Mathematical modelling Books
Cambridge University Press Computational Statistical Physics
Book SynopsisProviding a detailed and pedagogical account of the rapidly-growing field of computational statistical physics, this book covers both the theoretical foundations of equilibrium and non-equilibrium statistical physics, and also modern, computational applications such as percolation, random walks, magnetic systems, machine learning dynamics, and spreading processes on complex networks. A detailed discussion of molecular dynamics simulations is also included, a topic of great importance in biophysics and physical chemistry. The accessible and self-contained approach adopted by the authors makes this book suitable for teaching courses at graduate level, and numerous worked examples and end of chapter problems allow students to test their progress and understanding.Table of ContentsPreface; Part I. Stochastic Methods: 1. Random Numbers; 2. Random-Geometrical Models; 3. Equilibrium Systems; 4. Monte-Carlo Methods; 5. Phase Transitions; 6. Cluster Algorithms; 7. Histogram Methods; 8. Renormalization Group; 9. Learning and Optimizing; 10. Parallelization; 11. Non-Equilibrium Systems; Part II. Molecular Dynamics: 12. Basic Molecular Dynamics; 13. Optimizing Molecular Dynamics; 14. Dynamics of Composed Particles; 15. Long-Range Potentials; 16. Canonical Ensemble; 17. Inelastic Collisions in Molecular Dynamics; 18. Event-Driven Molecular Dynamics; 19. Non-Spherical Particles; 20. Contact Dynamics; 21. Discrete Fluid Models; 22. Ab-Initio Simulations; References; Index.
£59.99
World Scientific Europe Ltd Mathematical Modeling And Computation In Finance:
Book SynopsisThis book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.Supplementary Material:Solutions Manual is available to instructors who adopt this textbook for their courses. Please contact sales@wspc.com.
£999.99
Springer Nature Switzerland AG Special Relativity: An Introduction with 200
Book SynopsisThis textbook develops Special Relativity in a systematic way and offers problems with detailed solutions to empower students to gain a real understanding of this core subject in physics. This new edition has been thoroughly updated and has new sections on relativistic fluids, relativistic kinematics and on four-acceleration. The problems and solution section has been significantly expanded and short history sections have been included throughout the book.The approach is structural in the sense that it develops Special Relativity in Minkowski space following the parallel steps as the development of Newtonian Physics in Euclidian space. A second characteristic of the book is that it discusses the mathematics of the theory independently of the physical principles, so that the reader will appreciate their role in the development of the physical theory.The book is intended to be used both as a textbook for an advanced undergraduate teaching course in Special Relativity but also as a reference book for the future. Table of ContentsMathematical Part.- The Structure of the Theories of Physics.- Newtonian Physics.- The Foundation of Special Relativity.- The Physics of the Position Four-Vector.- Relativistic Kinematics.- Four-Acceleration.- Paradoxes.- Mass – Four-Momentum.- Relativistic Reactions.- Four-Force.- Irreducible Decompositions.- The Electromagnetic Field.- Relativistic Angular Momentum.- The Covariant Lorentz Transformation.- Geometric Description of Relativistic Interactions.
£72.64
Springer Nature Switzerland AG A Primer on Mathematical Modelling
Book SynopsisIn this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers.A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites.This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasioThis book is addressed to any student interested in learning how to construct and apply mathematical models.Trade Review“The book is extremely well written and is spectacular in its beauty. It is full with colorful pictures and figures, with many clear graphs, algorithms, codes (written in Octave) and tables, which makes reading the book a real joy. … This is a superb book for readers doing their initial steps in the wonderful world of modeling. I recommended it to my 17-year-old nephew, who is now reading it with great enthusiasm.” (Dan Givoli, IACM Expressions, Issue 50, July, 2022)“It is thus appropriate for junior college students. It is even suitable for self-study and independent research projects. … Professors Quarteroni and Gervasio have written a nice and fun book, which also constitutes a useful toolbox for anyone who wants to get acquainted with the methods of Applied Mathematics.” (Fernando Tohmé, zbMATH 1475.00018, 2022)“The book is an outstanding document from an educational point of view. ... The interaction of the simplicity of mathematical methods and the sophistication of the three main applications is very well done. In summary, this new book is highly recommended for both undergraduate and graduate students who are interested in mathematical modeling … .” (Thomas Wick, SIAM Review, Vol. 63 (3), September, 2021)Table of Contents1. A warm-up to models.- 2. Getting started.- 3. Reckoning with the computer.- 4. A virtual surfer for the web.- 5. A network of capillaries.- 6. Predators and preys in the maths ocean.- 7. Take-home message.- 8. Solutions to exercises.
£33.24
Springer Nature Switzerland AG Non-Local Cell Adhesion Models: Symmetries and
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.
£999.99
Springer Nature Switzerland AG Measuring Professional Competence for the
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.
£999.99
Springer Nature Switzerland AG Recent Advances in Industrial and Applied
Book SynopsisThis open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.Table of Contents1 M. Berger, Asteroid-Generated Tsunamis: A Review.- 2 A. Bermúdez, Some Case Studies in Environmental and Industrial Mathematics.- 3 Z. Cai et al., Hyperbolic Model Reduction for Kinetic Equations.- 4 A. Cohen et al., State Estimation - The Role of Reduced Models.- 5 C. Conca, Modelling Our Sense Of Smell.- 6 L. Edelstein-Keshet, Pattern formation inside living cells.- 7 M. Garzon et al., Efficient Algorithms for Tracking Moving Interfaces.- 8 K. Lauter, Private AI: Machine Learning on Encrypted Data.- 9 C. Le Bris, Mathematical approaches for contemporary materials science: Addressing defects in the microstructure.- 10 H. Leng et al., An iterative thresholding method for topology optimization for the Navier-Stokes flow.- 11 K. Sako, Cryptography and Digital Transformation.- 12 H. Suito et al., Numerical Study for Blood Flows in Thoracic Aorta.- 13 J.A.C. Weideman, Dynamics of Complex Singularities of Nonlinear PDEs: Analysis and Computation.
£33.24
Springer International Publishing AG Uncertain Rule-Based Fuzzy Systems: Introduction
Book SynopsisThe second edition of this textbook provides a fully updated approach to fuzzy sets and systems that can model uncertainty — i.e., “type-2” fuzzy sets and systems. The author demonstrates how to overcome the limitations of classical fuzzy sets and systems, enabling a wide range of applications from time-series forecasting to knowledge mining to control. In this new edition, a bottom-up approach is presented that begins by introducing classical (type-1) fuzzy sets and systems, and then explains how they can be modified to handle uncertainty. The author covers fuzzy rule-based systems – from type-1 to interval type-2 to general type-2 – in one volume. For hands-on experience, the book provides information on accessing MatLab and Java software to complement the content. The book features a full suite of classroom material.Table of ContentsIntroduction.- Part 1: Type-1 Fuzzy Sets and Systems.- Short Primers on Type-1 Fuzzy Sets and Fuzzy Logic.- Type-1 Fuzzy Logic Systems.- Part 2: Type-2 Fuzzy Sets.- Sources of Uncertainty.- Type-2 Fuzzy Sets.- Operations on and Properties OF Type-2 Fuzzy Sets.- Type-2 Relations and Compositions.- Centroid of a Type-2 Fuzzy Set: Type-Reduction.- Part 3: Type-2 Fuzzy Logic Systems.- Mamdani Interval Type-2 Fuzzy Logic Systems (IT2 FLSS).- TSK Interval Type-2 Fuzzy Logic Systems.- General Type-2 Fuzzy Logic Systems (GT2 FLSS).- Conclusion.
£74.99
Springer International Publishing AG Modeling Life: The Mathematics of Biological
Book SynopsisThis book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?Trade Review“The book can serve as an introduction to the field of modeling not only for university students but for any person interested in the field with little or no knowledge of calculus. … This book is a very interesting deviation from this prevailing paradigm. It takes the essence of calculus and presents it in a way which is accessible and usable in the practice of life sciences professionals.” (Svetoslav Markov, zbMATH 1397.92001, 2018)Table of Contents1. Modeling, Change, and Simulation.- 2. Derivatives and Integrals.- 3. Equilibrium Behavior.- 4. Non-Equilibrium Dynamics: Oscillation.- 5. Chaos.- 6. Linear Algebra.- 7. Multivariable Systems.- Bibliography.- Index.
£999.99
Springer International Publishing AG Modeling Life: The Mathematics of Biological
Book SynopsisThis book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?Trade Review“The book can serve as an introduction to the field of modeling not only for university students but for any person interested in the field with little or no knowledge of calculus. … This book is a very interesting deviation from this prevailing paradigm. It takes the essence of calculus and presents it in a way which is accessible and usable in the practice of life sciences professionals.” (Svetoslav Markov, zbMATH 1397.92001, 2018)Table of Contents1. Modeling, Change, and Simulation.- 2. Derivatives and Integrals.- 3. Equilibrium Behavior.- 4. Non-Equilibrium Dynamics: Oscillation.- 5. Chaos.- 6. Linear Algebra.- 7. Multivariable Systems.- Bibliography.- Index.
