A crucial problem in exploratory analysis of data is that it is difficult for computational methods to focus on interesting aspects of data. Traditional methods of unsupervised learning cannot differentiate between interesting and noninteresting variation, and hence may model, visualize, or cluster parts of data that are not interesting to the analyst. This wastes the computational power of the...

We introduce a class of metric perceptual distances between textures. The first metric is sensitive to both rotation and scale differences, and provides a basis for two other metrics, one invariant to rotation, and the other invariant to both rotation and scale. Our metrics are based on Earth Mover’s Distance computations on log-polar distributions of spatial frequency computed from Gabor filte...

Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic variant of the Hennessy-Milner logic. Our approach is based on the novel notions of mimicking formulae and distance between formulae. The former are a weak versi...

The global holomorphic α-invariant introduced by Tian is closely related to the existence of Kähler-Einstein metrics. We apply the result of Tian, Yau and Zelditch on polarized Kähler metrics to approximate plurisubharmonic functions and compute the α-invariant on CP 2#nCP 2 for n = 1, 2, 3.

In this paper, we compute Riemannian metrics on the Siegel-Jacobi space which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.