Mathematical modelling Books

Book SynopsisLearn to master basic programming tasks from scratch with real-life, scientifically relevant examples and solutions drawn from both science and engineering. Students and researchers at all levels are increasingly turning to the powerful Python programming language as an alternative to commercial packages and this fast-paced introduction moves from the basics to advanced concepts in one complete volume, enabling readers to gain proficiency quickly. Beginning with general programming concepts such as loops and functions within the core Python 3 language, and moving on to the NumPy, SciPy and Matplotlib libraries for numerical programming and data visualization, this textbook also discusses the use of Jupyter Notebooks to build rich-media, shareable documents for scientific analysis. The second edition features a new chapter on data analysis with the pandas library and comprehensive updates, and new exercises and examples. A final chapter introduces more advanced topics such as floating-pTable of ContentsAcknowledgments; 1. Introduction; 2. The core Python language I; 3. Interlude: simple plots and charts; 4. The core Python language II; 5. IPython and Jupyter Notebook; 6. NumPy; 7. Matplotlib; 8. SciPy; 9. Data analysis with pandas; 10. General scientific programming; Appendix A. Solutions; Appendix B. Differences between Python versions 2 and 3; Appendix C. SciPy's odeint ordinary differential equation solver; Glossary; Index.

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Book SynopsisNumerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them ''in action'' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.Trade Review'Computational general relativity has now become a central tool for the exploration of the astrophysical universe, and gravitational-wave astronomy would not be possible without it. A burgeoning or seasoned astrophysicist who wishes to be up to date must therefore acquire an awareness of the field's methods and main achievements. But where to begin? With this book! Baumgarte and Shapiro are leading experts (indeed, founding experts) of this field, and with their trademark lucid and engaging prose, they take us gently by the hand on a comprehensive guided tour. Mysterious notions (lapse, shift, extrinsic curvature, constraint equations) are introduced seamlessly, and the book features a gallery of the field's most important results to date. A superb achievement for the great benefit of the scientific community.' Eric Poisson, University of Guelph; author of A Relativist's Toolkit'Numerical relativity well deserves its reputation as a subject of great beauty yet prodigious conceptual difficulty and daunting technical complexity. This outstanding text, by two leading practitioners of the field, is a wonderful Rosetta Stone for those seeking an efficient path toward a working knowledge of the subject. For me it will serve as an essential reference. I'm sorry only that it was not available sooner.' Robert Eisenstein, Massachusetts Institute of Technology'This is an excellent book explaining the general relativistic two-body problem and its numerical treatment in a highly pedagogical manner to a broad scientific audience. Besides the main topic, readers will also gain some unexpected insight and new viewpoints on numerous wider aspects of Einstein's theory.' Ulrich Sperhake, University of Cambridge'Black holes and gravitational waves are, thanks to new observations, fast-advancing frontiers of astronomy that attract wide interest. Their implications are best addressed by powerful computers, so this text, by two acknowledged world experts, is especially welcome and timely.' Martin Rees, Astronomer Royal; author of Gravity's Fatal AttractionTable of ContentsPreface; 1. Newton's and Einstein's gravity; 2. Foliations of spacetime: constraint and evolution equations; 3. Solving the constraint equations; 4 Solving the evolution equations; 5. Numerical simulations of black-hole binaries; Epilogue; Appendix A. A brief review of tensor properties; Appendix B. A brief introduction to some numerical techniques; Appendix C. A very brief introduction to matter sources; Appendix D. A summary of important results; Appendix E. Answers to selected problems; References; Index.

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Book SynopsisThe study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors'' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.Trade Review'… a stylish, well-written and up to date introduction to complex variable methods for undergraduate (or early graduate) students in applied mathematics, science and engineering … I thoroughly enjoyed reading this book and warmly commend it to anyone seeking a brisk, well-organised account of complex variables with a practical focus on applications and calculational aspects.' Nick Lord, The Mathematical GazetteTable of Contents1. Complex numbers and elementary functions; 2. Analytic functions and integration; 3. Sequences, series and singularities of complex functions; 4. Residue calculus and applications of contour integration; 5. Conformal mappings and applications; Appendix. Answers to selected odd-numbered exercises; References; Index.

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Book SynopsisProvides an accessible foundation to Bayesian analysis using real world models This book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Each chapter comprises a description of the problem, the corresponding model, the computational method, results and inferences as well as the issues that arise in the implementation of these approaches. Case Studies in Bayesian Statistical Modelling and Analysis: Illustrates how to do Bayesian analysis in a clear and concise manner using real-world problems. Each chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods. Features approaches that can be used in a wide area of application, such as, health, the environment, genetics, information science, medicine, biology, industry and remote sensing.Trade Review “As such, this book can serve as a handy reference for proficient statisticians and programmers.” (The Quarterly Review of Biology, 1 October 2015) Table of Contents Preface xvii List of contributors xix 1 Introduction 1Clair L. Alston, Margaret Donald, Kerrie L. Mengersen and Anthony N. Pettitt 1.1 Introduction 1 1.2 Overview 1 1.3 Further reading 8 1.3.1 Bayesian theory and methodology 8 1.3.2 Bayesian methodology 10 1.3.3 Bayesian computation 10 1.3.4 Bayesian software 11 1.3.5 Applications 13 References 13 2 Introduction to MCMC 17Anthony N. Pettitt and Candice M. Hincksman 2.1 Introduction 17 2.2 Gibbs sampling 18 2.2.1 Example: Bivariate normal 18 2.2.2 Example: Change-point model 19 2.3 Metropolis–Hastings algorithms 19 2.3.1 Example: Component-wise MH or MH within Gibbs 20 2.3.2 Extensions to basic MCMC 21 2.3.3 Adaptive MCMC 22 2.3.4 Doubly intractable problems 22 2.4 Approximate Bayesian computation 24 2.5 Reversible jump MCMC 25 2.6 MCMC for some further applications 26 References 27 3 Priors: Silent or active partners of Bayesian inference? 30Samantha Low Choy 3.1 Priors in the very beginning 30 3.1.1 Priors as a basis for learning 32 3.1.2 Priors and philosophy 32 3.1.3 Prior chronology 33 3.1.4 Pooling prior information 34 3.2 Methodology I: Priors defined by mathematical criteria 35 3.2.1 Conjugate priors 35 3.2.2 Impropriety and hierarchical priors 37 3.2.3 Zellner’s g-prior for regression models 37 3.2.4 Objective priors 38 3.3 Methodology II: Modelling informative priors 40 3.3.1 Informative modelling approaches 40 3.3.2 Elicitation of distributions 42 3.4 Case studies 44 3.4.1 Normal likelihood: Time to submit research dissertations 44 3.4.2 Binomial likelihood: Surveillance for exotic plant pests 47 3.4.3 Mixture model likelihood: Bioregionalization 50 3.4.4 Logistic regression likelihood: Mapping species distribution via habitat models 53 3.5 Discussion 57 3.5.1 Limitations 57 3.5.2 Finding out about the problem 58 3.5.3 Prior formulation 59 3.5.4 Communication 60 3.5.5 Conclusion 61 Acknowledgements 61 References 61 4 Bayesian analysis of the normal linear regression model 66Christopher M. Strickland and Clair L. Alston 4.1 Introduction 66 4.2 Case studies 67 4.2.1 Case study 1: Boston housing data set 67 4.2.2 Case study 2: Production of cars and station wagons 67 4.3 Matrix notation and the likelihood 67 4.4 Posterior inference 68 4.4.1 Natural conjugate prior 69 4.4.2 Alternative prior specifications 73 4.4.3 Generalizations of the normal linear model 74 4.4.4 Variable selection 78 4.5 Analysis 81 4.5.1 Case study 1: Boston housing data set 81 4.5.2 Case study 2: Car production data set 85 References 88 5 Adapting ICU mortality models for local data: A Bayesian approach 90Petra L. Graham, Kerrie L. Mengersen and David A. Cook 5.1 Introduction 90 5.2 Case study: Updating a known risk-adjustment model for local use 91 5.3 Models and methods 92 5.4 Data analysis and results 96 5.4.1 Updating using the training data 96 5.4.2 Updating the model yearly 98 5.5 Discussion 100 References 101 6 A Bayesian regression model with variable selection for genome-wide association studies 103Carla Chen, Kerrie L. Mengersen, Katja Ickstadt and Jonathan M. Keith 6.1 Introduction 103 6.2 Case study: Case–control of Type 1 diabetes 104 6.3 Case study: GENICA 105 6.4 Models and methods 105 6.4.1 Main effect models 105 6.4.2 Main effects and interactions 108 6.5 Data analysis and results 109 6.5.1 WTCCC TID 109 6.5.2 GENICA 110 6.6 Discussion 112 Acknowledgements 115 References 115 6.A Appendix: SNP IDs 117 7 Bayesian meta-analysis 118Jegar O. Pitchforth and Kerrie L. Mengersen 7.1 Introduction 118 7.2 Case study 1: Association between red meat consumption and breast cancer 119 7.2.1 Background 119 7.2.2 Meta-analysis models 121 7.2.3 Computation 125 7.2.4 Results 125 7.2.5 Discussion 129 7.3 Case study 2: Trends in fish growth rate and size 130 7.3.1 Background 130 7.3.2 Meta-analysis models 131 7.3.3 Computation 134 7.3.4 Results 134 7.3.5 Discussion 135 Acknowledgements 137 References 138 8 Bayesian mixed effects models 141Clair L. Alston, Christopher M. Strickland, Kerrie L. Mengersen and Graham E. Gardner 8.1 Introduction 141 8.2 Case studies 142 8.2.1 Case study 1: Hot carcase weight of sheep carcases 142 8.2.2 Case study 2: Growth of primary school girls 142 8.3 Models and methods 146 8.3.1 Model for Case study 1 147 8.3.2 Model for Case study 2 148 8.3.3 MCMC estimation 149 8.4 Data analysis and results 150 8.5 Discussion 158 References 158 9 Ordering of hierarchies in hierarchical models: Bone mineral density estimation 159Cathal D. Walsh and Kerrie L. Mengersen 9.1 Introduction 159 9.2 Case study 160 9.2.1 Measurement of bone mineral density 160 9.3 Models 161 9.3.1 Hierarchical model 162 9.3.2 Model H1 163 9.3.3 Model H2 163 9.4 Data analysis and results 164 9.4.1 Model H1 164 9.4.2 Model H2 165 9.4.3 Implication of ordering 166 9.4.4 Simulation study 166 9.4.5 Study design 166 9.4.6 Simulation study results 167 9.5 Discussion 168 References 168 9.A Appendix: Likelihoods 170 10 Bayesian Weibull survival model for gene expression data 171Sri Astuti Thamrin, James M. McGree and Kerrie L. Mengersen 10.1 Introduction 171 10.2 Survival analysis 172 10.3 Bayesian inference for the Weibull survival model 174 10.3.1 Weibull model without covariates 174 10.3.2 Weibull model with covariates 175 10.3.3 Model evaluation and comparison 176 10.4 Case study 178 10.4.1 Weibull model without covariates 178 10.4.2 Weibull survival model with covariates 180 10.4.3 Model evaluation and comparison 182 10.5 Discussion 182 References 183 11 Bayesian change point detection in monitoring clinical outcomes 186Hassan Assareh, Ian Smith and Kerrie L. Mengersen 11.1 Introduction 186 11.2 Case study: Monitoring intensive care unit outcomes 187 11.3 Risk-adjusted control charts 187 11.4 Change point model 188 11.5 Evaluation 189 11.6 Performance analysis 190 11.7 Comparison of Bayesian estimator with other methods 194 11.8 Conclusion 194 References 195 12 Bayesian splines 197Samuel Clifford and Samantha Low Choy 12.1 Introduction 197 12.2 Models and methods 197 12.2.1 Splines and linear models 197 12.2.2 Link functions 198 12.2.3 Bayesian splines 198 12.2.4 Markov chain Monte Carlo 204 12.2.5 Model choice 206 12.2.6 Posterior diagnostics 207 12.3 Case studies 207 12.3.1 Data 207 12.3.2 Analysis 208 12.4 Conclusion 216 12.4.1 Discussion 216 12.4.2 Extensions 217 12.4.3 Summary 218 References 218 13 Disease mapping using Bayesian hierarchical models 221Arul Earnest, Susanna M. Cramb and Nicole M. White 13.1 Introduction 221 13.2 Case studies 224 13.2.1 Case study 1: Spatio-temporal model examining the incidence of birth defects 224 13.2.2 Case study 2: Relative survival model examining survival from breast cancer 225 13.3 Models and methods 225 13.3.1 Case study 1 225 13.3.2 Case study 2 229 13.4 Data analysis and results 230 13.4.1 Case study 1 230 13.4.2 Case study 2 231 13.5 Discussion 234 References 237 14 Moisture, crops and salination: An analysis of a three-dimensional agricultural data set 240Margaret Donald, Clair L. Alston, Rick Young and Kerrie L. Mengersen 14.1 Introduction 240 14.2 Case study 241 14.2.1 Data 242 14.2.2 Aim of the analysis 242 14.3 Review 243 14.3.1 General methodology 243 14.3.2 Computations 243 14.4 Case study modelling 243 14.4.1 Modelling framework 243 14.5 Model implementation: Coding considerations 246 14.5.1 Neighbourhood matrices and CAR models 246 14.5.2 Design matrices vs indexing 246 14.6 Case study results 247 14.7 Conclusions 249 References 250 15 A Bayesian approach to multivariate state space modelling: A study of a Fama–French asset-pricing model with time-varying regressors 252Christopher M. Strickland and Philip Gharghori 15.1 Introduction 252 15.2 Case study: Asset pricing in financial markets 253 15.2.1 Data 254 15.3 Time-varying Fama–French model 254 15.3.1 Specific models under consideration 255 15.4 Bayesian estimation 256 15.4.1 Gibbs sampler 256 15.4.2 Sampling Σε 257 15.4.3 Sampling β 1:n 257 15.4.4 Sampling Σ α 259 15.4.5 Likelihood calculation 260 15.5 Analysis 261 15.5.1 Prior elicitation 261 15.5.2 Estimation output 261 15.6 Conclusion 264 References 265 16 Bayesian mixture models: When the thing you need to know is the thing you cannot measure 267Clair L. Alston, Kerrie L. Mengersen and Graham E. Gardner 16.1 Introduction 267 16.2 Case study: CT scan images of sheep 268 16.3 Models and methods 270 16.3.1 Bayesian mixture models 270 16.3.2 Parameter estimation using the Gibbs sampler 273 16.3.3 Extending the model to incorporate spatial information 274 16.4 Data analysis and results 276 16.4.1 Normal Bayesian mixture model 276 16.4.2 Spatial mixture model 278 16.4.3 Carcase volume calculation 281 16.5 Discussion 284 References 284 17 Latent class models in medicine 287Margaret Rolfe, Nicole M. White and Carla Chen 17.1 Introduction 287 17.2 Case studies 288 17.2.1 Case study 1: Parkinson’s disease 288 17.2.2 Case study 2: Cognition in breast cancer 288 17.3 Models and methods 289 17.3.1 Finite mixture models 290 17.3.2 Trajectory mixture models 292 17.3.3 Goodness of fit 296 17.3.4 Label switching 297 17.3.5 Model computation 298 17.4 Data analysis and results 300 17.4.1 Case study 1: Phenotype identification in PD 300 17.4.2 Case study 2: Trajectory groups for verbal memory 302 17.5 Discussion 306 References 307 18 Hidden Markov models for complex stochastic processes: A case study in electrophysiology 310Nicole M. White, Helen Johnson, Peter Silburn, Judith Rousseau and Kerrie L. Mengersen 18.1 Introduction 310 18.2 Case study: Spike identification and sorting of extracellular recordings 311 18.3 Models and methods 312 18.3.1 What is an HMM? 312 18.3.2 Modelling a single AP: Application of a simple HMM 313 18.3.3 Multiple neurons: An application of a factorial HMM 315 18.3.4 Model estimation and inference 317 18.4 Data analysis and results 320 18.4.1 Simulation study 320 18.4.2 Case study: Extracellular recordings collected during deep brain stimulation 323 18.5 Discussion 326 References 327 19 Bayesian classification and regression trees 330Rebecca A. O’Leary, Samantha Low Choy, Wenbiao Hu and Kerrie L. Mengersen 19.1 Introduction 330 19.2 Case studies 332 19.2.1 Case study 1: Kyphosis 332 19.2.2 Case study 2: Cryptosporidium 332 19.3 Models and methods 334 19.3.1 CARTs 334 19.3.2 Bayesian CARTs 335 19.4 Computation 337 19.4.1 Building the BCART model – stochastic search 337 19.4.2 Model diagnostics and identifying good trees 339 19.5 Case studies – results 341 19.5.1 Case study 1: Kyphosis 341 19.5.2 Case study 2: Cryptosporidium 343 19.6 Discussion 345 References 346 20 Tangled webs: Using Bayesian networks in the fight against infection 348Mary Waterhouse and Sandra Johnson 20.1 Introduction to Bayesian network modelling 348 20.1.1 Building a BN 349 20.2 Introduction to case study 351 20.3 Model 352 20.4 Methods 354 20.5 Results 355 20.6 Discussion 357 References 359 21 Implementing adaptive dose finding studies using sequential Monte Carlo 361James M. McGree, Christopher C. Drovandi and Anthony N. Pettitt 21.1 Introduction 361 21.2 Model and priors 363 21.3 SMC for dose finding studies 364 21.3.1 Importance sampling 364 21.3.2 SMC 365 21.3.3 Dose selection procedure 367 21.4 Example 369 21.5 Discussion 371 References 372 21.A Appendix: Extra example 373 22 Likelihood-free inference for transmission rates of nosocomial pathogens 374Christopher C. Drovandi and Anthony N. Pettitt 22.1 Introduction 374 22.2 Case study: Estimating transmission rates of nosocomial pathogens 375 22.2.1 Background 375 22.2.2 Data 376 22.2.3 Objective 376 22.3 Models and methods 376 22.3.1 Models 376 22.3.2 Computing the likelihood 379 22.3.3 Model simulation 380 22.3.4 ABC 381 22.3.5 ABC algorithms 382 22.4 Data analysis and results 384 22.5 Discussion 385 References 386 23 Variational Bayesian inference for mixture models 388Clare A. McGrory 23.1 Introduction 388 23.2 Case study: Computed tomography (CT) scanning of a loin portion of a pork carcase 390 23.3 Models and methods 392 23.4 Data analysis and results 397 23.5 Discussion 399 References 399 23.A Appendix: Form of the variational posterior for a mixture of multivariate normal densities 401 24 Issues in designing hybrid algorithms 403Jeong E. Lee, Kerrie L. Mengersen and Christian P. Robert 24.1 Introduction 403 24.2 Algorithms and hybrid approaches 406 24.2.1 Particle system in the MCMC context 407 24.2.2 MALA 407 24.2.3 DRA 408 24.2.4 PS 409 24.2.5 Population Monte Carlo (PMC) algorithm 410 24.3 Illustration of hybrid algorithms 412 24.3.1 Simulated data set 412 24.3.2 Application: Aerosol particle size 415 24.4 Discussion 417 References 418 25 A Python package for Bayesian estimation using Markov chain Monte Carlo 421Christopher M. Strickland, Robert J. Denham, Clair L. Alston and Kerrie L. Mengersen 25.1 Introduction 421 25.2 Bayesian analysis 423 25.2.1 MCMC methods and implementation 424 25.2.2 Normal linear Bayesian regression model 433 25.3 Empirical illustrations 437 25.3.1 Example 1: Linear regression model – variable selection and estimation 438 25.3.2 Example 2: Loglinear model 441 25.3.3 Example 3: First-order autoregressive regression 446 25.4 Using PyMCMC efficiently 451 25.4.1 Compiling code in Windows 455 25.5 PyMCMC interacting with R 457 25.6 Conclusions 458 25.7 Obtaining PyMCMC 459 References 459 Index 461

