Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.

Real-time multiplex PCR assays for reliable detection of Clostridium perfringens toxin genes in animal isolates

Typing of Clostridium perfringens strains by PCR-based determination of toxin genes proved to be a reliable method for diagnosis of enterotoxaemia in various animal species. We report the establishment and validation of three real-time fluorogenic (TaqMan) multiplex PCRs for the detection of C. perfringens alpha-, beta-, beta2-, epsilon-, entero- and iota-toxin genes. The composition of the PCRs was chosen with regard to robustness of the assays and in order to increase sensitivity compared to the conventional simplex PCRs. The combination of probe dyes selected for the real-time assays (FAM/TAMRA, Cy-5/BHQ-2 and VIC/TAMRA) as well as the designation of the chromosome-borne alpha-toxin as internal positive control allowed the creation of highly specific and sensitive, as well as time and cost effective PCRs. One hundred and three strains of C. perfringens isolated in Switzerland derived from clinical or suspected cases of enterotoxaemia in 10 different animal species were tested. The toxin genotypes were in agreement in both the conventional PCRs and the newly designed multiplex PCRs. Furthermore, the real-time PCR carried out as simplex allows to quantitate the copy numbers of plasmid-borne toxin genes in relation to the chromosomally located alpha-toxin gene.

Comparison of multiplex ligation-dependent probe amplification and real-time PCR accuracy for gene copy number quantification using the beta-defensin locus

The reliable quantification of gene copy number variations is a precondition for future investigations regarding their functional relevance. To date, there is no generally accepted gold standard method for copy number quantification, and methods in current use have given inconsistent results in selected cohorts. In this study, we compare two methods for copy number quantification. beta-defensin gene copy numbers were determined in parallel in 80 genomic DNA samples by real-time PCR and multiplex ligation-dependent probe amplification (MLPA). The pyrosequencing-based paralog ratio test (PPRT) was used as a standard of comparison in 79 out of 80 samples. Realtime PCR and MPLA results confirmed concordant DEFB4, DEFB103A, and DEFB104A copy numbers within samples. These two methods showed identical results in 32 out of 80 samples; 29 of these 32 samples comprised four or fewer copies. The coefficient of variation of MLPA is lower compared with PCR. In addition, the consistency between MLPA and PPRT is higher than either PCR/MLPA or PCR/PPRT consistency. In summary, these results suggest that MLPA is superior to real-time PCR in beta-defensin copy number quantification.