Mathematical modelling Books

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisJust like humans, animals and plants suffer from infectious diseases, which can critically threaten biodiversity. This book describes key studies that have driven our understanding of the ecology and evolution of wildlife diseases. Each chapter introduces the host and disease, and explains how that system has aided our general understanding of the evolution and spread of wildlife diseases, through the development and testing of important epidemiological and evolutionary theories. Questions addressed include: How do hosts and parasites co-evolve? What determines how fast a disease spreads through a population? How do co-infecting parasites interact? Why do hosts vary in parasite burden? Which factors determine parasite virulence and host resistance? How do parasites influence the spread of invasive species? How do we control infectious diseases in wildlife? This book will provide a valuable introduction to students new to the topic, and novel insights to researchers, professionals and pTrade Review'Overall, this is a fascinating collection of studies that showcases why wildlife diseases are worthy of study and how combining field observations, experiments, mathematical models and the latest in genomic and molecular research provides not only research insight, but also contributes to effective conservation and management efforts.' Rob Robinson, British Trust for Ornithology'Advances in modeling, epidemiologic techniques, and genetics have been crucial in some examples treated by contributors, and the importance of long-term field studies, essential for understanding dynamic systems, is emphasized throughout the volume. Some studies are observational, some experimental, and some largely theoretical. All contributions are extensively referenced and effectively illustrated.' M. Gochfeld, Choice'Overall, this well-written book is, in my opinion, a valuable contribution that will encourage further collecting and analysing long-term data in the study of wildlife diseases. It also gives hope. The advances in our understanding of wildlife disease dynamics enable better planning of conservation and management efforts, as shown in the case of wild and farmed salmon or the bighorn sheep pneumonia. As such, it is undoubtedly of high value for researchers and managers working in the field of wildlife disease ecology, but also for advanced undergraduate students or academic lecturers who would like to broaden their knowledge. The book was a great company during the coronavirus lockdown and a fascinating journey through the realm of wildlife diseases. I highly recommend it!' Agata Mrugala, Basic and Applied Ecology'This book comes to fill an important niche in disease ecology: synthesizing the state of knowledge about wildlife disease ecology while integrating theoretical models with a wide variety empirical case studies … this book presents an invaluable synthesis of our knowledge of disease ecology in wildlife hosts.' Miguel A. Acevedo, The Quarterly Review of BiologyTable of ContentsPreface: wildlife disease ecology; Glossary of terms; Part I. Understanding Within-Host Processes: 1. Pollinator diseases: the Bombus-Crithidia system; 2. Genetic diversity and disease spread: epidemiological models and empirical studies of a snail-trematode system; 3. Wild rodents as a natural model to study within-host parasite interactions; 4. From population to individual host scale and back again: testing theories of infection and defence in the Soay sheep of St Kilda; 5. The causes and consequences of parasite interactions: African buffalo as a case study; 6. Effects of host lifespan on the evolution of age-specific resistance: a case study of anther-smut disease on wild carnations; 7. Sexually transmitted infections in natural populations: what have we learnt from beetles and beyond?; Part II. Understanding Between-Host Processes: 8. Using insect baculoviruses to understand how population structure affects disease spread; 9. Infection and invasion: study cases from aquatic communities; 10. Parasite mediated selection in red grouse – consequences for population dynamics and mate choice; 11. Emergence, transmission and evolution of an uncommon enemy: Tasmanian devil facial tumour disease; 12. Bovine tuberculosis in badgers: sociality, infection and demography in a social mammal; 13. Mycoplasma ovipneumoniae in bighorn sheep: from exploration to action; 14. Manipulating parasites in an Arctic herbivore: gastrointestinal nematodes and the population regulation of Svalbard reindeer; Part III. Understanding Wildlife Disease Ecology at the Community and Landscape Level: 15. The ecological and evolutionary trajectory of oak powdery mildew in Europe; 16. Healthy herds or predator spreaders? Insights from the plankton into how predators suppress and spread disease; 17. Multi-trophic interactions and migration behaviour determine the ecology and evolution of parasite infection in monarch butterflies; 18. When chytrid fungus invades: integrating theory and data to understand disease- induced amphibian declines; 19. Ecology of a marine ectoparasite in farmed and wild salmon; 20. Mycoplasmal conjunctivitis in house finches: the study of an emerging disease; 21. Heterogeneities in infection and transmission in a parasite-rabbit system: key issues for understanding disease dynamics and persistence; 22. Sylvatic plague in Central Asia: a case study of abundance thresholds.

