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Wavelets from a Statistical Perspective
by Maarten JansenWavelets from a Statistical Perspective offers a modern, 2nd generation look on wavelets, far beyond the rigid setting of the equispaced, dyadic wavelets in the early days. With the methods of this book, based on the lifting scheme, researchers can set up a wavelet or another multiresolution analysis adapted to their data, ranging from images to scattered data or other irregularly spaced observations. Whereas classical wavelets stand a bit apart from other nonparametric methods, this book adds a multiscale touch to your spline, kernel or local polynomial smoothing procedure, thereby extending its applicability to nonlinear, nonparametric processing for piecewise smooth data. One of the chapters of the book constructs B-spline wavelets on nonequispaced knots and multiscale local polynomial transforms. In another chapter, the link between wavelets and Fourier analysis, ubiquitous in the classical approach, is explained, but without being inevitable. In further chapters the discrete wavelet transform is contrasted with the continuous version, the nondecimated (or maximal overlap) transform taking an intermediate position. An important principle in designing a wavelet analysis through the lifting scheme is finding the right balance between bias and variance. Bias and variance also play a crucial role in the nonparametric smoothing in a wavelet framework, in finding well working thresholds or other smoothing parameters. The numerous illustrations can be reproduced with the online available, accompanying software. The software and the exercises can also be used as a starting point in the further exploration of the material.
Wavelets in Functional Data Analysis
by Pedro A. Morettin Aluísio Pinheiro Brani VidakovicWavelet-based procedures are key in many areas of statistics, applied mathematics, engineering, and science. This book presents wavelets in functional data analysis, offering a glimpse of problems in which they can be applied, including tumor analysis, functional magnetic resonance and meteorological data. Starting with the Haar wavelet, the authors explore myriad families of wavelets and how they can be used. High-dimensional data visualization (using Andrews' plots), wavelet shrinkage (a simple, yet powerful, procedure for nonparametric models) and a selection of estimation and testing techniques (including a discussion on Stein's Paradox) make this a highly valuable resource for graduate students and experienced researchers alike.
Wavelets in Medicine and Biology
by Michael Unser Akram AldroubiConsiderable attention from the international scientific community is currently focused on the wide ranging applications of wavelets. For the first time, the field's leading experts have come together to produce a complete guide to wavelet transform applications in medicine and biology. Wavelets in Medicine and Biology provides accessible, detailed, and comprehensive guidelines for all those interested in learning about wavelets and their applications to biomedical problems.
Wavelets in Neuroscience (Springer Series in Synergetics)
by Alexander E. Hramov Alexey A. Koronovskii Valeri A. Makarov Vladimir A. Maksimenko Alexey N. Pavlov Evgenia SitnikovaThis book illustrates how modern mathematical wavelet transform techniques offer fresh insights into the complex behavior of neural systems at different levels: from the microscopic dynamics of individual cells to the macroscopic behavior of large neural networks. It also demonstrates how and where wavelet-based mathematical tools can provide an advantage over classical approaches used in neuroscience. The authors well describe single neuron and populational neural recordings.This 2nd edition discusses novel areas and significant advances resulting from experimental techniques and computational approaches developed since 2015, and includes three new topics:• Detection of fEPSPs in multielectrode LFPs recordings.• Analysis of Visual Sensory Processing in the Brain and BCI for Human Attention Control;• Analysis and Real-time Classification of Motor-related EEG Patterns;The book is a valuable resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in these and related areas.
Wavelets in Neuroscience
by Alexander E. Hramov Alexey A. Koronovskii Valeri A. Makarov Alexey N. Pavlov Evgenia SitnikovaThis book examines theoretical and applied aspects of wavelet analysis in neurophysics, describing in detail different practical applications of the wavelet theory in the areas of neurodynamics and neurophysiology and providing a review of fundamental work that has been carried out in these fields over the last decade. Chapters 1 and 2 introduce and review the relevant foundations of neurophysics and wavelet theory, respectively, pointing on one hand to the various current challenges in neuroscience and introducing on the other the mathematical techniques of the wavelet transform in its two variants (discrete and continuous) as a powerful and versatile tool for investigating the relevant neuronal dynamics. Chapter 3 then analyzes results from examining individual neuron dynamics and intracellular processes. The principles for recognizing neuronal spikes from extracellular recordings and the advantages of using wavelets to address these issues are described and combined with approaches based on wavelet neural networks (chapter 4). The features of time-frequency organization of EEG signals are then extensively discussed, from theory to practical applications (chapters 5 and 6). Lastly, the technical details of automatic diagnostics and processing of EEG signals using wavelets are examined (chapter 7). The book will be a useful resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in the corresponding areas.
