Multichromosomal median and halving problems under different genomic distances

<p>Abstract</p> <p>Background</p> <p>Genome median and genome halving are combinatorial optimization problems that aim at reconstructing ancestral genomes as well as the evolutionary events leading from the ancestor to extant species. Exploring complexity issues is a first step towards devising efficient algorithms. The complexity of the median problem for unichromosomal genomes (permutations) has been settled for both the breakpoint distance and the reversal distance. Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances.</p> <p>Results</p> <p>We settle here the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halving problems in genomes with circular and linear chromosomes, showing that the multichromosomal problem is actually easier than the unichromosomal problem. Still other variants of these problems are NP-complete, including the DCJ double distance problem, previously mentioned as an open question. We list the remaining open problems.</p> <p>Conclusion</p> <p>This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.</p

Overlaps in dimensions of poverty

The Poverty and Social Exclusion Survey of Britain made it possible first time to explore poverty using three different measures applied at the same time on the same sample. The measures were: lacking socially perceived necessities; being subjectively poor and having a relatively low income. These approaches are all commonly used to identify the poor and to measure poverty but rarely if ever in combination. In this article we have found that there is little overlap in the group of people defined as poor by these dimensions. There are reasons for this lack of overlap, connected to the reliability and validity of the different measures. However the people who are defined as living in poverty by different measures of poverty are different. This inevitably means that the policy response to poverty will be different depending on which measure is employed. We have attempted to analyse overlap in two ways. First, by exploring the dimensions of poverty cumulatively, we have found that, the more dimensions people are poor on, the more they are unlike the non-poor and the poor on only one dimension, in their characteristics and in their social exclusion. Second, by treating particular dimensions as meriting more attention than others, we explored three permutations of this type and concluded that, while each permutation were more unlike the non-poor than those poor on a single dimension, they were not as unlike the non-poor as the cumulatively poor were. These results indicate that accumulation might be a better way of using overlapping measures of poverty than by giving priority to one dimension over another. The implication of the paper is that it is not safe to rely on one measure of poverty –the results obtained are just not reliable enough. Surveys, such as the Family Resources Survey or the European Community Household Panel, which are used to monitor the prevalence of poverty, need to be adapted to enable results to be triangulated – to incorporate a wider range of poverty measures

On testing the significance of sets of genes

This paper discusses the problem of identifying differentially expressed groups of genes from a microarray experiment. The groups of genes are externally defined, for example, sets of gene pathways derived from biological databases. Our starting point is the interesting Gene Set Enrichment Analysis (GSEA) procedure of Subramanian et al. [Proc. Natl. Acad. Sci. USA 102 (2005) 15545--15550]. We study the problem in some generality and propose two potential improvements to GSEA: the maxmean statistic for summarizing gene-sets, and restandardization for more accurate inferences. We discuss a variety of examples and extensions, including the use of gene-set scores for class predictions. We also describe a new R language package GSA that implements our ideas.Comment: Published at http://dx.doi.org/10.1214/07-AOAS101 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org