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Book SynopsisUpdated look at financial modeling and Monte Carlo simulation with software by Oracle Crystal Ball This revised and updated edition of the bestselling book on financial modeling provides the tools and techniques needed to perform spreadsheet simulation. It answers the essential question of why risk analysis is vital to the decision-making process, for any problem posed in finance and investment. This reliable resource reviews the basics and covers how to define and refine probability distributions in financial modeling, and explores the concepts driving the simulation modeling process. It also discusses simulation controls and analysis of simulation results. The second edition of Financial Modeling with Crystal Ball and Excel contains instructions, theory, and practical example models to help apply risk analysis to such areas as derivative pricing, cost estimation, portfolio allocation and optimization, credit risk, and cash flow analysis. It includes the resouTable of ContentsPreface xi Acknowledgments xvii About the Author xix Chapter 1 Introduction 1 1.1 Financial Modeling 2 1.2 Risk Analysis 2 1.3 Monte Carlo Simulation 4 1.4 Risk Management 8 1.5 Benefits and Limitations of Using Crystal Ball 9 Chapter 2 Analyzing Crystal Ball Forecasts 11 2.1 Simulating a 50–50 Portfolio 11 2.2 Varying the Allocations 22 2.3 Presenting the Results 27 Chapter 3 Building A Crystal Ball Model 29 3.1 Simulation Modeling Process 29 3.2 Defining Crystal Ball Assumptions and Forecasts 30 3.3 Running Crystal Ball 33 3.4 Sources of Error 34 3.5 Controlling Model Error 36 Chapter 4 Selecting Crystal Ball Assumptions 37 4.1 Crystal Ball’s Basic Distributions 37 4.2 Using Historical Data to Choose Distributions 55 4.3 Specifying Correlations 64 Chapter 5 Using Decision Variables 79 5.1 Defining Decision Variables 79 5.2 Decision Table with One Decision Variable 81 5.3 Decision Table with Two Decision Variables 87 5.4 Using OptQuest 98 Chapter 6 Selecting Run Preferences 105 6.1 Trials 105 6.2 Sampling 109 6.3 Speed 111 6.4 Options 113 6.5 Statistics 115 Chapter 7 Net Present Value and Internal Rate of Return 117 7.1 Deterministic NPV and IRR 117 7.2 Simulating NPV and IRR 119 7.3 Capital Budgeting 123 7.4 Customer Net Present Value 133 Chapter 8 Modeling Financial Statements 137 8.1 Deterministic Model 137 8.2 Tornado Chart and Sensitivity Analysis 138 8.3 Crystal Ball Sensitivity Chart 139 8.4 Conclusion 143 Chapter 9 Portfolio Models 145 9.1 Single-period Crystal Ball Model 145 9.2 Single-period Analytical Solution 148 9.3 Multi-period Crystal Ball Model 149 Chapter 10 Value at Risk 155 10.1 VaR 155 10.2 Shortcomings of VaR 157 10.3 Conditional Value at Risk 157 Chapter 11 Simulating Financial Time Series 163 11.1 White Noise 163 11.2 Random Walk 165 11.3 Autocorrelation 166 11.4 Additive Random Walk with Drift 170 11.5 Multiplicative Random Walk Model 173 11.6 Geometric Brownian Motion Model 176 11.7 Mean-reverting Model 180 Chapter 12 Financial Options 187 12.1 Types of Options 187 12.2 Risk-neutral Pricing and the Black-Scholes Model 188 12.3 Portfolio Insurance 192 12.4 American Option Pricing 194 12.5 Exotic Option Pricing 197 12.6 Bull Spread 201 12.7 Principal-protected Instrument 201 Chapter 13 Real Options 205 13.1 Financial Options and Real Options 205 13.2 Applications of Real Options Analysis 206 13.3 Black-Scholes Real Options Insights 209 13.4 Real Options Valuation Tool 211 Chapter 14 Credit Risk 221 14.1 Expected Loss 221 14.2 Credit Risk Simulation Model 223 14.3 Conditional Value at Risk 225 14.4 Using CVaR to Manage Credit Risk 227 Chapter 15 Construction Project Management 229 15.1 Project Description 229 15.2 Choosing Construction Methods 231 15.3 Risk Analysis 231 15.4 Stochastic Optimization 234 Chapter 16 Oil and GasExploration 235 16.1 Well Properties 235 16.2 Statistical Models 236 16.3 Conclusion 239 Appendix A Crystal Ball’s Probability Distributions 241 A.1 Bernoulli 241 A.2 Beta 243 A.3 Beta PERT 244 A.4 Binomial 246 A.5 Custom 247 A.6 Discrete Uniform 251 A.7 Exponential 252 A.8 Gamma 254 A.9 Geometric 255 A.10 Hypergeometric 257 A.11 Logistic 259 A.12 Lognormal 260 A.13 Maximum Extreme 262 A.14 Minimum Extreme 263 A.15 Negative Binomial 264 A.16 Normal 266 A.17 Pareto 267 A.18 Poisson 269 A.19 Student’s t 270 A.20 Triangular 272 A.21 Uniform 273 A.22 Weibull 275 A.23 Yes-No 276 Appendix B Generating Assumption Values 279 B.1 Generating Random Numbers 279 B.2 Generating Random Variates 282 B.3 Latin Hypercube Sampling 284 Appendix C Variance Reduction Techniques 287 C.1 Using Crystal Ball to Value an Asian Option 288 C.2 Antithetic Variates 289 C.3 Control Variates 289 C.4 Comparison 290 C.5 Conclusion 292 Appendix D About the Download 293 Glossary 297 References 301 Index 311

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Book SynopsisThis book is a Solutions Manual to Accompany Applied Mathematics and Modeling for Chemical Engineers. There are many examples provided as homework in the original text and the solution manual provides detailed solutions of many of these problems that are in the parent book Applied Mathematics and Modeling for Chemical Engineers.

