We construct continuous families of scattering manifolds with the same scattering phase. The manifolds are compactly supported metric perturbations of Euclidean R for n ≥ 8. The metric perturbation may have arbitrarily small support.

We show that the cyclic lamplighter group C2 oCn embeds into Hilbert space with distortion O ( √ log n ) . This matches the lower bound proved by Lee, Naor and Peres in [14], answering a question posed in that paper. Thus the Euclidean distortion of C2 o Cn is Θ ( √ log n ) . Our embedding is constructed explicitly in terms of the irreducible representations of the group. Since the optimal Eucl...

Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied fo...

We show that on Hilbert scheme of n points on C, the hyperkähler metric construsted by H. Nakajima via hyperkähler reduction is the Quasi-Asymptotically Locally Euclidean (QALE in short) metric constructed by D. Joyce.

Deformable models like snakes are a classical tool for image segmentation. Highly deformable models extend them with the ability to handle dynamic topological changes, and therefore to extract arbitrary complex shapes. However, the resolution of these models largely depends on the resolution of the image. As a consequence, their time and memory complexity increases at least as fast as the size ...

The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in Cγ domains, where γ(x) = bx log log(1/x)/ log log log(1/x), b small. A counterexample shows that this result is very nearly sharp.

As the essential content of intelligent animal husbandry, identifying each livestock is only way to achieve modern and refined scientific husbandry. This paper proposes a sheep face recognition method based on European spatial metrics realizes noncontact identity by training network using image samples in natural environment. The SheepBase data set was first proposed this process, which contain...