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Book SynopsisChapter 1: Introduction: The nature and structure of the inventory problem.- Chapter 2: Review of the literature.- Chapter 3: Methodology.- Chapter 4: Analysis of inventory behaviour of OECD countries.- Chapter 5: Stability of macroeconomic variables.- Chapter 6: Inventory developments in individual countries.- Chapter 7: Summary and conclusions.Table of ContentsChapter 1: Introduction: The nature and structure of the inventory problem.- Chapter 2: Review of the literature.- Chapter 3: Methodology.- Chapter 4: Analysis of inventory behaviour of OECD countries.- Chapter 5: Stability of macroeconomic variables.- Chapter 6: Inventory developments in individual countries.- Chapter 7: Summary and conclusions.

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Book SynopsisThis book focuses on a development of optimal, flexible, and efficient models and algorithms for cell formation in group technology. Its main aim is to provide a reliable tool that can be used by managers and engineers to design manufacturing cells based on their own preferences and constraints imposed by a particular manufacturing system.Trade Review“The book under review is a very good source … continuing the long term passion of Panos Pardalos and his collaborators in exact solution of difficult problems … . It also adds a very valuable contribution to the body of knowledge of the cell formation problem that can be used in both teaching and research including in bioinformatics.” (Boris Mirkin, Optimization Letters, 2015)Table of Contents1. The problem of cell formation.- 2. ​The p-Median problem.- 3. Application of the PMP to cell formation in group technology.- 4. The minimum multicut problem and an exact model for cell formation.- 5. Multiobjective nature of cell formation.- 6. Pattern-based heuristic for the cell formation problem in group technology.- 7. Branch-and-bound algorithm for bi-criterion cell formation problems.- 8. Summary and conclusions.- A. Solutions to the 35 CF instances from [71].- Index.- References.

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Book SynopsisStudies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas.Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics.A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to traditional local systems represented by partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives to as well as bridges to existing local continuum and discrete models.The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on existing discrete models and local continuum models and the connections between them.

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Book SynopsisDynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks.This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

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Book SynopsisMathematical models are very much in the news now, as they are used to make decisions about our response to such vital areas as COVID-19 and climate change. Frequently, they are blamed for a series of dubious decisions, creating much concern amongst the general public. However, without mathematical models, we would have none of the modern technology that we take for granted, nor would we have modern health care, be able to forecast the climate, cook a potato, have electricity to power our home, or go into space.By explaining technical mathematical concepts in a way that everyone can understand and appreciate, Climate, Chaos and COVID: How Mathematical Models Describe the Universe sets the record straight and lifts the lid off the mystery of mathematical models. It shows why they work, how good they can be, the advantages and disadvantages of using them and how they make the modern world possible. The readers will be able to see the impact that the use of these models has on their lives, and will be able to appreciate both their power and their limitations.The book includes a very large number of both short and long case studies, many of which are taken directly from the author's own experiences of working as a mathematical modeller in academia, in industry, and between the two. These include COVID-19 and climate and how maths saves the whales, powers our home, gives us the material we need to live, and takes us into space.

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Book SynopsisLinear systems have all the necessary elements (modeling, identification, analysis and control), from an educational point of view, to help us understand the discipline of automation and apply it efficiently. This book is progressive and organized in such a way that different levels of readership are possible. It is addressed both to beginners and those with a good understanding of automation wishing to enhance their knowledge on the subject. The theory is rigorously developed and illustrated by numerous examples which can be reproduced with the help of appropriate computation software. 60 exercises and their solutions are included to enable the readers to test and enhance their knowledge.Table of ContentsPreface xi Introduction xvii Chapter 1. Reminders and General Points 1 1.1. Lines 1 1.2. Adaptation and stationary waves 4 1.3. Smith chart 6 1.4. Power in a line 6 1.5. Line sections 7 1.6. Lines with losses 9 Chapter 2. Measurements in HF 11 2.1. Material 11 2.2. The power bench11 2.3. Measurements on the network analyzer 14 Chapter 3. Resonant Cavities 25 3.1. Resonance 25 3.2. Coaxial cavities 28 3.3. Quarter-wave cavities 29 Chapter 4. Fabrication and Tuning of Cavities 47 4.1. Standard structures 47 4.2. Materials 53 4.3. Assembly 56 4.4. Temperature stability 58 4.5. Cavity tuning 70 Chapter 5. The Band-pass Filter 83 5.1. The band-pass function 83 5.2. Calculation of a Tchebycheff band-pass 85 5.3. Technologies 87 Chapter 6. The Combline Filter 97 6.1. Architecture 97 6.2. Dimension calculations. Dishal’s Method 105 6.3. Tuning of filters 114 Chapter 7. Channel Multiplexing 129 7.1. Definitions 129 7.2. The duplexer 129 7.3. The combiner 140 Chapter 8. Auxiliary Devices 157 8.1. Introduction 157 8.2. Circulators 157 8.3. The antenna alarms 165 8.4. Loads and attenuators 170 8.5. Reception amplifiers 177 8.6. The impedance adaptor 186 8.7. The 2nd harmonic rejecter 186 Chapter 9. Directive Couplers 189 9.1. Introduction 189 9.2. Technologies 191 9.3. The hybrid transformer 194 9.4. The 180° hybrid ring 196 9.5. The wireline 198 9.6. The “groundless” coupler 199 9.7. The “catnose” coupler 201 9.8. Discrete-elements coupler 202 9.9. Numerical data 204 9.10. Applications 210 Chapter 10. Helical Resonators 213 10.1. Introduction 213 10.2. Functioning 214 10.3. Structures 215 10.4. Tapping and coupling 219 10.5. Quality coefficient 220 10.6. Set-up rules 223 10.7. Applications 224 Chapter 11. Multicouplers 225 11.1. Transmitter multicouplers (TX) 225 11.2. Receiver multicouplers (RX) 235 11.3. TX/RX multicouplers 236 11.4. TMA 240 11.5. Power and intermodulations 243 11.6. Multiband coupling 254 Chapter 12. Utilities 257 12.1. BASIC programs 257 12.2. Varia 264 Chapter 13. Various Questions and Exploratory Ways 271 13.1. The coupler without intrinsic loss 271 13.2. Infinite rejection band-pass 275 13.3. Helix TX multicoupler 276 13.4. Conclusion 278 Bibliography 281 Index 283

