Exact reconstruction with directional wavelets on the sphere

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux et al. (2005). The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation is firstly identified. A scale discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background (CMB) data, such as the imprint of topological defects, in particular cosmic strings, and for their reconstruction after separation from the other signal components.Comment: 22 pages, 2 figures. Version 2 matches version accepted for publication in MNRAS. Version 3 (identical to version 2) posted for code release announcement - "Steerable scale discretised wavelets on the sphere" - S2DW code available for download at http://www.mrao.cam.ac.uk/~jdm57/software.htm

Data compression on the sphere

Large data-sets defined on the sphere arise in many fields. In particular, recent and forthcoming observations of the anisotropies of the cosmic microwave background (CMB) made on the celestial sphere contain approximately three and fifty mega-pixels respectively. The compression of such data is therefore becoming increasingly important. We develop algorithms to compress data defined on the sphere. A Haar wavelet transform on the sphere is used as an energy compression stage to reduce the entropy of the data, followed by Huffman and run-length encoding stages. Lossless and lossy compression algorithms are developed. We evaluate compression performance on simulated CMB data, Earth topography data and environmental illumination maps used in computer graphics. The CMB data can be compressed to approximately 40% of its original size for essentially no loss to the cosmological information content of the data, and to approximately 20% if a small cosmological information loss is tolerated. For the topographic and illumination data compression ratios of approximately 40:1 can be achieved when a small degradation in quality is allowed. We make our SZIP program that implements these compression algorithms available publicly.Comment: 13 pages, 8 figures, accepted for publication by A&A; We make our SZIP program that implements these compression algorithms available publicly from http://www.szip.org.u

A scanner system for high-resolution quantification of variation in root growth dynamics of Brassica rapa genotypes

The potential exists to breed for root system architectures that optimize resource acquisition. However, this requires the ability to screen root system development quantitatively, with high resolution, in as natural an environment as possible, with high throughput. This paper describes the construction of a low-cost, high-resolution root phenotyping platform, requiring no sophisticated equipment and adaptable to most laboratory and glasshouse environments, and its application to quantify environmental and temporal variation in root traits between genotypes of Brassica rapa L. Plants were supplied with a complete nutrient solution through the wick of a germination paper. Images of root systems were acquired without manual intervention, over extended periods, using multiple scanners controlled by customized software. Mixed-effects models were used to describe the sources of variation in root traits contributing to root system architecture estimated from digital images. It was calculated that between one and 43 replicates would be required to detect a significant difference (95% CI 50% difference between traits). Broad-sense heritability was highest for shoot biomass traits (>0.60), intermediate (0.25–0.60) for the length and diameter of primary roots and lateral root branching density on the primary root, and lower (<0.25) for other root traits. Models demonstrate that root traits show temporal variations of various types. The phenotyping platform described here can be used to quantify environmental and temporal variation in traits contributing to root system architecture in B. rapa and can be extended to screen the large populations required for breeding for efficient resource acquisition

Computer-assisted mitotic count using a deep learning–based algorithm improves interobserver reproducibility and accuracy

The mitotic count (MC) is an important histological parameter for prognostication of malignant neoplasms. However, it has inter- and intraobserver discrepancies due to difficulties in selecting the region of interest (MC-ROI) and in identifying or classifying mitotic figures (MFs). Recent progress in the field of artificial intelligence has allowed the development of high-performance algorithms that may improve standardization of the MC. As algorithmic predictions are not flawless, computer-assisted review by pathologists may ensure reliability. In the present study, we compared partial (MC-ROI preselection) and full (additional visualization of MF candidates and display of algorithmic confidence values) computer-assisted MC analysis to the routine (unaided) MC analysis by 23 pathologists for whole-slide images of 50 canine cutaneous mast cell tumors (ccMCTs). Algorithmic predictions aimed to assist pathologists in detecting mitotic hotspot locations, reducing omission of MFs, and improving classification against imposters. The interobserver consistency for the MC significantly increased with computer assistance (interobserver correlation coefficient, ICC = 0.92) compared to the unaided approach (ICC = 0.70). Classification into prognostic stratifications had a higher accuracy with computer assistance. The algorithmically preselected hotspot MC-ROIs had a consistently higher MCs than the manually selected MC-ROIs. Compared to a ground truth (developed with immunohistochemistry for phosphohistone H3), pathologist performance in detecting individual MF was augmented when using computer assistance (F1-score of 0.68 increased to 0.79) with a reduction in false negatives by 38%. The results of this study demonstrate that computer assistance may lead to more reproducible and accurate MCs in ccMCTs

Terrace reconstruction and long profile projection: a case study from the Solent river system near Southampton, England

