Escape of mass in zero-range processes with random rates

We consider zero-range processes in ${\mathbb{Z}}^d$ with site dependent jump rates. The rate for a particle jump from site $x$ to $y$ in ${\mathbb{Z}}^d$ is given by $\lambda_xg(k)p(y-x)$, where $p(\cdot)$ is a probability in ${\mathbb{Z}}^d$, $g(k)$ is a bounded nondecreasing function of the number $k$ of particles in $x$ and $\lambda =\{\lambda_x\}$ is a collection of i.i.d. random variables with values in $(c,1]$, for some $c>0$. For almost every realization of the environment $\lambda$ the zero-range process has product invariant measures $\{{\nu_{\lambda, v}}:0\le v\le c\}$ parametrized by $v$, the average total jump rate from any given site. The density of a measure, defined by the asymptotic average number of particles per site, is an increasing function of $v$. There exists a product invariant measure ${\nu _{\lambda, c}}$, with maximal density. Let $\mu$ be a probability measure concentrating mass on configurations whose number of particles at site $x$ grows less than exponentially with $\|x\|$. Denoting by $S_{\lambda}(t)$ the semigroup of the process, we prove that all weak limits of $\{\mu S_{\lambda}(t),t\ge 0\}$ as $t\to \infty$ are dominated, in the natural partial order, by ${\nu_{\lambda, c}}$. In particular, if $\mu$ dominates ${\nu _{\lambda, c}}$, then $\mu S_{\lambda}(t)$ converges to ${\nu_{\lambda, c}}$. The result is particularly striking when the maximal density is finite and the initial measure has a density above the maximal.Comment: Published at http://dx.doi.org/10.1214/074921707000000300 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

A note on weak convergence results for uniform infinite causal triangulations

We discuss uniform infinite causal triangulations and equivalence to the size biased branching process measure - the critical Galton-Watson branching process distribution conditioned on non-extinction. Using known results from the theory of branching processes, this relation is used to prove weak convergence of the joint length-area process of a uniform infinite causal triangulations to a limiting diffusion. The diffusion equation enables us to determine the physical Hamiltonian and Green's function from the Feynman-Kac procedure, providing us with a mathematical rigorous proof of certain scaling limits of causal dynamical triangulations.Comment: 23 pages, 2 figure

Condensation for a fixed number of independent random variables

A family of m independent identically distributed random variables indexed by a chemical potential \phi\in[0,\gamma] represents piles of particles. As \phi increases to \gamma, the mean number of particles per site converges to a maximal density \rho_c<\infty. The distribution of particles conditioned on the total number of particles equal to n does not depend on \phi (canonical ensemble). For fixed m, as n goes to infinity the canonical ensemble measure behave as follows: removing the site with the maximal number of particles, the distribution of particles in the remaining sites converges to the grand canonical measure with density \rho_c; the remaining particles concentrate (condensate) on a single site.Comment: 6 page

Growth of uniform infinite causal triangulations

We introduce a growth process which samples sections of uniform infinite causal triangulations by elementary moves in which a single triangle is added. A relation to a random walk on the integer half line is shown. This relation is used to estimate the geodesic distance of a given triangle to the rooted boundary in terms of the time of the growth process and to determine from this the fractal dimension. Furthermore, convergence of the boundary process to a diffusion process is shown leading to an interesting duality relation between the growth process and a corresponding branching process.Comment: 27 pages, 6 figures, small changes, as publishe

Gene expression profiles in asbestos-exposed epithelial and mesothelial lung cell lines

