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.

Incidence of AIDS-Defining and Other Cancers in HIV-Positive Children in South Africa: Record Linkage Study.

BACKGROUND Little is known on the risk of cancer in HIV-positive children in sub-Saharan Africa. We examined incidence and risk factors of AIDS-defining and other cancers in pediatric antiretroviral therapy (ART) programs in South Africa. METHODS We linked the records of five ART programs in Johannesburg and Cape Town to those of pediatric oncology units, based on name and surname, date of birth, folder and civil identification numbers. We calculated incidence rates and obtained hazard ratios (HR) with 95% confidence intervals (CI) from Cox regression models including ART, sex, age, and degree of immunodeficiency. Missing CD4 counts and CD4% were multiply imputed. Immunodeficiency was defined according to World Health Organization 2005 criteria. RESULTS Data of 11,707 HIV-positive children were included in the analysis. During 29,348 person-years of follow-up 24 cancers were diagnosed, for an incidence rate of 82 per 100,000 person-years (95% CI 55-122). The most frequent cancers were Kaposi Sarcoma (34 per 100,000 person-years) and Non Hodgkin Lymphoma (31 per 100,000 person-years). The incidence of non AIDS-defining malignancies was 17 per 100,000. The risk of developing cancer was lower on ART (HR 0.29, 95%CI 0.09-0.86), and increased with age at enrolment (>10 versus <3 years: HR 7.3, 95% CI 2.2-24.6) and immunodeficiency at enrolment (advanced/severe versus no/mild: HR 3.5, 95%CI 1.1-12.0). The HR for the effect of ART from complete case analysis was similar but ceased to be statistically significant (p=0.078). CONCLUSIONS Early HIV diagnosis and linkage to care, with start of ART before advanced immunodeficiency develops, may substantially reduce the burden of cancer in HIV-positive children in South Africa and elsewhere.

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.

When to Monitor CD4 Cell Count and HIV RNA to Reduce Mortality and AIDS-Defining Illness in Virologically Suppressed HIV-Positive Persons on Antiretroviral Therapy in High-Income Countries: A Prospective Observational Study.

OBJECTIVE To illustrate an approach to compare CD4 cell count and HIV-RNA monitoring strategies in HIV-positive individuals on antiretroviral therapy (ART). DESIGN Prospective studies of HIV-positive individuals in Europe and the USA in the HIV-CAUSAL Collaboration and The Center for AIDS Research Network of Integrated Clinical Systems. METHODS Antiretroviral-naive individuals who initiated ART and became virologically suppressed within 12 months were followed from the date of suppression. We compared 3 CD4 cell count and HIV-RNA monitoring strategies: once every (1) 3 ± 1 months, (2) 6 ± 1 months, and (3) 9-12 ± 1 months. We used inverse-probability weighted models to compare these strategies with respect to clinical, immunologic, and virologic outcomes. RESULTS In 39,029 eligible individuals, there were 265 deaths and 690 AIDS-defining illnesses or deaths. Compared with the 3-month strategy, the mortality hazard ratios (95% CIs) were 0.86 (0.42 to 1.78) for the 6 months and 0.82 (0.46 to 1.47) for the 9-12 month strategy. The respective 18-month risk ratios (95% CIs) of virologic failure (RNA >200) were 0.74 (0.46 to 1.19) and 2.35 (1.56 to 3.54) and 18-month mean CD4 differences (95% CIs) were -5.3 (-18.6 to 7.9) and -31.7 (-52.0 to -11.3). The estimates for the 2-year risk of AIDS-defining illness or death were similar across strategies. CONCLUSIONS Our findings suggest that monitoring frequency of virologically suppressed individuals can be decreased from every 3 months to every 6, 9, or 12 months with respect to clinical outcomes. Because effects of different monitoring strategies could take years to materialize, longer follow-up is needed to fully evaluate this question.

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.

Defining barriers in caring for seriously-ill children in a resource-limited setting: An observational study of 2 children's hospitals in Haiti

Background. According to the WHO 2007 country report, Haiti lags behind the Millennium Development Goal of reducing child mortality and maintains the highest under-5 mortality rate in the Western hemisphere. 3 Overall, few studies exist that seek to better grasp barriers in caring for a seriously ill child in a resource-limited setting and only a handful propose sustainable, effective interventions. ^ Objectives. The objectives of this study are to describe the prevalence of serious illnesses among children hospitalized at 2 children's hospitals in Port au Prince, to determine the barriers faced when caring for seriously ill children, and to report hospital outcomes of children admitted with serious illnesses. ^ Methods. Data were gathered from 2 major children's hospitals in Port au Prince, Haiti (Grace Children's Hospital [GCH] and Hopital d l'Universite d'Etat d'Haiti [HUEH]) using a triangulated approach of focus group discussions, physician questionnaires, and retrospective chart review. 23 pediatric physicians participated in focus group discussions and completed a self-administered questionnaire evaluating healthcare provider knowledge, self-efficacy, and perceived barriers relating to the care of seriously ill children in a resource-limited setting. A sample of 240 patient charts meeting eligibility criteria was abstracted for pertinent elements including sociodemographics, documentation, treatment strategies, and outcomes. Factors associated with mortality were analyzed using χ2 test and Fisher exact test [Minitab v.15]. ^ Results. The most common primary diagnoses at admission were gastroenteritis with moderate dehydration (35.5%), severe malnutrition (25.8%), and pneumonia (19.3%) for GCH, and severe malnutrition (32.6%), sepsis (24.7%), and severe respiratory distress (18%) for HUEH. Overall, 12.9% and 27% of seriously ill patients presented with shock to GCH and HUEH, respectively. ^ Shortage of necessary materials and equipment represented the most commonly reported limitation (18/23 respondents). According to chart data, 9.4% of children presenting with shock did not receive a fluid bolus, and only 8% of patients presenting with altered mental status or seizures received a glucose check. 65% of patients with meningitis did not receive a lumbar puncture due to lack of materials. ^ Hospital mortality rates did not differ by gender or by institution. Children who died were more likely to have a history of prematurity (OR 4.97 [95% CI 1.32-18.80]), an incomplete vaccination record (OR 4.05 [95% CI 1.68-9.74]), or a weight for age ≤3rd percentile (OR 6.1 [95% CI 2.49-14.93]. Case-fatality rates were significantly higher among those who presented with signs of shock compared with those who did not (23.1% vs. 10.7%, RR=2.16, p=0.03). Caregivers did not achieve shock reversal in 21% of patients and did not document shock reversal in 50% of patients. ^ Conclusions. Many challenges face those who seek to optimize care for seriously ill children in resource-limited settings. Specifically, in Haiti, qualitative and quantitative data suggest major issues with lack of supplies, pre-hospital factors, including malnutrition as a comorbidity, and early recognition and management of shock. A tailored intervention designed to address these issues is needed in order to prospectively evaluate improvements in child mortality in a high-risk population.^

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.