Some combinatorial arrays related to the Lotka-Volterra system

The purpose of this paper is to investigate the connection between the Lotka-Volterra system and combinatorics. We study several context-free grammars associated with the Lotka-Volterra system. Some combinatorial arrays, involving the Stirling numbers of the second kind and Eulerian numbers, are generated by these context-free grammars. In particular, we present grammatical characterization of some statistics on cyclically ordered partitions.Comment: 15 page

Sensitivity analysis of permeability parameters of bovine nucleus pulposus obtained through inverse fitting of the nonlinear biphasic equation : effect of sampling strategy

Permeability controls the fluid flow into and out of soft tissue, and plays an important role in maintaining the health status of such tissue. Accurate determination of the parameters that define permeability is important for the interpretation of models that incorporate such processes. This paper describes the determination of strain-dependent permeability parameters from the nonlinear biphasic equation from experimental data of different sampling frequencies using the Nelder–Mead simplex method. The ability of this method to determine the global optimum was assessed by constructing the whole manifold arising from possible parameter combinations. Many parameter combinations yielded similar fits with the Nelder–Mead algorithm able to identify the global maximum within the resolution of the manifold. Furthermore, the sampling strategy affected the optimum values of the permeability parameters. Therefore, permeability parameter estimations arising from inverse methods should be utilised with the knowledge that they come with large confidence intervals

Rapid identification of mutations in GJC2 in primary lymphoedema using whole exome sequencing combined with linkage analysis with delineation of the phenotype.

Background: Primary lymphoedema describes a chronic, frequently progressive, failure of lymphatic drainage. This disorder is frequently genetic in origin, and a multigenerational family in which eight individuals developed postnatal lymphoedema of all four limbs was ascertained from the joint Lymphoedema/Genetic clinic at St George's Hospital. Methods: Linkage analysis was used to determine a locus, and exome sequencing was employed to look for causative variants. Results: Linkage analysis revealed cosegregation of a 16.1 Mb haplotype on chromosome 1q42 that contained 173 known or predicted genes. Whole exome sequencing in a single affected individual was undertaken, and the search for the causative variant was focused to within the linkage interval. This approach revealed two novel non-synonymous single nucleotide substitutions within the chromosome 1 locus, in NVL and GJC2. NVL and GJC2 were sequenced in an additional cohort of individuals with a similar phenotype and non-synonymous variants were found in GJC2 in four additional families. Conclusion: This report demonstrates the power of exome sequencing efficiently applied to a traditional positional cloning pipeline in disease gene discovery, and suggests that the phenotype produced by GJC2 mutations is predominantly one of 4 limb lymphoedema