Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps

We give three families of parabolic rational maps and show that every Cantor set of circles as the Julia set of a non-hyperbolic rational map must be quasisymmetrically equivalent to the Julia set of one map in these families for suitable parameters. Combining a result obtained before, we give a complete classification of the Cantor circles Julia sets in the sense of quasisymmetric equivalence. Moreover, we study the regularity of the components of the Cantor circles Julia sets and establish a sufficient and necessary condition when a component of a Cantor circles Julia set is a quasicircle.Comment: 39 pages, 10 figures and 1 table, to appear in Discrete and Continous Dynamical Systems-

Quality Classified Image Analysis with Application to Face Detection and Recognition

Motion blur, out of focus, insufficient spatial resolution, lossy compression and many other factors can all cause an image to have poor quality. However, image quality is a largely ignored issue in traditional pattern recognition literature. In this paper, we use face detection and recognition as case studies to show that image quality is an essential factor which will affect the performances of traditional algorithms. We demonstrated that it is not the image quality itself that is the most important, but rather the quality of the images in the training set should have similar quality as those in the testing set. To handle real-world application scenarios where images with different kinds and severities of degradation can be presented to the system, we have developed a quality classified image analysis framework to deal with images of mixed qualities adaptively. We use deep neural networks first to classify images based on their quality classes and then design a separate face detector and recognizer for images in each quality class. We will present experimental results to show that our quality classified framework can accurately classify images based on the type and severity of image degradations and can significantly boost the performances of state-of-the-art face detector and recognizer in dealing with image datasets containing mixed quality images.Comment: 6 page

On the Quantum Theory of Massless Spin-3/2 Field in Minkowski Spacetime

From the modern viewpoint and by the geometric method, this paper provides a concise foundation for the quantum theory of massless spin-3/2 field in Minkowski spacetime, which includes both the one-particle's quantum mechanics and the many-particle's quantum field theory. The explicit result presented here is useful for the investigation of spin-3/2 field in various circumstances such as supergravity, twistor programme, Casimir effect, and quantum inequality.Comment: 11 pages, typos corrected, accepted for publication in Int.J.Geom. Methods Mod. Phy