The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Recursive partitioning for tumor classification with gene expression microarray data

Precise classification of tumors is critically important for cancer diagnosis and treatment. It is also a scientifically challenging task. Recently, efforts have been made to use gene expression profiles to improve the precision of classification, with limited success. Using a published data set for purposes of comparison, we introduce a methodology based on classification trees and demonstrate that it is significantly more accurate for discriminating among distinct colon cancer tissues than other statistical approaches used heretofore. In addition, competing classification trees are displayed, which suggest that different genes may coregulate colon cancers.