400 research outputs found
A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds
The Newton iteration is a popular method for minimising a cost function on
Euclidean space. Various generalisations to cost functions defined on manifolds
appear in the literature. In each case, the convergence rate of the generalised
Newton iteration needed establishing from first principles. The present paper
presents a framework for generalising iterative methods from Euclidean space to
manifolds that ensures local convergence rates are preserved. It applies to any
(memoryless) iterative method computing a coordinate independent property of a
function (such as a zero or a local minimum). All possible Newton methods on
manifolds are believed to come under this framework. Changes of coordinates,
and not any Riemannian structure, are shown to play a natural role in lifting
the Newton method to a manifold. The framework also gives new insight into the
design of Newton methods in general.Comment: 36 page
Prospects for near-infrared characterisation of hot Jupiters with VSI
In this paper, we study the feasibility of obtaining near-infrared spectra of
bright extrasolar planets with the 2nd generation VLTI Spectro-Imager
instrument (VSI), which has the required angular resolution to resolve nearby
hot Extrasolar Giant Planets (EGPs) from their host stars. Taking into account
fundamental noises, we simulate closure phase measurements of several
extrasolar systems using four 8-m telescopes at the VLT and a low spectral
resolution (R = 100). Synthetic planetary spectra from T. Barman are used as an
input. Standard chi2-fitting methods are then used to reconstruct planetary
spectra from the simulated data. These simulations show that low-resolution
spectra in the H and K bands can be retrieved with a good fidelity for half a
dozen targets in a reasonable observing time (about 10 hours, spread over a few
nights). Such observations would strongly constrain the planetary temperature
and albedo, the energy redistribution mechanisms, as well as the chemical
composition of their atmospheres. Systematic errors, not included in our
simulations, could be a serious limitation to these performance estimations.
The use of integrated optics is however expected to provide the required
instrumental stability (around 10^-4 on the closure phase) to enable the first
thorough characterisation of extrasolar planetary emission spectra in the
near-infrared.Comment: 10 pages, 8 figures, Proc. SPIE conference 7013 "Optical and Infrared
Interferometry" (Marseille 2008
Improving Interferometric Null Depth Measurements using Statistical Distributions: Theory and First Results with the Palomar Fiber Nuller
A new "self-calibrated" statistical analysis method has been developed for
the reduction of nulling interferometry data. The idea is to use the
statistical distributions of the fluctuating null depth and beam intensities to
retrieve the astrophysical null depth (or equivalently the object's visibility)
in the presence of fast atmospheric fluctuations. The approach yields an
accuracy much better (about an order of magnitude) than is presently possible
with standard data reduction methods, because the astrophysical null depth
accuracy is no longer limited by the magnitude of the instrumental phase and
intensity errors but by uncertainties on their probability distributions. This
approach was tested on the sky with the two-aperture fiber nulling instrument
mounted on the Palomar Hale telescope. Using our new data analysis approach
alone-and no observations of calibrators-we find that error bars on the
astrophysical null depth as low as a few 10-4 can be obtained in the
near-infrared, which means that null depths lower than 10-3 can be reliably
measured. This statistical analysis is not specific to our instrument and may
be applicable to other interferometers
Evidence for a circumplanetary disk around protoplanet PDS 70 b
We present the first observational evidence for a circumplanetary disk around
the protoplanet PDS~70~b, based on a new spectrum in the band acquired with
VLT/SINFONI. We tested three hypotheses to explain the spectrum: Atmospheric
emission from the planet with either (1) a single value of extinction or (2)
variable extinction, and (3) a combined atmospheric and circumplanetary disk
model. Goodness-of-fit indicators favour the third option, suggesting
circumplanetary material contributing excess thermal emission --- most
prominent at m. Inferred accretion rates (-- yr) are compatible with observational
constraints based on the H and Br lines. For the planet, we
derive an effective temperature of 1500--1600 K, surface gravity , radius , mass , and possible thick clouds.
