Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
The Recurrence of the End Times: Voegelin, Hegel, and the Stop-History Movements explores the deep connection between modern political ideologies and the secular eschatological hopes and dreams of a post-Christian society. Focusing primarily upon the thought of 20th century German émigré political scientist Eric Voegelin, the book argues that we cannot understand the globalized world in which we live unless we appreciate the lasting influence of the various "End of History" speculators—specifically, G.W.F Hegel, Alexandre Kojève, and Francis Fukuyama. Through a Voegelinian lens, he dissects the relationship between these three thinkers, also claiming that while Voegelin may have misunderstood Hegel, his critiques of the Hegelian approach to history offer fresh and important perspectives on the contemporary world. This makes a forceful argument that the idea of history as a teleological path, leading toward some goal—whether perfect harmony between nations, a technocratic utopia, a return to some romanticized idyllic “state of nature,” or what Kojève and Fukuyama called the “universal and homogenous State”—has vast, and perverse, implications for the trajectory of American foreign and domestic policy.
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.
The idea that history repeats itself has a long and intriguing history. This volume is concerned with the period of time in the Western tradition when its expressions were most numerous and fervent. The author shows that this idea should not be confined to its cyclical version, for such notions as reenactment, retribution, and renaissance also belong under the wide umbrella of "recurrence." He argues, moreover, that not only the Greco-Roman but also the biblical tradition contributed to the history of this idea. The old contrast between Judeo-Christian linear views of history and Greco-Roman cyclical views is brought into question. Beginning with Polybius, Trompf examines the manifold forms of recurrence thinking in Greek and Roman historiography, then turns his attention to biblical views of historical change, arguing that in Luke-Acts and in earlier Jewish writings an interest in the idea of history repeating itself was clearly demonstrated. Jewish and early Christian writers initiated and foreshadowed an extensive synthesizing of recurrence notions and models from both traditions, although the syntheses could vary with the context and dogmatic considerations. The Renaissance and Reformation intertwine classical and biblical notions of recurrence most closely, yet even in the sixteenth century some ideas distinct to each tradition, such as the Polybian conception of a "cycle of governments" and hte biblical notion of the "reenactment of significant events," were revived in stark separation from each other. The Idea of Historical Recurrence in Western Thought deals with a continuing but not always fruitful "dialogue" between the two great traditions of Western thought, a dialogue that did not stop short in the days of Machiavelli, but has been carried on to the present day. This study is the first half of a long story to be continued in a second volume on the idea of historical recurrence from Giambattista Vico to Arnold Toynbee. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1979.
This work is a reading of the way humans have attempted to talk about the nature of time, in particular the idea of the periodic creation and destruction of the world and the cosmos--eternal recurrence.
This groundbreaking volume is the first to elaborate the theory of set families as a tool for studying the phenomenon of recurrence. The theory is implicit in such seminal works as Hillel Furstenberg's Recurrence in Ergodic Theory and Combinational Number Theory, but Ethan Akin's study elaborates it in detail, defining such elements of theory as: open families of special subsets the unification of several ideas associated with transitivity, ergodicity, and mixing the Ellis theory of enveloping semigroups for compact dynamical systems and new notions of equicontinuity, distality, and rigidity.
Repetition is constitutive of human life. Both the species and the individual develop through repetition. Unlike simple recall, repetition is permeated by the past and the present and is oriented toward the future. Repetition of central actions and events plays an important role in the lives of individuals and the life of society. It helps to create meaning and memory. Because repetition is a central aspect of human life, it plays a role in all social and cultural spheres. It is important for several branches of the humanities and social studies. This book presents studies of an array of repetitive phenomena and to show that repetition analysis is opening up a new field of study within single disciplines and interdisciplinary research. Recommended for scholars of literature, music, culture, and communication.
The analysis of recurrences in dynamical systems by using recurrence plots and their quantification is still an emerging field. Over the past decades recurrence plots have proven to be valuable data visualization and analysis tools in the theoretical study of complex, time-varying dynamical systems as well as in various applications in biology, neuroscience, kinesiology, psychology, physiology, engineering, physics, geosciences, linguistics, finance, economics, and other disciplines. This multi-authored book intends to comprehensively introduce and showcase recent advances as well as established best practices concerning both theoretical and practical aspects of recurrence plot based analysis. Edited and authored by leading researcher in the field, the various chapters address an interdisciplinary readership, ranging from theoretical physicists to application-oriented scientists in all data-providing disciplines.
As a follow-up to COVID-19 in New York City: an Ecology of Race and Class Oppression, which showed that decades of discriminatory public policies shaped the Bronx into the epicenter of the first wave of COVID-19, this book examines the build up to the crest and subsequent ebbing of the second wave of COVID-19 across the 62 counties of New York State (NYS) and 152 ZIP Code areas of the four central boroughs of New York City (NYC). Like its predecessor, the sequel examines the vulnerabilities that give rise to spikes in infection rates that form epicenters. Unlike the first wave, NYC was not the epicenter of the second wave; high-incident counties just outside NYS formed an extended initial epicenter and exported COVID-19 to neighboring counties of NYS. Rural NYS counties differed significantly from urban ones socioeconomically and in infection rates during the cresting period. Before the crest, no socioeconomic factor was associated with county infection rates; rather, the major associating factor was political and cultural: percent of the 2020 vote garnered by Trump. Rural counties voted heavily for Trump. This association disappeared post-crest by mid-January 2021. In NYC, the Bronx again behaved like a single high-incidence entity, unlike the other three boroughs that had patches of high and low infection incidence. Among the topics covered: The Second COVID Wave Washes Over New York State The Second Wave Storm-Surges Across New York City Discussion of County Data from the Second Wave of COVID-19 Parsing Meaning From the 152 ZIP Code Data The book closes with a prescription for pandemic response planning based on empowered communities and workers interacting with health departments as equals. The Recurrence of COVID-19 in New York State and New York City is a valuable resource for social epidemiologists, public health researchers of health disparities, those in public service tasked with addressing these problems, and infectious disease scientists who focus on spread in human populations of new zoonotic diseases. The brief also will find readership among students in these fields, civil rights scholars, science writers, medical anthropologists and sociologists, medical and public health historians, public health economists, and public policy scientists.
