Conformal Invariance in Percolation, Self-Avoiding Walks and Related Problems

Over the years, problems like percolation and self-avoiding walks have provided important testing grounds for our understanding of the nature of the critical state. I describe some very recent ideas, as well as some older ones, which cast light both on these problems themselves and on the quantum field theories to which they correspond. These ideas come from conformal field theory, Coulomb gas mappings, and stochastic Loewner evolution.Comment: Plenary talk given at TH-2002, Paris. 21 pages, 9 figure

The extreme vulnerability of interdependent spatially embedded networks

Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, while below this "critical dependency" (CD) a failure of few nodes leads only to small damage to the system. So far, the research has been focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically analyze the stability of systems consisting of interdependent spatially embedded networks modeled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no CD and \textit{any} small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice. Our results are important for understanding the vulnerabilities and for designing robust interdependent spatial embedded networks.Comment: 13 pages, 5 figure

Longitudinal analyses of the DNA methylome in deployed military servicemen identify susceptibility loci for post-traumatic stress disorder

In order to determine the impact of the epigenetic response to traumatic stress on post-traumatic stress disorder (PTSD), this study examined longitudinal changes of genome-wide blood DNA methylation profiles in relation to the development of PTSD symptoms in two prospective military cohorts (one discovery and one replication data set). In the first cohort consisting of male Dutch military servicemen (n=93), the emergence of PTSD symptoms over a deployment period to a combat zone was significantly associated with alterations in DNA methylation levels at 17 genomic positions and 12 genomic regions. Evidence for mediation of the relation between combat trauma and PTSD symptoms by longitudinal changes in DNA methylation was observed at several positions and regions. Bioinformatic analyses of the reported associations identified significant enrichment in several pathways relevant for symptoms of PTSD. Targeted analyses of the significant findings from the discovery sample in an independent prospective cohort of male US marines (n=98) replicated the observed relation between decreases in DNA methylation levels and PTSD symptoms at genomic regions in ZFP57, RNF39 and HIST1H2APS2. Together, our study pinpoints three novel genomic regions where longitudinal decreases in DNA methylation across the period of exposure to combat trauma marks susceptibility for PTSD

Longitudinal analyses of the DNA methylome in deployed military servicemen identify susceptibility loci for post-traumatic stress disorder.

In order to determine the impact of the epigenetic response to traumatic stress on post-traumatic stress disorder (PTSD), this study examined longitudinal changes of genome-wide blood DNA methylation profiles in relation to the development of PTSD symptoms in two prospective military cohorts (one discovery and one replication data set). In the first cohort consisting of male Dutch military servicemen (n=93), the emergence of PTSD symptoms over a deployment period to a combat zone was significantly associated with alterations in DNA methylation levels at 17 genomic positions and 12 genomic regions. Evidence for mediation of the relation between combat trauma and PTSD symptoms by longitudinal changes in DNA methylation was observed at several positions and regions. Bioinformatic analyses of the reported associations identified significant enrichment in several pathways relevant for symptoms of PTSD. Targeted analyses of the significant findings from the discovery sample in an independent prospective cohort of male US marines (n=98) replicated the observed relation between decreases in DNA methylation levels and PTSD symptoms at genomic regions in ZFP57, RNF39 and HIST1H2APS2. Together, our study pinpoints three novel genomic regions where longitudinal decreases in DNA methylation across the period of exposure to combat trauma marks susceptibility for PTSD