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Random Wireless Networks

Random Wireless Networks

Rahul Vaze

Cambridge University Press
2015
sidottu
This book discusses the theoretical limits of information transfer in random wireless networks or ad hoc networks, where nodes are distributed uniformly in space and there is no centralised control. It provides a detailed analysis of the two relevant notions of capacity for random wireless networks – transmission capacity and throughput capacity. The book starts with the transmission capacity framework that is first presented for the single-hop model and later extended to the multi-hop model with retransmissions. Reusing some of the tools developed for analysis of transmission capacity, a few key long-standing questions about the performance analysis of cellular networks are also provided for the benefit of students. The discussion goes further into the concept of hierarchical co-operation that allows throughput capacity to scale linearly with the number of nodes. The author finally discusses the concept of hierarchical co-operation that allows throughput capacity to scale linearly with the number of nodes.
Random Sets in Econometrics

Random Sets in Econometrics

Ilya Molchanov; Francesca Molinari

Cambridge University Press
2018
sidottu
Random set theory is a fascinating branch of mathematics that amalgamates techniques from topology, convex geometry, and probability theory. Social scientists routinely conduct empirical work with data and modelling assumptions that reveal a set to which the parameter of interest belongs, but not its exact value. Random set theory provides a coherent mathematical framework to conduct identification analysis and statistical inference in this setting and has become a fundamental tool in econometrics and finance. This is the first book dedicated to the use of the theory in econometrics, written to be accessible for readers without a background in pure mathematics. Molchanov and Molinari define the basics of the theory and illustrate the mathematical concepts by their application in the analysis of econometric models. The book includes sets of exercises to accompany each chapter as well as examples to help readers apply the theory effectively.
Random Graphs, Geometry and Asymptotic Structure

Random Graphs, Geometry and Asymptotic Structure

Michael Krivelevich; Konstantinos Panagiotou; Mathew Penrose; Colin McDiarmid

Cambridge University Press
2016
sidottu
The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.
Random Graphs and Complex Networks

Random Graphs and Complex Networks

Remco van der Hofstad

Cambridge University Press
2016
sidottu
This rigorous introduction to network science presents random graphs as models for real-world networks. Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. Designed for a master's-level course, where students may only have a basic background in probability, the text covers such important preliminaries as convergence of random variables, probabilistic bounds, coupling, martingales, and branching processes. Building on this base - and motivated by many examples of real-world networks, including the Internet, collaboration networks, and the World Wide Web - it focuses on several important models for complex networks and investigates key properties, such as the connectivity of nodes. Numerous exercises allow students to develop intuition and experience in working with the models.
Random Graphs and Complex Networks: Volume 2

Random Graphs and Complex Networks: Volume 2

Remco van der Hofstad

Cambridge University Press
2024
sidottu
Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.
Random Sets in Econometrics

Random Sets in Econometrics

Ilya Molchanov; Francesca Molinari

Cambridge University Press
2018
pokkari
Random set theory is a fascinating branch of mathematics that amalgamates techniques from topology, convex geometry, and probability theory. Social scientists routinely conduct empirical work with data and modelling assumptions that reveal a set to which the parameter of interest belongs, but not its exact value. Random set theory provides a coherent mathematical framework to conduct identification analysis and statistical inference in this setting and has become a fundamental tool in econometrics and finance. This is the first book dedicated to the use of the theory in econometrics, written to be accessible for readers without a background in pure mathematics. Molchanov and Molinari define the basics of the theory and illustrate the mathematical concepts by their application in the analysis of econometric models. The book includes sets of exercises to accompany each chapter as well as examples to help readers apply the theory effectively.
Random Walks and Heat Kernels on Graphs

Random Walks and Heat Kernels on Graphs

Martin T. Barlow

Cambridge University Press
2017
pokkari
This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincaré inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.
Random Recollections of an Old Publisher

