Periodic orbits from Δ-modulation of stable linear systems

The �-modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by cTx where c �Rn/{0} is a given, otherwise arbitrary, vector. We obtain necessary and sufficient conditions for the existence of periodic points of a finite order. Some concrete results about the existence of a certain order of periodic points are also derived. We also study the relationship between certain polyhedra and the periodicity of the �-modulated orbit

Stein factors for negative binomial approximation in Wasserstein distance

The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 (2006) 943-954). The bounds are used to quantify the accuracy of negative binomial approximation to parasite counts in hosts. Since the infectivity of a population can be expected to be proportional to its total parasite burden, the Wasserstein metric is the appropriate choice.Comment: Published at http://dx.doi.org/10.3150/14-BEJ595 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Recovering complete and draft population genomes from metagenome datasets.

Assembly of metagenomic sequence data into microbial genomes is of fundamental value to improving our understanding of microbial ecology and metabolism by elucidating the functional potential of hard-to-culture microorganisms. Here, we provide a synthesis of available methods to bin metagenomic contigs into species-level groups and highlight how genetic diversity, sequencing depth, and coverage influence binning success. Despite the computational cost on application to deeply sequenced complex metagenomes (e.g., soil), covarying patterns of contig coverage across multiple datasets significantly improves the binning process. We also discuss and compare current genome validation methods and reveal how these methods tackle the problem of chimeric genome bins i.e., sequences from multiple species. Finally, we explore how population genome assembly can be used to uncover biogeographic trends and to characterize the effect of in situ functional constraints on the genome-wide evolution

Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations

Quantum virial expansion provides an ideal tool to investigate the high-temperature properties of a strongly correlated Fermi gas. Here, we construct the virial expansion in the presence of spin population imbalance. Up to the third order, we calculate the high-temperature free energy of a unitary Fermi gas as a function of spin imbalance, with infinitely large, attractive or repulsive interactions. In the latter repulsive case, we show that there is no itinerant ferromagnetism when quantum virial expansion is applicable. We therefore estimate an upper bound for the ferromagnetic transition temperature $T_{c}$. For a harmonically trapped Fermi gas at unitarity, we find that $(T_{c})_{uppper}<T_{F}$, where $T_{F}$ is the Fermi temperature at the center of the trap. Our result for the high-temperature equations of state may confront future high-precision thermodynamic measurements.Comment: 7 pages, 5 figures, accepted in Phys. Rev.