We prove some results on the farthest points in convex metric spaces and in linear metric spaces. The continuity of the farthest point map and characterization of strictly convex linear metric spaces in terms of farthest points are also discussed.

Regular maps on non-orientable surfaces are considered with particular reference to the properties of inner reflectors, corresponding to symmetries of the 2-fold smooth orientable covering which project onto local reflections of the map itself. An example is given where no inner reflector is induced by an involution, and the existence of such involutions is related to questions of symmetry of c...

In this paper, we present a new single-channel noise reduction method that integrates compensation and soft masking into the same statistical model assumptions for noise-robust speech recognition. By utilizing a Gaussian mixture model(GMM) as a pre-knowledge of speech and added noise signals, the proposed method can effectively restore clean speech spectra and separate out ambient noises from a...

Many geometry processing applications are sensitive to noises and sharp features. Although there are a number of works on detecting noises and sharp features in the literature, they are heuristic. On the one hand, traditional denoising methods use filtering operators to remove the noises, however, may blur sharp features and shrink the object. On the other hand, noises make detection of feature...

In this paper, we propose a generic framework for intersubject non-linear registration of 4D time-series images. In this framework, spatio-temporal registration is defined by mapping trajectories of physical points as opposed to spatial registration that solely aims at mapping homologous points. First, we determine the trajectories we want to register in each sequence using a motion tracking al...

Ultra-cold atoms provide ideal platforms for interferometry. The macroscopic matter-wave property of ultra-cold leads to large coherent length and long time, which enable high accuracy sensitivity measurement. Here, we review our efforts improve the performance interferometer. We demonstrate a shortcut method manipulating in an optical lattice. Compared with traditional ones, this can reduce ma...