Biased-estimations of the Variance and Skewness

Nonlinear combinations of direct observables are often used to estimate quantities of theoretical interest. Without sufficient caution, this could lead to biased estimations. An example of great interest is the skewness $S_3$ of the galaxy distribution, defined as the ratio of the third moment \xibar_3 and the variance squared \xibar_2^2. Suppose one is given unbiased estimators for \xibar_3 and \xibar_2^2 respectively, taking a ratio of the two does not necessarily result in an unbiased estimator of $S_3$. Exactly such an estimation-bias affects most existing measurements of $S_3$. Furthermore, common estimators for \xibar_3 and \xibar_2 suffer also from this kind of estimation-bias themselves: for \xibar_2, it is equivalent to what is commonly known as the integral constraint. We present a unifying treatment allowing all these estimation-biases to be calculated analytically. They are in general negative, and decrease in significance as the survey volume increases, for a given smoothing scale. We present a re-analysis of some existing measurements of the variance and skewness and show that most of the well-known systematic discrepancies between surveys with similar selection criteria, but different sizes, can be attributed to the volume-dependent estimation-biases. This affects the inference of the galaxy-bias(es) from these surveys. Our methodology can be adapted to measurements of analogous quantities in quasar spectra and weak-lensing maps. We suggest methods to reduce the above estimation-biases, and point out other examples in LSS studies which might suffer from the same type of a nonlinear-estimation-bias.Comment: 28 pages of text, 9 ps figures, submitted to Ap

Non-Markovian Decay of a Three Level Cascade Atom in a Structured Reservoir

We present a formalism that enables the study of the non-Markovian dynamics of a three-level ladder system in a single structured reservoir. The three-level system is strongly coupled to a bath of reservoir modes and two quantum excitations of the reservoir are expected. We show that the dynamics only depends on reservoir structure functions, which are products of the mode density with the coupling constant squared. This result may enable pseudomode theory to treat multiple excitations of a structured reservoir. The treatment uses Laplace transforms and an elimination of variables to obtain a formal solution. This can be evaluated numerically (with the help of a numerical inverse Laplace transform) and an example is given. We also compare this result with the case where the two transitions are coupled to two separate structured reservoirs (where the example case is also analytically solvable)

Theory of Pseudomodes in Quantum Optical Processes

This paper deals with non-Markovian behaviour in atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in high Q cavities or photonic band gap materials. In cases such as the former, we show that the pseudo mode theory for single quantum reservoir excitations can be obtained by applying the Fano diagonalisation method to a system in which the atomic transitions are coupled to a discrete set of (cavity) quasimodes, which in turn are coupled to a continuum set of (external) quasimodes with slowly varying coupling constants and continuum mode density. Each pseudomode can be identified with a discrete quasimode, which gives structure to the actual reservoir of true modes via the expressions for the equivalent atom-true mode coupling constants. The quasimode theory enables cases of multiple excitation of the reservoir to now be treated via Markovian master equations for the atom-discrete quasimode system. Applications of the theory to one, two and many discrete quasimodes are made. For a simple photonic band gap model, where the reservoir structure is associated with the true mode density rather than the coupling constants, the single quantum excitation case appears to be equivalent to a case with two discrete quasimodes

Can Life develop in the expanded habitable zones around Red Giant Stars?

We present some new ideas about the possibility of life developing around sub-giant and red giant stars. Our study concerns the temporal evolution of the habitable zone. The distance between the star and the habitable zone, as well as its width, increases with time as a consequence of stellar evolution. The habitable zone moves outward after the star leaves the main sequence, sweeping a wider range of distances from the star until the star reaches the tip of the asymptotic giant branch. If life could form and evolve over time intervals from $5 \times 10^8$ to $10^9$ years, then there could be habitable planets with life around red giant stars. For a 1 M$_{\odot}$ star at the first stages of its post main-sequence evolution, the temporal transit of the habitable zone is estimated to be of several 10$^9$ years at 2 AU and around 10$^8$ years at 9 AU. Under these circumstances life could develop at distances in the range 2-9 AU in the environment of sub-giant or giant stars and in the far distant future in the environment of our own Solar System. After a star completes its first ascent along the Red Giant Branch and the He flash takes place, there is an additional stable period of quiescent He core burning during which there is another opportunity for life to develop. For a 1 M$_{\odot}$ star there is an additional $10^9$ years with a stable habitable zone in the region from 7 to 22 AU. Space astronomy missions, such as proposed for the Terrestrial Planet Finder (TPF) and Darwin should also consider the environments of sub-giants and red giant stars as potentially interesting sites for understanding the development of life

Eccentricity Evolution in Simulated Galaxy Clusters

Strong cluster eccentricity evolution for $z \le 0.13$ has appeared in a variety of observational data sets. We examine the evolution of eccentricity in simulated galaxy clusters using a variety of simulation methodologies, amplitude normalizations, and background cosmologies. We do not find find such evolution for $z < 0.1$ in any of our simulation ensembles. We suggest a systematic error in the form of a redshift-dependent selection effect in cluster catalogs or missing physics in cluster simulations important enough to modify the cluster morphology.Comment: Revised version to be published in ApJ. Moderate revisions, including additional N-body simulations with varying amplitude normalization and background matter density within OCDM and $\lambda$CDM scenarios reinforce our conclusion that observed clusters have recently relaxed much more rapidly than simulated one

