The Heat Asymptotics on Filtered Manifolds.

The short-time heat kernel expansion of elliptic operators provides a link between local and global features of classical geometries. For many geometric structures related to (non-)involutive distributions, the natural differential operators tend to be Rockland, hence hypoelliptic. In this paper, we establish a universal heat kernel expansion for formally self-adjoint non-negative Rockland differential operators on general closed filtered manifolds.

Regression analysis of group testing samples.

This paper develops a general regression methodology that relates the group testing responses to individual covariate information. It can be used to study samples from a group testing procedure and to deal with a wide range of regression problems. A detailed illustration of the methodology is provided for a group testing procedure proposed by Gastwirth and Hammick.

Recognizing circular decomposable metrics.

Circular decomposable metrics (CDMs) have been used in phylogenetic studies. The fastest algorithm for recognizing a CDM runs in time O(n5), given an n x n table of pairwise distances. We give an O(n2) time algorithm for this problem.