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Asymptotics for Associated Random Variables
by Paulo Eduardo OliveiraThe book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting the theory in a unified way, explaining relations and implications of the results. It will present basic definitions and characterizations, followed by a collection of relevant inequalities. These are then applied to characterize almost sure and weak convergence of sequences of associated variables. It will also cover applications of positive dependence to the characterization of asymptotic results in nonparametric statistics. The book is directed towards researchers in probability and statistics, with particular emphasis on people interested in nonparametric methods. It will also be of interest to graduate students in those areas. The book could also be used as a reference on association in a course covering dependent variables and their asymptotics. As prerequisite, readers should have knowledge of basic probability on the reals and on metric spaces. Some acquaintance with the asymptotics of random functions, such us empirical processes and partial sums processes, is useful but not essential.
Asymptotics, Nonparametrics, and Time Series
by Subir Ghosh"Contains over 2500 equations and exhaustively covers not only nonparametrics but also parametric, semiparametric, frequentist, Bayesian, bootstrap, adaptive, univariate, and multivariate statistical methods, as well as practical uses of Markov chain models."
Asymptotics of Elliptic and Parabolic PDEs: And Their Applications In Statistical Physics, Computational Neuroscience, And Biophysics (Applied Mathematical Sciences #199)
by Zeev Schuss David HolcmanThis is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.
Asymptotische Stochastik: Eine Einführung mit Blick auf die Statistik
by Norbert HenzeDieses Lehrbuch liefert einen verständnisorientierten Einstieg in die asymptotische Stochastik. Es ist vom Niveau her zu Beginn eines Mathematik-Masterstudiums angesiedelt und deckt den Stoff ab, der in einer vierstündigen Vorlesung mit zweistündigen Übungen vermittelt werden kann. Einzelne Kapitel eignen sich zudem für Seminare am Ende eines Bachelorstudiums.Neben eher grundständigen Themen wie der Momentenmethode zum Nachweis von Verteilungskonvergenz oder dem multivariaten zentralen Grenzwertsatz und der Delta-Methode werden unter anderem Grenzwertsätze für U-Statistiken und der Satz von Donsker sowie die Brown'sche Brücke mit Anwendungen auf die Statistik behandelt. Das Buch schließt mit einem zentralen Grenzwertsatz für hilbertraumwertige Zufallselemente mit Anwendungen auf gewichtete L²-Statistiken. Ein besonderes Merkmal des Buches sind mehr als 130 Selbstfragen, die am Ende des jeweiligen Kapitels beantwortet werden, sowie mehr als 180 Übungsaufgaben mit Lösungen. Hierdurch eignet sich dieses Werk sehr gut zum Selbststudium.Die 2. Auflage ist vollständig durchgesehen und thematisch unter anderem um die starke Konsistenz der Maximum-Likelihood-Schätzung sowie zentrale Grenzwertsätze für Dreiecksschemata von Zufallsvektoren und hilbertraumwertigen Zufallsvariablen erweitert. Hinzugekommen sind auch weitere Beispiele sowie 11 neue Aufgaben mit Lösungen.
At Home in the City: Growing Old in Urban America
by Stacy TorresUncovers how people aged 60 and older struggle, survive, and thrive in twenty-first-century urban America. To understand elders' experiences of aging in place, sociologist Stacy Torres spent five years with longtime New York City residents as they coped with health setbacks, depression, gentrification, financial struggles, the accumulated losses of neighbors, friends, and family, and other everyday challenges. The sensitive portrait Torres paints in At Home in the City moves us beyond stereotypes of older people as either rich and pampered or downtrodden and frail to capture the multilayered complexity of late life. These pages chronicle how a nondescript bakery in Manhattan served as a public living room, providing company to ease loneliness and a sympathetic ear to witness the monumental and mundane struggles of late life. Through years of careful observation, Torres peels away the layers of this oft-neglected social world and explores the constellation of relationships and experiences that Western culture often renders invisible or frames as a problem. At Home in the City strikes a realistic balance as it highlights how people find support, flex their resilience, and assert their importance in their communities in old age.
At the Intersection of Language, Logic, and Information: ESSLLI 2018 Student Session, Sofia, Bulgaria, August 6–17, 2018, Selected Papers (Lecture Notes in Computer Science #11667)
by Jennifer Sikos Eric PacuitThe European Summer School in Logic, Language and Information (ESSLLI) is organized every year by the Association for Logic, Language and Information (FoLLI) in different sites around Europe. The papers cover vastly dierent topics, but each fall in the intersection of the three primary topics of ESSLLI: Logic, Language and Computation. The 14 papers presented in this volume have been selected among 24 papers presented by talks or posters at the Student Sessions of the 30th edition of ESSLLI, held in 2018 in Sofia, Bulgaria.The Student Session is a forum for PhD and Master students to present their research at the interfaces of logic, language and computation. It features three tracks: Logic and Computation (LoCo), Logic and Language (LoLa), and Language and Computation (LaCo).
