Comment on Ricci Collineations of Static Spherically Symmetric Spacetimes

We present a counter example to a theorem given by Amir {\em et al.} J. Math. Phys. {\bf 35}, 3005 (1994). We also comment on a misleading statements of the same reference.Comment: 4 pages,LaTex fil

Role of Anisotropy and Refractive Index in Scattering and Whiteness Optimization

This is the final version. Available from Wiley via the DOI in this record.The ability to manipulate light–matter interaction to tailor the scattering properties of materials is crucial to many aspects of everyday life, from paints to lighting, and to many fundamental concepts in disordered photonics. Light transport and scattering in a granular disordered medium are dictated by the spatial distribution (structure factor) and the scattering properties (form factor and refractive index) of its building blocks. As yet, however, the importance of anisotropy in such systems has not been considered. Here, a systematic numerical survey that disentangles and quantifies the role of different kinds and degrees of anisotropy in scattering optimization is reported. It is shown that ensembles of uncorrelated, anisotropic particles with nematic ordering enables to increase by 20% the reflectance of low-refractive index media (n = 1.55), using only three-quarters of material compared to their isotropic counterpart. Additionally, these systems exhibit a whiteness comparable to conventionally used high-refractive index media, e.g., TiO2 (n = 2.60). Therefore, the findings not only provide an understanding of the role of anisotropy in scattering optimization, but they also showcase a novel strategy to replace inorganic white enhancers with sustainable and biocompatible products made of biopolymers.Biotechnology and Biological Sciences Research Council (BBSRC)European Research Council (ERC)Leverhulme Trus

Exploiting speckle correlations to improve the resolution of wide-field fluorescence microscopy

Fluorescence microscopy is indispensable in nanoscience and biological sciences. The versatility of labeling target structures with fluorescent dyes permits to visualize structure and function at a subcellular resolution with a wide field of view. Due to the diffraction limit, conventional optical microscopes are limited to resolving structures larger than 200 nm. The resolution can be enhanced by near-field and far-field super-resolution microscopy methods. Near-field methods typically have a limited field of view and far-field methods are limited by the involved conventional optics. Here, we introduce a combined high-resolution and wide-field fluorescence microscopy method that improves the resolution of a conventional optical microscope by exploiting correlations in speckle illumination through a randomly scattering high-index medium: Speckle correlation resolution enhancement (SCORE). As a test, we collect two-dimensional fluorescence images of 100-nm diameter dye-doped nanospheres. We demonstrate a deconvolved resolution of 130 nm with a field of view of 10 x 10 \text{\mu m}^2

Scattering Lens Resolves sub-100 nm Structures with Visible Light

The smallest structures that conventional lenses are able to optically resolve are of the order of 200 nm. We introduce a new type of lens that exploits multiple scattering of light to generate a scanning nano-sized optical focus. With an experimental realization of this lens in gallium phosphide we have succeeded to image gold nanoparticles at 97 nm optical resolution. Our work is the first lens that provides a resolution in the nanometer regime at visible wavelengths.Comment: 4 pages, 3 figure

Measurement of change in health status with Rasch models

Background: The traditional approach to the measurement of change presents important drawbacks (no information at individual level, ordinal scores, variance of the measurement instrument across time points), which Rasch models overcome. The article aims to illustrate the features of the measurement of change with Rasch models. Methods: To illustrate the measurement of change using Rasch models, the quantitative data of a longitudinal study of heart-surgery patients (N=98) were used. The scale "Perception of Positive Change" was used as an example of measurement instrument. All patients underwent cardiac rehabilitation, individual psychological intervention, and educational intervention. Nineteen patients also attended progressive muscle relaxation group trainings. The scale was administered before and after the interventions. Three Rasch approaches were used. Two separate analyses were run on the data from the two time points to test the invariance of the instrument. An analysis was run on the stacked data from both time points to measure change in a common frame of reference. Results of the latter analysis were compared with those of an analysis that removed the influence of local dependency on patient measures. Statistics t, \u3a72 and F were used for comparing the patient and item measures estimated in the Rasch analyses (a-priori \u3b1=.05). Infit, Outfit, R and item Strata were used for investigating Rasch model fit, reliability, and validity of the instrument. Results: Data of all 98 patients were included in the analyses. The instrument was reliable, valid, and substantively unidimensional (Infit, Outfit<2 for all items, R=.84, item Strata range=3.93-6.07). Changes in the functioning of the instrument occurred across the two time, which prevented the use of the two separate analyses to unambiguously measure change. Local dependency had a negligible effect on patient measures (p 65.8674). Thirteen patients improved, whereas 3 worsened. The patients who attended the relaxation group trainings did not report greater improvement than those who did not (p=.1007). Conclusions: Rasch models represent a valid framework for the measurement of change and a useful complement to traditional approaches. \ua9 Anselmi et al

Branching Lévy processes with inhomogeneous breeding potentials

The object of study in this thesis is a number of different models of branching Levy processes in inhomogeneous breeding potential. We employ some widely-used spine techniques to investigate various features of these models for their subsequent comparison. The thesis is divided into 5 chapters. In the first chapter we introduce the general framework for branching Markov processes within which we are going to present all our results. In the second chapter we consider a branching Brownian motion in the potential β|·|p, β> 0, p ≥0. We give a new proof of the result about the critical value of p for the explosion time of the population. The main advantage of the new proof is that it can be easily generalised to other models. The third chapter is devoted to continuous-time branching random walks in the potential β|·|p, β> 0, p ≥0. We give results about the explosion time and the right most particle behaviour comparing them with the known results for the branching Brownian motion. In the fourth chapter we look at general branching Levy processes in the potential β|·|p, β> 0, p ≥0. Subject to certain assumptions we prove some results about the explosion time and the rightmost particle. We exhibit how the corresponding results for the branching Brownian motion and and the branching random walk fit into the general structure. The last chapter considers a branching Brownian motion with branching taking place at the origin on the local time scale. We present some results about the population dynamics and the right most particle behaviour. We also prove the Strong Law of Large Numbers for this model.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Ricci Collineations for Non-Degenerate, Diagonal and Spherically Symmetric Ricci Tensors

The expression of the vector field generator of a Ricci Collineation for diagonal, spherically symmetric and non-degenerate Ricci tensors is obtained. The resulting expressions show that the time and radial first derivatives of the components of the Ricci tensor can be used to classify the collineation, leading to 64 families. Some examples illustrate how to obtain the collineation vector

Temporal Variations in the Usefulness of Normalized Difference Vegetation Index as a Predictor for Ixodes ricinus (Acari: Ixodidae) in a Borrelia lusitaniae Focus in Tuscany, Central Italy

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