A Mixture model with random-effects components for clustering correlated gene-expression profiles

Motivation: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. Results: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation) and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too.

Neighborhood environmental factors correlated with walking near home: Using SPACES

Purpose: The physical environment plays an important role in influencing participation in physical activity, although the specific factors that are correlated with different patterns of walking remain to be determined We examined correlations between physical environmental factors and self-reported walking for recreation and transport near home. Methods: The local neighborhood environments (defined as a 400-m radius from the respondent's home) of 1678 adults were assessed for their suitability for walking. The environmental data were collected during 2000 using the Systematic Pedestrian and Cycling Environmental Scan (SPACES) instrument together with information from other sources. We used logistic regression modeling to examine the relationship between the attributes of the physical environment and the self-reported walking behavior undertaken near home. Results: Functional features were correlated with both walking for recreation (odds ratio (OR) 1.62; 95% confidence interval (Cl): 1.20-2.19) and for transport (OR 1.30; 95% Cl: 0.97-1.73). A well-maintained walking surface was the main functional factor associated with walking for recreation (OR 2.04; 95% Cl: 1.43-2.91) and for transport (OR 2.13; 95% Cl: 1.53-2.96). Destination factors, such as shops and public transport, were significantly correlated with walking for transport (OR 1.80; 95% Cl: 1.33-2.44), but not recreation. Conclusion: The findings suggest that neighborhoods with pedestrian facilities that are attractive and comfortable and where there are local destinations (such as shops and public transport) are associated with walking near home.

On the distributed compression of quantum information

The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian-Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction.