In this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duality is rather special to 4-dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics. The book reviews some basic geometry, but is is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures.

This book examines different aspects of network security metrics and their application to enterprise networks. One of the most pertinent issues in securing mission-critical computing networks is the lack of effective security metrics which this book discusses in detail. Since “you cannot improve what you cannot measure”, a network security metric is essential to evaluating the relative effectiveness of potential network security solutions. The authors start by examining the limitations of existing solutions and standards on security metrics, such as CVSS and attack surface, which typically focus on known vulnerabilities in individual software products or systems. The first few chapters of this book describe different approaches to fusing individual metric values obtained from CVSS scores into an overall measure of network security using attack graphs. Since CVSS scores are only available for previously known vulnerabilities, such approaches do not consider the threat of unknown attacks exploiting the so-called zero day vulnerabilities. Therefore, several chapters of this book are dedicated to develop network security metrics especially designed for dealing with zero day attacks where the challenge is that little or no prior knowledge is available about the exploited vulnerabilities, and thus most existing methodologies for designing security metrics are no longer effective. Finally, the authors examine several issues on the application of network security metrics at the enterprise level. Specifically, a chapter presents a suite of security metrics organized along several dimensions for measuring and visualizing different aspects of the enterprise cyber security risk, and the last chapter presents a novel metric for measuring the operational effectiveness of the cyber security operations center (CSOC). Security researchers who work on network security or security analytics related areas seeking new research topics, as well as security practitioners including network administrators and security architects who are looking for state of the art approaches to hardening their networks, will find this book helpful as a reference. Advanced-level students studying computer science and engineering will find this book useful as a secondary text.

This monograph studies the problem of characterizing canonical metrics on Hermitian locally symmetric manifolds X of non-compact/compact types in terms of curvature conditions. The proofs of these metric rigidity theorems are applied to the study of holomorphic mappings between manifolds X of the same type. Moreover, a dual version of the generalized Frankel Conjecture on characterizing compact K„hler manifolds are also formulated.

This volume contains papers presented at the 27th Taniguchi International Symposium, held in Sanda, Japan - focusing on the study of moduli spaces of various geometric objects such as Einstein metrics, conformal structures, and Yang-Mills connections from algebraic and analytic points of view.;Written by over 15 authorities from around the world, Einstein Metrics and Yang-Mills Connections...: discusses current topics in Kaehler geometry, including Kaehler-Einstein metrics, Hermitian-Einstein connections and a new Kaehler version of Kawamata-Viehweg's vanishing theorem; explores algebraic geometric treatments of holomorphic vector bundles on curves and surfaces; addresses nonlinear problems related to Mong-Ampere and Yamabe-type equations as well as nonlinear equations in mathematical physics; and covers interdisciplinary topics such as twistor theory, magnetic monopoles, KP-equations, Einstein and Gibbons-Hawking metrics, and supercommutative algebras of superdifferential operators.;Providing a wide array of original research articles not published elsewhere Einstein Metrics and Yang-Mills Connections is for research mathematicians, including topologists and differential and algebraic geometers, theoretical physicists, and graudate-level students in these disciplines.

Bundles, connections, metrics and curvature are the lingua franca of modern differential geometry and theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, this book would suit a one-semester course on the subject of bundles and the associated geometry.

Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduate-level introduction to differential geometry of complex Finsler metrics. After reviewing real Finsler geometry stressing global results, complex Finsler geometry is presented introducing connections, Kählerianity, geodesics, curvature. Finally global geometry and complex Monge-Ampère equations are discussed for Finsler manifolds with constant holomorphic curvature, which are important in geometric function theory. Following E. Cartan, S.S. Chern and S. Kobayashi, the global approach carries the full strength of hermitian geometry of vector bundles avoiding cumbersome computations, and thus fosters applications in other fields.

As network science and technology continues to gain popularity, it becomes imperative to develop procedures to examine emergent network domains, as well as classical networks, to help ensure their overall optimization. Centrality Metrics for Complex Network Analysis: Emerging Research and Opportunities is a pivotal reference source for the latest research findings on centrality metrics and their broader applications for different categories of networks including wireless sensor networks, curriculum networks, social networks etc. Featuring extensive coverage on relevant areas, such as complex network graphs, node centrality metrics, and mobile sensor networks, this publication is an ideal resource for students, faculty, industry practitioners, and business professionals interested in theoretical concepts and current developments in network domains.