarization 52 3.3.1 Means, medians, and central tendency 52 3.3.2 Summarizing variation 56 3.3.3 Summarizing (bivariate) correlation 59 3.4 Data diagnostics and data transformation 60 3.4.1 Outlier analysis 60 3.4.2 Entropy∗ 62 3.4.3 Data transformation 64 3.5 Simple smoothing techniques 65 3.5.1 Binning 66 3.5.2 Moving averages∗ 67 3.5.3 Exponential smoothing∗ 69 4 Data visualization and statistical graphics 76 4.1 Univariate visualization 77 4.1.1 Strip charts and dot plots 77 4.1.2 Boxplots 79 4.1.3 Stem-and-leaf plots 81 4.1.4 Histograms and density estimators 83 4.1.5 Quantile plots 87 4.2 Bivariate and multivariate visualization 89 4.2.1 Pie charts and bar charts 90 4.2.2 Multiple boxplots and QQ plots 95 4.2.3 Scatterplots and bubble plots 98 4.2.4 Heatmaps 102 4.2.5 Time series plots∗ 105 5 Statistical inference 115 5.1 Parameters and likelihood 115 5.2 Point estimation 117 5.2.1 Bias 118 5.2.2 The method of moments 118 5.2.3 Least squares/weighted least squares 119 5.2.4 Maximum likelihood∗ 120 5.3 Interval estimation 123 5.3.1 Confidence intervals 123 5.3.2 Single-sample intervals for normal (Gaussian) parameters 124 5.3.3 Two-sample intervals for normal (Gaussian) parameters 128 5.3.4 Wald intervals and likelihood intervals∗ 131 5.3.5 Delta method intervals∗ 135 5.3.6 Bootstrap intervals∗ 137 5.4 Testing hypotheses 138 5.4.1 Single-sample tests for normal (Gaussian) parameters 140 5.4.2 Two-sample tests for normal (Gaussian) parameters 142 5.4.3 Walds tests, likelihood ratio tests, and ‘exact’ tests∗ 145 5.5 Multiple inferences∗ 148 5.5.1 Bonferroni multiplicity adjustment 149 5.5.2 False discovery rate 151 Part II Statistical Learning and Data Analytics 161 6 Techniques for supervised learning: simple linear regression 163 6.1 What is “supervised learning?” 163 6.2 Simple linear regression 164 6.2.1 The simple linear model 164 6.2.2 Multiple inferences and simultaneous confidence bands 171 6.3 Regression diagnostics 175 6.4 Weighted least squares (WLS) regression 184 6.5 Correlation analysis 187 6.5.1 The correlation coefficient 187 6.5.2 Rank correlation 190 7 Techniques for supervised learning: multiple linear regression 198 7.1 Multiple linear regression 198 7.1.1 Matrix formulation 199 7.1.2 Weighted least squares for the MLR model 200 7.1.3 Inferences under the MLR model 201 7.1.4 Multicollinearity 208 7.2 Polynomial regression 210 7.3 Feature selection 211 7.3.1 R2p plots 212 7.3.2 Information criteria: AIC and BIC 215 7.3.3 Automated variable selection 216 7.4 Alternative regression methods∗ 223 7.4.1 Loess 224 7.4.2 Regularization: ridge regression 230 7.4.3 Regularization and variable selection: the Lasso 238 7.5 Qualitative predictors: ANOVA models 242 8 Supervised learning: generalized linear models 258 8.1 Extending the linear regression model 258 8.1.1 Nonnormal data and the exponential family 258 8.1.2 Link functions 259 8.2 Technical details for GLiMs∗ 259 8.2.1 Estimation 260 8.2.2 The deviance function 261 8.2.3 Residuals 262 8.2.4 Inference and model assessment 264 8.3 Selected forms of GLiMs 265 8.3.1 Logistic regression and binary-data GLiMs 265 8.3.2 Trend testing with proportion data 271 8.3.3 Contingency tables and log-linear models 273 8.3.4 Gamma regression models 281 9 Supervised learning: classification 291 9.1 Binary classification via logistic regression 292 9.1.1 Logistic discriminants 292 9.1.2 Discriminant rule accuracy 296 9.1.3 ROC curves 297 9.2 Linear discriminant analysis (LDA) 297 9.2.1 Linear discriminant functions 297 9.2.2 Bayes discriminant/classification rules 302 9.2.3 Bayesian classification with normal data 303 9.2.4 Naïve Bayes classifiers 308 9.3 k-Nearest neighbor classifiers 308 9.4 Tree-based methods 312 9.4.1 Classification trees 312 9.4.2 Pruning 314 9.4.3 Boosting 321 9.4.4 Regression trees 321 9.5 Support vector machines∗ 322 9.5.1 Separable data 322 9.5.2 Nonseparable data 325 9.5.3 Kernel transformations 326 10 Techniques for unsupervised learning: dimension reduction 341 10.1 Unsupervised versus supervised learning 341 10.2 Principal component analysis 342 10.2.1 Principal components 342 10.2.2 Implementing a PCA 344 10.3 Exploratory factor analysis 351 10.3.1 The factor analytic model 351 10.3.2 Principal factor estimation 353 10.3.3 Maximum likelihood estimation 354 10.3.4 Selecting the number of factors 355 10.3.5 Factor rotation 356 10.3.6 Implementing an EFA 357 10.4 Canonical correlation analysis∗ 361 11 Techniques for unsupervised learning: clustering and association 373 11.1 Cluster analysis 373 11.1.1 Hierarchical clustering 376 11.1.2 Partitioned clustering 384 11.2 Association rules/market basket analysis 395 11.2.1 Association rules for binary observations 396 11.2.2 Measures of rule quality 397 11.2.3 The Apriori algorithm 398 11.2.4 Statistical measures of association quality 402 A Matrix manipulation 411 A.1 Vectors and matrices 411 A.2 Matrix algebra 412 A.3 Matrix inversion 414 A.4 Quadratic forms 415 A.5 Eigenvalues and eigenvectors 415 A.6 Matrix factorizations 416 A.6.1 QR decomposition 417 A.6.2 Spectral decomposition 417 A.6.3 Matrix square root 417 A.6.4 Singular value decomposition 418 A.7 Statistics via matrix operations 419 B Brief introduction to R 421 B.1 Data entry and manipulation 422 B.2 A turbo-charged calculator 426 B.3 R functions 427 B.3.1 Inbuilt R functions 427 B.3.2 Flow control 429 B.3.3 User-defined functions 429 B.4 R packages 430 References 432 Index 453

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Book SynopsisAn introduction to stochastic processes through the use of R Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences.Trade Review"This text provides an excellent introduction to stochastic processes and their applications"...."Examples are plentiful and well chosen, and help to organize the material and to move it forward. Each section contains a good supply of exercises, both calculational and theoretical" Thomas Polaski, Mathematical Reviews, Sept 2017Table of ContentsPreface xi Acknowledgments xv List of Symbols and Notation xvii About the Companion Website xxi 1 Introduction and Review 1 1.1 Deterministic and Stochastic Models 1 1.2 What is a Stochastic Process? 5 1.3 Monte Carlo Simulation 9 1.4 Conditional Probability 10 1.5 Conditional Expectation 18 Exercises 34 2 Markov Chains: First Steps 40 2.1 Introduction 40 2.2 Markov Chain Cornucopia 42 2.3 Basic Computations 52 2.4 Long-Term Behavior—the Numerical Evidence 59 2.5 Simulation 65 2.6 Mathematical Induction* 68 Exercises 70 3 Markov Chains for the Long Term 76 3.1 Limiting Distribution 76 3.2 Stationary Distribution 80 3.3 Can you Find the Way to State a? 94 3.4 Irreducible Markov Chains 103 3.5 Periodicity 106 3.6 Ergodic Markov Chains 109 3.7 Time Reversibility 114 3.8 Absorbing Chains 119 3.9 Regeneration and the Strong Markov Property* 133 3.10 Proofs of Limit Theorems* 135 Exercises 144 4 Branching Processes 158 4.1 Introduction 158 4.2 Mean Generation Size 160 4.3 Probability Generating Functions 164 4.4 Extinction is Forever 168 Exercises 175 5 Markov Chain Monte Carlo 181 5.1 Introduction 181 5.2 Metropolis–Hastings Algorithm 187 5.3 Gibbs Sampler 197 5.4 Perfect Sampling* 205 5.5 Rate of Convergence: the Eigenvalue Connection* 210 5.6 Card Shuffling and Total Variation Distance* 212 Exercises 219 6 Poisson Process 223 6.1 Introduction 223 6.2 Arrival, Interarrival Times 227 6.3 Infinitesimal Probabilities 234 6.4 Thinning, Superposition 238 6.5 Uniform Distribution 243 6.6 Spatial Poisson Process 249 6.7 Nonhomogeneous Poisson Process 253 6.8 Parting Paradox 255 Exercises 258 7 Continuous-Time Markov Chains 265 7.1 Introduction 265 7.2 Alarm Clocks and Transition Rates 270 7.3 Infinitesimal Generator 273 7.4 Long-Term Behavior 283 7.5 Time Reversibility 294 7.6 Queueing Theory 301 7.7 Poisson Subordination 306 Exercises 313 8 Brownian Motion 320 8.1 Introduction 320 8.2 Brownian Motion and Random Walk 326 8.3 Gaussian Process 330 8.4 Transformations and Properties 334 8.5 Variations and Applications 345 8.6 Martingales 356 Exercises 366 9 A Gentle Introduction to Stochastic Calculus* 372 9.1 Introduction 372 9.2 Ito Integral 378 9.3 Stochastic Differential Equations 385 Exercises 397 A Getting Started with R 400 B Probability Review 421 B.1 Discrete Random Variables 422 B.2 Joint Distribution 424 B.3 Continuous Random Variables 426 B.4 Common Probability Distributions 428 B.5 Limit Theorems 439 B.6 Moment-Generating Functions 440 C Summary of Common Probability Distributions 443 D Matrix Algebra Review 445 D.1 Basic Operations 445 D.2 Linear System 447 D.3 Matrix Multiplication 448 D.4 Diagonal, Identity Matrix, Polynomials 448 D.5 Transpose 449 D.6 Invertibility 449 D.7 Block Matrices 449 D.8 Linear Independence and Span 450 D.9 Basis 451 D.10 Vector Length 451 D.11 Orthogonality 452 D.12 Eigenvalue, Eigenvector 452 D.13 Diagonalization 453 Answers to Selected Odd-Numbered Exercises 455 References 470 Index 475

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Book SynopsisGraphs and Networks A unique blend of graph theory and network science for mathematicians and data science professionals alike. Featuring topics such as minors, connectomes, trees, distance, spectral graph theory, similarity, centrality, small-world networks, scale-free networks, graph algorithms, Eulerian circuits, Hamiltonian cycles, coloring, higher connectivity, planar graphs, flows, matchings, and coverings, Graphs and Networks contains modern applications for graph theorists and a host of useful theorems for network scientists. The book begins with applications to biology and the social and political sciences and gradually takes a more theoretical direction toward graph structure theory and combinatorial optimization. A background in linear algebra, probability, and statistics provides the proper frame of reference. Graphs and Networks also features: Applications to neuroscience, climate science, and the social and political sciencesA research outlook integrated directly into tTable of ContentsList of Figures iv Preface viii Chapter 1. From Königsberg to Connectomes 1 1.1. Introduction 1 1.2. Isomorphism 18 1.3. Minors and Constructions 25 Chapter 2. Fundamental Topics 39 2.1. Trees 39 2.2. Distance 44 2.3. Degree Sequences 52 2.4. Matrices 56 Chapter 3. Similarity and Centrality 70 3.1. Similarity Measures 70 3.2. Centrality Measures 74 3.3. Eigenvector and Katz Centrality 78 3.4. PageRank 84 Chapter 4. Types of Networks 91 4.1. Small-World Networks 91 4.2. Scale-Free Networks 95 4.3. Assortative Mixing 97 4.4. Covert Networks 102 Chapter 5. Graph Algorithms 107 5.1. Traversal Algorithms 107 5.2. Greedy Algorithms 113 5.3. Shortest Path Algorithms 118 Chapter 6. Structure, Coloring, Higher Connectivity 126 6.1. Eulerian Circuits 126 6.2. Hamiltonian Cycles 131 6.3. Coloring 136 6.4. Higher Connectivity 142 6.5. Menger's Theorem 148 Chapter 7. Planar Graphs 159 7.1. Properties of Planar Graphs 159 7.2. Euclid's Theorem on Regular Polyhedra 167 7.3. The Five Color Theorem 172 7.4. Invariants for Non-Planar Graphs 174 Chapter 8. Flows and Matchings 182 8.1. Flows in Networks 182 8.2. Stable Sets, Matchings, Coverings 188 8.3. Min-Max Theorems 192 8.4. Maximum Matching Algorithm 196 Appendix A. Linear Algebra 211 Appendix B. Probability and Statistics 215 Appendix C. Complexity of Algorithms 218 Appendix D. Stacks and Queues 222 Appendix. Bibliography 226

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Book SynopsisThe easy way to grasp customer analytics Ensuring your customers are having positive experiences with your company at all levels, including initial brand awareness and loyalty, is crucial to the success of your business.Table of ContentsIntroduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 2 Beyond the Book 3 Where to Go from Here 3 Part I: Getting Started with Customer Analytics 5 Chapter 1: Introducing Customer Analytics 7 Defining Customer Analytics 7 The benefits of customer analytics 8 Using customer analytics 11 Compiling Big and Small Data 12 Chapter 2: Embracing the Science and Art of Metrics 15 Adding up Quantitative Data 15 Discrete and continuous data 16 Levels of data 16 Variables 19 Quantifying Qualitative Data 20 Determining the Sample Size You Need 22 Estimating a confidence interval 24 Computing a 95% confidence interval 25 Determining What Data to Collect 27 Managing the Right Measure 28 Chapter 3: Planning a Customer Analytics Initiative 31 A Customer Analytics Initiative Overview 31 Defining the Scope and Outcome 33 Identifying the Metrics, Methods, and Tools 34 Setting a Budget 35 Determining the Correct Sample Size 36 Analyzing and Improving 37 Controlling the Results 38 Part II: Identifying Your Customers 41 Chapter 4: Segmenting Customers 43 Why Segment Customers 43 Segmenting by the Five W’s 47 Who 47 Where 48 What 49 When 52 Why 52 How 52 Analyzing the Data to Segment Your Customers 53 Step 1: Tabulate your data 53 Step 2: Cross-Tabbing 54 Step 3: Cluster Analysis 56 Step 4: Estimate the size of each segment 57 Step 5 Estimate the value of each segment 57 Chapter 5: Creating Customer Personas 61 Recognizing the Importance of Personas 61 Working with personas 64 Getting More Personal with Customer Data 66 Step 1: Collecting the appropriate data 66 Step 2: Dividing data 68 Step 3: Identifying and refining personas 68 Answering Questions with Personas 71 Chapter 6: Determining Customer Lifetime Value 75 Why your CLV is important 76 Applying CLV in Business 77 Calculating Lifetime Value 77 Estimating revenue 78 Calculating the CLV 80 Identifying profitable customers 82 Marketing to profitable customers 82 Part III: Analytics for the Customer Journey 85 Chapter 7: Mapping the Customer Journey 87 Working with the Traditional Marketing Funnel 87 What Is a Customer Journey Map? 91 Define the Customer Journey 93 Finding the data 93 Sketching the journey 94 Making the map more useful 101 Chapter 8: Determining Brand Awareness and Attitudes 103 Measuring Brand Awareness 103 Unaided awareness 104 Aided awareness 105 Measuring product or service knowledge 106 Measuring Brand Attitude 107 Identifying brand pillars 108 Checking brand affinity 108 Measuring Usage and Intent 110 Finding out past usage 110 Measuring future intent 110 Understanding the Key Drivers of Attitude 111 Structuring a Brand Assessment Survey 111 Chapter 9: Measuring Customer Attitudes 113 Gauging Customer Satisfaction 113 General satisfaction 114 Attitude versus satisfaction 115 Rating Usability with the SUS and SUPR-Q 117 System Usability Scale (SUS) 117 Standardized User Experience Percentile Rank Questionnaire (SUPR-Q) 120 Measuring task difficulty with SEQ 122 Scoring Brand Affection 123 Finding Expectations: Desirability and Luxury 125 Desirability 125 Luxury 125 Measuring Attitude Lift 126 Asking for Preferences 128 Finding Your Key Drivers of Customer Attitudes 129 Writing Effective Customer Attitude Questions 131 Chapter 10: Quantifying the Consideration and Purchase Phases 133 Identifying the Consideration Touchpoints 133 Company-driven touchpoints 134 Customer-driven touchpoints 134 Measuring the Customer-Driven Touchpoints 135 Measuring the Three R’s of Company-Driven Touchpoints 137 Reach 137 Resonance 137 Reaction 138 Measuring resonance and reaction 139 Tracking Conversions and Purchases 139 Tracking micro conversions 140 Creating micro-conversion opportunities 141 Setting up conversion tracking 142 Measuring conversion rates 142 Measuring Changes through A/ B Testing 143 Offline A/B testing 144 Online A/B testing 144 Testing multiple variables 148 Making the Most of Website Analytics 148 Chapter 11: Tracking Post-Purchase Behavior 151 Dealing with Cognitive Dissonance 152 Reducing dissonance 152 Turning dissonance into satisfaction 153 Tracking return rates 153 Measuring the Post-Purchase Touchpoints 154 Digging into the post-purchase touchpoints 155 Assessing post-purchase satisfaction ratings 158 Finding Problems Using Call Center Analysis 159 Finding the Root Cause with Cause-and-Effect Diagrams 160 Creating a cause-and-effect diagram 161 Chapter 12: Measuring Customer Loyalty 163 Measuring Customer Loyalty 164 Repurchase rate 164 Net Promoter Score 166 Bad profits 174 Finding Key Drivers of Loyalty 177 Valuing positive word of mouth 178 Valuing negative word of mouth 182 Part IV: Analytics for Product Development 185 Chapter 13: Developing Products That Customers Want 187 Gathering Input on Product Features 187 Finding Customers’ Top Tasks 188 Listing the tasks 189 Finding customers 189 Selecting five tasks 190 Graphing and analyzing 190 Taking an internal view 191 Conducting a Gap Analysis 193 Mapping Business Needs to Customer Requirements 194 Identifying customers’ wants and needs 195 Identifying the voice of the customer 196 Identifying the how’s (the voice of the company) 196 Building the relationship between the customer and company voices 197 Generating priorities 197 Examining priorities 198 Measuring Customer Delight with the Kano Model 199 Assessing the Value of Each Combination of Features 200 Finding Out Why Problems Occur 202 Chapter 14: Gaining Insights through a Usability Study 207 Recognizing the Principles of Usability 207 Conducting a Usability Test 208 Determining what you want to test 209 Identifying the goals 209 Outlining task scenarios 209 Recruiting users 212 Testing your users 215 Collecting metrics 216 Coding and analyzing your data 218 Summarizing and presenting the results 218 Considering the Different Types of Usability Tests 218 Finding and Reporting Usability Problems 221 Facilitating a Usability Study 225 Chapter 15: Measuring Findability and Navigation 231 Finding Your Areas of Findability 232 Identifying What Customers Want 233 Prepping for a Findability Test 235 Finding your baseline 235 Designing the study 235 Looking at your findability metrics 237 Conducting Your Findability Study 240 Determining sample size 240 Recruiting users 241 Analyzing the results 242 Improving Findability 244 Cross-linking products 244 Regrouping categories 245 Rephrasing the tasks 245 Measuring findability after changes 246 Chapter 16: Considering the Ethics of Customer Analytics 249 Getting Informed Consent 249 Facebook 250 OKCupid 251 Amazon and Orbitz 251 Mintcom 252 Deciding to Experiment 252 Part V: The Part of Tens 255 Chapter 17: Ten Customer Metrics You Should Collect 257 Chapter 18: Ten Methods to Improve the Customer Experience 263 Chapter 19: Ten Common Analytic Mistakes 267 Chapter 20: Ten Methods for Identifying Customer Needs 271 Appendix: Predicting with Customer Analytics 277 Finding Similarities and Associations 278 Visualizing associations 279 Quantifying the strength of a relationship 280 Associations between binary variables 284 Determining Causation 288 Randomized experimental study 288 Quasi-experimental design 289 Correlational study 290 Single-subjects study 290 Anecdotes 291 Predicting with Regression 291 Predicting with the regression line 293 Creating a regression equation in Excel 294 Multiple regression analysis 296 Predicting with binary data 300 Predicting Trends with Time Series Analysis 301 Exponential (non-linear) growth 304 Training and validation periods 306 Detecting Differences 308 Index 311

