Mathematical modelling Books

Book SynopsisThe human brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For more than a century, a diverse array of researchers searched for a language that could be used to capture the essence of what these neurons do and how they communicate and how those communications create thoughts, perceptions and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it.In Models of the Mind, author and computational neuroscientist Grace Lindsay explains how mathematical models have allowed scientists to understand and describe many of the brain''s processes, including decision-making, sensory processing, quantifying memory, and more. She introduces readers to the most important concepts in modern neuroscience, and highlights the tensions that arise when the abstract world of mathematical modelling collides with the messy details of biology. Each chapter of MoTrade ReviewGrace Lindsay provides a masterful tour of this important frontier, tackling intimidating topics with verve and wit. * Sean Carroll *This is a remarkable book … an excellent introduction to an area that few of us probably know anything about, and all the more fascinating because of that. * Popular Science *Models of the Mind is a grand tour through the history of computational neuroscience, from its humble beginnings in information theory and neuron structure up to its modern manifestations harnessing supercomputers to run large scale convolutional neural networks that model important brain systems. * Women You Should Know *The book is not only wide-ranging in its choice of topics but is also a lively journey through the history of these efforts and traces the lives of the eccentric and fascinating scientists who were instrumental in figuring out the brain’s working by using tools ranging from information theory and graph theory to Bayesian modeling and neural networks. * 3 Quarks Daily * ‘Enthralling, erudite and accessible … an engrossing history of science and an enlightening guide to neuroscience’s current frontiers.’ * Liam Drew, Neurobiologist and author of I, Mammal: The Story of What Makes Us Mammals *‘This book is an anthology of the scientific poetry that has illuminated our studies and conceptions of the brain.’ * Professor Larry Abbott, Center for Theoretical Neuroscience, Columbia University *Table of Contents1: Spherical Cows 2: How Neurons Get Their Spike 3: Learning to Compute 4: Making and Maintaining Memories 5: Excitation and Inhibition 6: Stages of Sight 7: Cracking the Neural Code 8: Movement in Low Dimensions 9: From Structure to Function 10: Making Rational Decisions 11: How Rewards Guide Actions 12: Grand Unified Theories of the Brain Mathematical Appendix Acknowledgements Bibliography Index

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Book SynopsisThe study of networks, including computer networks, social networks, and biological networks, has attracted enormous interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on an unprecedented scale, and the development of new theoretical tools has allowed us to extract knowledge from networks of many different kinds. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.Topics covered include the measurement of networks; methods for analyzing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms; mathematical models of networks, including random graph models and generative models; and theories of dynamical processes taking place on networks.Trade ReviewThis is the definitive book on networks, friendly enough for anyone to read and serious enough for researchers to find their way. [Newman] is one of the founders and leaders of the field and has updated the book with cutting-edge topics. * Professor Cris Moore, Santa Fe Institute *This is the definitive book on network science, by one of its most brilliant researchers and graceful expositors. The second edition of Mark Newman's Networks is clear, comprehensive, and fascinating. * Steven Strogatz, Department of Mathematics, Cornell University, USA *This is an excellent textbook by one of the preeminent scholars in the study of networks. I draw heavily from it when teaching my undergraduate course on networks, and I am very pleased to see a new edition of the book. Newman's clear exposition shines through in this textbook. * Mason Porter, Department of Mathematics, UCLA, USA *An extraordinarily comprehensive and clear exposition of network science from one of the giants in the field. Newman succeeds in making accessible to a broad readership even the most technical content. * Santo Fortunato, School of Informatics and Computing, Indiana University *Reviews from previous edition:Networks accomplishes two key goals: It provides a comprehensive introduction and presents the theoretic backbone of network science. [] The book is balanced in its presentation of theoretical concepts, computational techniques, and algorithms. The level of difficulty increases which each chapter [which] makes the book particularly valuable to physics students who wish to acquire a solid foundation based on their knowledge of basic linear algebra, calculus, and differential equations. * Physics Today *Newman has written a wonderful book that gives an extensive overview of the broadly interdisciplinary network-related developments that have occured in many fields, including mathematics, physics, computer science, biology, and the social sciences ... Overall, a valuable resource covering a wide-randing field. * Choice *Likely to become the standard introductory textbook for the study of networks [...] Overall, this is an excellent textbook for the growing field of networks. It is cleverly written and suitable as both an introduction for undergraduate students (particularly Parts 1 to 3) and as a roadmap for graduate students. [...] Being highly self-contained, computer scientists and professionals from other fields can also use the book - in fact, the author himself is a physicist. In short, this book is a delight for the inquisitive mind. * Computing Reviews *This book brings together, for the first time, the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong connections between work in different subject areas. * CERN Courier *Table of Contents1: Introduction Part I: The empirical study of networks 2: Technological networks 3: Networks of information 4: Social networks 5: Biological networks Part II: Fundamentals of network theory 6: Mathematics of networks 7: Measures and metrics 8: Computer algorithms 9: Network statistics and measurement error 10: The structure of real-world networks Part III: Network models 11: Random graphs 12: The configuration model 13: Models of network formation Part IV: Applications 14: Community structure 15: Percolation and network resilience 16: Epidemics on networks 17: Dynamical systems on networks 18: Network search

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Book SynopsisOutnumbered is a journey to the dark side of mathematics, from how it dictates our social media activities to our travel routes. Algorithms are running our society, and as Facebook''s Cambridge Analytica scandal has revealed, we don''t even realize how our data has been used against us. David Sumpter investigates whether mathematics is crossing dangerous lines when it comes to what we can make decisions about. Our increasing reliance on technology and the internet has opened a window for mathematicians and data researchers to gaze through into our lives. Using the data they are constantly collecting about where we travel, where we shop, what we buy, and what interests us, they can begin to predict our daily habits, and increasingly we are relinquishing our decision-making to algorithms. Are we giving this up too easily?Without understanding what mathematics can and can''t do it is impossible to get a handle on how it is changing our lives. In this book, DaTrade ReviewSumpter's [...] expertise and sceptical approach are brought alive with fascinating examples including Banksy and Space Invaders. * Financial Times *[David Sumpter] reckons with the sheer scales of the systems that manage much of our digital lives. Step by step he details the maths that underpins each of these systems, laying out the straightforward, if advanced, calculations that govern their outcomes – and their limitations. * Guardian *An important message. * Popular Science *As millions slowly wake up to the pitfalls of handing over their digital lives, Sumpter combines engaging hands-on demonstrations with stories from insiders to shed light on precisely how data alchemists seek to persuade and predict us, and whether their almighty algorithms are all they're hyped up to be. -- John Burn-Murdoch, data journalist, Financial TimesYou've heard about these algorithms that run your life and you want to know two things: how exactly do they work? And how much should I worry? With a refreshing mix of in-depth knowledge and personal honesty, David Sumpter answers both those questions. * Timandra Harkness, writer, comedian and broadcaster, and author of Big Data *A stellar book about the application of mathematics to the real world. Each chapter tells a fascinating story, and David's warm and witty style demonstrates that a mathematician can be so much more than just a machine for turning coffee into theorems. A riveting read. -- Kit Yates, Senior Lecturer, Department of Mathematical Sciences, University of BathTable of ContentsPART 1: ANALYSING US Chapter 1: Finding Banksy Chapter 2: Make Some Noise Chapter 3: The Principal Components of Friendship Chapter 4: One Hundred Dimensions of You Chapter 5: Cambridge Hyperbolytica Chapter 6: Impossibly Unbiased Chapter 7: The Data Alchemists PART 2: INFLUENCING US Chapter 8: Nate Silver vs the Rest of Us Chapter 9: We ‘Also Liked ’ the Internet Chapter 10: The Popularity Contest Chapter 11: Bubbling Up Chapter 12: Football Matters Chapter 13: Who Reads Fake News? PART 3: BECOMING US Chapter 14: Learning to be Sexist Chapter 15: The Only Thought Between the Decimal Chapter 16: Kick Your Ass at Space Invaders Chapter 17: The Bacterial Brain Chapter 18: Back to Reality Notes Acknowledgements Index

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Book SynopsisThis textbook is concerned with the mathematical modelling of biological and physiological phenomena for mathematically sophisticated students. A range of topics are discussed: diffusion population dynamics, autonomous differential equations and the stability of ecosystems, biogeography, pharmokinetics, biofluid mechanics, cardiac mechanics, the spectral analysis of heart sounds using FFT techniques. The last chapter deals with a wide variety of commonly used medical devices. This book is based on courses taught by the author over many years and the material is well class tested. The reader is aided by many exercises that examine key points and extend the presentation in the body of the text. All students of mathematical biology will find this book to be a highly useful resource.Trade Review'It can be highly recommended to biomedical engineers and all students of mathematical biology.' Acta CardiologicaTable of ContentsPreface; 1. Dimensional analysis in mathematical physiology; 2. The mathematics of diffusion; 3. Population biology; 4. Biogeography: mathematical analysis of wildlife reserves; 5. Pharmacokinetics: drug distribution in pharmacology; 6. Mathematical modelling in epidemiology; 7. Modelling the AIDS epidemic; 8. Biological fluid mechanics; 9. Analysis and applications of left ventricular mechanics; 10. Analysis and applications of heart valve vibration; 11. Medical devices; Glossary of terms; References; Index.