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Book SynopsisThe Simplex Algorithm.- Geometry.- The Duality Theorem.- Matrix Environment.- General Form.- Unsolvable Systems.- Geometry Revisited.- Game Theory.- Network Environment.- Combinatorics.- Economics.- Integer Optimization.Trade ReviewFrom the reviews:“In an effort at reform, Hurlbert (Arizona State) dubs his subject ‘linear optimization’ … . the author designs his work for discovery-based learning. … Ideally, this volume offers students the opportunity to recapitulate the Socratic process for reinforcement … . Summing Up: Recommended. Lower-division undergraduates.” (D. V. Feldman, Choice, Vol. 47 (9), May, 2010)“Hurlbert’s textbook focuses on the mathematics of linear programming and important connections to linear algebra, graph theory, convexity, and game theory. The author has adopted the Moore method in which students are given some basic terminology and definitions and are then asked to develop the subject by proving a series of theorems. … This textbook would be very suitable for an undergraduate course in linear programming that uses the Moore method.” (Brian Borchers, The Mathematical Association of America, February, 2010)“This text is … oriented toward duality as central to solving and understanding linear optimization problems. … Sequential steps in the ‘Workouts’ help guide the student through the discovery process. … this book would be an excellent choice for an instructor wishing to teach linear optimization to a motivated class. There is enough in here to sustain every taste and approach and create an excellent first course in optimization.” (Steven R. Dunbar, SIAM Review, Vol. 53 (3), 2011)Table of ContentsIntroduction.- The Simplex Algorithm.- Geometry.- The Duality Theorem.- Matrix Implementation.- General Form.- Unsolvable Systems.- Geometry Revisited.- Game Theory.- Network Implementation.- Combinatorics.- Economics.- Integer Optimization.- Appendix A: Linear Algebra Overview.- Appendix B: The Equivalence of the Auxiliary and Shortcut Methods.- Appendix C: Complexity.- Appendix D: LOP Catalog.

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Book SynopsisThis book contains a selection of the best theoretical and applied papers from the inaugural International Choice Modelling Conference. The conference was organised by the Institute for Transport Studies at the University of Leeds and held in Harrogate, North Yorkshire on 30 March to 1 April 2009. The conference brought together leading researchers and practitioners from across the many different areas in which choice modelling is a key technique for understanding behaviour and evaluating policy. The diversity of the field was reflected in presentations by both academics and practitioners, coming from six continents and a variety of fields including transport and economics. Key contributions include papers from Professor Daniel McFadden, from the University of California, Berkeley - Nobel Prize laureate in Economics and chief architect of random utility modelling. The conference also included keynote presentations by five other leading choice modellers, namely Professor Moshe Ben-Akiva, Professor Chandra Bhat, Professor Michel Bierlaire, Professor David Hensher, and Professor Riccardo Scarpa.Trade ReviewAn important collection of papers by many of the world's leading researchers in choice modeling. With topics that range from the conceptual basis of choice to the pragmatics of data collection, this volume provides a vivid snapshot of the current state of the field.A" Kenneth Train, University of California, Berkeley.Table of ContentsPART I: Guest Speaker Papers 1. Sociality, Rationality, and the Ecology of Choice - Daniel McFadden 2. Planning and Action in a Model of Choice - Moshe Ben-Akiva 3. Attribute Processing, Heuristics, and Preference Construction in Choice Analysis - David Hensher 4. The Multiple Discrete-Continuous Extreme Value (MDCEV) Model: Formulation and Applications - Chandra R. Bhat & Naveen Eluru 5. Capturing Human Perception of Facial Expressions by Discrete Choice Modelling - Matteo Sorci,Thomas Robin, Javier Cruz, Michel Bierlaire, J.-P. Thiran and Gianluca Antonini Part II: Data Collection 6. Serial Choice Conjoint Analysis for Estimating Discrete Choice Models - Michiel C.J. Bliemer and John M. Rose 7. Observed Efficiency of a D-Optimal Design in an Interactive Agency Choice Experiment - Sean M. Puckett and John M. Rose 8. Effects of Stated Choice Design Dimensions on Model Estimates - Phani Kumar Chintakayala, Stephane Hess, John M. Rose and Mark Wardman 9. Stated Choice Experimental Designs for Scheduling Models - Paul Koster and Yin-Yen Tseng Part III: Concepts & Methodology 10. Systematically Heterogeneous Covariance in Network GEV Models - Jeffrey P. Newman 11. On Estimation of Hybrid Choice Models - Denis Bolduc and Ricardo Alvarez-Daziano 12. A Model of Travel Happiness and Mode Switching - Maya Abou-Zeid and Moshe Ben-Akiva 13. On Path Generation Algorithms for Route Choice Models - Emma Frejinger and Michel Bierlaire Part IV: Endogeneity and Heterogeneity 14. Mode Choice Endogeneity in Value of Travel Time Estimation - Stefan L. Mabit and Mogens Fosgerau 15. Accommodating Coefficient Outliers in Discrete Choice Modelling: A Comparison of Discrete and Continuous Mixing Approaches - Danny Campbell, Stephane Hess, Riccardo Scarpa and John M. Rose 16. Addressing Endogeneity in Discrete Choice Models: Assessing Control-Function and Latent-Variable Methods - Cristian Angelo Guevara and Moshe Ben-Akiva 17. Latent Class and Mixed Logit Models with Endogenous Choice Set Formation Based on Compensatory Screening Rules - Matthieu de Lapparent Part V: Transport Matters 18. Transport Welfare Benefits in the Presence of an Income Effect - James Laird 19. Which Commuters will Car Share? An Examination of Alternative Approaches to Identifying Market Segments - Jon Crockett, Gerard Andrew Whelan, Caroline Louise Sinclair and Hugh Gillies 20. Modelling Choice in a Changing Environment: Assessing the Shock Effects of a New Transport System - Maria Francisca Yanez and Juan de Dios Ortuzar 21. What do We Really Know About Travellers' Response to Unreliability? - Yaron Hollander Part VI: Beyond Transport 22. Optimizing Product Portfolios Using Discrete Choice Modeling and TURF - Thomas J. Adler, Colin Smith and Jeffrey Dumont 23. Preference Stability: Modelling how Consumer Preferences Shift after Receiving New Product Information - Harmen Oppewal, Mark Morrison, Paul Wang and David Waller 24. Investigating Willingness to Pay -Willingness to Accept Asymmetry in Choice Experiments - Bruno Lanz, Allan Provins, Ian J. Bateman, Riccardo Scarpa, Ken Willis and Ece Ozdermiroglu 25. Clustering Ranked Preference Data Using Sociodemographic Covariates - Isobel Claire Gormley and Thomas Brendan Murphy 26. Continuous versus Discrete Representation of Investing Firm Heterogeneity in Modelling FDI Location Decisions - Simona Rasciute and Eric J. Pentecost 27. Development of Integrated Choice and Latent Variable (ICLV) Models for the Residential Relocation Decision in Island Areas - Eleni Kitrinou, Amalia Polydoropoulou and Denis Bolduc