£47.49
Springer Verlag, Singapore Stability and Control of Nonlinear Time-varying
Book SynopsisThis book presents special systems derived from industrial models, including the complex saturation nonlinear functions and the delay nonlinear functions. It also presents typical methods, such as the classical Liapunov and Integral Inequalities methods. Providing constructive qualitative and stability conditions for linear systems with saturated inputs in both global and local contexts, it offers practitioners more concise model systems for modern saturation nonlinear techniques, which have the potential for future applications. This book is a valuable guide for researchers and graduate students in the fields of mathematics, control, and engineering.Table of ContentsIntroduction.- Novel Mathematical Modeling and Stability Analysis of Linear Uncertain Systems Subject to Actuator Saturations.- Commuting Matrices, Equilibrium Points for Control Systems with Single Saturated Input.- Stability and Closed Trajectory for 2nd Order Control Systems with Single Saturated Input.- Equilibrium Points Analysis of 2nd Order Differential Systems with Single Saturated Input.- Stability Analysis for Lurie Nonlinear Systems with Time-varying Plant and Actuator under Time-varying Delay Feedback.- Several Stability Criteria on Differential Inclusions with Nonlinear Integral Delays.- Generalization of Integral Inequalities and (c1,c1) stability of Neutral Delay Differential Equations.- Several Integral Inequalities and Their Applications in Nonlinear Differential Systems.- Fuzzy Observer, Fuzzy Controller Design and Common Hurwitz Matrices Analysis for a class of Uncertain Nonlinear System.- The Three-stage Chaotic Communication System Based on The Unified Chaotic System.- Nonlinear Dynamic Model of 2K-H Planetary Gear Transmission System And Its Chaotic Characteristics.
£999.99
Springer Verlag, Singapore Risk-Based Engineering: An Integrated Approach to
Book SynopsisThe book comprehensively covers the various aspects of risk modeling and analysis in technological contexts. It pursues a systems approach to modeling risk and reliability concerns in engineering, and covers the key concepts of risk analysis and mathematical tools used to assess and account for risk in engineering problems. The relevance of incorporating risk-based structures in design and operations is also stressed, with special emphasis on the human factor and behavioral risks. The book uses the nuclear plant, an extremely complex and high-precision engineering environment, as an example to develop the concepts discussed. The core mechanical, electronic and physical aspects of such a complex system offer an excellent platform for analyzing and creating risk-based models. The book also provides real-time case studies in a separate section to demonstrate the use of this approach. There are many limitations when it comes to applications of risk-based approaches to engineering problems. The book is structured and written in a way that addresses these key gap areas to help optimize the overall methodology. This book serves as a textbook for graduate and advanced undergraduate courses on risk and reliability in engineering. It can also be used outside the classroom for professional development courses aimed at practicing engineers or as an introduction to risk-based engineering for professionals, researchers, and students interested in the field.Table of ContentsPreface.- Chapter 1: Introduction.- Chapter 2: Risk Characterization.- Chapter 3: Probabilistic Approach to Reliability Engineering.- Chapter 4: System Reliability Modelling.- Chapter 5: Life Prediction.- Chapter 6: Probabilistic Risk Assessment.- Chapter 7: Risk-based Design.- Chapter 8: Fatigue and Fracture Risk Assessment- A Probabilistic Framework.- Chapter 9: Uncertainty Modeling.- Chapter 10: Human Reliability Analysis.- Chapter 11: Digital system reliability.- Chapter 12: Physics of Failure.- Chapter 13: Prognostics and Health Management.- Chapter 14: Risk Informed Decisions.- Chapter 15: Risk-based / Risk-informed Applications.- Appendix: Statistical Tables.
£82.49
Oxford University Press Applied Statistics with R A Practical Guide for
Book SynopsisThis book uses the statistical language R, which is the choice of ecologists worldwide and is rapidly becoming the 'go-to' stats program throughout the life-sciences. Furthermore, by using a single, real-world dataset throughout the book, readers are encouraged to become deeply familiar with an imperfect but realistic set of data.Trade ReviewApplied Statistics with R will keep you engaged with its humor and humility while teaching the fundamentals of modern biological data analysis. * Morgan W. Tingley, The Quarterly Review of Biology *This book excels at...taking away the fear of coding that seems to be an epidemic among students. It is written in a very conversational tone and the author explains every line of code, avoiding any technical language. * Julia Balogh, Goethe-Universität Frankfurt am Main, Germany, ISBE Newsletter Vol 36 *Table of ContentsPreface 1: Introduction to R 2: Before You Begin (aka Thoughts on Proper Data Analysis) 3: Exploratory Data Analysis and Data Summarization 4: Introduction to Plotting 5: Basic Statistical Analyses using R 6: More Linear Models in R! 7: Generalized Linear Models 8: Mixed Effects Models 9: Advanced Data Wrangling and Plotting 10: Writing Loops and Functions in R 11: Final Thoughts
£999.99
Princeton University Press A Biologists Guide to Mathematical Modeling in
Book SynopsisServes as a how-to guide for developing mathematical models in biology. Starting at an elementary level of mathematical modeling, this title gradually builds from classic models in ecology and evolution to more intricate class-structured and probabilistic models. It provides primers with instructive exercises.Trade ReviewHonorable Mention for the 2007 Best Professional/Scholarly Book in Biological Sciences, Association of American Publishers "A gentle but thorough introduction to the mathematical techniques employed in ecological and evolutionary theory. Readers who ... finish this well-written book will be prepared to read and understand a sizeable fraction of the current literature."--Donald L. DeAngelis, Quarterly Review of Biology "At long last, Sally Otto and Troy Day have provided relief for biologists and epidemiologists in search of an easily read, practical, and thorough starting point from which to learn mathematical modeling... We would recommend this book over shorter texts that are labeled as 'introductory'... The depth and detail that Otto and Day have included in this text arc appealing rather than intimidating, and the structure of the text is empowering rather than didactic or formulaic."--Sanjay Basu and Alison P. Galvani, Siam Review "[T]he great value of the Otto/Day book is that it attempts pedagogical soundness, and so is useful for teaching. Besides being perfectly readable, it engages and impresses the reader quickly not only with the subject matter, but also with the quality of printing and layout which have to be seen to be believed. These praises may sound lavish by many a reader of these columns but first see the book or better still buy the volume and you will see our passion and rage for going all out in praise of this volume."--Current Engineering Practice "I highly recommend this book for every university biology department because it provides both a unique, and often uplifting, introduction and a comprehensive reference of techniques for building and analysing mathematical models."--Volker Grimm, Basic and Applied Ecology "I cannot help but think that future textbook authors will want to have Otto and Day front and center on the work desk, for this is a valuable source of material... This book stands out, and its contribution is quite apparent. In sum, this book is a valuable contribution to the literature, and one to which I expect to refer regularly in connection with my teaching and writing duties."--Steven G. Krantz, UMAP Journal "[A] great textbook... [M]asterful use of figures and illustrations and exercises ... provide the reader with valuable practice in constructing models and implementing related mathematical techniques. I certainly recommend this text and can attest to its usefulness for budding researchers in the biological sciences."