Qualitative differential games with two targets

So-called differential games of kind (qualitative games) were considered involving two or more players each of whom possesses a target toward which he wished to steer the response of a dynamical system that was under the control of all players. Sufficient conditions were derived, which assure termination on a particular player's target. In general, these conditions were constructive in that they permited construction of a winning (terminating) strategy for a player. The theory is illustrated by a pursuit-evasion problem

Coupled Two-Way Clustering Analysis of Gene Microarray Data

We present a novel coupled two-way clustering approach to gene microarray data analysis. The main idea is to identify subsets of the genes and samples, such that when one of these is used to cluster the other, stable and significant partitions emerge. The search for such subsets is a computationally complex task: we present an algorithm, based on iterative clustering, which performs such a search. This analysis is especially suitable for gene microarray data, where the contributions of a variety of biological mechanisms to the gene expression levels are entangled in a large body of experimental data. The method was applied to two gene microarray data sets, on colon cancer and leukemia. By identifying relevant subsets of the data and focusing on them we were able to discover partitions and correlations that were masked and hidden when the full dataset was used in the analysis. Some of these partitions have clear biological interpretation; others can serve to identify possible directions for future research

Super-paramagnetic clustering of yeast gene expression profiles

High-density DNA arrays, used to monitor gene expression at a genomic scale, have produced vast amounts of information which require the development of efficient computational methods to analyze them. The important first step is to extract the fundamental patterns of gene expression inherent in the data. This paper describes the application of a novel clustering algorithm, Super-Paramagnetic Clustering (SPC) to analysis of gene expression profiles that were generated recently during a study of the yeast cell cycle. SPC was used to organize genes into biologically relevant clusters that are suggestive for their co-regulation. Some of the advantages of SPC are its robustness against noise and initialization, a clear signature of cluster formation and splitting, and an unsupervised self-organized determination of the number of clusters at each resolution. Our analysis revealed interesting correlated behavior of several groups of genes which has not been previously identified

Statistical Mechanics of Semi-Supervised Clustering in Sparse Graphs

We theoretically study semi-supervised clustering in sparse graphs in the presence of pairwise constraints on the cluster assignments of nodes. We focus on bi-cluster graphs, and study the impact of semi-supervision for varying constraint density and overlap between the clusters. Recent results for unsupervised clustering in sparse graphs indicate that there is a critical ratio of within-cluster and between-cluster connectivities below which clusters cannot be recovered with better than random accuracy. The goal of this paper is to examine the impact of pairwise constraints on the clustering accuracy. Our results suggests that the addition of constraints does not provide automatic improvement over the unsupervised case. When the density of the constraints is sufficiently small, their only impact is to shift the detection threshold while preserving the criticality. Conversely, if the density of (hard) constraints is above the percolation threshold, the criticality is suppressed and the detection threshold disappears.Comment: 8 pages, 4 figure