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Book SynopsisThis book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing.Table of ContentsIntroduction.- The boundary integral equation.- Basis functions, B-splines.- Description of the geometry.- Getting geometry information from CAD programs.- Numerical treatment of integral equations.- Numerical integration.- Steady state potential problems.- Static linear solid mechanics.- Body force effects.- Treatment of inhomogeneities/inclusions.- Material non-linear behaviour.- Applications in geomechanics.- Viscous flow problems.- Time dependent problems.- Summary and outlook.- Appendix A: Fundamental solutions.

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Book SynopsisThis open access volume presents a novel computational framework for understanding how collections of excitable cells work. The key approach in the text is to model excitable tissue by representing the individual cells constituting the tissue. This is in stark contrast to the common approach where homogenization is used to develop models where the cells are not explicitly present. The approach allows for very detailed analysis of small collections of excitable cells, but computational challenges limit the applicability in the presence of large collections of cells.Table of ContentsDerivation of a cell-based mathematical model of excitable cells.- A cell-based model for ionic electrodiffusion in excitable tissue.- Modeling cardiac mechanics on a subcellular scale.- Operator splitting and finite difference schemes for solving the EMI model.- Solving the EMI equations using finite element methods.- Iterative solvers for EMI models.- Improving neural simulations with the EMI model.- Index.

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Book SynopsisThis monograph considers the mathematical modeling of cellular adhesion, a key interaction force in cell biology. While deeply grounded in the biological application of cell adhesion and tissue formation, this monograph focuses on the mathematical analysis of non-local adhesion models. The novel aspect is the non-local term (an integral operator), which accounts for forces generated by long ranged cell interactions. The analysis of non-local models has started only recently, and it has become a vibrant area of applied mathematics. This monograph contributes a systematic analysis of steady states and their bifurcation structure, combining global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the symmetries of the non-local term. These methods allow readers to analyze and understand cell adhesion on a deep level.Trade Review“Modelers who wish to use similar approaches in their modeling will find this a good source of base information, as well as a valuable guide for initiating similar analyses for their own models. Analysts wishing to expand our understanding … will find this book a fine building block. It could also prove a useful resource for graduate students looking for potential projects … . this monograph is an admirable attempt … and hopefully will inspire significant further study.” (Kevin Painter, SIAM Review, Vol. 64 (1), March, 2022)“The detailed analysis, as presented here, shows a stimulating interaction between model symmetries, mathematical analysis, and biological reality, which probably are inspired the authors and hopefully the readers of this book too.” (Andrey Zahariev, zbMATH 1473.92001, 2021)Table of ContentsIntroduction.- Preliminaries.- The Periodic Problem.- Basic Properties.- Local Bifurcation.- Global Bifurcation.- Non-local Equations with Boundary Conditions.- No-flux Boundary Conditions.- Discussion and future directions.

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Book SynopsisThis textbook deals with engineering, science, technical, legal, financial, ICT, logistics and people management topics necessary for managing engineered assets such as all man-made tools, gadgets, buildings, equipment, machines, infrastructure, large-scale physical and industrial facilities and systems which pervade all sectors of industry. By coalescing concepts, principles, practices, and practical issues from the relevant multi-disciplines, the book addresses the body of knowledge required for managing engineered assets in the 4IR and Society 5.0 era and beyond.The book is written for: Scholars and students who intend to strengthen or acquire knowledge about the concepts, principles, and practice of managing engineered assets; Managers of engineered assets in both the public and private sectors who aim to improve asset management practice for their organisational purposes and missions; Policymakers and regulators in order to improve policymaking, governance, assessment and evaluation frameworks on the management of engineered assets; The broader audience concerned about the sustainable management of engineered assets that constitute our built environment and provide the means for industry and livelihood. Table of ContentsDefinitions and Scope.- Value and Sustainability.- Technical Principles.- Practical Concepts.- Engineering Asset Management Framework.- Asset Acquisition Stage.- Asset Utilisation Stage.- Asset Retirement Stage.- SAMP and EAMBoK.