--Jason M. Graham, MAA ReviewsTable of ContentsPreface ix Chapter 1: Mathematical Modeling in Biology 1 1.1 Introduction 1 1.2 HIV 2 1.3 Models of HIV/AIDS 5 1.4 Concluding Message 14 Chapter 2: How to Construct a Model 17 2.1 Introduction 17 2.2 Formulate the Question 19 2.3 Determine the Basic Ingredients 19 2.4 Qualitatively Describe the Biological System 26 2.5 Quantitatively Describe the Biological System 33 2.6 Analyze the Equations 39 2.7 Checks and Balances 47 2.8 Relate the Results Back to the Question 50 2.9 Concluding Message 51 Chapter 3: Deriving Classic Models in Ecology and Evolutionary Biology 54 3.1 Introduction 54 3.2 Exponential and Logistic Models of Population Growth 54 3.3 Haploid and Diploid Models of Natural Selection 62 3.4 Models of Interactions among Species 72 3.5 Epidemiological Models of Disease Spread 77 3.6 Working Backward--Interpreting Equations in Terms of the Biology 79 3.7 Concluding Message 82 Primer 1: Functions and Approximations 89 P1.1 Functions and Their Forms 89 P1.2 Linear Approximations 96 P1.3 The Taylor Series 100 Chapter 4: Numerical and Graphical Techniques--Developing a Feeling for Your Model 110 4.1 Introduction 110 4.2 Plots of Variables Over Time 111 4.3 Plots of Variables as a Function of the Variables Themselves 124 4.4 Multiple Variables and Phase-Plane Diagrams 133 4.5 Concluding Message 145 Chapter 5: Equilibria and Stability Analyses--One-Variable Models 151 5.1 Introduction 151 5.2 Finding an Equilibrium 152 5.3 Determining Stability 163 5.4 Approximations 176 5.5 Concluding Message 184 Chapter 6: General Solutions and Transformations--One-Variable Models 191 6.1 Introduction 191 6.2 Transformations 192 6.3 Linear Models in Discrete Time 193 6.4 Nonlinear Models in Discrete Time 195 6.5 Linear Models in Continuous Time 198 6.6 Nonlinear Models in Continuous Time 202 6.7 Concluding Message 207 Primer 2: Linear Algebra 214 P2.1 An Introduction to Vectors and Matrices 214 P2.2 Vector and Matrix Addition 219 P2.3 Multiplication by a Scalar 222 P2.4 Multiplication of Vectors and Matrices 224 P2.5 The Trace and Determinant of a Square Matrix 228 P2.6 The Inverse 233 P2.7 Solving Systems of Equations 235 P2.8 The Eigenvalues of a Matrix 237 P2.9 The Eigenvectors of a Matrix 243 Chapter 7: Equilibria and Stability Analyses--Linear Models with Multiple Variables 254 7.1 Introduction 254 7.2 Models with More than One Dynamic Variable 255 7.3 Linear Multivariable Models 260 7.4 Equilibria and Stability for Linear Discrete-Time Models 279 7.5 Concluding Message 289 Chapter 8: Equilibria and Stability Analyses--Nonlinear Models with Multiple Variables 294 8.1 Introduction 294 8.2 Nonlinear Multiple-Variable Models 294 8.3 Equilibria and Stability for Nonlinear Discrete-Time Models 316 8.4 Perturbation Techniques for Approximating Eigenvalues 330 8.5 Concluding Message 337 Chapter 9: General Solutions and Tranformations--Models with Multiple Variables 347 9.1 Introduction 347 9.2 Linear Models Involving Multiple Variables 347 9.3 Nonlinear Models Involving Multiple Variables 365 9.4 Concluding Message 381 Chapter 10: Dynamics of Class-Structured Populations 386 10.1 Introduction 386 10.2 Constructing Class-Structured Models 388 10.3 Analyzing Class-Structured Models 393 10.4 Reproductive Value and Left Eigenvectors 398 10.5 The Effect of Parameters on the Long-Term Growth Rate 400 10.6 Age-Structured Models--The Leslie Matrix 403 10.7 Concluding Message 418 Chapter 11: Techniques for Analyzing Models with Periodic Behavior 423 11.1 Introduction 423 11.2 What Are Periodic Dynamics? 423 11.3 Composite Mappings 425 11.4 Hopf Bifurcations 428 11.5 Constants of Motion 436 11.6 Concluding Message 449 Chapter 12: Evolutionary Invasion Analysis 454 12.1 Introduction 454 12.2 Two Introductory Examples 455 12.3 The General Technique of Evolutionary Invasion Analysis 465 12.4 Determining How the ESS Changes as a Function of Parameters 478 12.5 Evolutionary Invasion Analyses in Class-Structured Populations 485 12.6 Concluding Message 502 Primer 3: Probability Theory 513 P3.1 An Introduction to Probability 513 P3.2 Conditional Probabilities and Bayes' Theorem 518 P3.3 Discrete Probability Distributions 521 P3.4 Continuous Probability Distributions 536 P3.5 The (Insert Your Name Here) Distribution 553 Chapter 13: Probabilistic Models 567 13.1 Introduction 567 13.2 Models of Population Growth 568 13.3 Birth-Death Models 573 13.4 Wright-Fisher Model of Allele Frequency Change 576 13.5 Moran Model of Allele Frequency Change 581 13.6 Cancer Development 584 13.7 Cellular Automata--A Model of Extinction and Recolonization 591 13.8 Looking Backward in Time--Coalescent Theory 594 13.9 Concluding Message 602 Chapter 14: Analyzing Discrete Stochastic Models 608 14.1 Introduction 608 14.2 Two-State Markov Models 608 14.3 Multistate Markov Models 614 14.4 Birth-Death Models 631 14.5 Branching Processes 639 14.6 Concluding Message 644 Chapter 15: Analyzing Continuous Stochastic Models--Diffusion in Time and Space 649 15.1 Introduction 649 15.2 Constructing Diffusion Models 649 15.3 Analyzing the Diffusion Equation with Drift 664 15.4 Modeling Populations in Space Using the Diffusion Equation 684 15.5 Concluding Message 687 Epilogue: The Art of Mathematical Modeling in Biology 692 Appendix 1: Commonly Used Mathematical Rules 695 A1.1 Rules for Algebraic Functions 695 A1.2 Rules for Logarithmic and Exponential Functions 695 A1.3 Some Important Sums 696 A1.4 Some Important Products 696 A1.5 Inequalities 697 Appendix 2: Some Important Rules from Calculus 699 A2.1 Concepts 699 A2.2 Derivatives 701 A2.3 Integrals 703 A2.4 Limits 704 Appendix 3: The Perron-Frobenius Theorem 709 A3.1: Definitions 709 A3.2: The Perron-Frobenius Theorem 710 Appendix 4: Finding Maxima and Minima of Functions 713 A4.1 Functions with One Variable 713 A4.2 Functions with Multiple Variables 714 Appendix 5: Moment-Generating Functions 717 Index of Definitions, Recipes, and Rules 725 General Index 727
£69.00
Kogan Page Ltd Neuro Design
Book SynopsisDarren Bridger is a consultant to designers and marketers, advising on using and analyzing data that tap into consumers' non-conscious thinking and motivations. He was one of the original pioneers of the Consumer Neuroscience industry, helping to pioneer two of the first companies in the field then joining the world's largest agency, Neurofocus (now part of the Nielsen company). He is currently Head of Insights at NeuroStrata. Trade Review"A super, easy-to-read book demystifying the world of neuro design, addressing the balance between the role of human creativity and that of neuroscience in modern design. If you think neuro design is about creating bland designs by deconstructing beauty, you need to read this book. It's not about that at all. Darren Bridger introduces all the major themes, key methods and tools underlying the science in engaging, manageable chunks. Any book that explains the allure of memes has to get five stars from me." * Jamie Croggon, Design Director, SharkNinja *"With solid science as the starting point, Darren Bridger provides an eminently practical guide to designing for your customer's brain. Neuro Design is packed with actionable strategies and techniques, and is a must-read for every marketer and designer." * Roger Dooley, author of Brainfluence *"A topic which should be of great importance to anyone in the business of retailing, advertising and marketing. Darren Bridger deals with complex topics in an engaging and practical manner, covering all aspects of the interplay between brain function and product design. Such an understanding is crucial for ensuring consumers stop and buy, rather than walking on by." * Dr David Lewis, Chairman of Mindlab International & Author of The Brain Sell *Table of Contents Section - 01: What is Neuro Design?; Section - 02: Neuroaesthetics; Section - 03: Processing Fluency; Section - 04: How First Impressions Work; Section - 05: Multisensory and Emotional Design; Section - 06: Visual Saliency Maps; Section - 07: Visual Persuasion and Behavioural Economics; Section - 08: Designing for Screens; Section - 09: Viral Designs; Section - 10: Designing Presentation Slides; Section - 11: Conducting Neuro Design Research; Section - 12: Conclusion;
£24.99
Cambridge University Press Entropy and Diversity
Book SynopsisThe global biodiversity crisis is one of humanity''s most urgent problems, but even quantifying biological diversity is a difficult mathematical and conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It was born of research in category theory, is given strength by information theory, and is fed by the ancient field of functional equations. It applies the power of the axiomatic method to a biological problem of pressing concern, but it also presents new theorems that stand up as mathematics in their own right, independently of any application. The question ''what is diversity?'' has surprising mathematical depth, and this book covers a wide breadth of mathematics, from functional equations to geometric measure theory, from probability theory to number theory. Despite this range, the mathematical prerequisites are few: the main narrative thread of this book requires no more than an undergraduate course in analysis.Trade Review'The book shows that the theory of diversity measurement is fertile soil for new mathematics, just as much as the neighboring but far more thoroughly worked field of information theory.' Hirokazu Nishimura, ZB Math Reviews'Each new mathematical concept is introduced from fundamental principles, in a lucid, engaging style, keeping the core biological application in the foreground … Leinster provides us with the tools to clearly assess what we are losing, so that we may focus better on what we can save.' Benjamin Allen, The Quarterly Review of Biology'The book is a welcome addition to the theory of biodiversity in that it covers the topics of entropy and diversity in a mathematically rigorous yet fairly accessible way … Recommended.' M. Bona, Choice MagazineTable of ContentsIntroduction; 1. Fundamental functional equations; 2. Shannon entropy; 3. Relative entropy; 4. Deformations of Shannon entropy; 5. Means; 6. Species similarity and magnitude; 7. Value; 8. Mutual information and metacommunities; 9. Probabilistic methods; 10. Information loss; 11. Entropy modulo a prime; 12. The categorical origins of entropy; Appendix A. Proofs of background facts; Appendix B. Summary of conditions; References; Index of notation; Subject index.
