Matrix Information Geometry

This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of pote

This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of pote

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemann

This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of appli

Information retrieval, IR, the science of extracting information from any potential source, can be viewed in a number of ways: logical, probabilistic and vector space models are some of the most important. In this book, the author, one of the leading researchers in the area, shows how these views can be reforged in the same framework used to formulate the general principles of quantum mechanics. All the usual quantum-mechanical notions have their IR-theoretic analogues, and the standard results can be applied to address problems in IR, such as pseudo-relevance feedback, relevance feedback and ostensive retrieval. The relation with quantum computing is also examined. To keep the book self-contained appendices with background material on physics and mathematics are included. Each chapter ends with bibliographic remarks that point to further reading. This is an important, ground-breaking book, with much new material, for all those working in IR, AI and natural language processing.

Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptogra

Reveals the ancient mathematical principles refuting the notion of the solar system as an accidental creation. Reveals how ancient civilizations encoded their secret knowledge of the sky in mythology,

In virtue of its features, Bohm's quantum potential introduces interesting and relevant perspectives towards a satisfactory geometrodynamic description of quantum processes. This book makes a comprehe

Identifies the patterns of our planet’s design within the natural landscape ‧ Explains the geometry inherent in the mountains and coasts on all continents ‧ Reveals how ancient monuments were built to

"Optimal Observation for Cyber-physical Systems" addresses the challenge, fundamental to the design of wireless sensor networks (WSNs), presented by the obligatory trade-off between precise estimates

The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and be

This brand new book includes the most up-to-date information on the Geometry Common Core Regents Exam. Students can use this review guide to prepare for their Geometry Regents Exams. Inside, separate

Engineering drawing is the "instrument of communication" upon which the designer must place all information necessary to define a new product. Computer-aided design (CAD) courses often involve teachin

SparkCharts?:The information you need-concisely, conveniently, and accurately. Created by Harvard students for students everywhere, these study companions and reference tools cover a wide range of col

The new QuickStudy Booklets cover the key information on some of the toughest courses today, helping students boost their grades. The books are presented in the clear, concise format readers have come

Matrices and kernels with positivity structures, and the question of entrywise functions preserving them, have been studied throughout the 20th century, attracting recent interest in connection to high-dimensional covariance estimation. This is the first book to systematically develop the theoretical foundations of the entrywise calculus, focusing on entrywise operations - or transforms - of matrices and kernels with additional structure, which preserve positive semidefiniteness. Designed as an introduction for students, it presents an in-depth and comprehensive view of the subject, from early results to recent progress. Topics include: structural results about, and classifying the preservers of positive semidefiniteness and other Loewner properties (monotonicity, convexity, super-additivity); historical connections to metric geometry; classical connections to moment problems; and recent connections to combinatorics and Schur polynomials. Based on the author's course, the book is struc