Streptococcus pneumoniae (the pneumococcus) is the world’s foremost bacterial pathogen in both morbidity and mortality. Switching between phenotypic forms (or ‘phases’) that favour asymptomatic carriage or invasive disease was first reported in 1933. Here, we show that the underlying mechanism for such phase variation consists of genetic rearrangements in a Type I restriction-modification system (SpnD39III). The rearrangements generate six alternative specificities with distinct methylation patterns, as defined by single-molecule, real-time (SMRT) methylomics. The SpnD39III variants have distinct gene expression profiles. We demonstrate distinct virulence in experimental infection and in vivo selection for switching between SpnD39III variants. SpnD39III is ubiquitous in pneumococci, indicating an essential role in its biology. Future studies must recognize the potential for switching between these heretofore undetectable, differentiated pneumococcal subpopulations in vitro and in vivo. Similar systems exist in other bacterial genera, indicating the potential for broad exploitation of epigenetic gene regulation.

Single-cell transcriptomic assays have enabled the de novo reconstruction of lineage differentiation trajectories, along with the characterization of cellular heterogeneity and state transitions. Several methods have been developed for reconstructing developmental trajectories from single-cell transcriptomic data, but efforts on analyzing single-cell epigenomic data and on trajectory visualization remain limited. Here we present STREAM, an interactive pipeline capable of disentangling and visualizing complex branching trajectories from both single-cell transcriptomic and epigenomic data. We have tested STREAM on several synthetic and real datasets generated with different single-cell technologies. We further demonstrate its utility for understanding myoblast differentiation and disentangling known heterogeneity in hematopoiesis for different organisms. STREAM is an open-source software package.

The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality . This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher’s discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction. This article is part of the theme issue ‘Hilbert’s sixth problem’.

The entropy maximum approach to constructing equilibria in lattice kinetic equations is revisited. For a suitable entropy function, we derive explicitly the hydrodynamic local equilibrium, prove the $H$ theorem for lattice Bhatnagar-Gross-Krook models, and develop a systematic method to account for additional constraints.

In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both randomized and deterministic, for selecting elements from these families that have been shown to ensure the rate of convergence in $L_2$ norm of order $O(1/N)$, where $N$ is the number of elements. We show that both randomized and deterministic procedures are successful if additional information about the families of functions to be approximated is provided. In the absence of such additional information one may observe exponential growth of the number of terms needed to approximate the function and/or extreme sensitivity of the outcome of the approximation to parameters. Implications of our analysis for applications of neural networks in modeling and control are illustrated with examples.Comment: arXiv admin note: text overlap with arXiv:0905.067