£46.27
John Murray Press Escape from Model Land: How Mathematical Models
Book SynopsisShortlisted for Best Maths Book of 2022 by Chaulkdust Magazine'A brilliant account of how models are so often abused and of how they should be used' John KayHow do mathematical models shape our world - and how can we harness their power for good?Models are at the centre of everything we do. Whether we use them or are simply affected by them, they act as metaphors that help us better understand the increasingly complex problems facing us in the modern world. Without models, we couldn't begin to tackle three of the major challenges facing modern society: regulation of the economy, climate change and the COVID-19 pandemic. Yet in recent years, the validity of the models we use has been hotly debated and there has been renewed awareness of the disastrous consequences when the makers and interpreters of models get things wrong.Drawing on contemporary examples from finance, climate and health policy, Erica Thompson explores what models are, why we need them, how they work and what happens when they go wrong. This is not a book that argues we should do away with models, but rather, that we need to properly understand how they are constructed - and how some of the assumptions that underlie the models we use can have significant unintended consequences. Unexpectedly humorous, thought-provoking and passionate, this is essential reading for everyone.Trade ReviewA brilliant account of how models are so often abused and of how they should be used -- John KayA wise, lucid and compelling guide to how mathematical modelling shapes our world. Dr Thompson teaches us how to go from being unthinking consumers of models to sophisticated users, combining a rich variety of vivid examples and case studies with deep conceptual expertise -- Stian Westlake, CEO, Royal Statistical SocietyDemystifies the process of making the mathematical models that are increasingly used to make decisions about our lives . . . A thought-provoking and helpful guide for data scientists and decision makers alike -- Stephanie Hare, author of TECHNOLOGY IS NOT NEUTRALCarefully researched and beautifully written . . . For an open-minded reader keen to expose, understand and potentially reconstruct their own worldview, Escape from Model Land is, at the same time, an uncomfortable and uplifting read. It shines a gentle light on many of our own norms and beliefs -- Kevin AndersonAn eye-opening account . . . Thompson offers a host of lessons . . . The result is a thoughtful, convincing look at how data works -- Publisher's WeeklyBrilliant . . . a highly engaging work of popular science -- E&T Magazine[A] healthy realism about data, algorithms and their limitations . . . Thompson asks data scientists to be conscious of the choices and values in a model's design . . . [offering] the basis for a constructive agenda -- The EconomistData, computing power, AI, and the models that use them will continue to proliferate. The wisdom, life experience, and humility to make the best use of those powerful tools will remain scarce. This delightfully wide-ranging book offers heaps of the latter to help us generate genuine insights from the former -- Charles J. Wheelan, bestselling author of NAKED STATISTICSOffers a contemplative, densely encapsulated summary of her reflection and research . . . it's up to us to learn from models without being drawn in by their seductive elegance, and to ensure that the lessons from Model Land find substantive expression where it actually matters: in our messy, material, magnificent world -- Wall Street Journal
£999.99
Springer International Publishing AG Graph Representation Learning
Book SynopsisGraph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning. Table of ContentsPreface.- Acknowledgments.- Introduction.- Background and Traditional Approaches.- Neighborhood Reconstruction Methods.- Multi-Relational Data and Knowledge Graphs.- The Graph Neural Network Model.- Graph Neural Networks in Practice.- Theoretical Motivations.- Traditional Graph Generation Approaches.- Deep Generative Models.- Conclusion.- Bibliography.- Author's Biography .
£22.99
Industrial Press Inc.,U.S. Guide to Mathematical Modelling
Book SynopsisOffering an introduction to Mathematical Modeling, this book encourages readers to participate in the investigation of various modeling examples.
£46.80
Nova Science Publishers Inc Mathematical Models of Economic Growth & Crises
Book SynopsisThe main goal of this book is to present coherent mathematical models to describe an economic growth and related economic issues. The book is a continuation of the authors previous book Mathematical Dynamics of Economic Markets (9781594545283), which presented mathematical models of economic forces acting on the markets. In his previous book, the author described a system of ordinary differential equations, which connected together economic forces behind the products demand, supply and prices on the market. The author focuses on a specific aspect of how to modify the said system of ordinary differential equations, in order to describe the phenomenon of economic growth. In order to achieve clarity, the author restricted himself to economic processes arising on the markets of a single-product economy. Economic growth is presented as a result of savings and investment occurring on the markets. The markets participants withdraw part of the product from markets in the form of savings and use the withdrawn product in production in the form of an investment. The withdrawal drives the products supply on the market down while at the same time driving the products price up, which in turn drives the products demand down. When an impact of the products price increase exceeds an impact of the products demand decrease, economic growth occurs. Contrarily, one observes an economic decline in the opposite situation. The author looks into various aspects that savings and investment exert on the market. He in particular discusses the models that examine an economic growth in situations when savings and investment were done in the form of a one-time withdrawal of the product, constant-rate withdrawal of product, constant-accelerated withdrawal of product, and exponential withdrawal of product from the market. The author further examines an impact of four economic concepts on economic growth -- demand, supply, investment, and debt. He presents mathematical models exploring interconnections among these concepts and studies their mutual impacts on both economic growth and decline. He builds a mathematical model in order to verify a hypothesis that weak recovery after the financial crisis could be attributed to the decline of investments that were not compensated by the decrease of an interest rate. The author also looks into the phenomenon of economic crises and builds a few mathematical models. The models of four economic crises are considered. The first model concerns the last financial crisis where an author tried to explain how relatively small disturbances on financial markets had produced a large impact on the real economy. His conclusion is that fluctuations on connected markets amplify each other, which is known as the resonance phenomenon. The second model relates to the monetary part of Japanese economic policy known as Abenomics, where the price of Japanese bonds decreases and the yield increases. The author builds a mathematical model to investigate this phenomenon. The third model is about a secular stagnation hypothesis advanced by Lawrence Summers. The author complements his model of economic growth with the external supply of product to the market. He found that external supply provided with either constant rate or constant acceleration can cause a restricted or unrestricted economic decline, respectively. The fourth model is a model describing the four stages of the Greek economic crisis (before the Eurozone, before the Euro crisis, after the Euro crisis, and during the austerity period) and two potential recovery stages (with austere and benign economic transformations).
£148.79
Nova Science Publishers Inc Concepts, Mathematical Modelling and Applications
Book SynopsisAlthough there are probably enough publications about mechanical circulatory support, they do not seem to address the theoretical aspects with sufficient details. A more detailed knowledge of the interaction between ventricular assist devices (VADs) and the cardiovascular system may help with their clinical management with a view to improve patients outcomes.The aim is a different approach based on the development of critical thinking that may generate further ideas in the context of current developments. We must understand the time-varying elastance theory, which has played a key role in cardiovascular modelling and is often used for numerical/hybrid simulations of a mechanically supported left ventricle. The limitations of the original concept have led to further modifications of the theory and alternative approaches worth exploring. Ventricular interactions have significant implications in cardiac mechanics and it is extremely important to understand their role during VAD support. We must understand the physiology of VAD support and their connection to the circulation. Aortic valve physiology during support with rotary blood pumps has important implications on device performance. The modelling approach to pneumatic pulsatile VADs and their current role is addressed. The principles behind magnetic levitation technology are explained in details in view of its contribution to the progress in this field. Trans-cutaneous external transmission energy system technology has great potential, but the physics behind it does not get explained enough. The potential of a simulation approach in the clinical environment is discussed in relation to optimization of device treatment, outcome prediction and training of medical and nursing staff. These are some of the key concepts being addressed in this book which biomedical engineers, clinicians and academics should hopefully find educational and helpful according to their needs.VADs have become the standard of care for patients in advanced heart failure, but we must understand their strengths and limitations in order to make further progress and achieve their full potential.