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Book SynopsisThis self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.Trade ReviewFrom the reviews: It explains its chosen topics clearly and simply, not including extraneous material, and is written at a level that can be understood and appreciated by undergraduate students. Indeed, the level of writing is superb in its clarity and elegance... Just as useful as the writing style are the appendices and hints. Not only does Britton give elementary presentations of some basic mathematical techniques (difference equations, ODEs and PDEs) he also gives extensive hints for the exercises, bordering on complete solutions in some cases. This is a resource that will surely prove extremely useful for all teachers of such a course...there is no denying that Essential Mathematical Biology is superbly designed for the purpose it serves, and will, I am sure, become a popular text book across the world. UK Nonlinear News Britton explains how difference and differential equations have been used to formulate theory and description in biology, but at a level accessible to undergraduate mathematics, physics or engineering majors. His very readable style achieves clear and largely jargon-free explanations with no sacrifice of mathematical rigour.....Clearly intended to be read and used as a course textbook, another attractive feature of this volume is the inclusion of interesting and relevant exercises after each subchapter section, together with an appendix of hints to help students work and understand them. Other appendixes efficiently review the mathematical techniques and concepts that are basic to the applications presented in the chapters....I believe that Essential Mathematical Biology will enrich the personal library of any scholar interested in applied differential equations. The Quarterly Review of Biology, Volume 79, No. 2 "This excellent monograph provides a very readable introduction to the most important aspects of mathematical biology. … The book contains numerous exercises, with hints for the solutions, a guide for further studies, and interesting historical comments. An index helps in finding the many concepts and equations introduced in the monograph. This is a most welcome addition to the literature." (Jean Mawhin, Bulletin of the Belgian Mathematical Society, Vol. 12 (1), 2005) "This book as a textbook covers a diversity of topics from mathematical biology. Its content is best summarized by the title of its eight substantial Chapters. … It poses questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. … includes many exercises as well as detailed solutions for them. … a good introduction for those beginners that are interested in the fast growing field of mathematical biology." (Lan-Sun Chen, Mathematical Reviews, 2003m) "Each chapter of this textbook provides a brief introduction into an important area of mathematical biology. … In addition, there are four appendices, comprising about one fourth of the whole text, which summarize important techniques … . The book is aimed at the undergraduate level … . Many exercises, together with hints for their solution, complement this text which will be useful as a first introduction." (R. Bürger, Monatshefte für Mathematik, Vol. 143 (4), 2004) "In brevity and simplicity lies the great strength of this book. It explains its chosen topics clearly and simply … that can be understood and appreciated by undergraduate students. Indeed, the level of writing is superb … . Just as useful as the writing style are the appendices and the hints. … will surely prove extremely useful for all teachers of such a course. … will, I am sure, become a popular text book across the world." (James Sneyd, UK Nonlinear News, June, 2004) "Britton writes a book that provides for an introductory account of mathematical biology. … Many examples are given … . The figures are clear and precise. All mathematical formulae, equations and models are complete, clear and readable. … The material in the book is clear and concise. The book provides the reader with a wealth of information and is well suited as a textbook for a course in mathematical biology. I highly recommend this book … . It makes a worthwhile addition." (Paul Johnson, New Zealand Mathematical Society Newsletter, Issue 90, April, 2004) "It was a great pleasure reading Essential Mathematical Biology. … the book is very well written without large jumps in the mathematical reasoning, it is also quite concise and covers a large amount of material. … The writing and style are very clear. The mathematical steps are laid out neatly with clear definitions and notation … . The book is a great contribution to students interested in mathematical biology … and a source of important insights for biological scientists." (D. Kault, The Australian Mathematical Society, Vol. 31 (1), 2004) "This book is a self-contained introduction to the fast-growing field of mathematical biology. … it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. A broad range of topics is covered … ." (L’Enseignement Mathematique, Vol. 49 (3-4), 2003) "Those of us in mathematical biology like to imagine our field on the verge of achieving critical opalescence … . it is a pleasure and challenge to share the wide spectrum of problems and approaches with eager undergraduates from various backgrounds … . Several textbooks are available, now including Essential Mathematical Biology by Nicholas Britton. The author … exemplifies interdisciplinary approaches … . Essential Mathematical Biology would serve well as a template for an advanced undergraduate or beginning graduate course … ." (Fred Adler, Physics Today, March, 2004) "Each of the eight chapters starts with a brief list of clearly expressed goals, questions or explanations, well motivating the reader to enter the chapter by introducing him into the essential biological problems and their importance. … I can fully recommend to use this ‘undergraduate mathematics textbook’ in any theoretical or practical computer course introducing into Mathematical Biology, but also for other teaching or education purposes within this interdisciplinary filed of growing importance between Mathematics, Scientific Computing, Bioinformatics, Systems Biology, Ecology, Physiology and Biomedicine." (Wolfgang Alt, Mathematical Biosciences, Vol. 208, 2007)Table of Contents1. Single Species Population Dynamics.- 2. Population Dynamics of Interacting Species.- 3. Infectious Diseases.- 4. Population Genetics and Evolution.- 5. Biological Motion.- 6. Molecular and Cellular Biology.- 7. Pattern Formation.- 8. Tumour Modelling.- Further Reading.- A. Some Techniques for Difference Equations.- A.1 First-order Equations.- A.1.1 Graphical Analysis.- A.1.2 Linearisation.- A.2 Bifurcations and Chaos for First-order Equations.- A.2.1 Saddle-node Bifurcations.- A.2.2 Transcritical Bifurcations.- A.2.3 Pitchfork Bifurcations.- A.2.4 Period-doubling or Flip Bifurcations.- A.3 Systems of Linear Equations: Jury Conditions.- A.4 Systems of Nonlinear Difference Equations.- A.4.1 Linearisation of Systems.- A.4.2 Bifurcation for Systems.- B. Some Techniques for Ordinary Differential Equations.- B.1 First-order Ordinary Differential Equations.- B.1.1 Geometric Analysis.- B.1.2 Integration.- B.1.3 Linearisation.- B.2 Second-order Ordinary Differential Equations.- B.2.1 Geometric Analysis (Phase Plane).- B.2.2 Linearisation.- B.2.3 Poincaré-Bendixson Theory.- B.3 Some Results and Techniques for rath Order Systems.- B.3.1 Linearisation.- B.3.2 Lyapunov Functions.- B.3.3 Some Miscellaneous Facts.- B.4 Bifurcation Theory for Ordinary Differential Equations.- B.4.1 Bifurcations with Eigenvalue Zero.- B.4.2 Hopf Bifurcations.- C. Some Techniques for Partial Differential Equations.- C.1 First-order Partial Differential Equations and Characteristics.- C.2 Some Results and Techniques for the Diffusion Equation.- C.2.1 The Fundamental Solution.- C.2.2 Connection with Probabilities.- C.2.3 Other Coordinate Systems.- C.3 Some Spectral Theory for Laplace’s Equation.- C.4 Separation of Variables in Partial Differential Equations.- C.5 Systems of Diffusion Equations with Linear Kinetics.- C.6 Separating the Spatial Variables from Each Other.- D. Non-negative Matrices.- D.1 Perron-Frobenius Theory.- E. Hints for Exercises.

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Book SynopsisThis book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited.This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields. Trade Review“Advanced mathematical concepts are presented in a logical and clear manner, making the book accessible to graduate students as well as non-mathematicians working on problems in continuum mechanics of solids. … The book is very well organized and well written. The mathematical results are clearly presented.” (Corina- Stefania Drapaca, Mathematical Reviews, November, 2019)Table of ContentsStatic Problems.- Description of Deformable Stressed Bodies.- Elastic Materials.- Polyconvex Materials: Existence Of Energy-Minimizing Deformations.- General Hyperelastic Materials: Existence/Nonexistence Results.- Linearized Elasticity.- Evolution Problems.- Linear Rheological Models at Small Strains.- Nonlinear Materials with Internal Variables at Small Strains.- Thermodynamics of Selected Materials and Processes.- Evolution at finite Strains.

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Book SynopsisThis volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text.Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful. Trade Review“The book can be of special interest to mathematicians, STEM students, and engineers working in multidisciplinary industry settings where the insight provided by differential-algebraic equations can be determinant in decision making.” (Andrzej Sokolowski, MAA Reviews, August 11, 2019)Table of ContentsGeneral Nonlinear Differential Algebraic Equations and Tracking Problems: A Robotics Example.- DAE Aspects in Vehicle Dynamics and Mobile Robotics.- Open-loop Control of Underactuated Mechanical Systems Using Servo-constraints: Analysis and Some Examples.- Systems of Differential Algebraic Equations in Computational Electromagnetics.- Gas Network Benchmark Models.- Topological Index Analysis Applied to Coupled Flow Networks.- Nonsmooth DAEs with Applications in Modeling Phase Changes.- Continuous, Semi-Discrete, and Fully Discretized Navier-Stokes Equations.

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Book SynopsisThe chapters in this contributed volume showcase current theoretical approaches in the modeling of ocular fluid dynamics in health and disease. By including chapters written by experts from a variety of fields, this volume will help foster a genuinely collaborative spirit between clinical and research scientists. It vividly illustrates the advantages of clinical and experimental methods, data-driven modeling, and physically-based modeling, while also detailing the limitations of each approach. Blood, aqueous humor, vitreous humor, tear film, and cerebrospinal fluid each have a section dedicated to their anatomy and physiology, pathological conditions, imaging techniques, and mathematical modeling. Because each fluid receives a thorough analysis from experts in their respective fields, this volume stands out among the existing ophthalmology literature.Ocular Fluid Dynamics is ideal for current and future graduate students in applied mathematics and ophthalmology who wish to explore the field by investigating open questions, experimental technologies, and mathematical models. It will also be a valuable resource for researchers in mathematics, engineering, physics, computer science, chemistry, ophthalmology, and more.Table of ContentsPart I. Introduction.- Mathematical and physical modeling principles of complex biological systems.- Part II. Blood.- Vascular Anatomy and Physiology of the Eye.- Pathological Consequences of Vascular Hemodynamic Alterations in the Eye.- Measurement of geometrical and functional parameters related to ocular blood flow.- Mathematical modeling of blood flow in the eye.- Part III. Aqueous Humor.- Changes in Parameters of Aqueous Humor Dynamics Throughout Life.- Aqueous Humor Dynamics and its Influence on Glaucoma.- Approaches to Aqueous Humor Outflow Imaging.

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Book SynopsisQuantum systems with many degrees of freedom are inherently difficult to describe and simulate quantitatively. The space of possible states is, in general, exponentially large in the number of degrees of freedom such as the number of particles it contains. Standard digital high-performance computing is generally too weak to capture all the necessary details, such that alternative quantum simulation devices have been proposed as a solution. Artificial neural networks, with their high non-local connectivity between the neuron degrees of freedom, may soon gain importance in simulating static and dynamical behavior of quantum systems. Particularly promising candidates are neuromorphic realizations based on analog electronic circuits which are being developed to capture, e.g., the functioning of biologically relevant networks. In turn, such neuromorphic systems may be used to measure and control real quantum many-body systems online. This thesis lays an important foundation for the realization of quantum simulations by means of neuromorphic hardware, for using quantum physics as an input to classical neural nets and, in turn, for using network results to be fed back to quantum systems. The necessary foundations on both sides, quantum physics and artificial neural networks, are described, providing a valuable reference for researchers from these different communities who need to understand the foundations of both.Table of ContentsIntroduction.- Quantum Mechanics and Spin Systems.- Artificial Neural Networks.- Discrete Truncated Wigner Approximation.- BM-Based Wave Function Parametrization.- Deep Neural Networks and Phase Reweighting.- Towards Neuromorphic Sampling of Quantum States.- Conclusion.

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Book SynopsisSimulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.Trade Review“By providing tools and current examples on modeling issues ... the book makes a contribution answering the becoming more and more prevalent presence of Mathematics in our daily lives. The examples come essentially from the physical and natural sciences, but the book can be relied on in other areas, including the humanities, aside seminal works on mathematical modeling ... . The journey consists in eight rigorous and enjoying chapters.” (Lisa Morhaim, zbMATH 1519.00001, 2023)Table of Contents1 The model, aka the magic box.- 2 Weather Forecast Models.- 3 Epidemics: the Mathematics of Contagion.- 4 Mathematical Hearth.- 5 Mathematics in the Wind.- 6 Flying on Sun Power.- 7 The taste for Mathematics.- 8 Conclusions.

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Book SynopsisThis contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics.The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.Table of ContentsPart I: Computational Science and Engineering.- Multirate Schemes — An Answer of Numerical Analysis to a Demand from Applications.- Electronic Circuit Simulation and the Development of New Krylov-Subspace Methods.- Modular time integration of coupled problems in system dynamics.- Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems.- Fast Numerical Methods to Compute Periodic Solutions of Electromagnetic Models.- Challenges in the Simulation of Radio Frequency Circuits.- An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics.- From rotating fluid masses and Ziegler’s paradox to Pontryagin- and Krein spaces and bifurcation theory.- Part II: Data Analysis and finance.- Topological Data Analysis.- Prediction Models with Functional Data for Variables related with Energy Production.- Quantization Methods for Stochastic Differential Equations.

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Book SynopsisSemi-supervised learning is a learning paradigm concerned with the study of how computers and natural systems such as humans learn in the presence of both labeled and unlabeled data. Traditionally, learning has been studied either in the unsupervised paradigm (e.g., clustering, outlier detection) where all the data are unlabeled, or in the supervised paradigm (e.g., classification, regression) where all the data are labeled. The goal of semi-supervised learning is to understand how combining labeled and unlabeled data may change the learning behavior, and design algorithms that take advantage of such a combination. Semi-supervised learning is of great interest in machine learning and data mining because it can use readily available unlabeled data to improve supervised learning tasks when the labeled data are scarce or expensive. Semi-supervised learning also shows potential as a quantitative tool to understand human category learning, where most of the input is self-evidently unlabeled. In this introductory book, we present some popular semi-supervised learning models, including self-training, mixture models, co-training and multiview learning, graph-based methods, and semi-supervised support vector machines. For each model, we discuss its basic mathematical formulation. The success of semi-supervised learning depends critically on some underlying assumptions. We emphasize the assumptions made by each model and give counterexamples when appropriate to demonstrate the limitations of the different models. In addition, we discuss semi-supervised learning for cognitive psychology. Finally, we give a computational learning theoretic perspective on semi-supervised learning, and we conclude the book with a brief discussion of open questions in the field. Table of Contents: Introduction to Statistical Machine Learning / Overview of Semi-Supervised Learning / Mixture Models and EM / Co-Training / Graph-Based Semi-Supervised Learning / Semi-Supervised Support Vector Machines / Human Semi-Supervised Learning / Theory and OutlookTable of ContentsIntroduction to Statistical Machine Learning.- Overview of Semi-Supervised Learning.- Mixture Models and EM.- Co-Training.- Graph-Based Semi-Supervised Learning.- Semi-Supervised Support Vector Machines.- Human Semi-Supervised Learning.- Theory and Outlook.

