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Gaussian Capacity Analysis
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Book Synopsis Gaussian Capacity Analysis by : Liguang Liu
Download or read book Gaussian Capacity Analysis written by Liguang Liu and published by Springer. This book was released on 2018-09-20 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space. Included in the text is a new geometric characterization of the Gaussian 1-capacity and the Gaussian Poincaré 1-inequality. Applications to function spaces and geometric measures are also presented. This book will be of use to researchers who specialize in potential theory, elliptic differential equations, functional analysis, probability, and geometric measure theory.
Book Synopsis Information Capacity of Gaussian Channels by : Charles R. Baker
Download or read book Information Capacity of Gaussian Channels written by Charles R. Baker and published by . This book was released on 1987 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information capacity of Gaussian channels is one of the basic problems of information theory. Shannon's results for white Gaussian channels and Fano's waterfilling analysis of stationary Gaussian channnels are two of the best-known works of early information theory. Results are given here which extend to a general framework these results and others due to Gallager and to Kadota, Zakai, and Ziv. The development applies to arbitrary Gaussian channels when the channel noise has sample paths in a separable Banach space, and to a large class of Gaussian channels when the noise has sample paths in a linear topological vector space. Solutions for the capacity are given for both matched and mismatched channels. Keywords: Gaussian channels; Channel capacity; Shannon theory; Information theory.
Book Synopsis Analysis On Gaussian Spaces by : Yaozhong Hu
Download or read book Analysis On Gaussian Spaces written by Yaozhong Hu and published by World Scientific. This book was released on 2016-08-30 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Written by a well-known expert in fractional stochastic calculus, this book offers a comprehensive overview of Gaussian analysis, with particular emphasis on nonlinear Gaussian functionals. In addition, it covers some topics that are not frequently encountered in other treatments, such as Littlewood-Paley-Stein, etc. This coverage makes the book a valuable addition to the literature. Many results presented in this book were hitherto available only in the research literature in the form of research papers by the author and his co-authors.'Mathematical Reviews ClippingsAnalysis of functions on the finite dimensional Euclidean space with respect to the Lebesgue measure is fundamental in mathematics. The extension to infinite dimension is a great challenge due to the lack of Lebesgue measure on infinite dimensional space. Instead the most popular measure used in infinite dimensional space is the Gaussian measure, which has been unified under the terminology of 'abstract Wiener space'.Out of the large amount of work on this topic, this book presents some fundamental results plus recent progress. We shall present some results on the Gaussian space itself such as the Brunn-Minkowski inequality, Small ball estimates, large tail estimates. The majority part of this book is devoted to the analysis of nonlinear functions on the Gaussian space. Derivative, Sobolev spaces are introduced, while the famous Poincaré inequality, logarithmic inequality, hypercontractive inequality, Meyer's inequality, Littlewood-Paley-Stein-Meyer theory are given in details.This book includes some basic material that cannot be found elsewhere that the author believes should be an integral part of the subject. For example, the book includes some interesting and important inequalities, the Littlewood-Paley-Stein-Meyer theory, and the Hörmander theorem. The book also includes some recent progress achieved by the author and collaborators on density convergence, numerical solutions, local times.
Book Synopsis Gaussian Harmonic Analysis by : Wilfredo Urbina-Romero
Download or read book Gaussian Harmonic Analysis written by Wilfredo Urbina-Romero and published by Springer. This book was released on 2019-06-21 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: harmonic analysis and probability. The book is intended for a very diverse audience, from graduate students all the way to researchers working in a broad spectrum of areas in analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of real analysis as well as with classical harmonic analysis, including Calderón-Zygmund theory; also some knowledge of basic orthogonal polynomials theory would be convenient. The monograph develops the main topics of classical harmonic analysis (semigroups, covering lemmas, maximal functions, Littlewood-Paley functions, spectral multipliers, fractional integrals and fractional derivatives, singular integrals) with respect to the Gaussian measure. The text provide an updated exposition, as self-contained as possible, of all the topics in Gaussian harmonic analysis that up to now are mostly scattered in research papers and sections of books; also an exhaustive bibliography for further reading. Each chapter ends with a section of notes and further results where connections between Gaussian harmonic analysis and other connected fields, points of view and alternative techniques are given. Mathematicians and researchers in several areas will find the breadth and depth of the treatment of the subject highly useful.
Book Synopsis Capacity of Gaussian Noise Channels with Side Information and Feedback by : Thierry Etienne Klein
Download or read book Capacity of Gaussian Noise Channels with Side Information and Feedback written by Thierry Etienne Klein and published by . This book was released on 2001 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Information Capacity of Peak and Average Power Constrained Gaussian Channels by : Joel Gorham Smith
Download or read book On the Information Capacity of Peak and Average Power Constrained Gaussian Channels written by Joel Gorham Smith and published by . This book was released on 1969 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mutual Information and Capacity of the Continuous Time Gaussian Channel with Feedback by : Shunsuke Ihara
Download or read book Mutual Information and Capacity of the Continuous Time Gaussian Channel with Feedback written by Shunsuke Ihara and published by . This book was released on 1991 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Gaussian Processes for Machine Learning by : Carl Edward Rasmussen
Download or read book Gaussian Processes for Machine Learning written by Carl Edward Rasmussen and published by MIT Press. This book was released on 2005-11-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
Book Synopsis Information Theory For Continuous Systems by : Shunsuke Ihara
Download or read book Information Theory For Continuous Systems written by Shunsuke Ihara and published by World Scientific. This book was released on 1993-09-23 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic mathematical analysis of entropy and stochastic processes, especially Gaussian processes, and its applications to information theory.The contents fall roughly into two parts. In the first part a unified treatment of entropy in information theory, probability theory and mathematical statistics is presented. The second part deals mostly with information theory for continuous communication systems. Particular emphasis is placed on the Gaussian channel.An advantage of this book is that, unlike most books on information theory, it places emphasis on continuous communication systems, rather than discrete ones.
