The ergodic decomposition of asymptotically mean stationary random sources

It is demonstrated how to represent asymptotically mean stationary (AMS) random sources with values in standard spaces as mixtures of ergodic AMS sources. This an extension of the well known decomposition of stationary sources which has facilitated the generalization of prominent source coding theorems to arbitrary, not necessarily ergodic, stationary sources. Asymptotic mean stationarity generalizes the definition of stationarity and covers a much larger variety of real-world examples of random sources of practical interest. It is sketched how to obtain source coding and related theorems for arbitrary, not necessarily ergodic, AMS sources, based on the presented ergodic decomposition.Comment: Submitted to IEEE Transactions on Information Theory, Apr. 200

Full-length de novo viral quasispecies assembly through variation graph construction

International audienceMotivation: Viruses populate their hosts as a viral quasispecies: a collection of genetically related mutant strains.Viral quasispecies assembly refers to reconstructing the strain-specific haplotypes from read data, and predicting their relative abundances within the mix of strains, an important step for various treatment-related reasons. Reference-genome-independent ("de novo") approaches have yielded benefits over reference-guided approaches, because reference-induced biases can become overwhelming when dealing with divergent strains. While being very accurate, extant de novo methods only yield rather short contigs. It remains to reconstruct full-length haplotypes together with their abundances from such contigs. Method: We first construct a variation graph, a recently popular, suitable structure for arranging and integrating several related genomes, from the short input contigs, without making use of a reference genome. To obtain paths through the variation graph that reflect the original haplotypes, we solve a minimization problem that yields a selection of maximal-length paths that is optimal in terms of being compatible with the read coverages computed for the nodes of the variation graph. We output the resulting selection of maximal length paths as the haplotypes, together with their abundances. Results: Benchmarking experiments on challenging simulated data sets show significant improvements in assembly contiguity compared to the input contigs, while preserving low error rates. As a consequence, our method outperforms all state-of-the-art viral quasispecies assem-blers that aim at the construction of full-length haplotypes, in terms of various relevant assembly measures. Our tool, Virus-VG, is publicly available at https://bitbucket.org/jbaaijens/ virus-vg

Robust inference of groups in gene expression time-courses using mixtures of HMMs

Motivation: Genetic regulation of cellular processes is frequently investigated using large-scale gene expression experiments to observe changes in expression over time. This temporal data poses a challenge to classical distance-based clustering methods due to its horizontal dependencies along the time-axis. We propose to use hidden Markov models (HMMs) to explicitly model these time-dependencies. The HMMs are used in a mixture approach that we show to be superior over clustering. Furthermore, mixtures are a more realistic model of the biological reality, as an unambiguous partitioning of genes into clusters of unique functional assignment is impossible. Use of the mixture increases robustness with respect to noise and allows an inference of groups at varying level of assignment ambiguity. A simple approach, partially supervised learning, allows to benefit from prior biological knowledge during the training. Our method allows simultaneous analysis of cyclic and non-cyclic genes and copes well with noise and missing values. Results: We demonstrate biological relevance by detection of phase-specific groupings in HeLa time-course data. A benchmark using simulated data, derived using assumptions independent of those in our method, shows very favorable results compared to the baseline supplied by k-means and two prior approaches implementing model-based clustering. The results stress the benefits of incorporating prior knowledge, whenever available

Automatic discovery of 100-miRNA signature for cancer classification using ensemble feature selection

International audienc