Regularity conditions in the realisability problem in applications to point processes and random closed sets

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive ex-tension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extens ion can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

3D documentation and visualization of external injury findings by integration of simple photography in CT/MRI data sets (IprojeCT).

This study evaluated the feasibility of documenting patterned injury using three dimensions and true colour photography without complex 3D surface documentation methods. This method is based on a generated 3D surface model using radiologic slice images (CT) while the colour information is derived from photographs taken with commercially available cameras. The external patterned injuries were documented in 16 cases using digital photography as well as highly precise photogrammetry-supported 3D structured light scanning. The internal findings of these deceased were recorded using CT and MRI. For registration of the internal with the external data, two different types of radiographic markers were used and compared. The 3D surface model generated from CT slice images was linked with the photographs, and thereby digital true-colour 3D models of the patterned injuries could be created (Image projection onto CT/IprojeCT). In addition, these external models were merged with the models of the somatic interior. We demonstrated that 3D documentation and visualization of external injury findings by integration of digital photography in CT/MRI data sets is suitable for the 3D documentation of individual patterned injuries to a body. Nevertheless, this documentation method is not a substitution for photogrammetry and surface scanning, especially when the entire bodily surface is to be recorded in three dimensions including all external findings, and when precise data is required for comparing highly detailed injury features with the injury-inflicting tool.

Automated 3D Lumbar Intervertebral Disc Segmentation from MRI Data Sets

This paper proposed an automated three-dimensional (3D) lumbar intervertebral disc (IVD) segmentation strategy from Magnetic Resonance Imaging (MRI) data. Starting from two user supplied landmarks, the geometrical parameters of all lumbar vertebral bodies and intervertebral discs are automatically extracted from a mid-sagittal slice using a graphical model based template matching approach. Based on the estimated two-dimensional (2D) geometrical parameters, a 3D variable-radius soft tube model of the lumbar spine column is built by model fitting to the 3D data volume. Taking the geometrical information from the 3D lumbar spine column as constraints and segmentation initialization, the disc segmentation is achieved by a multi-kernel diffeomorphic registration between a 3D template of the disc and the observed MRI data. Experiments on 15 patient data sets showed the robustness and the accuracy of the proposed algorithm.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

Effects of divergent selection for growth on egg quality traits in Japanese quail

The experiment was designed to investigate the impact of selection for increased body mass on external and internal egg quality traits of Japanese quail. Three hundred and sixty Japanese quail, divergently selected over three generations for different body mass at 4 weeks of age, were used. Quail were homogeneously divided into three groups each consisting of 120 birds: high body mass (HBM), low body mass (LBM) and Control. ANOVA was used to detect the effect of selection on egg quality. In addition, correlation between external and internal egg quality traits was measured. Our results revealed thatHBMquail laid heavier eggs (P = 0.03 compared with LBM but not significantly different with Control quail) with a higher external (shell thickness, shell weight, eggshell ratio and eggshell density, P = 0.0001) and internal egg quality score (albumen weight, P = 0.003; albumen ratio, P = 0.01; albumen height, yolk height, yolk index and Haugh unit, P = 0.0001) when compared with both the Control and LBM. The egg surface area and yolk diameter were significantly higher in HBM when compared with the LBM but not with the Control line. Egg weight was positively correlated with albumen weight (r = 0.54, P = 0.0001), albumen ratio (r = 0.14, P = 0.05), yolk height (r = 0.27, P = 0.0001), yolk weight (r = 0.23, P = 0.002), yolk diameter (r = 0.14, P = 0.05) and yolk index (r = 0.21, P = 0.005) but was negatively correlated with yolk ratio (r = –0.16, P = 0.03). Our results indicate that selection for higher body mass might result in heavier eggs and superior egg quality.

Fast Algorithms Using Minimal Data Structures for Common Topological Relationships in Large, Irregularly-spaced Topographic Data Sets

Digital terrain models (DTM) typically contain large numbers of postings, from hundreds of thousands to billions. Many algorithms that run on DTMs require topological knowledge of the postings, such as finding nearest neighbors, finding the posting closest to a chosen location, etc. If the postings are arranged irregu- larly, topological information is costly to compute and to store. This paper offers a practical approach to organizing and searching irregularly-space data sets by presenting a collection of efficient algorithms (O(N),O(lgN)) that compute important topological relationships with only a simple supporting data structure. These relationships include finding the postings within a window, locating the posting nearest a point of interest, finding the neighborhood of postings nearest a point of interest, and ordering the neighborhood counter-clockwise. These algorithms depend only on two sorted arrays of two-element tuples, holding a planimetric coordinate and an integer identification number indicating which posting the coordinate belongs to. There is one array for each planimetric coordinate (eastings and northings). These two arrays cost minimal overhead to create and store but permit the data to remain arranged irregularly.

Integrated Data Sets of the EU FP5 Research Project ORFOIS: Origin and fate of biogenic particle fluxes in the ocean and their interactions with atmospheric CO2 concentrations as well as the marine sediment

For a reliable simulation of the time and space dependent CO2 redistribution between ocean and atmosphere an appropriate time dependent simulation of particle dynamics processes is essential but has not been carried out so far. The major difficulties were the lack of suitable modules for particle dynamics and early diagenesis (in order to close the carbon and nutrient budget) in ocean general circulation models, and the lack of an understanding of biogeochemical processes, such as the partial dissolution of calcareous particles in oversaturated water. The main target of ORFOIS was to fill in this gap in our knowledge and prediction capability infrastructure. This goal has been achieved step by step. At first comprehensive data bases (already existing data) of observations of relevance for the three major types of biogenic particles, organic carbon (POC), calcium carbonate (CaCO3), and biogenic silica (BSi or opal), as well as for refractory particles of terrestrial origin were collated and made publicly available.

Contemporary genetic, historical genetic and morphological data sets for the Yellow-tufted Honeyeater Lichenostomus melanops

Understanding the evolutionary history of threatened populations can improve their conservation management. Re-establishment of past but recent gene flow could re-invigorate threatened populations and replenish genetic diversity, necessary for population persistence. One of the four nominal subspecies of the common yellow-tufted honeyeater, Lichenostomus melanops cassidix, is critically endangered despite substantial conservation efforts over 55 years. Using a combination of morphometric, genetic and modelling approaches we tested for its evolutionary distinctiveness and conservation merit. We confirmed that cassidix has at least one morphometric distinction. It also differs genetically from the other subspecies in allele frequencies but not phylogenetically, implying that its evolution was recent. Modelling historical distribution supported the lack of vicariance and suggested a possibility of gene flow among subspecies at least since the late Pleistocene. Multi-locus coalescent analyses indicated that cassidix diverged from its common ancestor with neighbouring subspecies gippslandicus sometime from the mid-Pleistocene to the Holocene, and that it has the smallest historical effective population size of all subspecies. It appears that cassidix diverged from its ancestor with gippslandicus through a combination of drift and local selection. From patterns of genetic subdivision on two spatial scales and morphological variation we concluded that cassidix, gippslandicus and (melanops + meltoni) are diagnosable as subspecies. Low genetic diversity and effective population size of cassidix may translate to low genetic fitness and evolutionary potential, thus managed gene flow from gippslandicus is recommended for its recovery.