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Book SynopsisThis open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analysis of the model. Teaching mathematical modelling is a cognitively challenging activity for (prospective) teachers. Thus, teacher education requires a detailed analysis of professional competence for teaching mathematical modelling. Measuring this competence requires theoretical models that accurately describe requirements placed upon teachers, as well as appropriate evaluation tools that adequately capture skills and abilities in this field. This book presents an instrument that measures the professional competences in a sample of 349 prospective teachers.Table of ContentsIntroduction.- Objectives and application areas.- Test development.- Implementation of the test.- Test quality.- Selected results.- References.- Attachment.- Modelling experiences.- Beliefs about mathematical modelling.- Self-efficacy about assesing mathematical modelling.- Modelling specific pedagogical content knowledge.- Test booklet.

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Book SynopsisThis monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes. The presentation includes a review of generalized additive models, additive kernels/Gaussian processes, generalized Tikhonov regularization, empirical mode decomposition, and Synchrosqueezing, which are all related to and generalizable under the proposed framework.Although kernel methods have strong theoretical foundations, they require the prior selection of a good kernel. While the usual approach to this kernel selection problem is hyperparameter tuning, the objective of this monograph is to present an alternative (programming) approach to the kernel selection problem while using mode decomposition as a prototypical pattern recognition problem. In this approach, kernels are programmed for the task at hand through the programming of interpretable regression networks in the context of additive Gaussian processes.It is suitable for engineers, computer scientists, mathematicians, and students in these fields working on kernel methods, pattern recognition, and mode decomposition problems.Table of ContentsIntroduction.- Review.- The mode decomposition problem.- Kernel mode decomposition networks (KMDNets).- Additional programming modules and squeezing.- Non-trigonometric waveform and iterated KMD.- Unknown base waveforms.- Crossing frequencies, vanishing modes, and noise.- Appendix.

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Book Synopsis.- Preliminaries..- First Look at QPLEX..- Part 1 QPLEX Modeling and Calculus..- Introduction to QPLEX Modeling and Calculus..- Simple Transition Dynamics..- Models with Simple Transition Dynamics..- Advanced Transition Dynamics..- Models with Advanced Transition Dynamics..- Conditional and Joint Probabilities..- Part 2 Graphical QPLEX Calculus..- Introduction to Graphical QPLEX Calculus..- Subsystem QPLEX Calculus..- Conditional Independence..- Information Structure..- Graphical QPLEX Calculus with Distributional Programs..- Efficient Calculation for Distributional Programs..- Part 3 Foundations..- Introduction to Foundations..- Optimality of QPLEX Iterates..- Exactness Results.

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Book SynopsisPreface.- The Root of Mind and Mathematics.- Equality, Similarity, and Transformations.- Mind and Mathematics in an Event-Centered Approach.- Symmetry, the Unconscious, and Imagination.- Imagination, Mathematics, and Mysticism.- Epilogue.- Index.

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Book SynopsisPreface.- The Starting Point: Lakoff and Núñez.- Image Schema Theory.- Related Processes.- Learning, Diagrams, and AI.- Index.

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Book Synopsis This book is unique to be the only one completely dedicated for battery modeling for all components of battery management system (BMS) applications. The contents of this book compliment the multitude of research publications in this domain by providing coherent fundamentals. An explosive market of Li ion batteries has led to aggressive demand for mathematical models for battery management systems (BMS). Researchers from multi-various backgrounds contribute from their respective background, leading to a lateral growth. Risk of this runaway situation is that researchers tend to use an existing method or algorithm without in depth knowledge of the cohesive fundamentals—often misinterpreting the outcome. It is worthy to note that the guiding principles are similar and the lack of clarity impedes a significant advancement. A repeat or even a synopsis of all the applications of battery modeling albeit redundant, would hence be a mammoth task, and cannot be done in a single offering. The authors believe that a pivotal contribution can be made by explaining the fundamentals in a coherent manner. Such an offering would enable researchers from multiple domains appreciate the bedrock principles and forward the frontier.Battery is an electrochemical system, and any level of understanding cannot ellipse this premise. The common thread that needs to run across—from detailed electrochemical models to algorithms used for real time estimation on a microchip—is that it be physics based. Build on this theme, this book has three parts. Each part starts with developing a framework—often invoking basic principles of thermodynamics or transport phenomena—and ends with certain verified real time applications. The first part deals with electrochemical modeling and the second with model order reduction. Objective of a BMS is estimation of state and health, and the third part is dedicated for that. Rules for state observers are derived from a generic Bayesian framework, and health estimation is pursued using machine learning (ML) tools. A distinct component of this book is thorough derivations of the learning rules for the novel ML algorithms. Given the large-scale application of ML in various domains, this segment can be relevant to researchers outside BMS domain as well.The authors hope this offering would satisfy a practicing engineer with a basic perspective, and a budding researcher with essential tools on a comprehensive understanding of BMS models.Table of ContentsLithium batteries and underlying electrochemical processes.- Electrochemical model (EM) for lithium batteries.- Electrochemical impedance spectroscopy (EIS) models.- Equivalent circuit models (ECM).- Reduced order models.- Battery management system – state estimator and algorithms.- Battery thermal models.- Battery life models.