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Book SynopsisMathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students'' physical intuition as he guides them through the mathematical methods required to study upper-level physics. Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material. It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions (''By the Ways'') as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, manTrade Review'Schramm's Mathematical Methods and Physical Insights is a very welcome new textbook in the area of pedagogical mathematical physics. The book contains numerous insightful and helpful examples from classical and modern physics, as well as unusual and interesting applications of the presented mathematical concepts within and beyond physics. I find the 'BTW' inserts, and the lively, unpretentious style of the book both exciting and entertaining. The material discussed in Schramm's textbook covers entirely the scope of our three-trimester-long Mathematical Methods offering, and additionally provides useful background material to 'even out' the often inhomogeneous preparation of students in these classes; I will definitely consider adopting this textbook for my next offerings of Mathematical Methods for Physics here at the University of California, Santa Cruz.' Professor Stefano Profumo, University of California, Santa Cruz'As the title suggests, Schramm's book distinguishes itself from traditional mathematical methods texts in its thematic approach that builds from unit to unit, using rich examples from physical systems that elucidate each topic. A must-read for physicists wanting to expand their mathematical toolkit as well as for mathematicians hoping to gain new insights from the physical world.' Professor Jason Detwiler, University of Washington'For students taking physics courses, one of the difficulties is how to apply appropriate mathematical skills in problem solving (e.g., using integration to find the electric field produced by a continuous charge distribution). This book introduces commonly used mathematical skills from the perspective of a physicist. Focusing on the topics in upper-level physics courses, it provides the mathematical skills for solving problems in each topic. The book is easy to read, and the problems at the end of each chapter offer plenty of exercises for students. The book is a valuable resource for undergraduate students taking upper-level physics courses, and instructors teaching such courses. It could also be a useful reference for graduate students.' Professor Hong Lin, Bates College'Physics and engineering students often struggle with mathematics texts that present the material in an abstract fashion, disconnected from practical applications. Schramm's text represents a refreshing and much needed change. Providing context and intuition throughout, with many worked examples, and in engaging prose, it does more than just explain mathematical methods; it infuses them with meaning and relevance.' Dr. Jochen Rau, RheinMain University of Applied Sciences, GermanyTable of ContentsPreface; Part I. Things You Just Gotta' Know: 1. Prelude: symbiosis; 2. Coordinating coordinates; 3. Complex numbers; 4. Index algebra; 5. Brandishing binomials; 6. Infinite series; 7. Interlude: orbits in a central potential; 8. Ten integration techniques and tricks; 9. The Dirac delta function; 10. Coda: statistical mechanics; Part II. The Calculus of Vector Fields: 11. Prelude: visualizing vector fields; 12. grad, div & curl; 13. Interlude: irrotational and incompressible; 14. Integrating scalar & vector fields; 15. The theorems of Gauss & Stokes; 16. Simply connected regions; 17. Coda: mostly Maxwell; Part III. Calculus in the Complex Plane: 18. Prelude: path independence in the complex plane; 19. Series, singularities & branches; 20. Interlude: conformal mapping; 21. The calculus of residues; 22. Coda: analyticity & causality; Part IV. Linear Algebra: 23. Prelude: superposition; 24. Vector space; 25. The inner product; 26. Interlude: rotations; 27. The Eigenvalue problem; 28. Coda: normal modes; Entr'acte: Tensors; 29. Cartesian tensors; 30. Beyond cartesian; Part V. Orthogonal Functions: 31. Prelude: 1 2 3 . . . infinity; 32. Eponymous polynomials; 33. Fourier series; 34. Convergence and completeness; 35. Interlude: beyond the straight & narrow; 36. Fourier transforms; 37. Coda: of time intervals and frequency bands; Part VI. Differential Equations: 38. Prelude: first order first; 39. Second-order ODEs; 40. Interlude: the Sturm-Liouville Eigenvalue problem; 41. Partial differential equations; 42. Green's functions; 43. Coda: quantum scattering; Appendix A. Curvilinear coordinates; Appendix B. Rotations in R3; Appendix C. The Bessel family of functions; References; Index.

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Book Synopsis'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

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Book SynopsisA Mezze of Mathematical Methods is Volume 1 of Science by Simulation. It is a recipe book of mathematical models that can be enlivened by the transmutation of equations into computer code. In this volume, the examples chosen are an eclectic mix of systems and stories rooted in common experience, rather than those normally associated with constrained courses on Physics, Chemistry or Biology which are taught in isolation and susceptible to going out of date in a few years. Rather than a 'what' of Science, this book is aimed at the 'how', readily applied to projects by students and professionals. Written in a friendly style based upon the author's expertise in teaching and pedagogy, this mathematically rigorous book is designed for readers to follow arguments step-by-step with stand-alone chapters which can be read independently. This approach will provide a tangible and readily accessible context for the development of a wide range of interconnected mathematical ideas and computing methods that underpin the practice of Science.

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Book SynopsisLearning Mathematics through Modelling and Simulation: An Investigative Approach, offers the readers a hands-on experience of discovering the beautiful aspects of mathematics through the use of technology. Three powerful tools falling into the categories of spreadsheet programs (Microsoft Excel),They are applied in the book to enable the readers to independently explore, visualise, conjecture, reason and solve problems.

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Book SynopsisSports analytics has gathered tremendous momentum as one of the most dynamic fields. Diving deep into the numbers of sports can be game changing or simply a fun exercise for fans. How do you get in the game with numbers? What questions can be explored? What actionable insights can be gleaned?Do you like sports? This book will detail ways to analyze athletics to gain insight that can otherwise be obscured. Like math? You'll find many mathematical topics not involving sports. You'll also see how sports analytics can train you broadly in mathematics.From coaching at the highest levels to national media broadcasts, analytics are becoming increasingly indispensable. Dive into the numbers behind soccer to basketball to baseball to boxing to swimming, dive into the numbers. Learn how to get in the game with sports and mathematics.

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Book SynopsisA bold, visionary, and mind-bending exploration of how the geometry of chaos can explain our uncertain world - from weather and pandemics to quantum physics and free willCovering a breathtaking range of topics - from climate change to the foundations of quantum physics, from economic modelling to conflict prediction, from free will to consciousness and spirituality - The Primacy of Doubt takes us on a unique journey through the science of uncertainty. A key theme that unifies these seemingly unconnected topics is the geometry of chaos: the beautiful and profound fractal structures that lie at the heart of much of modern mathematics. Royal Society Research Professor Tim Palmer shows us how the geometry of chaos not only provides the means to predict the world around us, it suggests new insights into some of the most astonishing aspects of our universe and ourselves. This important and timely book helps the reader makes sense of uncertainty in a rapidly changing world.Trade Reviewimportant book * Andrew Robinson, Nature *The Primacy of Doubt also contains very informative explanations as to the application of chaos theory in climate and meteorological models, and why meteorologists failed to predict southern Britain's 1987 hurricane. To my mind this were probably the book's strongest areas and are 'must reads' for those with an interest in climate forecasting. * Jonathan Cowie, SF2 Concatenation *Quite possibly the best popular science book I've ever read... The Primacy of Doubt is like getting off one of those exciting roller coaster rides, when your immediate inclination is to think 'I want to do that again, but I'll have a bit of a break first.' I will be reading this book again, without doubt. Remarkable. * Brian Clegg, Popular Science *delightful and substantive * William Hooke, Living on the Real World *The Primacy of Doubt provides a remarkably broad-ranging account of uncertainty in physics, in all its various aspects. I strongly recommend this highly thought-provoking book. * Roger Penrose, OM, FRS, winner of the 2020 Nobel Prize in Physics *Tim Palmer is a scientific polymath. It's hard to think of anyone else who could have written so authoritatively—and so accessibly—on themes extending from quantum gravity to climate modelling. This fascinating and important book offers some profoundly original speculations on conceptual linkages across different sciences. * Lord Martin Rees, Astronomer Royal of the United Kingdom *The Primacy of Doubt is an important book by one of the pioneers of dynamical weather prediction, indispensable for daily life. * Suki Manabe, winner of the 2021 Nobel Prize in Physics *In a whirlwind of a book that's partly scientific autobiography and partly the manifest of a visionary, Tim Palmer masterfillly weaves together climate change and quantum mechanics into one coherent whole. Using uncertainty as a unifring principle, Palmer puts forward new perspectives on old problems. A revolutionary thinker way ahead of his time. * Sabine Hossenfelder, author of Lost in Math *An exploration of the amorphous concept of uncertainty... [an] informative, ingenious book. * Kirkus Reviews *Physicist Palmer delivers a challenging but rewarding look at how uncertainty helps scientists make sense of the world... Despite the complexity of his arguments, the author succeeds at bringing complicated theories within reach of those who have a basic familiarity with physics. Science-minded readers, take note. * Publishers Weekly *Provocative... useful for scientists and non-scientists alike * Jessica Flack, Physics World *Table of ContentsPreface 1: The Primacy of Doubt DS From Two Perspectives Part I: The Science of Uncertainty and the Geometry of Chaos 2: Chaos, Chaos Everywhere 3: The Geometry of Chaos 4: Noisy, Million-Dollar Butterflies 5: Quantum Uncertainty DS Determinism Lost? Part II: The Science of Uncertainty to Predict Our Chaotic World 6: The Two Roads to Monte Carlo 7: Climate Change: Catastrophe or Just Lukewarm? 8: Pandemics 9: Financial Crashes 10: Deadly Conflict and the Digital Ensemble of Spaceship Earth 11: Decisions! Decisions! Part III: The Science of Uncertainty to Understand Our Chaotic World 12: Quantum Uncertainty: Determinism Regained? 13: Noisy Billion-Dollar Brains 14: Free Will, Consciousness and Theology Acknowledgements Bibliography

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Book SynopsisThis novel textbook addresses the shortcomings of current competition theory and suggests a more useful approach that can provide a basis for future models that have far greater predictive ability in both ecology and evolution.Trade ReviewThis book offers readers a compelling introduction to these complexities. * Mark A. McPeek, Biological Sciences, Dartmouth College, Hanover, New Hampshire, The Quarterly Review of Biology *

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Book SynopsisThis textbook provides an introduction to the world of numerical modeling in the physical sciences, focusing more specifically on earth and planetary sciences. It is designed to lead the reader through the process of defining the mathematical or physical model of interest and applying numerical methods to approximate and explore the solutions to these models, while also providing a quantitative assessment of the limitations, performance and quality of these approximations. The book is designed to provide a self-contained reference by including the mathematical foundations required to understand the models and their convergence. It includes a detailed discussion of models for ordinary systems of equation and partial differential equations, with pseudo-codes detailing the solution procedure. Examples are drawn from the fields of earth and planetary sciences, including, geochemical box models, non-linear ordinary differential equations describing the evolution of subvolcanic magma chambers, the mass conservation of cosmogenic nuclides in soils, diffusion in minerals, the hillslope equation, the advection-diffusion and wave equations and the shallow water equations. Featuring numerous examples drawn from earth and planetary sciences, the content of this book has been used by the author to teach numerical methods classes at the undergraduate and graduate levels over several years, and will provide an excellent resources for teachers and learners in this area.

