Hyperbolic angular statistics for globally coupled phase oscillators

We analytically discuss a multiplicative noise generalization of the Kuramoto-Sakaguchi dynamics for an assembly of globally coupled phase oscillators. In the mean field limit, the resulting class of invariant measures coincides with a generalized, two parameter family of angular von Mises probability distributions which is governed by the exit law from the unit disc of a hyperbolic drifted Brownian motion. Our dynamics offers a simple yet analytically tractable generalization of Kuramoto-Sakaguchi dynamics with two control parameters. We derive an exact and very compact relation between the two control parameters at the onset of phase oscillators synchronization.Comment: 8 page

Expanding the diversity of mycobacteriophages: Insights into genome architecture and evolution

Mycobacteriophages are viruses that infect mycobacterial hosts such as Mycobacterium smegmatis and Mycobacterium tuberculosis. All mycobacteriophages characterized to date are dsDNA tailed phages, and have either siphoviral or myoviral morphotypes. However, their genetic diversity is considerable, and although sixty-two genomes have been sequenced and comparatively analyzed, these likely represent only a small portion of the diversity of the mycobacteriophage population at large. Here we report the isolation, sequencing and comparative genomic analysis of 18 new mycobacteriophages isolated from geographically distinct locations within the United States. Although no clear correlation between location and genome type can be discerned, these genomes expand our knowledge of mycobacteriophage diversity and enhance our understanding of the roles of mobile elements in viral evolution. Expansion of the number of mycobacteriophages grouped within Cluster A provides insights into the basis of immune specificity in these temperate phages, and we also describe a novel example of apparent immunity theft. The isolation and genomic analysis of bacteriophages by freshman college students provides an example of an authentic research experience for novice scientists. © 2011 Hatfull et al