1,983 research outputs found
Random trees between two walls: Exact partition function
We derive the exact partition function for a discrete model of random trees
embedded in a one-dimensional space. These trees have vertices labeled by
integers representing their position in the target space, with the SOS
constraint that adjacent vertices have labels differing by +1 or -1. A
non-trivial partition function is obtained whenever the target space is bounded
by walls. We concentrate on the two cases where the target space is (i) the
half-line bounded by a wall at the origin or (ii) a segment bounded by two
walls at a finite distance. The general solution has a soliton-like structure
involving elliptic functions. We derive the corresponding continuum scaling
limit which takes the remarkable form of the Weierstrass p-function with
constrained periods. These results are used to analyze the probability for an
evolving population spreading in one dimension to attain the boundary of a
given domain with the geometry of the target (i) or (ii). They also translate,
via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main
modifications in Sect. 5-6 and conclusio
Confluence of geodesic paths and separating loops in large planar quadrangulations
We consider planar quadrangulations with three marked vertices and discuss
the geometry of triangles made of three geodesic paths joining them. We also
study the geometry of minimal separating loops, i.e. paths of minimal length
among all closed paths passing by one of the three vertices and separating the
two others in the quadrangulation. We concentrate on the universal scaling
limit of large quadrangulations, also known as the Brownian map, where pairs of
geodesic paths or minimal separating loops have common parts of non-zero
macroscopic length. This is the phenomenon of confluence, which distinguishes
the geometry of random quadrangulations from that of smooth surfaces. We
characterize the universal probability distribution for the lengths of these
common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding
paragraph and one reference added, and several other small correction
The redshift evolution of bias and baryonic matter distribution
We study the distribution of baryonic and luminous matter within the
framework of a hierarchical scenario. Using an analytical model for structure
formation which has already been checked against observations for galaxies,
Lyman- clouds, clusters and reionization processes, we present its
predictions for the bias of these objects. We describe its dependence on the
luminosity (for galaxies or quasars) or the column density (for Lyman-
absorbers) of the considered objects. We also study its redshift evolution,
which can exhibit an intricate behaviour. These astrophysical objects do not
trace the dark matter density field, the Lyman- forest clouds being
undercorrelated and the bright galaxies overcorrelated, while the intermediate
class of Lyman-limit systems is seen to sample the matter field quite well.
We also present the distribution of baryonic matter over these various
objects. We show that light does not trace baryonic mass, since bright galaxies
which contain most of the stars only form a small fraction of the mass
associated with virialized and cooled halos. We consider two cosmologies: a
critical density universe and an open universe. In both cases, our results
agree with observations and show that hierarchical scenarios provide a good
model for structure formation and can describe a wide range of objects which
spans at least the seven orders of magnitude in mass for which data exist. More
detailed observations, in particular of the clustering evolution of galaxies,
will constrain the astrophysical models involved.Comment: 13 pages, final version published in A&
Distance statistics in large toroidal maps
We compute a number of distance-dependent universal scaling functions
characterizing the distance statistics of large maps of genus one. In
particular, we obtain explicitly the probability distribution for the length of
the shortest non-contractible loop passing via a random point in the map, and
that for the distance between two random points. Our results are derived in the
context of bipartite toroidal quadrangulations, using their coding by
well-labeled 1-trees, which are maps of genus one with a single face and
appropriate integer vertex labels. Within this framework, the distributions
above are simply obtained as scaling limits of appropriate generating functions
for well-labeled 1-trees, all expressible in terms of a small number of basic
scaling functions for well-labeled plane trees.Comment: 24 pages, 9 figures, minor corrections, new added reference
Distance statistics in quadrangulations with a boundary, or with a self-avoiding loop
We consider quadrangulations with a boundary and derive explicit expressions
for the generating functions of these maps with either a marked vertex at a
prescribed distance from the boundary, or two boundary vertices at a prescribed
mutual distance in the map. For large maps, this yields explicit formulas for
the bulk-boundary and boundary-boundary correlators in the various encountered
scaling regimes: a small boundary, a dense boundary and a critical boundary
regime. The critical boundary regime is characterized by a one-parameter family
of scaling functions interpolating between the Brownian map and the Brownian
Continuum Random Tree. We discuss the cases of both generic and self-avoiding
boundaries, which are shown to share the same universal scaling limit. We
finally address the question of the bulk-loop distance statistics in the
context of planar quadrangulations equipped with a self-avoiding loop. Here
again, a new family of scaling functions describing critical loops is
discovered.Comment: 55 pages, 14 figures, final version with minor correction
Influence of an elliptic instability on the merging of a co-rotating vortex pair
