6,459 research outputs found
Exponential clogging time for a one dimensional DLA
When considering DLA on a cylinder it is natural to ask how many particles it
takes to clog the cylinder, e.g. modeling clogging of arteries. In this note we
formulate a very simple DLA clogging model and establish an exponential lower
bound on the number of particles arriving before clogging appears
Shape-based peak identification for ChIP-Seq
We present a new algorithm for the identification of bound regions from
ChIP-seq experiments. Our method for identifying statistically significant
peaks from read coverage is inspired by the notion of persistence in
topological data analysis and provides a non-parametric approach that is robust
to noise in experiments. Specifically, our method reduces the peak calling
problem to the study of tree-based statistics derived from the data. We
demonstrate the accuracy of our method on existing datasets, and we show that
it can discover previously missed regions and can more clearly discriminate
between multiple binding events. The software T-PIC (Tree shape Peak
Identification for ChIP-Seq) is available at
http://math.berkeley.edu/~vhower/tpic.htmlComment: 12 pages, 6 figure
A Deep WSRT 1.4 GHz Radio Survey of the Spitzer Space Telescope FLSv Region
The First Look Survey (FLS) is the first scientific product to emerge from
the Spitzer Space Telescope. A small region of this field (the verification
strip) has been imaged very deeply, permitting the detection of cosmologically
distant sources. We present Westerbork Synthesis Radio Telescope (WSRT)
observations of this region, encompassing a ~1 sq. deg field, centred on the
verification strip (J2000 RA=17:17:00.00, DEC=59:45:00.000). The radio images
reach a noise level of ~ 8.5 microJy/beam - the deepest WSRT image made to
date. We summarise here the first results from the project, and present the
final mosaic image, together with a list of detected sources. The effect of
source confusion on the position, size and flux density of the faintest sources
in the source catalogue are also addressed. The results of a serendipitous
search for HI emission in the field are also presented. Using a subset of the
data, we clearly detect HI emission associated with four galaxies in the
central region of the FLSv. These are identified with nearby, massive galaxies.Comment: 9 pages, 6 figures (fig.3 in a separate gif file). Accepted for
publication in A&A. The full paper and the related material can be downloaded
from http://www.astron.nl/wsrt/WSRTsurveys/WFLS
On the effect of adding epsilon-Bernoulli percolation to everywhere percolating subgraphs of Z^d
We show that adding epsilon-Bernoulli percolation to an everywhere
percolating subgraph of Z^2 results in a graph which has large scale geometry
similar to that of supercritical Bernoulli percolation, in various specific
senses. We conjecture similar behavior in higher dimensions.Comment: Author home pages: http://www.wisdom.weizmann.ac.il/~itai
http://www.math.chalmers.se/~olleh http://www.wisdom.weizmann.ac.il/~schram
Percolation in invariant Poisson graphs with i.i.d. degrees
Let each point of a homogeneous Poisson process in R^d independently be
equipped with a random number of stubs (half-edges) according to a given
probability distribution mu on the positive integers. We consider
translation-invariant schemes for perfectly matching the stubs to obtain a
simple graph with degree distribution mu. Leaving aside degenerate cases, we
prove that for any mu there exist schemes that give only finite components as
well as schemes that give infinite components. For a particular matching scheme
that is a natural extension of Gale-Shapley stable marriage, we give sufficient
conditions on mu for the absence and presence of infinite components
Exact Multifractal Exponents for Two-Dimensional Percolation
The harmonic measure (or diffusion field or electrostatic potential) near a
percolation cluster in two dimensions is considered. Its moments, summed over
the accessible external hull, exhibit a multifractal spectrum, which I
calculate exactly. The generalized dimensions D(n) as well as the MF function
f(alpha) are derived from generalized conformal invariance, and are shown to be
identical to those of the harmonic measure on 2D random walks or self-avoiding
walks. An exact application to the anomalous impedance of a rough percolative
electrode is given. The numerical checks are excellent. Another set of exact
and universal multifractal exponents is obtained for n independent
self-avoiding walks anchored at the boundary of a percolation cluster. These
exponents describe the multifractal scaling behavior of the average nth moment
of the probabity for a SAW to escape from the random fractal boundary of a
percolation cluster in two dimensions.Comment: 5 pages, 3 figures (in colors
A Sublinear Variance Bound for Solutions of a Random Hamilton Jacobi Equation
We estimate the variance of the value function for a random optimal control
problem. The value function is the solution of a Hamilton-Jacobi
equation with random Hamiltonian
in dimension . It is known that homogenization occurs as , but little is known about the statistical fluctuations of .
Our main result shows that the variance of the solution is bounded
by . The proof relies on a modified Poincar\'e
inequality of Talagrand
Excited Random Walk in One Dimension
We study the excited random walk, in which a walk that is at a site that
contains cookies eats one cookie and then hops to the right with probability p
and to the left with probability q=1-p. If the walk hops onto an empty site,
there is no bias. For the 1-excited walk on the half-line (one cookie initially
at each site), the probability of first returning to the starting point at time
t scales as t^{-(2-p)}. Although the average return time to the origin is
infinite for all p, the walk eats, on average, only a finite number of cookies
until this first return when p<1/2. For the infinite line, the probability
distribution for the 1-excited walk has an unusual anomaly at the origin. The
positions of the leftmost and rightmost uneaten cookies can be accurately
estimated by probabilistic arguments and their corresponding distributions have
power-law singularities near the origin. The 2-excited walk on the infinite
line exhibits peculiar features in the regime p>3/4, where the walk is
transient, including a mean displacement that grows as t^{nu}, with nu>1/2
dependent on p, and a breakdown of scaling for the probability distribution of
the walk.Comment: 14 pages, 13 figures, 2-column revtex4 format, for submission to J.
Phys.
Phase Transitions on Nonamenable Graphs
We survey known results about phase transitions in various models of
statistical physics when the underlying space is a nonamenable graph. Most
attention is devoted to transitive graphs and trees
The spectral dimension of generic trees
We define generic ensembles of infinite trees. These are limits as
of ensembles of finite trees of fixed size , defined in terms
of a set of branching weights. Among these ensembles are those supported on
trees with vertices of a uniformly bounded order. The associated probability
measures are supported on trees with a single spine and Hausdorff dimension
. Our main result is that their spectral dimension is , and
that the critical exponent of the mass, defined as the exponential decay rate
of the two-point function along the spine, is 1/3
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