A martingale approach to minimal surfaces

Digital cohomology groups of certain minimal surfaces

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

Minimal Surfaces: A Three Dimensional Segmentation Approach

A novel geometric approach for three dimensional object segmentation is presented. The scheme is based on geometric deformable surfaces moving towards the objects to be detected. We show that this model is equivalent to the computation of surfaces of minimal area (local minimal surfaces) in a Riemannian space. This space is deened by a metric induced from the three dimensional image in which th...

On the Minimal Martingale Measureand

A Martingale Approach to Regenerative Simulation

The standard regenerative method for estimating steady-state parameters is extended to permit cycles which begin and end in diierent states. This result is established using the Dynkin martingale and a related solution to Poisson's equation. We compare the variance constant which appears in the associated central limit theorem with that arising from cycles that begin and end in the same state. ...

A Martingale Approach to Scan Statistics

Scan statistics are commonly used in biology, medicine, engineering and other fields where interest is in the probability of observing clusters of events in a window at an unknown location. Due to the dependent nature of the number of events in a large number of overlapping window locations, even approximate solutions for the simplest scan statistics may require elaborate calculations. We propo...