51,637 research outputs found
Vector speckle grid: instantaneous incoherent speckle grid for high-precision astrometry and photometry in high-contrast imaging
Photometric and astrometric monitoring of directly imaged exoplanets will
deliver unique insights into their rotational periods, the distribution of
cloud structures, weather, and orbital parameters. As the host star is occulted
by the coronagraph, a speckle grid (SG) is introduced to serve as astrometric
and photometric reference. Speckle grids are implemented as diffractive
pupil-plane optics that generate artificial speckles at known location and
brightness. Their performance is limited by the underlying speckle halo caused
by evolving uncorrected wavefront errors. The speckle halo will interfere with
the coherent SGs, affecting their photometric and astrometric precision. Our
aim is to show that by imposing opposite amplitude or phase modulation on the
opposite polarization states, a SG can be instantaneously incoherent with the
underlying halo, greatly increasing the precision. We refer to these as vector
speckle grids (VSGs). We derive analytically the mechanism by which the
incoherency arises and explore the performance gain in idealised simulations
under various atmospheric conditions. We show that the VSG is completely
incoherent for unpolarized light and that the fundamental limiting factor is
the cross-talk between the speckles in the grid. In simulation, we find that
for short-exposure images the VSG reaches a 0.3-0.8\% photometric error
and astrometric error, which is a
performance increase of a factor 20 and 5, respectively.
Furthermore, we outline how VSGs could be implemented using liquid-crystal
technology to impose the geometric phase on the circular polarization states.
The VSG is a promising new method for generating a photometric and astrometric
reference SG that has a greatly increased astrometric and photometric
precision.Comment: Accepted for publication in A&
Wolbachia and arbovirus inhibition in mosquitoes
Wolbachia is a maternally inherited intracellular bacteria that can manipulate the reproduction of their insect hosts, and cytoplasmic incompatibility allows them to spread through mosquito populations. When particular strains of Wolbachia are transferred into certain Aedes mosquito species, the transmission capacity of important arthropod-borne viruses can be suppressed or abolished in laboratory challenges. Viral inhibition is associated with higher densities of transinfecting Wolbachia compared with wild-type strains of the bacterium. The upregulation of innate immune effectors can contribute to virus inhibition in Aedes aegypti, but does not seem to be required. Modulation of autophagy and lipid metabolism, and intracellular competition between viruses and bacteria for lipids, provide promising hypotheses for the mechanism of inhibition. Transinfecting virus-inhibiting strains can produce higher fitness costs than wild-type mosquito Wolbachia; however, this is not always the case, and the wMel strain has already been introduced to high frequency in wild Ae. aegypti populations
Statistical regularities of self-intersection counts for geodesics on negatively curved surfaces
Let be a compact, negatively curved surface. From the (finite)
set of all closed geodesics on of length , choose one, say
, at random and let be the number of its
self-intersections. It is known that there is a positive constant
depending on the metric such that in
probability as . The main results of this paper concern
the size of typical fluctuations of about . It
is proved that if the metric has constant curvature -1 then typical
fluctuations are of order , in particular,
converges weakly to a nondegenerate probability distribution. In contrast, it
is also proved that if the metric has variable negative curvature then
fluctuations of are of order , in particular, converges weakly to a Gaussian
distribution. Similar results are proved for generic geodesics, that is,
geodesics whose initial tangent vectors are chosen randomly according to
normalized Liouville measure
Critical scaling of stochastic epidemic models
In the simple mean-field SIS and SIR epidemic models, infection is
transmitted from infectious to susceptible members of a finite population by
independent coin tosses. Spatial variants of these models are proposed, in
which finite populations of size are situated at the sites of a lattice and
infectious contacts are limited to individuals at neighboring sites. Scaling
laws for both the mean-field and spatial models are given when the infection
parameter is such that the epidemics are critical. It is shown that in all
cases there is a critical threshold for the numbers initially infected: below
the threshold, the epidemic evolves in essentially the same manner as its
branching envelope, but at the threshold evolves like a branching process with
a size-dependent drift.Comment: Published at http://dx.doi.org/10.1214/074921707000000346 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Singularity of Data Analytic Operations
Statistical data by their very nature are indeterminate in the sense that if
one repeated the process of collecting the data the new data set would be
somewhat different from the original. Therefore, a statistical method, a map
taking a data set to a point in some space F, should be stable at
: Small perturbations in should result in a small change in .
Otherwise, is useless at or -- and this is important -- near . So
one doesn't want to have "singularities," data sets s.t.\ the the
limit of as approaches doesn't exist. (Yes, the same issue
arises elsewhere in applied math.)
However, broad classes of statistical methods have topological obstructions
of continuity: They must have singularities. We show why and give lower bounds
on the Hausdorff dimension, even Hausdorff measure, of the set of singularities
of such data maps. There seem to be numerous examples.
We apply mainly topological methods to study the (topological) singularities
of functions defined (on dense subsets of) "data spaces" and taking values in
spaces with nontrivial homology. At least in this book, data spaces are usually
compact manifolds. The purpose is to gain insight into the numerical
conditioning of statistical description, data summarization, and inference and
learning methods. We prove general results that can often be used to bound
below the dimension of the singular set. We apply our topological results to
develop lower bounds on Hausdorff measure of the singular set. We apply these
methods to the study of plane fitting and measuring location of data on
spheres.
\emph{This is not a "final" version, merely another attempt.}Comment: 325 pages, 8 figure
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