We obtain KSS, Strichartz and certain weighted Strichartz estimates for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metri...

In order to efficiently utilize limited radio resources, resource allocation schemes in OFDMA-based wireless networks have gained intensive attention recently. Instead of improving the throughput performance, the utility is adopted as the metric for resource allocation, which provides reasonable methods to build up the relationship between user experience and various quality-of-service (QoS) me...

Nearest Neighbour (NN) classification is a widely-used, effective method for both binary and multi-class problems. It relies on the assumption that class conditional probabilities are locally constant. However, this assumption becomes invalid in high dimensions, and severe bias can be introduced, which degrades the performance of the method. The employment of a locally adaptive distance metric ...

Two problems in the search of metric characteristics on weighted undirected graphs with non-negative edge weights are being considered. The first problem: a weighted undirected graph with non-negative edge weight is given. The radius, diameter and at least one center and one pair of peripheral vertices of the graph are to be found. In the second problem we have additionally calculated the dista...

Learning a distance metric from training samples is often a crucial step in machine learning and pattern recognition. Locality, compactness and consistency are considered as the key principles in distance metric learning. However, the existing metric learning methods just consider one or two of them. In this paper, we develop a multi-granularity distance learning technique. First, a new index, ...

A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric. Learning such a metric is a hot topic since more than ten years now, and a number of methods have been proposed to efficiently learn it. However, the nature ...

Trees with positively-weighted edges induce a natural metric on any subset of vertices, however not every metric is representable in this way. A problem arising in areas of classification, particularly in evolutionary biology, is how to approximate an arbitrary distance function by such a tree metric, and thereby estimate the underlying tree that generated the data. Such transformations, from d...

For example, IR with the regular Euclidean distance is a metric space. It is usually of interest to consider the finite case, where X is an n-point set. Then, the function d can be specified by ( n 2 ) real numbers. Alternatively, one can think about (X,d) is a weighted complete graph, where we specify positive weights on the edges, and the resulting weights on the edges comply with the triangl...

In this paper, we give a complete characterization of the class of weighted maximum multiflow problems whose dual polyhedra have bounded fractionality. This is a common generalization of two fundamental results of Karzanov. The first is a characterization of commodity graphs H for which the dual of maximum multiflow problem with respect to H has bounded fractionality, and the second is a charac...