Optimal PSF modeling for weak lensing: complexity and sparsity

We investigate the impact of point spread function (PSF) fitting errors on cosmic shear measurements using the concepts of complexity and sparsity. Complexity, introduced in a previous paper, characterizes the number of degrees of freedom of the PSF. For instance, fitting an underlying PSF with a model with low complexity will lead to small statistical errors on the model parameters, however these parameters could suffer from large biases. Alternatively, fitting with a large number of parameters will tend to reduce biases at the expense of statistical errors. We perform an optimisation of scatters and biases by studying the mean squared error of a PSF model. We also characterize a model sparsity, which describes how efficiently the model is able to represent the underlying PSF using a limited number of free parameters. We present the general case and illustrate it for a realistic example of PSF fitted with shapelet basis sets. We derive the relation between complexity and sparsity of the PSF model, signal-to-noise ratio of stars and systematic errors on cosmological parameters. With the constraint of maintaining the systematics below the statistical uncertainties, this lead to a relation between the required number of stars to calibrate the PSF and the sparsity. We discuss the impact of our results for current and future cosmic shear surveys. In the typical case where the biases can be represented as a power law of the complexity, we show that current weak lensing surveys can calibrate the PSF with few stars, while future surveys will require hard constraints on the sparsity in order to calibrate the PSF with 50 stars.Comment: accepted by A&A, 9 pages, 6 figure

Cosmic Shear Systematics: Software-Hardware Balance

Cosmic shear measurements rely on our ability to measure and correct the Point Spread Function (PSF) of the observations. This PSF is measured using stars in the field, which give a noisy measure at random points in the field. Using Wiener filtering, we show how errors in this PSF correction process propagate into shear power spectrum errors. This allows us to test future space-based missions, such as Euclid or JDEM, thereby allowing us to set clear engineering specifications on PSF variability. For ground-based surveys, where the variability of the PSF is dominated by the environment, we briefly discuss how our approach can also be used to study the potential of mitigation techniques such as correlating galaxy shapes in different exposures. To illustrate our approach we show that for a Euclid-like survey to be statistics limited, an initial pre-correction PSF ellipticity power spectrum, with a power-law slope of -3 must have an amplitude at l =1000 of less than 2 x 10^{-13}. This is 1500 times smaller than the typical lensing signal at this scale. We also find that the power spectrum of PSF size \dR^2) at this scale must be below 2 x 10^{-12}. Public code available as part of iCosmo at http://www.icosmo.orgComment: 5 pages, 3 figures. Submitted to MNRA

Information Gains from Cosmological Probes

In light of the growing number of cosmological observations, it is important to develop versatile tools to quantify the constraining power and consistency of cosmological probes. Originally motivated from information theory, we use the relative entropy to compute the information gained by Bayesian updates in units of bits. This measure quantifies both the improvement in precision and the 'surprise', i.e. the tension arising from shifts in central values. Our starting point is a WMAP9 prior which we update with observations of the distance ladder, supernovae (SNe), baryon acoustic oscillations (BAO), and weak lensing as well as the 2015 Planck release. We consider the parameters of the flat $\Lambda$CDM concordance model and some of its extensions which include curvature and Dark Energy equation of state parameter $w$. We find that, relative to WMAP9 and within these model spaces, the probes that have provided the greatest gains are Planck (10 bits), followed by BAO surveys (5.1 bits) and SNe experiments (3.1 bits). The other cosmological probes, including weak lensing (1.7 bits) and {$\rm H_0$} measures (1.7 bits), have contributed information but at a lower level. Furthermore, we do not find any significant surprise when updating the constraints of WMAP9 with any of the other experiments, meaning that they are consistent with WMAP9. However, when we choose Planck15 as the prior, we find that, accounting for the full multi-dimensionality of the parameter space, the weak lensing measurements of CFHTLenS produce a large surprise of 4.4 bits which is statistically significant at the 8 $\sigma$ level. We discuss how the relative entropy provides a versatile and robust framework to compare cosmological probes in the context of current and future surveys.Comment: 26 pages, 5 figure

iCosmo: an Interactive Cosmology Package

Aims: The interactive software package iCosmo, designed to perform cosmological calculations is described. Methods: iCosmo is a software package to perform interactive cosmological calculations for the low redshift universe. Computing distance measures, the matter power spectrum, and the growth factor is supported for any values of the cosmological parameters. It also computes derived observed quantities for several cosmological probes such as cosmic shear, baryon acoustic oscillations and type Ia supernovae. The associated errors for these observables can be derived for customised surveys, or for pre-set values corresponding to current or planned instruments. The code also allows for the calculation of cosmological forecasts with Fisher matrices which can be manipulated to combine different surveys and cosmological probes. The code is written in the IDL language and thus benefits from the convenient interactive features and scientific library available in this language. iCosmo can also be used as an engine to perform cosmological calculations in batch mode, and forms a convenient adaptive platform for the development of further cosmological modules. With its extensive documentation, it may also serve as a useful resource for teaching and for newcomers in the field of cosmology. Results: The iCosmo package is described with various examples and command sequences. The code is freely available with documentation at http://www.icosmo.org, along with an interactive web interface and is part of the Initiative for Cosmology, a common archive for cosmological resources.Comment: 6 pages including 2 tables and 4 figures. Accepted and published in Astronomy and Astrophysics. Public code and further resources available at http://www.icosmo.or

Optimized Principal Component Analysis on Coronagraphic Images of the Fomalhaut System

