Tensor Network Contractions

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Publisher : Springer Nature
ISBN 13 : 3030344894
Total Pages : 160 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Tensor Network Contractions by : Shi-Ju Ran

Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Tensor Network Contractions

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Publisher :
ISBN 13 : 9781013273636
Total Pages : 158 pages
Book Rating : 4.2/5 (736 download)

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Book Synopsis Tensor Network Contractions by : Maciej Lewenstein

Download or read book Tensor Network Contractions written by Maciej Lewenstein and published by . This book was released on 2020-10-08 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

Introduction to Tensor Network Methods

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Publisher : Springer
ISBN 13 : 3030014096
Total Pages : 172 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Introduction to Tensor Network Methods by : Simone Montangero

Download or read book Introduction to Tensor Network Methods written by Simone Montangero and published by Springer. This book was released on 2018-11-28 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter. The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.

Tensor Networks for Dimensionality Reduction and Large-Scale Optimization

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Publisher :
ISBN 13 : 9781680832761
Total Pages : 262 pages
Book Rating : 4.8/5 (327 download)

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Book Synopsis Tensor Networks for Dimensionality Reduction and Large-Scale Optimization by : Andrzej Cichocki

Download or read book Tensor Networks for Dimensionality Reduction and Large-Scale Optimization written by Andrzej Cichocki and published by . This book was released on 2017-05-28 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph builds on Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions by discussing tensor network models for super-compressed higher-order representation of data/parameters and cost functions, together with an outline of their applications in machine learning and data analytics. A particular emphasis is on elucidating, through graphical illustrations, that by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volume of data/parameters, thereby alleviating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification, generalized eigenvalue decomposition and in the optimization of deep neural networks. The monograph focuses on tensor train (TT) and Hierarchical Tucker (HT) decompositions and their extensions, and on demonstrating the ability of tensor networks to provide scalable solutions for a variety of otherwise intractable large-scale optimization problems. Tensor Networks for Dimensionality Reduction and Large-scale Optimization Parts 1 and 2 can be used as stand-alone texts, or together as a comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions. See also: Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions. ISBN 978-1-68083-222-8

Tensor Networks for Dimensionality Reduction and Large-scale Optimization

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Publisher :
ISBN 13 : 9781680832235
Total Pages : 180 pages
Book Rating : 4.8/5 (322 download)

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Book Synopsis Tensor Networks for Dimensionality Reduction and Large-scale Optimization by : Andrzej Cichocki

Download or read book Tensor Networks for Dimensionality Reduction and Large-scale Optimization written by Andrzej Cichocki and published by . This book was released on 2016 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern applications in engineering and data science are increasingly based on multidimensional data of exceedingly high volume, variety, and structural richness. However, standard machine learning algorithms typically scale exponentially with data volume and complexity of cross-modal couplings - the so called curse of dimensionality - which is prohibitive to the analysis of large-scale, multi-modal and multi-relational datasets. Given that such data are often efficiently represented as multiway arrays or tensors, it is therefore timely and valuable for the multidisciplinary machine learning and data analytic communities to review low-rank tensor decompositions and tensor networks as emerging tools for dimensionality reduction and large scale optimization problems. Our particular emphasis is on elucidating that, by virtue of the underlying low-rank approximations, tensor networks have the ability to alleviate the curse of dimensionality in a number of applied areas. In Part 1 of this monograph we provide innovative solutions to low-rank tensor network decompositions and easy to interpret graphical representations of the mathematical operations on tensor networks. Such a conceptual insight allows for seamless migration of ideas from the flat-view matrices to tensor network operations and vice versa, and provides a platform for further developments, practical applications, and non-Euclidean extensions. It also permits the introduction of various tensor network operations without an explicit notion of mathematical expressions, which may be beneficial for many research communities that do not directly rely on multilinear algebra. Our focus is on the Tucker and tensor train (TT) decompositions and their extensions, and on demonstrating the ability of tensor networks to provide linearly or even super-linearly (e.g., logarithmically) scalable solutions, as illustrated in detail in Part 2 of this monograph.

Emergent Phenomena in Correlated Matter

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Publisher : Forschungszentrum Jülich
ISBN 13 : 3893368841
Total Pages : 562 pages
Book Rating : 4.8/5 (933 download)

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Book Synopsis Emergent Phenomena in Correlated Matter by : Eva Pavarini

Download or read book Emergent Phenomena in Correlated Matter written by Eva Pavarini and published by Forschungszentrum Jülich. This book was released on 2013 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tensors: Geometry and Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 0821869078
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tensors: Geometry and Applications by : J. M. Landsberg

Download or read book Tensors: Geometry and Applications written by J. M. Landsberg and published by American Mathematical Soc.. This book was released on 2011-12-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

Quantum Computing: An Applied Approach

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Publisher : Springer Nature
ISBN 13 : 3030832740
Total Pages : 422 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Quantum Computing: An Applied Approach by : Jack D. Hidary

Download or read book Quantum Computing: An Applied Approach written by Jack D. Hidary and published by Springer Nature. This book was released on 2021-09-29 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book integrates the foundations of quantum computing with a hands-on coding approach to this emerging field; it is the first to bring these elements together in an updated manner. This work is suitable for both academic coursework and corporate technical training. The second edition includes extensive updates and revisions, both to textual content and to the code. Sections have been added on quantum machine learning, quantum error correction, Dirac notation and more. This new edition benefits from the input of the many faculty, students, corporate engineering teams, and independent readers who have used the first edition. This volume comprises three books under one cover: Part I outlines the necessary foundations of quantum computing and quantum circuits. Part II walks through the canon of quantum computing algorithms and provides code on a range of quantum computing methods in current use. Part III covers the mathematical toolkit required to master quantum computing. Additional resources include a table of operators and circuit elements and a companion GitHub site providing code and updates. Jack D. Hidary is a research scientist in quantum computing and in AI at Alphabet X, formerly Google X.

High-Dimensional Probability

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Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Physics of the Lorentz Group

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Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681740621
Total Pages : 173 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis Physics of the Lorentz Group by : Sibel Baskal

Download or read book Physics of the Lorentz Group written by Sibel Baskal and published by Morgan & Claypool Publishers. This book was released on 2015-11-01 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.

Entropy and Diversity

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Publisher : Cambridge University Press
ISBN 13 : 1108832709
Total Pages : 457 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Entropy and Diversity by : Tom Leinster

Download or read book Entropy and Diversity written by Tom Leinster and published by Cambridge University Press. This book was released on 2021-04-22 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.

A Concise Course in Algebraic Topology

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Publisher : University of Chicago Press
ISBN 13 : 9780226511832
Total Pages : 262 pages
Book Rating : 4.5/5 (118 download)

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Book Synopsis A Concise Course in Algebraic Topology by : J. P. May

Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Quantum Hamiltonian Complexity

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Publisher :
ISBN 13 : 9781680830064
Total Pages : 140 pages
Book Rating : 4.8/5 (3 download)

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Book Synopsis Quantum Hamiltonian Complexity by : Sevag Gharibian

Download or read book Quantum Hamiltonian Complexity written by Sevag Gharibian and published by . This book was released on 2015-09-30 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. It provides a computer science-oriented introduction to the subject in order to help bridge the language barrier between computer scientists and physicists in the field.

Information Processing in Medical Imaging

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Publisher : Springer Nature
ISBN 13 : 3030781917
Total Pages : 784 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Information Processing in Medical Imaging by : Aasa Feragen

Download or read book Information Processing in Medical Imaging written by Aasa Feragen and published by Springer Nature. This book was released on 2021-06-20 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 27th International Conference on Information Processing in Medical Imaging, IPMI 2021, which was held online during June 28-30, 2021. The conference was originally planned to take place in Bornholm, Denmark, but changed to a virtual format due to the COVID-19 pandemic. The 59 full papers presented in this volume were carefully reviewed and selected from 200 submissions. They were organized in topical sections as follows: registration; causal models and interpretability; generative modelling; shape; brain connectivity; representation learning; segmentation; sequential modelling; learning with few or low quality labels; uncertainty quantification and generative modelling; and deep learning.

A Relativist's Toolkit

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Publisher : Cambridge University Press
ISBN 13 : 1139451995
Total Pages : 253 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis A Relativist's Toolkit by : Eric Poisson

Download or read book A Relativist's Toolkit written by Eric Poisson and published by Cambridge University Press. This book was released on 2004-05-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.

An Introduction To Quantum Field Theory

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Publisher : CRC Press
ISBN 13 : 0429983182
Total Pages : 866 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis An Introduction To Quantum Field Theory by : Michael E. Peskin

Download or read book An Introduction To Quantum Field Theory written by Michael E. Peskin and published by CRC Press. This book was released on 2018-05-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

Data Fusion Methodology and Applications

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Publisher : Elsevier
ISBN 13 : 0444639853
Total Pages : 396 pages
Book Rating : 4.4/5 (446 download)

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Book Synopsis Data Fusion Methodology and Applications by : Marina Cocchi

Download or read book Data Fusion Methodology and Applications written by Marina Cocchi and published by Elsevier. This book was released on 2019-05-11 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data Fusion Methodology and Applications explores the data-driven discovery paradigm in science and the need to handle large amounts of diverse data. Drivers of this change include the increased availability and accessibility of hyphenated analytical platforms, imaging techniques, the explosion of omics data, and the development of information technology. As data-driven research deals with an inductive attitude that aims to extract information and build models capable of inferring the underlying phenomena from the data itself, this book explores the challenges and methodologies used to integrate data from multiple sources, analytical platforms, different modalities, and varying timescales. Presents the first comprehensive textbook on data fusion, focusing on all aspects of data-driven discovery Includes comprehensible, theoretical chapters written for large and diverse audiences Provides a wealth of selected application to the topics included