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Author: Razvan Gurau
Publisher: Oxford University Press
ISBN: 0198787936
Category : Mathematics
Languages : en
Pages : 345
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Book Description
This book introduces "Random Tensors," a framework for studying random geometries in any dimension. It provides a complete derivation of the key results in the field. Whatever form a theory of Quantum Gravity may take, it must incorporate random geometry.
Author: Razvan Gurau
Publisher: Oxford University Press
ISBN: 0198787936
Category : Mathematics
Languages : en
Pages : 345
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Book Description
This book introduces "Random Tensors," a framework for studying random geometries in any dimension. It provides a complete derivation of the key results in the field. Whatever form a theory of Quantum Gravity may take, it must incorporate random geometry.
Author: Wolfgang Hackbusch
Publisher: Springer Science & Business Media
ISBN: 3642280277
Category : Mathematics
Languages : en
Pages : 525
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Book Description
Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc.
Author: Dimitris Gritzalis
Publisher: Springer Nature
ISBN: 3031662458
Category :
Languages : en
Pages : 416
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Book Description
Author: Chengming Bai
Publisher: World Scientific
ISBN: 9814518565
Category : Mathematics
Languages : en
Pages : 665
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Book Description
This volume focuses on developments in the field of group theory in its broadest sense and is of interest to theoretical and experimental physicists, mathematicians, and scientists in related disciplines who are interested in the latest methods and applications. In an increasingly ultra-specialized world, this volume will demonstrate the interchange of ideas and methods in theoretical and mathematical physics.
Author: Francois Chollet
Publisher: Simon and Schuster
ISBN: 1638350094
Category : Computers
Languages : en
Pages : 502
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Book Description
Unlock the groundbreaking advances of deep learning with this extensively revised edition of the bestselling original. Learn directly from the creator of Keras and master practical Python deep learning techniques that are easy to apply in the real world. In Deep Learning with Python, Second Edition you will learn: Deep learning from first principles Image classification & image segmentation Timeseries forecasting Text classification and machine translation Text generation, neural style transfer, and image generation Deep Learning with Python has taught thousands of readers how to put the full capabilities of deep learning into action. This extensively revised second edition introduces deep learning using Python and Keras, and is loaded with insights for both novice and experienced ML practitioners. You’ll learn practical techniques that are easy to apply in the real world, and important theory for perfecting neural networks. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Recent innovations in deep learning unlock exciting new software capabilities like automated language translation, image recognition, and more. Deep learning is becoming essential knowledge for every software developer, and modern tools like Keras and TensorFlow put it within your reach, even if you have no background in mathematics or data science. About the book Deep Learning with Python, Second Edition introduces the field of deep learning using Python and the powerful Keras library. In this new edition, Keras creator François Chollet offers insights for both novice and experienced machine learning practitioners. As you move through this book, you’ll build your understanding through intuitive explanations, crisp illustrations, and clear examples. You’ll pick up the skills to start developing deep-learning applications. What's inside Deep learning from first principles Image classification and image segmentation Time series forecasting Text classification and machine translation Text generation, neural style transfer, and image generation About the reader For readers with intermediate Python skills. No previous experience with Keras, TensorFlow, or machine learning is required. About the author François Chollet is a software engineer at Google and creator of the Keras deep-learning library. Table of Contents 1 What is deep learning? 2 The mathematical building blocks of neural networks 3 Introduction to Keras and TensorFlow 4 Getting started with neural networks: Classification and regression 5 Fundamentals of machine learning 6 The universal workflow of machine learning 7 Working with Keras: A deep dive 8 Introduction to deep learning for computer vision 9 Advanced deep learning for computer vision 10 Deep learning for timeseries 11 Deep learning for text 12 Generative deep learning 13 Best practices for the real world 14 Conclusions
Author: Maolin Che
Publisher: Springer Nature
ISBN: 9811520593
Category : Mathematics
Languages : en
Pages : 258
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Book Description
The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective. A systematic description about how to extend the numerical linear algebra to the numerical multi-linear algebra is also delivered in this book. The authors design the neural network model for the computation of the rank-one approximation of real tensors, a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors and a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors, adaptive randomized algorithms for computing the approximate tensor decompositions, and the QR type method for computing U-eigenpairs of complex tensors. This book could be used for the Graduate course, such as Introduction to Tensor. Researchers may also find it helpful as a reference in tensor research.
Author: Edoardo Angelo Di Napoli
Publisher: Frontiers Media SA
ISBN: 2832504256
Category : Science
Languages : en
Pages : 192
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Book Description
Author: Luca Lionni
Publisher: Springer
ISBN: 3319960237
Category : Science
Languages : en
Pages : 233
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Book Description
This book provides a number of combinatorial tools that allow a systematic study of very general discrete spaces involved in the context of discrete quantum gravity. In any dimension D, we can discretize Euclidean gravity in the absence of matter over random discrete spaces obtained by gluing families of polytopes together in all possible ways. These spaces are then classified according to their curvature. In D=2, it results in a theory of random discrete spheres, which converge in the continuum limit towards the Brownian sphere, a random fractal space interpreted as a quantum random space-time. In this limit, the continuous Liouville theory of D=2 quantum gravity is recovered. Previous results in higher dimension regarded triangulations, converging towards a continuum random tree, or gluings of simple building blocks of small sizes, for which multi-trace matrix model results are recovered in any even dimension. In this book, the author develops a bijection with stacked two-dimensional discrete surfaces for the most general colored building blocks, and details how it can be used to classify colored discrete spaces according to their curvature. The way in which this combinatorial problem arrises in discrete quantum gravity and random tensor models is discussed in detail.
Author: Steffen Gielen
Publisher: MDPI
ISBN: 3039361783
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research.
Author: Arne Jensen
Publisher: World Scientific
ISBN: 9814449245
Category : Science
Languages : en
Pages : 743
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Book Description
This is an in-depth study of not just about Tan Kah-kee, but also the making of a legend through his deeds, self-sacrifices, fortitude and foresight. This revised edition sheds new light on his political agonies in Mao's China over campaigns against capitalists and intellectuals.
