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Book
Convex Optimization for Machine Learning.
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ISBN: 1638280533 1638280525 Year: 2022 Publisher: Norwell, MA : Now Publishers,

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Abstract

This book covers an introduction to convex optimization, one of the powerful and tractable optimization problems that can be efficiently solved on a computer. The goal of the book is tohelp develop a sense of what convex optimization is, and how it can be used in a widening array of practical contexts with a particular emphasis on machine learning.The first part of the book covers core concepts of convex sets, convex functions, and related basic definitions that serve understanding convex optimization and its corresponding models. The second part deals with one very useful theory, called duality, which enables us to: (1) gain algorithmic insights; and (2) obtain an approximate solution to non-convex optimization problems which are often difficult to solve. The last part focuses on modern applications in machine learning and deep learning.A defining feature of this book is that it succinctly relates the “story” of how convex optimization plays a role, via historical examples and trending machine learning applications. Another key feature is that it includes programming implementation of a variety of machine learning algorithms inspired by optimization fundamentals, together with a brief tutorial of the used programming tools. The implementation is based on Python, CVXPY, and TensorFlow.This book does not follow a traditional textbook-style organization, but is streamlined via a series of lecture notes that are intimately related, centered around coherent themes and concepts. It serves as a textbook mainly for a senior-level undergraduate course, yet is also suitable for a first-year graduate course. Readers benefit from having a good background in linear algebra, some exposure to probability, and basic familiarity with Python.


Book
The lateralized brain : the neuroscience and evolution of hemispheric asymmetries
Authors: ---
ISBN: 012803453X 9780128034538 9780128034521 0128034521 Year: 2018 Publisher: London, England : Academic Press,

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The Lateralized Brain: The Neuroscience and Evolution of Hemispheric Asymmetries is an up-to-date teaching resource for neuroscience faculty members that teach courses concerning hemispheric asymmetries. The book provides students with all relevant information on the subject, while also giving aspiring researchers in the field an up-to-date overview of relevant, previous work. It is ideal for courses on hemispheric asymmetries, that is, the functional or structural differences between the left and the right hemispheres of the brain, and also highlights how the widespread use of modern neuroimaging techniques, such as fMRI and DTI has completely changed the way hemispheric asymmetries are currently investigated. --

Particles and waves.
Author:
ISBN: 0198023006 1280525495 9786610525492 0195345053 9780198023005 9781280525490 0195065476 9780195065473 019506755X 9780195067552 019506755X 9780195067552 6610525498 9780195345056 0197731201 Year: 2023 Publisher: Oxford : Oxford University Press,

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A collection of essays by the scientific philosopher Peter Achinstein, representing the culmination of his examination of methodological issues arising from 19th century physics. He focuses on philosophical problems surrounding the postulation of unobservable entities such as light waves.


Book
The birth of string theory
Authors: --- --- ---
ISBN: 9781139379250 1139379259 0511977727 9780511977725 9781139374965 1139374966 9781139376396 113937639X 9780521197908 0521197902 1107223695 1280647213 9786613633262 1139377825 1139370979 Year: 2012 Publisher: Cambridge : Cambridge University Press,

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String theory is currently the best candidate for a unified theory of all forces and all forms of matter in nature. As such, it has become a focal point for physical and philosophical discussions. This unique book explores the history of the theory's early stages of development, as told by its main protagonists. The book journeys from the first version of the theory (the so-called dual resonance model) in the late sixties, as an attempt to describe the physics of strong interactions outside the framework of quantum field theory, to its reinterpretation around the mid-seventies as a quantum theory of gravity unified with the other forces, and its successive developments up to the superstring revolution in 1984. Providing important background information to current debates on the theory, this book is essential reading for students and researchers in physics, as well as historians and philosophers of science.

Pontryagin duality and the structure of locally compact abelian groups
Author:
ISBN: 1139883739 1107365783 1107370515 1107360870 1107369312 129940359X 1107363322 0511600720 9781107360877 9780511600722 0521215439 9780521215435 Year: 1977 Volume: 29 Publisher: Cambridge : Cambridge University Press,

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These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.


Book
Holographic Quantum Matter
Authors: --- ---
ISBN: 0262348020 0262348012 0262038439 Year: 2018 Publisher: Cambridge The MIT Press

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"Holographic Quantum Matter describes a new field that has emerged in the past decade at the interface of condensed matter physics and quantum gravity. Experimental discoveries in condensed matter have led to the identification of numerous materials--like high temperature superconductors (HTS)--in which the collective motion of electrons requires deeper understand of quantum effects at large length scales. HTS's act as a "strange metal" in which the charge and energy is not carried by quasiparticles. In the meantime, studies of quantum gravity using string theory led to a major breakthrough with the identification of a mathematical tool known as the holographic correspondence. The authors describe the developments that followed with the realization that states of quantum matter without quasiparticle excitations are precisely those that are efficiently described by the holographic correspondence. The book is addressed to graduate students in theoretical physics, especially those specializing in condensed matter, string theory, or quantum field theory. It presents the necessary background in the study of quantum matter and in string theory, so that students in both fields are apprised of recent developments in the other field. It connects this introductory discussion to what are the most important recent developments. It provides the tools and motivation for performing holographic computations. And it explains how the salient technical results from holographic studies have led to new insights into quantum matter"--


Book
A posteriori error analysis via duality theory : with applications in modeling and numerical approximations
Author:
ISBN: 1280613432 9786610613434 038723537X Year: 2005 Publisher: New York : Springer Science,

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This volume provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates. Audience This volume is suitable for researchers and graduate students in applied and computational mathematics, and in engineering.

Linear ray and wave optics in phase space : bridging ray and wave optics via the Wigner phase-space picture
Author:
ISBN: 1281036501 9786611036508 0080535534 0444517995 0444636080 9780080535531 9780444517999 Year: 2005 Publisher: Amsterdam ; Boston : Elsevier,

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Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the

Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations
Authors: ---
ISBN: 0521850649 9780521850643 9780511542855 0511130422 9780511130427 051112824X 9780511128240 0511128894 9780511128899 0511542852 1280416254 9781280416255 1107153662 9781107153660 9786610416257 6610416257 0511182104 9780511182105 0511199341 9780511199349 0511300026 9780511300028 Year: 2005 Volume: 167 Publisher: Cambridge : Cambridge University Press,

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Poincaré duality algebras originated in the work of topologists on the cohomology of closed manifolds, and Macaulay's dual systems in the study of irreducible ideals in polynomial algebras. These two ideas are tied together using basic commutative algebra involving Gorenstein algebras. Steenrod operations also originated in algebraic topology, but may best be viewed as a means of encoding the information often hidden behind the Frobenius map in characteristic p<>0. They provide a noncommutative tool to study commutative algebras over a Galois field. In this Tract the authors skilfully bring together these ideas and apply them to problems in invariant theory. A number of remarkable and unexpected interdisciplinary connections are revealed that will interest researchers in the areas of commutative algebra, invariant theory or algebraic topology.

Strings, branes and gravity
Authors: --- ---
ISBN: 981279963X 9789812799630 9789810247744 9810247745 Year: 2001 Publisher: Singapore River Edge, NJ World Scientific

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Many of the topics in this book are outgrowths of the spectacular new understanding of duality in string theory which emerged around 1995. They include the AdS/CFT correspondence and its relation to holography, the matrix theory formulation of M theory, the structure of black holes in string theory, the structure of D-branes and M-branes, and detailed development of dualities with N = 1 and N = 2 supersymmetry. In addition, there are lectures covering experimental and phenomenological aspects of the Standard Model and its extensions, and discussions on cosmology including both theoretical aspe

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