Wavelets Theory and Its Applications: A First Course (Forum for Interdisciplinary Mathematics)
by Mani MehraThis book provides comprehensive information on the conceptual basis of wavelet theory and it applications. Maintaining an essential balance between mathematical rigour and the practical applications of wavelet theory, the book is closely linked to the wavelet MATLAB toolbox, which is accompanied, wherever applicable, by relevant MATLAB codes. The book is divided into four parts, the first of which is devoted to the mathematical foundations. The second part offers a basic introduction to wavelets. The third part discusses wavelet-based numerical methods for differential equations, while the last part highlights applications of wavelets in other fields. The book is ideally suited as a text for undergraduate and graduate students of mathematics and engineering.
Waves in an Impossible Sea: How Everyday Life Emerges from the Cosmic Ocean
by Matt StrasslerA theoretical physicist takes readers on an awe-inspiring journey—found in "no other book" (Science)—to discover how the universe generates everything from nothing at all: "If you want to know what's really going on in the realms of relativity and particle physics, read this book" (Sean Carroll, author of The Biggest Ideas in the Universe). In Waves in an Impossible Sea, physicist Matt Strassler tells a startling tale of elementary particles, human experience, and empty space. He begins with a simple mystery of motion. When we drive at highway speeds with the windows down, the wind beats against our faces. Yet our planet hurtles through the cosmos at 150 miles per second, and we feel nothing of it. How can our voyage be so tranquil when, as Einstein discovered, matter warps space, and space deflects matter? The answer, Strassler reveals, is that empty space is a sea, albeit a paradoxically strange one. Much like water and air, it ripples in various ways, and we ourselves, made from its ripples, can move through space as effortlessly as waves crossing an ocean. Deftly weaving together daily experience and fundamental physics—the musical universe, the enigmatic quantum, cosmic fields, and the Higgs boson—Strassler shows us how all things, familiar and unfamiliar, emerge from what seems like nothing at all. Accessible and profound, Waves in an Impossible Sea is the ultimate guide to our place in the universe.
Waves in Continuous Media (Lecture Notes in Geosystems Mathematics and Computing)
by S. L. Gavrilyuk N.I. Makarenko S.V. SukhininStarting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g. how to recognize the hyperbolicity property, find characteristics, Riemann invariants and conservation laws for quasilinear systems of equations, construct and analyze solutions with weak or strong discontinuities, and how to investigate equations with dispersion and to construct travelling wave solutions for models reducible to nonlinear evolution equations. Chapter 3 deals with surface and internal waves in an incompressible fluid. The efficiency of mathematical methods is demonstrated on a hierarchy of approximate submodels generated from the Euler equations of homogeneous and non-homogeneous fluids. The self-contained presentations of the material is complemented by 200+ problems of different level of difficulty, numerous illustrations, and bibliographical recommendations.
Waves in Flows (Advances in Mathematical Fluid Mechanics)
by Tomáš Bodnár Giovanni P. Galdi Šárka NečasováThis volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. Based on lectures given at the summer school “Waves in Flows”, held in Prague from August 27-31, 2018, chapters are written by renowned experts in their respective fields. Featuring an accessible and flexible presentation, readers will be motivated to broaden their perspectives on the interconnectedness of mathematics and physics. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications. Specific topics covered include:Equatorial wave–current interactionsWater–wave problemsGravity wave propagationFlow–acoustic interactions Waves in Flows will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.
