Searching for the scale of homogeneity

We introduce a statistical quantity, known as the $K$ function, related to the integral of the two--point correlation function. It gives us straightforward information about the scale where clustering dominates and the scale at which homogeneity is reached. We evaluate the correlation dimension, $D_2$, as the local slope of the log--log plot of the $K$ function. We apply this statistic to several stochastic point fields, to three numerical simulations describing the distribution of clusters and finally to real galaxy redshift surveys. Four different galaxy catalogues have been analysed using this technique: the Center for Astrophysics I, the Perseus--Pisces redshift surveys (these two lying in our local neighbourhood), the Stromlo--APM and the 1.2 Jy {\it IRAS} redshift surveys (these two encompassing a larger volume). In all cases, this cumulant quantity shows the fingerprint of the transition to homogeneity. The reliability of the estimates is clearly demonstrated by the results from controllable point sets, such as the segment Cox processes. In the cluster distribution models, as well as in the real galaxy catalogues, we never see long plateaus when plotting $D_2$ as a function of the scale, leaving no hope for unbounded fractal distributions.Comment: 9 pages, 11 figures, MNRAS, in press; minor revision and added reference

Spatial variation of Anopheles-transmitted Wuchereria bancrofti and Plasmodium falciparum infection densities in Papua New Guinea.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.The spatial variation of Wuchereria bancrofti and Plasmodium falciparum infection densities was measured in a rural area of Papua New Guinea where they share anopheline vectors. The spatial correlation of W. bancrofti was found to reduce by half over an estimated distance of 1.7 km, much smaller than the 50 km grid used by the World Health Organization rapid mapping method. For P. falciparum, negligible spatial correlation was found. After mass treatment with anti-filarial drugs, there was negligible correlation between the changes in the densities of the two parasites

Gene expression meta-analysis of Parkinson’s disease and its relationship with Alzheimer’s disease

Abstract Parkinson’s disease (PD) and Alzheimer’s disease (AD) are the most common neurodegenerative diseases and have been suggested to share common pathological and physiological links. Understanding the cross-talk between them could reveal potentials for the development of new strategies for early diagnosis and therapeutic intervention thus improving the quality of life of those affected. Here we have conducted a novel meta-analysis to identify differentially expressed genes (DEGs) in PD microarray datasets comprising 69 PD and 57 control brain samples which is the biggest cohort for such studies to date. Using identified DEGs, we performed pathway, upstream and protein-protein interaction analysis. We identified 1046 DEGs, of which a majority (739/1046) were downregulated in PD. YWHAZ and other genes coding 14–3-3 proteins are identified as important DEGs in signaling pathways and in protein-protein interaction networks (PPIN). Perturbed pathways also include mitochondrial dysfunction and oxidative stress. There was a significant overlap in DEGs between PD and AD, and over 99% of these were differentially expressed in the same up or down direction across the diseases. REST was identified as an upstream regulator in both diseases. Our study demonstrates that PD and AD share significant common DEGs and pathways, and identifies novel genes, pathways and upstream regulators which may be important targets for therapy in both diseases

Bayesian quantile regression

The paper introduces the idea of Bayesian quantile regression employing a likelihood function that is based on the asymmetric Laplace distribution. It is shown that irrespective of the original distribution of the data, the use of the asymmetric Laplace distribution is a very natural and effective way for modelling Bayesian quantile regression. The paper also demonstrates that improper uniform priors for the unknown model parameters yield a proper joint posterior. The approach is illustrated via a simulated and two real data sets.Asymmetric Laplace distribution Bayesian inference Markov chain Monte Carlo methods Quantile regression

Correction: A World Malaria Map: Plasmodium falciparum Endemicity in 2007

BACKGROUND: Efficient allocation of resources to intervene against malaria requires a detailed understanding of the contemporary spatial distribution of malaria risk. It is exactly 40 y since the last global map of malaria endemicity was published. This paper describes the generation of a new world map of Plasmodium falciparum malaria endemicity for the year 2007. METHODS AND FINDINGS: A total of 8,938 P. falciparum parasite rate (PfPR) surveys were identified using a variety of exhaustive search strategies. Of these, 7,953 passed strict data fidelity tests for inclusion into a global database of PfPR data, age-standardized to 2–10 y for endemicity mapping. A model-based geostatistical procedure was used to create a continuous surface of malaria endemicity within previously defined stable spatial limits of P. falciparum transmission. These procedures were implemented within a Bayesian statistical framework so that the uncertainty of these predictions could be evaluated robustly. The uncertainty was expressed as the probability of predicting correctly one of three endemicity classes; previously stratified to be an informative guide for malaria control. Population at risk estimates, adjusted for the transmission modifying effects of urbanization in Africa, were then derived with reference to human population surfaces in 2007. Of the 1.38 billion people at risk of stable P. falciparum malaria, 0.69 billion were found in Central and South East Asia (CSE Asia), 0.66 billion in Africa, Yemen, and Saudi Arabia (Africa+), and 0.04 billion in the Americas. All those exposed to stable risk in the Americas were in the lowest endemicity class (PfPR(2−10) ≤ 5%). The vast majority (88%) of those living under stable risk in CSE Asia were also in this low endemicity class; a small remainder (11%) were in the intermediate endemicity class (PfPR(2−10) > 5 to < 40%); and the remaining fraction (1%) in high endemicity (PfPR(2−10) ≥ 40%) areas. High endemicity was widespread in the Africa+ region, where 0.35 billion people are at this level of risk. Most of the rest live at intermediate risk (0.20 billion), with a smaller number (0.11 billion) at low stable risk. CONCLUSIONS: High levels of P. falciparum malaria endemicity are common in Africa. Uniformly low endemic levels are found in the Americas. Low endemicity is also widespread in CSE Asia, but pockets of intermediate and very rarely high transmission remain. There are therefore significant opportunities for malaria control in Africa and for malaria elimination elsewhere. This 2007 global P. falciparum malaria endemicity map is the first of a series with which it will be possible to monitor and evaluate the progress of this intervention process

Contrasting patterns in the small-scale heterogeneity of human helminth infections in urban and rural environments in Brazil.

Marked heterogeneity exists in the patterns of parasitic infection between individuals, households and communities. Analysis of parasite distributions within populations is complicated by the fact that parasite distributions are highly aggregated and few studies have explicitly incorporated this distribution when investigating small-scale spatial heterogeneities. This study aimed to quantify the small-scale (within- and between-household) heterogeneity of helminth infection in an area of Minas Gerais State, Brazil, with rural and urban sectors. Parasitological data from a cross-sectional survey of 1,249 individuals aged 0-86 years from 242 households were analysed. Within-household clustering of infection was assessed using random effect logistic regression models and between-household spatial heterogeneity was assessed using a Bayesian negative binomial spatial model. The overall prevalence of hookworm (Necator americanus) was 66.9%, the prevalence of Schistosoma mansoni was 44.9% and the prevalence of Ascaris lumbricoides was 48.8%. Statistical analysis indicated significant (within) household and (between household) spatial clustering of hookworm in both rural and urban areas and of S. mansoni in rural areas. There was no evidence of either household or spatial clustering of S. mansoni in urban areas. The spatial correlation of S. mansoni was estimated to reduce by half over a distance of 700 m in the rural area. Rural hookworm had a much smaller half-distance (28 m) and urban hookworm showed an even smaller half-distance (12 m). We suggest that such species-specific differences in patterns of infection by environment are primarily due to variation in exposure and parasite life cycle, although host genetic factors cannot be ruled out