Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure

Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transformation to GFGCC and GSGCC are studied.Comment: 32 pages, 6 figure

Determinations of upper critical field in continuous Ginzburg-Landau model

Novel procedures to determine the upper critical field $B_{c2}$ have been proposed within a continuous Ginzburg-Landau model. Unlike conventional methods, where $B_{c2}$ is obtained through the determination of the smallest eigenvalue of an appropriate eigen equation, the square of the magnetic field is treated as eigenvalue problems so that the upper critical field can be directly deduced. The calculated $B_{c2}$ from the two procedures are consistent with each other and in reasonably good agreement with existing theories and experiments. The profile of the order parameter associated with $B_{c2}$ is found to be Gaussian-like, further validating the methodology proposed. The convergences of the two procedures are also studied.Comment: Revtex4, 8 pages, 4 figures, references modified, figures and table embedde

Tracking in a space variant active vision system

Without the ability to foveate on and maintain foveation, active vision for applications such as surveillance, object recognition and object tracking are difficult to build. Although foveation in cartesian coordinates is being actively pursued by many, multi-resolution high accuracy foveation in log polar space has not been given much attention. This paper addresses the use of foveation to track a single object as well as multiple objects for a simulated space variant active vision system. Complex logarithmic mapping is chosen firstly because it provides high resolution and wide angle viewing. Secondly, the spatially variant structure of log polar space leads to an object increasing in size as it moves towards the fovea. This is important as we know which object is closer to the fovea at any instant in time.<br /

The Gauge Hierarchy Problem and Higher Dimensional Gauge Theories

We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter fields, and a way to fix it dynamically is presented. We also point out that on the simply-connected space $S^2$ even the finite mass correction vanishes.Comment: LaTeX2e. 12 pages, 3 Postscript figures; Added references, some comment