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Book SynopsisThis book is about how climate science works and why you should absolutely trust some of its conclusions and absolutely distrust others. Climate change raises new, foundational challenges in science. It requires us to question what we know and how we know it. The subject is important for society but the science is young and history tells us that scientists can get things wrong before they get them right. How, then, can we judge what information is reliable and what is open to question? Stainforth goes to the heart of the climate change problem to answer this question. He describes the fundamental characteristics of climate change and shows how they undermine the application of traditional research methods, demanding new approaches to both scientific and societal questions. He argues for a rethinking of how we go about the study of climate change in the physical sciences, the social sciences, economics, and policy. The subject requires nothing less than a restructuring of academic reseaTrade ReviewClimate is, in some respects, highly predictable; yet, in other respects, highly unpredictable. But there is no contradiction. The resolution of this seeming paradox in Predicting Our Climate Future leads in turn to a vision for how humankind must respond to this most important problem of all time. * George Akerlof, Nobel Laureate in Economics, 2001 *A profound yet very accessible guide to climate science, highlighting the significant uncertainties without apology. This book explains clearly why doubt creates a greater and more urgent need to act now to build a better future. * Trevor Maynard, Executive Director of Systemic Risks, Cambridge Centre for Risk Studies *The immense complexity of the climate system raises deep questions about what science can usefully say about the future. David Stainforth navigates philosophical and mathematical questions that could hardly be of greater practical importance. He questions what it is reasonable to ask of climate scientists and his conclusions challenge the way in which science should be conducted in the future. * Jim Hall, Professor of Climate and Environmental Risk, University of Oxford *Is the science settled? Are climate models rubbish? Stainforth's book serves up nuanced answers to big questions in climate science, in an easy conversational style. * Cameron Hepburn, Professor of Environmental Economics, University of Oxford *A thoughtful exploration of the foundations and limitations of climate prediction that explains how its chaotic and probabilistic nature lead to deep uncertainty when assessing climate risk. * Ramalingam Saravanan, Professor of Atmospheric Sciences, Texas A&M University *Predicting Our Climate Future is an erudite and very personal reflection on climate change, the state of climate science, and their implications for the decisions society needs to take. It should be top of the reading list for scientists, practitioners and anyone who wants to truly comprehend the challenge of climate prediction. * Simon Dietz, Professor of Environmental Policy, London School of Economics and Political Science *A provocative contribution to the literature of climate change. * Kirkus *Predicting Our Climate Future is an ambitious exploration of a critical topic. It is a recommended read for climate scientists, especially those trying to model the future, for the researchers-in many disciplines-that are focused on understanding and forecasting the physical and human impacts of the coming climate changes, and for policy makers engaged in climate issues. * Steven Earle, New York Journal of Books *Intelligent, accessible, well reasoned and working very hard to get it's teeth into a complex but vitally important issue. * Irish Tech News *Fascinating...[there is a] a refreshing honesty [in Stainforth's writing] about the limitations we have with certain kinds of prediction. * Brian Clegg, Popular Science *Stainforth is good at explaining the complexities [of climate modelling], leavening the highly technical bits with ... lots of relatable real-world analogies. * Geordie Torr, The Geographical *Table of ContentsSection 1 Chapter 1: The obvious and the obscure Chapter 2: A problem of prediction Chapter 3: Going beyond what we've seen Chapter 4: The one-shot bet. Chapter 5: From chaos to pandemonium Chapter 6: The curse of bigger and better computers Chapter 7: Talking at cross purposes Chapter 8: Not just of academic interest Section 2 Challenge 1: How to balance justified arrogance with essential humility. Chapter 9 - Stepping up to the task of prediction Chapter 10 The Times They Are A Changin' Chapter 11 Starting from scratch Chapter 12 Are scientists being asked to answer impossible questions? Challenge 2: Tying down what we mean by climate and climate change. Chapter 13 The essence of climate Chapter 14 A Walk in Three Dimensions Chapter 15 A walk in three dimensions over a two dimensional sea Challenge 3: When is a study with a climate model a study of climate change? Chapter 16 Climate change in climate models Challenge 4: How can we measure what climate is now and how it has changed? Chapter 17 Measuring climate change Challenge 5: How can we relate what happens in a model to what will happen in reality? Chapter 18 - Can climate models be realistic? Chapter 19 More models, better information? Chapter 20 How bad is too bad? Challenge 6: How can we use today's climate science well? Chapter 21 - What we do with what we've got Challenge 7: Getting a grip on the scale of future changes in climate? Chapter 22 - Stuff of the Genesis myth Chapter 23 Things ... can only get hotter Challenge 8: How can we use the information we have, or could have, to design a future that is better than it would otherwise be? Chapter 24 - Making it personal Chapter 25 - Where physics and economics meet. Challenge 9: How can we build physical and social science that is up to the task of informing society about what matters for society? Chapter 26 - Controlling factors. Chapter 27 - Beyond comprehension? No, just new challenges for human intellect.

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Book SynopsisThis book is a comprehensive introduction to quantitative approaches to complex adaptive systems. Practically all areas of life on this planet are constantly confronted with complex systems, be it ecosystems, societies, traffic, financial markets, opinion formation and spreading, or the internet and social media. Complex systems are systems composed of many elements that interact strongly with each other, which makes them extremely rich dynamical systems showing a huge range of phenomena. Properties of complex systems that are of particular importance are their efficiency, robustness, resilience, and proneness to collapse.The quantitative tools and concepts needed to understand the co-evolutionary nature of networked systems and their properties are challenging. The book gives a self-contained introduction to these concepts, so that the reader will be equipped with a toolset that allows them to engage in the science of complex systems. Topics covered include random processes of path-deTrade ReviewWell written and structured * Ejay Nsugbe, Mathematics Today *The authors make an excellent job in describing their introduction to Complex Systems theory . . . The book is certainly an excellent start for students (who can find also a series of exercises in every chapter and for practioners). For scientists it is a useful handbook to find whatever needed to start their journey in Complexity Science. * Guido Caldarelli, IMT Alti Studi Lucca, Mathematics Magazine *It seems to me that the authors have succeeded admirably in their aims and that, by helping to train and enthuse the next generation of researchers on complex systems, their book will contribute substantially towards overcoming any possible bottleneck that is impeding further progress. * Peter V. E. McClintock, Department of Physics, Lancaster University, Contemporary Physics *This book is a comprehensive introduction to quantitative approaches to complex adaptive systems, starting from basic principles. It also equips the reader with a basic self-contained toolkit for engaging in complex systems science. It extends earlier classical literature in the field to summarize in a clear, structured, and comprehensive way the methodological progress made in complex systems science over the past 20 years. * Mathematical Reviews Clippings *This book will surely become a standard text for anyone who wants to seriously understand complexity no matter what their background or stage of career. It is written from a physicists perspective, stressing mechanism, underlying principles and mathematical rigour, yet is eminently readable and pedagogical. * Geoffrey West, Santa Fe Institute *Complexity until now has been lacking a strong theoretical underpinning. Now it has one. This book is a tour de force. Excellent! * W. Brian Arthur, Santa Fe Institute *Table of Contents1: Introduction to complex systems 2: Probability and random processes 3: Scaling 4: Networks 5: Evolutionary processes 6: Statistical mechanics & information theory for complex systems 7: The future of the science of complex systems? 8: Special functions and approximations

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Book SynopsisA report that provides a summary and evaluation of several modeling approaches, and their theoretical and empirical underpinnings, relative to complex land-change dynamics and processes, and identifies several opportunities for further advancing the science, data, and cyberinfrastructure involved in the land-change model (LCM) enterprise.Table of Contents1 Front Matter; 2 Summary; 3 1 The State of Land Change Modeling; 4 2 Land Change Modeling Approaches; 5 3 Improving Land Change Modeling; 6 References; 7 Appendixes; 8 Appendix A: List of Contributors; 9 Appendix B: Online Questionnaire; 10 Appendix C: Committee and Staff Biographies

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Book SynopsisThe high-order sensitivities of model responses with respect to model parameters are notoriously difficult to compute for large-scale models involving many parameters. The neglect of higher-order response sensitivities leads to substantial errors in predicting the moments (expectation, variance, skewness, kurtosis) of the model responseâs distribution in the phase-space of model parameters. The author expands on his theory of addressing high-order sensitivity analysis. The mathematical/computational models of physical systems comprise parameters, independent and dependent variables. Since the physical processes themselves are seldom known precisely and since most of the modelâs parameters stem from experimental procedures that are also subject to imprecision and/or uncertainties, the results predicted by these models are also imprecise, being affected by the uncertainties underlying the respective model. In the particular case of sensitivity analysis using conventional methods, the number of large-scale computations increases exponentially. For large-scale models involving many parameters, even the first-order sensitivities are computationally very expensive to determine accurately by conventional methods. Furthermore, the curse of dimensionality prohibits the accurate computation of higher-order sensitivities by conventional methods. Other books by the author, all published by CRC Press, include Sensitivity & Uncertainty Analysis, Volume: Theory (2003), and Sensitivity and Uncertainty Analysis, Volume II: Applications to Large-Scale Systems (Cacuci, et al., 2005), Computational Methods for Data Evaluation and Assimilation (Cacuci, et al.,2014). The Second-Order Adjoint Sensitivity Analysis Methodology (2018), and Advances in High-Order Predictive Modeling Methodologies and Illustrative Problems (2025).

