Modeling of evolving textures using granulometries

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Analysing Large Scale Structure: I. Weighted Scaling Indices and Constrained Randomisation

The method of constrained randomisation is applied to three-dimensional simulated galaxy distributions. With this technique we generate for a given data set surrogate data sets which have the same linear properties as the original data whereas higher order or nonlinear correlations are not preserved. The analysis of the original and surrogate data sets with measures, which are sensitive to nonlinearities, yields information about the existence of nonlinear correlations in the data. We demonstrate how to generate surrogate data sets from a given point distribution, which have the same linear properties (power spectrum) as well as the same density amplitude distribution. We propose weighted scaling indices as a nonlinear statistical measure to quantify local morphological elements in large scale structure. Using surrogates is is shown that the data sets with the same 2-point correlation functions have slightly different void probability functions and especially a different set of weighted scaling indices. Thus a refined analysis of the large scale structure becomes possible by calculating local scaling properties whereby the method of constrained randomisation yields a vital tool for testing the performance of statistical measures in terms of sensitivity to different topological features and discriminative power.Comment: 10 pages, 5 figures, accepted for publication in MNRA

Differing self-similarity in light scattering spectra: A potential tool for pre-cancer detection

The fluctuations in the elastic light scattering spectra of normal and dysplastic human cervical tissues analyzed through wavelet transform based techniques reveal clear signatures of self-similar behavior in the spectral fluctuations. Significant differences in the power law behavior ascertained through the scaling exponent was observed in these tissues. The strong dependence of the elastic light scattering on the size distribution of the scatterers manifests in the angular variation of the scaling exponent. Interestingly, the spectral fluctuations in both these tissues showed multi-fractality (non-stationarity in fluctuations), the degree of multi-fractality being marginally higher in the case of dysplastic tissues. These findings using the multi-resolution analysis capability of the discrete wavelet transform can contribute to the recent surge in the exploration for non-invasive optical tools for pre-cancer detection.Comment: 13 pages, 14 figure

Comparative performance of airyscan and structured illumination superresolution microscopy in the study of the surface texture and 3D shape of pollen

The visualization of taxonomically diagnostic features of individual pollen grains can be a challenge for many ecologically and phylogenetically important pollen types. The resolution of traditional optical microscopy is limited by the diffraction of light (250 nm), while high resolution tools such as electron microscopy are limited by laborious preparation and imaging workflows. Airyscan confocal superresolution and structured illumination superresolution (SR-SIM) microscopy are powerful new tools for the study of nanoscale pollen morphology and three-dimensional structure that can overcome these basic limitations. This study demonstrates their utility in capturing morphological details below the diffraction limit of light. Using three distinct pollen morphotypes (Croton hirtus, Dactylis glomerata, and Helianthus sp.) and contrast-enhancing fluorescent staining, we were able to assess the effectiveness of the Airyscan and SR-SIM. We further demonstrate that these new superresolution methods can be easily applied to the study of fossil pollen material

A comprehensive overview of the Cold Spot

The report of a significant deviation of the CMB temperature anisotropies distribution from Gaussianity (soon after the public release of the WMAP data in 2003) has become one of the most solid WMAP anomalies. This detection grounds on an excess of the kurtosis of the Spherical Mexican Hat Wavelet coefficients at scales of around 10 degrees. At these scales, a prominent feature --located in the southern Galactic hemisphere-- was highlighted from the rest of the SMHW coefficients: the Cold Spot. This article presents a comprehensive overview related to the study of the Cold Spot, paying attention to the non-Gaussianity detection methods, the morphological characteristics of the Cold Spot, and the possible sources studied in the literature to explain its nature. Special emphasis is made on the Cold Spot compatibility with a cosmic texture, commenting on future tests that would help to give support or discard this hypothesis.Comment: 21 pages, 14 figures. Accepted for publication in the Advances in Astronomy special issue "Testing the Gaussianity and Statistical Isotropy of the Universe