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

An Iron-Catalyzed Bond-Making/Bond-Breaking Cascade Merges Cycloisomerization and Cross-Coupling Chemistry

Treatment of readily available enynes with alkyl-Grignard reagents in the presence of catalytic amounts of Fe(acac)3 engenders a remarkably facile and efficient reaction cascade that results in the net formation of two new C−C bonds while a C−Z bond in the substrate backbone is broken. Not only does this new manifold lend itself to the extrusion of heteroelements (Z=O, NR), but it can even be used for the cleavage of activated C−C bonds. The reaction likely proceeds via metallacyclic intermediates, the iron center of which gains ate character before reductive elimination occurs. The overall transformation represents a previously unknown merger of cycloisomerization and cross-coupling chemistry. It provides ready access to highly functionalized 1,3-dienes comprising a stereodefined tetrasubstituted alkene unit, which are difficult to make by conventional means

Noncanonical Quantization of Gravity. I. Foundations of Affine Quantum Gravity

The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of constraints, a primary kinematical representation is derived in the form of a reproducing kernel and its associated reproducing kernel Hilbert space. Constraints are introduced following the projection operator method which involves no gauge fixing, no complicated moduli space, nor any auxiliary fields. The result, which is only qualitatively sketched in the present paper, involves another reproducing kernel with which inner products are defined for the physical Hilbert space and which is obtained through a reduction of the original reproducing kernel. Several of the steps involved in this general analysis are illustrated by means of analogous steps applied to one-dimensional quantum mechanical models. These toy models help in motivating and understanding the analysis in the case of gravity.Comment: minor changes, LaTeX, 37 pages, no figure

Further Evidence for Seed Size Variation in the Genus Zostera: Exploratory Studies with Z. japonica and Z. asiatica

Recent studies found seed size variation within the seagrass Zostera marina, one of nine species in the genus Zostera. The objectives of this study were to determine if variation also exists in the seeds of two other species Zostera japonica and Zostera asiatica within this genus. Results indicate that: (1) length and weight varied between two populations (one indigenous population from Akkeshi-Ko, Japan, and one exotic population from Willapa Bay, Washington, USA) of the small-bodied intertidal seagrass species Z. japonica, and (2) seed-size classes were discernable. Preliminary investigations were also initiated with a Japanese population of Z. asiatica, a large-bodied subtidal seagrass species. Z. japonica seeds from the exotic population were significantly (P \u3c 0.00 1) longer and heavier when compared to those from the indigenous population, a finding which may help explain both the process of the earlier introduction and the recent expansion of this exotic in the northeastern Pacific. Also, preliminary results indicate that Z. asiatica seeds are heavier than both those of Z. marina and Z. japonica, which suggests that larger seeds may be associated with large-bodied plants in this genus, an observation that should direct future seed ecology studies within the genus. These findings demonstrate that, similar to the study of terrestrial angiosperms, investigations designed to describe the comparative ecology of marine seed-bearing plants should include an evaluation of seed size

Nota sobre la pirofilita de Águilas (Murcia, SE de España)

Se hace un estudio previo del yacimiento de la pirofilita de Águilas (Provincia de Murcia, SE de España). Pirofilita, cuarzo, micas blancas y caolinita son los constituyentes de estas mineralizaciones filonianas que encajan enfisuras de las filitas del complejo Alpujárride. El origen de la pirofilita está relacionado con un proceso de metamorfismoregional de un material sedimentario rico en aluminio. La principal reacciónimplicada seria:1 Caolinita + 2 SiO2 = 1 Pirofilita + H2OSe contempla asimismo como posibilidad alternativa, un proceso de segregación metamórfica. Se dan datos ópticos, de análisis químico y de difracción de Rayos X

