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 $\sim$0.3-0.8\% photometric error and $\sim$$3-10\cdot10^{-3}$ $\lambda/D$ astrometric error, which is a performance increase of a factor $\sim$20 and $\sim$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 $\Upsilon$ be a compact, negatively curved surface. From the (finite) set of all closed geodesics on $\Upsilon$ of length $\leq L$, choose one, say $\gamma_{L}$, at random and let $N (\gamma_{L})$ be the number of its self-intersections. It is known that there is a positive constant $\kappa$ depending on the metric such that $N (\gamma_{L})/L^{2} \rightarrow \kappa$ in probability as $L\rightarrow \infty$. The main results of this paper concern the size of typical fluctuations of $N (\gamma_{L})$ about $\kappa L^{2}$. It is proved that if the metric has constant curvature -1 then typical fluctuations are of order $L$, in particular, $(N (\gamma_{L})-\kappa L^{2})/L$ converges weakly to a nondegenerate probability distribution. In contrast, it is also proved that if the metric has variable negative curvature then fluctuations of $N (\gamma_{L})$ are of order $L^{3/2}$, in particular, $(N (\gamma_{L})-\kappa L^{2})/L^{3/2}$ 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 $p-$coin tosses. Spatial variants of these models are proposed, in which finite populations of size $N$ 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 $p$ 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 $\Phi$ taking a data set $x$ to a point in some space F, should be stable at $x$: Small perturbations in $x$ should result in a small change in $\Phi(x)$. Otherwise, $\Phi$ is useless at $x$ or -- and this is important -- near $x$. So one doesn't want $\Phi$ to have "singularities," data sets $x$ s.t.\ the the limit of $\Phi(y)$ as $y$ approaches $x$ 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

Storeria dekayi

Number of Pages: 4Integrative BiologyGeological Science