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Book Synopsis...I know of no better book of its kind... (Journal of the Royal Statistical Society, Vol 169 (1), January 2006) A revised and updated edition of this bestselling introductory textbook to statistical analysis using the leading free software package R This new edition of a bestselling title offers a concise introduction to a broad array of statistical methods, at a level that is elementary enough to appeal to awide range of disciplines. Step-by-step instructionshelp the non-statistician to fully understand the methodology. The book covers the full range of statistical techniques likely to be needed to analyse the data from research projects, including elementary material like t--tests and chi--squared tests, intermediate methods like regression and analysis of variance, and more advanced techniques like generalized linear modelling. Includes numerous worked examples and exercises within each chapter.Table of ContentsPreface xi Chapter 1 Fundamentals 1 Everything Varies 2 Significance 3 Good and Bad Hypotheses 3 Null Hypotheses 3 p Values 3 Interpretation 4 Model Choice 4 Statistical Modelling 5 Maximum Likelihood 6 Experimental Design 7 The Principle of Parsimony (Occam’s Razor) 8 Observation, Theory and Experiment 8 Controls 8 Replication: It’s the ns that Justify the Means 8 How Many Replicates? 9 Power 9 Randomization 10 Strong Inference 14 Weak Inference 14 How Long to Go On? 14 Pseudoreplication 15 Initial Conditions 16 Orthogonal Designs and Non-Orthogonal Observational Data 16 Aliasing 16 Multiple Comparisons 17 Summary of Statistical Models in R 18 Organizing Your Work 19 Housekeeping within R 20 References 22 Further Reading 22 Chapter 2 Dataframes 23 Selecting Parts of a Dataframe: Subscripts 26 Sorting 27 Summarizing the Content of Dataframes 29 Summarizing by Explanatory Variables 30 First Things First: Get to Know Your Data 31 Relationships 34 Looking for Interactions between Continuous Variables 36 Graphics to Help with Multiple Regression 39 Interactions Involving Categorical Variables 39 Further Reading 41 Chapter 3 Central Tendency 42 Further Reading 49 Chapter 4 Variance 50 Degrees of Freedom 53 Variance 53 Variance: A Worked Example 55 Variance and Sample Size 58 Using Variance 59 A Measure of Unreliability 60 Confidence Intervals 61 Bootstrap 62 Non-constant Variance: Heteroscedasticity 65 Further Reading 65 Chapter 5 Single Samples 66 Data Summary in the One-Sample Case 66 The Normal Distribution 70 Calculations Using z of the Normal Distribution 76 Plots for Testing Normality of Single Samples 79 Inference in the One-Sample Case 81 Bootstrap in Hypothesis Testing with Single Samples 81 Student’s t Distribution 82 Higher-Order Moments of a Distribution 83 Skew 84 Kurtosis 86 Reference 87 Further Reading 87 Chapter 6 Two Samples 88 Comparing Two Variances 88 Comparing Two Means 90 Student’s t Test 91 Wilcoxon Rank-Sum Test 95 Tests on Paired Samples 97 The Binomial Test 98 Binomial Tests to Compare Two Proportions 100 Chi-Squared Contingency Tables 100 Fisher’s Exact Test 105 Correlation and Covariance 108 Correlation and the Variance of Differences between Variables 110 Scale-Dependent Correlations 112 Reference 113 Further Reading 113 Chapter 7 Regression 114 Linear Regression 116 Linear Regression in R 117 Calculations Involved in Linear Regression 122 Partitioning Sums of Squares in Regression: SSY = SSR + SSE 125 Measuring the Degree of Fit, r 2 133 Model Checking 134 Transformation 135 Polynomial Regression 140 Non-Linear Regression 142 Generalized Additive Models 146 Influence 148 Further Reading 149 Chapter 8 Analysis of Variance 150 One-Way ANOVA 150 Shortcut Formulas 157 Effect Sizes 159 Plots for Interpreting One-Way ANOVA 162 Factorial Experiments 168 Pseudoreplication: Nested Designs and Split Plots 173 Split-Plot Experiments 174 Random Effects and Nested Designs 176 Fixed or Random Effects? 177 Removing the Pseudoreplication 178 Analysis of Longitudinal Data 178 Derived Variable Analysis 179 Dealing with Pseudoreplication 179 Variance Components Analysis (VCA) 183 References 184 Further Reading 184 Chapter 9 Analysis of Covariance 185 Further Reading 192 Chapter 10 Multiple Regression 193 The Steps Involved in Model Simplification 195 Caveats 196 Order of Deletion 196 Carrying Out a Multiple Regression 197 A Trickier Example 203 Further Reading 211 Chapter 11 Contrasts 212 Contrast Coefficients 213 An Example of Contrasts in R 214 A Priori Contrasts 215 Treatment Contrasts 216 Model Simplification by Stepwise Deletion 218 Contrast Sums of Squares by Hand 222 The Three Kinds of Contrasts Compared 224 Reference 225 Further Reading 225 Chapter 12 Other Response Variables 226 Introduction to Generalized Linear Models 228 The Error Structure 229 The Linear Predictor 229 Fitted Values 230 A General Measure of Variability 230 The Link Function 231 Canonical Link Functions 232 Akaike’s Information Criterion (AIC) as a Measure of the Fit of a Model 233 Further Reading 233 Chapter 13 Count Data 234 A Regression with Poisson Errors 234 Analysis of Deviance with Count Data 237 The Danger of Contingency Tables 244 Analysis of Covariance with Count Data 247 Frequency Distributions 250 Further Reading 255 Chapter 14 Proportion Data 256 Analyses of Data on One and Two Proportions 257 Averages of Proportions 257 Count Data on Proportions 257 Odds 259 Overdispersion and Hypothesis Testing 260 Applications 261 Logistic Regression with Binomial Errors 261 Proportion Data with Categorical Explanatory Variables 264 Analysis of Covariance with Binomial Data 269 Further Reading 272 Chapter 15 Binary Response Variable 273 Incidence Functions 275 ANCOVA with a Binary Response Variable 279 Further Reading 284 Chapter 16 Death and Failure Data 285 Survival Analysis with Censoring 287 Further Reading 290 Appendix Essentials of the R Language 291 R as a Calculator 291 Built-in Functions 292 Numbers with Exponents 294 Modulo and Integer Quotients 294 Assignment 295 Rounding 295 Infinity and Things that Are Not a Number (NaN) 296 Missing Values (NA) 297 Operators 298 Creating a Vector 298 Named Elements within Vectors 299 Vector Functions 299 Summary Information from Vectors by Groups 300 Subscripts and Indices 301 Working with Vectors and Logical Subscripts 301 Addresses within Vectors 304 Trimming Vectors Using Negative Subscripts 304 Logical Arithmetic 305 Repeats 305 Generate Factor Levels 306 Generating Regular Sequences of Numbers 306 Matrices 307 Character Strings 309 Writing Functions in R 310 Arithmetic Mean of a Single Sample 310 Median of a Single Sample 310 Loops and Repeats 311 The ifelse Function 312 Evaluating Functions with apply 312 Testing for Equality 313 Testing and Coercing in R 314 Dates and Times in R 315 Calculations with Dates and Times 319 Understanding the Structure of an R Object Using str 320 Reference 322 Further Reading 322 Index 323

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Book SynopsisINTRODUCTION TO THEORETICAL AND MATHEMATICAL FLUID DYNAMICS A practical treatment of mathematical fluid dynamics In Introduction to Theoretical and Mathematical Fluid Dynamics, distinguished researcher Dr. Bhimsen K. Shivamoggi delivers a comprehensive and insightful exploration of fluid dynamics from a mathematical point of view. The book introduces readers to the mathematical study of fluid behavior and highlights areas of active research in fluid dynamics. With coverage of advances in the field over the last 15 years, this book provides in-depth examinations of theoretical and mathematical fluid dynamics with a particular focus on incompressible and compressible fluid flows. Introduction to Theoretical and Mathematical Fluid Dynamics includes practical applications and exercises to illustrate the concepts discussed within, and real-world examples are explained throughout the text. Clear and explanatory material accompanies the rigorous maTable of ContentsContents Preface to the Third Edition xv Acknowledgments xvii Part I Basic Concepts and Equations of Fluid Dynamics 1 1 Introduction to the Fluid Model 3 1.1 The Fluid State 4 1.2 Description of the Flow-Field 5 1.3 Volume Forces and Surface Forces 7 1.4 Relative Motion Near a Point 10 1.5 Stress–Strain Relations 13 2 Equations of Fluid Flows 15 2.1 The Transport Theorem 16 2.2 The Material Derivative 18 2.3 The Law of Conservation of Mass 18 2.4 Equation of Motion 19 2.5 The Energy Equation 19 2.6 The Equation of Vorticity 22 2.7 The Incompressible Fluid 23 2.8 Boundary Conditions 24 2.9 A Program for Analysis of the Governing Equations 25 3 Hamiltonian Formulation of Fluid-Flow Problems 27 3.1 Hamiltonian Dynamics of Continuous Systems 28 3.2 Three-Dimensional Incompressible Flows 32 3.3 Two-Dimensional Incompressible Flows 35 4 Surface Tension Effects 39 4.1 Shape of the Interface between Two Fluids 39 4.2 Capillary Rises in Liquids 41 Part II Dynamics of Incompressible Fluid Flows 45 5 Fluid Kinematics and Dynamics 47 5.1 Stream Function 47 5.2 Equations of Motion 50 5.3 Integrals of Motion 50 5.4 Capillary Waves on a Spherical Drop 51 5.5 Cavitation 54 5.6 Rates of Change of Material Integrals 55 5.7 The Kelvin Circulation Theorem 57 5.8 The Irrotational Flow 58 5.9 Simple-Flow Patterns 62 (i) The Source Flow 62 (ii) The Doublet Flow 63 (iii) The Vortex Flow 66 (iv) Doublet in a Uniform Stream 66 (v) Uniform Flow Past a Circular Cylinder with Circulation 67 6 The Complex-Variable Method 71 6.1 The Complex Potential 71 6.2 Conformal Mapping of Flows 74 6.3 Hydrodynamic Images 82 6.4 Principles of Free-Streamline Flow 84 (i) Schwarz-Christoffel Transformation 84 (ii) Hodograph Method 93 7 Three-Dimensional Irrotational Flows 99 7.1 Special Singular Solutions 99 (i) The Source Flow 99 (ii) The Doublet Flow 101 7.2 d’Alembert’s Paradox 104 7.3 Image of a Source in a Sphere 105 7.4 Flow Past an Arbitrary Body 107 7.5 Unsteady Flows 109 7.6 Renormalized (or Added) Mass of Bodies Moving through a Fluid 111 8 Vortex Flows 115 8.1 Vortex Tubes 115 8.2 Induced Velocity Field 117 8.3 Biot-Savart’s Law 117 8.4 von Kármán Vortex Street 121 8.5 Vortex Ring 124 8.6 Hill’s Spherical Vortex 129 8.7 Vortex Sheet 131 8.8 Vortex Breakdown: Brooke Benjamin’s Theory 135 9 Rotating Flows 143 9.1 Governing Equations and Elementary Results 143 9.2 Taylor-Proudman Theorem 144 9.3 Propagation of Inertial Waves in a Rotating Fluid 146 9.4 Plane Inertial Waves 147 9.5 Forced Wavemotion in a Rotating Fluid 150 (i) The Elliptic Case 153 (ii) The Hyperbolic Case 154 9.6 Slow Motion along the Axis of Rotation 155 9.7 Rossby Waves 160 10 Water Waves 167 10.1 Governing Equations 168 10.2 A Variational Principle for Surface Waves 169 10.3 Water Waves in a Semi-Infinite Fluid 171 10.4 Water Waves in a Fluid Layer of Finite Depth 172 10.5 Shallow-Water Waves 174 (i) Analogy with Gas Dynamics 175 (ii) Breaking of Waves 176 10.6 Water Waves Generated by an Initial Displacement over a Localized Region 176 10.7 Waves on a Steady Stream 182 (i) One-Dimensional Gravity Waves 183 (ii) One-Dimensional Capillary-Gravity Waves 184 (iii) Ship Waves 185 10.8 Gravity Waves in a Rotating Fluid 188 10.9 Theory of Tides 193 10.10 Hydraulic Jump 195 (i) Tidal Bores 195 (ii) The Dam-Break Problem 199 10.11 Nonlinear Shallow-Water Waves 202 (i) Solitary Waves 206 (ii) Periodic Cnoidal Waves 208 (iii) Interacting Solitary Waves 214 (iv) Stokes Waves 219 (v) Modulational Instability and Envelope Solutions 220 10.12 Nonlinear Capillary-Gravity Waves 230 (i) Resonant Three-Wave Interactions 230 (ii) Second-Harmonic Resonance 235 11 Applications to Aerodynamics 241 11.1 Airfoil Theory: Method of Complex Variables 242 (i) Force and Moments on an Arbitrary Body 242 (ii) Flow Past an Arbitrary Cylinder 245 (iii) Flow Around a Flat Plate 248 (iv) Flow Past an Airfoil 250 (v) The Joukowski Transformation 253 11.2 Thin Airfoil Theory 259 (i) Thickness Problem 262 (ii) Camber Problem 264 (iii) Flat Plate at an Angle of Attack 269 (iv) Combined Aerodynamic Characteristics 271 (v) The Leading-Edge Problem of a Thin Airfoil 271 11.3 Slender-Body Theory 275 11.4 Prandtl’s Lifting-Line Theory for Wings 277 11.5 Oscillating Thin-Airfoil Problem: Theodorsen’s Theory 282 Part III Dynamics of Compressible Fluid Flows 297 12 Review of Thermodynamics 299 12.1 Thermodynamic System and Variables of State 299 12.2 The First Law of Thermodynamics and Reversible and Irreversible Processes 300 12.3 The Second Law of Thermodynamics 303 12.4 Entropy 304 12.5 Liquid and Gaseous Phases 307 13 Isentropic Fluid Flows 309 13.1 Applications of Thermodynamics to Fluid Flows 309 13.2 Linear Sound Wave Propagation 310 13.3 The Energy Equation 310 13.4 Stream-Tube Area and Flow Velocity Relations 312 14 Potential Flows 317 14.1 Governing Equations 317 14.2 Streamline Coordinates 319 14.3 Conical Flows: Prandtl-Meyer Flow 320 14.4 Small Perturbation Theory 324 14.5 Characteristics 326 (i) Compatibility Conditions in Streamline Coordinates 328 (ii) A Singular-Perturbation Problem for Hyperbolic Systems 331 15 Nonlinear Theory of Plane Sound Waves 343 15.1 Riemann Invariants 343 15.2 Simple Wave Solutions 344 15.3 Nonlinear Propagation of a Sound Wave 352 15.4 Nonlinear Resonant Three-Wave Interactions of Sound Waves 355 15.5 Burgers Equation 361 16 Shock Waves 371 16.1 The Normal Shock Wave 371 16.2 The Oblique Shock Wave 384 16.3 Blast Waves: Taylor’s Self-similarity and Sedov’s Exact Solution 387 17 The Hodograph Method 393 17.1 The Hodograph Transformation of Potential Flow Equations 393 17.2 The Chaplygin Equation 394 17.3 The Tangent-Gas Approximation 396 17.4 The Lost Solution 401 17.5 The Limit Line 402 18 Applications to Aerodynamics 411 18.1 Thin Airfoil Theory 411 (i) Thin Airfoil in Linearized Supersonic Flows 411 (ii) Far-Field Behavior of Supersonic Flow Past a Thin Airfoil 414 (iii) Thin Airfoil in Transonic Flows 417 18.2 Slender Bodies of Revolution 420 18.3 Oscillating Thin Airfoil in Subsonic Flows: Possio’s Theory 427 18.4 Oscillating Thin Airfoils in Supersonic Flows: Stewartson’s Theory 435 Part IV Dynamics of Viscous Fluid Flows 439 19 Exact Solutions to Equations of Viscous Fluid Flows 441 19.1 Channel Flows 442 19.2 Decay of a Line Vortex: The Lamb-Oseen Vortex 443 19.3 Line Vortex in a Uniform Stream 446 19.4 Diffusion of a Localized Vorticity Distribution 446 19.5 Burgers Vortex 451 19.6 Flow Due to a Suddenly Accelerated Plane 453 19.7 The Round Laminar Jet: Landau-Squire Solution 456 19.8 Ekman Layer at a Free Surface in a Rotating Fluid 459 19.9 Centrifugal Flow Due to a Rotating Disk: von Kármán Solution 462 19.10 Shock Structure: Becker’s Solution 464 19.11 Couette Flow of a Gas 467 20 Flows at Low Reynolds Numbers 469 20.1 Dimensional Analysis 469 20.2 Stokes’ Flow Past a Rigid Sphere: Stokes’ Formula 470 20.3 Stokes’ Flow Past a Spherical Drop 474 20.4 Stokes’ Flow Past a Rigid Circular Cylinder: Stokes’ Paradox 478 20.5 Oseen’s Flow Past a Rigid Sphere 479 20.6 Oseen’s Approximation for Periodically Oscillating Wakes 483 21 Flows at High Reynolds Numbers 489 21.1 Prandtl’s Boundary-Layer Concept 489 21.2 The Method of Matched Asymptotic Expansions 490 21.3 Location and Nature of the Boundary Layers 497 21.4 Incompressible Flow Past a Flat Plate 500 (i) The Outer Expansion 501 (ii) The Inner Expansion 502 (iii) Flow Due to Displacement Thickness 507 21.5 Separation of Flow in a Boundary Layer: Landau’s Theory 509 21.6 Boundary Layers in Compressible Flows 512 (i) Crocco’s Integral 514 (ii) Flow Past a Flat Plate: Howarth-Dorodnitsyn Transformation 516 21.7 Flow in a Mixing Layer between Two Parallel Streams 517 (i) Geometrical Characteristics of the Mixing Flow 520 21.8 Narrow Jet: Bickley’s Solution 521 21.9 Wakes 524 21.10 Periodic Boundary Layer Flows 524 22 Jeffrey-Hamel Flow 529 22.1 The Exact Solution 529 (i) Only 𝑒1 Is Real and Positive 531 (ii) 𝑒1, 𝑒2, and 𝑒3 Are Real and Distinct 532 22.2 Flows at Low Reynolds Numbers 535 22.3 Flows at High Reynolds Numbers 541 References 545 Bibliography 549 Index 551

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Book SynopsisProvides an overview of the developments and advances in the field of network clustering and blockmodeling over the last 10 years This book offers an integrated treatment of network clustering and blockmodeling, covering all of the newest approaches and methods that have been developed over the last decade. Presented in a comprehensive manner, it offers the foundations for understanding network structures and processes, and features a wide variety of new techniques addressing issues that occur during the partitioning of networks across multiple disciplines such as community detection, blockmodeling of valued networks, role assignment, and stochastic blockmodeling. Written by a team of international experts in the field, Advances in Network Clustering and Blockmodeling offers a plethora of diverse perspectives covering topics such as: bibliometric analyses of the network clustering literature; clustering approaches to networks; label propagation for clustering; and treating missing nTable of ContentsList of Contributors xv 1 Introduction 1Patrick Doreian, Vladimir Batagelj, and Anuška Ferligoj 1.1 On the Chapters 1 1.2 Looking Forward 9 2 Bibliometric Analyses of the Network Clustering Literature 11Vladimir Batagelj, Anuška Ferligoj, and Patrick Doreian 2.1 Introduction 11 2.2 Data Collection and Cleaning 12 2.2.1 Most Cited/Citing Works 15 2.2.2 The Boundary Problem for Citation Networks 17 2.3 Analyses of the Citation Networks 19 2.3.1 Components 20 2.3.2 The CPM Path of the Main Citation Network 20 2.3.3 Key-Route Paths 20 2.3.4 Positioning Sets of Selected Works in a Citation Network 30 2.4 Link Islands in the Clustering Network Literature 35 2.4.1 Island 10: Community Detection and Blockmodeling 35 2.4.2 Island 7: Engineering Geology 36 2.4.3 Island 9: Geophysics 38 2.4.4 Island 2: Electromagnetic Fields and their Impact on Humans 38 2.4.5 Limitations and Extensions 40 2.5 Authors 41 2.5.1 Productivity Inside Research Groups 42 2.5.2 Collaboration 43 2.5.3 Citations Among Authors Contributing to the Network Partitioning Literature 45 2.5.4 Citations Among Journals 47 2.5.5 Bibliographic Coupling 50 2.5.6 Linking Through a Jaccard Network 58 2.6 Summary and Future Work 62 Acknowledgements 63 References 63 3 Clustering Approaches to Networks 65Vladimir Batagelj 3.1 Introduction 65 3.2 Clustering 66 3.2.1 The Clustering Problem 66 3.2.2 Criterion Functions 67 3.2.3 Cluster-Error Function/Examples 72 3.2.4 The Complexity of the Clustering Problem 75 3.3 Approaches to Clustering 76 3.3.1 Local Optimization 76 3.3.2 Dynamic Programming 79 3.3.3 Hierarchical Methods 79 3.3.4 Adding Hierarchical Methods 83 3.3.5 The Leaders Method 84 3.4 Clustering Graphs and Networks 87 3.5 Clustering in Graphs and Networks 89 3.5.1 An Indirect Approach 89 3.5.2 A Direct Approach: Blockmodeling 90 3.5.3 Graph Theoretic Approaches 90 3.6 Agglomerative Method for Relational Constraints 90 3.6.1 Software Support 95 3.7 Some Examples 95 3.7.1 The US Geographical Data, 2016 95 3.7.2 Citations Among Authors from the Network Clustering Literature 98 3.8 Conclusion 102 Acknowledgements 102 References 102 4 Different Approaches to Community Detection 105Martin Rosvall, Jean-Charles Delvenne, Michael T. Schaub, and Renaud Lambiotte 4.1 Introduction 105 4.2 Minimizing Constraint Violations: the Cut-based Perspective 107 4.3 Maximizing Internal Density: the Clustering Perspective 108 4.4 Identifying Structural Equivalence: the Stochastic Block Model Perspective 110 4.5 Identifying Coarse-grained Descriptions: the Dynamical Perspective 111 4.6 Discussion 114 4.7 Conclusions 116 Acknowledgements 116 References 116 5 Label Propagation for Clustering 121Lovro Šubelj 5.1 Label Propagation Method 121 5.1.1 Resolution of Label Ties 123 5.1.2 Order of Label Propagation 123 5.1.3 Label Equilibrium Criterium 124 5.1.4 Algorithm and Complexity 125 5.2 Label Propagation as Optimization 127 5.3 Advances of Label Propagation 128 5.3.1 Label Propagation Under Constraints 129 5.3.2 Label Propagation with Preferences 130 5.3.3 Method Stability and Complexity 133 5.4 Extensions to Other Networks 137 5.5 Alternative Types of Network Structures 139 5.5.1 Overlapping Groups of Nodes 139 5.5.2 Hierarchy of Groups of Nodes 140 5.5.3 Structural Equivalence Groups 142 5.6 Applications of Label Propagation 146 5.7 Summary and Outlook 146 References 147 6 Blockmodeling of Valued Networks 151Carl Nordlund and Aleš Žiberna 6.1 Introduction 151 6.2 Valued Data Types 153 6.3 Transformations 154 6.3.1 Scaling Transformations 155 6.3.2 Dichotomization 157 6.3.3 Normalization Procedures 157 6.3.4 Iterative Row-column Normalization 158 6.3.5 Transaction-flow and Deviational Transformations 159 6.4 Indirect Clustering Approaches 160 6.4.1 Structural Equivalence: Indirect Metrics 160 6.4.2 The CONCOR Algorithm 161 6.4.3 Deviational Structural Equivalence: Indirect Approach 162 6.4.4 Regular Equivalence: The REGE Algorithms 162 6.4.5 Indirect Approaches: Finding Clusters, Interpreting Blocks 163 6.5 Direct Approaches 164 6.5.1 Generalized Blockmodeling 164 6.5.2 Generalized Blockmodeling of Valued Networks 165 6.5.3 Deviational Generalized Blockmodeling 166 6.6 On the Selection of Suitable Approaches 167 6.7 Examples 168 6.7.1 EIES Friendship Data at Time 2 168 6.7.2 Commodity Trade Within EU/EFTA 2010 173 6.8 Conclusion 183 Acknowledgements 185 References 185 7 Treating Missing Network Data Before Partitioning 189Anja Žnidaršič, Patrick Doreian, and Anuška Ferligoj 7.1 Introduction 189 7.2 Types of Missing Network Data 190 7.2.1 Measurement Errors in Recorded (Or Reported) Ties 190 7.2.2 Item Non-Response 192 7.2.3 Actor Non-Response 192 7.3 Treatments of Missing Data (Due to Actor Non-Response) 193 7.3.1 Reconstruction 194 7.3.2 Imputations of the Mean Values of Incoming Ties 196 7.3.3 Imputations of the Modal Values of Incoming Ties 196 7.3.4 Reconstruction and Imputations Based on Modal Values of Incoming Ties 197 7.3.5 Imputations of the Total Mean 197 7.3.6 Imputations of Median of the Three Nearest Neighbors based on Incoming Ties 197 7.3.7 Null Tie Imputations 198 7.3.8 Blockmodel Results for the Whole and Treated Networks 198 7.4 A Study Design Examining the Impact of Non-Response Treatments on Clustering Results 200 7.4.1 Some Features of Indirect and Direct Blockmodeling 200 7.4.2 Design of the Simulation Study 201 7.4.3 The Real Networks Used in the Simulation Studies 201 7.5 Results 202 7.5.1 Indirect Blockmodeling of Real Valued Networks 202 7.5.2 Indirect Blockmodeling on Real Binary Networks 210 7.5.3 Direct Blockmodeling of Binary Real Networks 216 7.6 Conclusions 222 Acknowledgements 223 References 223 8 Partitioning Signed Networks 225Vincent Traag, Patrick Doreian, and Andrej Mrvar 8.1 Notation 225 8.2 Structural Balance Theory 226 8.2.1 Weak Structural Balance 230 8.3 Partitioning 232 8.3.1 Strong Structural Balance 233 8.3.2 Weak Structural Balance 237 8.3.3 Blockmodeling 238 8.3.4 Community Detection 239 8.4 Empirical Analysis 242 8.5 Summary and Future Work 247 References 248 9 Partitioning Multimode Networks 251Martin G Everett and Stephen P Borgatti 9.1 Introduction 251 9.2 Two-Mode Partitioning 252 9.3 Community Detection 253 9.4 Dual Projection 254 9.5 Signed Two-Mode Networks 257 9.6 Spectral Methods 258 9.7 Clustering 261 9.8 More Complex Data 262 9.9 Conclusion 263 References 263 10 Blockmodeling Linked Networks 267Aleš Žiberna 10.1 Introduction 267 10.2 Blockmodeling Linked Networks 268 10.2.1 Separate Analysis 269 10.2.2 A True Linked Blockmodeling Approach 269 10.2.3 Weighting of Different Parts of a Linked Network 270 10.3 Examples 270 10.3.1 Co-authorship Network at Two Time-points 270 10.3.2 A Multilevel Network of Participants at a Trade Fair for TV Programs 277 10.4 Conclusion 284 Acknowledgements 285 References 285 11 Bayesian Stochastic Blockmodeling 289Tiago P. Peixoto 11.1 Introduction 289 11.2 Structure Versus Randomness in Networks 290 11.3 The Stochastic Blockmodel 292 11.4 Bayesian Inference: The Posterior Probability of Partitions 294 11.5 Microcanonical Models and the Minimum Description Length Principle 298 11.6 The “Resolution Limit” Underfitting Problem and the Nested SBM 300 11.7 Model Variations 305 11.7.1 Model Selection 306 11.7.2 Degree Correction 306 11.7.3 Group Overlaps 310 11.7.4 Further Model Extensions 313 11.8 Efficient Inference Using Markov Chain Monte Carlo 314 11.9 To Sample or To Optimize? 317 11.10 Generalization and Prediction 321 11.11 Fundamental Limits of Inference: The Detectability–Indetectability Phase Transition 323 11.12 Conclusion 327 References 328 12 Structured Networks and Coarse-Grained Descriptions: A Dynamical Perspective 333Michael T. Schaub, Jean-Charles Delvenne, Renaud Lambiotte, and Mauricio Barahona 12.1 Introduction 333 12.2 Part I: Dynamics on and of Networks 337 12.2.1 General Setup 337 12.2.2 Consensus Dynamics 338 12.2.3 Diffusion Processes and Random Walks 340 12.3 Part II: The Influence of Graph Structure on Network Dynamics 342 12.3.1 Time Scale Separation in Partitioned Networks 342 12.3.2 Strictly Invariant Subspaces of the Network Dynamics and External Equitable Partitions 345 12.3.3 Structural Balance: Consensus on Signed Networks and Polarized Opinion Dynamics 348 12.4 Part III: Using Dynamical Processes to Reveal Network Structure 351 12.4.1 A Generic Algorithmic Framework for Dynamics-Based Network Partitioning and Coarse Graining 352 12.4.2 Extending the Framework by using other Measures 354 12.5 Discussion 357 Acknowledgements 358 References 358 13 Scientific Co-Authorship Networks 363Marjan Cugmas, Anuška Ferligoj, and Luka Kronegger 13.1 Introduction 363 13.2 Methods 364 13.2.1 Blockmodeling 365 13.2.2 Measuring the Obtained Blockmodels’ Stability 365 13.3 The Data 369 13.4 The Structure of Obtained Blockmodels 370 13.5 Stability of the Obtained Blockmodel Structures 378 13.5.1 Clustering of Scientific Disciplines According to Different Operationalizations of Core Stability 378 13.5.2 Explaining the Stability of Cores 382 13.6 Conclusions 384 Acknowledgements 386 References 386 14 Conclusions and Directions for Future Work 389Patrick Doreian, Anuška Ferligoj, and Vladimir Batagelj 14.1 Issues Raised within Chapters 390 14.2 Linking Ideas Found in Different Chapters 395 14.3 A Brief Summary and Conclusion 397 References 397 Topic Index 399 Person Index 407

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Book SynopsisExperimental Design and Statistical Analysis for Pharmacology and the Biomedical Sciences A practical guide to the use of basic principles of experimental design and statistical analysis in pharmacology Experimental Design and Statistical Analysis for Pharmacology and the Biomedical Sciences provides clear instructions on applying statistical analysis techniques to pharmacological data. Written by an experimental pharmacologist with decades of experience teaching statistics and designing preclinical experiments, this reader-friendly volume explains the variety of statistical tests that researchers require to analyze data and draw correct conclusions. Detailed, yet accessible, chapters explain how to determine the appropriate statistical tool for a particular type of data, run the statistical test, and analyze and interpret the results. By first introducing basic principles of experimental design and statistical analysis, the author then guides readers through descriptive and inferentiaTable of Contents Foreward 4 1 Introduction 6 2 So, what are data? 8 3 Numbers; counting and measuring, precision and accuracy 9 4 Data collection: Sampling and populations, different types of data, data distributions 12 5 Descriptive statistics: measures to describe and summarize data sets. 16 6 Testing for Normality and transforming skewed data sets 22 7 The Standard Normal Distribution 28 8 Non-Parametric Descriptive statistics 30 9 Summary of descriptive statistics; so, what values may I use to describe my data? 34 Decision Flowchart 1: Descriptive Statistics – Parametric v Non-parametric data 43 10 Introduction to Inferential statistics 44 11 Comparing 2 sets of data – Independent t-test 50 12 Comparing 2 sets of data – Paired t-test 55 13 Comparing 2 sets of data – Independent non-parametric data 58 14 Comparing 2 sets of data – Paired non-parametric data 62 15 Parametric 1-way Analysis of Variance 66 16 Repeated Measures Analysis of Variance 78 17 Complex Analysis of Variance models 86 18 Non-parametric ANOVA 102 Decision Flowchart 2: Inferential Statistics – Single and multiple pairwise comparisons 115 19 Correlation Analysis 116 20 Regression Analysis 126 21 Chi-Square Analysis 136 Decision Flowchart 3: Inferential Statistics –Tests of Association 145 22 Confidence Intervals 146 23 Permutation Test of Exact Inference 150 24 General Linear Model 152 Appendices Introduction to Appendices 155 A Data distribution: probability mass function and probability density functions A.1 Binomial Distribution 156 A.2 Exponential Distribution 157 A.3 Normal Distribution 158 A.4 Chi-square Distribution 159 A.5 Student t-Distribution 160 A.6 F Distribution 161 B Standard Normal Probabilities B.1 AUC values for z values below the mean (i.e. -z) 162 B.2 AUC values for z values above the mean (i.e. +z) 163 C Critical values of the t-distribution 164 D Critical values of the Mann-Whitney U statistic D.1 Critical values for U; One-tailed test, p = 0.05 165 D.2 Critical values for U; One-tailed test, p = 0.01 166 D.3 Critical values for U; Two-tailed test, p = 0.05 167 D.4 Critical values for U; Two-tailed test, p = 0.01 168 E Critical values of the F distribution E.1 Critical values of F, p = 0.05 169 E.2 Critical values of F, p = 0.01 170 E.3 Critical values of F, p = 0.001 171 F Critical values of the Chi-square distribution 172 G Critical z values for multiple non-parametric pairwise comparisons G.1 Critical values of z according to the number of comparisons 173 G.2 Alternative critical values of z according to the number of comparisons when all groups have an equal number of subjects 173 H Critical values of correlation coefficients H.1 Pearson Product Moment Correlation 174 H.2 Spearman Rank Correlation 174 H.3 Kendall’s Rank Correlation (Kendall’s tau) 175 Overall Decision Flowchart: Descriptive and Inferential Statistics 176 Index

