Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field

How to share underground reservoirs

Many resources, such as oil, gas, or water, are extracted from porous soils and their exploration is often shared among different companies or nations. We show that the effective shares can be obtained by invading the porous medium simultaneously with various fluids. Partitioning a volume in two parts requires one division surface while the simultaneous boundary between three parts consists of lines. We identify and characterize these lines, showing that they form a fractal set consisting of a single thread spanning the medium and a surrounding cloud of loops. While the spanning thread has fractal dimension ${1.55\pm0.03}$, the set of all lines has dimension ${1.69\pm0.02}$. The size distribution of the loops follows a power law and the evolution of the set of lines exhibits a tricritical point described by a crossover with a negative dimension at criticality

A Novel Acyl-CoA Beta-Transaminase Characterized from a Metagenome

BACKGROUND: Bacteria are key components in all ecosystems. However, our knowledge of bacterial metabolism is based solely on the study of cultivated organisms which represent just a tiny fraction of microbial diversity. To access new enzymatic reactions and new or alternative pathways, we investigated bacterial metabolism through analyses of uncultivated bacterial consortia. METHODOLOGY/PRINCIPAL FINDINGS: We applied the gene context approach to assembled sequences of the metagenome of the anaerobic digester of a municipal wastewater treatment plant, and identified a new gene which may participate in an alternative pathway of lysine fermentation. CONCLUSIONS: We characterized a novel, unique aminotransferase that acts exclusively on Coenzyme A (CoA) esters, and proposed a variant route for lysine fermentation. Results suggest that most of the lysine fermenting organisms use this new pathway in the digester. Its presence in organisms representative of two distinct bacterial divisions indicate that it may also be present in other organisms

Therapeutic Potential of HDL in Cardioprotection and Tissue Repair

Epidemiological studies support a strong association between high-density lipoprotein (HDL) cholesterol levels and heart failure incidence. Experimental evidence from different angles supports the view that low HDL is unlikely an innocent bystander in the development of heart failure. HDL exerts direct cardioprotective effects, which are mediated via its interactions with the myocardium and more specifically with cardiomyocytes. HDL may improve cardiac function in several ways. Firstly, HDL may protect the heart against ischaemia/reperfusion injury resulting in a reduction of infarct size and thus in myocardial salvage. Secondly, HDL can improve cardiac function in the absence of ischaemic heart disease as illustrated by beneficial effects conferred by these lipoproteins in diabetic cardiomyopathy. Thirdly, HDL may improve cardiac function by reducing infarct expansion and by attenuating ventricular remodelling post-myocardial infarction. These different mechanisms are substantiated by in vitro, ex vivo, and in vivo intervention studies that applied treatment with native HDL, treatment with reconstituted HDL, or human apo A-I gene transfer. The effect of human apo A-I gene transfer on infarct expansion and ventricular remodelling post-myocardial infarction illustrates the beneficial effects of HDL on tissue repair. The role of HDL in tissue repair is further underpinned by the potent effects of these lipoproteins on endothelial progenitor cell number, function, and incorporation, which may in particular be relevant under conditions of high endothelial cell turnover. Furthermore, topical HDL therapy enhances cutaneous wound healing in different models. In conclusion, the development of HDL-targeted interventions in these strategically chosen therapeutic areas is supported by a strong clinical rationale and significant preclinical data.status: publishe