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Book SynopsisAnswer Set Programming (ASP) is a declarative problem solving approach, initially tailored to modeling problems in the area of Knowledge Representation and Reasoning (KRR). More recently, its attractive combination of a rich yet simple modeling language with high-performance solving capacities has sparked interest in many other areas even beyond KRR. This book presents a practical introduction to ASP, aiming at using ASP languages and systems for solving application problems. Starting from the essential formal foundations, it introduces ASP's solving technology, modeling language and methodology, while illustrating the overall solving process by practical examples. Table of Contents: List of Figures / List of Tables / Motivation / Introduction / Basic modeling / Grounding / Characterizations / Solving / Systems / Advanced modeling / ConclusionsTable of ContentsList of Figures.- List of Tables.- Motivation.- Introduction.- Basic modeling.- Grounding.- Characterizations.- Solving.- Systems.- Advanced modeling.- Conclusions.

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Book SynopsisThis book addresses the state of the art of reduced order methods for modelling and computational reduction of complex parametrised systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in various fields.Consisting of four contributions presented at the CIME summer school, the book presents several points of view and techniques to solve demanding problems of increasing complexity. The focus is on theoretical investigation and applicative algorithm development for reduction in the complexity – the dimension, the degrees of freedom, the data – arising in these models.The book is addressed to graduate students, young researchers and people interested in the field. It is a good companion for graduate/doctoral classes.Table of Contents- 1. The Reduced Basis Method in Space and Time: Challenges, Limits and Perspectives. - 2. Inverse Problems: A Deterministic Approach Using Physics-Based Reduced Models. - 3. Model Order Reduction for Optimal Control Problems. - 4. Machine Learning Methods for Reduced Order Modeling.

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Book SynopsisThe purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.Table of Contents1 Review of Probability Theory.- 2 Applications to Mathematical Statistics.- 3 Conditional Probability and Conditional Expectation.- 4 Markov Chains.- 5 Sampling of Random Variables and Simulation.- 6 Brownian Motion.- 7 Introduction to Stochastic Calculus and Ito Integral.- 8 Introduction to Stochastic Differential Equations and Applications.- Bibliography.- Solutions.

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Book SynopsisThe research in this book looks at the likelihood and level of use of implemented technological components with regard to the adoption of different precision agricultural technologies. To identify the variables affecting farmers'' choices to embrace more precise technology, zero-inflated Poisson and negative binomial count data regression models are utilized. Outcomes from the count data analysis of a random sample of various farm operators show that various aspects, including farm dimension, farmer demographics, soil texture, urban impacts, farmer position of liabilities, and position of the farm in a state, were significantly associated with the approval severity and likelihood of precision farming technologies.Technical topics discussed in the book include: Precision agriculture Machine learning Wireless sensor networks IoT Deep learning

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Book SynopsisThe book covers a wide range of Artificial Intelligence (AI) and Mathematical Methods issues, research and applications in the area of pavement, geomechanical and few examples on geo-environmental systems: Application of Artificial Neural Networks; Data mining applications; Stochastic Finite Element; Fuzzy Set Theory; Artificial Immune Systems; Probabilistic Reasoning; System Identification Techniques; Image Processing. This collection of papers provides researchers and engineers with a current comprehensive look at available and emerging AI and Mathematical Methods within pavement and geomechanical systems.

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Book SynopsisThis book discusses the importance of knowledge as an intangible asset, separate from physical entities, that can enable us to understand and/or change the world. It provides a thorough treatment of knowledge, one that is free of ideological and philosophical preconceptions, and which relies exclusively on concepts and principles from the theory of computing and logic. It starts with an introduction to knowledge as truthful and useful information, and its development and management by computers and humans. It analyses the relationship between computational processes and physical phenomena, as well as the processes of knowledge production and application by humans and computers. In turn, the book presents autonomous systems that are called upon to replace humans in complex operations as a step toward strong AI, and discusses the risks – real or hypothetical – of the careless use of these systems. It compares human and machine intelligence, attempting to answer the question of whether and to what extent computers, as they stand today, can approach human-level situation awareness and decision-making. Lastly, the book explains the functioning of individual consciousness as an autonomous system that manages short- and long-term objectives on the basis of value criteria and accumulated knowledge. It discusses how individual values are shaped in society and the role of institutions in fostering and maintaining a common set of values for strengthening social cohesion. The book differs from books on the philosophy of science in many respects, e.g. by considering knowledge in its multiple facets and degrees of validity and truthfulness. It follows the dualist tradition of logicians, emphasizing the importance of logic and language and considering an abstract concept of information very different from the one used in the physical sciences. From this perspective, it levels some hopefully well-founded criticism at approaches that consider information and knowledge as nothing more than the emergent properties of physical phenomena. The book strikes a balance between popular books that sidestep fundamental issues and focus on sensationalism, and scientific or philosophical books that are not accessible to non-experts. As such, it is intended for a broad audience interested in the role of knowledge as a driver for change and development, and as a common good whose production and application could shape the future of humanity.Trade Review​In Understanding and Changing the World: From Information to Knowledge and Intelligence, Joseph Sifakis (a 2007 Turing Award recipient) amasses a lifetime of knowledge as a deep thinker and effective practitioner of computer science—indeed, collecting a civilization’s wisdom—to provide a valuable framework that is rooted in the philosophy of science and society."Akash Deshpande, SIAM News, https://sinews.siam.org/Details-Page/intelligence-whence-and-whitherTable of Contents1. Introduction.- Part I For a Gnoseological View of the World.- 2. Fundamental Questions about Knowledge.- 3. Information and Knowledge.- 4. The Development and Application of Knowledge.- Part II Computing, Knowledge and Intelligence.- 5. Physical Phenomena and Computational Processes.- 6. Human vs Artificial Intelligence.- Part III Consciousness and Society.- 7. Consciousness.- 8. Value Systems and Society.- 9. Epilogue.- Index.

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Book SynopsisTrade Review“Beautifully bringing together historical and contemporary research on representations in science with themes from aesthetics and the philosophy of art, Suárez’s book is an outstanding interdisciplinary contribution to the philosophy of science. It is essential reading for anyone interested in modeling practices, their connections with the arts, and what this insightful combination of science, art, and practice might bring to the epistemology of science.” -- Chiara Ambrosio, University College London“Suárez has been a leading voice in the philosophy of modeling for the last two decades. This book is a wonderfully clear and compelling presentation of his ‘inferentialist theory of representation.’ The book will be a central resource for advanced undergraduate and graduate students, and required reading for every philosopher of science.” -- Martin Kusch, University of Vienna“Suárez has written a brilliant account of the inferential conception of scientific representation, its historical roots, and its application to contemporary scientific modeling. What stands out is his deflationist approach toward metaphysics, the streamlined account in terms of representational force and inferential capacity, and the connection to the phenomenology of artistic perception. A magnificent work.” -- Bas C. van Fraassen, Princeton University“Inference and Representation makes a strong case for an inferential conception of scientific modeling. It argues that the effectiveness of a model lies in its providing an orientation that facilitates fruitful scientific reasoning. It is a valuable contribution to the literature on modeling.” -- Catherine Z. Elgin, Harvard University“This much-anticipated book is the culmination of over twenty years of pioneering work by Suárez. It is a must-read for anyone wishing to think carefully about models and representations in science. Suárez gives a careful, insightful, and comprehensive exposition and defence of his inferential conception of representation, and he now develops it in an expressly pragmatist direction with a helpful focus on the uses of models. What emerges is a compelling deflationary account of ‘representation without metaphysics,’ engaging fully with the complex realities of inferential practices. Suárez argues that common notions of representation based on similarity or isomorphism are ill-fitting and inadequate, and shows how the activity of representation pervades all sorts of scientific practices. His discussion is clear and systematic throughout, and successfully combines philosophical acuity and historical awareness. In the course of presenting his own position he also gives a fair, critical summing-up and evaluation of the considerable existing literature on models and representation. This landmark work should appeal to philosophers, historians of science and practicing scientists alike.” -- Hasok Chang, University of Cambridge“During the past quarter-century, philosophers of science have come to appreciate the importance of models and modeling practices in the sciences. Suárez has been one of the pioneers in this work, specifically in investigating how models represent aspects of the world. The present book is the culmination of insights accumulated over more than two decades. It provides a convincing account of representation, one emphasizing the uses to which models are put and the inferences they allow. Suárez develops his views with welcome precision, focuses on an admirably wide range of types of models, and offers numerous insights about the historical development of modeling. His final two chapters explore the notion of representation more broadly, with a lucid and well-informed discussion of representation in visual art, and draw out the implications for several large issues in the philosophy of science. This book is an outstanding contribution to the field.” -- Philip Kitcher, Columbia UniversityTable of ContentsPreface and Acknowledgments 1 Introducing Scientific Representation Part I Modeling 2 The Modeling Attitude: A Genealogy 3 Models and Their Uses Part II Representation 4 Theories of Representation 5 Against Substance 6 Scientific Theories and Deflationary Representation 7 Representation as Inference Part III Implications 8 Lessons from the Philosophy of Art 9 Scientific Epistemology Transformed Notes References Index