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Book SynopsisBrings mathematics to bear on your real-world, scientific problems Mathematical Methods in Interdisciplinary Sciencesprovides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics. The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include: Structural static and vibration problemsHeat conduction and diffusion problemsFluid dynamics problems The book also covers topics as diverse as soft Table of ContentsNotes on Contributors xv Preface xxv Acknowledgments xxvii 1 Connectionist Learning Models for Application Problems Involving Differential and Integral Equations 1Susmita Mall, Sumit Kumar Jeswal, and Snehashish Chakraverty 1.1 Introduction 1 1.1.1 Artificial Neural Network 1 1.1.2 Types of Neural Networks 1 1.1.3 Learning in Neural Network 2 1.1.4 Activation Function 2 1.1.4.1 Sigmoidal Function 3 1.1.5 Advantages of Neural Network 3 1.1.6 Functional Link Artificial Neural Network (FLANN) 3 1.1.7 Differential Equations (DEs) 4 1.1.8 Integral Equation 5 1.1.8.1 Fredholm Integral Equation of First Kind 5 1.1.8.2 Fredholm Integral Equation of Second Kind 5 1.1.8.3 Volterra Integral Equation of First Kind 5 1.1.8.4 Volterra Integral Equation of Second Kind 5 1.1.8.5 Linear Fredholm Integral Equation System of Second Kind 6 1.2 Methodology for Differential Equations 6 1.2.1 FLANN-Based General Formulation of Differential Equations 6 1.2.1.1 Second-Order Initial Value Problem 6 1.2.1.2 Second-Order Boundary Value Problem 7 1.2.2 Proposed Laguerre Neural Network (LgNN) for Differential Equations 7 1.2.2.1 Architecture of Single-Layer LgNN Model 7 1.2.2.2 Training Algorithm of Laguerre Neural Network (LgNN) 8 1.2.2.3 Gradient Computation of LgNN 9 1.3 Methodology for Solving a System of Fredholm Integral Equations of Second Kind 9 1.3.1 Algorithm 10 1.4 Numerical Examples and Discussion 11 1.4.1 Differential Equations and Applications 11 1.4.2 Integral Equations 16 1.5 Conclusion 20 References 20 2 Deep Learning in Population Genetics: Prediction and Explanation of Selection of a Population 23Romila Ghosh and Satyakama Paul 2.1 Introduction 23 2.2 Literature Review 23 2.3 Dataset Description 25 2.3.1 Selection and Its Importance 25 2.4 Objective 26 2.5 Relevant Theory, Results, and Discussions 27 2.5.1 automl 27 2.5.2 Hypertuning the Best Model 28 2.6 Conclusion 30 References 30 3 A Survey of Classification Techniques in Speech Emotion Recognition 33Tanmoy Roy, Tshilidzi Marwala, and Snehashish Chakraverty 3.1 Introduction 33 3.2 Emotional Speech Databases 33 3.3 SER Features 34 3.4 Classification Techniques 35 3.4.1 Hidden Markov Model 36 3.4.1.1 Difficulties in Using HMM for SER 37 3.4.2 Gaussian Mixture Model 37 3.4.2.1 Difficulties in Using GMM for SER 38 3.4.3 Support Vector Machine 38 3.4.3.1 Difficulties with SVM 39 3.4.4 Deep Learning 39 3.4.4.1 Drawbacks of Using Deep Learning for SER 41 3.5 Difficulties in SER Studies 41 3.6 Conclusion 41 References 42 4 Mathematical Methods in Deep Learning 49Srinivasa Manikant Upadhyayula and Kannan Venkataramanan 4.1 Deep Learning Using Neural Networks 49 4.2 Introduction to Neural Networks 49 4.2.1 Artificial Neural Network (ANN) 50 4.2.1.1 Activation Function 52 4.2.1.2 Logistic Sigmoid Activation Function 52 4.2.1.3 tanh or Hyperbolic Tangent Activation Function 53 4.2.1.4 ReLU (Rectified Linear Unit) Activation Function 54 4.3 Other Activation Functions (Variant Forms of ReLU) 55 4.3.1 Smooth ReLU 55 4.3.2 Noisy ReLU 55 4.3.3 Leaky ReLU 55 4.3.4 Parametric ReLU 56 4.3.5 Training and Optimizing a Neural Network Model 56 4.4 Backpropagation Algorithm 56 4.5 Performance and Accuracy 59 4.6 Results and Observation 59 References 61 5 Multimodal Data Representation and Processing Based on Algebraic System of Aggregates 63Yevgeniya Sulema and Etienne Kerre 5.1 Introduction 63 5.2 Basic Statements of ASA 64 5.3 Operations on Aggregates and Multi-images 65 5.4 Relations and Digital Intervals 72 5.5 Data Synchronization 75 5.6 Fuzzy Synchronization 92 5.7 Conclusion 96 References 96 6 Nonprobabilistic Analysis of Thermal and Chemical Diffusion Problems with Uncertain Bounded Parameters 99Sukanta Nayak, Tharasi Dilleswar Rao, and Snehashish Chakraverty 6.1 Introduction 99 6.2 Preliminaries 99 6.2.1 Interval Arithmetic 99 6.2.2 Fuzzy Number and Fuzzy Arithmetic 100 6.2.3 Parametric Representation of Fuzzy Number 101 6.2.4 Finite Difference Schemes for PDEs 102 6.3 Finite Element Formulation for Tapered Fin 102 6.4 Radon Diffusion and Its Mechanism 105 6.5 Radon Diffusion Mechanism with TFN Parameters 107 6.5.1 EFDM to Radon Diffusion Mechanism with TFN Parameters 108 6.6 Conclusion 112 References 112 7 Arbitrary Order Differential Equations with Fuzzy Parameters 115Tofigh Allahviranloo and Soheil Salahshour 7.1 Introduction 115 7.2 Preliminaries 115 7.3 Arbitrary Order Integral and Derivative for Fuzzy-Valued Functions 116 7.4 Generalized Fuzzy Laplace Transform with Respect to Another Function 118 References 122 8 Fluid Dynamics Problems in Uncertain Environment 125Perumandla Karunakar, Uddhaba Biswal, and Snehashish Chakraverty 8.1 Introduction 125 8.2 Preliminaries 126 8.2.1 Fuzzy Set 126 8.2.2 Fuzzy Number 126 8.2.3 𝛿-Cut 127 8.2.4 Parametric Approach 127 8.3 Problem Formulation 127 8.4 Methodology 129 8.4.1 Homotopy Perturbation Method 129 8.4.2 Homotopy Perturbation Transform Method 130 8.5 Application of HPM and HPTM 131 8.5.1 Application of HPM to Jeffery–Hamel Problem 131 8.5.2 Application of HPTM to Coupled Whitham–Broer–Kaup Equations 134 8.6 Results and Discussion 136 8.7 Conclusion 142 References 142 9 Fuzzy Rough Set Theory-Based Feature Selection: A Review 145Tanmoy Som, Shivam Shreevastava, Anoop Kumar Tiwari, and Shivani Singh 9.1 Introduction 145 9.2 Preliminaries 146 9.2.1 Rough Set Theory 146 9.2.1.1 Rough Set 146 9.2.1.2 Rough Set-Based Feature Selection 147 9.2.2 Fuzzy Set Theory 147 9.2.2.1 Fuzzy Tolerance Relation 148 9.2.2.2 Fuzzy Rough Set Theory 149 9.2.2.3 Degree of Dependency-Based Fuzzy Rough Attribute Reduction 149 9.2.2.4 Discernibility Matrix-Based Fuzzy Rough Attribute Reduction 149 9.3 Fuzzy Rough Set-Based Attribute Reduction 149 9.3.1 Degree of Dependency-Based Approaches 150 9.3.2 Discernibility Matrix-Based Approaches 154 9.4 Approaches for Semisupervised and Unsupervised Decision Systems 154 9.5 Decision Systems with Missing Values 158 9.6 Applications in Classification, Rule Extraction, and Other Application Areas 158 9.7 Limitations of Fuzzy Rough Set Theory 159 9.8 Conclusion 160 References 160 10 Universal Intervals: Towards a Dependency-Aware Interval Algebra 167Hend Dawood and Yasser Dawood 10.1 Introduction 167 10.2 The Need for Interval Computations 169 10.3 On Some Algebraic and Logical Fundamentals 170 10.4 Classical Intervals and the Dependency Problem 174 10.5 Interval Dependency: A Logical Treatment 176 10.5.1 Quantification Dependence and Skolemization 177 10.5.2 A Formalization of the Notion of Interval Dependency 179 10.6 Interval Enclosures Under Functional Dependence 184 10.7 Parametric Intervals: How Far They Can Go 186 10.7.1 Parametric Interval Operations: From Endpoints to Convex Subsets 186 10.7.2 On the Structure of Parametric Intervals: Are They Properly Founded? 188 10.8 Universal Intervals: An Interval Algebra with a Dependency Predicate 192 10.8.1 Universal Intervals, Rational Functions, and Predicates 193 10.8.2 The Arithmetic of Universal Intervals 196 10.9 The S-Field Algebra of Universal Intervals 201 10.10 Guaranteed Bounds or Best Approximation or Both? 209 Supplementary Materials 210 Acknowledgments 211 References 211 11 Affine-Contractor Approach to Handle Nonlinear Dynamical Problems in Uncertain Environment 215Nisha Rani Mahato, Saudamini Rout, and Snehashish Chakraverty 11.1 Introduction 215 11.2 Classical Interval Arithmetic 217 11.2.1 Intervals 217 11.2.2 Set Operations of Interval System 217 11.2.3 Standard Interval Computations 218 11.2.4 Algebraic Properties of Interval 219 11.3 Interval Dependency Problem 219 11.4 Affine Arithmetic 220 11.4.1 Conversion Between Interval and Affine Arithmetic 220 11.4.2 Affine Operations 221 11.5 Contractor 223 11.5.1 SIVIA 223 11.6 Proposed Methodology 225 11.7 Numerical Examples 230 11.7.1 Nonlinear Oscillators 230 11.7.1.1 Unforced Nonlinear Differential Equation 230 11.7.1.2 Forced Nonlinear Differential Equation 232 11.7.2 Other Dynamic Problem 233 11.7.2.1 Nonhomogeneous Lane–Emden Equation 233 11.8 Conclusion 236 References 236 12 Dynamic Behavior of Nanobeam Using Strain Gradient Model 239Subrat Kumar Jena, Rajarama Mohan Jena, and Snehashish Chakraverty 12.1 Introduction 239 12.2 Mathematical Formulation of the Proposed Model 240 12.3 Review of the Differential Transform Method (DTM) 241 12.4 Application of DTM on Dynamic Behavior Analysis 242 12.5 Numerical Results and Discussion 244 12.5.1 Validation and Convergence 244 12.5.2 Effect of the Small-Scale Parameter 245 12.5.3 Effect of Length-Scale Parameter 247 12.6 Conclusion 248 Acknowledgment 249 References 250 13 Structural Static and Vibration Problems 253M. Amin Changizi and Ion Stiharu 13.1 Introduction 253 13.2 One-parameter Groups 254 13.3 Infinitesimal Transformation 254 13.4 Canonical Coordinates 254 13.5 Algorithm for Lie Symmetry Point 255 13.6 Reduction of the Order of the ODE 255 13.7 Solution of First-Order ODE with Lie Symmetry 255 13.8 Identification 256 13.9 Vibration of a Microcantilever Beam Subjected to Uniform Electrostatic Field 258 13.10 Contact Form for the Equation 259 13.11 Reducing in the Order of the Nonlinear ODE Representing the Vibration of a Microcantilever Beam Under Electrostatic Field 260 13.12 Nonlinear Pull-in Voltage 261 13.13 Nonlinear Analysis of Pull-in Voltage of Twin Microcantilever Beams 266 13.14 Nonlinear Analysis of Pull-in Voltage of Twin Microcantilever Beams of Different Thicknesses 268 References 272 14 Generalized Differential and Integral Quadrature: Theory and Applications 273Francesco Tornabene and Rossana Dimitri 14.1 Introduction 273 14.2 Differential Quadrature 274 14.2.1 Genesis of the Differential Quadrature Method 274 14.2.2 Differential Quadrature Law 275 14.3 General View on Differential Quadrature 277 14.3.1 Basis Functions 278 14.3.1.1 Lagrange Polynomials 281 14.3.1.2 Trigonometric Lagrange Polynomials 282 14.3.1.3 Classic Orthogonal Polynomials 282 14.3.1.4 Monomial Functions 291 14.3.1.5 Exponential Functions 291 14.3.1.6 Bernstein Polynomials 291 14.3.1.7 Fourier Functions 292 14.3.1.8 Bessel Polynomials 292 14.3.1.9 Boubaker Polynomials 292 14.3.2 Grid Distributions 293 14.3.2.1 Coordinate Transformation 293 14.3.2.2 𝛿-Point Distribution 293 14.3.2.3 Stretching Formulation 293 14.3.2.4 Several Types of Discretization 293 14.3.3 Numerical Applications: Differential Quadrature 297 14.4 Generalized Integral Quadrature 310 14.4.1 Generalized Taylor-Based Integral Quadrature 312 14.4.2 Classic Integral Quadrature Methods 314 14.4.2.1 Trapezoidal Rule with Uniform Discretization 314 14.4.2.2 Simpson’s Method (One-third Rule) with Uniform Discretization 314 14.4.2.3 Chebyshev–Gauss Method (Chebyshev of the First Kind) 314 14.4.2.4 Chebyshev–Gauss Method (Chebyshev of the Second Kind) 314 14.4.2.5 Chebyshev–Gauss Method (Chebyshev of the Third Kind) 315 14.4.2.6 Chebyshev–Gauss Method (Chebyshev of the Fourth Kind) 315 14.4.2.7 Chebyshev–Gauss–Radau Method (Chebyshev of the First Kind) 315 14.4.2.8 Chebyshev–Gauss–Lobatto Method (Chebyshev of the First Kind) 315 14.4.2.9 Gauss–Legendre or Legendre–Gauss Method 315 14.4.2.10 Gauss–Legendre–Radau or Legendre–Gauss–Radau Method 315 14.4.2.11 Gauss–Legendre–Lobatto or Legendre–Gauss–Lobatto Method 316 14.4.3 Numerical Applications: Integral Quadrature 316 14.4.4 Numerical Applications: Taylor-Based Integral Quadrature 320 14.5 General View: The Two-Dimensional Case 324 References 340 15 Brain Activity Reconstruction by Finding a Source Parameter in an Inverse Problem 343Amir H. Hadian-Rasanan and Jamal Amani Rad 15.1 Introduction 343 15.1.1 Statement of the Problem 344 15.1.2 Brief Review of Other Methods Existing in the Literature 345 15.2 Methodology 346 15.2.1 Weighted Residual Methods and Collocation Algorithm 346 15.2.2 Function Approximation Using Chebyshev Polynomials 349 15.3 Implementation 353 15.4 Numerical Results and Discussion 354 15.4.1 Test Problem 1 355 15.4.2 Test Problem 2 357 15.4.3 Test Problem 3 358 15.4.4 Test Problem 4 359 15.4.5 Test Problem 5 362 15.5 Conclusion 365 References 365 16 Optimal Resource Allocation in Controlling Infectious Diseases 369A.C. Mahasinghe, S.S.N. Perera, and K.K.W.H. Erandi 16.1 Introduction 369 16.2 Mobility-Based Resource Distribution 370 16.2.1 Distribution of National Resources 370 16.2.2 Transmission Dynamics 371 16.2.2.1 Compartment Models 371 16.2.2.2 SI Model 371 16.2.2.3 Exact Solution 371 16.2.2.4 Transmission Rate and Potential 372 16.2.3 Nonlinear Problem Formulation 373 16.2.3.1 Piecewise Linear Reformulation 374 16.2.3.2 Computational Experience 374 16.3 Connection–Strength Minimization 376 16.3.1 Network Model 376 16.3.1.1 Disease Transmission Potential 376 16.3.1.2 An Example 376 16.3.2 Nonlinear Problem Formulation 377 16.3.2.1 Connection Strength Measure 377 16.3.2.2 Piecewise Linear Approximation 378 16.3.2.3 Computational Experience 379 16.4 Risk Minimization 379 16.4.1 Novel Strategies for Individuals 379 16.4.1.1 Epidemiological Isolation 380 16.4.1.2 Identifying Objectives 380 16.4.2 Minimizing the High-Risk Population 381 16.4.2.1 An Example 381 16.4.2.2 Model Formulation 382 16.4.2.3 Linear Integer Program 383 16.4.2.4 Computational Experience 383 16.4.3 Minimizing the Total Risk 384 16.4.4 Goal Programming Approach 384 16.5 Conclusion 386 References 387 17 Artificial Intelligence and Autonomous Car 391Merve Arıtürk, Sırma Yavuz, and Tofigh Allahviranloo 17.1 Introduction 391 17.2 What is Artificial Intelligence? 391 17.3 Natural Language Processing 391 17.4 Robotics 393 17.4.1 Classification by Axes 393 17.4.1.1 Axis Concept in Robot Manipulators 393 17.4.2 Classification of Robots by Coordinate Systems 394 17.4.3 Other Robotic Classifications 394 17.5 Image Processing 395 17.5.1 Artificial Intelligence in Image Processing 395 17.5.2 Image Processing Techniques 395 17.5.2.1 Image Preprocessing and Enhancement 396 17.5.2.2 Image Segmentation 396 17.5.2.3 Feature Extraction 396 17.5.2.4 Image Classification 396 17.5.3 Artificial Intelligence Support in Digital Image Processing 397 17.5.3.1 Creating a Cancer Treatment Plan 397 17.5.3.2 Skin Cancer Diagnosis 397 17.6 Problem Solving 397 17.6.1 Problem-solving Process 397 17.7 Optimization 399 17.7.1 Optimization Techniques in Artificial Intelligence 399 17.8 Autonomous Systems 400 17.8.1 History of Autonomous System 400 17.8.2 What is an Autonomous Car? 401 17.8.3 Literature of Autonomous Car 402 17.8.4 How Does an Autonomous Car Work? 405 17.8.5 Concept of Self-driving Car 406 17.8.5.1 Image Classification 407 17.8.5.2 Object Tracking 407 17.8.5.3 Lane Detection 408 17.8.5.4 Introduction to Deep Learning 408 17.8.6 Evaluation 409 17.9 Conclusion 410 References 410 18 Different Techniques to Solve Monotone Inclusion Problems 413Tanmoy Som, Pankaj Gautam, Avinash Dixit, and D. R. Sahu 18.1 Introduction 413 18.2 Preliminaries 414 18.3 Proximal Point Algorithm 415 18.4 Splitting Algorithms 415 18.4.1 Douglas–Rachford Splitting Algorithm 416 18.4.2 Forward–Backward Algorithm 416 18.5 Inertial Methods 418 18.5.1 Inertial Proximal Point Algorithm 419 18.5.2 Splitting Inertial Proximal Point Algorithm 421 18.5.3 Inertial Douglas–Rachford Splitting Algorithm 421 18.5.4 Pock and Lorenz’s Variable Metric Forward–Backward Algorithm 422 18.5.5 Numerical Example 428 18.6 Numerical Experiments 429 References 430 Index 433

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Book SynopsisCalculus Essentials For Dummies(9781119591207) was previously published asCalculus Essentials For Dummies (9780470618356). While this version features a newDummiescover and design, the content is the same as the prior release and should not be considered a new or updated product. Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option.Calculus Essentials For Dummiesprovides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material,Calculus Essentials For Dummiessticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also Table of ContentsIntroduction 1 About This Book 1 Conventions Used in This Book 2 Foolish Assumptions 2 Icons Used in This Book 3 Where to Go from Here 3 Chapter 1: Calculus: No Big Deal 5 So What is Calculus Already? 5 Real-World Examples of Calculus 7 Differentiation 8 Integration 9 Why Calculus Works 11 Limits: Math microscopes 11 What happens when you zoom in 12 Chapter 2: Limits and Continuity 15 Taking it to the Limit 15 Three functions with one limit 15 One-sided limits 17 Limits and vertical asymptotes 18 Limits and horizontal asymptotes 18 Instantaneous speed 19 Limits and Continuity 21 The hole exception 22 Chapter 3: Evaluating Limits 25 Easy Limits 25 Limits to memorize 25 Plug-and-chug limits 26 “Real” Limit Problems 26 Factoring 27 Conjugate multiplication 27 Miscellaneous algebra 28 Limits at Infinity 29 Horizontal asymptotes 30 Solving limits at infinity 31 Chapter 4: Differentiation Orientation 33 The Derivative: It’s Just Slope 34 The slope of a line 35 The derivative of a line 36 The Derivative: It’s Just a Rate 36 Calculus on the playground 36 The rate-slope connection 38 The Derivative of a Curve 39 The Difference Quotient 40 Average and Instantaneous Rate 46 Three Cases Where the Derivative Does Not Exist 47 Chapter 5: Differentiation Rules 49 Basic Differentiation Rules 49 The constant rule 49 The power rule 49 The constant multiple rule 50 The sum and difference rules 51 Differentiating trig functions 52 Exponential and logarithmic functions 52 Derivative Rules for Experts 53 The product and quotient rules 53 The chain rule 54 Differentiating Implicitly 59 Chapter 6: Differentiation and the Shape of Curves 61 A Calculus Road Trip 61 Local Extrema 63 Finding the critical numbers 63 The First Derivative Test 65 The Second Derivative Test 66 Finding Absolute Extrema on a Closed Interval 69 Finding Absolute Extrema over a Function’s Entire Domain 71 Concavity and Inflection Points 73 Graphs of Derivatives 75 The Mean Value Theorem 78 Chapter 7: Differentiation Problems 81 Optimization Problems 81 The maximum area of a corral 81 Position, Velocity, and Acceleration 83 Velocity versus speed 84 Maximum and minimum height 86 Velocity and displacement 87 Speed and distance travelled 88 Acceleration 89 Tying it all together 90 Related Rates 91 A calculus crossroads 91 Filling up a trough 94 Linear Approximation 97 Chapter 8: Introduction to Integration 101 Integration: Just Fancy Addition 101 Finding the Area under a Curve 103 Dealing with negative area 105 Approximating Area 105 Approximating area with left sums 105 Approximating area with right sums 108 Approximating area with midpoint sums 110 Summation Notation 112 Summing up the basics 112 Writing Riemann sums with sigma notation 113 Finding Exact Area with the Definite Integral 116 Chapter 9: Integration: Backwards Differentiation 119 Antidifferentiation: Reverse Differentiation 119 The Annoying Area Function 121 The Fundamental Theorem 124 Fundamental Theorem: Take Two 126 Antiderivatives: Basic Techniques 128 Reverse rules 128 Guess and check 130 Substitution 132 Chapter 10: Integration for Experts 137 Integration by Parts 137 Picking your u 139 Tricky Trig Integrals 141 Sines and cosines 141 Secants and tangents 144 Cosecants and cotangents 147 Trigonometric Substitution 147 Case 1: Tangents 148 Case 2: Sines 150 Case 3: Secants 151 Partial Fractions 152 Case 1: The denominator contains only linear factors 152 Case 2: The denominator contains unfactorable quadratic factors 153 Case 3: The denominator contains repeated factors 155 Equating coefficients 155 Chapter 11: Using the Integral to Solve Problems 157 The Mean Value Theorem for Integrals and Average Value 158 The Area between Two Curves 160 Volumes of Weird Solids 162 The meat-slicer method 162 The disk method 163 The washer method 165 The matryoshka doll method 166 Arc Length 168 Improper Integrals 171 Improper integrals with vertical asymptotes 171 Improper integrals with infinite limits of integration 173 Chapter 12: Eight Things to Remember 175 a2- b2 = (a - b)(a + b) 175 0/5 = 0 But 5/0 is Undefined 175 SohCahToa 175 Trig Values to Know 176 sin2ϴ + cos2ϴ = 1 176 The Product Rule 176 The Quotient Rule 176 Your Sunglasses 176 Index 177