Book Synopsis Gaussian Channels and Their Capacity by : Kenjiro Yanagi
Download or read book Gaussian Channels and Their Capacity written by Kenjiro Yanagi and published by . This book was released on 1980 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topics in Non-Gaussian Signal Processing by : Edward J. Wegman
Download or read book Topics in Non-Gaussian Signal Processing written by Edward J. Wegman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-Gaussian Signal Processing is a child of a technological push. It is evident that we are moving from an era of simple signal processing with relatively primitive electronic cir cuits to one in which digital processing systems, in a combined hardware-software configura. tion, are quite capable of implementing advanced mathematical and statistical procedures. Moreover, as these processing techniques become more sophisticated and powerful, the sharper resolution of the resulting system brings into question the classic distributional assumptions of Gaussianity for both noise and signal processes. This in turn opens the door to a fundamental reexamination of structure and inference methods for non-Gaussian sto chastic processes together with the application of such processes as models in the context of filtering, estimation, detection and signal extraction. Based on the premise that such a fun damental reexamination was timely, in 1981 the Office of Naval Research initiated a research effort in Non-Gaussian Signal Processing under the Selected Research Opportunities Program.
Book Synopsis The Capacity of the Gaussian Channel with Scalar, Multidimensional, Or Band-limited Binary Input by : Ahmed Omar Nasif
Download or read book The Capacity of the Gaussian Channel with Scalar, Multidimensional, Or Band-limited Binary Input written by Ahmed Omar Nasif and published by . This book was released on 2005 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Capacity of Gaussian Feedback Channels with Memory by : Bernd Neumann
Download or read book Capacity of Gaussian Feedback Channels with Memory written by Bernd Neumann and published by . This book was released on 1971 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Industrial Data Analytics for Diagnosis and Prognosis by : Shiyu Zhou
Download or read book Industrial Data Analytics for Diagnosis and Prognosis written by Shiyu Zhou and published by John Wiley & Sons. This book was released on 2021-07-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover data analytics methodologies for the diagnosis and prognosis of industrial systems under a unified random effects model In Industrial Data Analytics for Diagnosis and Prognosis - A Random Effects Modelling Approach, distinguished engineers Shiyu Zhou and Yong Chen deliver a rigorous and practical introduction to the random effects modeling approach for industrial system diagnosis and prognosis. In the book’s two parts, general statistical concepts and useful theory are described and explained, as are industrial diagnosis and prognosis methods. The accomplished authors describe and model fixed effects, random effects, and variation in univariate and multivariate datasets and cover the application of the random effects approach to diagnosis of variation sources in industrial processes. They offer a detailed performance comparison of different diagnosis methods before moving on to the application of the random effects approach to failure prognosis in industrial processes and systems. In addition to presenting the joint prognosis model, which integrates the survival regression model with the mixed effects regression model, the book also offers readers: A thorough introduction to describing variation of industrial data, including univariate and multivariate random variables and probability distributions Rigorous treatments of the diagnosis of variation sources using PCA pattern matching and the random effects model An exploration of extended mixed effects model, including mixture prior and Kalman filtering approach, for real time prognosis A detailed presentation of Gaussian process model as a flexible approach for the prediction of temporal degradation signals Ideal for senior year undergraduate students and postgraduate students in industrial, manufacturing, mechanical, and electrical engineering, Industrial Data Analytics for Diagnosis and Prognosis is also an indispensable guide for researchers and engineers interested in data analytics methods for system diagnosis and prognosis.
Book Synopsis The Capacity of the Gaussian Broadcast Channel with Feedback by : Stanford University. Department of Statistics
Download or read book The Capacity of the Gaussian Broadcast Channel with Feedback written by Stanford University. Department of Statistics and published by . This book was released on 1977 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Upper Bound to the Capacity of a Linear Timevarying Channel with Additive Gaussian Noise by : G. David Forney (Jr)
Download or read book Upper Bound to the Capacity of a Linear Timevarying Channel with Additive Gaussian Noise written by G. David Forney (Jr) and published by . This book was released on 1962 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis is concerned with the evaluation of the upper bound to the capacity of a linear time-varying channel obtained by finding the capacity of the same channel when its behavior at all times is known a priori. Numerical evaluation turns out to depend on the ditribution of the eigenvalues of a random infinite-dimensional matrix, which is apparently an unsolved mathematical problem. Evaluation is possible in two special ases: first, where the channel is not time-varying in which case the capacity formula reduces to that formerly known; second, when the channel has no memory, that is y = ax + u, where a is random and n is white and gaussian. 9author).
Book Synopsis Information Theoretic Security and Privacy of Information Systems by : Rafael F. Schaefer
Download or read book Information Theoretic Security and Privacy of Information Systems written by Rafael F. Schaefer and published by Cambridge University Press. This book was released on 2017-06-16 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn how information theoretic approaches can inform the design of more secure information systems and networks with this expert guide. Covering theoretical models, analytical results, and the state of the art in research, it will be of interest to researchers, graduate students, and practitioners working in communications engineering.