£999.99
Nova Science Publishers Inc Mathematical Modeling for the Solution of
Book SynopsisThese books are intended for undergraduate, graduate researchers and practitioners in computational sciences, and as reference books for an advanced computational methods course. We have included new results for iterative procedures in abstract spaces general enough for handling inverse problems in various situations related to real life problems through mathematical modeling. These books contain a plethora of updated bibliography and provide comparison between various investigations made in recent years in the field of computational mathematics in the wide sense. Iterative processes are the tools used to generate sequences approximating solutions of equations describing the real life problems stated above and others originating from biosciences, engineering, mathematical economics, mathematical biology, mathematical chemistry, mathematical physics medicine, mathematical programming, and other disciplines. These books also provide, recent advancements on the study of iterative procedures, and can be used as a source from which one can obtain the proper method to use in order to solve a problem. The books require a fundamental background in mathematical statistics, linear algebra and numerical analysis. It may be used as a self-study reference or as a supplementary text for an advanced course in biosciences, engineering and computational sciences.Table of ContentsFor more information, please visit our website at:https://novapublishers.com/shop/mathematical-modeling-for-the-solution-of-equations-and-systems-of-equations-with-applications-volume-iii/
£191.19
Nova Science Publishers Inc Mathematics & Modelling
Book SynopsisMathematics & Modelling
£120.79
Nova Science Publishers Inc Mathematical Modelling in the Theory of
Book SynopsisMathematical Modelling in the Theory of Multivelocity Continuum
£117.59
Nova Science Publishers Inc Mathematical Models in Environmental Policy
Book SynopsisPresents mathematical ideas and models that can be used to facilitate rational environmental policy making. Describes classical models for biological community performance, ecological system stability, and population dynamics, presents air pollution models and methods for solving emission problems, and highlights major results of the application of
£106.39
Nova Science Publishers Inc Differential Equations & Mathematical Modelling
Book SynopsisThis book presents translations of selected Russian papers on the theoretical aspects of differential equations and applications of mathematical methods to modelling. These papers have been selected for their high scientific standards, innovative approaches, and topical interests.
£92.79
Nova Science Publishers Inc Applied Mathematical Modeling
Book SynopsisThis new book focuses on important research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. It includes heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimisation; finite volume, finite element, and boundary element procedures; decision sciences in an industrial and manufacturing context; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering.
£159.99
Nova Science Publishers Inc Leading-Edge Applied Mathematical Modeling
Book SynopsisThis book covers new and significant research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. It includes heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimisation; finite volume, finite element, and boundary element procedures; decision sciences in an industrial and manufacturing context; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering.
£159.99
Nova Science Publishers Inc Environmental Modelling: New Research
Book SynopsisEnvironment models seek to re-create what occurs during some event in nature. It is much easier and practical to create computer models to run certain experiments than it is to go out and do the same experiment again and again. Computer models take equations which were usually formulated through testing under natural conditions, and put them into computer programs where they can be run quickly and easily. A model can then output the results of doing these equations into a form which can be output to a screen for the user to view. The aim is to improve the capacity to represent, understand, predict or manage the behaviour of environmental systems at all practical scales. This book presents the latest research from around the globe.
£86.99
Nova Science Publishers Inc Efficient Algorithms of Time Series Processing &
Book SynopsisThis book presents works on processing time series of observations in problems of meteorology, ichthyology, medical geography, epidemiology and demography. These works have been published by the authors within the last 4 years in the Russian journals and reported at various Russian and international conferences. The basic methods of processing of time series in the collected works are developed algorithms for: recognition of images, classifications, estimations of dispersions of fluctuations concerning a trend. The idea of construction of the first two algorithms consists in studying large outliers in time series. Such approach has allowed to construct quite simple for understanding and rather fast, as to computing, algorithms of recognition of images and classifications and to apply them in the problems that are characterised by large volumes of empirical information. The third of the specified algorithms is based on special transformations of time series to problems with a small trend and greater fluctuations. Application of traditional algorithms in the considered arrays of the empirical information demands complex calculations. The problems described in presented works, are actual and that''s why the using in them of the offered algorithms carries not illustrative, but substantial character. The problems in question: influence of meteorological factors on critical values: catch of fish(hunchback salmon) in the Amur river, freezing in the Tatar strait, numbers infected by tick-borne [vernal] encephalitis and other epidemic diseases in Primorye Territory, influence of economic transformations on various age groups of the population and on dynamics of a population in cities of the Primorye Territory, influence of global warming on fluctuations of surface temperature in various areas of the Far East.
£999.99
Nova Science Publishers Inc Mathematical Modelling
Book Synopsis
£999.99
Imperial College Press Modeling Coastal And Offshore Processes
Book SynopsisModeling is now a major tool for important environmental strategies. This book allows the non-specialist reader to understand and criticize current models of the shallow sea and coastal environments. Sufficient background on mathematics and statistics is covered, but readers disinclined to spend time on this may use the book as a reference guide in modeling. Topics include the numerical schemes used, modeling the sea bed, modeling shallow sea dynamics and, unusually for this type of book, modeling ecosystems and animals.Table of ContentsModeling Preliminaries; Modeling Techniques; Mathematical Foundations; Numerical Methods.
£67.45
Springer Nature Switzerland AG Computational Methods for Deep Learning Theoretic
Book SynopsisIntegrating concepts from deep learning, machine learning, and artificial neural networks, this highly unique textbook presents content progressively from easy to more complex, orienting its content about knowledge transfer from the viewpoint of machine intelligence. It adopts the methodology from graphical theory, mathematical models, and algorithmic implementation, as well as covers datasets preparation, programming, results analysis and evaluations.Beginning with a grounding about artificial neural networks with neurons and the activation functions, the work then explains the mechanism of deep learning using advanced mathematics. In particular, it emphasizes how to use TensorFlow and the latest MATLAB deep-learning toolboxes for implementing deep learning algorithms.As a prerequisite, readers should have a solid understanding especially of mathematical analysis, linear algebra, numerical analysis, optimizations, differential geometry, manifold, and information theory, as well as basic algebra, functional analysis, and graphical models. This computational knowledge will assist in comprehending the subject matter not only of this text/reference, but also in relevant deep learning journal articles and conference papers.This textbook/guide is aimed at Computer Science research students and engineers, as well as scientists interested in deep learning for theoretic research and analysis. More generally, this book is also helpful for those researchers who are interested in machine intelligence, pattern analysis, natural language processing, and machine vision.Dr. Wei Qi Yan is an Associate Professor in the Department of Computer Science at Auckland University of Technology, New Zealand. His other publications include the Springer title, Visual Cryptography for Image Processing and Security.
£52.24
Mathematical Society of Japan Hierarchy Of Semiconductor Equations: Relaxation
Book SynopsisThis volume provides a recent study of mathematical research on semiconductor equations. With recent developments in semiconductor technology, several mathematical models have been established to analyze and to simulate the behavior of electron flow in semiconductor devices. Among them, a hydrodynamic, an energy-transport and a drift-diffusion models are frequently used for the device simulation with the suitable choice, depending on the purpose of the device usage. Hence, it is interesting and important not only in mathematics but also in engineering to study a model hierarchy, relations among these models. The model hierarchy has been formally understood by relaxation limits letting the physical parameters, called relaxation times, tend to zero. The main concern of this volume is the mathematical justification of the relaxation limits. Precisely, we show that the time global solution for the hydrodynamic model converges to that for the energy-transport model as a momentum relaxation time tends to zero. Moreover, it is shown that the solution for the energy-transport model converges to that for the drift-diffusion model as an energy relaxation time tends to zero. For beginners' help, this volume also presents the physical background of the semiconductor devices, the derivation of the models, and the basic mathematical results such as the unique existence of time local solutions.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all marketsTable of ContentsIntroduction: Structure of Semiconductor Device; Mathematical Models; Review of Previous Results; Notation; Mathematical Problem and Main Results: Intial Boundary Value Problem for Hydrodynamic Model; Formal Computation of Relaxation Limits; Asymptotic Behavior of Hydrodynamic Model; Relaxation Time Limits; Outline of Proofs; Stationary Solutions: Unique Existence of Stationary Solutions; Relaxation Limits of Stationary Solutions; Energy-Transport Model: Uniform Estimate of Local Solution; Semi-Global Existence of Solution; Global Existence of Solution; Energy Relaxation Limit; Additional Regularity; Hydrodynamic Model: Uniform Estimate of Local Solution; Semi-Global Existence of Solution; Global Existence of Solution; Momentum and Energy Relaxation Limits; Appendices: Time Local Solvability of Energy-Transport Model; Time Local Solvability of Hydrodynamic Model.