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Book SynopsisA balanced introduction to the theoretical foundations and real-world applications of mathematical finance The ever-growing use of derivative products makes it essential for financial industry practitioners to have a solid understanding of derivative pricing. To cope with the growing complexity, narrowing margins, and shortening life-cycle of the individual derivative product, an efficient, yet modular, implementation of the pricing algorithms is necessary. Mathematical Finance is the first book to harmonize the theory, modeling, and implementation of today''s most prevalent pricing models under one convenient cover. Building a bridge from academia to practice, this self-contained text applies theoretical concepts to real-world examples and introduces state-of-the-art, object-oriented programming techniques that equip the reader with the conceptual and illustrative tools needed to understand and develop successful derivative pricing models. Utilizing almost tweTrade Review"…very useful to practitioners and students…" (MAA Reviews, December 26, 2007) "An excellent textbook for students in mathematical finance, computational finance, and derivative pricing courses at the upper undergraduate or beginning graduate level." (Mathematical Reviews 2007)Table of Contents1. Introduction. 1.1 Theory, Modeling and Implementation. 1.2 Interest Rate Models and Interest Rate Derivatives. 1.3 How to Read this Book. 1.3.1 Abridged Versions. 1.3.2 Special Sections. 1.3.3 Notation. I: FOUNDATIONS. 2. Foundations. 2.1 Probability Theory. 2.2 Stochastic Processes. 2.3 Filtration. 2.4 Brownian Motion. 2.5 Wiener Measure, Canonical Setup. 2.6 Itô Calculus. 2.6.1 Itô Integral. 2.6.2 Itô Process. 2.6.3 Itô Lemma and Product Rule. 2.7 Brownian Motion with Instantaneous Correlation. 2.8 Martingales. 2.8.1 Martingale Representation Theorem. 2.9 Change of Measure (Girsanov, Cameron, Martin). 2.10 Stochastic Integration. 2.11 Partial Differential Equations (PDE). 2.11.1 Feynman-Kac Theorem . 2.12 List of Symbols. 3. Replication. 3.1 Replication Strategies. 3.1.1 Introduction. 3.1.2 Replication in a discrete Model. 3.2 Foundations: Equivalent Martingale Measure. 3.2.1 Challenge and Solution Outline. 3.2.2 Steps towards the Universal Pricing Theorem. 3.3 Excursus: Relative Prices and Risk Neutral Measures. 3.3.1 Why relative prices? 3.3.2 Risk Neutral Measure. II: FIRST APPLICATIONS. 4. Pricing of a European Stock Option under the Black-Scholes Model. 5. Excursus: The Density of the Underlying of a European Call Option. 6. Excursus: Interpolation of European Option Prices. 6.1 No-Arbitrage Conditions for Interpolated Prices. 6.2 Arbitrage Violations through Interpolation. 6.2.1 Example (1): Interpolation of four Prices. 6.2.2 Example (2): Interpolation of two Prices. 6.3 Arbitrage-Free Interpolation of European Option Prices. 7. Hedging in Continuous and Discrete Time and the Greeks. 7.1 Introduction. 7.2 Deriving the Replications Strategy from Pricing Theory. 7.2.1 Deriving the Replication Strategy under the Assumption of a Locally Riskless Product. 7.2.2 The Black-Scholes Differential Equation. 7.2.3 The Derivative V(t) as a Function of its Underlyings S i(t). 7.2.4 Example: Replication Portfolio and PDE under a Black-Scholes Model. 7.3 Greeks. 7.3.1 Greeks of a European Call-Option under the Black-Scholes model. 7.4 Hedging in Discrete Time: Delta and Delta-Gamma Hedging. 7.4.1 Delta Hedging. 7.4.2 Error Propagation. 7.4.3 Delta-Gamma Hedging. 7.4.4 Vega Hedging. 7.5 Hedging in Discrete Time: Minimizing the Residual Error (Bouchaud-Sornette Method). 7.5.1 Minimizing the Residual Error at Maturity T. 7.5.2 Minimizing the Residual Error in each Time Step. III: INTEREST RATE STRUCTURES, INTEREST RATE PRODUCTS AND ANALYTIC PRICING FORMULAS. Motivation and Overview. 8. Interest Rate Structures. 8.1 Introduction. 8.1.1 Fixing Times and Tenor Times. 8.2 Definitions. 8.3 Interest Rate Curve Bootstrapping. 8.4 Interpolation of Interest Rate Curves. 8.5 Implementation. 9. Simple Interest Rate Products. 9.1 Interest Rate Products Part 1: Products without Optionality. 9.1.1 Fix, Floating and Swap. 9.1.2 Money-Market Account. 9.2 Interest Rate Products Part 2: Simple Options. 9.2.1 Cap, Floor, Swaption. 9.2.2 Foreign Caplet, Quanto. 10. The Black Model for a Caplet. 11. Pricing of a Quanto Caplet (Modeling the FFX). 11.1 Choice of Numéraire. 12. Exotic Derivatives. 12.1 Prototypical Product Properties. 12.2 Interest Rate Products Part 3: Exotic Interest Rate Derivatives. 12.2.1 Structured Bond, Structured Swap, Zero Structure. 12.2.2 Bermudan Option. 12.2.3 Bermudan Callable and Bermudan Cancelable. 12.2.4 Compound Options. 12.2.5 Trigger Products. 12.2.6 Structured Coupons. 12.2.7 Shout Options. 12.3 Product Toolbox. IV: DISCRETIZATION AND NUMERICAL VALUATION METHODS. Motivation and Overview. 13. Discretization of time and state space. 13.1 Discretization of Time: The Euler and the Milstein Scheme. 13.1.1 Definitions. 13.1.2 Time-Discretization of a Lognormal Process. 13.2 Discretization of Paths (Monte-Carlo Simulation) . 13.2.1 Monte-Carlo Simulation. 13.2.2 Weighted Monte-Carlo Simulation. 13.2.3 Implementation. 13.2.4 Review. 13.3 Discretization of State Space. 13.3.1 Definitions. 13.3.2 Backward-Algorithm. 13.3.3 Review. 13.4 Path Simulation through a Lattice: Two Layers. 14. Numerical Methods for Partial Differential Equations. 15. Pricing Bermudan Options in a Monte Carlo Simulation. 15.1 Introduction. 15.2 Bermudan Options: Notation. 15.2.1 Bermudan Callable. 15.2.2 Relative Prices. 15.3 Bermudan Option as Optimal Exercise Problem. 15.3.1 Bermudan Option Value as single (unconditioned) Expectation: The Optimal Exercise Value. 15.4 Bermudan Option Pricing - The Backward Algorithm. 15.5 Re-simulation. 15.6 Perfect Foresight. 15.7 Conditional Expectation as Functional Dependence. 15.8 Binning. 15.8.1 Binning as a Least-Square Regression. 15.9 Foresight Bias. 15.10 Regression Methods - Least Square Monte-Carlo. 15.10.1 Least Square Approximation of the Conditional Expectation. 15.10.2 Example: Evaluation of a Bermudan Option on a Stock (Backward Algorithm with Conditional Expectation Estimator). 15.10.3 Example: Evaluation of a Bermudan Callable. 15.10.4 Implementation. 15.10.5 Binning as linear Least-Square Regression. 15.11 Optimization Methods. 15.11.1 Andersen Algorithm for Bermudan Swaptions. 15.11.2 Review of the Threshold Optimization Method. 15.11.3 Optimization of Exercise Strategy: A more general Formulation. 15.11.4 Comparison of Optimization Method and Regression. Method. 15.12 Duality Method: Upper Bound for Bermudan Option Prices. 15.12.1 Foundations. 15.12.2 American Option Evaluation as Optimal Stopping Problem. 15.13 Primal-Dual Method: Upper and Lower Bound. 16. Pricing Path-Dependent Options in a Backward Algorithm. 16.1 Evaluation of a Snowball / Memory in a Backward Algorithm. 16.2 Evaluation of a Flexi Cap in a Backward Algorithm. 17. Sensitivities (Partial Derivatives) of Monte Carlo Prices. 17.1 Introduction. 17.2 Problem Description. 17.2.1 Pricing using Monte-Carlo Simulation. 17.2.2 Sensitivities from Monte-Carlo Pricing. 17.2.3 Example: The Linear and the Discontinuous Payout. 17.2.4 Example: Trigger Products. 17.3 Generic Sensitivities: Bumping the Model. 17.4 Sensitivities by Finite Differences. 17.4.1 Example: Finite Differences applied to Smooth and Discontinuous Payout. 17.5 Sensitivities by Pathwise Differentiation. 17.5.1 Example: Delta of a European Option under a Black-Scholes Model. 17.5.2 Pathwise Differentiation for Discontinuous Payouts. 17.6 Sensitivities by Likelihood Ratio Weighting. 17.6.1 Example: Delta of a European Option under a Black-Scholes Model using Pathwise Derivative. 17.6.2 Example: Variance Increase of the Sensitivity when using Likelihood Ratio Method for Smooth Payouts. 17.7 Sensitivities by Malliavin Weighting. 17.8 Proxy Simulation Scheme. 18. Proxy Simulation Schemes for Monte Carlo Sensitivities and Importance Sampling. 18.1 Full Proxy Simulation Scheme. 18.1.1 Calculation of Monte-Carlo weights. 18.2 Sensitivities by Finite Differences on a Proxy Simulation Scheme. 18.2.1 Localization. 18.2.2 Object-Oriented Design. 18.3 Importance Sampling. 18.3.1 Example. 18.4 Partial Proxy Simulation Schemes. 18.4.1 Linear Proxy Constraint. 18.4.2 Comparison to Full Proxy Scheme Method. 18.4.3 Non-Linear Proxy Constraint. 18.4.4 Transition Probability from a Nonlinear Proxy Constraint. 18.4.5 Sensitivity with respect to the Diffusion Coefficients - Vega. 18.4.6 Example: LIBOR Target Redemption Note. 18.4.7 Example: CMS Target Redemption Note. V: PRICING MODELS FOR INTEREST RATE DERIVATIVES. 19. LIBOR Market Models. 19.1 LIBOR Market Model. 19.1.1 Derivation of the Drift Term. 19.1.2 The Short Period Bond P(Tm(t)+1;t) . 19.1.3 Discretization and (Monte-Carlo) Simulation. 19.1.4 Calibration - Choice of the free Parameters. 19.1.5 Interpolation of Forward Rates in the LIBOR Market Model. 19.2 Object Oriented Design. 19.2.1 Reuse of Implementation. 19.2.2 Separation of Product and Model. 19.2.3 Abstraction of Model Parameters. 19.2.4 Abstraction of Calibration. 19.3 Swap Rate Market Models (Jamshidian 1997). 19.3.1 The Swap Measure. 19.3.2 Derivation of the Drift Term. 19.3.3 Calibration - Choice of the free Parameters. 20. Swap Rate Market Models. 20.1 Definitions. 20.2 Terminal Correlation examined in a LIBOR Market Model Example. 20.2.1 De-correlation in a One-Factor Model. 20.2.2 Impact of the Time Structure of the Instantaneous Volatility on Caplet and Swaption Prices. 20.2.3 The Swaption Value as a Function of Forward Rates. 20.3 Terminal Correlation is dependent on the Equivalent Martingale Measure. 20.3.1 Dependence of the Terminal Density on the Martingale Measure. 21. Excursus: Instantaneous Correlation and Terminal Correlation. 21.1 Short Rate Process in the HJM Framework. 21.2 The HJM Drift Condition. 22.Heath-Jarrow-Morton Framework: Foundations. 22.1 Introduction. 22.2 The Market Price of Risk. 22.3 Overview: Some Common Models. 22.4 Implementations. 22.4.1 Monte-Carlo Implementation of Short-Rate Models. 22.4.2 Lattice Implementation of Short-Rate Models. 23. Short-Rate Models. 23.1 Short Rate Models in the HJM Framework. 23.1.1 Example: The Ho-Lee Model in the HJM Framework. 23.1.2 Example: The Hull-White Model in the HJM Framework. 23.2 LIBOR Market Model in the HJM Framework. 23.2.1 HJM Volatility Structure of the LIBOR Market Model. 23.2.2 LIBOR Market Model Drift under the QB Measure. 23.2.3 LIBOR Market Model as a Short Rate Model. 24 Heath-Jarrow-Morton Framwork: Immersion of Short-Rate Models and LIBOR Market Model. 24.1 Model. 24.2 Interpretation of the Figures. 24.3 Mean Reversion. 24.4 Factors. 24.5 Exponential Volatility Function. 24.6 Instantaneous Correlation. 25. Excursus: Shape of teh Interst Rate Curve under Mean Reversion and a Multifactor Model. 25.1 Introduction. 25.2 Cheyette Model. 26. Ritchken-Sakarasubramanian Framework: JHM with Low Markov Dimension. 26.1 Introduction. 26.1.1 The Markov Functional Assumption (independent of the model considered) . 26.1.2 Outline of this Chapter . 26.2 Equity Markov Functional Model. 26.2.1 Markov Functional Assumption. 26.2.2 Example: The Black-Scholes Model. 26.2.3 Numerical Calibration to a Full Two-Dimensional European Option Smile Surface. 26.2.4 Interest Rates. 26.2.5 Model Dynamics. 26.2.6 Implementation. 26.3 LIBOR Markov Functional Model. 26.3.1 LIBOR Markov Functional Model in Terminal Measure. 26.3.2 LIBOR Markov Functional Model in Spot Measure. 26.3.3 Remark on Implementation. 26.3.4 Change of numéraire in a Markov-Functional Model. 26.4 Implementation: Lattice. 26.4.1 Convolution with the Normal Probability Density. 26.4.2 State space discretization. Markov Functional Models. PART VI: Extended Models. 27.1 Introduction - Different Types of Spreads. 27.1.1 Spread on a Coupon. 27.1.2 Credit Spread. 27.2 Defaultable Bonds. 27.3 Integrating deterministic Credit Spread into a Pricing Model. 27.3.1 Deterministic Credit Spread. 27.3.2 Implementation. 27.4 Receiver’s and Payer’s Credit Spreads. 27.4.1 Example: Defaultable Forward Starting Coupon Bond. 27.4.2 Example: Option on a Defaultable Coupon Bond. 28. Credit Spreads. 28.1 Cross Currency LIBOR Market Model. 28.1.1 Derivation of the Drift Term under Spot-Measure. 28.1.2 Implementation. 28.2 Equity Hybrid LIBOR Market Model. 28.2.1 Derivation of the Drift Term under Spot-Measure. 28.2.2 Implementation. 28.3 Equity-Hybrid Cross-Currency LIBOR Market Model. 28.3.1 Summary. 28.3.2 Implementation. 29. Hybrid Models. 29.1 Elements of Object Oriented Programming: Class and Objects. 29.1.1 Example: Class of a Binomial Distributed Random Variable. 29.1.2 Constructor. 29.1.3 Methods: Getter, Setter, Static Methods. 29.2 Principles of Object Oriented Programming. 29.2.1 Encapsulation and Interfaces. 29.2.2 Abstraction and Inheritance. 29.2.3 Polymorphism. 29.3 Example: A Class Structure for One Dimensional Root Finders. 29.3.1 Root Finder for General Functions. 29.3.2 Root Finder for Functions with Analytic Derivative: Newton Method. 29.3.3 Root Finder for Functions with Derivative Estimation: Secant Method. 29.4 Anatomy of a Java™ Class. 29.5 Libraries. 29.5.1 Java™2 Platform, Standard Edition (j2se). 29.5.2 Java™2 Platform, Enterprise Edition (j2ee). 29.5.3 Colt. 29.5.4 Commons-Math: The Jakarta Mathematics Library. 29.6 Some Final Remarks. 29.6.1 Object Oriented Design (OOD) / Unified Modeling Language. PART VII: Implementation 30. Object-Oriented Implementatin in JavaTM. PART VIII: Appendices. A: A small Collection of Common Misconceptions. B: Tools (Selection). B.1 Linear Regression. B.2 Generation of Random Numbers. B.2.1 Uniform Distributed Random Variables. B.2.2 Transformation of the Random Number Distribution via the Inverse Distribution Function. B.2.3 Normal Distributed Random Variables. B.2.4 Poisson Distributed Random Variables. B.2.5 Generation of Paths of an n-dimensional Brownian Motion. B.3 Factor Decomposition - Generation of Correlated Brownian Motion. B.4 Factor Reduction. B.5 Optimization (one-dimensional): Golden Section Search. B.6 Convolution with Normal Density. C: Exercises. D: List of Symbols. E: Java™ Source Code (Selection). E.1 Java™ Classes for Chapter 29. List of Figures. List of Tables. List of Listings. Bibliography. Index.

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Book SynopsisAn accessible and multidisciplinaryintroduction to cellular automata As the applicability of cellular automata broadens and technology advances, there is a need for a concise, yet thorough, resource that lays the foundation of key cellularautomata rules and applications. In recent years, Stephen Wolfram''s A New Kind of Science has brought the modeling power that lies in cellular automata to the attentionof the scientific world, and now, Cellular Automata: A Discrete View of the World presents all the depth, analysis, and applicability of the classic Wolfram text in a straightforward, introductory manner. This book offers an introduction to cellular automata as a constructive method for modeling complex systems where patterns of self-organization arising from simple rules are revealed in phenomena that exist across a wide array of subject areas, including mathematics, physics, economics, and the social sciences. The book begins with a preliminary introduction to cellular autTrade Review"The book is well produced and a good introduction to its subject." (Computing Reviews, January 30, 2009) "An interesting read and worth browsing by somebody interested in getting a general background on CA. The examples are many and varied, and the numerous citations--both to electronic and printed media--are very helpful." (Computing Reviews, November 11, 2008) "An interesting read and worth browsing by somebody interested in getting a general background on CA. The examples are many and varied, and the numerous citations--both to electronic and printed media--are very helpful." (Computing Reviews, Nov 2008) "Schiff suppresses most mathematical details, rendering his book highly accessible, informative, and entertaining, but leaving open niches for a textbook treatment with exercises or an advanced monograph with proofs." (CHOICE, October 2008) "This book serves as a valuable resource for undergraduate and graduate students in the physical, biological, and social sciences and may also be of interest to any reader with a scientific or basic mathematical ground." (Mathematical Reviews, 2008m) "Schiff suppresses most mathematical details, rendering his book highly accessible, informative, and entertaining, but leaving open niches for a textbook treatment with exercises or an advanced monograph with proofs." (CHOICE Oct 2008) "This book serves as a valuable resource for undergraduate and graduate students in the physical, biological, and social sciences and may also be of interest to any reader with a scientific or basic mathematical ground." (Mathematical Reviews 2008)Table of ContentsPreface. 1. Preliminaries. 2. Dynamical Systems. 3. One-Dimensional Cellular Automata. 4. Two-Dimensional Automata. 5. Applications. 6. Complexity. Appendix A. References. Index.