We present the results of a study to optimize the principal component analysis (PCA) algorithm for planet detection, a new algorithm complementing ADI and LOCI for increasing the contrast achievable next to a bright star. The stellar PSF is constructed by removing linear combinations of principal components, allowing the flux from an extrasolar planet to shine through. The number of principal components used determines how well the stellar PSF is globally modelled. Using more principal components may decrease the number of speckles in the final image, but also increases the background noise. We apply PCA to Fomalhaut VLT NaCo images acquired at 4.05 micron with an apodized phase plate. We do not detect any companions, with a model dependent upper mass limit of 13-18 M_Jup from 4-10 AU. PCA achieves greater sensitivity than the LOCI algorithm for the Fomalhaut coronagraphic data by up to 1 magnitude. We make several adaptations to the PCA code and determine which of these prove the most effective at maximizing the signal-to-noise from a planet very close to its parent star. We demonstrate that optimizing the number of principal components used in PCA proves most effective for pulling out a planet signal.Comment: Accepted for publication in ApJ, 7 pages, 9 figure

Figures of Merit for Testing Standard Models: Application to Dark Energy Experiments in Cosmology

Given a standard model to test, an experiment can be designed to: (i) measure the standard model parameters; (ii) extend the standard model; or (iii) look for evidence of deviations from the standard model. To measure (or extend) the standard model, the Fisher matrix is widely used in cosmology to predict expected parameter errors for future surveys under Gaussian assumptions. In this article, we present a frame- work that can be used to design experiments such that it maximises the chance of finding a deviation from the standard model. Using a simple illustrative example, discussed in the appendix, we show that the optimal experimental configuration can depend dramatically on the optimisation approach chosen. We also show some simple cosmology calculations, where we study Baryonic Acoustic Oscillation and Supernove surveys. In doing so, we also show how external data, such as the positions of the CMB peaks measured by WMAP, and theory priors can be included in the analysis. In the cosmological cases that we have studied (DETF Stage III), we find that the three optimisation approaches yield similar results, which is reassuring and indicates that the choice of optimal experiment is fairly robust at this level. However, this may not be the case as we move to more ambitious future surveys.Comment: Submitted to MNRAS. 12 pages, 9 figure

Back to Natural Fiber: Wool Color Influences Its Sensitivity to Enzymatic Treatment

There are many missed biotechnological opportunities in the developmental countries. Wool quality improvement is one of them. This study is concerning with improving the wool quality using technical enzymes. White wool proves to be more susceptible to the enzymatic treatment than blackish brown wool. This proves that the enzymatic reaction is sensitive to the natural color differences between wool fibers. A simple enzymatic method has been used to improve the wool quality as well as to investigate the changes happened in the wool fibers. Geobacillus stearothermophilus has been used under mesophilic and static cultivation conditions using wool as the main carbon source. These conditions prove to be more suitable for maintaining the fiber structure, less expensive, and reliable as an in-house biotechnological process that can be adapted everywhere. The enzyme activity in case of white wool was 4 Units/ml and for blackish brown wool was 1.5 Units/ml. Electron microscope has been used to evaluate the end result. By following the process included in this paper using probable microbial strain(s), the wool quality improvement can be applied globally and can add another value to the economy of the developmental countries

Composition et structure des Gastéropodes dans les stations à Retama raetam (Fabaceae) dans la région de Naâma (Algérie)

La région de Naâma est située au sud-ouest algérien et se caractérise par un bioclimat aride. Une approche de la diversité de la malacofaune associée à Retama raetam a été réalisée dans trois stations appartenant à cette région de janvier à juin 2012. La richesse spécifique des Gastéropodes est de quatre (04) réparties entre deux familles : celle des Sphincterochilidae et celle des Helicidae. La seconde comprend deux sous-familles dont celle des Helicinae et celle des Helicellinae. Deux espèces sont constantes, une seule est accessoire et la dernière est accidentelle. L’importance relative des escargots fluctue selon les stations et suivant les mois et les saisons. En hiver, dans la deuxième station la richesse malacologique est nulle. En avril, mai et juin la richesse spécifique est relativement importante dans la 3ème station avec une valeur égale à 4. Sphincterochila candididissima (Sphincterochilidae) possède une fréquence de 83% dans la station 3 et a une abondance de 5.87% dans la première station. Helicella pyramidata a une abondance de 1.34% dans la même station.Mots-clés : Retama raetam, malacofaune, diversité, bioécologie, saisons, mois, répartition verticale, région de Naâma.Composition and structure of gastropods in stations Retama raetam (Fabaceae) in the area of Naâma (Algeria)Naâma is situated in the south West of Algeria and characterized by an arid climat. An approach to the diversity of malacofauna associated with Retama raetam was conducted in three stations in this area from January to June 2012. Species richness of gastropods is 04 divided into two families: the Sphincterochilidae and that of Helicidae. The second consists of two sub-families of the Helicinae and that of Helicellinae Two species are constant, one is accessory and the latter is accidental. The relative importance of snails varies depending on the station and following the months and seasons. In winter, the second in the station malacological wealth is zero. In April, May and June the species richness is relatively high in the third station with a value equal to 4. Sphincterochila candididissima (Sphincterochilidae) has a frequency of 83% in station 3 and has an abundance of 5.87% in the first station. Helicella pyramidata has an abundance of 1.34% in the same station.Keywords : Retama raetam, malacofauna, diversity, bio-ecology, seasons, months, vertical distribution, Naama region