Waves in Flows: The 2018 Prague-Sum Workshop Lectures (Advances in Mathematical Fluid Mechanics)
by Tomáš Bodnár Giovanni P. Galdi Šárka NečasováThis volume explores a range of recent advances in mathematical fluid mechanics, covering theoretical topics and numerical methods. Chapters are based on the lectures given at a workshop in the summer school Waves in Flows, held in Prague from August 27-31, 2018. A broad overview of cutting edge research is presented, with a focus on mathematical modeling and numerical simulations. Readers will find a thorough analysis of numerous state-of-the-art developments presented by leading experts in their respective fields. Specific topics covered include:ChemorepulsionCompressible Navier-Stokes systemsNewtonian fluidsFluid-structure interactions Waves in Flows: The 2018 Prague-Sum Workshop Lectures will appeal to post-doctoral students and scientists whose work involves fluid mechanics.
Way Out in the Desert
by T. J. Marsh Jennifer WardThis toe-tapping text will have you singing along with the lovable creatures of the desert in no time! Filled with vibrant illustrations of many of the charming plants and animals that call the Sonoran Desert home, Way Out in the Desert is a wonderful teaching tool that takes you on a trip down memory lane. If you remember singing Over in the Meadow as a child, now you can give your children their own memories of this timeless tune. So take a child on a trip where Way out in the desert having fun in the sun lived a mother horned toad and her little toady one...
The Way to a Great Country: A Macroscopic View on Chinese Population in the 21st Century (China Perspectives)
by Tian XueyuanPopulation is the most influential factor in social development and economic growth, especially in China. In this book, author Tian Xueyuan provides macro illustrations of the main issues confronting China’s population and development in the 21st century and advises on facing population development challenges to sustainable future development. This book explores issues such as the relation between the change of population and consumption, how the age of the working population affects economic structure and transition when above or below the Lewis turning point, the impact of population aging on growth speed and the pension system, how to remove the urban– rural dual structure, how to reform exam- oriented education, and how to balance relations between population, resource, environment, and sustainable growth. The discussions on population– consumption relations, labor– economy relations, urbanization and rural– urban relations, and beyond provide insightful judgment on and prospects for China’s future development. This book is helpful for international audiences to better understand China’s population and development challenges and strategies.
Ways of Thinking in STEM-based Problem Solving: Teaching and Learning in a New Era
by Lyn D. English Timothy LehmannTaking a future-oriented approach, this book addresses students’ ways of thinking in STEM-based problem solving. It provides a rich set of chapters that explore how we can advance important thinking skills in STEM education for K-12 students. STEM education is essential to understanding and solving many of the world’s major challenges. However, the kind of interdisciplinary modes of thinking required to tackle such unforeseen problems is lacking in most STEM education delivery. This book examines the various ways of thinking that can be applied to effective STEM-based problem solving across K-12 education. These include design and design-based thinking, systems thinking and modeling, critical thinking, innovative and adaptive thinking, intuition in problem solving, and computational and algorithmic thinking. Across the chapters, the authors’ interdisciplinary perspectives give further depth to understanding how students learn and apply their thinking to solve STEM-based problems. The book also provides guidance on how to assess ways of thinking in STEM education, to ensure educators can recognize students’ progress and development.Bringing together a team of international experts, this book is essential reading for pre-service teachers, teacher educators, and researchers in STEM education.
Ways Out Of Social Isolation For Older People In The Context Of New Media: CONNECT-ED – A Project to Improve Social Participation
by Britta Thege Juliane Köchling-Farahwaran Sonja Börm Stephan DettmersThe book introduces the concept of encounter CONNECT-ED from the practice of working with the elderly to impart media skills and presents empirical data on the social participation and quality of life of the participants. The research results show the potential of the Internet for older people and open up perspectives for gender- and age-sensitive advanced training opportunities.