BACKGROUND: Asbestos has been shown to cause chromosomal damage and DNA aberrations. Exposure to asbestos causes many lung diseases e.g. asbestosis, malignant mesothelioma, and lung cancer, but the disease-related processes are still largely unknown. We exposed the human cell lines A549, Beas-2B and Met5A to crocidolite asbestos and determined time-dependent gene expression profiles by using Affymetrix arrays. The hybridization data was analyzed by using an algorithm specifically designed for clustering of short time series expression data. A canonical correlation analysis was applied to identify correlations between the cell lines, and a Gene Ontology analysis method for the identification of enriched, differentially expressed biological processes. RESULTS: We recognized a large number of previously known as well as new potential asbestos-associated genes and biological processes, and identified chromosomal regions enriched with genes potentially contributing to common responses to asbestos in these cell lines. These include genes such as the thioredoxin domain containing gene (TXNDC) and the potential tumor suppressor, BCL2/adenovirus E1B 19kD-interacting protein gene (BNIP3L), GO-terms such as "positive regulation of I-kappaB kinase/NF-kappaB cascade" and "positive regulation of transcription, DNA-dependent", and chromosomal regions such as 2p22, 9p13, and 14q21. We present the complete data sets as Additional files. CONCLUSION: This study identifies several interesting targets for further investigation in relation to asbestos-associated diseases

Potentiality in Aristotle's psychology and ethics

The distinction between potentiality and actuality in Aristotle has its origin in Platonic ethics. In his psychological and ethical works Aristotle’s notion of potentiality is embedded in a causal framework that is characteristic of life in general. A key theme is the distinction of various meanings of ‘to know’. In his early work the possession of knowledge is distinguished from its use. In De anima Aristotle adds the potentiality for acquiring knowledge as characteristic of the genus human being. He argues that the stages of actualization of knowledge are instances of a more comprehensive biological and ethical development. Life is the fulfillment of soul as formal, efficient and final cause, with the potentiality of body as material cause. The unity of body and soul is derived from the causal nexus of potentiality and actuality, like a power and the instrument in which it resides. In such cases potentiality is complex and depends on numerous conditions. Failure of full realization may occur when any of the necessary conditions of the development and realization of the fulfillment of human life are lacking, whether in the environment (e.g. climate), the body (illness, drunkenness), or the soul (natural virtue, firm character, attention).Political Philosophy and Ethic

Multi-genome identification and characterization of chlamydiae-specific type III secretion substrates: the Inc proteins

<p>Abstract</p> <p>Background</p> <p><it>Chlamydiae </it>are obligate intracellular bacteria that multiply in a vacuolar compartment, the inclusion. Several chlamydial proteins containing a bilobal hydrophobic domain are translocated by a type III secretion (TTS) mechanism into the inclusion membrane. They form the family of Inc proteins, which is specific to this phylum. Based on their localization, Inc proteins likely play important roles in the interactions between the microbe and the host. In this paper we sought to identify and analyze, using bioinformatics tools, all putative Inc proteins in published chlamydial genomes, including an environmental species.</p> <p>Results</p> <p>Inc proteins contain at least one bilobal hydrophobic domain made of two transmembrane helices separated by a loop of less than 30 amino acids. Using bioinformatics tools we identified 537 putative Inc proteins across seven chlamydial proteomes. The amino-terminal segment of the putative Inc proteins was recognized as a functional TTS signal in 90% of the <it>C. trachomatis </it>and <it>C. pneumoniae </it>sequences tested, validating the data obtained <it>in silico</it>. We identified a <it>macro </it>domain in several putative Inc proteins, and observed that Inc proteins are enriched in segments predicted to form coiled coils. A surprisingly large proportion of the putative Inc proteins are not constitutively translocated to the inclusion membrane in culture conditions.</p> <p>Conclusions</p> <p>The Inc proteins represent 7 to 10% of each proteome and show a great degree of sequence diversity between species. The abundance of segments with a high probability for coiled coil conformation in Inc proteins support the hypothesis that they interact with host proteins. While the large majority of Inc proteins possess a functional TTS signal, less than half may be constitutively translocated to the inclusion surface in some species. This suggests the novel finding that translocation of Inc proteins may be regulated by as-yet undetermined mechanisms.</p