This book is a very timely exposition of part of an important subject which goes under the general name of “inverse problems”. The analogous problem for continuous media has been very much studied, with a great deal of difficult mathematics involved, especially partial differential equations. Some of the researchers working on the inverse conductivity problem for continuous media (the problem of recovering the conductivity inside from measurements on the outside) have taken an interest in the authors' analysis of this similar problem for resistor networks.The authors' treatment of inverse problems for electrical networks is at a fairly elementary level. It is accessible to advanced undergraduates, and mathematics students at the graduate level. The topics are of interest to mathematicians working on inverse problems, and possibly to electrical engineers. A few techniques from other areas of mathematics have been brought together in the treatment. It is this amalgamation of such topics as graph theory, medial graphs and matrix algebra, as well as the analogy to inverse problems for partial differential equations, that makes the book both original and interesting.
Annotation This book is a very timely exposition of part of an important subject which goes under the general name of "inverse problems". The analogous problem for continuous media has been very much studied, with a great deal of difficult mathematics involved, especially partial differential equations. Some of the researchers working on the inverse conductivity problem for continuous media (the problem of recovering the conductivity inside from measurements on the outside) have taken an interest in the authors' analysis of this similar problem for resistor networks. The authors' treatment of inverse problems for electrical networks is at a fairly elementary level. It is accessible to advanced undergraduates, and mathematics students at the graduate level. The topics are of interest to mathematicians working on inverse problems, and possibly to electrical engineers. A few techniques from other areas of mathematics have been brought together in the treatment. It is this amalgamation of such topics as graphtheory, medial graphs and matrix algebra, as well as the analogy to inverse problems for partial differential equations, that makes the book both original and interesting.
While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic.
In this thesis, we take a general view on the study of networks from inverse perspectives. By proposing a general representation for the dynamics of networks in terms of explicit dependencies among units, we develop new concepts for understanding, among other things, (i) how disparate networks achieve identical dynamics, and (ii) how we may reconstruct the structural connectivity of networks regardless of the type of network under study (e.g. gene regulatory networks, metabolic networks or neural networks). Specifically, here we heavily rely on concepts and tools coming from nonlinear dynam...
'The traditional analysis of infrastructure networks has provided the conceptual rationalization for centralized monopolies for a century. In recent years, liberalization has shown that much wider participation can be beneficial. Innovative development in decentralized networks can be driven from below if government policies permit it, as vividly demonstrated by the Internet. This book contributes to a much needed exploration into the characteristics and implications of decentralized networks being driven from below, introducing new perspectives on the conception and analysis of infrastructure networks.' William H. Melody, Aalborg University, Denmark and Delft University of Technology, The Netherlands The notion of inverse infrastructures that is, bottom-up, user-driven, self-organizing networks gives us a fresh perspective on the omnipresent infrastructure systems that support our economy and structure our way of living. This fascinating book considers the emergence of inverse infrastructures as a new phenomenon that will have a vast impact on consumers, industry and policy. Using a wide range of theories, from institutional economics to complex adaptive systems, it explores the mechanisms and incentives for the rise of these alternatives to large-scale infrastructures and points to their potential disruptive effect on conventional markets and governance models. The approach in this unique book challenges the existing literature on infrastructures, which primarily focuses on large technical systems (LTSs). Rather, this study highlights unprecedented developments, analyzing the differences and complementarity between LTSs and inverse infrastructures. It illustrates that even large infrastructures need not require a blueprint design or top-down and centralized control to run efficiently. The expert contributors draw upon a captivating and wide-ranging set of case studies, including: Wikipedia; wind energy cooperatives, Wireless Leiden, rural telecom in developing countries, local radio and television distribution, the collection of waste paper, syngas infrastructure design, and e-government projects. The book discusses the feasibility of temporary infrastructures and unheard of ownership arrangements, and concludes that inverse networks represent a critical transformation of the accepted model of infrastructure development. Laying a foundation for future research in the area and suggesting ways to bridge the gap between policy and practice, this path-breaking book will prove a riveting read for academics, students and researchers across a number of disciplines including economics, business, management, innovation, and technology and policy studies.
This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition Optical flow calculation and video compression algorithms Image models with bounded variation functions Bayes and Minimax theories for signal estimation 200 pages rewritten and most illustrations redrawn More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics
This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.
Modeling and Inverse Problems in the Presence of Uncertainty collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation i
