62,063 research outputs found
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 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
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 and 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 . 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
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 . In words, this equation means
that for all values of the parameter , 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 , 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
) with external field , 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
Sharpness of the percolation transition in the two-dimensional contact process
For ordinary (independent) percolation on a large class of lattices it is
well known that below the critical percolation parameter the cluster size
distribution has exponential decay and that power-law behavior of this
distribution can only occur at . This behavior is often called ``sharpness
of the percolation transition.'' For theoretical reasons, as well as motivated
by applied research, there is an increasing interest in percolation models with
(weak) dependencies. For instance, biologists and agricultural researchers have
used (stationary distributions of) certain two-dimensional contact-like
processes to model vegetation patterns in an arid landscape (see [20]). In that
context occupied clusters are interpreted as patches of vegetation. For some of
these models it is reported in [20] that computer simulations indicate
power-law behavior in some interval of positive length of a model parameter.
This would mean that in these models the percolation transition is not sharp.
This motivated us to investigate similar questions for the ordinary (``basic'')
contact process with parameter . We show, using techniques from
Bollob\'{a}s and Riordan [8, 11], that for the upper invariant measure
of this process the percolation transition is sharp. If
is such that (-a.s.) there are no infinite
clusters, then for all parameter values below the cluster-size
distribution has exponential decay.Comment: Published in at http://dx.doi.org/10.1214/10-AAP702 the Annals of
Applied Probability (http://www.imstat.org/aap/) 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 fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function
We study the fixed point for a non-linear transformation in the set of
Hausdorff moment sequences, defined by the formula: . We determine the corresponding measure , which has an increasing
and convex density on , and we study some analytic functions related to
it. The Mellin transform of extends to a meromorphic function in the
whole complex plane. It can be characterized in analogy with the Gamma function
as the unique log-convex function on satisfying and the
functional equation .Comment: 29 pages,1 figur
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
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
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