Athanasius Kircher, the Mysteries of the Geocosmos, Magnetism, and the Universe
by Agustín UdíasAthanasius Kircher, the eminent 17th-century German Jesuit professor of mathematics at the Roman College emerges as a captivating figure within the pages of this monograph by Agustín Udías. Aptly deemed 'the man who knew everything,' Kircher's thirty-two comprehensive works, spanning an array of subjects, provide a unique lens into his visionary perspectives. This book delves into three selected works where Kircher unveils his conceptualization of the Earth, termed the 'Geocosmos,' treated magnetism as a cosmic and spiritual force, and embarks on a cosmic exploration from Earth to the stars. From his groundbreaking speculations on the Earth's interior, attributing earthquakes and volcanoes to intricate channels of air, water, and fire, to his cosmic journey accompanied by the ethereal spirit Cosmiel, Kircher's enduring allure persists. Despite variance from contemporary knowledge, situated at the beginning of modern science, Kircher's proposals of the structure of the Earth’s interior, cosmic magnetic theories, and space journey to the stars offer a compelling glimpse into the intellectual landscape of a bygone era, making this book an essential exploration for scholars seeking a nuanced understanding of Kircher's profound influence.
The Atiyah-Patodi-Singer Index Theorem (Research Notes in Mathematics)
by null Richard MelroseBased on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.
An Atlas of Edge-Reversal Dynamics (Chapman & Hall/CRC Research Notes in Mathematics Series)
by null V.C. BarbosaThis important resource offers the first in-depth account of the graph dynamics system SER (Scheduling by Edge Reversal),. In Part 1: Edge-Reversal Dynamics, the author discusses the main applications and properties of SER, provides data from statistics and correlations computed over several graph classes, and gives an overview of the algorithmic aspects of the construction of the catalogue. Part 2: The Atlas comprises the atlas proper-a catalogue of graphical representations of all basins of attraction generated by the SER mechanism for all graphs in selected classes.
The Atlas of Environmental Migration
by Dina Ionesco Daria Mokhnacheva François GemenneAs climate change and extreme weather events increasingly threaten traditional landscapes and livelihoods of entire communities the need to study its impact on human migration and population displacement has never been greater. The Atlas of Environmental Migration is the first illustrated publication mapping this complex phenomenon. It clarifies terminology and concepts, draws a typology of migration related to environment and climate change, describes the multiple factors at play, explains the challenges, and highlights the opportunities related to this phenomenon. Through elaborate maps, diagrams, illustrations, case studies from all over the world based on the most updated international research findings, the Atlas guides the reader from the roots of environmental migration through to governance. In addition to the primary audience of students and scholars of environment studies, climate change, geography and migration it will also be of interest to researchers and students in politics, economics and international relations departments.
An Atlas of Functions: with Equator, the Atlas Function Calculator
by Keith B. Oldham Jerome Spanier Jan MylandThis second edition of An Atlas of Functions, with Equator, the Atlas Function Calculator, provides comprehensive information on several hundred functions or function families, of interest to all those scientists, engineers and mathematicians who are concerned with the quantitative aspects of their field. Beginning with simple integer-valued functions, the book progresses to polynomials, exponential, trigonometric, Bessel, and hypergeometric functions, as well as many more. The 65 chapters are arranged roughly in order of increasing complexity, mathematical sophistication being kept to a minimum while utility is stressed throughout. In addition to providing definitions and simple properties for every function, each chapter catalogs more complex interrelationships as well as the derivatives, integrals, Laplace transforms and other characteristics of the function. Numerous color figures in 2 or 3 dimensions depict their shape and qualitative features and flesh out the reader's familiarity with the functions. In many instances, the chapter concludes with a concise exposition on a topic in applied mathematics associated with the particular function or function family. Features that make the Atlas an invaluable reference tool, yet simple to use, include: full coverage of those functions--elementary and "special"--that meet everyday needsa standardized chapter format, making it easy to locate needed information on such aspects as: nomenclature, general behavior, definitions, intrarelationships, expansions, approximations, limits, and response to operations of the calculusextensive cross-referencing and comprehensive indexing, with useful appendicesthe inclusion of innovative software--Equator, the Atlas Function Calculatorthe inclusion of new material dealing with interesting applications of many of the function families, building upon the favorable responses to similar material in the first edition.