£17.00
World Scientific Publishing Co Pte Ltd Computational Methods In Large Scale Simulation
Book SynopsisThis volume documents the research carried out by visiting scientists attached to the Institute for Mathematical Sciences (IMS) at the National University of Singapore and the Institute of High Performance Computing (IHPC) under the program “Advances and Mathematical Issues in Large Scale Simulation.” From 2002 to 2003, researchers from various countries gathered to initiate interesting and innovative work on various themes related to multiscale simulation and fast algorithms.Today, modeling and simulation are used extensively to solve complex problems and to reduce the use of experimentation during the design and analysis stage. It is important to know the various issues that have to be considered in the successful development of computational methodologies for such work.This volume is a compilation of the research by various visiting scientists in the area of modeling and multiscale simulation. Each article covers a major project and documents how computational methodology, mathematical modeling, high performance computing and simulation are combined in a multiscale scheme to solve a variety of complex problems. Some of these include the design, synthesis, processing, characterization and manufacture of nanomaterials and nanostructures, new algorithms for computational work, and grid computing.Through the included examples, readers can realize the vast potential of computational modeling and large scale simulation for the solution of problems in a variety of disciplines and applications.Table of Contents# Methods of Multiscale Modeling in Mechanics (W A Curtin) # Efficient and Accurate Boundary Methods for Computational Optics (C Hafner & J Smajic) # Finite Element Modeling of Periodic Structures (Z Lou & J-M Jin) # Factorization of Potential and Field Distributions without Utilizing the Addition Theorem (A-R Baghi-Wadji & E Li) # Virtualization-Aware Application Framework for Hierarchical Multiscale Simulations on a Grid (A Nakano et al.) # Molecular Dynamics Simulation and Local Quantities (T Ikeshoji) # Recent Advances in Modeling and Simulation of High-Speed Interconnects (M Nakhla & R Achar) # Multiscale Modeling of Degradation and Failure of Interconnect Lines Driven by Electromigration and Stress Gradients (R Atkinson & A M Cuitino)
£133.95
World Scientific Publishing Co Pte Ltd Global Derivatives: Products, Theory And Practice
Book SynopsisThis book provides a broad description of the financial derivatives business from a practitioner's point of view, with a particular emphasis on fixed income derivatives, a specific development on fixed income derivatives and a practical approach to the field. With particular emphasis on the concrete usage of mathematical models, numerical methods and the pricing methodology, this book is an essential reading for anyone considering a career in derivatives either as a trader, a quant or a structurer.Table of ContentsStandard Products and Markets; The Vanilla Products; Introduction to Financial Modeling; The Black-Scholes Model; Fixed Income Basis; European Options; Technical Toolbox; Yield Curve Modeling; Numerical Methods; Inflation; Hybrid Models; Product Catalog and Usage; 3rd Generation Trading System.
£100.70
World Scientific Publishing Co Pte Ltd Mathematical Understanding Of Infectious Disease
Book SynopsisThe Institute for Mathematical Sciences at the National University of Singapore hosted a research program on Mathematical Modeling of Infectious Diseases: Dynamics and Control from 15 August to 9 October 2005. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.This invaluable volume is a collection of three expanded lecture notes of those tutorials which cover a wide range of topics including basic mathematical details for various epidemic models, statistical distribution theory, and applications with real-life examples with implications for health policy makers.Table of ContentsThe Basic Epidemiology Models: Models, Expressions for R0, Parameter Estimation and Applications (H W Hethcote); Epidemiology Models with Variable Population Size (H W Hethcote); Age-Structured Epidemiology Models and Expressions for R0 (H W Hethcote); Non-Identifiables and Invariant Quantities in Infectious Disease Models (P Yan); Clinical and Public Health Applications of Mathematical Models (J W Glasser).
£90.25
World Scientific Publishing Co Pte Ltd Advances In Numerical Simulation Of Nonlinear
Book SynopsisMost of the Earth's surface is covered by water. Many aspects of our everyday lives and activities may be affected by water waves in some way. Sometimes, the waves can cause disaster. One of the examples was the tsunami that occurred in the Indian Ocean on 26 December 2004. This indicates how important it is for us to fully understand water waves, in particular the very large ones. One way to do so is to perform numerical simulation based on the nonlinear theory. Considerable research advances have been made in this area over the past decade by developing various numerical methods and applying them to emerging problems; however, until now there has been no comprehensive book to reflect these advances. This unique volume aims to bridge this gap.This book contains 18 self-contained chapters written by more than 50 authors from 12 different countries, many of whom are world-leading experts in the field. Each chapter is based mainly on the pioneering work of the authors and their research teams over the past decades. The chapters altogether deal with almost all numerical methods that have been employed so far to simulate nonlinear water waves and cover many important and very interesting applications, such as overturning waves, breaking waves, waves generated by landslides, freak waves, solitary waves, tsunamis, sloshing waves, interaction of extreme waves with beaches, interaction with fixed structures, and interaction with free-response floating structures. Therefore, this book provides a comprehensive overview of the state-of-the-art research and key achievements in numerical modeling of nonlinear water waves, and serves as a unique reference for postgraduates, researchers and senior engineers working in industry.Table of ContentsA Model for Fully Nonlinear Ocean Wave Simulations in Three Dimensions Derived by Using Fourier Inversion of Boundary Integral Equations (J Grue & D Fructus); Numerical Simulations of the Dynamics of Water Waves: Rogue Waves and Frequency Downshifting (C Kharif & J Touboul); Numerical Progress in Fully Nonlinear Potential Flow Modeling of 3D Extreme Ocean Waves (S T Grilli et al.); Time-Domain Simulation of Nonlinear Water Waves Using Spectral Methods (F Bonnefoy et al.); QALE-FEM Method and Its Applications to Simulation of Free-Response Floating Structures and Overturning Waves (Q W Ma & S Yan); Velocity Recovery Techniques in Finite Element Based on MEL Formulation (V Sriram et al.); Method of Fundamental Solutions for Fully Nonlinear Water Waves (D L Young et al.); A Review of Boussinesq Formulations for Water Waves (P A Madsen); Inter-Comparisons of Different Forms of Higher-Order Boussinesq Equations (Z L Zou et al.); Application of the Finite Volume Method to the Simulation of Nonlinear Water Waves (D Greaves); Developments in Multi-Fluid Finite Volume Cartesian Cut Cell Free Surface Capturing Methods (D M Causon et al.); Numerical Computation Methods for Extremely Nonlinear Wave-Body Interactions (M Kashiwagi et al.); Smoothed Particle Hydrodynamics for Nonlinear Water Waves (R A Dalrymple et al.); Modeling Nonlinear Water Waves with Eddy-Viscosity Turbulent SPH Models (R Issa & D Violeau); MLPG_R Method and Its Applications to Various Nonlinear Water Waves (Q W Ma); Large Eddy Simulation of Hydrodynamics Generated by Breaking Waves (P Lubin & J-P Caltagirone); Recent Development in Turbulence Models Applied to Unsteady Breaking Waves (Q Zhao & S Armfield); Freak Waves and Their Interaction with Structures (G Clauss).
£209.00
Springer-Verlag New York Inc. An Introduction to Mathematical Finance with
Book SynopsisThis textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student's conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper.The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probTrade Review“The book is thick with rich with applications and solid justifications of all concepts. … If you are a financial mathematics instructor, this book is for you. It progresses through easier topics to more advanced topics very well and is practical, meaningful, and more importantly, relevant to the 21st century financial student. … can be used as the one standard book for your class but can also be a springboard to research projects with your more advanced and curious students.” (Peter T. Olszewski, MAA Reviews, August, 2017)“This self-contained book is well organized and covers a broad range of classical topics of financial mathematics. A rich source of examples and exercises, the book is an ideal textbook for both undergraduate and graduate students that are interested in mathematical models in finance. The book can also be used for mathematically trained students and individuals in actuarial science to prepare for professional exams.” (Zhuo Jin, Mathematical Reviews, May, 2017)“The book is an undergraduate textbook in mathematical finance with applications. … The textbook is aimed at advanced undergraduates, and also at master's degree students who want a more rigorous treatment of the mathematical models in finance. This text will be a very good textbook for a year-long course on introductory mathematical finance.” (Anatoliy Swishchuk, zbMATH 1348.91002, 2016)Table of ContentsPreface.- 1. Preliminaries and Financial Markets.- 2. The Time Value of Money.- 3. Markowitz Portfolio Theory.- 4. Capital Market Theory and Portfolio Risk Measures.- 5. Binomial Trees and Security Pricing Modeling.- 6. Stochastic Calculus and Geometric Brownian Motion Model.- 7. Derivatives: Forwards, Futures, Swaps and Options.- 8. The BSM Model and European Option Pricing.- Index.
£999.99
Society for Industrial & Applied Mathematics,U.S. Piecewise Affine Control: Continuous-Time,
Book SynopsisEngineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements.The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications.Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.Trade ReviewPiecewise affine systems are widely used as modeling and design tools across a number of applications, ranging from robotics to systems biology. These systems require a delicate touch as they can exhibit complex and sometimes surprising features. This impressive book navigates the world of such systems with clarity, technical depth, and elegance.”- Professor Magnus Egerstedt, Georgia Institute of Technology
£78.20
Springer Carbon Nanostructured Materials
Book SynopsisThis book provides a concise yet comprehensive look at carbon nanostructured materials, focusing on synthesis methodologies, applications, and fundamental principles.