The Northern Sky Optical Cluster Survey II: An Objective Cluster Catalog for 5800 Square Degrees

We present a new, objectively defined catalog of candidate galaxy clusters based on the galaxy catalogs from the Digitized Second Palomar Observatory Sky Survey (DPOSS). This cluster catalog, derived from the best calibrated plates in the high latitude (|b|>30) Northern Galactic Cap region, covers 5,800 square degrees, and contains 8,155 candidate clusters. A simple adaptive kernel density mapping technique, combined with the SExtractor object detection algorithm, is used to detect galaxy overdensities, which we identify as clusters. Simulations of the background galaxy distribution and clusters of varying richnesses and redshifts allow us to optimize detection parameters, and measure the completeness and contamination rates for our catalog. Cluster richnesses and photometric redshifts are measured, using integrated colors and magnitudes for each cluster. An extensive spectroscopic survey is used to confirm the photometric results. This catalog, with well-characterized sample properties, provides a sound basis for future studies of cluster physics and large scale structure.Comment: 49 pages, 16 figures. Accepted to AJ; appearing in April. Version with full resolution figures, and full length tables available at http://dposs.caltech.edu:8080/NoSOCS.htm

Medication adherence during adjunct therapy with statins and ACE inhibitors in adolescents with type 1 diabetes

OBJECTIVE: Suboptimal adherence to insulin treatment is a main issue in adolescents with type 1 diabetes. However, to date, there are no available data on adherence to adjunct noninsulin medications in this population. Our aim was to assess adherence to ACE inhibitors and statins and explore potential determinants in adolescents with type 1 diabetes. RESEARCH DESIGN AND METHODS:There were 443 adolescents with type 1 diabetes recruited into the Adolescent Type 1 Diabetes Cardio-Renal Intervention Trial (AdDIT) and exposed to treatment with two oral drugs—an ACE inhibitor and a statin—as well as combinations of both or placebo for 2–4 years. Adherence was assessed every 3 months with the Medication Event Monitoring System (MEMS) and pill count. RESULTS: Median adherence during the trial was 80.2% (interquartile range 63.6–91.8) based on MEMS and 85.7% (72.4–92.9) for pill count. Adherence based on MEMS and pill count dropped from 92.9% and 96.3%, respectively, at the first visit to 76.3% and 79.0% at the end of the trial. The percentage of study participants with adherence ≥75% declined from 84% to 53%. A good correlation was found between adherence based on MEMS and pill count (r = 0.82, P < 0.001). Factors associated with adherence were age, glycemic control, and country. CONCLUSIONS: We report an overall good adherence to ACE inhibitors and statins during a clinical trial, although there was a clear decline in adherence over time. Older age and suboptimal glycemic control at baseline predicted lower adherence during the trial, and, predictably, reduced adherence was more prevalent in subjects who subsequently dropped out

Steps toward the power spectrum of matter. I.The mean spectrum of galaxies

We calculate the mean power spectrum of galaxies using published power spectra of galaxies and clusters of galaxies. On small scales we use the power spectrum derived from the 2-dimensional distribution of APM galaxies, on large scales we use power spectra derived from 3-dimensional data for galaxy and cluster samples. Spectra are reduced to real space and to the amplitude of the power spectrum of APM galaxies. Available data indicate the presence of two different populations in the nearby Universe. Clusters of galaxies sample a relatively large region in the Universe where rich, medium and poor superclusters are well represented. Their mean power spectrum has a spike on scale 120 h^{-1}Mpc, followed by an approximate power-law spectrum of index n = -1.9 towards small scales. The power spectrum found from LCRS and IRAS 1.2 Jy surveys is flatter around the maximum, which may represent regions of the Universe with medium-rich and poor superclusters.Comment: LaTex (sty files added), 35 pages, 5 PostScript figures and Table with mean power spectrum embedded, Astrophysical Journal (accepted

A Personal Construct Psychology based investigation into a Product Service System for renting pushchairs to consumers

This is the peer-reviewed version of the following article: Maurizio Catulli and Nick Reed, ‘A Personal Construct Psychology Based Investigation Into a Product Service System for Renting Pushchairs to Consumers’, Business Strategy and the Environment, Vol. 26(5): 656-671, February 2017, which has been published in final form at DOI: 10.1002/bse.1944. Under embargo. Embargo end date: 1 February 2019. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.This paper explores how consumers construe a Product Service System (PSS) for the supply of pushchairs. A PSS is a system of products, services, networks of actors and supporting infrastructure designed to be more sustainable than traditional business models. PSS face an implementation challenge in consumer markets and this case based research explores some reasons for this. The study applies Personal Construct Psychology (in particular, Repertory Grid Technique) which has not previously been used in relation to researching PSS. Results suggest that PSS might be difficult to implement in relation to pushchairs. Renting pre-used equipment may meet resistance because of a perceived risk that acquisition by this means might endanger infants. Participants in the study construed buying new products from specialist infant product shops as being the best way of acquiring them. Accordingly PSS providers may, for instance, have to implement certified quality assurance processes in order to reassure consumers.Peer reviewedFinal Accepted Versio