Listing 1 - 10 of 79 | << page >> |
Sort by
|
Choose an application
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.
Choose an application
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. --
Cerebral dominance. --- Brain --- Duality. --- Anatomy. --- Dominance, Cerebral --- Functional asymmetry (Brain) --- Hemispheric dominance (Brain) --- Lateralization (Brain) --- Left and right brain --- Right and left brain --- Cerebral hemispheres --- Dual-brain psychology --- Laterality --- Whole brain learning --- Cerebral dominance --- Duality --- Anatomy --- Brain - Duality --- Brain - Anatomy
Choose an application
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.
Science --- Physics --- Wave-particle duality --- Dualism, Wave-particle --- Duality principle (Physics) --- Wave-corpuscle duality --- Complementarity (Physics) --- Electromagnetic waves --- Matter --- Radiation --- Wave mechanics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Philosophy --- History. --- Methodology --- Constitution --- Science - Philosophy - History. --- Physics - Methodology - History. --- Wave-particle duality - History.
Choose an application
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.
String models. --- Duality (Nuclear physics) --- Nuclear reactions --- Scattering (Physics) --- Models, String --- String theory
Choose an application
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.
Locally compact Abelian groups. --- Duality theory (Mathematics) --- Algebra --- Mathematical analysis --- Topology --- Compact Abelian groups --- Locally compact groups --- Topological groups --- Groupes abéliens localement compacts --- Locally compact Abelian groups --- Pontrjagin duality --- 517.986.6 --- Pontryagin duality --- 517.986.6 Harmonic analysis of functions of groups and homogeneous spaces --- Harmonic analysis of functions of groups and homogeneous spaces --- Pontrjagin duality. --- Topological groups. Lie groups --- Duality theory (Mathematics). --- Groupes abéliens localement compacts. --- Groupes topologiques --- Groupes localement compacts
Choose an application
"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"--
Holography. --- Duality (Nuclear physics) --- Condensed matter. --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Nuclear reactions --- Scattering (Physics) --- Laser photography --- Lensless photography --- Photography, Lensless --- Wavefront reconstruction imaging --- Diffraction --- Holographic interferometry --- Interference (Light) --- Interferometry --- Laser recording --- Photonics --- Speckle metrology --- Three-dimensional display systems --- quantum matter --- holographic --- condensed matter --- condensed matter physics --- quantum --- quantum field theory --- holographic duality --- duality --- black hole --- superconductors --- theoretical physics --- quantum gravity --- holographic principle --- gauge theory --- string theory --- cosmology --- adSCFT correspondence --- anti-de Sitterconformal field theory correspondence --- Maldacena duality --- gaugegravity duality --- holographic correspondence
Choose an application
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.
Error analysis (Mathematics) --- Duality theory (Mathematics) --- Algebra --- Mathematical analysis --- Topology --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Numerical analysis --- Statistics
Choose an application
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
Wave theory of light. --- Wigner distribution. --- Geometrical optics --- Mathematics. --- Optics, Geometrical --- Optics --- Distribution (Probability theory) --- Racah algebra --- Light, Wave theory of --- Wave-motion, Theory of --- Wave-particle duality
Choose an application
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.
Duality theory (Mathematics) --- Steenrod algebra --- Poincaré series --- Poincaré series. --- Steenrod algebra. --- Algebra, Steenrod --- Algebraic topology --- Algebra --- Mathematical analysis --- Topology --- Series, Poincaré
Choose an application
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
Black holes (Astronomy) --- Branes --- Compactifications --- Duality (Nuclear physics) --- Gravity --- String models --- Supersymmetry --- Geophysics --- Mechanics --- Pendulum --- Nuclear reactions --- Scattering (Physics) --- Topology --- p-branes --- Superstring theories
Listing 1 - 10 of 79 | << page >> |
Sort by
|