£42.74
Oxford University Press Statistical Analysis of Molecular and Genomic
Book SynopsisThe field of molecular and genomic evolution has been catalysed by the ever increasing availability of high throughput data such as transcriptome evolution, genotype-phenotype evolution, and genetic robustness. However, there is also an urgent requirement for the emergence of new paradigms (universally accepted scientific frameworks) supported by conceptual breakthroughs, since there is now widespread agreement that genome evolution research should be far more than a static pattern characterized by some well-known arguments and yet more big data for testing or extension. Furthermore, while the internet has made a vast body of literature and data widely accessible, researchers are increasingly facing significant challenges in how to select from this huge reserve appropriately and systematically. Statistical Analysis of Molecular and Genomic Evolution sets out to provide a solution to the most frequently asked question by next-generation young researchers in the area of evolutionary genomics: What is the knowledge that is essential for moving the research forward and where can it be found? Although the book incorporates the latest research foci, it is written at the simplest mathematical level whilst sophisticated enough to provide a deep understanding of current principles and methods. Technical issues are described only briefly, mathematical derivations are kept to a minimum, and it is structured and presented in a way that encourages its use as a graduate textbook. Mindful of the steep learning curve that some biologist readers may face, online appendices review basic mathematical and statistical concepts used in the book, and provide further examples and practical exercises.This is an advanced textbook suitable for graduate level students as well as professional researchers (both empiricists and theoreticians) in the fields of molecular phylogenetics, evolutionary biology, bioinformatics, mathematics, and statistics.
£999.99
The University of Chicago Press Mathematical Models of Social Evolution A Guide
Book SynopsisMathematical models have become central to the study of social evolution, both in biology and the social sciences. A primer on behavioral modeling that includes both mathematics and evolutionary theory, this book aims to make the student and professional researcher in biology and the social sciences fully conversant in the language of the field.Trade Review"Evolutionary arguments are increasingly used as explanations in a wide range of human sciences - psychology, economics, anthropology - as well as in biology itself. However, these arguments are frequently employed on the basis of a secondhand understanding of the principles by which they are derived. This is the first book to provide a thorough but accessible grounding in the methods underlying the major topics in the evolution of social behavior. It should become required study for graduate students in evolution and human behavior." - Daniel Nettle, Newcastle University"
£76.00
Taylor & Francis Ltd Mathematical and Numerical Modeling in Porous
Book SynopsisPorous media are broadly found in nature and their study is of high relevance in our present lives. In geosciences porous media research is fundamental in applications to aquifers, mineral mines, contaminant transport, soil remediation, waste storage, oil recovery and geothermal energy deposits. Despite their importance, there is as yet no complete understanding of the physical processes involved in fluid flow and transport. This fact can be attributed to the complexity of the phenomena which include multicomponent fluids, multiphasic flow and rock-fluid interactions. Since its formulation in 1856, Darcyâs law has been generalized to describe multi-phase compressible fluid flow through anisotropic and heterogeneous porous and fractured rocks. Due to the scarcity of information, a high degree of uncertainty on the porous medium properties is commonly present. Contributions to the knowledge of modeling flow and transport, as well as to the characterization of porous media at field scale are of great relevance. This book addresses several of these issues, treated with a variety of methodologies grouped into four parts:I Fundamental conceptsII Flow and transportIII Statistical and stochastic characterizationIV WavesThe problems analyzed in this book cover diverse length scales that range from small rock samples to field-size porous formations. They belong to the most active areas of research in porous media with applications in geosciences developed by diverse authors.This book was written for a broad audience with a prior and basic knowledge of porous media. The book is addressed to a wide readership, and it will be useful not only as an authoritative textbook for undergraduate and graduate students but also as a reference source for professionals including geoscientists, hydrogeologists, geophysicists, engineers, applied mathematicians and others working on porous media.Table of ContentsSection 1: Fundamental concepts Section 2: Flow and transport Section 3: Statistical and stochastic characterization Section 4: Waves
£237.50
John Wiley & Sons Inc Modeling and Simulation in the Medical and Health
Book SynopsisDetailing the link between computational models and physical models, Modeling and Simulation in the Medical and Health Sciences encourages a more uniform discussion of simulation within both the engineering and medical domains.Table of ContentsContributors. Foreword. Preface. Part One Fundamentals of Medical and Health Sciences Modeling and Simulation. 1 Introduction to Modeling and Simulation in the Medical and Health Sciences (Catherine M. Banks). 2 The Practice of Modeling and Simulation: Tools of the Trade (John A. Sokolowski). Part Two. Modeling for the Medical and Health Sciences. 3 Mathematical Models of Tumor Growth and Wound Healing (John A. Adam). 4 Physical Modeling (Stacie I. Ringleb). Part Three. Modeling and Simulation Applications. 5 Humans as Models (C. Donald Combs). 6 Modeling the Human System (Mohammed Ferdjallah and Gyu Tae Kim). 7 Robotics (Richard Lee). 8 Training (Paul E. Phrampus). 9 Patient Care (Eugene Santos Jr, Joseph Rosen, Keum Joo Kim, Fei Yu, Dequing Li, Elizabeth Jacob, Lindsay Katona). 10 Future of Modeling and Simulation in the Medical and Health Sciences (Richard M. Satava). Appendix. Index.
£76.46
Taylor & Francis Ltd hyperbolicsetsshadowingandpersistencefornoninverti
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
£170.00
Princeton University Press Topics in Mathematical Modeling
Book SynopsisTeaches how simple mathematics can help formulate and solve real problems of research interest in a range of fields, including biology, ecology, computer science, geophysics, engineering, and the social sciences. This book also includes traditional modeling topics such as predator-prey interaction, harvesting, and wars of attrition.Trade Review"This beautifully produced book should provide a joyful and stimulating reading experience for any layman who is curious about real-life events in the context of mathematical modelling, and it provides an excellent entry point to more advanced areas such as mathematical biology or climate modelling."--Z. Q. John Lu, Significance "What do global warming, predator-prey interactions, and the World Wide Web have in common? All of these disparate phenomena can be modeled using mathematics. In Topics in Mathematical Modeling, K. K. Tung demonstrates math's relevance to problems of current research interest in biology, ecology, computer science, geophysics, engineering, and the social sciences."--Scientific American Book Club "[T]his is a good introductory book about the nature and purpose of mathematical modeling. The topics chosen and the way in which they have been motivated and presented will help a wide range of students to 'see the point' and thereby arouse and stimulate their confidence about their mathematical problem solving skills."--Bob Anderssen, Australian Mathematics Society "I was so impressed by the breadth of examples contained in its 336 pages that I immediately set about using it to update one of my own undergraduate courses... A wonderful source book for all kinds of undergraduate mathematical activities... Extremely clear... It is highly recommended."