Models with variable extinction lead to slightly worse fits. However, the
amplitude (mag) and timescale of variation
(~years) required for the extinction would also suggest
circumplanetary material.Comment: 8 pages, 2 figures, 1 table. This is a pre-copyedited,
author-produced PDF of an article accepted for publication in ApJL on 2019
May 1
Low-rank optimization for semidefinite convex problems
We propose an algorithm for solving nonlinear convex programs defined in
terms of a symmetric positive semidefinite matrix variable . This algorithm
rests on the factorization , where the number of columns of Y fixes
the rank of . It is thus very effective for solving programs that have a low
rank solution. The factorization evokes a reformulation of the
original problem as an optimization on a particular quotient manifold. The
present paper discusses the geometry of that manifold and derives a second
order optimization method. It furthermore provides some conditions on the rank
of the factorization to ensure equivalence with the original problem. The
efficiency of the proposed algorithm is illustrated on two applications: the
maximal cut of a graph and the sparse principal component analysis problem.Comment: submitte
Integrated scheme of rapid environmental assessment for shallow water acoustics
Predicting sound propagation in shallow or very shallow water environments requires that the frequency-dependent acoustic properties be assessed for all components of the waveguide, i.e., the water column, sea bottom and sea surface interface. During the Maritime Rapid Environmental Assessment MREA?BP'07 sea trial in April-May 2007, south of Elba Island in the Mediterranean Sea, an integrated MREA scheme has been implemented to provide a full 4D (3D+T) environmental picture that is directly exploitable by acoustic propagation models. Based on a joint multi-disciplinary effort, several standard and advanced techniques of environmental characterization covering the fields of underwater acoustics, physical oceanography and geophysics have been combined within a coherent scheme of data acquisition, processing and assimilation. The paper presents the whole architecture of the implemented scheme. Based on a preliminary analysis of MREA?BP'07 data, advantages and drawbacks of the approach will be discussed. Ways ahead for further improvement and perspectives are finally drawn
A geometric Newton method for Oja's vector field
Newton's method for solving the matrix equation runs
up against the fact that its zeros are not isolated. This is due to a symmetry
of by the action of the orthogonal group. We show how
differential-geometric techniques can be exploited to remove this symmetry and
obtain a ``geometric'' Newton algorithm that finds the zeros of . The
geometric Newton method does not suffer from the degeneracy issue that stands
in the way of the original Newton method
Direct exoplanet detection and characterization using the ANDROMEDA method: Performance on VLT/NaCo data
Context. The direct detection of exoplanets with high-contrast imaging
requires advanced data processing methods to disentangle potential planetary
signals from bright quasi-static speckles. Among them, angular differential
imaging (ADI) permits potential planetary signals with a known rotation rate to
be separated from instrumental speckles that are either statics or slowly
variable. The method presented in this paper, called ANDROMEDA for ANgular
Differential OptiMal Exoplanet Detection Algorithm is based on a maximum
likelihood approach to ADI and is used to estimate the position and the flux of
any point source present in the field of view. Aims. In order to optimize and
experimentally validate this previously proposed method, we applied ANDROMEDA
to real VLT/NaCo data. In addition to its pure detection capability, we
investigated the possibility of defining simple and efficient criteria for
automatic point source extraction able to support the processing of large
surveys. Methods. To assess the performance of the method, we applied ANDROMEDA
on VLT/NaCo data of TYC-8979-1683-1 which is surrounded by numerous bright
stars and on which we added synthetic planets of known position and flux in the
field. In order to accommodate the real data properties, it was necessary to
develop additional pre-processing and post-processing steps to the initially
proposed algorithm. We then investigated its skill in the challenging case of a
well-known target, Pictoris, whose companion is close to the detection
limit and we compared our results to those obtained by another method based on
principal component analysis (PCA). Results. Application on VLT/NaCo data
demonstrates the ability of ANDROMEDA to automatically detect and characterize
point sources present in the image field. We end up with a robust method
bringing consistent results with a sensitivity similar to the recently
published algorithms, with only two parameters to be fine tuned. Moreover, the
companion flux estimates are not biased by the algorithm parameters and do not
require a posteriori corrections. Conclusions. ANDROMEDA is an attractive
alternative to current standard image processing methods that can be readily
applied to on-sky data
Auto-RSM: An automated parameter-selection algorithm for the RSM map exoplanet detection algorithm
Context. Most of the high-contrast imaging (HCI) data-processing techniques used over the last 15 years have relied on the angular differential imaging (ADI) observing strategy, along with subtraction of a reference point spread function (PSF) to generate exoplanet detection maps. Recently, a new algorithm called regime switching model (RSM) map has been proposed to take advantage of these numerous PSF-subtraction techniques; RSM uses several of these techniques to generate a single probability map. Selection of the optimal parameters for these PSF-subtraction techniques as well as for the RSM map is not straightforward, is time consuming, and can be biased by assumptions made as to the underlying data set. Aims: We propose a novel optimisation procedure that can be applied to each of the PSF-subtraction techniques alone, or to the entire RSM framework. Methods: The optimisation procedure consists of three main steps: (i) definition of the optimal set of parameters for the PSF-subtraction techniques using the contrast as performance metric, (ii) optimisation of the RSM algorithm, and (iii) selection of the optimal set of PSF-subtraction techniques and ADI sequences used to generate the final RSM probability map. Results: The optimisation procedure is applied to the data sets of the exoplanet imaging data challenge, which provides tools to compare the performance of HCI data-processing techniques. The data sets consist of ADI sequences obtained with three state-of-the-art HCI instruments: SPHERE, NIRC2, and LMIRCam. The results of our analysis demonstrate the interest of the proposed optimisation procedure, with better performance metrics compared to the earlier version of RSM, as well as to other HCI data-processing techniques.EPIC; NNEx
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