Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

Numerical Study of Length Spectra and Low-lying Eigenvalue Spectra of Compact Hyperbolic 3-manifolds

In this paper, we numerically investigate the length spectra and the low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero eigenvalues have been successfully computed using the periodic orbit sum method, which are compared with various geometric quantities such as volume, diameter and length of the shortest periodic geodesic of the manifolds. The deviation of low-lying eigenvalue spectra of manifolds converging to a cusped hyperbolic manifold from the asymptotic distribution has been measured by $\zeta-$ function and spectral distance.Comment: 19 pages, 18 EPS figures and 2 GIF figures (fig.10) Description of cusped manifolds in section 2 is correcte

Expansion in perfect groups

Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an integer q, denote by Ga_q the subgroup of Ga consisting of the elements that project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q with respect to the generating set S form a family of expanders when q ranges over square-free integers with large prime divisors if and only if the connected component of the Zariski-closure of Ga is perfect.Comment: 62 pages, no figures, revision based on referee's comments: new ideas are explained in more details in the introduction, typos corrected, results and proofs unchange

Universal Prefactor of Activated Conductivity in the Quantum Hall Effect

The prefactor of the activated dissipative conductivity in a plateau range of the quantum Hall effect is studied in the case of a long-range random potential. It is shown that due to long time it takes for an electron to drift along the perimeter of a large percolation cluster, phonons are able to maintain quasi-equilibrium inside the cluster. The saddle points separating such clusters may then be viewed as ballistic point contacts between electron reservoirs with different electrochemical potentials. The prefactor is universal and equal to 2$e^2/h$ at an integer filling factor $\nu$ and to 2$e^2/q^{2}h$ at $\nu=p/q$.Comment: 4 pages + 2 figures by reques

Prolonged fixed dose rate infusion of gemcitabine with autologous haemopoietic support in advanced pancreatic adenocarcinoma

This study aimed to define the maximum-tolerated dose (MTD) of fixed dose rate (FDR) of gemcitabine (2′-2′-difluorodeoxycitidine) infusion with circulating haemopoietic progenitor support and to evaluate the activity of the treatment. Secondary end points were pharmacokinetic of gemcitabine and difluorodeoxyuridina (dFdU) measured at first course and the activity andexpression profile of cytidine deaminase (CdA) on circulating mononuclear cells. Patients with advanced pancreatic carcinoma received escalating dose of gemcitabine 10 mg m−2 min−1 every 2 weeks with circulating haemopoietic progenitor support. First dose level was 3000 mg m−2 and the doses were increased by 500 mg m−2 until MTD. In all, 23 patients were enrolled. Toxicities were mild or moderate; the only patient treated at 7000 mg m−2 died because of toxicity; therefore; the MTD was established at 6500 mg m−2. The overall response rate was 22.2%. The AUC of gemcitabine showed a dose-dependent increase, while the AUC of dFdU reached a plateau at 4500 mg m−2. A significant relationship was found between the AUC of dFdU and CdA expression and activity (P<0.05). Moreover, progression rate and survival were significantly related to CdA expression and activity levels. The activity of high-dose gemcitabine is not superior to that reported with less intensive FDR schedules. The predictive role of CdA expression and activity on outcome deserves further investigation

SuperTriplets: a triplet-based supertree approach to phylogenomics

Motivation: Phylogenetic tree-building methods use molecular data to represent the evolutionary history of genes and taxa. A recurrent problem is to reconcile the various phylogenies built from different genomic sequences into a single one. This task is generally conducted by a two-step approach whereby a binary representation of the initial trees is first inferred and then a maximum parsimony (MP) analysis is performed on it. This binary representation uses a decomposition of all source trees that is usually based on clades, but that can also be based on triplets or quartets. The relative performances of these representations have been discussed but are difficult to assess since both are limited to relatively small datasets

Sex differences in the genetics of sarcoidosis across European and African ancestry populations

BackgroundSex differences in the susceptibility of sarcoidosis are unknown. The study aims to identify sex-dependent genetic variations in two clinical sarcoidosis phenotypes: Löfgren’s syndrome (LS) and non-Löfgren’s syndrome (non-LS).MethodsA meta-analysis of genome-wide association studies was conducted on Europeans and African Americans, totaling 10,103 individuals from three population-based cohorts, Sweden (n = 3,843), Germany (n = 3,342), and the United States (n = 2,918), followed by an SNP lookup in the UK Biobank (UKB, n = 387,945). A genome-wide association study based on Immunochip data consisting of 141,000 single nucleotide polymorphisms (SNPs) was conducted in the sex groups. The association test was based on logistic regression using the additive model in LS and non-LS sex groups independently. Additionally, gene-based analysis, gene expression, expression quantitative trait loci (eQTL) mapping, and pathway analysis were performed to discover functionally relevant mechanisms related to sarcoidosis and biological sex.ResultsWe identified sex-dependent genetic variations in LS and non-LS sex groups. Genetic findings in LS sex groups were explicitly located in the extended Major Histocompatibility Complex (xMHC). In non-LS, genetic differences in the sex groups were primarily located in the MHC class II subregion and ANXA11. Gene-based analysis and eQTL enrichment revealed distinct sex-specific gene expression patterns in various tissues and immune cell types. In LS sex groups, a pathway map related to antigen presentation machinery by IFN-gamma. In non-LS, pathway maps related to immune response lectin-induced complement pathway in males and related to maturation and migration of dendritic cells in skin sensitization in females were identified.ConclusionOur findings provide new evidence for a sex bias underlying sarcoidosis genetic architecture, particularly in clinical phenotypes LS and non-LS. Biological sex likely plays a role in disease mechanisms in sarcoidosis