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The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on ellip...
Learn How to Properly Use the Latest Analytics Approaches in Your Organization Computational Business Analytics presents tools and techniques for descriptive, predictive, and prescriptive analytics applicable across multiple domains. Through many examples and challenging case studies from a variety of fields, practitioners easily see the connections to their own problems and can then formulate their own solution strategies. The book first covers core descriptive and inferential statistics for analytics. The author then enhances numerical statistical techniques with symbolic artificial intelligence (AI) and machine learning (ML) techniques for richer predictive and prescriptive analytics. Wit...
Explains the material step-by-step starting from meaningful examples Steps detailed with R code in the spirit of reproducible research Real world data analyses from a Science paper reproduced and explained in detail Examples span a variety of fields across social and life sciences Overview of available software in and outside R
This is an integrated view of the most important aspects of autonomic control of circulation: the factors that determine the generation of signals at the sensory endings, the central nervous influence of the impulses, and the reflex responses of the efferent limb of the autonomic system. Abnormalities at any or all of these sites may be important in heart failure, hypertension, myocardial infarction, and arrhythmias. This book lays the groundwork for further understanding of basic mechanisms and improved appreciation by both clinicians and investigators of the pathophysiologic and therapeutic implications of these mechanisms.
This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics. The first part of the book discusses the basic numerical methods. The second part concentrates on simulation of classical and quantum systems. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multi-step methods and the class of Verlet methods, which is introduced by studying the motion in Liouville space. A general chapter on the numerical treatment of differential equations provides methods of finite differences, finite volumes, finite elements and boundary elements together with spectral methods and weighted residual based methods. The book gives simple but non trivial examples from a broad range of physical topics trying to give the reader insight into not only the numerical treatment but also simulated problems. Different methods are compared with regard to their stability and efficiency. The exercises in the book are realised as computer experiments.
It is the organization and presentation of the material, however, which make the peculiar appeal of the book. This is no mere compendium of results--the subject has been completely reworked and the proofs recast with the skill and elegance which come only from years of devotion. --Bulletin of the American Mathematical Society The very clear and simple presentation gives the reader easy access to the more difficult parts of the theory. --Jahrbuch uber die Fortschritte der Mathematik In 1937, the theory of matrices was seventy-five years old. However, many results had only recently evolved from special cases to true general theorems. With the publication of his Colloquium Lectures, Wedderburn ...
Graphics systems. Ghaphics facilities. Algorithms for line and curve generation. Graphics languages and data structures. Hidden-line removal algorithms. Generation of halftone images. Computer animation. Freeform surfaces.