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.

Metric regularity, tangent sets, and second-order optimality conditions

Abstract: A strong regularity theorem is proved, which shows that the usual constraint qualification conditions ensuring the regularity of the set-valued maps expressing feasibility in optimization problems, are in fact minimal assumptions. These results are then used to derive calculus rules for second-order tangent sets, allowing us in turn to obtain a second-order (Lagrangian) necessary condition for optimality which completes the usual one of positive semidefiniteness on the Hessian of the Lagrangian function.

Channel quality estimation and rate adaptation for cellular mobile radio

Abstract: We propose a technique to measure channel quality in terms of signal-to-interference plus noise ratio (SINR) for the transmission of signals over fading channels The Euclidean distance (ED) metric, associated with the decoded information sequence or a suitable modification thereof, is used as a channel quality measure Simulations show that the filtered or averaged metric is a reliable channel quality measure which remains consistent across different coded modulation schemes and at different mobile speeds The average scaled ED metric can be mapped to the SINR per symbol We propose the use of this SINR estimate for data rate adaptation, in addition to mobile assisted handoff (MAHO) and power control We particularly focus on data rate adaptation and propose a set of coded modulation schemes which utilize the SINR estimate to adapt between modulations, thus improving the data throughput Simulation results show that the proposed metric works well across the entire range of Dopplers to provide near-optimal rate adaptation to average SINR This method of adaptation averages out short-term variations due to Rayleigh fading and adapts to the long-term effects such as shadowing At low Dopplers, the metric can track Rayleigh fading and match the rate to a short-term average of the SINR, thus further increasing throughput

Another look at forecast-accuracy metrics for intermittent demand

Abstract: Some traditional measurements of forecast accuracy are unsuitable for intermittent demand data because they can give infinite or undefined values. Rob Hyndman summarizes these forecast accuracy metrics and explains their potential failings. He also introduces a new metric-the mean absolute scaled error (MASE)-which is more appropriate for intermittent-demand data. More generally, he believes that the MASE should become the standard metric for comparing forecast accuracy across multiple time series. Copyright International Institute of Forecasters, 2006

Quadric-based polygonal surface simplification

Abstract: Many applications in computer graphics and related fields can benefit from automatic simplification of complex polygonal surface models. Applications are often confronted with either very densely over-sampled surfaces or models too complex for the limited available hardware capacity. An effective algorithm for rapidly producing high-quality approximations of the original model is a valuable tool for managing data complexity. In this dissertation, I present my simplification algorithm, based on iterative vertex pair contraction. This technique provides an effective compromise between the fastest algorithms, which often produce poor quality results, and the highest-quality algorithms, which are generally very slow. For example, a 1000 face approximation of a 100,000 face model can be produced in about 10 seconds on a PentiumPro 200. The algorithm can simplify both the geometry and topology of manifold as well as non-manifold surfaces. In addition to producing single approximations, my algorithm can also be used to generate multiresolution representations such as progressive meshes and vertex hierarchies for view-dependent refinement. The foundation of my simplification algorithm, is the quadric error metric which I have developed. It provides a useful and economical characterization of local surface shape, and I have proven a direct mathematical connection between the quadric metric and surface curvature. A generalized form of this metric can accommodate surfaces with material properties, such as RGB color or texture coordinates. I have also developed a closely related technique for constructing a hierarchy of well-defined surface regions composed of disjoint sets of faces. This algorithm involves applying a dual form of my simplification algorithm to the dual graph of the input surface. The resulting structure is a hierarchy of face clusters which is an effective multiresolution representation for applications such as radiosity.