On the Complexity of Ordinal Clustering

Given a set of pairwise distances on a set of n points, constructing an edgeweighted tree whose leaves are these n points such that the tree distances would mimic the original distances under some criteria is a fundamental problem. One such criterion is to preserve the ordinal relation between the pairwise distances. The ordinal relation can be of the form of total order on the distances or it can be some partial order specified on the pairwise distances. We show that the problem of finding a weighted tree, if it exists, which would preserve the total order on pairwise distances is NP-hard. We also show the NP-hardness of the problem of finding a weighted tree which would preserve a particular kind of partial order called a triangle order, one of the most fundamental partial orders considered in computational biology.     

The extent of linkage disequilibrium in Arabidopsis thaliana.

Linkage disequilibrium (LD), the nonrandom occurrence of alleles in haplotypes, has long been of interest to population geneticists. Recently, the rapidly increasing availability of genomic polymorphism data has fueled interest in LD as a tool for fine-scale mapping, in particular for human disease loci. The chromosomal extent of LD is crucial in this context, because it determines how dense a map must be for associations to be detected and, conversely, limits how finely loci may be mapped. Arabidopsis thaliana is expected to harbor unusually extensive LD because of its high degree of selfing. Several polymorphism studies have found very strong LD within individual loci, but also evidence of some recombination. Here we investigate the pattern of LD on a genomic scale and show that in global samples, LD decays within approximately 1 cM, or 250 kb. We also show that LD in local populations may be much stronger than that of global populations, presumably as a result of founder events. The combination of a relatively high level of polymorphism and extensive haplotype structure bodes well for developing a genome-wide LD map in A. thaliana.     

Superoxide activates mitochondrial uncoupling proteins.

Uncoupling protein 1 (UCP1) diverts energy from ATP synthesis to thermogenesis in the mitochondria of brown adipose tissue by catalysing a regulated leak of protons across the inner membrane. The functions of its homologues, UCP2 and UCP3, in other tissues are debated. UCP2 and UCP3 are present at much lower abundance than UCP1, and the uncoupling with which they are associated is not significantly thermogenic. Mild uncoupling would, however, decrease the mitochondrial production of reactive oxygen species, which are important mediators of oxidative damage. Here we show that superoxide increases mitochondrial proton conductance through effects on UCP1, UCP2 and UCP3. Superoxide-induced uncoupling requires fatty acids and is inhibited by purine nucleotides. It correlates with the tissue expression of UCPs, appears in mitochondria from yeast expressing UCP1, and is absent in skeletal muscle mitochondria from UCP3 knockout mice. Our findings indicate that the interaction of superoxide with UCPs may be a mechanism for decreasing the concentrations of reactive oxygen species inside mitochondria.     

A survey of expressed genes in Caenorhabditis elegans.

As an adjunct to the genomic sequencing of Caenorhabditis elegans, we have investigated a representative cDNA library of 1,517 clones. A single sequence read has been obtained from the 5' end of each clone, allowing its characterization with respect to the public databases, and the clones are being localized on the genome map. The result is the identification of about 1,200 of the estimated 15,000 genes of C. elegans. More than 30% of the inferred protein sequences have significant similarity to existing sequences in the databases, providing a route towards in vivo analysis of known genes in the nematode. These clones also provide material for assessing the accuracy of predicted exons and splicing patterns and will lead to a more accurate estimate of the total number of genes in the organism than has hitherto been available.     

A new method of scenario analysis for strategic planning

We first present scenario analysis as a qualitative forecasting technique useful for strategic planning. Then we develop an overview of the two classes of methods for scenario analysis described in the literature. Based on both classes, a new method is developed which especially fits the needs of strategic planning. The method can be divided into three stages: 1. Determination of compatible scenarios, 2. Determination of scenario probabilities, and 3. Determination of main scenarios. An example is given to illustrate the method.