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

Estimation and Testing for Unit Root Processes with GARCH(1,1) Errors: Theory and Monte Carlo Evidence,

Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition alpha + beta

"Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence"

Least squares (LS) and maximum likelihood (ML) estimation are con-sidered for unit root processes with GARCH (1, 1) errors. The asymp-totic distributions of LS and ML estimators are derived under the con-dition ƒ¿ + ƒÀ

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