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

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

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Book SynopsisThis book provides a user-friendly, hands-on introduction to the Nonlinear Mixed Effects Modeling (NONMEM) system, the most powerful tool for pharmacokinetic / pharmacodynamic analysis. Introduces requisite background to using Nonlinear Mixed Effects Modeling (NONMEM), covering data requirements, model building and evaluation, and quality control aspects Provides examples of nonlinear modeling concepts and estimation basics with discussion on the model building process and applications of empirical Bayesian estimates in the drug development environment Includes detailed chapters on data set structure, developing control streams for modeling and simulation, model applications, interpretation of NONMEM output and results, and quality control Has datasets, programming code, and practice exercises with solutions, available on a supplementary websiteTrade Review“This book may make the “User Guide V experience” a story from the good old times for the next generation of pharmacometricians.” (CPT: Pharmacometrics & Systems Pharmacology, 22 December 2014)Table of ContentsPreface xiii CHAPTER 1 The Practice of Pharmacometrics 1 1.1 Introduction 1 1.2 Applications of Sparse Data Analysis 2 1.3 Impact of Pharmacometrics 4 1.4 Clinical Example 5 CHAPTER 2 Population Model Concepts and Terminology 9 2.1 Introduction 9 2.2 Model Elements 10 2.3 Individual Subject Models 11 2.4 Population Models 12 2.4.1 Fixed-Effect Parameters 13 2.4.2 Random-Effect Parameters 14 2.5 Models of Random Between-Subject Variability (L1) 17 2.5.1 Additive Variation 17 2.5.2 Constant Coefficient of Variation 18 2.5.3 Exponential Variation 18 2.5.4 Modeling Sources of Between-Subject Variation 19 2.6 Models of Random Variability in Observations (L2) 19 2.6.1 Additive Variation 20 2.6.2 Constant Coefficient of Variation 21 2.6.3 Additive Plus CCV Model 22 2.6.4 Log-Error Model 24 2.6.5 Relationship Between RV Expressions and Predicted Concentrations 24 2.6.6 Significance of the Magnitude of RV 25 2.7 Estimation Methods 26 2.8 Objective Function 26 2.9 Bayesian Estimation 27 CHAPTER 3 NONMEM Overview and Writing an NM-TRAN Control Stream 28 3.1 Introduction 28 3.2 Components of the NONMEM System 28 3.3 General Rules 30 3.4 Required Control Stream Components 31 3.4.1 $PROBLEM Record 31 3.4.2 The $DATA Record 32 3.4.3 The $INPUT Record 35 3.5 Specifying the Model in NM-TRAN 35 3.5.1 Calling PREDPP Subroutines for Specific PK Models 35 3.5.2 Specifying the Model in the $PK Block 38 3.5.3 Specifying Residual Variability in the $ERROR Block 45 3.5.4 Specifying Models Using the $PRED Block 49 3.6 Specifying Initial Estimates with $THETA, $OMEGA, and $SIGMA 50 3.7 Requesting Estimation and Related Options 56 3.8 Requesting Estimates of the Precision of Parameter Estimates 62 3.9 Controlling the Output 63 CHAPTER 4 Datasets 66 4.1 Introduction 66 4.2 Arrangement of the Dataset 68 4.3 Variables of the Dataset 71 4.3.1 TIME 71 4.3.2 DATE 71 4.3.3 ID 72 4.3.4 DV 74 4.3.5 MDV 74 4.3.6 CMT 74 4.3.7 EVID 75 4.3.8 AMT 76 4.3.9 RATE 77 4.3.10 ADDL 78 4.3.11 II 79 4.3.12 SS 80 4.4 Constructing Datasets with Flexibility to Apply Alternate Models 80 4.5 Examples of Event Records 81 4.5.1 Alternatives for Specifying Time 81 4.5.2 Infusions and Zero-Order Input 81 4.5.3 Using ADDL 82 4.5.4 Steady-State Approach 83 4.5.5 Samples Before and After Achieving Steady State 83 4.5.6 Unscheduled Doses in a Steady-State Regimen 84 4.5.7 Steady-State Dosing with an Irregular Dosing Interval 84 4.5.8 Multiple Routes of Administration 85 4.5.9 Modeling Multiple Dependent Variable Data Types 86 4.5.10 Dataset for $PRED 86 4.6 Beyond Doses and Observations 87 4.6.1 Other Data Items 87 4.6.2 Covariate Changes over Time 88 4.6.3 Inclusion of a Header Row 89 CHAPTER 5 Model Building: Typical Process 90 5.1 Introduction 90 5.2 Analysis Planning 90 5.3 Analysis Dataset Creation 92 5.4 Dataset Quality Control 93 5.5 Exploratory Data Analysis 94 5.5.1 EDA: Population Description 95 5.5.2 EDA: Dose-Related Data 99 5.5.3 EDA: Concentration-Related Data 99 5.5.4 EDA: Considerations with Large Datasets 111 5.5.5 EDA: Summary 115 5.6 Base Model Development 116 5.6.1 Standard Model Diagnostic Plots and Interpretation 116 5.6.2 Estimation of Random Effects 130 5.6.3 Precision of Parameter Estimates (Based on $COV Step) 137 5.7 Covariate Evaluation 138 5.7.1 Covariate Evaluation Methodologies 140 5.7.2 Statistical Basis for Covariate Selection 141 5.7.3 Diagnostic Plots to Illustrate Parameter-Covariate Relationships 143 5.7.4 Typical Functional Forms for Covariate-Parameter Relationships 148 5.7.5 Centering Covariate Effects 156 5.7.6 Forward Selection Process 160 5.7.7 Evaluation of the Full Multivariable Model 167 5.7.8 Backward Elimination Process 169 5.7.9 Other Covariate Evaluation Approaches 171 5.8 Model Refinement 172 CHAPTER 6 Interpreting the NONMEM Output 178 6.1 Introduction 178 6.2 Description of the Output Files 178 6.3 The NONMEM Report File 179 6.3.1 NONMEM-Related Output 179 6.3.2 PREDPP-Related Output 180 6.3.3 Output from Monitoring of the Search 180 6.3.4 Minimum Value of the Objective Function and Final Parameter Estimates 182 6.3.5 Covariance Step Output 186 6.3.6 Additional Output 187 6.4 Error Messages: Interpretation and Resolution 188 6.4.1 NM-TRAN Errors 188 6.4.2 $ESTIMATION Step Failures 189 6.4.3 $COVARIANCE Step Failures 190 6.4.4 PREDPP Errors 191 6.4.5 Other Types of NONMEM Errors 192 6.4.6 FORTRAN Compiler or Other Run-Time Errors 193 6.5 General Suggestions for Diagnosing Problems 193 CHAPTER 7 App lications Using Parameter Estimates from the Individual 198 7.1 Introduction 198 7.2 Bayes Theorem and Individual Parameter Estimates 200 7.3 Obtaining Individual Parameter Estimates 202 7.4 Applications of Individual Parameter Estimates 204 7.4.1 Generating Subject-Specific Exposure Estimates 204 7.4.2 Individual Exposure Estimates for Group Comparisons 210 CHAPTER 8 Introduction to Model Evaluation 212 8.1 Introduction 212 8.2 Internal Validation 212 8.3 External Validation 213 8.4 Predictive Performance Assessment 214 8.5 Objective Function Mapping 217 8.6 Leverage Analysis 220 8.7 Bootstrap Procedures 222 8.8 Visual and Numerical Predictive Check Procedures 223 8.8.1 The VPC Procedure 223 8.8.2 Presentation of VPC Results 225 8.8.3 The Numerical Predictive Check (NPC) Procedure 229 8.9 Posterior Predictive Check Procedures 229 CHAPTER 9 User-Written Models 232 9.1 Introduction 232 9.2 $MODEL 235 9.3 $SUBROUTINES 236 9.3.1 General Linear Models (ADVAN5 and ADVAN7) 236 9.3.2 General Nonlinear Models (ADVAN6, ADVAN8, ADVAN9, and ADVAN13) 238 9.3.3 $DES 238 9.4 A Series of Examples 240 9.4.1 Defined Fractions Absorbed by Zero- and First-Order Processes 240 9.4.2 Sequential Absorption with First-Order Rates, without Defined Fractions 242 9.4.3 Parallel Zero-Order and First-Order Absorption, without Defined Fractions 243 9.4.4 Parallel First-Order Absorption Processes, without Defined Fractions 245 9.4.5 Zero-Order Input into the Depot Compartment 246 9.4.6 Parent and Metabolite Model: Differential Equations 247 CHAPTER 10 PK/PD Models 250 10.1 Introduction 250 10.2 Implementation of PD Models in NONMEM 251 10.3 $PRED 252 10.3.1 Direct-Effect PK/PD Examples: PK Concentrations in the Dataset 253 10.3.2 Direct-Effect PK/PD Example: PK from Computed Concentrations 255 10.4 $PK 256 10.4.1 Specific ADVANs (ADVAN1–ADVAN4 and ADVAN10–ADVAN12) 256 10.4.2 General ADVANs (ADVAN5–ADVAN9 and ADVAN13) 257 10.4.3 PREDPP: Effect Compartment Link Model Example (PD in $ERROR) 257 10.4.4 PREDPP: Indirect Response Model Example: PD in $DES 259 10.5 Odd-Type Data: Analysis of Noncontinuous Data 261 10.6 PD Model Complexity 262 10.7 Communication of Results 263 CHAPTER 11 Simulation Basics 265 11.1 Introduction 265 11.2 The Simulation Plan 265 11.2.1 Simulation Components 266 11.2.2 The Input–Output Model 266 11.2.3 The Covariate Distribution Model 270 11.2.4 The Trial Execution Model 273 11.2.5 Replication of the Study 274 11.2.6 Analysis of the Simulated Data 275 11.2.7 Decision Making Using Simulations 275 11.3 Miscellaneous Other Simulation-Related Considerations 276 11.3.1 The Seed Value 276 11.3.2 Consideration of Parameter Uncertainty 277 11.3.3 Constraining Random Effects or Responses 278 CHAPTER 12 Quality Control 285 12.1 Introduction 285 12.2 QC of the Data Analysis Plan 285 12.3 Analysis Dataset Creation 286 12.3.1 Exploratory Data Analysis and Its Role in Dataset QC 287 12.3.2 QC in Data Collection 287 12.4 QC of Model Development 288 12.4.1 QC of NM-TRAN Control Streams 289 12.4.2 Model Diagnostic Plots and Model Evaluation Steps as QC 290 12.5 Documentation of QC Efforts 290 12.6 Summary 291 References 292 Index 293

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

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

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

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Book SynopsisCUTTING-EDGE DEVELOPMENTS IN HIGH-FREQUENCY FINANCIAL ECONOMETRICS In recent years, the availability of high-frequency data and advances in computing have allowed financial practitioners to design systems that can handle and analyze this information. Handbook of Modeling High-Frequency Data in Finance addresses the many theoretical and practical questions raised by the nature and intrinsic properties of this data. A one-stop compilation of empirical and analytical research, this handbook explores data sampled with high-frequency finance in financial engineering, statistics, and the modern financial business arena. Every chapter uses real-world examples to present new, original, and relevant topics that relate to newly evolving discoveries in high-frequency finance, such as: Designing new methodology to discover elasticity and plasticity of price evolution Constructing microstructure simulation models Table of Contents Preface xi Contributors xiii Part One Analysis of Empirical Data 1 1 Estimation of NIG and VG Models for High Frequency Financial Data 3 José E. Figueroa-López Steven R. Lancette Kiseop Lee and Yanhui mi 1.1 Introduction 3 1.2 The Statistical Models 6 1.3 Parametric Estimation Methods 9 1.4 Finite-Sample Performance via Simulations 14 1.5 Empirical Results 18 1.6 Conclusion 22 References 24 2 A Study of Persistence of Price Movement using High Frequency Financial Data 27 Dragos Bozdog Ionuţ Florescu Khaldoun Khashanah and Jim Wang 2.1 Introduction 27 2.2 Methodology 29 2.3 Results 35 2.4 Rare Events Distribution 41 2.5 Conclusions 44 References 45 3 Using Boosting for Financial Analysis and Trading 47 Germán Creamer 3.1 Introduction 47 3.2 Methods 48 3.3 Performance Evaluation 53 3.4 Earnings Prediction and Algorithmic Trading 60 3.5 Final Comments and Conclusions 66 References 69 4 Impact of Correlation Fluctuations on Securitized structures 75 Eric Hillebrand Ambar N. Sengupta and Junyue Xu 4.1 Introduction 75 4.2 Description of the Products and Models 77 4.3 Impact of Dynamics of Default Correlation on Low-Frequency Tranches 79 4.4 Impact of Dynamics of Default Correlation on High-Frequency Tranches 87 4.5 Conclusion 92 References 94 5 Construction of Volatility Indices Using A Multinomial Tree Approximation Method 97 Dragos Bozdog Ionuţ Florescu Khaldoun Khashanah and Hongwei Qiu 5.1 Introduction 97 5.2 New Methodology 99 5.3 Results and Discussions 101 5.4 Summary and Conclusion 110 References 115 Part Two Long Range Dependence Models 117 6 Long Correlations Applied to the Study of Memory Effects in High Frequency (TICK) Data the Dow Jones Index and International Indices 119 Ernest Barany and Maria Pia Beccar Varela 6.1 Introduction 119 6.2 Methods Used for Data Analysis 122 6.3 Data 128 6.4 Results and Discussions 132 6.5 Conclusion 150 References 160 7 Risk Forecasting with GARCH Skewed t Distributions and Multiple Timescales 163 Alec N. Kercheval and Yang Liu 7.1 Introduction 163 7.2 The Skewed t Distributions 165 7.3 Risk Forecasts on a Fixed Timescale 176 7.4 Multiple Timescale Forecasts 185 7.5 Backtesting 188 7.6 Further Analysis: Long-Term GARCH and Comparisons using Simulated Data 203 7.7 Conclusion 216 References 217 8 Parameter Estimation and Calibration for Long-Memory Stochastic Volatility Models 219 Alexandra Chronopoulou 8.1 Introduction 219 8.2 Statistical Inference Under the LMSV Model 222 8.3 Simulation Results 227 8.4 Application to the S&P Index 228 8.5 Conclusion 229 References 230 Part Three Analytical Results 233 9 A Market Microstructure Model of Ultra High Frequency Trading 235 Carlos A. Ulibarri and Peter C. Anselmo 9.1 Introduction 235 9.2 Microstructural Model 237 9.3 Static Comparisons 239 9.4 Questions for Future Research 241 References 242 10 Multivariate Volatility Estimation with High Frequency Data Using Fourier Method 243 MariaElviraMancinoandSimonaSanfelici 10.1 Introduction 243 10.2 Fourier Estimator of Multivariate Spot Volatility 246 10.3 Fourier Estimator of Integrated Volatility in the Presence of Microstructure Noise 252 10.4 Fourier Estimator of Integrated Covariance in the Presence of Microstructure Noise 263 10.5 Forecasting Properties of Fourier Estimator 272 10.6 Application: Asset Allocation 286 References 290 11 The ‘‘Retirement’’ Problem 295 Cristian Pasarica 11.1 Introduction 295 11.2 The Market Model 296 11.3 Portfolio and Wealth Processes 297 11.4 Utility Function 299 11.5 The Optimization Problem in the Case π (τT ] ≡ 0 299 11.6 Duality Approach 300 11.7 Infinite Horizon Case 305 References 324 12 Stochastic Differential Equations and Levy Models with Applications to High Frequency Data 327 Ernest Barany and Maria Pia Beccar Varela 12.1 Solutions to Stochastic Differential Equations 327 12.2 Stable Distributions 334 12.3 The Levy Flight Models 336 12.4 Numerical Simulations and Levy Models: Applications to Models Arising in Financial Indices and High Frequency Data 340 12.5 Discussion and Conclusions 345 References 346 13 Solutions to Integro-Differential Parabolic Problem Arising on Financial Mathematics 347 Maria C. Mariani Marc Salas and Indranil SenGupta 13.1 Introduction 347 13.2 Method of Upper and Lower Solutions 351 13.3 Another Iterative Method 364 13.4 Integro-Differential Equations in a Lévy Market 375 References 380 14 Existence of Solutions for Financial Models with Transaction Costs and Stochastic Volatility 383 Maria C. Mariani Emmanuel K. Ncheuguim and Indranil SenGupta 14.1 Model with Transaction Costs 383 14.2 Review of Functional Analysis 386 14.3 Solution of the Problem (14.2) and (14.3) in Sobolev Spaces 391 14.4 Model with Transaction Costs and Stochastic Volatility 400 14.5 The Analysis of the Resulting Partial Differential Equation 408 References 418 Index 421