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Book SynopsisPresenting a comprehensive resource for the mastery of network analysis in R, the goal of Network Analysis with R is to introduce modern network analysis techniques in R to social, physical, and health scientists. The mathematical foundations of network analysis are emphasized in an accessible way and readers are guided through the basic steps of network studies: network conceptualization, data collection and management, network description, visualization, and building and testing statistical models of networks. As with all of the books in the Use R! series, each chapter contains extensive R code and detailed visualizations of datasets. Appendices will describe the R network packages and the datasets used in the book. An R package developed specifically for the book, available to readers on GitHub, contains relevant code and real-world network datasets as well.Table of ContentsIntroducing Network Analysis in R.- The Network Analysis "5 Number Summary".- Network Data Management in R.- Basic Network Plotting and Layout.- Effective Network Graphic Design.- Advanced Network Graphics.- Actor Prominence.- Subgroups.- Affiliation Networks.- Random Network Models.- Statistical Network Models.- Dynamic Network Models.- Simulations.

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Book SynopsisPresenting a practitioner's guide to capabilities and best practices of quality control systems using the R programming language, this volume emphasizes accessibility and ease-of-use through detailed explanations of R code as well as standard statistical methodologies. In the interest of reaching the widest possible audience of quality-control professionals and statisticians, examples throughout are structured to simplify complex equations and data structures, and to demonstrate their applications to quality control processes, such as ISO standards. The volume balances its treatment of key aspects of quality control, statistics, and programming in R, making the text accessible to beginners and expert quality control professionals alike. Several appendices serve as useful references for ISO standards and common tasks performed while applying quality control with R. Trade Review Table of Contents

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Book SynopsisThis book focuses on the applications of convex optimization and highlights several topics, including support vector machines, parameter estimation, norm approximation and regularization, semi-definite programming problems, convex relaxation, and geometric problems. All derivation processes are presented in detail to aid in comprehension. The book offers concrete guidance, helping readers recognize and formulate convex optimization problems they might encounter in practice.Trade Review“Selected Applications of Convex Optimization is a brief book, only 140 pages, and includes exercises with each chapter. It would be a good supplemental text for an optimization or machine learning course.” (John D. Cook, MAA Reviews, maa.org, December, 2015)Table of ContentsPreliminary Knowledge.- Support Vector Machines.- Parameter Estimations.- Norm Approximation and Regulariztion.- Semi-Definite Programing and Linear Matrix Inequalities.- Convex Relaxation.- Geometric Problems.

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Book SynopsisReal world investors differ in their tastes and attitudes and they do not have, in general, perfect information about the future prospects of the economy. Most theoretical models, however, assume to the contrary that investors are homogeneous and perfectly informed about the market. In this book, an attempt is made to overcome these shortcomings. In three different case studies, the effect of heterogeneous time preferences, heterogeneous beliefs and imperfect information about the economy's growth on the term structure of interest rates are studied. The initial chapter gives an introduction to the theory of financial markets in continuous time under imperfect information and establishes the existence of an equilibrium with complete markets.Table of ContentsInformation.- Equilibrium with Imperfect Information and Complete Asset Markets in Continuous Time: Introduction; A Competitive Financial Market with Imperfect Information; Martingale Representation Theorem for the Innovation Process; The Existence of an Arrow-Debreu Equilibrium, Pareter Efficiency and the Representation Agent; Completeness of the Market and Existence of a Financial Equilibrium; Pricing Redundant Securities and the Term Structure of Interest Rates.- Heterogeneous Time Preferences - Preferred Habitat Theory Revisited: Modeling Preferred Habitat Time Preferences; A Model with Heterogeneous Time Preferences; Equilibrium; Analysis of the Term Structure; The Demand for Long-Term Bonds.- Imperfect Information: The Term Structure when the Growth Rate is Unknown: The Model; Estimating the Drift; Equilibrium with Perfect and Imperfect Information; The Yield Curve with Normal and Bernoulli Prior Beliefs; General Prior Beliefs.- Bulls and Bears: Heterogeneous Expectations: Setup; Equilibrium; Two Examples.

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Book SynopsisThis book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.Table of ContentsIntroduction: Uncertainty Quantification and Propagation.- Basic Formulations.- Spectral Expansions.- Non-intrusive Methods.- Galerkin Methods.- Detailed Elementary Applications.- Application to Navier-Stokes Equations.- Advanced topics.- Solvers for Stochastic Galerkin Problems.- Wavelet and Multiresolution Analysis Schemes.- Adaptive Methods.- Epilogue.

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Book SynopsisPHIL PICTON is a Reader in Engineering Control Systems at Nene College in Northampton. Prior to this he was a lecturer at the Open University where he contributed to distance learning courses on control engineering, electronics, mechatronics and artificial intelligence. His research interests include patten recognition, intelligent control and logic design.