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Book SynopsisTable of ContentsList of Variables with Common Example Units xvii Preface to Second Edition xxvii Preface to First Edition xxix 1 Introduction 1 1.1 Risk Analysis 2 1.2 Risk 4 1.3 Contaminants in the Environment 8 1.4 Uses of Environmental Risk Assessment 9 1.5 Risk Assessment Process 13 1.5.1 Problem Statement 13 1.5.2 System Description 14 1.5.3 Risk Calculation 14 1.5.4 Integration and Iteration 18 References 19 Additional Reading 20 Problems 21 2 Fundamental Aspects of Environmental Modeling 23 2.1 Introduction 23 2.2 Modeling Process 24 2.2.1 Model Development 24 2.2.2 Modeling Assurance 28 2.2.3 Environmental Modeling in Phases 30 2.3 Physical and Mathematical Basis for Risk Assessment Models 31 2.3.1 Mass Balances 31 2.3.2 Simple Models 40 2.4 Contaminant Transport Equation 47 2.4.1 Transport Processes 48 2.4.2 Derivation of the Contaminant Transport Equation 49 2.4.3 Zero-dimensional Solutions of the Contaminant Transport Equation 52 References 58 Additional Reading 59 Problems 59 3 Release Assessment 64 3.1 Introduction 64 3.2 Conceptual Model 65 3.3 Contaminant Identification 66 3.4 Emission-Rate Quantification 72 3.4.1 Release Probability 74 3.4.2 Contaminant Emission Rate 79 References 83 Additional Reading 84 Problems 84 4 Environmental Transport Theory 87 4.1 Introduction 87 4.2 One-Dimensional Solutions of the Contaminant Transport Equation 89 4.2.1 One-dimensional Advection 89 4.2.2 One-dimensional Advection and Dispersion 95 4.3 Three-Dimensional Contaminant Transport 99 4.4 Advanced Solution Methods 100 4.4.1 Numerical Techniques 100 4.4.2 Superposition Integral 101 References 103 Additional Reading 104 Problems 104 5 Surface Water Transport 107 5.1 Introduction 107 5.2 Types of Surface Water Bodies 109 5.2.1 Rivers and Streams 109 5.2.2 Lakes 111 5.2.3 Reservoirs on Rivers 111 5.2.4 Estuaries 111 5.2.5 Oceans 111 5.3 Sorption 112 5.3.1 Distribution Coefficient 112 5.3.2 Fraction Sorbed 116 5.3.3 Inclusion of Sorption in Transport Models 117 5.4 Transport Modeling 119 5.4.1 Lakes 119 5.4.2 Rivers and Streams 123 References 128 Additional Reading 129 Problems 129 6 Groundwater Transport 132 6.1 Introduction 132 6.2 Subsurface Characterization 134 6.3 Saturated Flow in Porous Media 135 6.3.1 Groundwater Speed and Direction 135 6.3.2 Porosity and Hydraulic Conductivity 138 6.3.3 Dispersion 138 6.4 Sorption 143 6.5 Subsurface Contaminant Transport Modeling 144 6.5.1 Linear Equilibrium Model of Subsurface Contaminant Transport 144 6.5.2 Saturated-Zone Transport Solutions 148 6.6 Other Considerations in Groundwater Transport 153 6.6.1 Vadose Zone Transport 153 6.6.2 Colloidal Transport 155 6.6.3 Transformations 155 6.6.4 NonAqueous-Phase Liquids 156 References 158 Additional Reading 159 Problems 159 7 Atmospheric Transport 163 7.1 Introduction 163 7.2 Atmospheric Dispersion 164 7.3 Atmospheric Transport Models 168 7.3.1 Constant Emission Rate: Gaussian Plume Model 168 7.3.2 Long-Term Averages 175 7.3.3 Infinite Line Source 179 7.3.4 Instantaneous Emission: Gaussian Puff Model 179 7.4 Other Considerations 180 7.4.1 Effective Release Height and Plume Rise 180 7.4.2 Building Wake 181 7.4.3 Release with Inversion Aloft 182 7.4.4 Nonconservative Processes 184 References 186 Additional Reading 187 Problems 187 8 Food Chain Transport 191 8.1 Introduction 191 8.2 Concentration in Soil 195 8.2.1 Conceptual Model 195 8.2.2 Atmospheric Deposition 197 8.2.3 Irrigation Deposition 197 8.2.4 Atmospheric Resuspension 198 8.3 Concentration in Vegetation 199 8.4 Concentration in Animals 204 References 206 Additional Reading 207 Problems 207 9 Exposure Assessment 210 9.1 Introduction 210 9.2 Dose 212 9.2.1 Chemical Dose 212 9.2.2 Radiological Dose 214 9.3 Contaminant Intake 215 9.3.1 Inhalation 216 9.3.2 Ingestion 216 9.3.3 Dermal Absorption 218 9.4 Dose Calculations 220 9.4.1 Chemical Dose Calculations 220 9.4.2 Radiological Dose Calculations 222 References 227 Additional Reading 228 Problems 228 10 Basic Human Toxicology 230 10.1 Introduction 230 10.2 Fundamentals of Anatomy and Physiology 231 10.2.1 Cellular Anatomy and Physiology 232 10.2.2 Cellular Mechanisms of Toxicity 237 10.2.3 Major Organ Systems 239 10.3 Mechanisms and Effects of Toxicity 250 10.3.1 Systemic Effects 250 10.3.2 Carcinogenic Effects 252 10.3.3 Teratogenic Effects 256 10.3.4 Hereditary Effects 258 References 259 Problems 261 11 Dose–Response and Risk Characterization 263 11.1 Introduction 263 11.2 Biological Basis of Dose–Response Modeling 264 11.3 Elements of Quantitative Dose–Response Analysis 266 11.3.1 Factors Affecting Toxicity 266 11.3.2 Quantification of Responses 272 11.3.3 Sources of Dose–Response Data 274 11.4 Dose–Response Modeling 279 11.4.1 Animal-to-Human Extrapolation 280 11.4.2 Dose–response models and high- to low-dose extrapolation 283 11.5 Risk Characterization 287 11.5.1 Margin of Exposure 287 11.5.2 Cancer Slope Factors and Unit Risk 289 11.6 Regulatory Implementation 290 11.6.1 The Benchmark Dose (BMD) Approach 291 11.6.2 Deterministic (Noncancer) Endpoints 293 11.6.3 Stochastic (Non-threshold) Endpoints 299 References 305 Additional Reading 308 Problems 308 12 Uncertainty and Sensitivity Analyses 311 12.1 Introduction 311 12.2 Types and Sources of Uncertainty 312 12.2.1 Qualitative and Quantitative Considerations 312 12.2.2 Sources of Uncertainty 313 12.2.3 Types of Uncertainty 314 12.3 Statistics Fundamentals 317 12.3.1 Random Variables and Distribution Functions 317 12.3.2 Characterization of PDFs 319 12.3.3 Determination of Distributions 320 12.4 Uncertainty Propagation 324 12.4.1 Sensitivity Analysis 325 12.4.2 Methods for Uncertainty Propagation 327 References 340 Problems 343 13 Screening and Computational Resources 348 13.1 Introduction 348 13.2 Screening Tools 349 13.2.1 COMPLY/COMPLY-R 349 13.2.2 DandD 350 13.2.3 Groundwater Transport Calculator 350 13.2.4 RSL and RML 350 13.2.5 RAIS PRG Calculators 351 13.2.6 RAIS Risk Calculators 351 13.2.7 SERAFM 351 13.3 Surface Water Transport 352 13.3.1 BASINS 352 13.3.2 EFDC 352 13.3.3 LADTAP II 353 13.3.4 QUAL2K 353 13.3.5 WASP 354 13.3.6 SMS 13 354 13.4 Groundwater Transport 354 13.4.1 3DFEMWATER/3DLEWASTE 354 13.4.2 EPACMTP 355 13.4.3 GMS 355 13.4.4 HELP 355 13.4.5 MODFLOW 6 356 13.4.6 PORFLOW 356 13.4.7 STOMP 357 13.4.8 TOUGHREACT 357 13.5 Atmospheric Transport 357 13.5.1 AERMOD 358 13.5.2 ALOHA 358 13.5.3 CTDMPLUS 359 13.5.4 HOTSPOT 359 13.5.5 HYSPLIT 359 13.5.6 PAVAN 360 13.5.7 RASCAL 360 13.5.8 XOQDOQ 360 13.6 Food Chain Transport 361 13.6.1 BASS 361 13.6.2 CAP-88 PC 361 13.6.3 GASPAR II 362 13.6.4 MILDOS 4 362 13.7 Transport, Exposure, and Consequence Assessment Tools 363 13.7.1 CalTOX 363 13.7.2 FRAMES-2.0 363 13.7.3 GENII 364 13.7.4 GOLDSIM 364 13.7.5 MEPAS 364 13.7.6 RESRAD 365 13.7.7 Risk Analyst 366 13.8 Geochemical Speciation Modeling 367 13.8.1 GWB 367 13.8.2 MINEQL+ 368 13.8.3 MINTEQA2/VISUAL MINTEQ 368 13.8.4 PHREEQC 368 13.9 Uncertainty 369 13.10 Other Useful Computational Resources 370 13.10.1 RESRAD-BUILD 370 13.10.2 SADA 370 13.10.3 VSP 370 13.10.4 BMDS 370 References 370 14 Case Studies 376 14.1 Introduction 376 14.2 PFAS 376 14.2.1 Background 377 14.2.2 Wilbur Earl Tenant’s Farm (EPA 2001, Bilott 2019) 377 14.2.3 Parkersburg and EPA (EPA 2001, Bilott 2019) 378 14.2.4 Epilogue 379 14.3 Arsenic in Drinking Water 380 14.3.1 Introduction 380 14.3.2 Risk Calculation 381 14.3.3 Risk Assessment 381 14.4 MCHM 382 14.4.1 Background 382 14.4.2 Calculation of MCHM Concentration 383 14.4.3 Epilogue 386 14.5 Releases from Rocky Flats 387 14.5.1 Introduction 388 14.5.2 1957 Plutonium Fire Basic Risk Assessment 388 14.5.3 Rocky Flats Comprehensive Risk Assessment 390 14.5.4 Comparisons for 1957 Plutonium Fire 391 14.5.5 Epilogue 393 References 393 Problems 395 15 Ethics, Stakeholder Involvement, and Risk Communication 396 15.1 Introduction 396 15.2 Ethics 397 15.2.1 Overview 397 15.2.2 Ethical Theories 397 15.2.3 Environmental Ethics 398 15.3 Stakeholder Involvement 400 15.3.1 Motivation 400 15.3.2 Potential Benefits and Detriments 401 15.3.3 Scope of Stakeholder Involvement 403 15.3.4 Legal Basis and Requirements 405 15.3.5 Methods and Approaches 405 15.4 Risk Communication 410 15.4.1 Scientific Basis 411 15.4.2 Practical Considerations 416 15.4.3 Unresolved Issues 417 References 418 Problems 422 16 Environmental Risk Management 423 16.1 Introduction 423 16.2 Risk Management Process 423 16.3 Risk Management Methods 424 16.3.1 Approaches to Risk Management 424 16.3.2 Fundamentals of Decision Analysis 426 16.3.3 Methods for Decision Analysis Under Certainty 433 16.3.4 Methods for Decision Analysis Under Risk 438 References 441 Problems 442 17 Environmental Laws and Regulations 444 17.1 Introduction 444 17.2 General Legal and Regulatory Structure for Environmental Protection 444 17.2.1 U.S. Governmental Structure 444 17.2.2 Regulatory Hierarchy 445 17.3 Major Federal Environmental Laws and Regulations 446 17.3.1 National Environmental Policy Act 447 17.3.2 CERCLA and SARA 449 17.3.3 Resource Conservation and Recovery Act 452 17.3.4 Toxic Substances Control Act 453 17.3.5 Clean Air Act 454 17.3.6 Clean Water Act 456 17.4 CERCLA Process 457 17.4.1 Remedial Actions Under CERCLA 457 17.4.2 Risk Assessment in the RI/FS Process 458 17.5 Additional Regulations 459 References 460 Problems 461 Appendix A Mathematical Tools 462 A. 1 Special Functions 462 A.1. 1 Dirac Delta Function 462 A.1. 2 Heaviside Unit Step Function 463 A.1. 3 Error Function and Complementary Error Function 463 A.1. 4 Gamma Function 464 A. 2 Laplace Transforms 465 A.2. 1 Definitions and Notation 465 A.2. 2 Basic Transforms and Properties 466 A.2. 3 Solution of Differential Equations with Laplace Transforms 467 A. 3 Exact Solutions to the One-Dimensional Contaminant Transport Equation 470 References 473 Additional Reading 474 Appendix B Degradation and Decay Parameters 475 Index 477

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Book SynopsisTable of ContentsIntroduction xxi Part I Display Data on a Dashboard 1 Chapter 1 Dashboard Basics 3 Determining When to Use a Dashboard 3 What Is a Dashboard? 5 Key Performance Indicators 6 Establishing User Requirements 6 Types of End Users 7 Assembling the Data 8 PivotTables 8 The GETPIVOTDATA Worksheet Function 13 Worksheet Functions 14 The VLOOKUP Function 14 The XLOOKUP Function 15 The INDEX and MATCH Functions 16 The SUMPRODUCT Function 17 Array Formulas 19 Tables 20 Structured Table Referencing 23 Text to Columns 24 Removing Duplicates 26 Building the Dashboard 28 Organizing Elements 28 Varying Elements 30 Showing Trends 31 Formatting the Dashboard 33 Number Formats 36 Chapter 2 Dashboard Case Studies 39 Monitoring Progress 39 Case Study: Monitoring a Software Project 40 Planning and Layout 40 Collecting the Data 42 Building the Visual Elements 43 Laying Out the Dashboard 54 Displaying Key Performance Indicators 55 Case Study: Human Resources KPIs 55 Planning and Layout 56 Collecting the Data 57 Building the Visual Elements 58 Laying Out the Dashboard 69 Reporting Financial Information 72 Case Study: Financial Information and Ratios 72 Planning and Layout 72 Collecting the Data 73 Building the Visual Elements 75 Laying Out the Dashboard 83 Chapter 3 Organizing Data for Dashboards 87 Separating Data Layers 87 Source Data Layer 89 Staging and Analysis Layer 90 Presentation Layer 91 Working with External Data 92 Power Query vs. Power Pivot 92 Text Files 92 Excel Files 98 Access Databases 105 SQL Server Databases 111 Transforming Data in Power Query 114 Managing Columns and Rows 116 Transforming Columns 119 Transforming Data Types 119 Transforming Numbers 121 Splitting Columns 123 Part II Visualization Primer 127 Chapter 4 The Fundamentals of Eff ective Visualization 129 Creating an Effective Visualization 129 Keep It to a Single Screen 130 Make It Attractive 131 Tell the Story Quickly 131 Make the Story Consistent with the Data 133 Choose the Proper Chart 135 Driving Meaning with Color 137 How to Use Color 137 Varying Color as Data Values Vary 137 Using Sharp Contrast to Highlight Data 138 Grouping Data with Color 139 Tips on Color Use 140 Use White Space 140 Use a Simple Color Pallet 141 Use Colors That Are Consistent with the Data 141 Use Enough Contrast 141 Use Non-data Pixels When Necessary 142 Focusing Attention on Text 142 Fonts 142 Legends 143 Axes 144 Data Labels 145 Showing Insights with Charts 146 Comparisons 146 Compositions 147 Relationships 149 Chapter 5 Non-chart Visualizations 151 Understanding Custom Number Formats 151 The Four Sections of a Format 152 Special Characters 153 Digit Placeholders 153 Commas and Periods 154 Text 154 Underscore 155 Asterisk 156 Escaping Special Characters 156 The Accounting Number Format 156 Date and Time Formats 158 Conditional Custom Number Formats 159 Using Icons 160 Color Scales 160 Data Bars 165 Icon Sets 167 Creating Sparklines 170 Types of Sparklines 170 Creating a Sparkline 171 Sparkline Groups 172 Customize a Sparkline 172 Changing the Source Data 173 Changing the Color and Thickness 174 Adjusting the Axis 175 Chapter 6 Using Shapes to Create Infographics 179 Working with Shapes 179 Inserting Shapes 180 Customizing Shapes 182 Framing Data with Shapes 185 Creating a Banner 186 Creating a Binder Tab 188 Working with Multiple Shapes 191 Creating Simple Charts with Shapes 193 Creating Custom Infographics 195 Adding Other Illustrations 196 Part III Tell a Story with Visualization 203 Chapter 7 Visualizing Performance Comparisons 205 Single Measurements 206 Column Charts 207 Case Study: Sales by Quarter 210 Bullet Charts 212 Case Study: Expenses vs. Budget 212 Clustered Column Charts 216 Case Study: Production Defects 217 Funnel Charts 218 Case Study: Sales Conversion 219 XY Charts 221 Case Study: Temperature vs. Sales 222 Bubble Charts 225 Case Study: Home Mortgages 226 Dot Plot Charts 228 Case Study: Production Output 229 Chapter 8 Visualizing Parts of a Whole 239 Pie Charts 239 Doughnut Charts 241 Case Study: Sales by Region 242 Waffle Charts 244 Case Study: Employee Participation by Benefit 245 Sunburst Charts 249 Case Study: Manufacturing Process Time Study 250 Histograms 252 Case Study: Restaurant Ticket Totals 254 Treemap Charts 256 Case Study: Insurance Policy Averages 257 Waterfall Charts 259 Case Study: Net Income 261 Chapter 9 Visualizing Changes Over Time 265 Line Charts 266 Case Study: Sales by Product Category 268 Column Charts with Variances 273 Case Study: Houses Sold by Month 274 Combination Charts 280 Case Study: Freight Revenue vs. Miles 281 Line Charts with Differences 284 Case Study: Current vs. Prior Quarter Revenue 285 Side-by-Side Box Plots 288 Case Study: Salaries by Department 290 Animated Charts 292 PivotCharts 293 Staging Area Formulas 295 Chart Animation Macros 299 Chart Automation 302 Manipulating Chart Objects 302 Creating Panel Charts 307 Index 317

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Book SynopsisTable of ContentsChapter 1. Precalculus Review. 1.1 What is Calculus? 1.2 Review of Elementary Mathematics. 1.3 Review of Inequalities. 1.4 Coordinate Plane; Analytic Geometry. 1.5 Functions. 1.6 The Elementary Functions. 1.7 Combinations of Functions. 1.8 A Note on Mathematical Proof; Mathematical Induction. Chapter 2. Limits and Continuity. 2.1 The Limit Process (An Intuitive Introduction). 2.2 Definition of Limit. 2.3 Some Limit Theorems. 2.4 Continuity. 2.5 The Pinching Theorem; Trigonometric Limits. 2.6 Two Basic Theorems. Chapter 3. The Derivative; The Process of Differentiation. 3.1 The Derivative. 3.2 Some Differentiation Formulas. 3.3 The d/dx Notation; Derivatives of Higher Order. 3.4 The Derivative as a Rate of Change. 3.5 The Chain Rule. 3.6 Differentiating the Trigonometric Functions. 3.7 Implicit Differentiation; Rational Powers. Chapter 4. The Mean-Value Theorem; Applications of the First and Second Derivatives. 4.1 The Mean-Value Theorem. 4.2 Increasing and Decreasing Functions. 4.3 Local Extreme Values. 4.4 Endpoint Extreme Values; Absolute Extreme Values. 4.5 Some Max-Min Problems. 4.6 Concavity and Points of Inflection. 4.7 Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps. 4.8 Some Curve Sketching. 4.9 Velocity and Acceleration; Speed. 4.10 Related Rates of Change Per Unit Time. 4.11 Differentials. 4.12 Newton-Raphson Approximations. Chapter 5. Integration. 5.1 An Area Problem; A Speed-Distance Problem. 5.2 The Definite Integral of a Continuous Function. 5.3 The Function f(x) = Integral from a to x of f(t) dt. 5.4 The Fundamental Theorem of Integral Calculus. 5.5 Some Area Problems. 5.6 Indefinite Integrals. 5.7 Working Back from the Chain Rule; the u-Substitution. 5.8 Additional Properties of the Definite Integral. 5.9 Mean-Value Theorems for Integrals; Average Value of a Function. Chapter 6. Some Applications of the Integral. 6.1 More on Area. 6.2 Volume by Parallel Cross-Sections; Discs and Washers. 6.3 Volume by the Shell Method. 6.4 The Centroid of a Region; Pappus’s Theorem on Volumes. 6.5 The Notion of Work. 6.6 Fluid Force. Chapter 7. The Transcendental Functions. 7.1 One-to-One Functions; Inverse Functions. 7.2 The Logarithm Function, Part I. 7.3 The Logarithm Function, Part II. 7.4 The Exponential Function. 7.5 Arbitrary Powers; Other Bases. 7.6 Exponential Growth and Decay. 7.7 The Inverse Trigonometric Functions. 7.8 The Hyperbolic Sine and Cosine. 7.9 The Other Hyperbolic Functions. Chapter 8. Techniques of Integration. 8.1 Integral Tables and Review. 8.2 Integration by Parts. 8.3 Powers and Products of Trigonometric Functions. 8.4 Integrals Featuring Square Root of (a^2 – x^2), Square Root of (a^2 + x^2), and Square Root of (x^2 – a^2). 8.5 Rational Functions; Partial Functions. 8.6 Some Rationalizing Substitutions. 8.7 Numerical Integration. Chapter 9. Differential Equations. 9.1 First-Order Linear Equations. 9.2 Integral Curves; Separable Equations. 9.3 The Equation y′′ + ay′+ by = 0. Chapter 10. The Conic Sections; Polar Coordinates; Parametric Equations. 10.1 Geometry of Parabola, Ellipse, Hyperbola. 10.2 Polar Coordinates. 10.3 Graphing in Polar Coordinates. 10.4 Area in Polar Coordinates. 10.5 Curves Given Parametrically. 10.6 Tangents to Curves Given Parametrically. 10.7 Arc Length and Speed. 10.8 The Area of a Surface of Revolution; Pappus’s Theorem on Surface Area. Chapter 11. Sequences; Indeterminate Forms; Improper Integrals. 11.1 The Least Upper Bound Axiom. 11.2 Sequences of Real Numbers. 11.3 The Limit of a Sequence. 11.4 Some Important Limits. 11.5 The Indeterminate Forms (0/0). 11.6 The Indeterminate Form (∞/∞); Other Indeterminate Forms. 11.7 Improper Integrals. Chapter 12. Infinite Series. 12.1 Sigma Notation. 12.2 Infinite Series. 12.3 The Integral Test; Basic Comparison, Limit Comparison. 12.4 The Root Test; The Ratio Test. 12.5 Absolute and Conditional Convergence; Alternating Series. 12.6 Taylor Polynomials in x; Taylor Series in x. 12.7 Taylor Polynomials and Taylor Series in x – a. 12.8 Power Series. 12.9 Differentiation and Integration of Power Series. Chapter 13. Vectors. 13.1 Rectangular Space Coordinates. 13.2 Vectors in Three-Dimensional Space. 13.3 The Dot Product. 13.4 The Cross Product. 13.5 Lines. 13.6 Planes. 13.7 Higher Dimensions. Chapter 14. Vector Calculus. 14.1 Limit, Continuity, Vector Derivative. 14.2 The Rules of Differentiation. 14.3 Curves. 14.4 Arc Length. 14.5 Curvilinear Motion; Curvature. 14.6 Vector Calculus in Mechanics. 14.7 Planetary Motion. Chapter 15. Functions of Several Variables. 15.1 Elementary Examples. 15.2 A Brief Catalogue of Quadric Surfaces; Projections. 15.3 Graphs; Level Curves and Level Surfaces. 15.4 Partial Derivatives. 15.5 Open Sets and Closed Sets. 15.6 Limits and Continuity; Equality of Mixed Partials. Chapter 16. Gradients; Extreme Values; Differentials. 16.1 Differentiability and Gradient. 16.2 Gradients and Directional Derivatives. 16.3 The Mean-Value Theorem; the Chain Rule. 16.4 The Gradient as a Normal; Tangent Lines and Tangent Planes. 16.5 Local Extreme Values. 16.6 Absolute Extreme Values. 16.7 Maxima and Minima with Side Conditions. 16.8 Differentials. 16.9 Reconstructing a Function from Its Gradient. Chapter 17. Multiple Integrals. 17.1 Multiple-Sigma Notation. 17.2 Double Integrals. 17.3 The Evaluation of Double Integrals by Repeated Integrals. 17.4 The Double Integral as the Limit or Riemann Sums; Polar Coordinates. 17.5 Further Applications of Double Integration. 17.6 Triple Integrals. 17.7 Reduction to Repeated Integrals. 17.8 Cylindrical Coordinates. 17.9 The Triple Integral as the Limit of Riemann Sums; Spherical Coordinates. 17.10 Jacobians; Changing Variables in Multiple Integration. Chapter 18. Line Integrals and Surface Integrals. 18.1 Line Integrals. 18.2 The Fundamental Theorem for Line Integrals. 18.3 Work-Energy Formula; Conservation of Mechanical Energy. 18.4 Another Notation for Line Integrals; Line Integrals with Respect to Arc Length. 18.5 Green’s Theorem. 18.6 Parametrized Surfaces; Surface Area. 18.7 Surface Integrals. 18.8 The Vector Differential Operator Ñ. 18.9 The Divergence Theorem. 18.10 Stokes’s Theorem. Chapter 19. Additional Differential Equations. 19.1 Bernoulli Equations; Homogeneous Equations. 19.2 Exact Differential Equations; Integrating Factors. 19.3 Numerical Methods. 19.4 The Equation y′′ + ay′+ by = ø(x). 19.5 Mechanical Vibrations. Appendix A. Some Additional Topics. A.1 Rotation of Axes; Eliminating the xy-Term. A.2 Determinants. Appendix B. Some Additional Proofs. B.1 The Intermediate-Value Theorem. B.2 Boundedness; Extreme-Value Theorem. B.3 Inverses. B.4 The Integrability of Continuous Functions. B.5 The Integral as the Limit of Riemann Sums.