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Book SynopsisQuantitative Finance with Case Studies in Python: A Practical Guide to Investment Management, Trading and Financial Engineering bridges the gap between the theory of mathematical finance and the practical applications of these concepts for derivative pricing and portfolio management. The book provides students with a very hands-on, rigorous introduction to foundational topics in quant finance, such as options pricing, portfolio optimization and machine learning. Simultaneously, the reader benefits from a strong emphasis on the practical applications of these concepts for institutional investors.This new edition includes brand new material on data science and AI concepts, including large language models, as well as updated content to reflect the transition from Libor to SOFR to bring the text right up to date. It also includes expanded material on inflation and mortgage-backed securitie, more trade ideas embedded in each chapter and also via a dedicated chapter analyzing a set of derivatives trades. There are additional examples throughout based on recent market dynamics, including the post-Covid inflation shock and its impact on risk parity strategies.Overall, the new edition is designed to be even more of a practical tool than the first edition, and more firmly rooted in real-world data, applications, and examples.Features Useful as both a teaching resource and as a practical tool for professional investors Ideal textbook for first year graduate students in quantitative finance programs, such as those in masterâs programs in Mathematical Finance, Quant Finance or Financial Engineering Includes a perspective on the future of quant finance techniques, and in particular covers concepts of Machine Learning and Artificial Intelligence Free-to-access repository with Python codes available at www.routledge.com/ 9781032014432 and on https://github.com/lingyixu/Quant-Finance-With-Python-Code.[CK1]

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Book SynopsisOffers what you need to make the most of building information modeling. If you're looking to get involved in the world of BIM, but don't quite know where to start, this book helps you in collaborative building using one coherent system of computer models rather than as separate sets of drawings.Trade Review“Building Information Modeling For Dummies is an excellent reference on current state-of-the-art BIM processes.” (3D Visualization World, November 2015)Table of ContentsIntroduction 1 Part I: Getting Started with Building Information Modeling 5 Chapter 1: Defining Building Information Modeling (BIM) 7 Chapter 2: Explaining the Building Part of BIM: It’s Not Just Buildings 15 Chapter 3: Examining the Information Part of BIM 25 Chapter 4: Discussing the Modeling Part of BIM (and Management Too) 41 Chapter 5: Grasping the Fundamentals and Understanding What BIM Is 51 Part II: Creating the Foundations for BIM 69 Chapter 6: Looking at the Digital World Around You 71 Chapter 7: Preparing the Foundations for BIM 89 Chapter 8: Setting Up a Collaborative BIM Workflow 105 Part III: Understanding BIM Requirements and Developing BIM Processes 121 Chapter 9: Mandating BIM in the UK and across the Globe 123 Chapter 10: Standardizing the Modeling of BIM Objects 149 Chapter 11: Collaborating through BIM Requirements 171 Chapter 12: Encouraging BIM in Your Office or On‐Site 187 Chapter 13: Developing BIM Plans and Strategies 203 Chapter 14: Considering the Issues that BIM Presents 219 Part IV: Measuring the Real‐World Benefits of BIM 233 Chapter 15: Evaluating BIM Benefits and Investment 235 Chapter 16: Using BIM On‐Site and BIM for Health and Safety 247 Chapter 17: Identifying All the Users of BIM 265 Part V: Exploring the Future of BIM 285 Chapter 18: Building the Future of Construction 287 Chapter 19: Eyeing the Possibilities: The Future of BIM 303 Chapter 20: Forecasting How New Technology Will Drive BIM 321 Part VI: The Part of Tens 335 Chapter 21: Ten Types of BIM Tools, Software, and Platforms to Consider 337 Chapter 22: Ten of the Best BIM Resources 341 Chapter 23: Ten (or So) Myth‐Busting Questions and Answers 349 Appendix A: Glossary 355 Appendix B: Your Handy BIM Checklist 363 Appendix C: Examining BIM and Education 365 Index 369

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Book SynopsisDavid Sandwell developed this advanced textbook over a period of nearly 30 years for his graduate course at Scripps Institution of Oceanography. The book augments the classic textbook Geodynamics by Don Turcotte and Jerry Schubert, presenting more complex and foundational mathematical methods and approaches to geodynamics. The main new tool developed in the book is the multi-dimensional Fourier transform for solving linear partial differential equations. The book comprises nineteen chapters, including: the latest global data sets; quantitative plate tectonics; plate driving forces associated with lithospheric heat transfer and subduction; the physics of the earthquake cycle; postglacial rebound; and six chapters on gravity field development and interpretation. Each chapter has a set of student exercises that make use of the higher-level mathematical and numerical methods developed in the book. Solutions to the exercises are available online for course instructors, on request.Trade Review'Advanced Geodynamics brings the unique perspective of a leading geophysicist to the solution of a wide array of problems in geodynamics. The approach emphasizes the use of advanced mathematics, in particular the Fourier transform, to obtain a quantitative understanding of the processes involved in shaping the Earth's surface. The advanced mathematical approach not only enhances the elegance of the solutions, but it enables the consideration of many problems not accessible with less sophisticated mathematical methods. The choice of problems benefits from the deep physical insights of the author to their solutions. The book discusses the physical processes involved in plate tectonics and the earthquake cycle and provides the latest relevant observational data sets. An emphasis is also placed on the use of gravity data to learn about these processes. The book is the product of decades of teaching by the author and is a must read for students of the physics of the Earth with the appropriate mathematical background.' Gerald Schubert, University of California, Los Angeles; co-author of Geodynamics'Most authors would find writing a sequel to Turcotte and Schubert's classic book on Geodynamics a daunting task. Not so for David Sandwell, whose first book is a wonderful mix of observations and theory, elegant mathematics and a focus on the oceans and the Fourier method which together help illuminate some of the fundamental physical processes that underlie plate tectonics.' Tony Watts, University of Oxford; author of Isostasy and Flexure of the Lithosphere'Advanced Geodynamics: The Fourier Transform Method by David Sandwell is a godsend for advanced undergraduate students, graduate students, and researchers actively engaged in the broad area of geodynamics. It complements the classic Geodynamics book by Turcotte & Schubert in a way nothing else could: by elevating the treatment to real, cutting-edge research problems via Fourier transforms that deliver simple and elegant solutions to complicated science problems.' Paul Wessel, University of HawaiiTable of Contents1. Observations Related to Plate Tectonics; 2. Fourier Transform Methods in Geophysics; 3. Plate Kinematics; 4. Marine Magnetic Anomalies; 5. Cooling of the Oceanic Lithosphere; 6. A Brief Review of Elasticity; 7. Crustal Structure, Isostasy, Swell Push Force, and Rheology; 8. Flexure of the Lithosphere; 9. Flexure Examples; 10. Elastic Solutions for Strike-Slip Faulting; 11. Heat Flow Paradox; 12. The Gravity Field of the Earth, Part I; 13. Reference Earth Model: WGS84; 14. Laplace's Equation in Spherical Coordinates; 15. Laplace's Equation in Cartesian Coordinates and Satellite Altimetry; 16. Poisson's Equation in Cartesian Coordinates; 17. Gravity/Topography Transfer Function and Isostatic Geoid Anomalies; 18. Postglacial Rebound; 19. Driving Forces of Plate Tectonics; References; Index.

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Book SynopsisThis comprehensive textbook/reference provides an in-depth overview of the key aspects of transportation analysis, with an emphasis on modeling real transportation systems and executing the models.Table of ContentsComputational Foundation in Transportation and Transportation Systems Modeling Transportation ModelsTraffic Assignment to Transportation NetworksIntegration Framework and Empirical EvaluationSimulation Tools in TransportationTransportation Use Cases

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Book SynopsisAn Observer Book of the Year A Times Science Book of the Year A New Statesman Book of the Year A Financial Times Science Book of the Year 'Astonishingly bold' Daily Mail 'It is hard to imagine a more timely book ... much of the modern world will make more sense having read it.' The Times We live in a world that's more interconnected than ever before. Our lives are shaped by outbreaks - of disease, of misinformation, even of violence - that appear, spread and fade away with bewildering speed. To understand them, we need to learn the hidden laws that govern them. From 'superspreaders' who might spark a pandemic or bring down a financial system to the social dynamics that make loneliness catch on, The Rules of Contagion offers compelling insights into human behaviour and explains how we can get better at predicting what happens next. Along the way, Adam Kucharski explores how innovations spread through friendship networks, what links computer viruses with folk stories - and why the most useful predictions aren't necessarily the ones that come true. Now revised and updated with content on Covid-19.Trade ReviewAstonishingly bold * Daily Mail *Perfect timing * Financial Times *Popular science at its best ... sparkling and clear. The subject is deeply fascinating and highly relevant ... Once you have read it, you will want to make sure others read it too. -- Alex Bellos, author * Alex's Adventures in Numberland *An impressively fluent, fascinating and accessible introduction to how epidemics, trends, behaviours and ideas start, spread - and end ... a work of contemporary relevance that Malcolm Gladwell devotees would enjoy. * New Statesman *It is hard to imagine a more timely book ... much of the modern world will make more sense having read it. * The Times *Adam Kucharski [is] fast becoming a key voice of reason in the media circus surrounding the virus ... Here he gives a clear, calm, historical overview of the mathematical ideas at the forefront of our pandemic response, where they came from and how well they stand up when you put them to the test. -- Hannah Fry * Guardian *This is a hell of a moment for a book like this to come out ... the principles of contagion, which, Kucharski argues, can be applied to everything from folk stories and financial crises to itching and loneliness, are suddenly of pressing interest to all of us. * Sunday Times *Rich in stories, The Rules of Contagion is a down-to-earth account of how mathematical approaches can help us better understand and, in turn, better respond to contagion in all its dynamic forms. Tackling issues from pandemics and gun violence, to financial crises and misinformation, Adam Kucharski inspires us all to think like mathematicians. A must read for anybody interested in epidemics and other crises. -- Peter Piot, Director of the London School of Hygiene & Tropical MedicineFor anyone wanting to know how diseases spread, Adam Kucharski's book, The Rules of Contagion is a timely introduction. * Irish Independent *For now Adam Kucharski's The Rules of Contagion is the book you want to reach for ... interesting and topical -- Laura Spinney * Guardian *Illuminating ... Coronavirus has prompted hot-headed public and media reaction; this book offers comfort in the form of cold, hard facts. * Prospect Magazine *One of the Economist's 'five books of science and history that cast light on covid-19': This book charts the history of this now-pivotal science, from its origins in understanding the spread of malaria at the turn of the 20th century, to its central role in predicting the dissemination of everything from diseases to fake news in the 21st. * Economist *The Rules of Contagion is a timely reminder of the importance of disease modelling. Without such models, we would be in far greater trouble battling COVID-19. * Lancet *Lively, intriguing and elegant * Spectator *A geeky but fascinating exploration of the mathematics of things that go viral-not least of them viruses ... Kucharski takes his readers down provocative detours, such as the use of public-health models of disease transmission to examine how social networks figure in urban gun violence, with algorithms that take into account such things as 'age, gang affiliations, and prior arrests.'... Utterly timely and readable. * Kirkus *Essential reading to truly process the pandemic -- Anjana Ahuja * New Statesman *Perhaps no commentator has been in greater demand this year than Adam Kucharski ... The Rules of Contagion is an accessible guide to the mathematical rules that govern the spread of infectious diseases in populations ... [which] makes a convincing case that just as mathematics can predict the arc of an epidemic, so it can also help us understand how social contagions, from financial panics to vaccine conspiracy theories, "go viral". -- Gaia Vince, winner of the Royal Society Prize and author of Adventures in the Anthropocene * Observer *

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Book SynopsisThis book introduces the reader to multiscale mathematical modeling that starts by describing a physical process at the microscopic level, and is followed by the macroscopic description of that process. There are two preliminary chapters introducing the main equations of mathematical physics and serves as revision of all of the necessary mathematical notions needed to navigate the domain of multiscale research.The author gives a rigorous presentation of the tools of mathematical modeling, as well as an evaluation of the errors of the method. This allows readers to analyze the limitations and accuracy of the method.The book is accessible to a wide range of readers, from specialists in engineering to applied mathematicians working in the applications of materials science, biophysics and medicine.

