1,957 research outputs found
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
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