River terrace sequences are important frameworks for archaeological evidence and as such it is important to produce robust correlations between what are often fragmentary remnants of ancient terraces. This paper examines both conceptual and practical issues related to such correlations, using a case study from the eastern part of the former Solent River system near Southampton, England. In this region two recent terrace schemes have been constructed using different data to describe the terrace deposits: one based mainly on terrace surfaces; the other on gravel thicknesses, often not recording the terrace surface itself. The utility of each of these types of data in terrace correlation is discussed in relation to the complexity of the record, the probability of post-depositional alteration of surface sediments and comparison of straight-line projections with modern river long profiles. Correlation using age estimates is also discussed, in relation to optically-stimulated luminescence dating of sand lenses within terrace gravels in this region during the PASHCC project. It is concluded that the need for replication at single sites means that this approach has limited use for correlative purposes, although dating of sediments is important for understanding wider landscape evolution and patterns of human occupation

A high-significance detection of non-Gaussianity in the WMAP 1-year data using directional spherical wavelets

A directional spherical wavelet analysis is performed to examine the Gaussianity of the WMAP 1-year data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows one to probe orientated structure in the data. Significant deviations from Gaussianity are detected in the skewness and kurtosis of spherical elliptical Mexican hat and real Morlet wavelet coefficients for both the WMAP and Tegmark et al. (2003) foreground-removed maps. The previous non-Gaussianity detection made by Vielva et al. (2003) using the spherical symmetric Mexican hat wavelet is confirmed, although their detection at the 99.9% significance level is only made at the 95.3% significance level using our most conservative statistical test. Furthermore, deviations from Gaussianity in the skewness of spherical real Morlet wavelet coefficients on a wavelet scale of 550 arcmin (corresponding to an effective global size on the sky of approximately 26 degrees and an internal size of 3 degrees) at an azimuthal orientation of 72 degrees, are made at the 98.3% significance level, using the same conservative method. The wavelet analysis inherently allows one to localise on the sky those regions that introduce skewness and those that introduce kurtosis. Preliminary noise analysis indicates that these detected deviation regions are not atypical and have average noise dispersion. Further analysis is required to ascertain whether these detected regions correspond to secondary or instrumental effects, or whether in fact the non-Gaussianity detected is due to intrinsic primordial fluctuations in the cosmic microwave background.Comment: 14 pages, 10 figures, references added, replaced to match version accepted by MNRA

Quantum entanglement with acousto-optic modulators: 2-photon beatings and Bell experiments with moving beamsplitters

We present an experiment testing quantum correlations with frequency shifted photons. We test Bell inequality with 2-photon interferometry where we replace the beamsplitters by acousto-optic modulators, which are equivalent to moving beamsplitters. We measure the 2-photon beatings induced by the frequency shifts, and we propose a cryptographic scheme in relation. Finally, setting the experiment in a relativistic configuration, we demonstrate that the quantum correlations are not only independent of the distance but also of the time ordering between the two single-photon measurements.Comment: 14 pages, 16 figure

Carbohydrate Intake in the Etiology of Crohn's Disease and Ulcerative Colitis

Background: Diet may have a role in the etiology of inflammatory bowel disease. In previous studies, the associations between increased intakes of carbohydrates, sugar, starch, and inflammatory bowel disease are inconsistent. However, few prospective studies have investigated the associations between these macronutrients and incident Crohn's disease (CD) or ulcerative colitis (UC). Methods: A total of 401,326 men and women were recruited between 1991 and 1998. At recruitment, dietary intakes of carbohydrate, sugar, and starch were measured using validated food frequency questionnaires. The cohort was monitored identifying participants who developed incident CD or UC. Cases were matched with 4 controls, and odds ratios were calculated for quintiles of total carbohydrate, sugar, and starch intakes adjusted for total energy intake, body mass index, and smoking. Results: One hundred ten participants developed CD, and 244 participants developed UC during follow-up. The adjusted odds ratio for the highest versus the lowest quintiles of total carbohydrate intake for CD was 0.87, 95% CI = 0.24 to 3.12 and for UC 1.46, 95% CI = 0.62 to 3.46, with no significant trends across quintiles for either (CD, Ptrend = 0.70; UC, Ptrend = 0.41). Similarly, no associations were observed with intakes of total sugar (CD, Ptrend = 0.50; UC, Ptrend = 0.71) or starch (CD, Ptrend = 0.69; UC, Ptrend = 0.17). Conclusions: The lack of associations with these nutrients is in agreement with many case–control studies that have not identified associations with CD or UC. As there is biological plausibility for how specific carbohydrates could have an etiological role in inflammatory bowel disease, future epidemiological work should assess individual carbohydrates, although there does not seem to be a macronutrient effect