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Book SynopsisAn Introduction to Cochran-Mantel-Haenszel Testing and Nonparametric ANOVA Complete reference for applied statisticians and data analysts that uniquely covers the new statistical methodologies that enable deeper data analysis An Introduction to Cochran-Mantel-Haenszel Testing and Nonparametric ANOVA provides readers with powerful new statistical methodologies that enable deeper data analysis. The book offers applied statisticians an introduction to the latest topics in nonparametrics. The worked examples with supporting R code provide analysts the tools they need to apply these methods to their own problems. Co-authored by an internationally recognised expert in the field and an early career researcher with broad skills including data analysis and R programming, the book discusses key topics such as: NP ANOVA methodologyCochran-Mantel-Haenszel (CMH) methodology and designLatin squares and balanced incomplete block designsParametric ANOVA F tests for continuous dataNonparametric rank tests (the Kruskal-Wallis and Friedman tests)CMH MS tests for the nonparametric analysis of categorical response data Applied statisticians and data analysts, as well as students and professors in data analysis, can use this book to gain a complete understanding of the modern statistical methodologies that are allowing for deeper data analysis.Table of ContentsPreface xiii 1 Introduction 1 1.1 What are the CMH and NP ANOVA tests? 1 1.2 Outline 3 1.3 5 1.4 Examples 6 2 The Basic CMH Tests 13 2.1 Genesis: Cochran (1954), and Mantel and Haenszel (1959) 13 2.2 The basic CMH tests 18 2.3 The Nominal CMH tests 22 2.4 The CMH mean scores test 26 2.5 The CMH correlation test 28 3 The Completely Randomised Design 41 3.1 Introduction 41 3.2 The design and parametric model 42 3.3 The Kruskal-Wallis tests 43 3.4 Relating the Kruskal-Wallis and ANOVA F tests 47 3.5 The CMH tests for the CRD 49 3.6 The KW tests are CMH MS tests 52 3.7 Relating the CMH MS and ANOVA F tests 54 3.8 Simulation study 58 3.9 Wald test statistics in the CRD 61 4 The Randomised Block Design 71 4.1 Introduction 71 4.2 The design and parametric model 72 4.3 The Friedman tests 74 4.4 The CMH test statistics in the RBD 77 4.5 The Friedman tests are CMH MS tests 86 4.6 Relating the CMH MS and ANOVA F tests 88 4.7 Simulation study 91 4.8 Wald test statistics in the RBD 94 5 The Balanced Incomplete Block Design 101 5.1 Introduction 101 5.2 The Durbin tests 101 5.3 The relationship between the adjusted Durbin statistic and the ANOVA F statistic 103 5.4 Simulation study 110 5.5 Orthogonal contrasts for balanced designs with ordered treatments 113 5.6 A CMH MS analogue test statistic for the BIBD 124 6 Unconditional Analogues of CMH Tests 129 6.1 Introduction 129 6.2 Unconditional univariate moment tests 132 6.3 Generalised correlations 137 6.4 Unconditional bivariate moment tests 147 6.5 Unconditional general association tests 152 6.6 Stuart’s Test 163 7 Higher Moment Extensions To The Ordinal CMH Tests 167 7.1 Introduction 167 7.2 Extensions to the CMH mean scores test 168 7.3 Extensions to the CMH correlation test 172 7.4 Examples 176 8 Unordered Nonparametric ANOVA 183 8.1 Introduction 183 8.2 Unordered NP ANOVA for the CMH design 187 8.3 Singly ordered three-way tables 189 8.4 The Kruskal-Wallis and Friedman tests are NP ANOVA tests 193 8.5 Are the CMH MS and extensions NP ANOVA tests? 197 8.6 Extension to other designs 199 8.7 Latin squares 202 8.8 Balanced incomplete blocks 204 9 The Latin Square Design 207 9.1 Introduction 207 9.2 The Latin square design and parametric model 208 9.3 The RL test 210 9.4 Alignment 212 9.5 Simulation study 216 9.6 Examples 225 9.7 Orthogonal trend contrasts for ordered treatments 232 9.8 Technical derivation of the RL test 238 10 Ordered Nonparametric ANOVA 243 10.1 Introduction 243 10.2 Ordered NP ANOVA for the CMH design 247 10.3 Doubly ordered three-way tables 249 10.4 Extension to other designs 252 10.5 Latin square rank tests 255 10.6 Modelling the moments of the response variable 257 10.7 Lemonade sweetness data 262 10.8 Breakfast cereal data revisited 271 11 Conclusion 275 11.1 CMH or NP ANOVA? 275 11.2 Homosexual marriage data revisited for the last time! 277 11.3 Job satisfaction data 280 11.4 The end 286 A Appendix 289 A.1 Kronecker Products and Direct Sums 289 A.2 The Moore-Penrose Generalised Inverse 292

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Book SynopsisAn Introduction to Optimization Accessible introductory textbook on optimization theory and methods, with an emphasis on engineering design, featuring MATLAB exercises and worked examples Fully updated to reflect modern developments in the field, the Fifth Edition of An Introduction to Optimization fills the need for an accessible, yet rigorous, introduction to optimization theory and methods, featuring innovative coverage and a straightforward approach. The book begins with a review of basic definitions and notations while also providing the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. In addition, the book includes an introduction to artificial neural networks, convex optimization, multi-objective optimization, and applications of optimization in machine learning. Numerous diagrams andTable of ContentsPreface xv About the Companion Website xviii Part I Mathematical Review 1 1 Methods of Proof and Some Notation 3 1.1 Methods of Proof 3 1.2 Notation 5 Exercises 5 2 Vector Spaces and Matrices 7 2.1 Vector and Matrix 7 2.2 Rank of a Matrix 11 2.3 Linear Equations 16 2.4 Inner Products and Norms 18 Exercises 20 3 Transformations 23 3.1 Linear Transformations 23 3.2 Eigenvalues and Eigenvectors 24 3.3 Orthogonal Projections 26 3.4 Quadratic Forms 27 3.5 Matrix Norms 32 Exercises 35 4 Concepts from Geometry 39 4.1 Line Segments 39 4.2 Hyperplanes and Linear Varieties 39 4.3 Convex Sets 41 4.4 Neighborhoods 43 4.5 Polytopes and Polyhedra 44 Exercises 45 5 Elements of Calculus 47 5.1 Sequences and Limits 47 5.2 Differentiability 52 5.3 The Derivative Matrix 54 5.4 Differentiation Rules 57 5.5 Level Sets and Gradients 58 5.6 Taylor Series 61 Exercises 65 Part II Unconstrained Optimization 67 6 Basics of Set-Constrained and Unconstrained Optimization 69 6.1 Introduction 69 6.2 Conditions for Local Minimizers 70 Exercises 78 7 One-Dimensional Search Methods 87 7.1 Introduction 87 7.2 Golden Section Search 87 7.3 Fibonacci Method 91 7.4 Bisection Method 97 7.5 Newton’s Method 98 7.6 Secant Method 101 7.7 Bracketing 103 7.8 Line Search in Multidimensional Optimization 103 Exercises 105 8 Gradient Methods 109 8.1 Introduction 109 8.2 Steepest Descent Method 110 8.3 Analysis of Gradient Methods 117 Exercises 126 9 Newton’s Method 133 9.1 Introduction 133 9.2 Analysis of Newton’s Method 135 9.3 Levenberg–Marquardt Modification 138 9.4 Newton’s Method for Nonlinear Least Squares 139 Exercises 142 10 Conjugate Direction Methods 145 10.1 Introduction 145 10.2 Conjugate Direction Algorithm 146 10.2.1 Basic Conjugate Direction Algorithm 146 10.3 Conjugate Gradient Algorithm 151 10.4 Conjugate Gradient Algorithm for Nonquadratic Problems 154 Exercises 156 11 Quasi-Newton Methods 159 11.1 Introduction 159 11.2 Approximating the Inverse Hessian 160 11.3 Rank One Correction Formula 162 11.4 DFP Algorithm 166 11.5 BFGS Algorithm 170 Exercises 173 12 Solving Linear Equations 179 12.1 Least-Squares Analysis 179 12.2 Recursive Least-Squares Algorithm 187 12.3 Solution to a Linear Equation with Minimum Norm 190 12.4 Kaczmarz’s Algorithm 191 12.5 Solving Linear Equations in General 194 Exercises 201 13 Unconstrained Optimization and Neural Networks 209 13.1 Introduction 209 13.2 Single-Neuron Training 211 13.3 Backpropagation Algorithm 213 Exercises 222 14 Global Search Algorithms 225 14.1 Introduction 225 14.2 Nelder–Mead Simplex Algorithm 225 14.3 Simulated Annealing 229 14.3.1 Randomized Search 229 14.3.2 Simulated Annealing Algorithm 229 14.4 Particle Swarm Optimization 231 14.4.1 Basic PSO Algorithm 232 14.4.2 Variations 233 14.5 Genetic Algorithms 233 14.5.1 Basic Description 233 14.5.1.1 Chromosomes and Representation Schemes 234 14.5.1.2 Selection and Evolution 234 14.5.2 Analysis of Genetic Algorithms 238 14.5.3 Real-Number Genetic Algorithms 243 Exercises 244 Part III Linear Programming 247 15 Introduction to Linear Programming 249 15.1 Brief History of Linear Programming 249 15.2 Simple Examples of Linear Programs 250 15.3 Two-Dimensional Linear Programs 256 15.4 Convex Polyhedra and Linear Programming 258 15.5 Standard Form Linear Programs 260 15.6 Basic Solutions 264 15.7 Properties of Basic Solutions 267 15.8 Geometric View of Linear Programs 269 Exercises 273 16 Simplex Method 277 16.1 Solving Linear Equations Using Row Operations 277 16.2 The Canonical Augmented Matrix 283 16.3 Updating the Augmented Matrix 284 16.4 The Simplex Algorithm 285 16.5 Matrix Form of the Simplex Method 291 16.6 Two-Phase Simplex Method 294 16.7 Revised Simplex Method 297 Exercises 301 17 Duality 309 17.1 Dual Linear Programs 309 17.2 Properties of Dual Problems 316 17.3 Matrix Games 321 Exercises 324 18 Nonsimplex Methods 331 18.1 Introduction 331 18.2 Khachiyan’s Method 332 18.3 Affine Scaling Method 334 18.3.1 Basic Algorithm 334 18.3.2 Two-Phase Method 337 18.4 Karmarkar’s Method 339 18.4.1 Basic Ideas 339 18.4.2 Karmarkar’s Canonical Form 339 18.4.3 Karmarkar’s Restricted Problem 341 18.4.4 From General Form to Karmarkar’s Canonical Form 342 18.4.5 The Algorithm 345 Exercises 349 19 Integer Linear Programming 351 19.1 Introduction 351 19.2 Unimodular Matrices 351 19.3 The Gomory Cutting-Plane Method 358 Exercises 366 Part IV Nonlinear Constrained Optimization 369 20 Problems with Equality Constraints 371 20.1 Introduction 371 20.2 Problem Formulation 373 20.3 Tangent and Normal Spaces 374 20.4 Lagrange Condition 379 20.5 Second-Order Conditions 387 20.6 Minimizing Quadratics Subject to Linear Constraints 390 Exercises 394 21 Problems with Inequality Constraints 399 21.1 Karush–Kuhn–Tucker Condition 399 21.2 Second-Order Conditions 406 Exercises 410 22 Convex Optimization Problems 417 22.1 Introduction 417 22.2 Convex Functions 419 22.3 Convex Optimization Problems 426 22.4 Semidefinite Programming 431 22.4.1 Linear Matrix Inequalities and Their Properties 431 22.4.2 LMI Solvers 435 22.4.2.1 Finding a Feasible Solution Under LMI Constraints 436 22.4.2.2 Minimizing a Linear Objective Under LMI Constraints 438 22.4.2.3 Minimizing a Generalized Eigenvalue Under LMI Constraints 440 Exercises 442 23 Lagrangian Duality 449 23.1 Overview 449 23.2 Notation 449 23.3 Primal–Dual Pair 450 23.4 General Duality Properties 451 23.4.1 Convexity of Dual Problem 451 23.4.2 Primal Objective in Terms of Lagrangian 451 23.4.3 Minimax Inequality Chain 452 23.4.4 Optimality of Saddle Point 452 23.4.5 Weak Duality 453 23.4.6 Duality Gap 453 23.5 Strong Duality 454 23.5.1 Strong Duality ⇔ Minimax Equals Maximin 454 23.5.2 Strong Duality ⇒ Primal Unconstrained Minimization 455 23.5.3 Strong Duality ⇒ Optimality 455 23.5.4 Strong Duality ⇒ KKT (Including Complementary Slackness) 455 23.5.5 Strong Duality ⇒ Saddle Point 456 23.6 Convex Case 456 23.6.1 Convex Case: KKT ⇒ Strong Duality 456 23.6.2 Convex Case: Regular Optimal Primal ⇒ Strong Duality 457 23.6.3 Convex Case: Slater’s Condition ⇒ Strong Duality 457 23.7 Summary of Key Results 457 Exercises 458 24 Algorithms for Constrained Optimization 459 24.1 Introduction 459 24.2 Projections 459 24.3 Projected Gradient Methods with Linear Constraints 462 24.4 Convergence of Projected Gradient Algorithms 465 24.4.1 Fixed Points and First-Order Necessary Conditions 466 24.4.2 Convergence with Fixed Step Size 468 24.4.3 Some Properties of Projections 469 24.4.4 Armijo Condition 470 24.4.5 Accumulation Points 471 24.4.6 Projections in the Convex Case 472 24.4.7 Armijo Condition in the Convex Case 474 24.4.8 Convergence in the Convex Case 480 24.4.9 Convergence Rate with Line-Search Step Size 481 24.5 Lagrangian Algorithms 483 24.5.1 Lagrangian Algorithm for Equality Constraints 484 24.5.2 Lagrangian Algorithm for Inequality Constraints 486 24.6 Penalty Methods 489 Exercises 495 25 Multiobjective Optimization 499 25.1 Introduction 499 25.2 Pareto Solutions 499 25.3 Computing the Pareto Front 501 25.4 From Multiobjective to Single-Objective Optimization 505 25.5 Uncertain Linear Programming Problems 508 25.5.1 Uncertain Constraints 508 25.5.2 Uncertain Objective Function Coefficients 511 25.5.3 Uncertain Constraint Coefficients 513 25.5.4 General Uncertainties 513 Exercises 513 Part V Optimization in Machine Learning 517 26 Machine Learning Problems and Feature Engineering 519 26.1 Machine Learning Problems 519 26.1.1 Data with Labels and Supervised Learning 519 26.1.2 Data Without Labels and Unsupervised Learning 521 26.2 Data Normalization 522 26.3 Histogram of Oriented Gradients 524 26.4 Principal Component Analysis and Linear Autoencoder 526 26.4.1 Singular Value Decomposition 526 26.4.2 Principal Axes and Principal Components of a Data Set 527 26.4.3 Linear Autoencoder 529 Exercises 530 27 Stochastic Gradient Descent Algorithms 537 27.1 Stochastic Gradient Descent Algorithm 537 27.2 Stochastic Variance Reduced Gradient Algorithm 540 27.3 Distributed Stochastic Variance Reduced Gradient 542 27.3.1 Distributed Learning Environment 542 27.3.2 SVRG in Distributed Optimization 543 27.3.3 Communication Versus Computation 545 27.3.4 Data Security 545 Exercises 546 28 Linear Regression and Its Variants 553 28.1 Least-Squares Linear Regression 553 28.1.1 A Linear Model for Prediction 553 28.1.2 Training the Model 554 28.1.3 Computing Optimal ̂w 554 28.1.4 Optimal Predictor and Performance Evaluation 555 28.1.5 Least-Squares Linear Regression for Data Sets with Vector Labels 556 28.2 Model Selection by Cross-Validation 559 28.3 Model Selection by Regularization 562 Exercises 564 29 Logistic Regression for Classification 569 29.1 Logistic Regression for Binary Classification 569 29.1.1 Least-Squares Linear Regression for Binary Classification 569 29.1.2 Logistic Regression for Binary Classification 570 29.1.3 Interpreting Logistic Regression by Log Error 572 29.1.4 Confusion Matrix for Binary Classification 573 29.2 Nonlinear Decision Boundary via Linear Regression 575 29.2.1 Least-Squares Linear Regression with Nonlinear Transformation 576 29.2.2 Logistic Regression with Nonlinear Transformation 578 29.3 Multicategory Classification 580 29.3.1 One-Versus-All Multicategory Classification 580 29.3.2 Softmax Regression for Multicategory Classification 581 Exercises 584 30 Support Vector Machines 589 30.1 Hinge-Loss Functions 589 30.1.1 Geometric Interpretation of the Linear Model 589 30.1.2 Hinge Loss for Binary Data Sets 590 30.1.3 Hinge Loss for Multicategory Data Sets 592 30.2 Classification by Minimizing Hinge Loss 593 30.2.1 Binary Classification by Minimizing Average Hinge Loss 593 30.2.2 Multicategory Classification by Minimizing E hww or E hcs 594 30.3 Support Vector Machines for Binary Classification 596 30.3.1 Hard-Margin Support Vector Machines 596 30.3.2 Support Vectors 598 30.3.3 Soft-Margin Support Vector Machines 599 30.3.4 Connection to Hinge-Loss Minimization 602 30.4 Support Vector Machines for Multicategory Classification 602 30.5 Kernel Trick 603 30.5.1 Kernels 603 30.5.2 Kernel Trick 604 30.5.3 Learning with Kernels 605 30.5.3.1 Regularized Logistic Regression with Nonlinear Transformation for Binary Classification 605 30.5.3.2 Regularized Hinge-Loss Minimization for Binary Classification 606 Exercises 607 31 K-Means Clustering 611 31.1 K-Means Clustering 611 31.2 K-Means++ forCenterInitialization 615 31.3 Variants of K-Means Clustering 617 31.3.1 K-Means Clustering Based on 1-Norm Regularization 617 31.3.2 PCA-Guided K-Means Clustering 619 31.4 Image Compression by Vector Quantization and K-Means Clustering 622 Exercises 623 References 627 Index 635