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

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

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Book SynopsisThis book is dedicated to modern approaches to mathematical modeling of reflexive processes in control. The authors consider reflexive games that describe the gametheoretical interaction of agents making decisions based on a hierarchy of beliefs regarding (1) essential parameters (informational reflexion), (2) decision principles used by opponents (strategic reflexion), (3) beliefs about beliefs, and so on. Informational and reflexive equilibria in reflexive games generalize a series of well-known equilibrium concepts in noncooperative games and models of collective behavior. These models allow posing and solving the problems of informational and reflexive control in organizational, economic, social and other systems, in military applications, etc. (the interested reader will find in the book over 30 examples of possible applications in these fields) and describing uniformly many psychological/sociological phenomena connected with reflexion, viz., implicit control, informational control via the mass media, reflexion in chess, art works, etc. The present book is intended for experts in decision making and control of systems of an interdisciplinary nature, as well as for undergraduates and postgraduates.Table of ContentsIntroduction. 1. Reflexion in decision-making 2. Informational reflexion and control 3. Strategic reflexion and control 4. Applied models of informational and reflexive control. Conclusion.

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Book SynopsisStochastic Communities presents a theory of biodiversity by analyzing the distribution of abundances among species in the context of a community. The basis of this theory is a distribution called the J distribution. This distribution is a pure hyperbola and mathematically implied by the stochastic species hypothesis assigning equal probabilities of birth and death within the population of each species over varying periods of time. The J distribution in natural communities has strong empirical support resulting from a meta-study and strong theoretical support from a theorem that is mathematically implied by the stochastic species hypothesis.Trade Review"The science of ecology suffers from a disconnect between theory and direct observation. Mathematicians have thought that simple equations could explain ecology. Field ecologists have assumed the mathematicians are right. Thus, empirical ecological understanding and prediction have suffered. Dewdney is an exceptions; he does field work and he is a mathematician. In his wonderful book, he takes advantage of both parts of ecology. And if Dewdney has done his math right, this book opens a whole new door to understanding biodiversity and its myriad causes."- Daniel Botkin, Professor Emeritus in the Department of Ecology, Evolution, and Marine Biology at the University of California, Santa Barbara, and President of the Center for the Study of the Environment"… development of a theory and guide to sampling, … it will be of great interest to both empirical and theoretical ecologists." - Trends in Ecology and EvolutionTable of ContentsThe J-curve and the J distribution. The J-distribution and its variations. Sampling in practice and in theory. Compiling and analysing field data. Predictions from data. Extending the sample. Stochastic systems and the stochastic community. The metastudy: A review. Fossil J-curves. Summary of theory and open problems. Appendix A: Mathematical Notes and Computer Tools. Appendix B: Results of the metastudy for the J distribution. Appendix C: Results of the test for the J distribution in taxonomic data.

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Book SynopsisStochastic Modeling for Medical Image Analysis provides a brief introduction to medical imaging, stochastic modeling, and model-guided image analysis.Today, image-guided computer-assisted diagnostics (CAD) faces two basic challenging problems. The first is the computationally feasible and accurate modeling of images from different modalities to obtain clinically useful information. The second is the accurate and fast inferring of meaningful and clinically valid CAD decisions and/or predictions on the basis of model-guided image analysis.To help address this, this book details original stochastic appearance and shape models with computationally feasible and efficient learning techniques for improving the performance of object detection, segmentation, alignment, and analysis in a number of important CAD applications.The book demonstrates accurate descriptions of visual appearances and shapes of the goal objects and their background to help solve aTable of ContentsMedical Imaging Modalities. From Images to Graphical Models. IRF Models: Estimating Marginals. Markov-Gibbs Random Field Models: Estimating Signal Interactions. Applications: Image Alignment. Segmenting Multimodal Images. Segmenting with Deformable Models. Segmenting with Shape and Appearance Priors. Cine Cardiac MRI Analysis. Sizing Cardiac Pathologies.

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Book SynopsisThis book focuses on process simulation in chemical engineering with a numerical algorithm based on the moving finite element method (MFEM). It offers new tools and approaches for modeling and simulating time-dependent problems with moving fronts and with moving boundaries described by time-dependent convection-reaction-diffusion partial differential equations in one or two-dimensional space domains. It provides a comprehensive account of the development of the moving finite element method, describing and analyzing the theoretical and practical aspects of the MFEM for models in 1D, 1D+1d, and 2D space domains. Mathematical models are universal, and the book reviews successful applications of MFEM to solve engineering problems. It covers a broad range of application algorithm to engineering problems, namely on separation and reaction processes presenting and discussing relevant numerical applications of the moving finite element method derived from real-world process simulations.Table of Contents1. Modeling and Simulation in Chemical Engineering. 2. The Moving Finite Elements Method. 3. Solving 1D Time-Dependent Models. 4. Solving 2D Time-Dependent Problems. 5. Solving Two Scales 1D+1d Time-Dependent Problems. 6. Solving Moving Boundary Problems. 7. Looking Ahead. 8. Index

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Book SynopsisThe book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional impulsive differential equations, and fractional impulsive functional differential equations, which have not been covered by other books. It manifests different constructive methods by demonstrating how these techniques can be applied to investigate qualitative properties of the solutions of fractional systems. Since many applications have been included, the demonstrated techniques and models can be used in training students in mathematical modeling and in the study and development of fractional-order models.Table of ContentsIntroduction. Preliminary Notes. Qualitative Properties Definitions. Lyapunov Functions and their Fractional Derivatives. Fractional Comparison Lemmas. Stability and Boundedness. Lyapunov Stability. Theorems on Boundedness. Global Stability. Mittag-Leffler Stability. Practical Stability. Lipschitz Stability. Stability of Sets. Stability of Integral Manifolds. Almost Periodicity. Almost Periodic Solutions. Lyapunov Method for Almost Periodic Solutions. Uncertain Fractional Differential Systems. Applications. Fractional Impulsive Neural Networks. Stability and Synchronization. Almost Periodic Solutions. The Uncertain Case. Fractional Impulsive Biological Models. Lasota-Wazewska Models. Lotka-Volterra Models. Kolmogorov-type Models. Fractional Impulsive Models in Economics.