--Chris Howls, Times Higher Education "Tung's preface shows that he is a dyed-in-the-wool teacher of considerable talent whose only mission is to show the student how to take raw empirical data and turn it into a mathematical paradigm that can be analyzed. His prerequisites are solid but minimal: calculus and a smattering of ordinary differential equations (ODEs). He is wise to provide an appendix with a quick treatment of ODEs for those whose background is deficient. Tung also describes in the preface a clear path for those who wish to avoid the differential equations altogether. Tung covers some of the usual modeling topics but also many others that are surprising and refreshing."--Steven G. Krantz, UMAP JournalTable of ContentsPreface xiii Chapter 1: Fibonacci Numbers, the Golden Ratio, and Laws of Nature? 1.1 Leonardo Fibonacci 1 1.2 The Golden Ratio 7 1.3 The Golden Rectangle and Self-Similarity 10 1.4 Phyllotaxis 12 1.5 Pinecones, Sunflowers, and Other Seed Heads 15 1.6 The Hofmeister Rule 17 1.7 A DynamicalModel 20 1.8 Concluding Remarks 21 1.9 Exercises 22 Chapter 2: Scaling Laws of Life, the Internet, and Social Networks 2.1 Introduction 27 2.2 Law of Quarter Powers 27 2.3 A Model of Branching Vascular Networks 30 2.4 Predictions of theModel 35 2.5 Complications andModifications 36 2.6 The Fourth Fractal Dimension of Life 38 2.7 Zipf's Law of Human Language, of the Size of Cities, and Email 39 2.8 TheWorldWideWeb and the Actor's Network 42 2.9 MathematicalModeling of Citation Network and theWeb 44 2.10 Exercises 47 Chapter 3: Modeling Change One Step at a Time 3.1 Introduction 54 3.2 Compound Interest and Mortgage Payments 54 Your Bank Account 54 Your Mortgage Payments,Monthly Interest Compounding 56 Your Mortgage Payments, Daily Interest Compounding 57 3.3 Some Examples 58 3.4 Compounding Continuously 58 Continuous Compounding 59 Double My Money: "Rule of 72," or Is It "Rule of 69"? 60 3.5 Rate of Change 62 Continuous Change 63 3.6 Chaotic Bank Balances 63 3.7 Exercises 65 Chapter 4: Differential Equation Models: Carbon Dating, Age of the Universe, HIV Modeling 4.1 Introduction 68 4.2 Radiometric Dating 68 4.3 The Age of Uranium in Our Solar System 70 4.4 The Age of the Universe 71 4.5 Carbon Dating 74 4.6 HIV Modeling 77 4.7 Exercises 79 Chapter 5: Modeling in the Physical Sciences, Kepler, Newton, and Calculus 5.1 Introduction 84 5.2 Calculus, Newton, and Leibniz 87 5.3 Vector Calculus Needed 88 5.4 Rewriting Kepler's Laws Mathematically 90 5.5 Generalizations 93 5.6 Newton and the Elliptical Orbit 95 5.7 Exercises 96 Chapter 6: Nonlinear Population Models: An Introduction to Qualitative Analysis Using Phase Planes 6.1 Introduction 98 6.2 PopulationModels 98 6.3 Qualitative Analysis 100 6.4 HarvestingModels 101 6.5 Economic Considerations 103 6.6 Depensation Growth Models 104 6.7 Comments 108 6.8 Exercises 108 Chapter 7: Discrete Time Logistic Map, Periodic and Chaotic Solutions 7.1 Introduction 113 Logistic Growth for Nonoverlapping Generations 114 7.2 DiscreteMap 115 7.3 Nonlinear Solution 117 7.4 Sensitivity to Initial Conditions 120 7.5 Order Out of Chaos 121 7.6 Chaos Is Not Random 122 7.7 Exercises 122 Chapter 8: Snowball Earth and Global Warming 8.1 Introduction 126 8.2 Simple ClimateModels 128 Incoming Solar Radiation 129 Albedo 130 Outward Radiation 130 Ice Dynamics 132 Transport 132 TheModel Equation 133 8.3 The Equilibrium Solutions 134 Ice-Free Globe 135 Ice-Covered Globe 136 Partially Ice-Covered Globe 137 Multiple Equilibria 138 8.4 Stability 139 The Slope-Stability Theorem 140 The Stability of the Ice-Free and Ice-Covered Globes 141 Stability and Instability of the Partially Ice-Covered Globe 141 How Does a Snowball Earth End? 143 8.5 Evidence of a Snowball Earth and Its Fiery End 144 8.6 The GlobalWarming Controversy 146 8.7 A Simple Equation for Climate Perturbation 150 8.8 Solutions 153 Equilibrium GlobalWarming 153 Time-Dependent GlobalWarming 154 Thermal Inertia of the Atmosphere-Ocean System 155 8.9 Exercises 157 Chapter 9: Interactions: Predator-Prey, Spraying of Pests, Carnivores in Australia 9.1 Introduction 161 9.2 The Nonlinear System and Its Linear Stability 162 9.3 Lotka-Volterra Predator-Prey Model 165 Linear Analysis 167 Nonlinear Analysis 170 9.4 Harvesting of Predator and Prey 172 Indiscriminate Spraying of Insects 173 9.5 The Case of theMissing Large Mammalian Carnivores 173 9.6 Comment 176 9.7 More Examples of Interactions 178 9.8 Exercises 182 Chapter 10: Marriage and Divorce 10.1 Introduction 191 10.2 Mathematical Modeling 195 Self-interaction 196 Marital Interactions 197 10.3 Data 198 10.4 An Example of a Validating Couple 199 10.5 Why Avoiding Conflicts Is an Effective Strategy in Marriage 201 10.6 Terminology 202 10.7 General Equilibrium Solutions 203 10.8 Conclusion 206 10.9 Assignment 206 10.10 Exercises 210 Chapter 11: Chaos in Deterministic Continuous Systems, Poincar and Lorenz 11.1 Introduction 212 11.2 Henri Poincare 212 11.3 Edward Lorenz 214 11.4 The Lorenz Equations 216 11.5 Comments on Lorenz Equations as aModel of Convection 224 11.6 ChaoticWaterwheel 225 11.7 Exercises 226 Chapter 12: El Nino and the Southern Oscillation 12.1 Introduction 229 12.2 Bjerknes' Hypothesis 231 12.3 A SimpleMathematicalModel of El Nino 233 The Atmosphere 233 Air-Sea Interaction 234 Ocean Temperature Advection 235 12.4 OtherModels of El Nino 239 12.5 Appendix: The Advection Equation 240 12.6 Exercises 241 Chapter 13: Age of the Earth: Lord Kelvin's Model 13.1 Introduction 243 13.2 The Heat Conduction Problem 245 13.3 Numbers 250 13.4 Exercises 251 Chapter 14: Collapsing Bridges: Broughton and Tacoma Narrows 14.1 Introduction 254 14.2 Marching Soldiers on a Bridge: A SimpleModel 254 Resonance 259 A Different Forcing Function 260 14.3 Tacoma Narrows Bridge 261 Assignment 262 14.4 Exercises 262 APPENDIX A: Differential Equations and Their Solutions A.1 First- and Second-Order Equations 267 A.2 Nonhomogeneous Ordinary Differential Equations 273 First-Order Equations 273 Second-Order Equations 275 A.3 Summary of ODE Solutions 277 A.4 Exercises 278 A.5 Solutions to Exercises 279 APPENDIX B: MATLAB Codes B.1 MATLAB Codes for Lorenz Equations 282 B.2 MATLAB Codes for Solving Vallis's Equations 284 Bibliography 287 Index 293
£70.40
Princeton University Press Bayesian Models
Book SynopsisBayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods--in language ecologists can understand. Unlike other books on the subject, this one emphasTrade Review"A refreshing and solid read for anyone confused or distracted by Bayesian recipe books."--Carsten F. Dormann, Quarterly Review of BiologyTable of ContentsPreface ix I Fundamentals 1 1 PREVIEW 3 1.1 A Line of Inference for Ecology 4 1.2 An Example Hierarchical Model 11 1.3 What Lies Ahead? 15 2 DETERMINISTIC MODELS 17 2.1 Modeling Styles in Ecology 17 2.2 A Few Good Functions 21 3 PRINCIPLES OF PROBABILITY 29 3.1 Why Bother with First Principles? 29 3.2 Rules of Probability 31 3.3 Factoring Joint Probabilities 36 3.4 Probability Distributions 39 4 LIKELIHOOD 71 4.1 Likelihood Functions 71 4.2 Likelihood Profiles 74 4.3 Maximum Likelihood 76 4.4 The Use of Prior Information in Maximum Likelihood 77 5 SIMPLE BAYESIAN MODELS 79 5.1 Bayes' Theorem 81 5.2 The Relationship between Likelihood and Bayes' 85 5.3 Finding the Posterior Distribution in Closed Form 86 5.4 More about Prior Distributions 90 6 HIERARCHICAL BAYESIAN MODELS 107 6.1 What Is a Hierarchical Model? 108 6.2 Example Hierarchical Models 109 6.3 When Are Observation and Process Variance Identifiable? 141 II Implementation 143 7 MARKOV CHAIN MONTE CARLO 145 7.1 Overview 145 7.2 How Does MCMC Work? 146 7.3 Specifics of the MCMC Algorithm 150 7.4 MCMC in Practice 177 8 INFERENCE FROM A SINGLE MODEL 181 8.1 Model Checking 181 8.2 Marginal Posterior Distributions 190 8.3 Derived Quantities 194 8.4 Predictions of Unobserved Quantities 196 8.5 Return to the Wildebeest 201 9 INFERENCE FROM MULTIPLE MODELS 209 9.1 Model Selection 210 9.2 Model Probabilities and Model Averaging 222 9.3 Which Method to Use? 227 III Practice in Model Building 231 10 WRITING BAYESIAN MODELS 233 10.1 A General Approach 233 10.2 An Example of Model Building: Aboveground Net Primary Production in Sagebrush Steppe 237 11 PROBLEMS 243 11.1 Fisher's Ticks 244 11.2 Light Limitation of Trees 245 11.3 Landscape Occupancy of Swiss Breeding Birds 246 11.4 Allometry of Savanna Trees 247 11.5 Movement of Seals in the North Atlantic 248 12 SOLUTIONS 251 12.1 Fisher's Ticks 251 12.2 Light Limitation of Trees 256 12.3 Landscape Occupancy of Swiss Breeding Birds 259 12.4 Allometry of Savanna Trees 264 12.5 Movement of Seals in the North Atlantic 268 Afterword 273 Acknowledgments 277 A Probability Distributions and Conjugate Priors 279 Bibliography 283 Index 293
£42.50
