In this note we address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct self-dual L2 harmonic 2-forms on the space. Gibbons found a non-topological L2 harmonic form in the Taub-NUT metric, leading to Abelian instantons with continuous energy. We imitate his construction in the case of the Euclidean Schwarzschild manif...

In this paper we study the structure of extremals ν : [0, T ] → Rn of variational problems with large enough T , fixed end points and an integrand f from a complete metric space of functions. We will establish the turnpike property for a generic integrand f . Namely, we will show that for a generic integrand f , any small ε > 0 and an extremal ν : [0, T ] → Rn of the variational problem with la...

Textures are one of the basic features in visual searching and computational vision. In the literature, most of the attention has been focussed on the texture features with minimal consideration of the noise models. In this paper we investigated the problem of texture classification from a maximum likelihood perspective. We took into account the texture model, the noise distribution, and the in...

The finite-sample risk of the k nearest neighbor classifier that uses a weighted Lpmetric as a measure of class similarity is examined. For a family of classification problems with smooth distributions in Rn, an asymptotic expansion for the risk is obtained in decreasing fractional powers of the reference sample size. An analysis of the leading expansion coefficients reveals that the optimal we...

Most of today’s multi-core processors feature shared L2 caches. A major problem faced by such architectures is cache contention, where multiple cores compete for usage of the single shared L2 cache. Uncontrolled sharing leads to scenarios where one core evicts useful L2 cache content belonging to another core. To address this problem, we have implemented a software mechanism in the operating sy...

The assessment of how well one image matches another forms a critical component both of models of human visual processing and of many image analysis systems. Two of the most commonly used norms for quantifying image similarity are L1 and L2, which are specific instances of the Minkowski metric. However, there is often not a principled reason for selecting one norm over the other. One way to add...

In this paper we study notions of distance between behaviors of linear differential systems. We introduce four metrics on the space of all controllable behaviors which generalize existing metrics on the space of input-output systems represented by transfer matrices. Three of these are defined in terms of gaps between closed subspaces of the Hilbert space L2(R). In particular we generalize the ‘...

Embeddings of finite metric spaces into Euclidean space have been studied in several contexts: The local theory of Banach spaces, the design of approximation algorithms, and graph theory. The emphasis is usually on embeddings with the least possible distortion. That is, one seeks an embedding that minimizes the bi-Lipschitz constant of the mapping. This question has also been asked for embeddin...

We present a new metric between histograms such as SIFT descriptors and a linear time algorithm for its computation. It is common practice to use the L2 metric for comparing SIFT descriptors. This practice assumes that SIFT bins are aligned, an assumption which is often not correct due to quantization, distortion, occlusion etc. In this paper we present a new Earth Mover’s Distance (EMD) varian...

Recently, in [1], it has been proved that if B is an open unit ball in a Cartesian product l2 × l2 furnished with the lp-norm ‖ · ‖ and kB is the Kobayashi distance on B, then the metric space (B,kB) is locally uniformly convex in linear sense. Our construction of domains, which are locally uniformly convex in their Kobayashi distances, is based on the ideas from [1]. Such domains play an impor...