Cluster Analysis of Gene Expression Data

The expression levels of many thousands of genes can be measured simultaneously by DNA microarrays (chips). This novel experimental tool has revolutionized research in molecular biology and generated considerable excitement. A typical experiment uses a few tens of such chips, each dedicated to a single sample—such as tissue extracted from a particular tumor. The results of such an experiment contain several hundred thousand numbers, that come in the form of a table, of several thousand rows (one for each gene) and 50–100 columns (one for each sample). We developed a clustering methodology to mine such data. In this review I provide a very basic introduction to the subject, aimed at a physics audience with no prior knowledge of either gene expression or clustering methods. I explain what genes are, what is gene expression and how it is measured by DNA chips. Next I explain what is meant by clustering and how we analyze the massive amounts of data from such experiments, and present results obtained from analysis of data from colon cancer, brain tumors and breast cancer.     

Potts ferromagnets on coexpressed gene networks: identifying maximally stable partitions

Clustering gene expression data by exploiting phase transitions in granular ferromagnets requires transforming the data to a granular substrate. We present a method using the recently introduced homogeneity order parameter Lambda [H. Agrawal, Phys. Rev. Lett. 89, 268702 (2002)]] for optimizing the parameter controlling the "granularity" and thus the stability of partitions. The model substrates obtained for gene expression data have a highly granular structure. We explore properties of phase transition in high q ferromagnetic Potts models on these substrates and show that the maximum of the width of superparamagnetic domain, corresponding to maximally stable partitions, coincides with the minimum of Lambda.     

An Exact Solution for the Optical Absorbance of Thin Films

The electric and magnetic fields within optical thin films are obtained exactly in closed form as solutions of a system of difference equations presented by Berning and utilized by Dill, Neureuther, Tuttle, and Walker in their sample program for modeling optical lithography. The solution allows an explicit closed form expression for the absorbance.     

Resonance in a Quantum Chain

A resonance of a magnetic impurity with a quantum spin-chain is studied. A Fresnel diffraction pattern is found.     

Spectral Dependence of Rise Time in Gas Filled Phototubes: Implications concerning Possible Miniaturization of Gas Discharge Detectors of Electromagnetic Radiation

The rise time of a gas-filled photodiode at blue-green wavelengths is found to be less than that at red wavelengths. As photoionization of excited atoms in such devices increases response to light of decreasing wavelength over that provided by the photocathode, spectral differences in rise time are also attributed to the same mechanism. It is suggested that these phenomena decrease parasitic inductance of the tube. This implies that rise times in glow discharge detectors of EM radiation can be improved through miniaturization of inter-electrode spacing.     

Duality relations and equivalences for models with O(N) and cubic symmetry

Formal expression for high-temperature series are derived for models with O(N) and cubic symmetry, with a special form of nearest neighbor interactions on the honeycomb lattice. By deriving low-temperature series for a class of generalized solid-on-solid and cubic models, a duality relation is established. Equivalences between cubic and SOS type models are also found. In the large-N limit, the series reduce to those of the hard hexagon model.     

Ising Chain with Random Magnetic Moments

The Ising chain with random magnetic moments is discussed, and the thermodynamic functions are computed.     

Ising model with variable bond strength

The partition function of the two-dimensional Ising model with variable bond strength along one dimension is computed exactly.     

On the interdependence of van der waals and double layer forces

We study the effect of coupling the electrostatic and low frequency electrodynamic responses of colloidal systems. Exact results are reported for the van der Waals free energy of interaction of non-uniform electrolyte across planar dielectric and planar charged dielectric across non-uniform electrolyte. In both cases, the results depend on the double layer repulsion.     

Neural networks: A biased overview

An overview of recent activity in the field of neural networks is presented. The long-range aim of this research is to understand how the brain works. First some of the problems are stated and terminology defined; then an attempt is made to explain why physicists are drawn to the field, and their main potential contribution. In particular, in recent years some interesting models have been introduced by physicists. A small subset of these models is described, with particular emphasis on those that are analytically soluble. Finally a brief review of the history and recent developments of single- and multilayer perceptrons is given, bringing the situation up to date regarding the central immediate problem of the field: search for a learning algorithm that has an associated convergence theorem.