In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is

We present the recent work on the noncommutative Fourier transform for subfactors and locally compact quantum groups, a Survey.We give a short introduction to subfactors and locally compact quantum groups and their properties;the Hausdorff-Young inequality and its extremal functions;Young's inequality and its extremal pairs;uncertainty principles and its minimizers;a noncommutative sum set theorem.

We consider an electron with an anomalous magnetic moment, <i>g</i> &gt; &gt; 2, confined to a plane and interacting with a nonhomogeneous magnetic field <i>B</i>, and investigate the corresponding Pauli Hamiltonian. We prove a lower bound on the number of bound states for the case when <i>B</i> is of a compact support and the related flux is <i>N</i> + <i></i>, <i></i>(0, 1]. In particular, there are at least <i>N</i> + 1 bound states if <i>B</i> does not change sign. We also consider the situation where the magnetic field is due to a localized rotationally symmetric electric current vortex in the plane. In this case the flux is zero; there is a pair of bound states for a weak coupling, and higher orbital-momentum spin-down states appearing as the current strength increases.

We propose a graph cut based global minimization method for image segmentation by representing the segmentation label function with a series of nested binary super-level set functions. This representation enables us to use K-1 binary functions to partition any images into K phases. Both continuous and discretized formulations will be treated. For the discrete model, we propose a new graph cut algorithm which is faster than the existing graph cut methods to obtain the exact global solution. In the continuous case, we further improve the segmentation accuracy using a number of techniques that are unique to the continuous segmentation models. With the convex relaxation and the dual method, the related continuous dual model is convex and we can mathematically show that the global minimization can be achieved. The corresponding continuous max-flow algorithms are easy and stable. Experimental results

We discuss discuss spectral and scattering properties of a particle confined to a straight Dirichlet tube in R''with a family of point interactions.