Multivariate Lagrange inversion formula and the cycle lemma

International audienceWe give a multitype extension of the cycle lemma of (Dvoretzky and Motzkin 1947). This allows us to obtain a combinatorial proof of the multivariate Lagrange inversion formula that generalizes the celebrated proof of (Raney 1963) in the univariate case, and its extension in (Chottin 1981) to the two variable case. Until now, only the alternative approach of (Joyal 1981) and (Labelle 1981) via labelled arborescences and endofunctions had been successfully extended to the multivariate case in (Gessel 1983), (Goulden and Kulkarni 1996), (Bousquet et al. 2003), and the extension of the cycle lemma to more than 2 variables was elusive. The cycle lemma has found a lot of applications in combinatorics, so we expect our multivariate extension to be quite fruitful: as a first application we mention economical linear time exact random sampling for multispecies trees

Multidimensional Gaussian sums arising from distribution of Birkhoff sums in zero entropy dynamical systems

A duality formula, of the Hardy and Littlewood type for multidimensional Gaussian sums, is proved in order to estimate the asymptotic long time behavior of distribution of Birkhoff sums $S_n$ of a sequence generated by a skew product dynamical system on the $\mathbb{T}^2$ torus, with zero Lyapounov exponents. The sequence, taking the values $\pm 1$, is pairwise independent (but not independent) ergodic sequence with infinite range dependence. The model corresponds to the motion of a particle on an infinite cylinder, hopping backward and forward along its axis, with a transversal acceleration parameter $\alpha$. We show that when the parameter $\alpha /\pi$ is rational then all the moments of the normalized sums $E((S_n/\sqrt{n})^k)$, but the second, are unbounded with respect to n, while for irrational $\alpha /\pi$, with bounded continuous fraction representation, all these moments are finite and bounded with respect to n.Comment: To be published in J. Phys.

Alignathon: A competitive assessment of whole-genome alignment methods

© 2014 Earl et al. Multiple sequence alignments (MSAs) are a prerequisite for a wide variety of evolutionary analyses. Published assessments and benchmark data sets for protein and, to a lesser extent, global nucleotide MSAs are available, but less effort has been made to establish benchmarks in the more general problem of whole-genome alignment (WGA). Using the same model as the successful Assemblathon competitions, we organized a competitive evaluation in which teams submitted their alignments and then assessments were performed collectively after all the submissions were received. Three data sets were used: Two were simulated and based on primate and mammalian phylogenies, and one was comprised of 20 real fly genomes. In total, 35 submissions were assessed, submitted by 10 teams using 12 different alignment pipelines. We found agreement between independent simulation-based and statistical assessments, indicating that there are substantial accuracy differences between contemporary alignment tools. We saw considerable differences in the alignment quality of differently annotated regions and found that few tools aligned the duplications analyzed. We found that many tools worked well at shorter evolutionary distances, but fewer performed competitively at longer distances. We provide all data sets, submissions, and assessment programs for further study and provide, as a resource for future benchmarking, a convenient repository of code and data for reproducing the simulation assessments

The clinical features of the piriformis syndrome: a systematic review

Piriformis syndrome, sciatica caused by compression of the sciatic nerve by the piriformis muscle, has been described for over 70 years; yet, it remains controversial. The literature consists mainly of case series and narrative reviews. The objectives of the study were: first, to make the best use of existing evidence to estimate the frequencies of clinical features in patients reported to have PS; second, to identify future research questions. A systematic review was conducted of any study type that reported extractable data relevant to diagnosis. The search included all studies up to 1 March 2008 in four databases: AMED, CINAHL, Embase and Medline. Screening, data extraction and analysis were all performed independently by two reviewers. A total of 55 studies were included: 51 individual and 3 aggregated data studies, and 1 combined study. The most common features found were: buttock pain, external tenderness over the greater sciatic notch, aggravation of the pain through sitting and augmentation of the pain with manoeuvres that increase piriformis muscle tension. Future research could start with comparing the frequencies of these features in sciatica patients with and without disc herniation or spinal stenosis

Transforming Growth Factor-β1 Suppresses Hepatitis B Virus Replication by the Reduction of Hepatocyte Nuclear Factor-4α Expression

Several studies have demonstrated that cytokine-mediated noncytopathic suppression of hepatitis B virus (HBV) replication may provide an alternative therapeutic strategy for the treatment of chronic hepatitis B infection. In our previous study, we showed that transforming growth factor-beta1 (TGF-β1) could effectively suppress HBV replication at physiological concentrations. Here, we provide more evidence that TGF-β1 specifically diminishes HBV core promoter activity, which subsequently results in a reduction in the level of viral pregenomic RNA (pgRNA), core protein (HBc), nucleocapsid, and consequently suppresses HBV replication. The hepatocyte nuclear factor 4alpha (HNF-4α) binding element(s) within the HBV core promoter region was characterized to be responsive for the inhibitory effect of TGF-β1 on HBV regulation. Furthermore, we found that TGF-β1 treatment significantly repressed HNF-4α expression at both mRNA and protein levels. We demonstrated that RNAi-mediated depletion of HNF-4α was sufficient to reduce HBc synthesis as TGF-β1 did. Prevention of HNF-4α degradation by treating with proteasome inhibitor MG132 also prevented the inhibitory effect of TGF-β1. Finally, we confirmed that HBV replication could be rescued by ectopic expression of HNF-4α in TGF-β1-treated cells. Our data clarify the mechanism by which TGF-β1 suppresses HBV replication, primarily through modulating the expression of HNF-4α gene

Identification of novel conserved peptide uORF homology groups in Arabidopsis and rice reveals ancient eukaryotic origin of select groups and preferential association with transcription factor-encoding genes

Abstract Background Upstream open reading frames (uORFs) can mediate translational control over the largest, or major ORF (mORF) in response to starvation, polyamine concentrations, and sucrose concentrations. One plant uORF with conserved peptide sequences has been shown to exert this control in an amino acid sequence-dependent manner but generally it is not clear what kinds of genes are regulated, or how extensively this mechanism is invoked in a given genome. Results By comparing full-length cDNA sequences from Arabidopsis and rice we identified 26 distinct homology groups of conserved peptide uORFs, only three of which have been reported previously. Pairwise Ka/Ks analysis showed that purifying selection had acted on nearly all conserved peptide uORFs and their associated mORFs. Functions of predicted mORF proteins could be inferred for 16 homology groups and many of these proteins appear to have a regulatory function, including 6 transcription factors, 5 signal transduction factors, 3 developmental signal molecules, a homolog of translation initiation factor eIF5, and a RING finger protein. Transcription factors are clearly overrepresented in this data set when compared to the frequency calculated for the entire genome (p = 1.2 × 10-7). Duplicate gene pairs arising from a whole genome duplication (ohnologs) with a conserved uORF are much more likely to have been retained in Arabidopsis (Arabidopsis thaliana) than are ohnologs of other genes (39% vs 14% of ancestral genes, p = 5 × 10-3). Two uORF groups were found in animals, indicating an ancient origin of these putative regulatory elements. Conclusion Conservation of uORF amino acid sequence, association with homologous mORFs over long evolutionary time periods, preferential retention after whole genome duplications, and preferential association with mORFs coding for transcription factors suggest that the conserved peptide uORFs identified in this study are strong candidates for translational controllers of regulatory genes.</p