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Book SynopsisLinear algebra and matrix theory are among the most important and most frequently applied branches of mathematics. They are especially important in solving engineering and economic models, where either the model is assumed linear, or the nonlinear model is approximated by a linear model, and the resulting linear model is examined.This book is mainly a textbook, that covers a one semester upper division course or a two semester lower division course on the subject.The second edition will be an extended and modernized version of the first edition. We added some new theoretical topics and some new applications from fields other than economics. We also added more difficult exercises at the end of each chapter which require deep understanding of the theoretical issues. We also modernized some proofs in the theoretical discussions which give better overview of the study material. In preparing the manuscript we also corrected the typos and errors, so the second edition will be a corrected, extended and modernized new version of the first edition.

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Book SynopsisThis book’s aim is to study the mathematical and computational models to analyze the progress, prognosis, prevention, and panacea of breast cancer. The book discusses application of Markov chains and transient mappings, Charlie–Simpson numerical algorithm, models represented by nonlinear reaction–diffusion-type partial differential equations, and related techniques. The book also attempts to design mathematical model of targeted strategic treatments by using Skilled Killer Drugs (SKD1 and SKD2) to suggest the improvisation of future cancer treatments. Both graduate students and researchers of computational biology and oncologists will benefit by studying this book. Researchers of cancer studies and biological sciences will also find this work helpful.Table of ContentsIntroduction.- Statistics: The Backgrounds & The Basis.- Attacker & Defender Model: The Dynamics of the Immune System.- Mathematical Modeling of Metastatic Cancer.- Mathematical/Computational Modeling of Advanced Immunotherapy.- Mathematical Modeling & Computational Studies On The War Against Breast Cancer.- Gene Therapy.- The Smartest Fighters.- Nutritional Therapy.- The Fateful Code & The Future Course.- Conclusion.

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Book Synopsis"Modeling the Environment" was the first textbook in an emerging field - the modeling techniques that allow managers and researchers to see in advance the consequences of actions and policies in environmental management. This new edition brings the book thoroughly up to date and reaffirms its status as the leading introductory text on the subject. System dynamics is one of the most widely used methods of modeling. The fundamental principles of this approach are demonstrated here with a wide range of examples, including geohydrology, population biology, epidemiology, and economics. The applications demonstrate the transferability of the systems approach across disciplines, across spatial scales, and across time scales. All of the models are implemented with stock and flow software programs such as Stella and Vensim, which are easy for students to learn and use.

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Book SynopsisIntended for advanced undergraduate and beginning graduate courses on Modeling, this book introduces a variety of mathematical models for biological systems, and presents the mathematical theory and techniques useful in analyzing those models. Its material is organized according to the mathematical theory rather than the biological application.Table of ContentsPreface xi 1 LINEAR DIFFERENCE EQUATIONS, THEORY, AND EXAMPLES 1 1.1 Introduction 1 1.2 Basic Definitions and Notation 2 1.3 First-Order Equations 6 1.4 Second-Order and Higher-Order Equations 8 1.5 First-Order Linear Systems 14 1.6 An Example: Leslie’s Age-Structured Model 18 1.7 Properties of the Leslie Matrix 20 1.8 Exercises for Chapter 1 28 1.9 References for Chapter 1 33 1.10 Appendix for Chapter 1 34 1.10.1 Maple Program:Turtle Model 34 1.10.2 MATLAB® Program:Turtle Model 34 2 NONLINEAR DIFFERENCE EQUATIONS, THEORY, AND EXAMPLES 36 2.1 Introduction 36 2.2 Basic Definitions and Notation 37 2.3 Local Stability in First-Order Equations 40 2.4 Cobwebbing Method for First-Order Equations 45 2.5 Global Stability in First-Order Equations 46 2.6 The Approximate Logistic Equation 52 2.7 Bifurcation Theory 55 2.7.1 Types of Bifurcations 56 2.7.2 Liapunov Exponents 60 2.8 Stability in First-Order Systems 62 2.9 Jury Conditions 67 2.10 An Example: Epidemic Model 69 2.11 Delay Difference Equations 73 2.12 Exercises for Chapter 2 76 2.13 References for Chapter 2 82 2.14 Appendix for Chapter 2 84 2.14.1 Proof of Theorem 2.1 84 2.14.2 A Definition of Chaos 86 2.14.3 Jury Conditions (Schur-Cohn Criteria) 86 2.14.4 Liapunov Exponents for Systems of Difference Equations 87 2.14.5 MATLAB Program: SIR Epidemic Model 88 3 BIOLOGICAL APPLICATIONS OF DIFFERENCE EQUATIONS 89 3.1 Introduction 89 3.2 Population Models 90 3.3 Nicholson-Bailey Model 92 3.4 Other Host-Parasitoid Models 96 3.5 Host-Parasite Model 98 3.6 Predator-Prey Model 99 3.7 Population Genetics Models 103 3.8 Nonlinear Structured Models 110 3.8.1 Density-Dependent Leslie Matrix Models 110 3.8.2 Structured Model for Flour Beetle Populations 116 3.8.3 Structured Model for the Northern Spotted Owl 118 3.8.4 Two-Sex Model 121 3.9 Measles Model with Vaccination 123 3.10 Exercises for Chapter 3 127 3.11 References for Chapter 3 134 3.12 Appendix for Chapter 3 138 3.12.1 Maple Program: Nicholson-Bailey Model 138 3.12.2 Whooping Crane Data 138 3.12.3 Waterfowl Data 139 4 LINEAR DIFFERENTIAL EQUATIONS: THEORY AND EXAMPLES 141 4.1 Introduction 141 4.2 Basic Definitions and Notation 142 4.3 First-Order Linear Differential Equations 144 4.4 Higher-Order Linear Differential Equations 145 4.4.1 Constant Coefficients 146 4.5 Routh-Hurwitz Criteria 150 4.6 Converting Higher-Order Equations to First-OrderSystems 152 4.7 First-Order Linear Systems 154 4.7.1 Constant Coefficients 155 4.8 Phase-Plane Analysis 157 4.9 Gershgorin’s Theorem 162 4.10 An Example: Pharmacokinetics Model 163 4.11 Discrete and Continuous Time Delays 165 4.12 Exercises for Chapter 4 169 4.13 References for Chapter 4 172 4.14 Appendix for Chapter 4 173 4.14.1 Exponential of a Matrix 173 4.14.2 Maple Program: Pharmacokinetics Model 175 5 NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS: THEORY AND EXAMPLES 176 5.1 Introduction 176 5.2 Basic Definitions and Notation 177 5.3 Local Stability in First-Order Equations 180 5.3.1 Application to Population Growth Models 181 5.4 Phase Line Diagrams 184 5.5 Local Stability in First-Order Systems 186 5.6 Phase Plane Analysis 191 5.7 Periodic Solutions 194 5.7.1 Poincaré-Bendixson Theorem 194 5.7.2 Bendixson’s and Dulac’s Criteria 197 5.8 Bifurcations 199 5.8.1 First-Order Equations 200 5.8.2 Hopf Bifurcation Theorem 201 5.9 Delay Logistic Equation 204 5.10 Stability Using Qualitative Matrix Stability 211 5.11 Global Stability and Liapunov Functions 216 5.12 Persistence and Extinction Theory 221 5.13 Exercises for Chapter 5 224 5.14 References for Chapter 5 232 5.15 Appendix for Chapter 5 234 5.15.1 Subcritical and Supercritical Hopf Bifurcations 234 5.15.2 Strong Delay Kernel 235 6 BIOLOGICAL APPLICATIONS OF DIFFERENTIAL EQUATIONS 237 6.1 Introduction 237 6.2 Harvesting a Single Population 238 6.3 Predator-Prey Models 240 6.4 Competition Models 248 6.4.1 Two Species 248 6.4.2 Three Species 250 6.5 Spruce Budworm Model 254 6.6 Metapopulation and Patch Models 260 6.7 Chemostat Model 263 6.7.1 Michaelis-Menten Kinetics 263 6.7.2 Bacterial Growth in a Chemostat 266 6.8 Epidemic Models 271 6.8.1 SI, SIS, and SIR Epidemic Models 271 6.8.2 Cellular Dynamics of HIV 276 6.9 Excitable Systems 279 6.9.1 Van der Pol Equation 279 6.9.2 Hodgkin-Huxley and FitzHugh-Nagumo Models 280 6.10 Exercises for Chapter 6 283 6.11 References for Chapter 6 292 6.12 Appendix for Chapter 6 296 6.12.1 Lynx and Fox Data 296 6.12.2 Extinction in Metapopulation Models 296 7 PARTIAL DIFFERENTIAL EQUATIONS: THEORY, EXAMPLES, AND APPLICATIONS 299 7.1 Introduction 299 7.2 Continuous Age-Structured Model 300 7.2.1 Method of Characteristics 302 7.2.2 Analysis of the Continuous Age-Structured Model 306 7.3 Reaction-Diffusion Equations 309 7.4 Equilibrium and Traveling Wave Solutions 316 7.5 Critical Patch Size 319 7.6 Spread of Genes and Traveling Waves 321 7.7 Pattern Formation 325 7.8 Integrodifference Equations 330 7.9 Exercises for Chapter 7 331 7.10 References for Chapter 7 336 Index 339

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Book SynopsisThis novel and accessible textbook focuses on the intimate interplay between ecological and evolutionary processes as populations spread through time and space. It provides both a survey of the field a story about the history and development of our understanding as well as a synthesis of the new developments.

