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Tensor Network Contractions
Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.
Elements of Applied Bifurcation Theory
Author: Yuri Kuznetsov
language: en
Publisher: Springer Science & Business Media
Release Date: 2004-06-29
Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
The Diabetic Foot
The incidence of diabetes is increasing both in the western world and in developing countries; type 2 diabetes increase is partly the result of greater obesity. Diabetes can cause two major problems to the foot – diabetic neuropathy resulting in nerve damage and peripheral vascular disease reducing the flow of blood. These can result in ulceration of the foot which needs careful management to avoid the possibility of amputation. This management is best undertaken by multidisciplinary teams using the latest evidence to support their practice. This book presents a comprehensive and authoritative coverage of the latest evidence-based investigations, techniques and management of the diabetic foot. Evidenced-based management of the diabetic foot International, multidisciplinary team of editors and contributors Comprehensive reference for all health professionals involved in the care of diabetic foot problems