Random Recollections of an Old Publisher

William Tinsley

Cambridge University Press
2010
pokkari
William Tinsley (1830–1900) was a noted Victorian publisher whose catalogue included works by such celebrated novelists as Thomas Hardy and Wilkie Collins. This two-volume autobiography, first published in 1900, traces his life from his rural childhood to the establishment and rise of the Tinsley Brothers company in 1858, and its later collapse. Each chapter contains a series of brief sketches of authors and other contemporaries. Volume 1 spans Tinsley's early days and travels to London, along with his first encounters with the publishing world. It includes detailed portraits of Mary Elizabeth Braddon and H. J. Byron, and incorporates material on the development of transport and general commerce in the Victorian era. Based on Tinsley's personal recollections, and incorporating letters as well as anecdotal information, these volumes will fascinate anyone interested in the history of publishing and the development of the nineteenth-century novel.
Random Recollections of an Old Publisher

Random Recollections of an Old Publisher

William Tinsley

Cambridge University Press
2010
pokkari
William Tinsley (1830–1900) was a noted Victorian publisher whose catalogue included works by such celebrated novelists as Thomas Hardy and Wilkie Collins. This two-volume autobiography, first published in 1900, traces his life from his rural childhood to the establishment and rise of the Tinsley Brothers company in 1858, and its later collapse. Each chapter contains a series of brief sketches of authors and other contemporaries. Volume 2 charts Tinsley's later career, and features several lengthier portraits of some of the personalities he encountered. It also includes information on Victorian playwrights and actors, along with a detailed section on the history of Sadler's Wells theatre. Based on Tinsley's personal recollections, and incorporating letters as well as anecdotal information, these volumes will fascinate anyone interested in the history of publishing and the development of the nineteenth-century novel.
Random Processes in Physics

Random Processes in Physics

Tobias Galla; Fred Loebinger; Helen Gleeson

Wiley-Blackwell (an imprint of John Wiley Sons Ltd)
2024
nidottu
This succinct book is unique in that it covers topics starting from the very basics of probability theory leading up to applications in (equilibrium) statistical physics, quantum theory and complex systems. The overarching aim of the book is to present probabilistic concepts, in a way accessible to physics undergraduates and with applications in physics in mind. The book is split into three parts: Part I: Fundamentals - The starting point of the book will present basic concepts in probability theory including discussions about general motivation, the difficulties in dealing with probabilities and a number of basic examples. This part will include some of the general mathematical concepts underpinning probability theory. This will be followed by a discussion of joint probabilities and topics relating to Bayes theorem. Lastly I will discuss how computers generate (pseudo-) random numbers, a topic which is key in any modern view on random processes for physicists. Part II: Specific probability distributions - The second part of the book will focus on the probability distributions most important for applications in physics including discussions about the Central Limit Theorem, the Gaussian distribution, Poissonian distributions and the connection with exponential random variables. Chapters on Levy flights, selfsimilarity, power law distributions (including applications) and on extreme value statistics (e.g. Gumbel and Weibull distributions) will complete Part II of the book.Part III: Applications in and beyond physics - The final part of the book will explore specific applications of random process modelling in physics and in selected adjacent disciplines, specifically applications in quantum theory, viewed specifically from the perspective of random processes and probability theory. Chapters will contain a derivation of the standard ensembles of classical statistical physics, from the point of view of information theory. This is then extended to quantum statistical physics and density matrices. Finally we will discuss simple Markov chains and Monte Carlo simulations, as well as applications of probability theory to a selected set of topics in complex systems. These will be described at a level suitable for undergraduate students in the first and second year.
Random Circulant Matrices

Random Circulant Matrices

Arup Bose; Koushik Saha

CRC Press
2018
sidottu
Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed. Arup Bose obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph.D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014.
Random Signal Processing

Random Signal Processing

Shaila Dinkar Apte

CRC Press
2017
nidottu
This book covers random signals and random processes along with estimation of probability density function, estimation of energy spectral density and power spectral density. The properties of random processes and signal modelling are discussed with basic communication theory estimation and detection. MATLAB simulations are included for each concept with output of the program with case studies and project ideas. The chapters progressively introduce and explain the concepts of random signals and cover multiple applications for signal processing.The book is designed to cater to a wide audience starting from the undergraduates (electronics, electrical, instrumentation, computer, and telecommunication engineering) to the researchers working in the pertinent fields.Key Features: • Aimed at random signal processing with parametric signal processing-using appropriate segment size.• Covers speech, image, medical images, EEG and ECG signal processing.• Reviews optimal detection and estimation.• Discusses parametric modeling and signal processing in transform domain.• Includes MATLAB codes and relevant exercises, case studies and solved examples including multiple choice questions