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Book SynopsisIn this work, Martin H. Krieger seeks to show what physicists really do behind the nearly impenetrable cloud of mathematical models they use as research tools. He argues that the technical details of these complex calculations also reveal key aspects of the physical properties they model.Table of ContentsList of Figures Preface 1: Modeling the Constitutions of Matter 2: Analysis: The Stability of Bulk Matter 3: Mathematics: Infinite Volume Limits and Thermodynamics 4: Formalism: Constituting Bulk Matter: Solutions to the Ising Model, and Duality in Those Solutions 5: Analysis: Generic, Formal, Model-Independent Accounts of the Constitution of Matter as Philosophical 6: Formalism: Technical Devices Doing the Work of Physics 7: Physics and Mathematics: Finding the Right Mechanism and Choosing the Right Functions 8: The Physics and the Mathematics Appendix: Two Papers by Lars Onsager A: Electrostatic Interaction of Molecules (1939) B: Crystal Statistics, Part I: A Two-Dimensional Model with an Order-Disorder Transition (1944) Notes References Index

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

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Book SynopsisThe origami introduced in this book is based on simple techniques. Some were previously known by origami artists and some were discovered by the author. Curved-Folding Origami Design shows a way to explore new area of origami composed of curved folds. Each technique is introduced in a step-by-step fashion, followed by some beautiful artwork examples. A commentary explaining the theory behind the technique is placed at the end of each chapter.Features Explains the techniques for designing curved-folding origami in seven chapters Contains many illustrations and photos (over 140 figures), with simple instructions Contains photos of 24 beautiful origami artworks, as well as their crease patterns Some basic theories behind the techniques are introduced Trade Review"This is a beautiful book; the lovely photographs and copious examples of curved-folding concepts make it the perfect jumping-off point for the curved-folding artist."-Robert J. Lang, author of Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami"Mitani-san's concise book is a must-have for anyone wishing to learn the science and art of curved folding. He has the enviable knack of making this enigmatic technique easy to control, fun to try and visually dazzling." -Paul Jackson, http://www.origami-artist.com/"Curved folding for everyone who ever wondered how the paper magic is done. This fascinating book explains the secrets of curved folding for everyone. You can open a whole new world of curved folding with this beautifully illustrated book. Must have for both origami enthusiasts and wide range of designers." -Ekaterina Lukasheva, http://www.kusudama.me/"Comprised of profusely illustrated instructions for twenty-four original origami artworks, "Curved-Folding Origami Design" is thoroughly 'user friendly' in organization and presentation, making it an ideal introduction to the novice and of immense interest to seasoned practitioners of origami art. While highly recommended for both community and academic library collections."-Margaret Lane- Wisconsin Bookwatch"This is a beautiful book; the lovely photographs and copious examples of curved-folding concepts make it the perfect jumping-off point for the curved-folding artist." -Robert J. Lang, author of Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami"Mitani-san's concise book is a must-have for anyone wishing to learn the science and art of curved folding. He has the enviable knack of making this enigmatic technique easy to control, fun to try and visually dazzling." -Paul Jackson, http://www.origami-artist.com/Curved folding for everyone who ever wondered how the paper magic is done. This fascinating book explains the secrets of curved folding for everyone. You can open a whole new world of curved folding with this beautifully illustrated book. Must have for both origami enthusiasts and wide range of designers. -Ekaterina Lukasheva, http://www.kusudama.me/Table of ContentsPrologueChapter 1 Fold a CurveChapter 2 Aligning CurvesChapter 3 Aligning Rotated CurvesChapter 4 TuckingChapter 5 Folding ConesChapter 6 Folding Back at Straight LineChapter 7 Other TechniquesAfterword

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Book SynopsisReliability and maintenance modeling with optimization is the most fundamental and interdisciplinary research area that can be applied to every technical and management field. Reliability and Maintenance Modeling with Optimization: Advances and Applications aims at providing the most recent advances and achievements in reliability and maintenance.The book discusses replacement, repair, and inspection, offers estimation and statistical tests, covers accelerated life testing, explores warranty analysis manufacturing, and includes service reliability.The targeted readers are researchers interested in reliability and maintenance engineering. The book can serve as supplemental reading in professional seminars for engineers, designers, project managers, and graduate students.

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Book SynopsisAn accessible and self-contained introduction to statistical models-now in a modernized new edition Generalized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various construction, application, and computational aspects. A clear introduction to the basic ideas of fixed effects models, random effects models, and mixed models is maintained throughout, and each chapter illustrates how these models are applicable in a wide array of contexts. In addition, a discussion of general methods for the analysis of such models is presented with an emphasis on the method of maximum likelihood for the estimation of parameters. The authors also provide comprehensive coverage of the lateTable of ContentsPreface. Preface to the First Edition. 1. Introduction. 1.1 Models. 1.2 Factors, Levels, Cells, Effects And Data. 1.3 Fixed Effects Models. 1.4 Random Effects Models. 1.5 Linear Mixed Models (Lmms). 1.6 Fixed Or Random? 1.7 Inference. 1.8 Computer Software. 1.9 Exercises. 2. One-Way Classifications. 2.1 Normality And Fixed Effects. 2.2 Normality, Random Effects And MLE. 2.3 Normality, Random Effects And REM1. 2.4 More On Random Effects And Normality. 2.5 Binary Data: Fixed Effects. 2.6 Binary Data: Random Effects. 2.7 Computing. 2.8 Exercises. 3. Single-Predictor Regression. 3.1 Introduction. 3.2 Normality: Simple Linear Regression. 3.3 Normality: A Nonlinear Model. 3.4 Transforming Versus Linking. 3.5 Random Intercepts: Balanced Data. 3.6 Random Intercepts: Unbalanced Data. 3.7 Bernoulli - Logistic Regression. 3.8 Bernoulli - Logistic With Random Intercepts. 3.9 Exercises. 4. Linear Models (LMs). 4.1 A General Model. 4.2 A Linear Model For Fixed Effects. 4.3 Mle Under Normality. 4.4 Sufficient Statistics. 4.5 Many Apparent Estimators. 4.6 Estimable Functions. 4.7 A Numerical Example. 4.8 Estimating Residual Variance. 4.9 Comments On The 1- And 2-Way Classifications. 4.10 Testing Linear Hypotheses. 4.11 T-Tests And Confidence Intervals. 4.12 Unique Estimation Using Restrictions. 4.13 Exercises. 5. Generalized Linear Models (GLMs). 5.1 Introduction. 5.2 Structure Of The Model. 5.3 Transforming Versus Linking. 5.4 Estimation By Maximum Likelihood. 5.5 Tests Of Hypotheses. 5.6 Maximum Quasi-Likelihood. 5.7 Exercises. 6. Linear Mixed Models (LMMs). 6.1 A General Model. 6.2 Attributing Structure To VAR(y). 6.3 Estimating Fixed Effects For V Known. 6.4 Estimating Fixed Effects For V Unknown. 6.5 Predicting Random Effects For V Known. 6.6 Predicting Random Effects For V Unknown. 6.7 Anova Estimation Of Variance Components. 6.8 Maximum Likelihood (Ml) Estimation. 6.9 Restricted Maximum Likelihood (REMl). 6.10 Notes And Extensions. 6.11 Appendix For Chapter 6. 6.12 Exercises. 7. Generalized Linear Mixed Models. 7.1 Introduction. 7.2 Structure Of The Model. 7.3 Consequences Of Having Random Effects. 7.4 Estimation By Maximum Likelihood. 7.5 Other Methods Of Estimation. 7.6 Tests Of Hypotheses. 7.7 Illustration: Chestnut Leaf Blight. 7.8 Exercises. 8. Models for Longitudinal data. 8.1 Introduction. 8.2 A Model For Balanced Data. 8.3 A Mixed Model Approach. 8.4 Random Intercept And Slope Models. 8.5 Predicting Random Effects. 8.6 Estimating Parameters. 8.7 Unbalanced Data. 8.8 Models For Non-Normal Responses. 8.9 A Summary Of Results. 8.10 Appendix. 8.11 Exercises. 9. Marginal Models. 9.1 Introduction. 9.2 Examples Of Marginal Regression Models. 9.3 Generalized Estimating Equations. 9.4 Contrasting Marginal And Conditional Models. 9.5 Exercises. 10. Multivariate Models. 10.1 Introduction. 10.2 Multivariate Normal Outcomes. 10.3 Non-Normally Distributed Outcomes. 10.4 Correlated Random Effects. 10.5 Likelihood Based Analysis. 10.6 Example: Osteoarthritis Initiative. 10.7 Notes And Extensions. 10.8 Exercises. 11. Nonlinear Models. 11.1 Introduction. 11.2 Example: Corn Photosynthesis. 11.3 Pharmacokinetic Models. 11.4 Computations For Nonlinear Mixed Models. 11.5 Exercises. 12. Departures From Assumptions. 12.1 Introduction. 12.2 Misspecifications Of Conditional Model For Response. 12.3 Misspecifications Of Random Effects Distribution. 12.4 Methods To Diagnose And Correct For Misspecifications. 12.5 Exercises. 13. Prediction. 13.1 Introduction. 13.2 Best Prediction (BP). 13.3 Best Linear Prediction (BLP). 13.4 Linear Mixed Model Prediction (BLUP). 13.5 Required Assumptions. 13.6 Estimated Best Prediction. 13.7 Henderson’s Mixed Model Equations. 13.8 Appendix. 13.9 Exercises. 14. Computing. 14.1 Introduction. 14.2 Computing Ml Estimates For LMMs. 14.3 Computing Ml Estimates For GLMMs. 14.4 Penalized Quasi-Likelihood And Laplace. 14.5 Exercises. Appendix M: Some Matrix Results. M.1 Vectors And Matrices Of Ones. M.2 Kronecker (Or Direct) Products. M.3 A Matrix Notation. M.4 Generalized Inverses. M.5 Differential Calculus. Appendix S: Some Statistical Results. S.1 Moments. S.2 Normal Distributions. S.3 Exponential Families. S.4 Maximum Likelihood. S.5 Likelihood Ratio Tests. S.6 MLE Under Normality. References. Index.

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Book SynopsisThis general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics.Trade Review'… It gives an excellent general introduction to epidemic modelling, starting with an interesting historical account and then describing the most important and useful models which can be used.' Robert MacMillan, Mathematical Gazette'The book will be accessible … and its study highly rewarding, to anyone with an interest in epidemic models…' V. S. Isham, Short Book Reviews'Daley and Gani's monograph is a concise and useful presentation of a variety of epidemiological models.' Daniel Haydon, Trends in Ecology and Evolution'… gives an excellent general introduction to epidemic modelling … should certainly be available to undergraduates.' Robert MacMillan, The Mathematical Gazette'This book had us hooked … [it] remains an important reference in our library and is frequently consulted for advice on how to think about modelling in related contexts.' Darfiana Nur and Kerrie L. Mengersen, The Australian and New Zealand Journal of Statistics'… the book is clear and well written … could serve as course literature for graduate, or possibly last year undergraduate, course in epidemic modelling.' Statistics in Medicine'I found the book very clear, concise and useful … I recommend the book very strongly as a teaching tool and as a research tool to academics and scientists who are interested in epidemic modeling. I also strongly recommend the book to applied mathematicians who are intetrested in stochastic models in general.' Mathematics TodayTable of ContentsPreface; 1. Some history; 2. Deterministic models; 3. Stochastic models in continuous time; 4. Stochastic models in discrete time; 5. Rumours: modelling spread and its cessation; 6. Fitting epidemic data; 7. The control of epidemics; References and author index; Subject index.

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Book SynopsisThis book focuses on the practical needs of applied statisticians and experimenters engaged in design, implementation and analysis in a variety of disciplines, including biological and physical sciences, engineering, medicine and agriculture. It contains numerous exercises and a wide range of examples drawn from real experiments.Table of Contents1. Introduction; 2. Elementary ideas of blocking: the randomised complete block design; 3. Elementary ideas of treatment structure; 4. General principles of linear models for the analysis of experimental data; 5. Experimental units; 6. Replication; 7. Blocking and control; 8. Multiple blocking systems and crossover designs; 9. Multiple levels of information; 10. Randomisation; 11. Restricted randomisation; 12. Experimental objectives, treatments and treatment structures; 13. Factorial structure and particular forms of effects; 14. Fractional replication; 15. Incomplete block size for factorial experiments; 16. Quantitative factors and response functions; 17. Multifactorial designs for quantitative factors; 18. Split unit designs; 19. Multiple experiments and new variation; 20. Sequential aspects of experiments and experimental programmes; 21. Designing useful experiments.

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Book SynopsisQueueing systems and networks are being applied to many areas of technology today, including telecommunications, computers, satellite systems, and traffic processes. This timely book, written by 26 of the most respected and influential researchers in the field, provides an overview of fundamental queueing systems and networks as applied to these technologies.Frontiers in Queueing: Models and Applications in Science and Engineering was written with more of an engineering slant than its predecessor, Advances in Queueing: Theory, Methods, and Open Problems. The earlier book was primarily concerned with methods, and was more theoretically oriented. This new volume, meant to be a sequel to the first book, was written by scientists and queueing theorists whose expertise is in technology and engineering, allowing readers to answer questions regarding the technicalities of related methods from the earlier book.Each chapter in the book surveys the classes of queueing models and networksTrade Review"The editor is to be congratulated for the selection of topics and assuring the high quality of articles."- Joseph Glaz, University of Connecticut, in Technometrics"The overall editing and production are excellent… Frontiers in Queueing may be less theoretical than Advances in Queueing,… but it is equal to it in terms of the high quality of its scholarship…As in the other book, these authors are all experts, and all of their contributions authoritatively reflect the current state of the art….My only compensation for reviewing Frontiers in Queueing is getting to keep the review copy. Considering that this is an excellent book, I think I got a very good deal.-Computing Reviews, December 1998Table of ContentsProgress of Classical Queueing Models: A Personal View of Queueing Theory. Retrial Queues Revisited. Some Results for the Mean Waiting-Time and Workload in GI/GI/k Queues. Queues with State Dependent Parameters. Telecommunications and Computer Networks: Queueing Analysis of Polling Models: Progress in 1990-1994. Product-Form Loss Networks. Sojourn Time Distributions in Non-Product Form Queueing Networks. Traffic Processes: Stochastic Geometry Models of Mobile Communication Networks. Fractal Queueing Models. Stochastic Modeling of Traffic Processes. Fluid Models for Single Buffer Systems. Applied Techniques and Statistical Inference in Queueing Models: Computational Methods in Queueing. Statistical Analysis of Queueing Systems. Perturbation Analysis for Control and Optimization of Queueing Systems: An Overview and the State of the Art. Polynomial Time Algorithms for Estimation of Rare Events in Queueing Models. Parametric Statistical Inference for Tail Probabilities of Queues. Index.

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Book SynopsisBringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. The second edition of this introductory book features several new codes and 140 new problems (many on physics applications), as well as new sections on the singular-value decomposition, derivative-free optimization, Bayesian linear regression, neural networks, and partial differential equations. The last section in each chapter is an in-depth project, tackling physics problems that cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the numerical methods often used in the subject.Trade Review'A fantastic addition as an introductory textbook for computational physics. The book is timely, and the author made thoughtful and, in my view, many wise choices. The book is comprehensive and yet accessible to undergraduate students.' Shiwei Zhang, the Flatiron Institute and the College of William & Mary'Gezerlis' book Numerical Methods in Physics with Python is a beautiful example of how an established subject can be brought to the next level by making it very accessible and by introducing several insightful and interdisciplinary applications. This second edition considerably extends the set of exercises, resulting in an extremely useful resource for both students and teachers. Strongly recommended!' Sonia Bacca, Johannes Gutenberg-Universität Mainz'This new edition of Numerical Methods… is another great example of Gezerlis' passion for teaching and for doing so carefully and precisely. Especially welcome, in my view, are the addition of problems at the end of each chapter and the discussion of singular value decomposition (SVD) and Bayesian methods. The SVD is one of the crown jewels of linear algebra which modern students interested in machine learning will surely find beneficial. To physics, computer science, or engineering students mesmerized by the fast Fourier transform, Gezerlis' excellent explanation of it in Chapter 6 is likely to shed some light on the underlying divide-and-conquer algorithm, which is an essential classic.' Joaquin Drut, University of North Carolina at Chapel HillPraise for the first edition: 'I enthusiastically recommend Numerical Methods in Physics with Python by Professor Gezerlis to any advanced undergraduate or graduate student who would like to acquire a solid understanding of the basic numerical methods used in physics. The methods are demonstrated with Python, a relatively compact, accessible computer language, allowing the reader to focus on understanding how the methods work rather than on how to program them. Each chapter offers a self-contained, clear, and engaging presentation of the relevant numerical methods, and captivates the reader with well-motivated physics examples and interesting physics projects. Written by a leading expert in computational physics, this outstanding textbook is unique in that it focuses on teaching basic numerical methods while also including a number of modern numerical techniques that are usually not covered in computational physics textbooks.' Yoram Alhassid, Yale University'In Numerical Methods in Physics with Python by Gezerlis, one finds a resource that has been sorely missing! As the usage of Python has become widespread, it is too often the case that students take libraries, functions, and codes and apply them without a solid understanding of what is truly being done 'under the hood' and why. Gezerlis' book fills this gap with clarity and rigor by covering a broad number of topics relevant for physics, describing the underlying techniques, and implementing them in detail. It should be an important resource for anyone applying numerical techniques to study physics.' Luis Lehner, Perimeter Institute for Theoretical Physics'Gezerlis' text takes a venerable subject - numerical techniques in physics - and brings it up to date and makes it accessible to modern undergraduate curricula through a popular, open-source programming language. Although the focus remains squarely on numerical techniques, each new lesson is motivated by topics commonly encountered in physics and concludes with a practical hands-on project to help cement the students' understanding. The net result is a textbook which fills an important and unique niche in pedagogy and scope, as well as a valuable reference for advanced students and practicing scientists.' Brian Metzger, Columbia UniversityTable of ContentsPreface; 1. Idiomatic Python; 2. Numbers; 3. Derivatives; 4. Matrices; 5. Zeroes and minima; 6. Approximation; 7. Integrals; 8. Differential equations; Appendix A. Installation and setup; Appendix B. Number representations; Appendix C. Math background; Bibliography; Index.

