Two-Dimensional Critical Percolation: The Full Scaling Limit

We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice -- that is, the scaling limit of the set of all interfaces between different clusters. Some properties of the loop process, including conformal invariance, are also proved.Comment: 45 pages, 12 figures. This is a revised version of math.PR/0504036 without the appendice

A lower bound for the mass of axisymmetric connected black hole data sets

We present a generalisation of the Brill-type proof of positivity of mass for axisymmetric initial data to initial data sets with black hole boundaries. The argument leads to a strictly positive lower bound for the mass of simply connected, connected axisymmetric black hole data sets in terms of the mass of a reference Schwarzschild metric

Injectivity of sections of convex harmonic mappings and convolution theorems

In the article the authors consider the class ${\mathcal H}_0$ of sense-preserving harmonic functions $f=h+\overline{g}$ defined in the unit disk $|z|<1$ and normalized so that $h(0)=0=h'(0)-1$ and $g(0)=0=g'(0)$, where $h$ and $g$ are analytic in the unit disk. In the first part of the article we present two classes $\mathcal{P}_H^0(\alpha)$ and $\mathcal{G}_H^0(\beta)$ of functions from ${\mathcal H}_0$ and show that if $f\in \mathcal{P}_H^0(\alpha)$ and $F\in\mathcal{G}_H^0(\beta)$, then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters $\alpha$ and $\beta$ are satisfied. In the second part we study the harmonic sections (partial sums) $$s_{n, n}(f)(z)=s_n(h)(z)+\overline{s_n(g)(z)},$$ where $f=h+\overline{g}\in {\mathcal H}_0$, $s_n(h)$ and $s_n(g)$ denote the $n$-th partial sums of $h$ and $g$, respectively. We prove, among others, that if $f=h+\overline{g}\in{\mathcal H}_0$ is a univalent harmonic convex mapping, then $s_{n, n}(f)$ is univalent and close-to-convex in the disk $|z|< 1/4$ for $n\geq 2$, and $s_{n, n}(f)$ is also convex in the disk $|z|< 1/4$ for $n\geq2$ and $n\neq 3$. Moreover, we show that the section $s_{3,3}(f)$ of $f\in {\mathcal C}_H^0$ is not convex in the disk $|z|<1/4$ but is shown to be convex in a smaller disk.Comment: 16 pages, 3 figures; To appear in Czechoslovak Mathematical Journa

Global Genotype-Phenotype Correlations in Pseudomonas aeruginosa

Once the genome sequence of an organism is obtained, attention turns from identifying genes to understanding their function, their organization and control of metabolic pathways and networks that determine its physiology. Recent technical advances in acquiring genome-wide data have led to substantial progress in identifying gene functions. However, we still do not know the function of a large number of genes and, even when a gene product has been assigned to a functional class, we cannot normally predict its contribution to the phenotypic behaviour of the cell or organism - the phenome. In this study, we assessed bacterial growth parameters of 4030 non-redundant PA14 transposon mutants in the pathogenic bacterium Pseudomonas aeruginosa. The genome-wide simultaneous analysis of 119 distinct growth-related phenotypes uncovered a comprehensive phenome and provided evidence that most genotypes are not phenotypically isolated but rather define specific complex phenotypic clusters of genotypes. Since phenotypic overlap was demonstrated to reflect the relatedness of genotypes on a global scale, knowledge of an organism's phenome might significantly contribute to the advancement of functional genomics

Sensory Input Pathways and Mechanisms in Swallowing: A Review

Over the past 20 years, research on the physiology of swallowing has confirmed that the oropharyngeal swallowing process can be modulated, both volitionally and in response to different sensory stimuli. In this review we identify what is known regarding the sensory pathways and mechanisms that are now thought to influence swallowing motor control and evoke its response. By synthesizing the current state of research evidence and knowledge, we identify continuing gaps in our knowledge of these mechanisms and pose questions for future research

Non-real zeros of derivatives of meromorphic functions

A number of results are proved concerning non-real zeros of derivatives of real and strictly non-real meromorphic functions in the plane