Metric (mathematics)

About: Metric (mathematics) is a research topic. Over the lifetime, 42617 publications have been published within this topic receiving 836571 citations. The topic is also known as: distance function & metric.

Energy conservation in heterogeneous server clusters

Abstract: The previous research on cluster-based servers has focused on homogeneous systems. However, real-life clusters are almost invariably heterogeneous in terms of the performance, capacity, and power consumption of their hardware components. In this paper, we argue that designing efficient servers for heterogeneous clusters requires defining an efficiency metric, modeling the different types of nodes with respect to the metric, and searching for request distributions that optimize the metric. To concretely illustrate this process, we design a cooperative Web server for a heterogeneous cluster that uses modeling and optimization to minimize the energy consumed per request. Our experimental results for a cluster comprised of traditional and blade nodes show that our server can consume 42% less energy than an energy-oblivious server, with only a negligible loss in throughput. The results also show that our server conserves 45% more energy than an energy-conscious server that was previously proposed for homogeneous clusters.

The application of machine learning to structural health monitoring

Abstract: In broad terms, there are two approaches to damage identification Model-driven methods establish a high-fidelity physical model of the structure, usually by finite element analysis, and then establish a comparison metric between the model and the measured data from the real structure If the model is for a system or structure in normal (ie undamaged) condition, any departures indicate that the structure has deviated from normal condition and damage is inferred Data-driven approaches also establish a model, but this is usually a statistical representation of the system, eg a probability density function of the normal condition Departures from normality are then signalled by measured data appearing in regions of very low density The algorithms that have been developed over the years for data-driven approaches are mainly drawn from the discipline of pattern recognition, or more broadly, machine learning The object of this paper is to illustrate the utility of the data-driven approach to damage identification by means of a number of case studies

Metric Spaces, Convexity and Nonpositive Curvature

Abstract: This is the second edition of a book which appeared in 2005. The new edition is an expanded and revised version. The book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function is convex. We have also included a systematic introduction to the theory of geodesics and related matters in metric spaces, as well as a detailed presentation of a few facets of convexity theory that are useful in the study of nonpositive curvature. The exposition starts from first principles and we give full proofs. Examples and applications are spread throughout the book, and they come from hyperbolic geometry, from the theory of Teichmuller spaces and from Hilbert geometry. At the end of each chapter there are historical notes and other notes on further developments.