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Book SynopsisTable of ContentsPreface xiii About the Companion Website xix 1 Teaching Methods for This Textbook 1 Synopsis 1 1.1 Education in Civil and Environmental Engineering 1 1.2 Machine Learning as an Educational Material 2 1.3 Possible Pathways for Course/Material Delivery 3 1.4 Typical Outline for Possible Means of Delivery 7 Chapter Blueprint 8 Questions and Problems 8 References 8 2 Introduction to Machine Learning 11 Synopsis 11 2.1 A Brief History of Machine Learning 11 2.2 Types of Learning 12 2.3 A Look into ML from the Lens of Civil and Environmental Engineering 15 2.4 Let Us Talk a Bit More about ML 17 2.5 ML Pipeline 18 2.6 Conclusions 27 Definitions 27 Chapter Blueprint 29 Questions and Problems 29 References 30 3 Data and Statistics 33 Synopsis 33 3.1 Data and Data Science 33 3.2 Types of Data 34 3.3 Dataset Development 37 3.4 Diagnosing and Handling Data 37 3.5 Visualizing Data 38 3.6 Exploring Data 59 3.7 Manipulating Data 66 3.8 Manipulation for Computer Vision 68 3.9 A Brief Review of Statistics 68 3.10 Conclusions 76 4 Machine Learning Algorithms 81 Synopsis 81 4.1 An Overview of Algorithms 81 4.2 Conclusions 127 5 Performance Fitness Indicators and Error Metrics 133 Synopsis 133 5.1 Introduction 133 5.2 The Need for Metrics and Indicators 134 5.3 Regression Metrics and Indicators 135 5.4 Classification Metrics and Indicators 142 5.5 Clustering Metrics and Indicators 142 5.6 Functional Metrics and Indicators* 151 5.7 Other Techniques (Beyond Metrics and Indicators) 154 5.8 Conclusions 159 6 Coding-free and Coding-based Approaches to Machine Learning 169 Synopsis 169 6.1 Coding-free Approach to ML 169 6.2 Coding-based Approach to ML 280 6.3 Conclusions 322 7 Explainability and Interpretability 327 7 Synopsis 327 7.1 The Need for Explainability 327 7.2 Explainability from a Philosophical Engineering Perspective* 329 7.3 Methods for Explainability and Interpretability 331 7.4 Examples 335 7.5 Conclusions 428 8 Causal Discovery and Causal Inference 433 Synopsis 433 8.1 Big Ideas Behind This Chapter 433 8.2 Re-visiting Experiments 434 8.3 Re-visiting Statistics and ML 435 8.4 Causality 436 8.5 Examples 451 8.6 A Note on Causality and ML 475 8.7 Conclusions 475 9 Advanced Topics (Synthetic and Augmented Data, Green ML, Symbolic Regression, Mapping Functions, Ensembles, and AutoML) 481 Synopsis 481 9.1 Synthetic and Augmented Data 481 9.2 Green ML 488 9.3 Symbolic Regression 498 9.4 Mapping Functions 529 9.5 Ensembles 539 9.6 AutoML 548 9.7 Conclusions 552 10 Recommendations, Suggestions, and Best Practices 559 Synopsis 559 10.1 Recommendations 559 10.2 Suggestions 564 10.3 Best Practices 566 11 Final Thoughts and Future Directions 573 Synopsis 573 11.1 Now 573 11.2 Tomorrow 573 11.3 Possible Ideas to Tackle 575 11.4 Conclusions 576 References 576 Index 577

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Book SynopsisA novel presentation of rank and permutation tests, with accessible guidance to applications in R Nonparametric testing problems are frequently encountered in many scientific disciplines, such as engineering, medicine and the social sciences. This book summarizes traditional rank techniques and more recent developments in permutation testing as robust tools for dealing with complex data with low sample size. Key Features: Examines the most widely used methodologies of nonparametric testing. Includes extensive software codes in R featuring worked examples, and uses real case studies from both experimental and observational studies. Presents and discusses solutions to the most important and frequently encountered real problems in different fields. Features a supporting website (www.wiley.com/go/hypothesis_testing) containing all of the data sets examined in the book along with ready to use R software codesTrade Review“The book combines an up to date overview with useful practical guidance to applications in R, and will be a valuable resource for practitioners and researchers working in a wide range of scientific fields including engineering, biostatistics, psychology and medicine.” (Zentralblatt MATH, 1 October 2014) Table of ContentsPresentation of the book xi Preface xiii Notation and abbreviations xvii 1 One- and two-sample location problems, tests for symmetry and tests on a single distribution 1 1.1 Introduction 1 1.2 Nonparametric tests 2 1.2.1 Rank tests 2 1.2.2 Permutation tests and combination based tests 3 1.3 Univariate one-sample tests 5 1.3.1 The Kolmogorov goodness-of-fit test 6 1.3.2 A univariate permutation test for symmetry 10 1.4 Multivariate one-sample tests 15 1.4.1 Multivariate rank test for central tendency 15 1.4.2 Multivariate permutation test for symmetry 18 1.5 Univariate two-sample tests 20 1.5.1 The Wilcoxon (Mann–Whitney) test 21 1.5.2 Permutation test on central tendency 27 1.6 Multivariate two-sample tests 29 1.6.1 Multivariate tests based on rank 29 1.6.2 Multivariate permutation test on central tendency 34 References 37 2 Comparing variability and distributions 38 2.1 Introduction 38 2.2 Comparing variability 39 2.2.1 The Ansari–Bradley test 40 2.2.2 The permutation Pan test 43 2.2.3 The permutation O’Brien test 46 2.3 Jointly comparing central tendency and variability 49 2.3.1 The Lepage test 50 2.3.2 The Cucconi test 52 2.4 Comparing distributions 56 2.4.1 The Kolmogorov–Smirnov test 56 2.4.2 The Cram´er–von Mises test 59 References 61 3 Comparing more than two samples 65 3.1 Introduction 65 3.2 One-way ANOVA layout 66 3.2.1 The Kruskal–Wallis test 67 3.2.2 Permutation ANOVA in the presence of one factor 73 3.2.3 The Mack–Wolfe test for umbrella alternatives 76 3.2.4 Permutation test for umbrella alternatives 83 3.3 Two-way ANOVA layout 87 3.3.1 The Friedman rank test for unreplicated block design 87 3.3.2 Permutation test for related samples 89 3.3.3 The Page test for ordered alternatives 91 3.3.4 Permutation analysis of variance in the presence of two factors 93 3.4 Pairwise multiple comparisons 95 3.4.1 Rank-based multiple comparisons for the Kruskal–Wallis test 96 3.4.2 Permutation tests for multiple comparisons 98 3.5 Multivariate multisample tests 99 3.5.1 A multivariate multisample rank-based test 99 3.5.2 A multivariate multisample permutation test 103 References 105 4 Paired samples and repeated measures 107 4.1 Introduction 107 4.2 Two-sample problems with paired data 108 4.2.1 The Wilcoxon signed rank test 108 4.2.2 A permutation test for paired samples 114 4.3 Repeated measures tests 116 4.3.1 Friedman rank test for repeated measures 117 4.3.2 A permutation test for repeated measures 120 References 122 5 Tests for categorical data 124 5.1 Introduction 124 5.2 One-sample tests 125 5.2.1 Binomial test on one proportion 125 5.2.2 The McNemar test for paired data (or bivariate responses) with binary variables 128 5.2.3 Multivariate extension of the McNemar test 131 5.3 Two-sample tests on proportions or 2 × 2 contingency tables 134 5.3.1 The Fisher exact test 135 5.3.2 A permutation test for comparing two proportions 138 5.4 Tests for R × C contingency tables 139 5.4.1 The Anderson–Darling permutation test for R × C contingency tables 140 5.4.2 Permutation test on moments 145 5.4.3 The chi-square permutation test 148 References 151 6 Testing for correlation and concordance 153 6.1 Introduction 153 6.2 Measuring correlation 154 6.3 Tests for independence 156 6.3.1 The Spearman test 157 6.3.2 The Kendall test 160 6.4 Tests for concordance 166 6.4.1 The Kendall–Babington Smith test 167 6.4.2 A permutation test for concordance 172 References 174 7 Tests for heterogeneity 176 7.1 Introduction 176 7.2 Statistical heterogeneity 177 7.3 Dominance in heterogeneity 178 7.3.1 Geographical heterogeneity 180 7.3.2 Market segmentation 184 7.4 Two-sided and multisample test 188 7.4.1 Customer satisfaction 189 7.4.2 Heterogeneity as a measure of uncertainty 191 7.4.3 Ethnic heterogeneity 194 7.4.4 Reliability analysis 196 References 197 Appendix A Selected critical values for the null distribution of the peak-known Mack–Wolfe statistic 201 Appendix B Selected critical values for the null distribution of the peak-unknown Mack–Wolfe statistic 203 Appendix C Selected upper-tail probabilities for the null distribution of the Page L statistic 206 Appendix D R functions and codes 213 Index 219

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Book SynopsisThis book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 900 pages--two-thirds the size of Stewart's other calculus texts, and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, www.StewartCalculus.com. Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart's other books. ESSENTIAL CALCULUS: EARLY TRANSCENDENTATable of Contents1. FUNCTIONS AND LIMITS. Functions and Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity. 2. DERIVATIVES. Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials. 3. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS. Exponential Functions. Inverse Functions and Logarithms. Derivatives of Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l'Hospital's Rule. 4. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton's Method. Antiderivatives. 5. INTEGRALS. Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule. 6. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. 7. APPLICATIONS OF INTEGRATION. Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area of a Surface of Revolution. Applications to Physics and Engineering. Differential Equations. 8. SERIES. Sequences. Series. The Integral and Comparison Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials. 9. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. 10. VECTORS AND THE GEOMETRY OF SPACE. Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Equations of Lines and Planes. Cylinders and Quadric Surfaces. Vector Functions and Space Curves. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. 11. PARTIAL DERIVATIVES. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximations. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Lagrange Multipliers. 12. MULTIPLE INTEGRALS. Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Change of Variables in Multiple Integrals. 13. VECTOR CALCULUS. Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes' Theorem. The Divergence Theorem. Appendix A. Trigonometry. Appendix B. Proofs. Appendix C. Sigma Notation. Appendix D. The Logarithm Defined as an Integral

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Book SynopsisIn this book Michael Potter offers a fresh and compelling portrait of the birth of modern analytic philosophy, viewed through the lens of a detailed study of the work of the four philosophers who contributed most to shaping it: Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein, and Frank Ramsey. It covers the remarkable period of discovery that began with the publication of Frege's Begriffsschrift in 1879 and ended with Ramsey's death in 1930. Potterâone of the most influential scholars of this period in philosophyâpresents a deep but accessible account of the break with absolute idealism and neo-Kantianism, and the emergence of approaches that exploited the newly discovered methods in logic. Like his subjects, Potter focusses principally on philosophical logic, philosophy of mathematics, and metaphysics, but he also discusses epistemology, meta-ethics, and the philosophy of language. The book is an essential starting point for any student attempting to understand the workTrade Review"The book is an impressive achievement, and it will be an important contribution to the literature on Frege, Russell, Wittgenstein, Ramsey, and the history of early analytic philosophy. I thoroughly enjoyed reading it and learned a lot from it. It is not only a state-of-the-art contribution to scholarship but will also be a valuable textbook for courses on the history of early analytic philosophy, or on the work of one or more of the four philosophers discussed."--David G. Stern, University of Iowa, USA"This book is a significant contribution to studies in the history of analytic philosophy and will benefit upper-level undergraduates studying this material for the first time, as well as active researchers in the area."--James Levine, Trinity College Dublin, IrelandTable of ContentsIntroductionPart I Frege Biography Logic before 1879 Begriffsschrift I: Foundations of logic Begriffsschrift II: Propositional logic Begriffsschrift III: Quantification Begriffsschrift IV: Identity Begriffsschrift V: The ancestral Early philosophy of logic The Hierarchy Grundlagen I: The context principle Grundlagen II: Arithmetical truth Grundlagen III: Numbers Grundlagen IV: The formal project Sense and reference I: Singular terms Sense and reference II: Sentences Sense anad references III: Concept-words Grundgesetze I: Types Grundgesetze II: Extensions The Frege-Hilbert correspondence Later writings Frege's Legacy Part II Russell Biography Bradley Geometry McTaggart German Mathematics Whitehead Moore Leibniz Peano Early logicism Denoting concepts The contradiction On denoting Truth Types Middle logicism Acquaintance Matter Pre-war judgement Facts Late logicism Post-war judgement Neutral monism Russell’s legacy III Wittgenstein Biography Facts Pictures Propositions Sense Wittgenstein’s concept-script Objects Identity Solipsism Ordinary language Minds Logic The metaphysical subject Arithmetic Science Ethics The mystical The legacy of the Tractatus IV Ramsey Biography Truth Knowledge The foundations of mathematics I: Types The foundations of mathematics II: Logicism Universals Degrees of belief Facts and propositions Last papers Ramsey’s legacy Bibliography

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Book SynopsisThe Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spacesâstretching studentsâ minds as they learn to visualize new possibilities for the shape of our universe.Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space.Features of the Third Edition: Full-color figures throughout Picture proofs have replaced algebraic proofs Simpler handles-and-crosscaps approach to surfaces Updated discussiTable of ContentsPart I Surfaces and Three-Manifolds Flatland Gluing Vocabulary Orientability Classification of Surfaces Products Flat Manifolds Orientability vs. Two-Sidedness Part II Geometries on Surfaces The Sphere The Hyperbolic Plane Geometries on Surfaces Gauss-Bonnet Formula and Euler Number Part III Geometries on Three-Manifolds Four-Dimensional Space The Hypersphere Hyperbolic Space Geometries on Three-Manifolds I Bundles Geometries on Three-Manifolds II Part IV The Universe The Universe The History of Space Appendix A: Answers Appendix B: Bibliography Appendix C: Conway’s ZIP Proof

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Book SynopsisIn spite of being nearly 500 years old, the subject of complex analysis is still today a vital and active part of mathematics. There are important applications in physics, engineering, and other aspects of technology. This Handbook presents contributed chapters by prominent mathematicians, including the new generation of researchers. More than a compilation of recent results, this book offers students an essential stepping-stone to gain an entry into the research life of complex analysis. Classes and seminars play a role in this process. More, though, is needed for further study. This Handbook will play that role. This book is also a reference and a source of inspiration for more seasoned mathematiciansboth specialists in complex analysis and others who want to acquaint themselves with current modes of thought.The chapters in this volume are authored by leading experts and gifted expositors. They are carefully crafted presentations of diverse aspects of the fielTable of ContentsPreface1.Something about poisson and dirichlet2.The Cauchy-Leray operator for convex domains3.Fractional linear maps and some applications. An “Augenblick” 4.Biholomorphic transformations5.Positivity in the @-Neumann Problem6.Symmetry and art 7.A glimpse into invariant distances in complex analysis8.Variations on the (eternal) theme of analytic continuation9.Complex convexity10.Reproducing kernels in complex analysis11.The Green’s function method on the Riemann mapping theorem12.Polynomial trace identities in quaternion algebras and two-generator Kleinian groups13.Boundary value problems on klein surfacesBibliographyIndex

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Book SynopsisBusiness Psychology and Organizational Behaviour introduces principles and concepts in psychology and organizational behaviour with emphasis on relevance and applications. Well organised and clearly written, it draws on a sound theoretical and applied base, and utilizes real-life examples, theories, and research findings of relevance to the world of business and work. The new edition of this best-selling textbook has been revised and updated with expanded and new material, including: proactive personality and situational theory in personality; theory of purposeful work behaviour; emotional and social anxiety in communication; decision biases and errors; and right brain activity and creativity, to name a few. There are numerous helpful features such as learning outcomes, chapter summaries, review questions, a glossary, and a comprehensive bibliography. Illustrations of practice and relevant theory and research also take the reader through individual, group, andTrade Review"This new up-to-date edition of Eugene McKenna’s highly respected textbook exceeds expectations. It is my book of choice both for teaching and for reference on business psychology and organizational behavior. It brings together relevant insights from past and present research, and it clarifies how the contributions of psychology relate to those of other disciplines. What may appear to be a formidably comprehensive book is actually easy to read due to its clear style and the many summaries and examples provided." - John Child, D.Sc., FBA, Professor of Commerce, Birmingham Business School, University of Birmingham, UK"This new edition of Business Psychology and Organizational Behaviour is outstanding. Not only does it cover thoroughly and up-to-date all the areas of business psychology and OB, but also develops new ones as well (e.g., business ethics). The standout for me are the international case studies, and particularly practitioner perspectives. A must-buy textbook in the field of OB by a renowned author and scholar." — Sir Cary Cooper, CBE, 50th Anniversary Professor of Organizational Psychology & Health at the ALLIANCE Manchester Business School, University of Manchester, UKPraise for the Fifth Edition: "The content of the book covers all the usual areas of business psychology. McKenna’s approach is scholarly, presenting research evidence for and against controversial topics before arriving at well-considered conclusions. A text such as this earns its place on the bookshelf of psychology undergraduates as a comprehensive core text." – Anne Kearns, Chartered Psychologist, The Psychologist "This new edition of Business Psychology and Organizational Behaviour is outstanding. Not only does it cover thoroughly and up-to-date all the areas of business psychology and OB, but also develops new ones as well (e.g., business ethics). The standout for me are the international case studies, and particularly practitioner perspectives. A must-buy textbook in the field of OB by a renowned author and scholar." — Sir Cary Cooper, CBE, 50th Anniversary Professor of Organizational Psychology & Health at the ALLIANCE Manchester Business School, University of Manchester, UK"This new up-to-date edition of Eugene McKenna’s highly respected textbook exceeds expectations. It is my book of choice both for teaching and for reference on business psychology and organizational behavior. It brings together relevant insights from past and present research, and it clarifies how the contributions of psychology relate to those of other disciplines. What may appear to be a formidably comprehensive book is actually easy to read due to its clear style and the many summaries and examples provided." - John Child, D.Sc., FBA, Professor of Commerce, Birmingham Business School, University of Birmingham, UK Praise for the Fifth Edition: "The content of the book covers all the usual areas of business psychology. McKenna’s approach is scholarly, presenting research evidence for and against controversial topics before arriving at well-considered conclusions. A text such as this earns its place on the bookshelf of psychology undergraduates as a comprehensive core text." – Anne Kearns, Chartered Psychologist, The PsychologistTable of ContentsAcknowledgments Preface PART I PERSPECTIVES AND ENQUIRY1. Historical Influences and Research MethodologyPART II THE INDIVIDUAL2. Personality and Intelligence3. Psychological Testing, Selection and Appraisal4. Motivation, Job Design and Extrinsic Rewards5. Perception and Communication6. Learning, Memory and Training7. Individual Decision Making and Creativity8. Attitudes, Values, Job Satisfaction, and CommitmentPART III THE GROUP9. Groups10. Teambuilding11. Leadership and Management Style12. Power, Politics, and ConflictPART IV THE ORGANIZATION13. Organizational Structure and Design14. Organizational Culture15. Organizational Change and Development16. Health and Work: StressGlossaryReferencesAuthor IndexSubject Index

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Book SynopsisForces shaping human history are complex, but the course of history is undeniably changed on many occasions by conscious acts. These may be premeditated or responsive, calmly calculated or performed under great pressure. They may also be successful or catastrophic, but how are historians to make such judgements and appeal to evidence in support of their conclusions? Further, and crucially, how exactly are we to distinguish probable unrealized alternatives from improbable ones? This book describes some of the modern statistical techniques that can begin to answer this question, as well as some of the difficulties in doing so. Using simple, well-quantified cases drawn from military history, we claim that statistics can now help us to navigate the near-truths, the envelope around the events with which any meaningful historical analysis must deal, and to quantify the basis of such analysis. Quantifying Counterfactual Military History is intended for a general audience who are intTable of Contents1. Could History Have Been Otherwise? 2. Could the Germans Have Won the Battle of Jutland? 3. Could the Germans Have Won the Battle of Britain? 4. Could the United States Have Prevailed in Vietnam? 5. The Road to Able Archer: Counterfactual Reasoning and the Dangerous History of Nuclear Deterrence 1945–1983 6. Conclusions

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Book SynopsisThe book has been tested and refined through years of classroom teaching experience. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. This textbook provides complete coverage of continuous-time financial models that form the cornerstones of financial derivative pricing theory. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives.Key features: In-depth coverage of continuous-time theory and methodology Numerous, fully worked out examples and exercises in every chapter Mathematically rigorous and consistent, yet bridging various basic and more advanced concepts Judicious balance of financial theory and mathematiTable of ContentsPart I: Stochastic Calculus with Brownian Motion. 1. One-Dimensional Brownian Motion and Related Processes. 2. Introduction to Continuous-Time Stochastic Calculus. Part II Continuous-Time Modelling. 3. Risk-Neutral Pricing in the (B; S) Economy: One Underlying Stock. 4. Risk-Neutral Pricing in a Multi-Asset Economy. 5. American Options. 6. Interest-Rate Modelling and Derivative Pricing. 7. Alternative Models of Asset Price Dynamics. A. Essentials of General Probability Theory. B. Some Useful Integral (Expectation) Identities and Symmetry Properties of Normal Random Variables. C. Answers and Hints to Exercises. D. Glossary of Symbols and Abbreviations. Greek Alphabet. References. Index.