We Are Generation Z: How Identity, Attitudes, and Perspectives Are Shaping Our Future
by Vivek PanditA young author shares an insider’s perspective on what it means to be Generation Z—and what Generation Z means for the world.Born at the turn of the millennium, the members of Generation Z are no strangers to today’s fast-paced, hyperconnected world. They were born in the Digital Age. They grew up online. Their identities, attitudes, and perspectives have all been uniquely integrated with technology. Now, as they stand at the brink of adulthood, it’s time for the world to discover: Who is Generation Z?Vivek Pandit understands firsthand what it means to be a digital native, and he has a unique view of the road ahead. By exploring the forces that have shaped him and his peers, he gives insight into how they may go on to shape the world.Winner of the Moonbeam Children’s Book Award Gold Medal in the Youth Author (under 18) category
We Just Averaged over Two Trillion Cross-Country Growth Regressions
by Eduardo Ley Mark F.J. SteelA report from the International Monetary Fund.
We Reason & We Prove for ALL Mathematics: Building Students’ Critical Thinking, Grades 6-12 (Corwin Mathematics Series)
by Michael Steele Gabriel J. Stylianides Fran Arbaugh Margaret Peg Smith Justin D. BoyleSharpen concrete teaching strategies that empower students to reason-and-prove What does reasoning-and-proving instruction look like and how can teachers support students’ capacity to reason-and-prove? Designed as a learning tool for mathematics teachers in grades 6-12, this book transcends all mathematical content areas with a variety of activities for teachers that include Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work Modifying curriculum materials and evaluating learning environments to better support students to reason-and-prove No other book tackles reasoning-and-proving with such breath, depth, and practical applicability.
We Reason & We Prove for ALL Mathematics: Building Students’ Critical Thinking, Grades 6-12 (Corwin Mathematics Series)
by Michael Steele Gabriel J. Stylianides Fran Arbaugh Margaret Peg Smith Justin D. BoyleSharpen concrete teaching strategies that empower students to reason-and-prove What does reasoning-and-proving instruction look like and how can teachers support students’ capacity to reason-and-prove? Designed as a learning tool for mathematics teachers in grades 6-12, this book transcends all mathematical content areas with a variety of activities for teachers that include Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work Modifying curriculum materials and evaluating learning environments to better support students to reason-and-prove No other book tackles reasoning-and-proving with such breath, depth, and practical applicability.
Weak and Measure-Valued Solutions to Evolutionary PDEs
by J. Necas J. Malek M. Rokyta M. RuzickaThis book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering
Weakly Stationary Random Fields, Invariant Subspaces and Applications
by Vidyadhar S. Mandrekar David A. RedettThe first book to examine weakly stationary random fields and their connections with invariant subspaces (an area associated with functional analysis). It reviews current literature, presents central issues and most important results within the area. For advanced Ph.D. students, researchers, especially those conducting research on Gaussian theory.
Weakly Wandering Sequences in Ergodic Theory
by Stanley Eigen Arshag Hajian Yuji Ito Vidhu PrasadThe appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant and deep properties of ergodic transformations that preserve an infinite measure. This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinite measure. Connections of these sequences to additive number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory is adequate for the reader.
Wealth, Income Inequalities, and Demography
by Luigi PaganettoIn this book, leading experts take a long-term view of the trends and policies of most relevance in achieving the structural readjustment required by the current crisis, which for too long has been viewed merely as an economic recession. A wide variety of issues are addressed, including the implications of the massive movement of wealth from advanced countries to emerging ones and the increasing income inequality evident within many countries. Prospects for growth toward the mid-century and beyond are discussed, with consideration of lessons from the past and the impact of various constraints, including corruption. The policies and reforms required to restore economic dynamism within the EU and more generally, to foster the "Good Economy" are discussed, recognizing the need for measures to promote innovation, entrepreneurship, well-being and high levels of environmental performance. The book comprises a selection of contributions presented at the XXV Villa Mondragone International Economic Seminar. For the past quarter of a century, this seminar has brought together leading experts to engage in debates on pressing economic questions. This book, based on the most recent gathering, will be of interest to all who are concerned about the challenges to growth, well-being and social inclusion that will have to be confronted in the coming decades.
