The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

Topological Aspects of Gauge Fixing Yang-Mills Theory on S4

For an $S_4$ space-time manifold global aspects of gauge-fixing are investigated using the relation to Topological Quantum Field Theory on the gauge group. The partition function of this TQFT is shown to compute the regularized Euler character of a suitably defined space of gauge transformations. Topological properties of the space of solutions to a covariant gauge conditon on the orbit of a particular instanton are found using the $SO(5)$ isometry group of the $S_4$ base manifold. We obtain that the Euler character of this space differs from that of an orbit in the topologically trivial sector. This result implies that an orbit with Pontryagin number \k=\pm1 in covariant gauges on $S_4$ contributes to physical correlation functions with a different multiplicity factor due to the Gribov copies, than an orbit in the trivial \k=0 sector. Similar topological arguments show that there is no contribution from the topologically trivial sector to physical correlation functions in gauges defined by a nondegenerate background connection. We discuss possible physical implications of the global gauge dependence of Yang-Mills theory.Comment: 13 pages, uuencoded and compressed LaTeX file, no figure

Polymorphisms in Gag spacer peptide 1 confer varying levels of resistance to the HIV- 1maturation inhibitor bevirimat

Background: The maturation inhibitor bevirimat (BVM) potently inhibits human immunodeficiency virus type 1 (HIV-1) replication by blocking capsid-spacer peptide 1 (CA-SP1) cleavage. Recent clinical trials demonstrated that a significant proportion of HIV-1-infected patients do not respond to BVM. A patient’s failure to respond correlated with baseline polymorphisms at SP1 residues 6-8. Results: In this study, we demonstrate that varying levels of BVM resistance are associated with point mutations at these residues. BVM susceptibility was maintained by SP1-Q6A, -Q6H and -T8A mutations. However, an SP1-V7A mutation conferred high-level BVM resistance and SP1-V7M and T8Δ mutations conferred intermediate levels of BVM resistance. Conclusions: Future exploitation of the CA-SP1 cleavage site as an antiretroviral drug target will need to overcome the baseline variability in the SP1 region of Gag.Publisher PDFPeer reviewe

Dynamics of heteropolymers in dilute solution: effective equation of motion and relaxation spectrum

The dynamics of a heteropolymer chain in solution is studied in the limit of long chain length. Using functional integral representation we derive an effective equation of motion, in which the heterogeneity of the chain manifests itself as a time-dependent excluded volume effect. At the mean field level, the heteropolymer chain is therefore dynamically equivalent to a homopolymer chain with both time-independent and time-dependent excluded volume effects. The perturbed relaxation spectrum is also calculated. We find that heterogeneity also renormalizes the relaxation spectrum. However, we find, to the lowest order in heterogeneity, that the relaxation spectrum does not exhibit any dynamic freezing, at the point when static (equilibrium) ``freezing'' transition occurs in heteropolymer. Namely, the breaking of fluctuation-dissipation theorem (FDT) proposed for spin glass dynamics does not have dynamic effect in heteropolymer, as far as relaxation spectrum is concerned. The implication of this result is discussed

A Genome-Wide Analysis of Promoter-Mediated Phenotypic Noise in Escherichia coli

Gene expression is subject to random perturbations that lead to fluctuations in the rate of protein production. As a consequence, for any given protein, genetically identical organisms living in a constant environment will contain different amounts of that particular protein, resulting in different phenotypes. This phenomenon is known as “phenotypic noise.” In bacterial systems, previous studies have shown that, for specific genes, both transcriptional and translational processes affect phenotypic noise. Here, we focus on how the promoter regions of genes affect noise and ask whether levels of promoter-mediated noise are correlated with genes' functional attributes, using data for over 60% of all promoters in Escherichia coli. We find that essential genes and genes with a high degree of evolutionary conservation have promoters that confer low levels of noise. We also find that the level of noise cannot be attributed to the evolutionary time that different genes have spent in the genome of E. coli. In contrast to previous results in eukaryotes, we find no association between promoter-mediated noise and gene expression plasticity. These results are consistent with the hypothesis that, in bacteria, natural selection can act to reduce gene expression noise and that some of this noise is controlled through the sequence of the promoter region alon

A Simple Screen to Identify Promoters Conferring High Levels of Phenotypic Noise

Genetically identical populations of unicellular organisms often show marked variation in some phenotypic traits. To investigate the molecular causes and possible biological functions of this phenotypic noise, it would be useful to have a method to identify genes whose expression varies stochastically on a certain time scale. Here, we developed such a method and used it for identifying genes with high levels of phenotypic noise in Salmonella enterica ssp. I serovar Typhimurium (S. Typhimurium). We created a genomic plasmid library fused to a green fluorescent protein (GFP) reporter and subjected replicate populations harboring this library to fluctuating selection for GFP expression using fluorescent-activated cell sorting (FACS). After seven rounds of fluctuating selection, the populations were strongly enriched for promoters that showed a high amount of noise in gene expression. Our results indicate that the activity of some promoters of S. Typhimurium varies on such a short time scale that these promoters can absorb rapid fluctuations in the direction of selection, as imposed during our experiment. The genomic fragments that conferred the highest levels of phenotypic variation were promoters controlling the synthesis of flagella, which are associated with virulence and host–pathogen interactions. This confirms earlier reports that phenotypic noise may play a role in pathogenesis and indicates that these promoters have among the highest levels of noise in the S. Typhimurium genome. This approach can be applied to many other bacterial and eukaryotic systems as a simple method for identifying genes with noisy expression

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum