Parking functions, labeled trees and DCJ sorting scenarios

In genome rearrangement theory, one of the elusive questions raised in recent years is the enumeration of rearrangement scenarios between two genomes. This problem is related to the uniform generation of rearrangement scenarios, and the derivation of tests of statistical significance of the properties of these scenarios. Here we give an exact formula for the number of double-cut-and-join (DCJ) rearrangement scenarios of co-tailed genomes. We also construct effective bijections between the set of scenarios that sort a cycle and well studied combinatorial objects such as parking functions and labeled trees.Comment: 12 pages, 3 figure

Genomic Distances under Deletions and Insertions

As more and more genomes are sequenced, evolutionary biologists are becoming increasingly interested in evolution at the level of whole genomes, in scenarios in which the genome evolves through insertions, deletions, and movements of genes along its chromosomes. In the mathematical model pioneered by Sankoff and others, a unichromosomal genome is represented by a signed permutation of a multiset of genes; Hannenhalli and Pevzner showed that the edit distance between two signed permutations of the same set can be computed in polynomial time when all operations are inversions. El-Mabrouk extended that result to allow deletions (or conversely, a limited form of insertions which forbids duplications). In this paper we extend El-Mabrouk's work to handle duplications as well as insertions and present an alternate framework for computing (near) minimal edit sequences involving insertions, deletions, and inversions. We derive an error bound for our polynomial-time distance computation under various assumptions and present preliminary experimental results that suggest that performance in practice may be excellent, within a few percent of the actual distance

On the DCJ Median Problem

As many whole genomes are sequenced, comparative genomics is moving from pairwise comparisons to multiway comparisons framed within a phylogenetic tree. A central problem in this process is the inference of data for internal nodes of the tree from data given at the leaves. When phrased as an optimization problem, this problem reduces to computing a median of three genomes under the operations (evolutionary changes) of interest. We focus on the universal rearrangement operation known as double-cut-and join (DCJ) and present three contributions to the DCJ median problem. First, we describe a new strategy to find so-called adequate subgraphs in the multiple breakpoint graph, using a seed genome. We show how to compute adequate subgraphs w.r.t. this seed genome using a network flow formulation. Second, we prove that the upper bound of the median distance computed from the triangle inequality is tight. Finally, we study the question of whether the median distance can reach its lower and upper bounds. We derive a necessary and sufficient condition for the median distance to reach its lower bound and a necessary condition for it to reach its upper bound and design algorithms to test for these conditions

Small Bowel Obstruction Due to Enterolith in a Patient with Diffuse Jejuno-Ileal Diverticulosis

We report an unusual case of small bowel obstruction caused by a large enterolith released from small bowel diverticulitis in a 81-year-old patient with occult massive Diffuse Jejuno-Ileal Diverticulosis (DJID). DJID is a rare condition whose symptoms are usually absent or non-specific. In most cases, the diagnosis of DJID is incidentally made or consecutive to secondary complications comprising obstruction, haemorrhage, diverticulitis and perforation. We shortly review the clinical and imaging features and complications of DJID

Biodiversity of soil biota and plants in abandoned arable fields and grasslands under restoration management

The currently widespread abandoning of agricultural land use in Western Europe offers new opportunities for ecological restoration and nature conservation. This is illustrated for abandoned arable fields and for permanent grasslands cut for hay after the cessation of fertilizer application. Although initiated by a sudden reduction of nutrient input to the system, the changing nutrient supply from the soil is considered to be the main driving force of succession. The soil nutrient supply is affected by soil organisms, both directly (root symbionts and herbivores) and indirectly (nutrient mineralization from dead organic matter). It is argued that because of the close association of changes in species diversity with changes in the functioning of ecosystems, biodiversity has to be studied in an ecosystem ecology context.