We study the nonlinear evolution of the elliptic instability and its influence on the merging process of two corotating Batchelor vortices using a spectral DNS approach. First, we analyse the nonlinear saturation of the elliptic instability for a single strained vortex, with and without axial jet, for moderate Reynolds numbers (Re= Gamma/nu approx= 12500, where Gamma is the circulation and nu the kinematic viscosity). We show that the vortex deformation induced by the instability remains limited to the vortex core region. The second part of our work focuses on the influence of the elliptic instability on the merging process. We compare three cases : no instability (2D), elliptic instability without axial jet, and elliptic instability with axial jet, the latter case being relevant to aircraft wakes. Qualitative and quantitative differences between the three different cases are pointed out and discussed in the context of aircraft vortices
Multicritical continuous random trees
We introduce generalizations of Aldous' Brownian Continuous Random Tree as
scaling limits for multicritical models of discrete trees. These discrete
models involve trees with fine-tuned vertex-dependent weights ensuring a k-th
root singularity in their generating function. The scaling limit involves
continuous trees with branching points of order up to k+1. We derive explicit
integral representations for the average profile of this k-th order
multicritical continuous random tree, as well as for its history distributions
measuring multi-point correlations. The latter distributions involve
non-positive universal weights at the branching points together with fractional
derivative couplings. We prove universality by rederiving the same results
within a purely continuous axiomatic approach based on the resolution of a set
of consistency relations for the multi-point correlations. The average profile
is shown to obey a fractional differential equation whose solution involves
hypergeometric functions and matches the integral formula of the discrete
approach.Comment: 34 pages, 12 figures, uses lanlmac, hyperbasics, eps
Characterization of Norovirus and Other Human Enteric Viruses in Sewage and Stool Samples Through Next-Generation Sequencing.
This study aimed to optimize a method to identify human enteric viruses in sewage and stool samples using random primed next-generation sequencing. We tested three methods, two employed virus enrichment based on the binding properties of the viral capsid using pig-mucin capture or by selecting viral RNA prior to library preparation through a capture using the SureSelect target enrichment. The third method was based on a non-specific biophysical precipitation with polyethylene glycol. Full genomes of a number of common human enteric viruses including norovirus, rotavirus, husavirus, enterovirus and astrovirus were obtained. In stool samples full norovirus genome were detected as well as partial enterovirus genome. A variety of norovirus sequences was detected in sewage samples, with genogroup II being more prevalent. Interestingly, the pig-mucin capture enhanced not only the recovery of norovirus and rotavirus but also recovery of astrovirus, sapovirus and husavirus. Documenting sewage virome using these methods provides information for molecular epidemiology and may be useful in developing strategies to prevent further spread of viruses
Assessment of human enteric viruses in cultured and wild bivalve molluscs
Standard and real-time reverse transcription-PCR (rRT-PCR) procedures were used to monitor cultured and wild bivalve molluscs from the Ría de Vigo (NW Spain) for the main human enteric RNA viruses, specifically, norovirus (NoV), hepatitis Avirus (HAV), astrovirus (AsV), rotavirus (RT), enterovirus (EV), and Aichi virus (AiV). The results showed the presence of at least one enteric virus in 63.4% of the 41 samples analyzed. NoV GII was the most prevalent virus, detected in 53.7% of the samples, while NoV GI, AsV, EV, and RV were found at lower percentages (7.3, 12.2, 12.2, and 4.9%, respectively). In general, samples obtained in the wild were more frequently contaminated than those from cultured (70.6 vs. 58.3%) molluscs and were more readily contaminated with more than one virus. However, NoV GI was detected in similar amounts in cultured and wild samples (6.4 × 102 to 3.3 × 103 RNA copies per gram of digestive tissue) while the concentrations of NoV GII were higher in cultured (from 5.6 × 101 to 1.5 × 104 RNA copies per gram of digestive tissue) than in wild (from 1.3 × 102 to 3.4 × 104 RNA copies per gram of digestive tissue) samples. [Int Microbiol 2009; 12(3):145-151
Loop models on random maps via nested loops: case of domain symmetry breaking and application to the Potts model
We use the nested loop approach to investigate loop models on random planar
maps where the domains delimited by the loops are given two alternating colors,
which can be assigned different local weights, hence allowing for an explicit
Z_2 domain symmetry breaking. Each loop receives a non local weight n, as well
as a local bending energy which controls loop turns. By a standard cluster
construction that we review, the Q = n^2 Potts model on general random maps is
mapped to a particular instance of this problem with domain-non-symmetric
weights. We derive in full generality a set of coupled functional relations for
a pair of generating series which encode the enumeration of loop configurations
on maps with a boundary of a given color, and solve it by extending well-known
complex analytic techniques. In the case where loops are fully-packed, we
analyze in details the phase diagram of the model and derive exact equations
for the position of its non-generic critical points. In particular, we
underline that the critical Potts model on general random maps is not self-dual
whenever Q \neq 1. In a model with domain-symmetric weights, we also show the
possibility of a spontaneous domain symmetry breaking driven by the bending
energy.Comment: 44 pages, 13 figure
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