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

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

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Book SynopsisThe first comprehensive review of the theory and practice of one oftoday''s most powerful optimization techniques. The explosive growth of research into and development of interiorpoint algorithms over the past two decades has significantlyimproved the complexity of linear programming and yielded some oftoday''s most sophisticated computing techniques. This book offers acomprehensive and thorough treatment of the theory, analysis, andimplementation of this powerful computational tool. Interior Point Algorithms provides detailed coverage of all basicand advanced aspects of the subject. Beginning with an overview offundamental mathematical procedures, Professor Yinyu Ye movesswiftly on to in-depth explorations of numerous computationalproblems and the algorithms that have been developed to solve them.An indispensable text/reference for students and researchers inapplied mathematics, computer science, operations research,management science, and engineering, Interior PoinTable of ContentsGeometry of Convex Inequalities. Computation of Analytic Center. Linear Programming Algorithms. Worst-Case Analysis. Average-Case Analysis. Asymptotic Analysis. Convex Optimization. Nonconvex Optimization. Implementation Issues. Bibliography. Index.

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Book SynopsisThis comprehensive text links abstract mathematics to engineering applications in order to provide a clear and thorough exploration of fluid dynamics. Focus is on the development of mathematical models of physical phenomena and the wide range of technologies available to students.Table of ContentsWhat is Fluid Dynamics? Statics, Dynamics, and Surface Tension. Forces On, and Within, a Flowing Medium. Conservation of Mass and Momentum in a Continuous Fluid. Dimensional Analysis and Dynamic Similarity. Nearly Parallel Flows. Unsteady Flows. The Stream Function. Turbulent Flow and the Laminar Boundary Layer. Flow through Porous Media. Macroscopic Balances. Appendix. Index.

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

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

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Book SynopsisA considerable body of knowledge has grown in the search for effective ways to obtain nonlinear dynamic models from stimulus-response data in a practical context. This book summarizes some 30 years of research progress in that arena, and details the most recent methodologies that offer practical solutions to this daunting problem.Trade Review"...a perfect research tool, as reference book, and even as a textbook. I highly recommend it to everyone interested in nonlinear dynamics." (Journal of Intelligent & Fuzzy Systems, Vol. 16, No. 2, 2005) "...a well-written methodology book...a useful addition to [researchers, engineers and graduate students']...personal libraries." (E-STREAMS, September 2005)Table of ContentsPrologue xiii 1 Introduction 1 1.1 Purpose of this Book 1 1.2 Advocated Approach 4 1.3 The Problem of System Modeling in Physiology 6 1.3.1 Model Specification and Estimation 10 1.3.2 Nonlinearity and Nonstationarity 12 1.3.3 Definition of the Modeling Problem 13 1.4 Types of Nonlinear Models of Physiological Systems 13 Example 1.1. Vertebrate Retina 15 Example 1.2. Invertebrate Photoreceptor 18 Example 1.3. Volterra analysis of Riccati Equation 19 Example 1.4. Glucose-Insulin Minimal Model 21 Example 1.5. Cerebral Autoregulation 22 1.5 Deductive and Inductive Modeling 24 Historical Note #1: Hippocratic and Galenic Views of 26 Integrative Physiology 2 Nonparametric Modeling 29 2.1 Volterra Models 31 2.1.1 Examples of Volterra Models 37 Example 2.1. Static Nonlinear System 37 Example 2.2. L–N Cascade System 38 Example 2.3. L–N–M “Sandwich” System 39 Example 2.4. Riccati System 40 2.1.2 Operational Meaning of the Volterra Kernels 41 Impulsive Inputs 42 Sinusoidal Inputs 43 Remarks on the Meaning of Volterra Kernels 45 2.1.3 Frequency-Domain Representation of the Volterra Models 45 2.1.4 Discrete-Time Volterra Models 47 2.1.5 Estimation of Volterra Kernels 49 Specialized Test Inputs 50 Arbitrary Inputs 52 Fast Exact Orthogonalization and Parallel-Cascade Methods 55 Iterative Cost-Minimization Methods for Non-Gaussian 55 Residuals 2.2 Wiener Models 57 2.2.1 Relation between Volterra and Wiener Models 60 The Wiener Class of Systems 62 Examples of Wiener Models 63 Comparison of Volterra/Wiener Model Predictions 64 2.2.2 Wiener Approach to Kernel Estimation 67 2.2.3 The Cross-Correlation Technique for Wiener Kernel Estimation 72 Estimation of h0 73 Estimation of h1 (𝜏) 73 Estimation of h2 (𝜏1, 𝜏2) 74 Estimation of h3 (𝜏1, 𝜏2, 𝜏3) 75 Some Practical Considerations 77 Illustrative Example 78 Frequency-Domain Estimation of Wiener Kernels 78 2.2.4 Quasiwhite Test Inputs 80 CSRS and Volterra Kernels 84 The Diagonal Estimability Problem 85 An Analytical Example 86 Comparison of Model Prediction Errors 88 Discrete-Time Representation of the CSRS Functional Series 89 Pseudorandom Signals Based on m-Sequences 89 Comparative Use of GWN, PRS, and CSRS 92 2.2.5 Apparent Transfer Function and Coherence Measurements 93 Example 2.5. L–N Cascade System 96 Example 2.6. Quadratic Volterra System 97 Example 2.7. Nonwhite Gaussian Inputs 98 Example 2.8. Duffing System 98 Concluding Remarks 99 2.3 Efficient Volterra Kernel Estimation 100 2.3.1 Volterra Kernel Expansions 101 Model Order Determination 104 2.3.2 The Laguerre Expansion Technique 107 Illustrative Examples 112 2.3.3 High-Order Volterra Modeling with Equivalent Networks 122 2.4 Analysis of Estimation Errors 125 2.4.1 Sources of Estimation Errors 125 2.4.2 Estimation Errors Associated with the Cross-Correlation 127 Technique Estimation Bias 128 Estimation Variance 130 Optimization of Input Parameters 131 Noise Effects 134 Erroneous Scaling of Kernel Estimates 136 2.4.3 Estimation Errors Associated with Direct Inversion Methods 137 2.4.4 Estimation Errors Associated with Iterative 139 Cost-Minimization Methods Historical Note #2: Vito Volterra and Norbert Wiener 140 3 Parametric Modeling 145 3.1 Basic Parametric Model Forms and Estimation Procedures 146 3.1.1 The Nonlinear Case 150 3.1.2 The Nonstationary Case 152 3.2 Volterra Kernels of Nonlinear Differential Equations 153 Example 3.1. The Riccati Equation 157 3.2.1 Apparent Transfer Functions of Linearized Models 158 Example 3.2. Illustrative Example 160 3.2.2 Nonlinear Parametric Models with Intermodulation 161 3.3 Discrete-Time Volterra Kernels of NARMAX Models 164 3.4 From Volterra Kernel Measurements to Parametric Models 167 Example 3.3. Illustrative Example 169 3.5 Equivalence Between Continuous and Discrete Parametric Models 171 Example 3.4. Illustrative Example 175 3.5.1 Modular Representation 177 4 Modular and Connectionist Modeling 179 4.1 Modular Form of Nonparametric Models 179 4.1.1 Principal Dynamic Modes 180 Illustrative Examples 186 4.1.2 Volterra Models of System Cascades 191 The L–N–M, L–N, and N–M Cascades 194 4.1.3 Volterra Models of Systems with Lateral Branches 198 4.1.4 Volterra Models of Systems with Feedback Branches 200 4.1.5 Nonlinear Feedback Described by Differential Equations 202 Example 1. Cubic Feedback Systems 204 Example 2. Sigmoid Feedback Systems 209 Example 3. Positive Nonlinear Feedback 213 Example 4. Second-Order Kernels of Nonlinear 215 Feedback Systems Nonlinear Feedback in Sensory Systems 216 Concluding Remarks on Nonlinear Feedback 220 4.2 Connectionist Models 223 4.2.1 Equivalence between Connectionist and Volterra Models 223 Relation with PDM Modeling 230 Illustrative Examples 232 4.2.2 Volterra-Equivalent Network Architectures for Nonlinear 235 System Modeling Equivalence with Volterra Kernels/Models 238 Selection of the Structural Parameters of the VEN Model 238 Convergence and Accuracy of the Training Procedure 240 The Pseudomode-Peeling Method 244 Nonlinear Autoregressive Modeling (Open-Loop) 246 4.3 The Laguerre-Volterra Network 246 Illustrative Example of LVN Modeling 249 Modeling Systems with Fast and Slow Dynamic (LVN-2) 251 Illustrative Examples of LVN-2 Modeling 255 4.4 The VWM Model 260 5 A Practitioner’s Guide 265 5.1 Practical Considerations and Experimental Requirements 265 5.1.1 System Characteristics 266 System Bandwidth 266 System Memory 267 System Dynamic Range 267 System Linearity 268 System Stationarity 268 System Ergodicity 268 5.1.2 Input Characteristics 269 5.1.3 Experimental Characteristics 270 5.2 Preliminary Tests and Data Preparation 272 5.2.1 Test for System Bandwidth 272 5.2.2 Test for System Memory 272 5.2.3 Test for System Stationarity and Ergodicity 273 5.2.4 Test for System Linearity 274 5.2.5 Data Preparation 275 5.3 Model Specification and Estimation 276 5.3.1 The MDV Modeling Methodology 277 5.3.2 The VEN/VWM Modeling Methodology 278 5.4 Model Validation and Interpretation 279 5.4.1 Model Validation 279 5.4.2 Model Interpretation 281 Interpretation of Volterra Kernels 281 Interpretation of the PDM Model 282 5.5 Outline of Step-by-Step Procedure 283 5.5.1 Elaboration of the Key Step # 5 284 6 Selected Applications 285 6.1 Neurosensory Systems 286 6.1.1 Vertebrate Retina 287 6.1.2 Invertebrate Retina 396 6.1.3 Auditory Nerve Fibers 302 6.1.4 Spider Mechanoreceptor 307 6.2 Cardiovascular System 320 6.3 Renal System 333 6.4 Metabolic-Endocrine System 342 7 Modeling of Multiinput/Multioutput Systems 359 7.1 The Two-Input Case 360 7.1.1 The Two-Input Cross-Correlation Technique 362 7.1.2 The Two-Input Kernel-Expansion Technique 362 7.1.3 Volterra-Equivalent Network Models with Two Inputs 364 Illustrative Example 366 7.2 Applications of Two-Input Modeling to Physiological Systems 369 7.2.1 Motion Detection in the Invertebrate Retina 369 7.2.2 Receptive Field Organization in the Vertebrate Retina 370 7.2.3 Metabolic Autoregulation in Dogs 378 7.2.4 Cerebral Autoregulation in Humans 380 7.3 The Multiinput Case 389 7.3.1 Cross-Correlation-Based Method for Multiinput Modeling 390 7.3.2 The Kernel-Expansion Method for Multiinput Modeling 393 7.3.3 Network-Based Multiinput Modeling 393 7.4 Spatiotemporal and Spectrotemporal Modeling 395 7.4.1 Spatiotemporal Modeling of Retinal Cells 398 7.4.2 Spatiotemporal Modeling of Cortical Cells 401 8 Modeling of Neuronal Systems 407 8.1 A General Model of Membrane and Synaptic Dynamics 408 8.2 Functional Integration in the Single Neuron 414 8.2.1 Neuronal Modes and Trigger Regions 417 Illustrative Examples 427 8.2.2 Minimum-Order Modeling of Spike-Output Systems 432 The Reverse-Correlation Technique 432 Minimum-Order Wiener Models 435 Illustrative Example 439 8.3 Neuronal Systems with Point-Process Inputs 439 8.3.1 The Lag-Delta Representation of P–V or P–W Kernels 445 8.3.2 The Reduced P–V or P–W Kernels 446 8.3.3 Examples from the Hippocampal Formation 450 Single-Input Stimulation in Vivo and Cross-Correlation 450 Technique Single-Input Stimulation in Vitro and Laguerre-Expansion 455 Technique Dual-Input Stimulation in the Hippocampal Slice 457 Nonlinear Modeling of Synaptic Dynamics 461 8.4 Modeling of Neuronal Ensembles 463 9 Modeling of Nonstationary Systems 467 9.1 Quasistationary and Recursive Tracking Methods 468 9.2 Kernel Expansion Method 469 9.2.1 Illustrative Example 474 9.2.2 A Test of Nonstationarity 475 9.2.3 Linear Time-Varying Systems with Arbitrary Inputs 479 9.3 Network-Based Methods 480 9.3.1 Illustrative Examples 481 9.4 Applications to Nonstationary Physiological Systems 484 10 Modeling of Closed-Loop Systems 489 10.1 Autoregressive Form of Closed-Loop Model 490 10.2 Network Model Form of Closed-Loop Systems 491 Appendix I Function Expansions 495 Appendix II Gaussian White Noise 499 Appendix III Construction of the Wiener Series 503 Appendix IV Stationarity, Ergodicity, and Autocorrelation Functions of Random Processes 505 References 507 Index 535

