The p-periodicity of the groups GL (n, Os(K)) and SL(n, Os(K))

In this paper we investigate the p-periodicity of the S-arithmetic groups G = GL(n, Os(K)) and G1 = SL(n, Os(K)) where Os(K) is the ring of S-integers of a number field K (cf. [12, 13]; S is a finite set of places in K including the infinite places). These groups are known to be virtually of finite (cohomological) dimension, and thus the concept of p-periodicity is defined; it refers to a rational prime p and to the p-primary component Ĥi(G, A, p) of the Farrell-Tate cohomology Ĥi(G, A) with respect to an arbitrary G-module A. We recall that Ĥi coincides with the usual cohomology Hi for all i above the virtual dimension of G, and that in the case of a finite group (i.e., a group of virtual dimension zero) the Ĥi, i , are the usual Tate cohomology groups. The group G is called p-periodic if Ĥi(G, A, p) is periodic in i, for all A, and the smallest corresponding period is then simply called the p-period of G. If G has no p-torsion, the p-primary component of all its Ĥi is 0, and thus G is trivially p-periodi

Temperature Profiles in Hamiltonian Heat Conduction

We study heat transport in the context of Hamiltonian and related stochastic models with nearest-neighbor coupling, and derive a universal law for the temperature profiles of a large class of such models. This law contains a parameter $\alpha$, and is linear only when $\alpha=1$. The value of $\alpha$ depends on energy-exchange mechanisms, including the range of motion of tracer particles and their times of flight.Comment: Revised text, same results Second revisio

How to avoid potential pitfalls in recurrence plot based data analysis

Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis

The cytoplasmic poly(A) polymerases GLD-2 and GLD-4 promote general gene expression via distinct mechanisms

Post-transcriptional gene regulation mechanisms decide on cellular mRNA activities. Essential gatekeepers of post-transcriptional mRNA regulation are broadly conserved mRNA-modifying enzymes, such as cytoplasmic poly(A) polymerases (cytoPAPs). Although these non-canonical nucleotidyltransferases efficiently elongate mRNA poly(A) tails in artificial tethering assays, we still know little about their global impact on poly(A) metabolism and their individual molecular roles in promoting protein production in organisms. Here, we use the animal model Caenorhabditis elegans to investigate the global mechanisms of two germline-enriched cytoPAPs, GLD-2 and GLD-4, by combining polysome profiling with RNA sequencing. Our analyses suggest that GLD-2 activity mediates mRNA stability of many translationally repressed mRNAs. This correlates with a general shortening of long poly(A) tails in gld-2-compromised animals, suggesting that most if not all targets are stabilized via robust GLD-2-mediated polyadenylation. By contrast, only mild polyadenylation defects are found in gld-4-compromised animals and few mRNAs change in abundance. Interestingly, we detect a reduced number of polysomes in gld-4 mutants and GLD-4 protein co-sediments with polysomes, which together suggest that GLD-4 might stimulate or maintain translation directly. Our combined data show that distinct cytoPAPs employ different RNA-regulatory mechanisms to promote gene expression, offering new insights into translational activation of mRNAs

Remarks on Bootstrap Percolation in Metric Networks

We examine bootstrap percolation in d-dimensional, directed metric graphs in the context of recent measurements of firing dynamics in 2D neuronal cultures. There are two regimes, depending on the graph size N. Large metric graphs are ignited by the occurrence of critical nuclei, which initially occupy an infinitesimal fraction, f_* -> 0, of the graph and then explode throughout a finite fraction. Smaller metric graphs are effectively random in the sense that their ignition requires the initial ignition of a finite, unlocalized fraction of the graph, f_* >0. The crossover between the two regimes is at a size N_* which scales exponentially with the connectivity range \lambda like_* \sim \exp\lambda^d. The neuronal cultures are finite metric graphs of size N \simeq 10^5-10^6, which, for the parameters of the experiment, is effectively random since N<< N_*. This explains the seeming contradiction in the observed finite f_* in these cultures. Finally, we discuss the dynamics of the firing front

A numerical study of infinitely renormalizable area-preserving maps

It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these Cantor sets for any two infinitely renormalizable maps is conjugated by a transformation that extends to a differentiable function whose derivative is Holder continuous of exponent alpha>0. In this paper we investigate numerically the specific value of alpha. We also present numerical evidence that the normalized derivative cocycle with the base dynamics in the Cantor set is ergodic. Finally, we compute renormalization eigenvalues to a high accuracy to support a conjecture that the renormalization spectrum is real

ELMO1 has an essential role in the internalization of Salmonella Typhimurium into enteric macrophages that impacts disease outcome.

Backgrounds and aims4-6 million people die of enteric infections each year. After invading intestinal epithelial cells, enteric bacteria encounter phagocytes. However, little is known about how phagocytes internalize the bacteria to generate host responses. Previously, we have shown that BAI1 (Brain Angiogenesis Inhibitor 1) binds and internalizes Gram-negative bacteria through an ELMO1 (Engulfment and cell Motility protein 1)/Rac1-dependent mechanism. Here we delineate the role of ELMO1 in host inflammatory responses following enteric infection.MethodsELMO1-depleted murine macrophage cell lines, intestinal macrophages and ELMO1 deficient mice (total or myeloid-cell specific) was infected with Salmonella enterica serovar Typhimurium. The bacterial load, inflammatory cytokines and histopathology was evaluated in the ileum, cecum and spleen. The ELMO1 dependent host cytokines were detected by a cytokine array. ELMO1 mediated Rac1 activity was measured by pulldown assay.ResultsThe cytokine array showed reduced release of pro-inflammatory cytokines, including TNF-α and MCP-1, by ELMO1-depleted macrophages. Inhibition of ELMO1 expression in macrophages decreased Rac1 activation (~6 fold) and reduced internalization of Salmonella. ELMO1-dependent internalization was indispensable for TNF-α and MCP-1. Simultaneous inhibition of ELMO1 and Rac function virtually abrogated TNF-α responses to infection. Further, activation of NF-κB, ERK1/2 and p38 MAP kinases were impaired in ELMO1-depleted cells. Strikingly, bacterial internalization by intestinal macrophages was completely dependent on ELMO1. Salmonella infection of ELMO1-deficient mice resulted in a 90% reduction in bacterial burden and attenuated inflammatory responses in the ileum, spleen and cecum.ConclusionThese findings suggest a novel role for ELMO1 in facilitating intracellular bacterial sensing and the induction of inflammatory responses following infection with Salmonella

Laplacian growth with separately controlled noise and anisotropy

Conformal mapping models are used to study competition of noise and anisotropy in Laplacian growth. For that, a new family of models is introduced with the noise level and directional anisotropy controlled independently. Fractalization is observed in both anisotropic growth and the growth with varying noise. Fractal dimension is determined from cluster size scaling with its area. For isotropic growth we find d = 1.7, both at high and low noise. For anisotropic growth with reduced noise the dimension can be as low as d = 1.5 and apparently is not universal. Also, we study fluctuations of particle areas and observe, in agreement with previous studies, that exceptionally large particles may appear during the growth, leading to pathologically irregular clusters. This difficulty is circumvented by using an acceptance window for particle areas.Comment: 13 pages, 15 figure

On Turing dynamical systems and the Atiyah problem

Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental l^2-Betti number with respect to an action of the threefold direct product of the lamplighter group Z/2 wr Z. The main new idea is embedding Turing machines into integral group rings. The main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio