Most known examples of isospectral manifolds can be constructed through variations of Sunada’s method or Gordon’s torus method. In this paper we explore these two techniques in the framework of equivariant isospectrality. We begin by establishing an equivariant version of Sunada’s technique and then we observe that many examples arising from the torus method are equivariantly isospectral. Using...

In order to improve the real-time quality and precision of object tracking, an algrithm using distance metric learning is studied. First, instances are selected around the objects, and features vectors are extracted by using the compress sensing theory. Second, distance metric is trained according to the random projection theory. Finally, the Mahalanobis distance of target object and possible i...

The knowledge of the metric entropy of precompact subsets of operators on finite dimensional Euclidean space is important in particular in the probabilistic methods developped by E. D. Gluskin and S. Szarek for constructing certain random Banach spaces. We give a new argument for estimating the metric entropy of some subsets such as the Grassmann manifold equipped with natural metrics. Here, th...

Abstract. Sticky particle solutions to the one-dimensional pressureless gas dynamics equations can be constructed by a suitable metric projection onto the cone of monotone maps, as was shown in recent work by Natile and Savaré. Their proof uses a discrete particle approximation and stability properties for first order differential inclusions. Here we give a more direct proof that relies on a re...

A stochastic flow is constructed on a frame bundle adapted to a Riemannian foliation on a compact manifold. The generator A of the resulting transition semigroup is shown to preserve the basic functions and forms, and there is an essentially unique strictly positive smooth function φ satisfying Aφ = 0. This function is used to perturb the metric, and an application of the ergodic theorem shows ...

For any hyperbolic complex X and a ∈ X we construct a visual metric ď = ďa on ∂X that makes the Isom(X)-action on ∂X bi-Lipschitz, Möbius, symmetric and conformal. We define a stereographic projection of ďa and show that it is a metric conformally equivalent to ďa. We also introduce a notion of hyperbolic dimension for hyperbolic spaces with group actions. Problems related to hyperbolic dimensi...

In this paper, we first detail the geodesic matching of images which consists in minimizing an energy resulting from a Riemannian metric on a manifold of images, which itself comes from the projection of a Riemannian metric on a deformation group onto the image manifold. We will then present an energy minimization technique based on a wavelet analysis of the deformation and finally some applica...

Most metric learning methods are characterized by diverse loss functions and projection methods, which naturally begs the question: is there a wider framework that can generalize many of these methods? In addition, ever persistent issues are those of scalability to large data sets and the question of kernelizability. We propose a unified approach to Mahalanobis metric learning: an online regula...

A study is made of differentiability of the metric projection P onto a closed convex subset K of a Hubert space H. When K has nonempty interior, the Gateaux or Fréchet smoothness of its boundary can be related with some precision to Gateaux or Fréchet differentiability properties of P. For instance, combining results in §3 with earlier work of R. D. Holmes shows that K has a C2 boundary if and ...

The differentiability properties of the metric projection Pc on a closed convex set C in Hilbert space are characterized in terms of the smoothness type of the boundary of C. Our approach is based on using variational type second derivatives as a sufficiently flexible tool to describe the boundary struc ture of the set C with regard to the differentiability of Pc. We extend results by R.B. Holm...