On l-adic representations for a space of noncongruence cuspforms

This paper is concerned with a compatible family of 4-dimensional \ell-adic representations \rho_{\ell} of G_\Q:=\Gal(\bar \Q/\Q) attached to the space of weight 3 cuspforms S_3 (\Gamma) on a noncongruence subgroup \Gamma \subset \SL. For this representation we prove that: 1.)It is automorphic: the L-function L(s, \rho_{\ell}^{\vee}) agrees with the L-function for an automorphic form for \text{GL}_4(\mathbb A_{\Q}), where \rho_{\ell}^{\vee} is the dual of \rho_{\ell}. 2.) For each prime p \ge 5 there is a basis h_p = \{h_p ^+, h_p ^- \} of S_3 (\Gamma) whose expansion coefficients satisfy 3-term Atkin and Swinnerton-Dyer (ASD) relations, relative to the q-expansion coefficients of a newform f of level 432. The structure of this basis depends on the class of p modulo 12. The key point is that the representation $\rho_{\ell}$ admits a quaternion multiplication structure in the sense of a recent work of Atkin, Li, Liu and Long.Comment: Second revised version. To appear: Proceedings of the American Mathematical Societ

A Note on Topological M5-branes and String-Fivebrane Duality

We derive the stability conditions for the M5-brane in topological M-theory using kappa-symmetry. The non-linearly self-dual 3-form on the world-volume is necessarily non-vanishing, as is the case also for the 2-form field strengths on coisotropic branes in topological string theory. It is demonstrated that the self-duality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) in G_2. The double dimensional reduction of the M5-brane is the D4-brane, and its direct reduction is an NS5-brane. We show that the equation of motion for the 3-form on the NS5-brane wrapping a Calabi-Yau space is exactly the Kodaira-Spencer equation, providing support for a string-fivebrane duality in topological string theory.Comment: 11 pp, plain te

The ChIP-seq-defined networks of Bcl-3 gene binding support its required role in skeletal muscle atrophy

NF-kappaB transcriptional activation is required for skeletal muscle disuse atrophy. We are continuing to study how the activation of NF-kB regulates the genes that encode the protein products that cause atrophy. Using ChIP-sequencing we found that Bcl-3, an NF-kB transcriptional activator required for atrophy, binds to the promoters of a number of genes whose collective function describes two major aspects of muscle wasting. By means of bioinformatics analysis of ChIP-sequencing data we found Bcl-3 to be directing transcription networks of proteolysis and energy metabolism. The proteolytic arm of the Bcl-3 networks includes many E3 ligases associated with proteasomal protein degradation, including that of the N-end rule pathway. The metabolic arm appears to be involved in organizing the change from oxidative phosphorylation to glycolysis in atrophying muscle. For one gene, MuRF1, ChIP-sequencing data identified the location of Bcl-3 and p50 binding in the promoter region which directed the creation of deletant and base-substitution mutations of MuRF1 promoter constructs to determine the effect on gene transcription. The results provide the first direct confirmation that the NF-kB binding site is involved in the muscle unloading regulation of MuRF1. Finally, we have combined the ChIP-sequencing results with gene expression microarray data from unloaded muscle to map several direct targets of Bcl-3 that are transcription factors whose own targets describe a set of indirect targets for NF-kB in atrophy. ChIP-sequencing provides the first molecular explanation for the finding that Bcl3 knockout mice are resistant to disuse muscle atrophy. Mapping the transcriptional regulation of muscle atrophy requires an unbiased analysis of the whole genome, which we show is now possible with ChIP-sequencing.R01 AR041705 - NIAMS NIH HHS; R01 AR060217 - NIAMS NIH HHS; AR041705 - NIAMS NIH HHS; AR060217 - NIAMS NIH HH

Peer crowd affiliation as a segmentation tool for young adult tobacco use.

BackgroundIn California, young adult tobacco prevention is of prime importance; 63% of smokers start by the age of 18 years, and 97% start by the age of 26 years. We examined social affiliation with 'peer crowd' (eg, Hipsters) as an innovative way to identify high-risk tobacco users.MethodsCross-sectional surveys were conducted in 2014 (N=3368) among young adult bar patrons in 3 California cities. We examined use rates of five products (cigarettes, e-cigarettes, hookah, cigars and smokeless tobacco) by five race/ethnicity categories. Peer crowd affiliation was scored based on respondents' selecting pictures of young adults representing those most and least likely to be in their friend group. Respondents were classified into categories based on the highest score; the peer crowd score was also examined as a continuous predictor. Logistic regression models with each tobacco product as the outcome tested the unique contribution of peer crowd affiliation, controlling for race/ethnicity, age, sex, sexual orientation and city.ResultsRespondents affiliating with Hip Hop and Hipster peer crowds reported significantly higher rates of tobacco use. As a categorical predictor, peer crowd was related to tobacco use, independent of associations with race/ethnicity. As a continuous predictor, Hip Hop peer crowd affiliation was also associated with tobacco use, and Young Professional affiliation was negatively associated, independent of demographic factors.ConclusionsTobacco product use is not the same across racial/ethnic groups or peer crowds, and peer crowd predicts tobacco use independent of race/ethnicity. Antitobacco interventions targeting peer crowds may be an effective way to reach young adult tobacco users.Trial registration numberNCT01686178, Pre-results

Reduction of the radar cross section of arbitrarily shaped cavity structures

The problem of the reduction of the radar cross section (RCS) of open-ended cavities was studied. The issues investigated were reduction through lossy coating materials on the inner cavity wall and reduction through shaping of the cavity. A method was presented to calculate the RCS of any arbitrarily shaped structure in order to study the shaping problem. The limitations of this method were also addressed. The modal attenuation was studied in a multilayered coated waveguide. It was shown that by employing two layers of coating, it was possible to achieve an increase in both the magnitude of attenuation and the frequency band of effectiveness. The numerical method used in finding the roots of the characteristic equation breaks down when the coating thickness is very lossy and large in terms of wavelength. A new method of computing the RCS of an arbitrary cavity was applied to study the effects of longitudinal bending on RCS reduction. The ray and modal descriptions for the fields in a parallel plate waveguide were compared. To extend the range of validity of the Shooting and Bouncing Ray (SBR) method, the simple ray picture must be modified to account for the beam blurring

A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors,

This paper provides a review of some recent theoretical results for time series models with GARCH errors, and is directed towards practitioners. Starting with the simple ARCH model and proceeding to the GARCH model, some results for stationary and nonstationary ARMA-GARCH are summarized. Various new ARCH-type models, including double threshold ARCH and GARCH, ARFIMA-GARCH, CHARMA and vector ARMA-GARCH, are also reviewed.