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

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

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

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Book SynopsisDPSM - Distributed Point Source Method for Modeling Engineering Problems is the first book that describes the theory of DPSM in detail and cover its applications in ultrasonic, magnetic, electrostatic, electromagnetic and thermal engineering problems.Table of ContentsChapter 1. Basic Theory of Distributed Point Source Method (DPSM) and its Application to Some Simple Problems (D. Placko and T. Kundu). 1.1 Introduction and Historical Development of DPSM. 1.2 Basic Principles of DPSM Modeling. 1.2.1 The fundamental idea. 1.2.1.1 Basic equations. 1.2.1.2 Boundary conditions. 1.2.2 Example in the case of a magnetic open core sensor. 1.2.2.1 Governing equations and solution. 1.2.2.2 Solution of coupling equations. 1.2.2.3 Results and discussion. 1.3 Examples from Ultrasonic Transducer Modeling. 1.3.1 Justification of modeling a finite plane source by a distribution of point sources . 1.3.2 Planar piston transducer in a fluid. 1.3.2.1 Conventional surface integral technique. 1.3.2.2 Alternative distributed point source method (DPSM) for computing the ultrasonic field. 1.3.2.2.1 Matrix formulation. 1.3.2.3 Restrictions on rS for point source distribution. 1.3.3 Focused transducer in a homogeneous fluid. 1.3.4 Ultrasonic field in a non-homogeneous fluid in presence of an interface. 1.3.4.1 Pressure field computation in fluid 1 at point P. 1.3.4.2 Pressure field computation in fluid 2 at point Q. 1.3.5 DPSM technique for ultrasonic field modeling in non-homogeneous fluid. 1.3.5.1 Field computation in fluid 1. 1.3.5.1.1 Approximations in computing the field. 1.3.5.2 Field in fluid 2. 1.3.6 Ultrasonic field in presence of a scatterer. 1.3.7 Numerical results. 1.3.7.1 Ultrasonic field in a homogeneous fluid. 1.3.7.2 Ultrasonic field in a non-homogeneous fluid - DPSM technique. 1.3.7.3 Ultrasonic field in a non-homogeneous fluid - surface integral method. 1.3.7.4 Ultrasonic field in presence of a finite size scatterer. References. Chapter 2. Advanced Theory of DPSM - Modeling Multi-Layered Medium and Inclusions of Arbitrary Shape (T. Kundu and D. Placko). 2.1 Introduction. 2.2 Theory of Multi-Layered Medium Modeling. 2.2.1 Transducer faces not coinciding with any interface. 2.2.1.1 Source strength determination from boundary and interface conditions. 2.2.2 Transducer faces coinciding with the interface - Case 1: Transducer faces modeled separately. 2.2.2.1 Source strength determination from interface and boundary conditions. 2.2.2.2 Counting number of equations and number of unknowns. 2.2.3 Transducer faces coinciding with the interface - Case 2: Transducer faces are part of the interface. 2.2.3.1 Source strength determination from interface and boundary conditions. 2.2.4 Special case involving one interface and one transducer only. 2.3 Theory for Multi-layered Medium Considering the Interaction Effect on the Transducer Surface . 2.3.1 Source strength determination from interface conditions. 2.3.2 Counting number of equations and number of unknowns. 2.4 Interference between two Transducers: Step-by-Step Analysis of Multiple Reflection. 2.5 Scattering by an Inclusion of Arbitrary Shape. 2.6 Scattering by an Inclusion of Arbitrary Shape - An Alternative Approach. 2.7 Electric Field in a Multi-Layered Medium. 2.8 Ultrasonic Field in a Multi-Layered Fluid Medium. 2.8.1 Ultrasonic field developed in a three-layered medium. 2.8.2 Ultrasonic field developed in a four-layered fluid medium. References. Chapter 3. Ultrasonic Modeling in Fluid Media (T. Kundu, R. Ahmad, N. Alnuaimi and D. Placko). 3.1 Introduction. 3.2 Primary and Secondary Sources. 3.3 Modeling Ultrasonic Transducers of Finite Dimension Immersed in a Homogeneous Fluid. 3.3.1 Numerical results - ultrasonic transducers of finite dimension immersed in fluid. 3.4 Modeling Ultrasonic Transducers of Finite Dimension Immersed in a Non-Homogeneous Fluid. 3.4.1 Obtaining the strengths of active and passive source layers. 3.4.1.1 Computation of the source strength vectors when multiple reflection between the transducer and the interface are ignored. 3.4.1.2 Computation of the source strength vectors considering the interaction effects between the transducer and the interface . 3.4.2 Numerical results - ultrasonic transducer immersed in non-homogeneous fluid. 3.5 Reflection at a Fluid-Solid Interface - Ignoring Multiple Reflections between the Transducer Surface and the Interface. 3.5.1 Numerical results for fluid-solid interface. 3.6 Modeling Ultrasonic Field in Presence of a Thin Scatterer of Finite Dimension. 3.7 Modeling Ultrasonic Field inside a Multi-Layered Fluid Medium. 3.8 Modeling Phased-Array Transducers Immersed in a Fluid. 3.8.1 Description and use of phased array transducers. 3.8.2 Theory of phased array transducer modeling. 3.8.3 Dynamic focusing and time lag determination. 3.8.4 Interaction between two transducers in a homogeneous fluid . 3.8.5 Numerical results for phased array transducer modeling. 3.8.5.1 Dynamic steering and focusing. 3.8.5.2 Interaction between two phased array transducers placed face to face. Reference. Chapter 4. Advanced Applications of Distributed Point Source Method - Ultrasonic Field Modeling in Solid Media (S. Banerjee and T. Kundu). 4.1 Introduction. 4.2 Calculation of Displacement and Stress Green’s Functions in Solids. 4.2.1 Point source excitation in a solid. 4.2.2 Calculation of displacement Green’s function. 4.2.3 Calculation of stress Green’s function. 4.3 Elemental Point Source in a Solid. 4.3.1 Displacement and stress Green’s functions. 4.3.2 Differentiation of displacement Green’s function with respect to x1, x2, x3. 4.3.3 Computation of displacements and stresses in the solid for multiple point sources. 4.3.4 Matrix representation. 4.4 Calculation of Pressure and Displacement Green’s Functions in the Fluid Adjacent to the Solid Half-Space. 4.4.1 Displacement and potential Green’s functions in the fluid. 4.4.2 Computation of displacement and pressure in the fluid. 4.4.3 Matrix representation. 4.5 Application 1: Ultrasonic Field Modeling near Fluid-Solid Interface [Banerjee et al. 2006]. 4.5.1 Matrix formulation to calculate source strengths. 4.5.2 Boundary conditions. 4.5.3 Solution. 4.5.4 Numerical results on ultrasonic field modeling near fluid-solid interface. 4.6 Application 2: Ultrasonic Field Modeling in a Solid Plate [Banerjee and Kundu 2006a]. 4.6.1 Ultrasonic field modeling in a homogeneous solid plate. 4.6.2 Matrix formulation to calculate source strengths. 4.6.3 Boundary and continuity conditions. 4.6.4 Solution. 4.6.5 Numerical results on ultrasonic field modeling in solid plates. 4.7 Application 3: Ultrasonic Fields in Solid Plates with Inclusion or Horizontal Cracks [Banerjee and Kundu 2006b]. 4.7.1 Problem geometry. 4.7.2 Matrix formulation. 4.7.3 Boundary and continuity conditions. 4.7.4 Solution. 4.7.5 Numerical results on ultrasonic fields in solid plate with horizontal crack. 4.8 Application 4: Ultrasonic Field Modeling in Sinusoidally Corrugated Wave Guides [Banerjee and Kundu 2006c]. 4.8.1 Theory. 4.8.2 Numerical results on ultrasonic fields in sinusoidal corrugated wave guides. 4.9 Calculation of Green’s Functions in Transversely Isotropic and Anisotropic Solids. 4.9.1 Governing differential equation for Green’s function calculation. 4.9.2 Radon transform. 4.9.3 Basic properties of Radon transform. 4.9.4 Displacement and stress Green’s functions. References. Chapter 5. DPSM Formulation for Basic Magnetic Problems (N. Liebeaux and D. Placko). 5.1 Introduction . 5.2 DPSM Formulation for Magnetic Problems. 5.2.1 The Biot-Savart law as a DPSM current source definition. 5.2.1.1 Wire of infinite length. 5.2.1.2 Current loop. 5.2.2 Current loops above a semi-infinite conductive target. 5.2.3 Current loops above a semi-infinite magnetic target. 5.2.4 Current loop circling a magnetic core. 5.2.4.1 Geometry. 5.2.4.2 DPSM formulation. 5.2.4.3 Results. 5.2.5 Finite Element Simulation - Comparisons. 5.3 Conclusion. References. Chapter 6. Advanced Magnetodynamic and Electromagnetic Problems(D. Placko and N. Liebeaux). 6.1 Introduction. 6.2 DPSM Formulation using Green’s Sources. 6.2.1 Green’s theory. 6.2.2 Green’s function in free homogeneous space. 6.3 Green’s Functions and DPSM Formulation. 6.3.1 Expressions of the magnetic and electric fields. 6.3.2 Boundary conditions. 6.4 Example of Application. 6.4.1 Target in aluminum (σ= 50 Ms/m), frequency = 1000 Hz. 6.4.2 Target in aluminum (σ= 50 Ms/m), frequency = 100 Hz, inclined excitation loop. 6.4.3 Dielectric target (&epsi;r = 5), frequency = 3 GHz, 10° tilted excitation loop. 6.5 Conclusion. References. Chapter 7. Electrostatic Modeling and Basic Applications (G. Lissorgues, A. Cruau and D. Placko). 7.1 Introduction. 7.2 Modeling by DPSM. 7.2.1 Digitalization of the problem. 7.2.2 DPSM meshing considerations. 7.2.3 Matrix formulation. 7.3 Solving the System. 7.3.1 Synthesizing electrostatic field and potential. 7.3.2 Capacitance calculation. 7.4 Examples Based on Parallel-Plate Capacitors. 7.4.1 Description. 7.4.2 Equations. 7.4.3 Results of simulation. 7.4.4 Gap-tuning variable capacitor. 7.4.5 Surface-tuning variable capacitor. 7.5 Summary. References. Chapter 8. Advanced Electrostatic Problems: Multi-Layered Dielectric Medium and Masking Issues (G. Lissorgues, A. Cruau and D. Placko). 8.1 Introduction. 8.2 Multi-Layered Systems. 8.3 Examples of Multi-Material Electrostatic Structure. 8.3.1 Parallel-plate capacitor with two dielectric layers. 8.3.2 Permittivity-tuning varactors. 8.4 Multi-Conductor Systems: Masking Issues. 8.4.1 Example of multi-conductor system. References. Chapter 9. Basic Electromagnetic Problems (M. Lemistre and D. Placko). 9.1 Introduction. 9.2 Theoretical Considerations. 9.2.1 Maxwell’s equations. 9.2.2 Radiation of dipoles. 9.2.2.1 Electromagnetic field radiated by a current distribution. 9.2.2.2 Electric dipole. 9.2.2.3 Magnetic dipole. 9.2.3 The surface impedance. 9.2.4 Diffraction by a circular aperture. 9.2.5 Eddy currents. 9.2.6 Polarization of dielectrics. 9.3 Principle of Electromagnetic Probe for NDE. 9.3.1 Application to dielectric materials. 9.3.2 Application to conductive materials. 9.3.2.1 Magnetic method. 9.3.2.2 Hybrid method. 9.4 Electromagnetic Method for Structural Health Monitoring Applications. 9.4.1 Generalities. 9.4.2 Hybrid method. 9.4.3 Electric method. References. Chapter 10. Advanced Electromagnetic Problems with Industrial Applications (M. Lemistre and D. Placko). 10.1 Introduction. 10.2 Modeling the Sources. 10.2.1 Generalities. 10.2.2 Primary source. 10.2.3 Boundary conditions. 10.3 Modeling a Defect Inside the Structure. 10.4 Solving the Inverse Problem. 10.5 Conclusion. Chapter 11. DPSM Beta Program User’s Manual (A. Cruau and D. Placko). 11.1 Introduction. 11.2 Glossary. 11.3 Modeling Preparation. 11.4 Program Steps. 11.5 Conclusion. Index.

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

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

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