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Book SynopsisThis is the sixth edition of a popular textbook on multivariate analysis. Well-regarded for its practical and accessible approach, with excellent examples and good guidance on computing, the book is particularly popular for teaching outside statistics, i.e. in epidemiology, social science, business, etc. The sixth edition has been updated with a new chapter on data visualization, a distinction made between exploratory and confirmatory analyses and a new section on generalized estimating equations and many new updates throughout. This new edition will enable the book to continue as one of the leading textbooks in the area, particularly for non-statisticians. Key Features: Provides a comprehensive, practical and accessible introduction to multivariate analysis. Keeps mathematical details to a minimum, so particularly geared toward a non-statistical audience. Includes lots of detailed worked examples, guidance on computiTrade Review"This book is an excellent resource for students and researchers of all levels. I have used earlier editions repeatedly in data-analysis courses for advanced undergraduates and graduate students in applied fields. The level of mathematical presentation is well matched to such settings. Not only are there excellent examples from biostatistics and public health, but there are also some very good business financial examples. The new chapter on Data Visualization in the new, sixth edition will be especially useful. Overall, the book is exceptionally well written and readable."- Stanley Sclove, University of Illinois at Chicago "Editions of Practical Multivariate Analysis have been the mainstay of my graduate-level service course in applied data-analysis since 1985. It remains an extraordinary book -- packed with excellent examples, clear explanation and fine advice -- and has my highest possible recommendation. Among many reasons it remains so extraordinary, are three signaled directly in its title: it is practical rather than theoretical, analytic rather than technical, and it embodies a broader-than-usual conception of utilitarian multivariate methods. Practical Multivariate Analysis connects readily to its audience’s reality. It uses concrete research questions and real data to motivate its content, illustrated by exemplary analyses using R, SAS, SPSS and STATA. It models how complex findings can be made comprehensible to a broader community. It reaches beyond the typical spectrum of multivariate methods. It begins sensibly, discussing how multivariate data can be explored and displayed before complex analysis. Then come chapters on useful extensions to multiple regression analysis. While not usually considered “multivariate,” these latter methods connect an incoming audience to earlier acquired skills and extend them. Then follow the core chapters on “standard” multivariate methods, including canonical correlation, discriminant, principal-components, factor and cluster analyses. All are clearly presented, and then extended by excellent chapters on logistic regression, survival and log-linear analyses, and multilevel modeling, techniques that have proven useful and ubiquitous throughout social-science research.In my view, Practical Multivariate Analysis is an excellent roadmap for conducting such analyses, and a fine model for ensuring that their complex findings can be communicated successfully to others."- John B. Willett, Charles William Eliot Research Professor, Harvard University Graduate School of Education "The Practical Multivariate Analysis is a fun statistical modeling book to read. I enjoyed the rich insights the book has provided, which can only be accumulated through years of experience with the complexity in real data. It covers a large collection of statistical methods and models with a clear focus on application. Always discussing a model or method along with data examples, the book helps readers focus on important perspectives in applying the model, from choice of appropriate methods to interpretation of the results, while it still manages to maintain thetechnique details at a minimal level. Readers with different backgrounds can all benefit from this book. It is valuable for researchers who are interested in analyzing their data with classical statistical models and interpreting the results. It is a good reading for new graduates in statistics who have not had a lot of experience with real data as the book provides many importance guidance in handling real data as well as watch-out advices. It can be used by applied data scientists and serve as a resourceful reference book for experienced consultants."- Xia Wang, University of Cincinnati "The monograph belongs to the series Texts in Statistical Science and presents the sixth upgraded edition of the popular manual. It was first issued in 1984, and from that time won recognition as one of the best textbooks on the applied statistical modeling and analysis...Most of chapters of the first part of the textbook contain such subsections as “Introduction” or “Definition,” “Discussion” or “Examples,” “Summary” and “Problems”...This structure makes the book very reader-friendly written, helping to students and researchers in various fields to understand what for a statistical tool can serve, how to apply it, and to interpret computer outputs. There is not much of mathematical and statistical derivation, neither modern statistical techniques, but plenty of examples oriented to the easy “know-how” practical implementations of the classical multivariate methods."- Stan Lipovetsky, Technometrics, Vol 62"The authors wrote the sixth edition of this book for biomedical scientists, behavioural scientists, and academic researchers, who wish to perform and understand the results of multivariate statistical analyses. The book also describes when to ask for help from a statistical expert on multivariate analysis...The sixth edition has been updated with, in particular, a new chapter on data visualization, a distinction made between exploratory and confirmatory analyses, and a new section on generalized estimating equations. This new edition will enable the book to continue as one of the leading textbooks in the area, particularly for non-statisticians, since it provides a comprehensive, practical, and accessible introduction to multivariate analysis whilst keeping mathematical details to a minimum...The book is an excellent roadmap for multivariate analysis and a fine model for ensuring that complex findings can be successfully communicated in a paper."- Luca Bertolaccini, ISCB News, July 2020 "This book is an excellent resource for students and researchers of all levels. I have used earlier editions repeatedly in data-analysis courses for advanced undergraduates and graduate students in applied fields. The level of mathematical presentation is well matched to such settings. Not only are there excellent examples from biostatistics and public health, but there are also some very good business financial examples. The new chapter on Data Visualization in the new, sixth edition will be especially useful. Overall, the book is exceptionally well written and readable."- Stanley Sclove, University of Illinois at Chicago "Editions of Practical Multivariate Analysis have been the mainstay of my graduate-level service course in applied data-analysis since 1985. It remains an extraordinary book -- packed with excellent examples, clear explanation and fine advice -- and has my highest possible recommendation. Among many reasons it remains so extraordinary, are three signaled directly in its title: it is practical rather than theoretical, analytic rather than technical, and it embodies a broader-than-usual conception of utilitarian multivariate methods. Practical Multivariate Analysis connects readily to its audience’s reality. It uses concrete research questions and real data to motivate its content, illustrated by exemplary analyses using R, SAS, SPSS and STATA. It models how complex findings can be made comprehensible to a broader community. It reaches beyond the typical spectrum of multivariate methods. It begins sensibly, discussing how multivariate data can be explored and displayed before complex analysis. Then come chapters on useful extensions to multiple regression analysis. While not usually considered “multivariate,” these latter methods connect an incoming audience to earlier acquired skills and extend them. Then follow the core chapters on “standard” multivariate methods, including canonical correlation, discriminant, principal-components, factor and cluster analyses. All are clearly presented, and then extended by excellent chapters on logistic regression, survival and log-linear analyses, and multilevel modeling, techniques that have proven useful and ubiquitous throughout social-science research.In my view, Practical Multivariate Analysis is an excellent roadmap for conducting such analyses, and a fine model for ensuring that their complex findings can be communicated successfully to others."- John B. Willett, Charles William Eliot Research Professor, Harvard University Graduate School of Education "The Practical Multivariate Analysis is a fun statistical modeling book to read. I enjoyed the richinsights the book has provided, which can only be accumulated through years of experience withthe complexity in real data. It covers a large collection of statistical methods and models with aclear focus on application. Always discussing a model or method along with data examples, thebook helps readers focus on important perspectives in applying the model, from choice ofappropriate methods to interpretation of the results, while it still manages to maintain thetechnique details at a minimal level.Readers with different backgrounds can all benefit from this book. It is valuable for researcherswho are interested in analyzing their data with classical statistical models and interpreting theresults. It is a good reading for new graduates in statistics who have not had a lot of experiencewith real data as the book provides many importance guidance in handling real data as well aswatch-out advices. It can be used by applied data scientists and serve as a resourceful referencebook for experienced consultants."- Xia Wang, University of Cincinnati "The monograph belongs to the series Texts in Statistical Science and presents the sixth upgraded edition of the popular manual. It was first issued in 1984, and from that time won recognition as one of the best textbooks on the applied statistical modeling and analysis...Most of chapters of the first part of the textbook contain such subsections as “Introduction” or “Definition,” “Discussion” or “Examples,” “Summary” and “Problems”...This structure makes the book very reader-friendly written, helping to students and researchers in various fields to understand what for a statistical tool can serve, how to apply it, and to interpret computer outputs. There is not much of mathematical and statistical derivation, neither modern statistical techniques, but plenty of examples oriented to the easy “know-how” practical implementations of the classical multivariate methods."- Stan Lipovetsky, Technometrics, Vol 62 Table of ContentsPart I: Preparation for Analysis. What is Multivariate Analysis? Characterizing Data for Analysis. Preparing for Data Analysis. Data Visualization. Data Screening and Transformations. Data Visualization. Selecting Appropriate Analyses. Part II: Regression Analysis. Simple Regression and Correlation. Multiple Regression and Correlation. Variable Selection in Regression. Special Regression Topics. Discriminant analysis. Logistic Regression. Regression Analysis with Survival Data. Principal Components Analysis. Factor Analysis. Cluster Analysis. Log-Linear Analysis. Correlated Outcomes Regression.

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Book SynopsisThe second edition of the Handbook of Induction Heating reflects the number of substantial advances that have taken place over the last decade in theory, computer modeling, semi-conductor power supplies, and process technology of induction heating and induction heat treating. This edition continues to be a synthesis of information, discoveries, and technical insights that have been accumulated at Inductoheat Inc. With an emphasis on design and implementation, the newest edition of this seminal guide provides numerous case studies, ready-to-use tables, diagrams, rules-of-thumb, simplified formulas, and graphs for working professionals and students.Trade Review"The 2nd Edition of the Handbook for Induction Heating is equivalent to having 3 world class experts on staff without paying high priced consulting fees. For your seasoned, and probably more importantly, your new and emerging manufacturing and process engineers, this comprehensive guide provides the details your company needs to compete around the world. Significant technical achievements have occurred since 2002 with the last edition. Rudnev, Loveless, and Cook have compiled an indispensable, world class text replete with the basics and advanced concepts of induction heating. The case studies also illustrate and inspire the design and deployment of innovative concepts which transform theory into application. If you are not reading and using this tour de force, it is safe to say that your competitors have read and marked up their copies."—Jon D. Tirpak, PE, FASM; Executive Director, Forging Defense Manufacturing Consortium, and Past President, ASM International (2015 – 2016)"As an automotive plant we are performing several heat treatment processes, among them induction hardening. Rear axle shafts, ring gears, couplers, etc. … all require induction hardening in order to obtain the required material properties like case depth, surface hardness, … . Although we have decades of experience, it is of crucial importance to have -theoretical and practical- technical support from specialists. The Handbook of Induction Heating is an exceptional help and reference work for everyone that is involved in IH. Not only when everything goes fine, but also when you face problems like undesirable or unexplainable results after IH, machine issues, etc. This book has given us the answer to many questions over the years and it will continue to do that. The 2nd edition is even more enhanced, and contains again a wide spectrum of many different issues that belong to the world of the practitioners of IH. One more thing to add: in the seldom event that one of the problems you face is not mentioned in the book, you can easily turn to the authors and ask them your question. This is what we experienced and appreciate enormously."—Mike Bogaerts, Supervisor Materials and Chemical Lab, CNH Industrial, Antwerp, Belgium"Induction heating is used in many applications which include heat treatment, forging, extrusion, rolling, bonding, brazing, sealing, shrink fitting, drying, and bending. A thorough knowledge of the process enables one to optimize its use in ever-increasing number of applications. This handbook assimilates the broad experience of the authors to accomplish this need." — Tirupathi R. Chandrupatla, Rowan University, New Jersey, USA"A very comprehensive, must-have textbook that heat treatment engineers should definitely read. You can learn every aspect of induction hardening and become an expert starting from scratch."—Tusaş Motor Sanayii, Ali Fırat Dinler, Turkey"The 2nd Edition of the Handbook for Induction Heating is equivalent to having 3 world class experts on staff without paying high priced consulting fees. For your seasoned, and probably more importantly, your new and emerging manufacturing and process engineers, this comprehensive guide provides the details your company needs to compete around the world. Significant technical achievements have occurred since 2002 with the last edition. Rudnev, Loveless, and Cook have compiled an indispensable, world class text replete with the basics and advanced concepts of induction heating. The case studies also illustrate and inspire the design and deployment of innovative concepts which transform theory into application. If you are not reading and using this tour de force, it is safe to say that your competitors have read and marked up their copies."—Jon D. Tirpak, PE, FASM; Executive Director, Forging Defense Manufacturing Consortium, and Past President, ASM International (2015 – 2016)"As an automotive plant we are performing several heat treatment processes, among them induction hardening. Rear axle shafts, ring gears, couplers, etc. … all require induction hardening in order to obtain the required material properties like case depth, surface hardness, … . Although we have decades of experience, it is of crucial importance to have -theoretical and practical- technical support from specialists. The Handbook of Induction Heating is an exceptional help and reference work for everyone that is involved in IH. Not only when everything goes fine, but also when you face problems like undesirable or unexplainable results after IH, machine issues, etc. This book has given us the answer to many questions over the years and it will continue to do that. The 2nd edition is even more enhanced, and contains again a wide spectrum of many different issues that belong to the world of the practitioners of IH. One more thing to add: in the seldom event that one of the problems you face is not mentioned in the book, you can easily turn to the authors and ask them your question. This is what we experienced and appreciate enormously."—Mike Bogaerts, Supervisor Materials and Chemical Lab, CNH Industrial, Antwerp, Belgium"Induction heating is used in many applications which include heat treatment, forging, extrusion, rolling, bonding, brazing, sealing, shrink fitting, drying, and bending. A thorough knowledge of the process enables one to optimize its use in ever-increasing number of applications. This handbook assimilates the broad experience of the authors to accomplish this need." — Tirupathi R. Chandrupatla, Rowan University, New Jersey, USA"A very comprehensive, must-have textbook that heat treatment engineers should definitely read. You can learn every aspect of induction hardening and become an expert starting from scratch."—Tusaş Motor Sanayii, Ali Fırat Dinler, TurkeyTable of ContentsIntroduction. Industrial Applications of Induction Heating. Theoretical Background. Heat Treatment by Induction. Joining Applications. Induction Mass Heating. Power Supplies for Modern Induction Heating. Epilogue. Appendix A. References. Index.

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Book SynopsisTough Test Questions? Missed Lectures? Not Enough Time? Textbook too Pricey?Fortunately, there's Schaum's. This all-in-one-package includes more than 650 fully-solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand.Schaumâs Outline of Geometry, Sixth Edition fTable of Contents 1. Fundamentals of Algebra: Laws and Operations2. Fundamentals of Algebra: Equations and Formulas3. Lines, Angles, and Triangles4. Methods of Proof5. Congruent Triangles6. Parallel Lines, Distances, and Angle Sums7. Parallelograms, Trapezoids, Medians, and Midpoints8. Circles9. Similarity10. Areas11. Regular Polygons and the Circle12. Locus13. Inequalities and Indirect Reasoning14. Improvement of Reasoning15. Constructions16. Proofs of Important Theorems17. Transformational Geometry 18. Conics

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Book SynopsisThis step-by-step approach helps you learn algebra quickly and easily!For many studentsâwhether they're kids in middle school or adults returning to collegeâalgebra is a difficult subject that only gets tougher as more concepts are learned. That's why Easy Algebra Step-by-Step, Third Edition is so effective at helping you succeed where other, drill-heavy guides fail. Using an original, step-by-step approach, this write-in workbook gives you a solid foundation in the basicsâthe fastest, easiest way to learn algebra.You'll learn essential concepts first, allowing you to grasp the subject almost immediately. You'll then gradually progress to more challenging skills, learning how to solve practical problems more easily with the help of clear, step-by-step instructions. Learning the key concepts in order (e.g., learning rational/irrational numbers before roots and radicals, exponents, and so on) ensures that you'll get a soli

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Book Synopsis Considered a classic by many, A First Course in Abstract Algebra is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialised work by emphasising an understanding of the nature of algebraic structures.Table of Contents 0. Sets and Relations. I. GROUPS AND SUBGROUPS. 1. Introduction and Examples. 2. Binary Operations. 3. Isomorphic Binary Structures. 4. Groups. 5. Subgroups. 6. Cyclic Groups. 7. Generators and Cayley Digraphs. I. PERMUTATIONS, COSETS, AND DIRECT PRODUCTS. 8. Groups of Permutations. 9. Orbits, Cycles, and the Alternating Groups. 10. Cosets and the Theorem of Lagrange. 11. Direct Products and Finitely Generated Abelian Groups. 12. Plane Isometries. III. HOMOMORPHISMS AND FACTOR GROUPS. 13. Homomorphisms. 14. Factor Groups. 15. Factor-Group Computations and Simple Groups. 16. Group Action on a Set. 17. Applications of G-Sets to Counting. IV. RINGS AND FIELDS. 18. Rings and Fields. 19. Integral Domains. 20. Fermat's and Euler's Theorems. 21. The Field of Quotients of an Integral Domain. 22. Rings of Polynomials. 23. Factorization of Polynomials over a Field. 24. Noncommutative Examples. 25. Ordered Rings and Fields. V. IDEALS AND FACTOR RINGS. 26. Homomorphisms and Factor Rings. 27. Prime and Maximal Ideas. 28. Gröbner Bases for Ideals. VI. EXTENSION FIELDS. 29. Introduction to Extension Fields. 30. Vector Spaces. 31. Algebraic Extensions. 32. Geometric Constructions. 33. Finite Fields. VII. ADVANCED GROUP THEORY. 34. Isomorphism Theorems. 35. Series of Groups. 36. Sylow Theorems. 37. Applications of the Sylow Theory. 38. Free Abelian Groups. 39. Free Groups. 40. Group Presentations. VIII.. AUTOMORPHISMS AND GALOIS THEORY. 41. Automorphisms of Fields. 42. The Isomorphism Extension Theorem. 43. Splitting Fields. 44. Separable Extensions. 45. Totally Inseparable Extensions. 46. Galois Theory. 47. Illustrations of Galois Theory. 48. Cyclotomic Extensions. 49. Insolvability of the Quintic. Appendix: Matrix Algebra. Notations. Index.

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Book SynopsisMark Dugopolski was born in Menominee, Michigan. After receiving a BS from Michigan State University, he taught high school in Illinois for four years. He received an MS in mathematics from Northern Illinois University at DeKalb. He then received a PhD in the area of topology and an MS in statistics from the University of Illinois at ChampaignUrbana. Mark taught mathematics at Southeastern Louisiana University in Hammond for twenty-five years and now holds the rank of Professor Emeritus of Mathematics. He has been writing textbooks since 1988. He is married and has two daughters. In his spare time he enjoys tennis, jogging, bicycling, fishing, kayaking, gardening, bridge, and motorcycling.Table of ContentsP. Prerequisites P.1 Real Numbers and Their Properties P.2 Integral Exponents and Scientific Notation P.3 Rational Exponents and Radicals P.4 Polynomials P.5 Factoring Polynomials P.6 Rational Expressions P.7 Complex Numbers 1. Equations, Inequalities, and Modeling 1.1 Linear, Rational, and Absolute Value Equations 1.2 Constructing Models to Solve Problems 1.3 Equations and Graphs in Two Variables 1.4 Linear Equations in Two Variables 1.5 Quadratic Equations 1.6 Miscellaneous Equations 1.7 Linear and Absolute Value Inequalities 2. Functions and Graphs 2.1 Functions 2.2 Graphs of Relations and Functions 2.3 Families of Functions, Transformations, and Symmetry 2.4 Operations with Functions 2.5 Inverse Functions 2.6 Constructing Functions with Variation 3. Polynomial and Rational Functions 3.1 Quadratic Functions and Inequalities 3.2 Zeros of Polynomial Functions 3.3 The Theory of Equations 3.4 Graphs of Polynomial Functions 3.5 Rational Functions and Inequalities 4. Exponential and Logarithmic Functions 4.1 Exponential Functions and Their Applications 4.2 Logarithmic Functions and Their Applications 4.3 Rules of Logarithms 4.4 More Equations and Applications 5. Systems of Equations and Inequalities 5.1 Systems of Linear Equations in Two Variables 5.2 Systems of Linear Equations in Three Variables 5.3 Nonlinear Systems of Equations 5.4 Partial Fractions 5.5 Inequalities and Systems of Inequalities in Two Variables 5.6 The Linear Programming Model 6. Matrices and Determinants 6.1 Solving Linear Systems Using Matrices 6.2 Operations with Matrices 6.3 Multiplication of Matrices 6.4 Inverses of Matrices 6.5 Solution of Linear Systems in Two Variables Using Determinants 6.6 Solution of Linear Systems in Three Variables Using Determinants 7. The Conic Sections 7.1 The Parabola 7.2 The Ellipse and the Circle 7.3 The Hyperbola 8. Sequences, Series, and Probability 8.1 Sequences and Arithmetic Sequences 8.2 Series and Arithmetic Series 8.3 Geometric Sequences and Series 8.4 Counting and Permutations 8.5 Combinations, Labeling, and the Binomial Theorem 8.6 Probability 8.7 Mathematical Induction

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Book Synopsis

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Book Synopsis

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