Products of Random Matrices

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewness. The distribution may have importance as an uncommitted prior in statistical image analysis.Comment: 9 pages, 1 figur

Gene duplications in prokaryotes can be associated with environmental adaptation

<p>Abstract</p> <p>Background</p> <p>Gene duplication is a normal evolutionary process. If there is no selective advantage in keeping the duplicated gene, it is usually reduced to a pseudogene and disappears from the genome. However, some paralogs are retained. These gene products are likely to be beneficial to the organism, e.g. in adaptation to new environmental conditions. The aim of our analysis is to investigate the properties of paralog-forming genes in prokaryotes, and to analyse the role of these retained paralogs by relating gene properties to life style of the corresponding prokaryotes.</p> <p>Results</p> <p>Paralogs were identified in a number of prokaryotes, and these paralogs were compared to singletons of persistent orthologs based on functional classification. This showed that the paralogs were associated with for example energy production, cell motility, ion transport, and defence mechanisms. A statistical overrepresentation analysis of gene and protein annotations was based on paralogs of the 200 prokaryotes with the highest fraction of paralog-forming genes. Biclustering of overrepresented gene ontology terms versus species was used to identify clusters of properties associated with clusters of species. The clusters were classified using similarity scores on properties and species to identify interesting clusters, and a subset of clusters were analysed by comparison to literature data. This analysis showed that paralogs often are associated with properties that are important for survival and proliferation of the specific organisms. This includes processes like ion transport, locomotion, chemotaxis and photosynthesis. However, the analysis also showed that the gene ontology terms sometimes were too general, imprecise or even misleading for automatic analysis.</p> <p>Conclusions</p> <p>Properties described by gene ontology terms identified in the overrepresentation analysis are often consistent with individual prokaryote lifestyles and are likely to give a competitive advantage to the organism. Paralogs and singletons dominate different categories of functional classification, where paralogs in particular seem to be associated with processes involving interaction with the environment.</p

Innate secretory antibodies protect against natural Salmonella typhimurium infection

The production of IgA is induced in an antigen-unspecific manner by commensal flora. These secretory antibodies (SAbs) may bind multiple antigens and are thought to eliminate commensal bacteria and self-antigens to avoid systemic recognition. In this study, we addressed the role of “innate” SAbs, i.e., those that are continuously produced in normal individuals, in protection against infection of the gastrointestinal tract. We used polymeric immunoglobulin receptor (pIgR−/−) knock-out mice, which are unable to bind and actively transport dimeric IgA and pentameric IgM to the mucosae, and examined the role of innate SAbs in protection against the invasive pathogen Salmonella typhimurium. In vitro experiments suggested that innate IgA in pIgR−/− serum bound S. typhimurium in a cross-reactive manner which inhibited epithelial cell invasion. Using a “natural” infection model, we demonstrated that pIgR−/− mice are profoundly sensitive to infection with S. typhimurium via the fecal-oral route and, moreover, shed more bacteria that readily infected other animals. These results imply an important evolutionary role for innate SAbs in protecting both the individual and the herd against infections, and suggest that the major role of SAbs may be to prevent the spread of microbial pathogens throughout the population, rather than protection of local mucosal surfaces

Role of breast regression protein 39 (BRP-39)/chitinase 3-like-1 in Th2 and IL-13–induced tissue responses and apoptosis

Mouse breast regression protein 39 (BRP-39; Chi3l1) and its human homologue YKL-40 are chitinase-like proteins that lack chitinase activity. Although YKL-40 is expressed in exaggerated quantities and correlates with disease activity in asthma and many other disorders, the biological properties of BRP-39/YKL-40 have only been rudimentarily defined. We describe the generation and characterization of BRP-39−/− mice, YKL-40 transgenic mice, and mice that lack BRP-39 and produce YKL-40 only in their pulmonary epithelium. Studies of these mice demonstrated that BRP-39−/− animals have markedly diminished antigen-induced Th2 responses and that epithelial YKL-40 rescues the Th2 responses in these animals. The ability of interleukin13 to induce tissue inflammation and fibrosis was also markedly diminished in the absence of BRP-39. Mechanistic investigations demonstrated that BRP-39 and YKL-40 play an essential role in antigen sensitization and immunoglobulin E induction, stimulate dendritic cell accumulation and activation, and induce alternative macrophage activation. These proteins also inhibit inflammatory cell apoptosis/cell death while inhibiting Fas expression, activating protein kinase B/AKT, and inducing Faim 3. These studies establish novel regulatory roles for BRP-39/YKL-40 in the initiation and effector phases of Th2 inflammation and remodeling and suggest that these proteins are therapeutic targets in Th2- and macrophage-mediated disorders