Atlas of Gender and Health Inequalities in India (Demographic Transformation and Socio-Economic Development #16)
by Christophe Z. GuilmotoHow will the world's largest population approach its inequality challenges? This volume addresses this question by unraveling different strands of India's emerging health and gender geographies. It is the first book to offer a comparative study of these disparities in India, stressing the deep interaction between health challenges and patriarchal features. Most themes explored in this book illustrate the entangled nature of the social and regional determinants of gender and health imbalances in India. Through its rich cartography of contemporary India, the book represents the first Atlas exploiting district-level figures drawn from the latest sociodemographic survey conducted in 2019-21. After an initial methodological synopsis, the book is built around twenty chapters—illustrated by 75 original maps, figures, and tables prepared by thirty authors—and concludes with a synthesis of India's spatial patterns. Chapters engage with major themes of gender and health inequalities and explore an array of innovative indicators such as access to menstrual hygiene, cesarean deliveries, health insurance, son preference in fertility, female landownership, patrilocal systems, hypertension, anemia, hysterectomy, girl-only or single-child families, or traditional contraception. Together, they provide an often surprising glimpse into the present and future of India's gender and health landscape, highlighting the considerable progress accomplished over the last two decades alongside persistent gaps and emerging issues.
An Atlas of the Smaller Maps in Orientable and Nonorientable Surfaces (Discrete Mathematics and Its Applications)
by David Jackson Terry I. VisentinMaps are beguilingly simple structures with deep and ubiquitous properties. They arise in an essential way in many areas of mathematics and mathematical physics, but require considerable time and computational effort to generate. Few collected drawings are available for reference, and little has been written, in book form, about their enumerative a
Atomicity through Fractal Measure Theory: Mathematical and Physical Fundamentals with Applications
by Alina Gavriluţ Ioan Mercheş Maricel AgopThis book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems.The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potential applications in life sciences, are opened.
Atomistic Computer Simulations: A Practical Guide
by Veronika Brazdova David R. BowlerMany books explain the theory of atomistic computer simulations; this book teaches you how to run themThis introductory "how to" title enables readers to understand, plan, run, and analyze their own independent atomistic simulations, and decide which method to use and which questions to ask in their research project. It is written in a clear and precise language, focusing on a thorough understanding of the concepts behind the equations and how these are used in the simulations. As a result, readers will learn how to design the computational model and which parameters of the simulations are essential, as well as being able to assess whether the results are correct, find and correct errors, and extract the relevant information from the results. Finally, they will know which information needs to be included in their publications.This book includes checklists for planning projects, analyzing output files, and for troubleshooting, as well as pseudo keywords and case studies.The authors provide an accompanying blog for the book with worked examples, and additional material and references: http://www.atomisticsimulations.org/.
Attacking Probability and Statistics Problems
by David S. KahnConcise and highly focused, this volume offers everything high school and beginning college students need to know to handle problems in probability and statistics. Numerous rigorously tested examples and coherent, to-the-point explanations are presented in an easy-to-follow format.The treatment is organized in a way that permits readers to advance sequentially or skip around between chapters. An essential companion volume to the author's Attacking Trigonometry Problems and Attacking Problems in Logarithms and Exponential Functions, this book will equip students with the skills they will need to successfully approach the problems in probability and statistics that they will encounter on exams.
Attacking Problems in Logarithms and Exponential Functions (Dover Books on Mathematics)
by David S. KahnThis original volume offers a concise, highly focused review of what high school and beginning college students need to know in order to solve problems in logarithms and exponential functions. Numerous rigorously tested examples and coherent to-the-point explanations, presented in an easy-to-follow format, provide valuable tools for conquering this challenging subject. The treatment is organized in a way that permits readers to advance sequentially or skip around between chapters. An essential companion volume to the author's Attacking Trigonometry Problems, this book will equip students with the skills they will need to successfully approach the problems in logarithms and exponential functions that they will encounter on exams.
Attacking Trigonometry Problems (Dover Books on Mathematics)
by David S. KahnThis volume offers a concise, highly focused review of what high school and beginning college undergraduates need to know to successfully solve the trigonometry problems they will encounter on exams. Rigorously tested examples and coherent, to-the-point explanations are presented in an accessible form and will provide valuable assistance in conquering this challenging subject.Rather than serving as a text or treatise, the book focuses on the essentials of trigonometry. All fourteen sections are organized in a manner that allows readers to advance sequentially or to skip around. The approach encourages memorization of ratios and formulas, and the practice problems offer ample opportunities to become comfortable with applying the trig ratios to a variety of settings.
Attacks, Defenses and Testing for Deep Learning
by Jinyin Chen Ximin Zhang Haibin ZhengThis book provides a systematic study on the security of deep learning. With its powerful learning ability, deep learning is widely used in CV, FL, GNN, RL, and other scenarios. However, during the process of application, researchers have revealed that deep learning is vulnerable to malicious attacks, which will lead to unpredictable consequences. Take autonomous driving as an example, there were more than 12 serious autonomous driving accidents in the world in 2018, including Uber, Tesla and other high technological enterprises. Drawing on the reviewed literature, we need to discover vulnerabilities in deep learning through attacks, reinforce its defense, and test model performance to ensure its robustness. Attacks can be divided into adversarial attacks and poisoning attacks. Adversarial attacks occur during the model testing phase, where the attacker obtains adversarial examples by adding small perturbations. Poisoning attacks occur during the model training phase, wherethe attacker injects poisoned examples into the training dataset, embedding a backdoor trigger in the trained deep learning model. An effective defense method is an important guarantee for the application of deep learning. The existing defense methods are divided into three types, including the data modification defense method, model modification defense method, and network add-on method. The data modification defense method performs adversarial defense by fine-tuning the input data. The model modification defense method adjusts the model framework to achieve the effect of defending against attacks. The network add-on method prevents the adversarial examples by training the adversarial example detector. Testing deep neural networks is an effective method to measure the security and robustness of deep learning models. Through test evaluation, security vulnerabilities and weaknesses in deep neural networks can be identified. By identifying and fixing these vulnerabilities, the security and robustness of the model can be improved. Our audience includes researchers in the field of deep learning security, as well as software development engineers specializing in deep learning.
Attitudes, Beliefs, Motivation and Identity in Mathematics Education: An Overview of the Field and Future Directions (ICME-13 Topical Surveys)
by Markku S. Hannula Pietro Di Martino Marilena Pantziara Qiaoping Zhang Francesca Morselli Einat Heyd-Metzuyanim Sonja Lutovac Raimo Kaasila James A. Middleton Amanda Jansen Gerald A GoldinThis book records the state of the art in research on mathematics-related affect. It discusses the concepts and theories of mathematics-related affect along the lines of three dimensions. The first dimension identifies three broad categories of affect: motivation, emotions, and beliefs. The book contains one chapter on motivation, including discussions on how emotions and beliefs relate to motivation. There are two chapters that focus on beliefs and a chapter on attitude which cross-cuts through all these categories. The second dimension covers a rapidly fluctuating state to a more stable trait. All chapters in the book focus on trait-type affect and the chapter on motivation discusses both these dimensions. The third dimension regards the three main levels of theorizing: physiological (embodied), psychological (individual) and social. All chapters reflect that mathematics-related affect has mainly been studied using psychological theories.
Attracting Science And Mathematics Ph.d.s To Secondary School Education
by National Research CouncilThe National Research Council conducted a study to identify a set of incentives that state governments and local school districts can use to attract Ph.D. scientists and mathematicians to secondary school teaching positions. This project investigated the career ambitions of Ph.D.s in the physical and life sciences through focus groups and a national survey to determine the kinds of work conditions and compensation packages that would induce them to take positions teaching physics, chemistry, biology, and various electives in public high schools or positions developing secondary school science and mathematics curricula. The study conducted interviews with Ph.D.s who are already teaching in secondary schools to ascertain information from their experiences, with local school district administrators to assess what they are realistically willing to offer Ph.D. scientists to attract them, and with higher education administrators to explore programmatic changes they would need to institute to provide Ph.D.s with skills tailored to secondary school teaching. These investigations led to this report which describes the incentives local school districts could use in establishing pilot programs in this area.
Attraction in Numerical Minimization: Iteration Mappings, Attractors, and Basins of Attraction (SpringerBriefs in Optimization)
by Adam B. LevyNumerical minimization of an objective function is analyzed in this book to understand solution algorithms for optimization problems. Multiset-mappings are introduced to engineer numerical minimization as a repeated application of an iteration mapping. Ideas from numerical variational analysis are extended to define and explore notions of continuity and differentiability of multiset-mappings, and prove a fixed-point theorem for iteration mappings. Concepts from dynamical systems are utilized to develop notions of basin size and basin entropy. Simulations to estimate basins of attraction, to measure and classify basin size, and to compute basin are included to shed new light on convergence behavior in numerical minimization. Graduate students, researchers, and practitioners in optimization and mathematics who work theoretically to develop solution algorithms will find this book a useful resource.
Attractors Under Discretisation (SpringerBriefs in Mathematics)
by Peter Kloeden Xiaoying HanThis work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained - by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes - results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
Attraktiver Mathematikunterricht: Motivierende Beispiele aus der Praxis
by Jürgen MaaßDieses Sachbuch zeigt Wege zu einem attraktiveren Mathematikunterricht in Beispielen auf, die als Abschlussarbeiten seiner ehemaliger Studenten (und Coautoren) praxiserprobt sind. Das Buch lädt zur Reflexion der eigenen Erfahrungen mit Mathematikunterricht und einer Diskussion darüber ein. Farbige Kästen fordern zur aktiven Teilnahme oder Weiterführung der Projekte auf.