A Wealth of Numbers
by Benjamin WardhaughDespite what we may sometimes imagine, popular mathematics writing didn't begin with Martin Gardner. In fact, it has a rich tradition stretching back hundreds of years. This entertaining and enlightening anthology--the first of its kind--gathers nearly one hundred fascinating selections from the past 500 years of popular math writing, bringing to life a little-known side of math history. Ranging from the late fifteenth to the late twentieth century, and drawing from books, newspapers, magazines, and websites, A Wealth of Numbers includes recreational, classroom, and work mathematics; mathematical histories and biographies; accounts of higher mathematics; explanations of mathematical instruments; discussions of how math should be taught and learned; reflections on the place of math in the world; and math in fiction and humor. Featuring many tricks, games, problems, and puzzles, as well as much history and trivia, the selections include a sixteenth-century guide to making a horizontal sundial; "Newton for the Ladies" (1739); Leonhard Euler on the idea of velocity (1760); "Mathematical Toys" (1785); a poetic version of the rule of three (1792); "Lotteries and Mountebanks" (1801); Lewis Carroll on the game of logic (1887); "Maps and Mazes" (1892); "Einstein's Real Achievement" (1921); "Riddles in Mathematics" (1945); "New Math for Parents" (1966); and "PC Astronomy" (1997). Organized by thematic chapters, each selection is placed in context by a brief introduction. A unique window into the hidden history of popular mathematics, A Wealth of Numbers will provide many hours of fun and learning to anyone who loves popular mathematics and science.
Weaponized Lies: How to Think Critically in the Post-Truth Era
by Daniel J. LevitinPreviously Published as A Field Guide to Lies We're surrounded by fringe theories, fake news, and pseudo-facts. These lies are getting repeated. New York Times bestselling author Daniel Levitin shows how to disarm these socially devastating inventions and get the American mind back on track. Here are the fundamental lessons in critical thinking that we need to know and share now. Investigating numerical misinformation, Daniel Levitin shows how mishandled statistics and graphs can give a grossly distorted perspective and lead us to terrible decisions. Wordy arguments on the other hand can easily be persuasive as they drift away from the facts in an appealing yet misguided way. The steps we can take to better evaluate news, advertisements, and reports are clearly detailed. Ultimately, Levitin turns to what underlies our ability to determine if something is true or false: the scientific method. He grapples with the limits of what we can and cannot know. Case studies are offered to demonstrate the applications of logical thinking to quite varied settings, spanning courtroom testimony, medical decision making, magic, modern physics, and conspiracy theories. This urgently needed book enables us to avoid the extremes of passive gullibility and cynical rejection. As Levitin attests: Truth matters. A post-truth era is an era of willful irrationality, reversing all the great advances humankind has made. Euphemisms like "fringe theories," "extreme views," "alt truth," and even "fake news" can literally be dangerous. Let's call lies what they are and catch those making them in the act.
Weaponized Lies: How to Think Critically in the Post-Truth Era
by Daniel J. LevitinIt's raining fringe theories, fake news, and pseudo-facts. These lies are getting repeated. New York Times bestselling author Daniel Levitin shows how to disarm these socially devastating inventions and get the American mind back on track. Here are the fundamental lessons in critical thinking (previously published as A Field Guide to Lies) that we need to know and share now. Investigating numerical misinformation, Daniel Levitin shows how mishandled statistics and graphs can give a grossly distorted perspective and lead us to terrible decisions. Wordy arguments on the other hand can easily be persuasive as they drift away from the facts in an appealing yet misguided way. The steps we can take to better evaluate news, advertisements, and reports are clearly detailed. Ultimately, Levitin turns to what underlies our ability to determine if something is true or false: the scientific method. He grapples with the limits of what we can and cannot know. Case studies are offered to demonstrate the applications of logical thinking to quite varied settings, spanning courtroom testimony, medical decision making, magic, modern physics, and conspiracy theories.This urgently needed book enables us to avoid the extremes of passive gullibility and cynical rejection. As Levitin attests: Truth matters. A post-truth era is an era of willful irrationality, reversing all the great advances humankind has made. Euphemisms like "fringe theories," "extreme views," "alt truth," and even "fake news" can literally be dangerous. Let's call lies what they are and catch those making them in the act.