Lagrangian one-particle velocity statistics in a turbulent flow

We present Lagrangian one-particle statistics from the Risoe PTV experiment of a turbulent flow. We estimate the Lagrangian Kolmogorov constant $C_0$ and find that it is affected by the large scale inhomogeneities of the flow. The pdf of temporal velocity increments are highly non-Gaussian for small times which we interpret as a consequence of intermittency. Using Extended Self-Similarity we manage to quantify the intermittency and find that the deviations from Kolmogorov 1941 similarity scaling is larger in the Lagrangian framework than in the Eulerian. Through the multifractal model we calculate the multifractal dimension spectrum.Comment: 22 pages, 14 figure

Approximate zero-one laws and sharpness of the percolation transition in a class of models including two-dimensional Ising percolation

One of the most well-known classical results for site percolation on the square lattice is the equation $p_c+p_c^*=1$. In words, this equation means that for all values $\neq p_c$ of the parameter $p$, the following holds: either a.s. there is an infinite open cluster or a.s. there is an infinite closed "star" cluster. This result is closely related to the percolation transition being sharp: below $p_c$, the size of the open cluster of a given vertex is not only (a.s.) finite, but has a distribution with an exponential tail. The analog of this result has been proven by Higuchi in 1993 for two-dimensional Ising percolation (at fixed inverse temperature $\beta<\beta_c$) with external field $h$, the parameter of the model. Using sharp-threshold results (approximate zero-one laws) and a modification of an RSW-like result by Bollob\'{a}s and Riordan, we show that these results hold for a large class of percolation models where the vertex values can be "nicely" represented (in a sense which will be defined precisely) by i.i.d. random variables. We point out that the ordinary percolation model obviously belongs to this class and we also show that the Ising model mentioned above belongs to it.Comment: Published in at http://dx.doi.org/10.1214/07-AOP380 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The lowest crossing in 2D critical percolation

We study the following problem for critical site percolation on the triangular lattice. Let A and B be sites on a horizontal line e separated by distance n. Consider, in the half-plane above e, the lowest occupied crossing R from the half-line left of A to the half-line right of B. We show that the probability that R has a site at distance smaller than m from AB is of order (log (n/m))^{-1}, uniformly in 1 <= m < n/2. Much of our analysis can be carried out for other two-dimensional lattices as well.Comment: 16 pages, Latex, 2 eps figures, special macros: percmac.tex. Submitted to Annals of Probabilit

The Population Genetic Signature of Polygenic Local Adaptation

Adaptation in response to selection on polygenic phenotypes may occur via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed knowledge about the specific loci underlying polygenic traits has begun to emerge from genome-wide association studies (GWAS). Here we combine this knowledge from GWAS with robust population genetic modeling to identify traits that may have been influenced by local adaptation. We exploit the fact that GWAS provide an estimate of the additive effect size of many loci to estimate the mean additive genetic value for a given phenotype across many populations as simple weighted sums of allele frequencies. We first describe a general model of neutral genetic value drift for an arbitrary number of populations with an arbitrary relatedness structure. Based on this model we develop methods for detecting unusually strong correlations between genetic values and specific environmental variables, as well as a generalization of $Q_{ST}/F_{ST}$ comparisons to test for over-dispersion of genetic values among populations. Finally we lay out a framework to identify the individual populations or groups of populations that contribute to the signal of overdispersion. These tests have considerably greater power than their single locus equivalents due to the fact that they look for positive covariance between like effect alleles, and also significantly outperform methods that do not account for population structure. We apply our tests to the Human Genome Diversity Panel (HGDP) dataset using GWAS data for height, skin pigmentation, type 2 diabetes, body mass index, and two inflammatory bowel disease datasets. This analysis uncovers a number of putative signals of local adaptation, and we discuss the biological interpretation and caveats of these results.Comment: 42 pages including 8 figures and 3 tables; supplementary figures and tables not included on this upload, but are mostly unchanged from v

Genetic analysis of rare disorders: Bayesian estimation of twin concordance rates

Twin concordance rates provide insight into the possibility of a genetic background for a disease. These concordance rates are usually estimated within a frequentistic framework. Here we take a Bayesian approach. For rare diseases, estimation methods based on asymptotic theory cannot be applied due to very low cell probabilities. Moreover, a Bayesian approach allows a straightforward incorporation of prior information on disease prevalence coming from non-twin studies that is often available. An MCMC estimation procedure is tested using simulation and contrasted with frequentistic analyses. The Bayesian method is able to include prior information on both concordance rates and prevalence rates at the same time and is illustrated using twin data on cleft lip and rheumatoid arthritis

SU(2) potentials in quantum gravity

We present investigations of the potential between static charges from a simulation of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.Comment: 3 pages, contribution to Lattice 94 conference, uuencoded compressed postscript fil

Sharpness versus robustness of the percolation transition in 2D contact processes

We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [17] for vegetation patterns in arid landscapes, we focus on percolation under invariant measures of such processes. We prove that the percolation transition is sharp (for one of our models this requires a reasonable assumption). This is shown to contradict a form of 'robust critical behaviour' with power law cluster size distribution for a range of parameter values, as suggested in [17].Comment: 31 pages, to appear in Stochastic Processes and their Application

Influent Wastewater Microbiota and Temperature Influence Anaerobic Membrane Bioreactor Microbial Community

Sustainable municipal wastewater recovery scenarios highlight benefits of anaerobic membrane bioreactors (AnMBRs). However, influences of continuous seeding by influent wastewater and temperature on attached-growth AnMBRs are not well understood. In this study, four bench-scale AnMBR operated at 10 and 25 °C were fed synthetic (SPE) and then real (PE) primary effluent municipal wastewater. Illumina sequencing revealed different bacterial communities in each AnMBR in response to temperature and bioreactor configuration, whereas differences were not observed in archaeal communities. Activity assays revealed hydrogenotrophic methanogenesis was the dominant methanogenic pathway at 10 °C. The significant relative abundance of Methanosaeta at 10 °C concomitant with low acetoclastic methanogenic activity may indicate possible Methanosaeta-Geobacter direct interspecies electron transfer. When AnMBR feed was changed to PE, continual seeding with wastewater microbiota caused AnMBR microbial communities to shift, becoming more similar to PE microbiota. Therefore, influent wastewater microbiota, temperature and reactor configuration influenced the AnMBR microbial community