8,974 research outputs found
Point Process Algorithm: A New Bayesian Approach for Planet Signal Extraction with the Terrestrial Planet Finder
The capability of the Terrestrial Planet Finder Interferometer (TPF-I) for
planetary signal extraction, including both detection and spectral
characterization, can be optimized by taking proper account of instrumental
characteristics and astrophysical prior information. We have developed the
Point Process Algorithm (PPA), a Bayesian technique for extracting planetary
signals using the sine-chopped outputs of a dual nulling interferometer. It is
so-called because it represents the system being observed as a set of points in
a suitably-defined state space, thus providing a natural way of incorporating
our prior knowledge of the compact nature of the targets of interest. It can
also incorporate the spatial covariance of the exozodi as prior information
which could help mitigate against false detections. Data at multiple
wavelengths are used simultaneously, taking into account possible spectral
variations of the planetary signals. Input parameters include the RMS
measurement noise and the a priori probability of the presence of a planet. The
output can be represented as an image of the intensity distribution on the sky,
optimized for the detection of point sources. Previous approaches by others to
the problem of planet detection for TPF-I have relied on the potentially
non-robust identification of peaks in a "dirty" image, usually a correlation
map. Tests with synthetic data suggest that the PPA provides greater
sensitivity to faint sources than does the standard approach (correlation map +
CLEAN), and will be a useful tool for optimizing the design of TPF-I.Comment: 17 pages, 6 figures. AJ in press (scheduled for Nov 2006
Dependence of chaotic diffusion on the size and position of holes
A particle driven by deterministic chaos and moving in a spatially extended
environment can exhibit normal diffusion, with its mean square displacement
growing proportional to the time. Here we consider the dependence of the
diffusion coefficient on the size and the position of areas of phase space
linking spatial regions (`holes') in a class of simple one-dimensional,
periodically lifted maps. The parameter dependent diffusion coefficient can be
obtained analytically via a Taylor-Green-Kubo formula in terms of a functional
recursion relation. We find that the diffusion coefficient varies
non-monotonically with the size of a hole and its position, which implies that
a diffusion coefficient can increase by making the hole smaller. We derive
analytic formulas for small holes in terms of periodic orbits covered by the
holes. The asymptotic regimes that we observe show deviations from the standard
stochastic random walk approximation. The escape rate of the corresponding open
system is also calculated. The resulting parameter dependencies are compared
with the ones for the diffusion coefficient and explained in terms of periodic
orbits.Comment: 12 pages, 5 figure
Fast Bayesian Optimal Experimental Design for Seismic Source Inversion
We develop a fast method for optimally designing experiments in the context
of statistical seismic source inversion. In particular, we efficiently compute
the optimal number and locations of the receivers or seismographs. The seismic
source is modeled by a point moment tensor multiplied by a time-dependent
function. The parameters include the source location, moment tensor components,
and start time and frequency in the time function. The forward problem is
modeled by elastodynamic wave equations. We show that the Hessian of the cost
functional, which is usually defined as the square of the weighted L2 norm of
the difference between the experimental data and the simulated data, is
proportional to the measurement time and the number of receivers. Consequently,
the posterior distribution of the parameters, in a Bayesian setting,
concentrates around the "true" parameters, and we can employ Laplace
approximation and speed up the estimation of the expected Kullback-Leibler
divergence (expected information gain), the optimality criterion in the
experimental design procedure. Since the source parameters span several
magnitudes, we use a scaling matrix for efficient control of the condition
number of the original Hessian matrix. We use a second-order accurate finite
difference method to compute the Hessian matrix and either sparse quadrature or
Monte Carlo sampling to carry out numerical integration. We demonstrate the
efficiency, accuracy, and applicability of our method on a two-dimensional
seismic source inversion problem
Fast Point Spread Function Modeling with Deep Learning
Modeling the Point Spread Function (PSF) of wide-field surveys is vital for
many astrophysical applications and cosmological probes including weak
gravitational lensing. The PSF smears the image of any recorded object and
therefore needs to be taken into account when inferring properties of galaxies
from astronomical images. In the case of cosmic shear, the PSF is one of the
dominant sources of systematic errors and must be treated carefully to avoid
biases in cosmological parameters. Recently, forward modeling approaches to
calibrate shear measurements within the Monte-Carlo Control Loops ()
framework have been developed. These methods typically require simulating a
large amount of wide-field images, thus, the simulations need to be very fast
yet have realistic properties in key features such as the PSF pattern. Hence,
such forward modeling approaches require a very flexible PSF model, which is
quick to evaluate and whose parameters can be estimated reliably from survey
data. We present a PSF model that meets these requirements based on a fast
deep-learning method to estimate its free parameters. We demonstrate our
approach on publicly available SDSS data. We extract the most important
features of the SDSS sample via principal component analysis. Next, we
construct our model based on perturbations of a fixed base profile, ensuring
that it captures these features. We then train a Convolutional Neural Network
to estimate the free parameters of the model from noisy images of the PSF. This
allows us to render a model image of each star, which we compare to the SDSS
stars to evaluate the performance of our method. We find that our approach is
able to accurately reproduce the SDSS PSF at the pixel level, which, due to the
speed of both the model evaluation and the parameter estimation, offers good
prospects for incorporating our method into the framework.Comment: 25 pages, 8 figures, 1 tabl
Using quantum key distribution for cryptographic purposes: a survey
The appealing feature of quantum key distribution (QKD), from a cryptographic
viewpoint, is the ability to prove the information-theoretic security (ITS) of
the established keys. As a key establishment primitive, QKD however does not
provide a standalone security service in its own: the secret keys established
by QKD are in general then used by a subsequent cryptographic applications for
which the requirements, the context of use and the security properties can
vary. It is therefore important, in the perspective of integrating QKD in
security infrastructures, to analyze how QKD can be combined with other
cryptographic primitives. The purpose of this survey article, which is mostly
centered on European research results, is to contribute to such an analysis. We
first review and compare the properties of the existing key establishment
techniques, QKD being one of them. We then study more specifically two generic
scenarios related to the practical use of QKD in cryptographic infrastructures:
1) using QKD as a key renewal technique for a symmetric cipher over a
point-to-point link; 2) using QKD in a network containing many users with the
objective of offering any-to-any key establishment service. We discuss the
constraints as well as the potential interest of using QKD in these contexts.
We finally give an overview of challenges relative to the development of QKD
technology that also constitute potential avenues for cryptographic research.Comment: Revised version of the SECOQC White Paper. Published in the special
issue on QKD of TCS, Theoretical Computer Science (2014), pp. 62-8
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