The role of the mother as a para-professional helper in the pre-school setting

The present study compared deployment of working—class mothers,\ud teachers and nursery nurses in day—to—day activities in pre—school set—\ud tings. Naturalistic observation was used in two pre—schools run on\ud free—play lines located in socially deprived areas. Mothers were\ud observed in the room their "Own" children attended. Teachers and mothers\ud were studied alone and with the other present in order to discover the\ud extent to which the presence of one affects the behaviour of the other.\ud Time spent by mothers in direct contact; indirect contact, dealing with\ud equipment, interaction with adults and not involved was compared with\ud that spent by the other two groups. Direct and indirect contact were\ud analysed at two different levels: (a) all time mothers spent with chil—\ud dren was considered, (b) time spent with "Own" children was disregarded.\ud Significantly larger within group differences were observed for mothers\ud when compared with teachers and nursery nurses in direct contact and no\ud activity. Significant differences in direct contact were observed for\ud mothers compared with the other two groups. Significant differences in\ud direct contact were due to: (a) wider within group differences for the\ud group of mothers than nursery nurses; (b) more time spent by teachers\ud than mothers. Time spent involved in no activity showed: (a) signifi—\ud cantly more varied behaviour than teachers, (b) significantly more time\ud than nursery nurses. Behaviours observed for mothers appeared to be\ud influenced by how they became involved; those invited by teachers show—\ud ing more time with the children and less not involved. It was also\ud found that teachers spent little time with "Own" children (large within\ud group differences were found). However, teacher—"Own" child interaction\ud was found to be somewhat lessened for some children due to the presence\ud of the mothers. Mothers in both conditions spent significantly more time\ud with their "Own" children than teachers and nursery nurses

Essays on productivity, economic geography and trade : the case of Chile

This dissertation investigates the relative importance of firm-specific and geographic characteristics for export behavior in the Chilean primary and processed food industries. The first essay develops a new method for measuring geographic characteristics to account for economic activity in adjacent, but separate spatial units. In the application to the Chilean manufacturing industry, the proposed index better identifies the presence of locational forces (e.g., technological spillovers or natural advantages) than do traditional indexes. Results suggest a higher geographic concentration of Chilean manufacturing firms through technological spillovers in highly populated areas, and access to natural resources in areas that are farther from large cities. The second essay analyzes the determinants of Chilean farms’ decision to produce exportables, i.e., export participation. An export behavior model is estimated using farm-level data from the Chilean Census of Agriculture and a two-stage conditional maximum likelihood procedure. Results show that a farm’s efficiency or productivity is more important than its location for its export participation. When a high-productivity farm locates in a region with better geographic characteristics, its likelihood of producing for export markets is higher. On the other hand, an opposite result is obtained when a low-productivity farm locates in regions with better geographic attributes. The latter suggests that farms must achieve a minimum level of efficiency for geographic characteristics to positively affect their export participation. The third essay investigates firms’ decision to export as well as that on how much to export (intensity) in the Chilean processed food industries. Results show the relative importance of sunk costs, foreign ownership and firm size in the Chilean firms’ export decision. Productivity and geography play a more prominent role in firms’ export-intensity decision in selected industries. In general, firm-specific characteristics appear to be more important than geographic attributes for export behavior. The three essays contribute to a better understanding of firms’ export behavior, in particular those in the Chilean agriculture and processed food industries. By providing insights into factors affecting export behavior, these three essays have implications for public policies to encourage firms’ participation in global markets

Composición química de la Alcachofa de Tudela a lo largo de su desarrollo.

En el presente trabajo se ha estudiado la composición química -K, N, Ca, P, Mg, Fe, Mn, Zn y Cu- de la planta entera de alcachofa de Tudela, a lo largo de todas las fases de su ciclo vital, cultivada sobre suelo agrícola, en dos parcelas distintas. Así mismo, se han realizado dos análisis completos de los suelos de ambas parcelas. Con este estudio se pretende adquirir un conocimiento básico que pueda servir de comparación en otros estudios aplicados con vistas a la denominación de calidad. Se ha observado que cerca del 55% de variación de la diversidad del conjunto de los contenidos en elementos a lo largo del ciclo vital, queda explicada por N, P, Zn y Cu, y un 29% por Mn, Ca y K; el Mg y Fe tienen comportamiento diferente en las plantas de las distintas parcelas. Y además que, existe una gran similitud en las concentraciones de los 9 elementos en las distintas alcachofas