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Book SynopsisElastic plates form a class of very important mechanical structures that appear in a wide range of practical applications, from building bodies to microchip production. As the sophistication of industrial designs has increased, so has the demand for greater accuracy in analysis. This in turn has led modelers away from Kirchoff's classical theory for thin plates and toward increasingly refined models that yield not only the deflection of the middle section, but also account for transverse shear deformation. The improved performance of these models is achieved, however, at the expense of a much more complicated system of governing equations and boundary conditions.In this Monograph, the authors conduct a rigorous mathematical study of a number of boundary value problems for the system of partial differential equations that describe the equilibrium bending of an elastic plate with transverse shear deformation. Specifically, the authors explore the existence, uniqueness, and continuous dependence of the solution on the data. In each case, they give the variational formulation of the problems and discuss their solvability in Sobolev spaces. They then seek the solution in the form of plate potentials and reduce the problems to integral equations on the contour of the domain.This treatment covers an extensive range of problems and presents the variational method and the boundary integral equation method applied side-by-side. Readers will find that this feature of the book, along with its clear exposition, will lead to a firm and useful understanding of both the model and the methods.Trade Review"It is amazing that the authors have managed to cover so many fundamental boundary-value problems and present the variational method and the boundary integral equation method applied side-by-side in a single volume…This feature of the book will certainly strengthen understanding of both the model and the methods. The writing style is very clear, the book is self-contained and easy to read, and it should be extremely valuable to researchers interested in applied analysis and mathematical models in elasticity."-Proceedings of the Edinburgh Mathematical Society (2002, vol. 45) "This book will be useful for mathematicians, theoretical engineers, and all interested in mathematical modeling in elasticity."-European Mathematical Society Newsletter, No. 40 (June 2001)Table of ContentsIntroduction. Formulation of the Problems. Variational Formulation of the Dirichlet and Neumann Problems. Boundary Integral Equations for the Dirichlet and Neumann Problems. Transmission Boundary Value Problems. Plate Weakened by a Crack. Boundary Value Problems with Other Types of Boundary Conditions. Plate on a Generalized Elastic Foundation. Appendix.

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Book SynopsisIn this book on mathematical programming, the postulate spacial-time certainty of economic process at uncertainty conditions in finite-dimensional vector space and the principle piecewise-linear homogeneity of economic process at uncertainty conditions in finite-dimensional vector space are first suggested. A special theory on constructing piecewise-linear economic-mathematical models was developed, and a criterion of multivariate prediction of economic process and their control at uncertainty conditions in a finite-dimensional vector space was suggested. A packet of numerical programs for computer simulation in constructing and multivariate prediction of economic state with the help of n-element piecewise-linear economic-mathematical models with regard to the uncertainty factors effect in m-dimensional vector space is also suggested.This book is intended for students of economic and administrative specialties as well as for research associates in the sphere of economic-mathematical methods, management, and banking.Table of ContentsBrief Information on Finite-Dimensional Vector Space and its Application in Economics. Bases of Piecewise-Linear Economic-Mathematical Models with Regard to Influence of Unaccounted Factors in Finite-Dimensional Vector Space. Piecewise Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence in Three-Dimensional Vector Space. Piecewise-Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence on a Plane. Bases of Software for Computer Simulation and Multivariant Prediction of Economic Even at Uncertainty Conditions on the Base of N-Component Piecewise-Linear Economic-Mathematical Models in M-Dimensional Vector Space. Index.

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Book Synopsis„Was ist Mathematik?” – auf diese Frage gibt dieses dicke Buch zahllose Antworten. Mathematik ist eben viel mehr als ein Schul- und Studienfach oder Rechnen: Es ist Teil der menschlichen Kultur, ein riesiges aktives Forschungsgebiet und ein nützlicher Werkzeugkasten. „Was ist Mathematik?” – statt einer einzelnen Antwort zeichnen die Autoren ein Panorama, bunt und vielfältig. Da geht es um Philosophie, Beweise, große und kleine Probleme, fundamentale Konzepte, Teilgebiete, Forschungspraxis, Anwendungen der Mathematik. Und um Geschichten aus der Geschichte. Das Buch richtet sich an alle, die wissen und darüber nachdenken wollen, was Mathematik ist, insbesondere auch an Studierende der Mathematik. Es begleitet eine Vorlesung, die an der Freien Universität Berlin jährlich vor allem für Lehramtsstudierende angeboten wird.Table of ContentsWas ist Mathematik?- Mathematische Forschung.- Beweise.- Formeln, Zeichnungen und Bilder.- Philosophie der Mathematik.- Primzahlen.- Zahlenbereiche.- Unendlichkeit.- Dimensionen.- Zufall – Wahrscheinlichkeiten – Statistik.- Funktionen.- Anwendungen.- Rechnen.- Algorithmen und Komplexität.- Mathematik in der Öffentlichkeit.

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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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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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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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