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.

Microscopy is at the forefront of multidisciplinary research. It was developed by physicists, made specific by chemists, and applied by biologists and doctors to better understand how the human body works. For this very reason, the field has been revolutionized in past decades. The objective of Optical Nanoscopy and Novel Microscopy Techniques is to choose some of those revolutionary ideas and serve a general audience from broad disciplines to achieve a fundamental understanding of these technologies and to better apply them in their daily research. The book begins with coverage of super-resolution optical microscopy, which discusses targeted modulation such as STED and SIM or localization methods such as PALM. It then discusses novel development of fluorescent probes, such as organic small-molecule probes, fluorescent proteins, and inorganic labels such as quantum dots. Finally, it describes advanced optical microscopy, such as fluorescence lifetime imaging, fiber optic microscopy, scanning ion conductance microscopy, and the joining of optics and acoustics-photoacoustic microscopy. Following each chapter, a detailed list of references is provided. Problems at the end of each chapter are also included.