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Book SynopsisMathematical Modeling in Biology: A Research Methods Approach is a textbook written primarily for advanced mathematics and science undergraduate students and graduate-level biology students. Although the applications center on ecology, the expertise of the authors, the methodology can be imported to any other science, including social science and economics. The aim of the book, beyond being a useful aid to teaching and learning the core modeling skills needed for mathematical biology, is to encourage students to think deeply and clearly about the meaning of mathematics in science and to learn significant research methods. Most importantly, it is hoped that students will experience some of the excitement of doing research.Features Minimal pre-requisites beyond a solid background in calculus, such as a calculus I course. Suitable for upper division mathematics and sciences students and graduate-level biology students. Provides sample MATLAB codes and instruction in Appendices along with datasets available on https://bit.ly/3fcLF3D Trade Review"Without hesitation, we highly recommend this book for Mathematics and Science Undergraduate Students and Graduate-Level Biology Students as well as researchers who are interested in biological research using a Mathematical Modeling approach. Apart from providing information for readers, this book is also equipped with exercises in almost every chapter to train readers to understand the contents of the book and this book is also equipped with various case studies that can be studied to understand the concepts of Mathematical Modeling in Biology. We greatly appreciate the authors who have contributed to writing this book which is the first edition of CRC Press for the Mathematical Biology Series. The enormous potential of Mathematical Modeling as a statistical approach in research methods can be predicted that this book will become a fundamental need for current and future research in the field of biology and several related fields."- TechnometricsTable of ContentsI. Introduction to Modeling 1. Mathematical Modeling. 1.1. What You Should Know About This Chapter. 1.2 The modeling cycle. 1.3. Biology. 1.4. Mathematics. 1.5. Statistics. 1.6. Epistemology: How We Know. 1.7. Exercises. 2. Avian Bone Growth: A Case Study. 2.1. What you should know about this chapter. 2.2. Scientific Problem. 2.3. Translation into Mathematics. 2.4. Model Parametrization. 2.5. Model Selection. 2.6. Model Validation. 2.7. Exercises. II. Discrete-Time Models. 3. Discrete-Time Maps. 3.1. What you should know about this chapter. 3.2. Compartmental Model. 3.3. Linear Maps. 3.4. Nonlinear Maps. 3.5. Linearization. 3.6. The Ricker Nonlinearity. 3.7. Exercises. 4. Chaos: Simple Rules Can Generate Complex Results. 4.1. What you should know about this chapter. 4.2. Ricker Model Revisited. 4.3. New Paradigms Associated from Chaos. 4.4. May’s Hypothesis. 4.5. Exercises. 5. Higher Dimensional Discrete-time Models. 5.1. What you should know about this chapter. 5.2. Intraspecific Interactions. 5.3. Interspecific Interactions. 5.4. Example of an Age-structured Single-Species Model. 5.5. Example of a Two-Species Model. 5.6. n-dimensional Linear Difference Equations. 5.7. Solving Linear Systems of Difference Equations. 5.8. Nonlinear Systems. 5.9. Exercises. 6. Flour Beetle Dynamics: A Case Study. 6.1. What you should know about this chapter. 6.2. Flour Beetles. 6.3. Data. 6.4. Assumptions. 6.5. Alternative Deterministic Models. 6.6. Stochastic Models. 6.7. Model Parametrization. 6.8. Model Selection. 6.9. Model Validation. 6.10. The "Hunt for Chaos" Experiments. 6.11. Exercises. III. Continuous-time Models 7. Introduction to Differential Equations. 7.1. What you should know about this chapter. 7.2. Compartmental Models. 7.3. Exercises. 8. Scalar Differential Equations. 8.1. What you should know about this chapter. 8.2. Linear Equations. 8.3. Nonlinear Equations. 8.4. Bifurcations. 8.5. Exercises. 9. Systems of Differential Equations. 9.1. What you should know about this chapter. 9.2. Linear Systems of ODEs and Phase Plane Analysis. 9.3. Nonlinear Systems of ODEs. 9.4. Limit Cycles, Cycle Chains, and Bifurcations. 9.5. Lotka-Volterra Models and Nullcline Analysis. 9.6. Exercises. 10. Seabird Behavior: A Case Study. 10.1. What you should know about this chapter. 10.2. The Scientific Problem. 10.3. Historical Data. 10.4. General Model. 10.5. Alternative Models. 10.6. Model Parametrization. 10.7. Model Selection. 10.8. Model Validation. 10.9. Test of a priori predictions. 10.10. Steady-state model. 10.11. Discussion. Exercises. IV. Regression Models. 11. Regression Models. 11.1. What You Should Know About This Chapter. 11.2. Linear Regression. 11.3. Logistic Regression. 11.4. Generalized Linear Models (GLMs). 11.5. Interaction Terms. 11.6. Exercises. 12. Climate Change and Seabird Cannibalism: A Case Study. 12.1. What You Should Know About This Chapter. 12.2. The Scientific Problem. 12.3. Data. 12.4. Logistic Regression Analysis. 12.5. Model Validation. 12.6. Outcomes. 12.7. Climate Change, Cannibalism, and Reproductive Synchrony. 12.8. Exercises. V. Appendix. A. Linear Algebra Basics. B. MATLAB: The Basics. C. Connecting Models to Data: A Brief Summary with Sample Codes.

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Book SynopsisThis textbook intends to be a comprehensive and substantially self-contained two-volume book covering performance, reliability, and availability evaluation subjects. The volumes focus on computing systems, although the methods may also be applied to other systems. The first volume covers Chapter 1 to Chapter 14, whose subtitle is ``Performance Modeling and Background. The second volume encompasses Chapter 15 to Chapter 25 and has the subtitle ``Reliability and Availability Modeling, Measuring and Workload, and Lifetime Data Analysis.This text is helpful for computer performance professionals for supporting planning, design, configuring, and tuning the performance, reliability, and availability of computing systems. Such professionals may use these volumes to get acquainted with specific subjects by looking at the particular chapters. Many examples in the textbook on computing systems will help them understand the concepts covered in each chapter. The text may also be helpful for the instructor who teaches performance, reliability, and availability evaluation subjects. Many possible threads could be configured according to the interest of the audience and the duration of the course. Chapter 1 presents a good number of possible courses programs that could be organized using this text.Volume II is composed of the last two parts. Part III examines reliability and availability modeling by covering a set of fundamental notions, definitions, redundancy procedures, and modeling methods such as Reliability Block Diagrams (RBD) and Fault Trees (FT) with the respective evaluation methods, adopts Markov chains, Stochastic Petri nets and even hierarchical and heterogeneous modeling to represent more complex systems. Part IV discusses performance measurements and reliability data analysis. It first depicts some basic measuring mechanisms applied in computer systems, then discusses workload generation. After, we examine failure monitoring and fault injection, and finally, we discuss a set of techniques for reliability and maintainability data analysis.

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Book SynopsisSpreadsheet Problem Solving and Programming for Engineers and Scientists provides a comprehensive resource essential to a full understanding of modern spreadsheet skills needed for engineering and scientific computations.Beginning with the basics of spreadsheets and programming, this book builds on the authors' decades of experience teaching spreadsheets and programming to both university students and professional engineers and scientists. Following on from this, it covers engineering economics, key numerical methods, and applied statistics. Finally, this book details the Visual Basic for Applications (VBA) programming system that accompanies Excel.With each chapter including examples and a set of exercises, this book is an ideal companion for all engineering courses and also for self-study. Based on the latest version of Excel (Microsoft Excel for Microsoft 365), it is also compatible with earlier versions of Excel dating back to Version 2013. Including numerTable of ContentsChapter 1 Spreadsheet Basics Chapter 2 Charts and GraphsChapter 3 Engineering and Scientific FormulasChapter 4 Table-based CalculationsChapter 5 Case Studies and TargetingChapter 6 Financial CalculationsChapter 7 Numerical MethodsChapter 8 Applied StatisticsChapter 9 Introduction to VBA and MacrosChapter 10 User-defined FunctionsChapter 11 VBA ProgrammingChapter 12 User InterfacesAppendix A: Matrix Algebra ReviewAppendix B: Shortcut Keys and Key Combinations

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Book SynopsisMechatronics is a mongrel, a crossbreed of classic mechanical engineering, the relatively young pup of computer science, the energetic electrical engineering, the pedigree mathematics and the bloodhound of Control Theory.All too many courses in control theory consist of a diet of Everything you could ever need to know about the Laplace Transform' rather than answering What happens when your servomotor saturates?' Topics in this book have been selected to answer the questions that the mechatronics student is most likely to raise.That does not mean that the mathematical aspects have been left out, far from it. The diet here includes matrices, transforms, eigenvectors, differential equations and even the dreaded z transform. But every effort has been made to relate them to practical experience, to make them digestible. They are there for what they can do, not to support pages of mathematical rigour that defines their origins.The theme running throughout theTable of Contents1. Why Do You Need Control Theory? 2. Modelling Time .3. A Simulation Environment 4. Step Length Considerations. 5. Modelling a Second-Order System .6. The Complication of Motor Drive Limits. 7. Practical Controller Design 8. Adding Dynamics to the Controller 9. Sensors and Actuators. 10. Analogue Simulation. 11. Matrix State Equations. 12. Putting It into Practice. 13. Observers 14. More about the Mathematics 15. Transfer Functions 16. Solving the State Equations 17. Discrete Time and the z Operator. 18. Root locus. 19. More about the Phase Plane. 20. Optimisation and an Experiment. 21. Problem Systems. 22. Final Comments.

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Book SynopsisThis book is designed as an introduction to neural dynamics through an intuitive exploration of fundamental dynamic motifs - the recurring dynamical concepts essential for understanding computational neuroscience. This concise, hands-on guide bridges the gap between mathematics and neuroscience, providing clear explanations of the key dynamical systems concepts that appear repeatedly in the computational/mathematical neuroscience literature.Key Features: Geometric and intuitive descriptions that minimize mathematical formality while preserving clarity Interactive Explorations that reinforce concepts through computer-based exercises Complete solutions to all Explorations, allowing for self-guided learning Accessible approach suitable for both experimental neuroscientists and mathematicians Focused coverage of essential concepts that serve as building blocks for understanding complex neural models This book serves as an ideal entry point into computational neuroscience for two distinct audiences: experimental neuroscientists seeking to understand computational techniques for collaboration, and mathematicians or mathematics students looking to apply their knowledge to neuroscience. Through its unique combination of concise text and hands-on exploration, readers will quickly develop the knowledge and skills needed to navigate the computational neuroscience literature with confidence.

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Book SynopsisIdeal for teaching and self study, this practical book demonstrates how cognitive scientists can conduct Bayesian analyses for many real-life modeling problems. Supported by examples, exercises, computer code and additional resources available online, readers will learn to take full advantage of the exciting possibilities that the Bayesian approach affords.Trade Review'This book provides the best practical guide to date on how to do Bayesian modeling in cognitive science.' Jay Myung, Ohio State University'This is a very powerful exposition of how Bayesian methods, and WinBUGS in particular, can be used to deal with cognitive models that are apparently intractable. When we produced WinBUGS, we had no idea it could be used like this - it's amazing and gratifying to see these applications.' David Spiegelhalter, Winton Professor for the Public Understanding of Risk, Statistical Laboratory, Centre for Mathematical Sciences, CambridgeTable of ContentsPart I. Getting Started: 1. The basics of Bayesian analysis; 2. Getting started with WinBUGS; Part II. Parameter Estimation: 3. Inferences with binomials; 4. Inferences with Gaussians; 5. Some examples of data analysis; 6. Latent mixture models; Part III. Model Selection: 7. Bayesian model comparison; 8. Comparing Gaussian means; 9. Comparing binomial rates; Part IV. Case Studies: 10. Memory retention; 11. Signal detection theory; 12. Psychophysical functions; 13. Extrasensory perception; 14. Multinomial processing trees; 15. The SIMPLE model of memory; 16. The BART model of risk taking; 17. The GCM model of categorization; 18. Heuristic decision-making; 19. Number concept development.

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