Geodesic grassfire for computing mixed-dimensional skeletons

Skeleton descriptors are commonly used to represent, understand and process shapes. While existing methods produce skeletons at a fixed dimension, such as surface or curve skeletons for a 3D object, often times objects are better described using skeleton geometry at a mixture of dimensions. In this paper we present a novel algorithm for computing mixed-dimensional skeletons. Our method is guided by a continuous analogue that extends the classical grassfire erosion. This analogue allows us to identify medial geometry at multiple dimensions, and to formulate a measure that captures how well an object part is described by medial geometry at a particular dimension. Guided by this analogue, we devise a discrete algorithm that computes a topology-preserving skeleton by iterative thinning. The algorithm is simple to implement, and produces robust skeletons that naturally capture shape components. Under Revie

Computational Geometry Teaching Tool

When students are taking Computational Geometry course which covers many geometry algorithms, most of them are difficult to follow because these algorithms are very abstract even if authors draw pictures to illustrate. In order to help students to get a better understanding of these algorithms, we decide to design Computational Geometry Teaching Tool. This tool is a web application that covers 8 geometry algorithms : Graham Scan, Quick Hull, Line Segment Intersection, Dual, Line Arrangement, Voronoi Diagram, Incremental Delaunay Triangulation and Kd Tree. First, this tool is developed by using JavaScript so that users don\u27t need to install any software or package. Furthermore, it breaks down the algorithm and go step by step so that students can move forward and backward on their own pace. Finally, all demos in this tool have same layout so that when students learn how to use the first one, they will know how to use others

Smooth Surface Reconstruction using Charts for Medical Data

We present a surface reconstruction technique that constructs a smooth analytic surface from scattered data. The technique is robust to noise and both poorly and non-uniformly sampled data, making it well-suited for use in medical applications. In addition, the surface can be parameterized in multiple ways, making it possible to represent additional data, such as electromagnetic potential, in a different (but related) coordinate system to the geometric one. The parameterization technique also supports consistent parameterizations of multiple data sets

Conformally prescribed scalar curvature on orbifolds

We study the prescribed scalar curvature problem in a conformal class on orbifolds with isolated singularities. We prove a compactness theorem in dimension $4$, and an existence theorem which holds in dimensions $n \geq 4$. This problem is more subtle than the manifold case since the positive mass theorem does not hold for ALE metrics in general. We also determine the $\rm{U}(2)$-invariant Leray-Schauder degree for a family of negative-mass orbifolds found by LeBrun.Comment: 39 page

Metabolism and function of hepatitis B virus cccDNA: Implications for the development of cccDNA-targeting antiviral therapeutics.

Persistent hepatitis B virus (HBV) infection relies on the stable maintenance and proper functioning of a nuclear episomal form of the viral genome called covalently closed circular (ccc) DNA. One of the major reasons for the failure of currently available antiviral therapeutics to achieve a cure of chronic HBV infection is their inability to eradicate or inactivate cccDNA. In this review article, we summarize our current understanding of cccDNA metabolism in hepatocytes and the modulation of cccDNA by host pathophysiological and immunological cues. Perspectives on the future investigation of cccDNA biology, as well as strategies and progress in therapeutic elimination and/or transcriptional silencing of cccDNA through rational design and phenotypic screenings, are also discussed. This article forms part of a symposium in Antiviral Research on “An unfinished story: from the discovery of the Australia antigen to the development of new curative therapies for hepatitis B.

Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpi\'nski gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpi\'{n}ski gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with $0 \leq$J$_b/$J$_a<1$, and an interesting crossover behavior between different phases at J$_b/$J$_a=1$ is unveiled, whose dynamics can be described by the J$_b/$J$_a$-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpi\'{n}ski gasket are obtained in both the $1/3$ plateau disordered phase and the $5/9$ plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpi\'{n}ski gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.Comment: 9 pages, 12 figure