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Graph Theoretic Methods in Multiagent Networks
This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems.
The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.
The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.
This book has been adopted as a textbook at the following universities:
University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA
eBook
Information and action : using variables
\"This book demonstrates how we organize information and objects in our daily lives and how these real-world examples can shed light on how computer programs work\"--Amazon.com.
Book
Clustering/Distribution Analysis and Preconditioned Krylov Solvers for the Approximated Helmholtz Equation and Fractional Laplacian in the Case of Complex-Valued, Unbounded Variable Coefficient Wave Number Iμ/I
We consider the Helmholtz equation and the fractional Laplacian in the case of the complex-valued unbounded variable coefficient wave number μ, approximated by finite differences. In a recent analysis, singular value clustering and eigenvalue clustering have been proposed for a τ preconditioning when the variable coefficient wave number μ is uniformly bounded. Here, we extend the analysis to the unbounded case by focusing on the case of a power singularity. Several numerical experiments concerning the spectral behavior and convergence of the related preconditioned GMRES are presented.
Journal Article
Matrices, Moments and Quadrature with Applications
This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.
eBook
Higher moments of Banach space valued random variables
We define the
We study both the projective and injective
tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations:
Bochner integrals, Pettis integrals and Dunford integrals.
One of the problems studied is whether two random variables with the
same injective moments (of a given order) necessarily have the same projective moments; this is of interest in applications. We show
that this holds if the Banach space has the approximation property, but not in general.
Several chapters are devoted to results
in special Banach spaces, including Hilbert spaces,
One of the main motivations of this paper is the application to Zolotarev metrics and
their use in the contraction method. This is sketched in an appendix.
eBook
Concentration of Measure for the Analysis of Randomized Algorithms
Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern applications. This book presents a coherent and unified treatment of probabilistic techniques for obtaining high probability estimates on the performance of randomized algorithms. It covers the basic toolkit from the Chernoff–Hoeffding bounds to more sophisticated techniques like martingales and isoperimetric inequalities, as well as some recent developments like Talagrand's inequality, transportation cost inequalities and log-Sobolev inequalities. Along the way, variations on the basic theme are examined, such as Chernoff–Hoeffding bounds in dependent settings. The authors emphasise comparative study of the different methods, highlighting respective strengths and weaknesses in concrete example applications. The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, thus making the book accessible to computer scientists as well as probabilists and discrete mathematicians.
eBook
Robust Optimization
Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.
eBook
Properties of Coordinated Ih/Isub.1,Ih/Isub.2-Convex Functions of Two Variables Related to the Hermite - Hadamard - Fejer Type Inequalities
In this paper, we prove the Hermite–Hadamard–Fejér type inequalities for coordinated (h[sub.1] ,h[sub.2] )-convex functions on the rectangle from the plane R[sup.2] . Some generalizations of the Hermite–Hadamard-type inequalities of two variables are also obtained as a consequence. Some properties of two functionals which are connected with the coordinated (h[sub.1] ,h[sub.2] )-convex functions are provided as well. Finally, we give applications of the acquired results to special means of positive real numbers.
Journal Article