Analysis of the Bayesian Cramer-Rao lower bound in astrometry: Studying the impact of prior information in the location of an object

Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims. We analyse bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (i.e., the position is a random variable) from observations that are statistically dependent on the position. Methods. We characterize the Bayesian Cramer-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background. Results. We quantify and analyse the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.Comment: 17 pages, 12 figures. Accepted for publication on Astronomy & Astrophysic

Assessment of Neuropsychological Trajectories in Longitudinal Population-Based Studies of Children

This paper provides a strategy for the assessment of brain function in longitudinal cohort studies of children. The proposed strategy invokes both domain-specific and omnibus intelligence test approaches. In order to minimise testing burden and practice effects, the cohort is divided into four groups with one-quarter tested at 6-monthly intervals in the 0–2-year age range (at ages 6 months, 1.0, 1.5 and 2.0 years) and at annual intervals from ages 3–20 (one-quarter of the children at age 3, another at age 4, etc). This strategy allows investigation of cognitive development and of the relationship between environmental influences and development at each age. It also allows introduction of new domains of function when age-appropriate. As far as possible, tests are used that will provide a rich source of both longitudinal and cross-sectional data. The testing strategy allows the introduction of novel tests and new domains as well as piloting of tests when the test burden is relatively light. In addition to the recommended tests for each age and domain, alternative tests are described. Assessment methodology and knowledge about child cognitive development will change over the next 20 years, and strategies are suggested for altering the proposed test schedule as appropriate

A note on the cylindrical collapse of counter-rotating dust

We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that--for the classes of solutions discussed herein--from regular initial data a curvature singularity inevitably develops, and no apparent horizons form, thus in accord with the spirit of the hoop conjecture.Comment: 8 pages, LaTeX, ijmpd macros (included), 1 eps figure; accepted for publication in Int. J. Mod. Phys.

Path Integrals, Density Matrices, and Information Flow with Closed Timelike Curves

Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and superposition using a path integral. Deutsch's density matrix approach is causal but typically destroys coherence. For each of these formulations I demonstrate that there are yet further alternatives in prescribing the handling of information flow (inequivalent to previous analyses) that have implications for any system in which unitarity or coherence are not preserved.Comment: 25 pages, phyzzx, CALT-68-188

Good and bad practices in pv plants

The PVCROPS project (PhotoVolta ic Cost r€duction, Reliability, Operational performance, Prediction and Simulation), cofinanced by European Commission in the frame of Seventh Framework Programme, has compiled in the “Good and bad practices: Manual to improve the quality and reduce the cost of PV systems” a collection of good and bad practices in actual PV plants . All the situations it collects represent the state-of-the-art of existing PV installations all around Europe. They show how the different parts of an installation can be implem ented properly or not. The aim of this manual is to represent a reference text which can help any PV actor (installers, electricians, maintenance operators, owners, etc.) not only to check and improve an already existing installation but will also, and mainly, avoid the previously known bad practices for the construction of a new PV installation. Thus, solving a priori the known errors, new PV installations will be more reliable, efficient and cost-effective and can recover the initial investment in a shorter time. The manual is going to be free available in the PVCROPS website in several languages

An Effective Search Method for Gravitational Ringing of Black Holes

We develop a search method for gravitational ringing of black holes. The gravitational ringing is due to complex frequency modes called the quasi-normal modes that are excited when a black hole geometry is perturbed. The detection of it will be a direct confirmation of the existence of a black hole. Assuming that the ringdown waves are dominated by the fundamental mode with least imaginary part, we consider matched filtering and develop an optimal method to search for the ringdown waves that have damped sinusoidal wave forms. When we use the matched filtering method, the data analysis with a lot of templates required. Here we have to ensure a proper match between the filter as a template and the real wave. It is necessary to keep the detection efficiency as high as possible under limited computational costs. First, we consider the white noise case for which the matched filtering can be studied analytically. We construct an efficient method for tiling the template space. Then, using a fitting curve of the TAMA300 DT6 noise spectrum, we numerically consider the case of colored noise. We find our tiling method developed for the white noise case is still valid even if the noise is colored.Comment: 17 pages, 9 figures. Accepted to Phys. Rev. D, Note correction to Eq. (3-25), A few comments added and minor typos correcte

Unitarity Restoration in the Presence of Closed Timelike Curves

A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations, this proposal is causal, linear in the initial density matrix and preserves probability. It provides a physically reasonable interpretation of invertible nonunitary evolution by redefining the final Hilbert space so that the evolution is unitary or equivalently by removing the nonunitary part of the evolution operator using a polar decomposition.Comment: LaTeX, 17pp, Revisions: Title change, expanded and clarified presentation of original proposal, esp. with regard to Heisenberg picture and remaining in original Hilbert spac

Simple Quantum Systems in Spacetimes with Closed Timelike Curves

Three simple examples illustrate properties of path integral amplitudes in fixed background spacetimes with closed timelike curves: non-relativistic potential scattering in the Born approximation is non-unitary, but both an example with hard spheres and the exact solution of a totally discrete model are unitary.Comment: 15 pages, CALT-68-180