SELF-DESTRUCTING SPIRAL WAVES: GLOBAL SIMULATIONS OF A SPIRAL-WAVE INSTABILITY IN ACCRETION DISKS

This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575. The authors acknowledge the San Diego Supercomputer Center at University of California, San Diego and the Texas Advanced Computing Center at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper. This work used the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC Operations grant ST/K0003259/1. DiRAC is part of the national E-Infrastructure

Tips for implementing multigrid methods on domains containing holes

As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised regions), via the multigrid method. We consider as a test case the Poisson equation with a nonlinear term added, as a means of illustrating the principles involved, and move to a "real world" 3-dimensional problem which is the solution of the conformally flat Hamiltonian constraint with Dirichlet and Robin boundary conditions. Using our vertex-centered multigrid code, we demonstrate globally second-order-accurate solutions of elliptic equations over domains containing holes, in two and three spatial dimensions. Keys to the success of this method are the choice of the restriction operator near the holes and definition of the location of the inner boundary. In some cases (e.g. two holes in two dimensions), more and more smoothing may be required as the mesh spacing decreases to zero; however for the resolutions currently of interest to many numerical relativists, it is feasible to maintain second order convergence by concentrating smoothing (spatially) where it is needed most. This paper, and our publicly available source code, are intended to serve as semi-pedagogical guides for those who may wish to implement similar schemes.Comment: 18 pages, 11 figures, LaTeX. Added clarifications and references re. scope of paper, mathematical foundations, relevance of work. Accepted for publication in Classical & Quantum Gravit

Modelling the exposure of wildlife to radiation: key findings and activities of IAEA working groups

The International Atomic Energy Agency (IAEA) established the Biota Working Group (BWG) as part of its Environmental Modelling for Radiation Safety (EMRAS) programme in 2004 (http://www-ns.iaea.org/projects/emras/emras-biota-wg.htm). At that time both the IAEA and the International Commission on Radiological Protection (ICRP) were addressing environmental protection (i.e. protection of non-human biota or wildlife) within the on-going revisions to the Basic Safety Standards and Recommendations respectively. Furthermore, some countries (e.g. the USA, UK) were already conducting assessments in accordance with national guidelines. Consequently, a number of assessment frameworks/models had been or were being developed. The BWG was established recognising these developments and the need to improve Member State’s capabilities with respect to protection of the environment from ionizing radiation. The work of the BWG was continued within the IAEA’s EMRAS II programme by the Biota Modelling Group (http://wwwns. iaea.org/projects/emras/emras2/working-groups/working-group-four.asp)

Giant Planet Formation and Migration

© 2018, The Author(s). Planets form in circumstellar discs around young stars. Starting with sub-micron sized dust particles, giant planet formation is all about growing 14 orders of magnitude in size. It has become increasingly clear over the past decades that during all stages of giant planet formation, the building blocks are extremely mobile and can change their semimajor axis by substantial amounts. In this chapter, we aim to give a basic overview of the physical processes thought to govern giant planet formation and migration, and to highlight possible links to water delivery.S.-J. Paardekooper is supported by a Royal Society University Research Fellowship. A. Johansen is supported by the Knut and Alice Wallenberg Foundation, the Swedish Research Council (grant 2014-5775) and the European Research Council (ERC Starting Grant 278675-PEBBLE2PLANET)

Astrophysical turbulence modeling

The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy, and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non coarse-grained) fields.Comment: 88 pages, 26 figures, published in Reports on Progress in Physic