Gauged M-flation After BICEP2

In view of the recent BICEP2 results [arXiv:1403.3985] which may be attributed to the observation of B-modes polarization of the CMB with tensor-to-scalar ratio $r=0.2_{-0.05}^{+0.07}$, we revisit M-flation model. Gauged M-flation is a string theory motivated inflation model with Matrix valued scalar inflaton fields in the adjoint representation of a $U(N)$ Yang-Mills theory. In continuation of our previous works, we show that in the M-flation model induced from a supersymmetric 10d background probed by a stack of $N$ D3-branes, the "effective inflaton" $\phi$ has a double-well Higgs-like potential, with minima at $\phi=0,\mu$. We focus on the $\phi>\mu$, symmetry-breaking region. We thoroughly examine predictions of the model for $r$ in the $2\sigma$ region allowed for $n_S$ by the Planck experiment. As computed in [arXiv:0903.1481], for $N_e=60$ and $n_S=0.96$ we find $r\simeq 0.2$, which sits in the sweet spot of BICEP2 region for $r$. We find that with increasing $\mu$ arbitrarily, $n_S$ cannot go beyond $\simeq 0.9670$. As $n_S$ varies in the $2\sigma$ range which is allowed by Planck and could be reached by the model, $r$ varies in the range $[0.1322,0.2623]$. Future cosmological experiments, like the CMBPOL, that confines $n_S$ with $\sigma(n_S)=0.0029$ can constrain the model further. Also, in this region of potential, for $n_S=0.9603$, we find that the largest isocurvature mode, which is uncorrelated with curvature perturbations, has a power spectrum with the amplitude of order $10^{-11}$ at the end of inflation. We also discuss the range of predictions of $r$ in the hilltop region, $\phi< \mu$.Comment: v1:16 pages, 9 figures; v2: matched the published versio

Boundary Conditions as Dirac Constraints

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a new feature in the context of constrained systems. Constructing the Dirac brackets and the reduced phase space structure for different boundary conditions, we show why mode expanding and then quantizing a field theory with boundary conditions is the proper way. We also show that in a quantized field theory subjected to the mixed boundary conditions, the field components are noncommutative.Comment: 18 pp, Latex, minor changes, typos correcte

Influence of Islam on smoking among Muslims

Smoking prevalence is generally high among Muslims. An awareness of their religious beliefs and rulings might increase the effectiveness of antismoking campaign

Analysis of overfitting in the regularized Cox model

The Cox proportional hazards model is ubiquitous in the analysis of time-to-event data. However, when the data dimension p is comparable to the sample size $N$, maximum likelihood estimates for its regression parameters are known to be biased or break down entirely due to overfitting. This prompted the introduction of the so-called regularized Cox model. In this paper we use the replica method from statistical physics to investigate the relationship between the true and inferred regression parameters in regularized multivariate Cox regression with L2 regularization, in the regime where both p and N are large but with p/N ~ O(1). We thereby generalize a recent study from maximum likelihood to maximum a posteriori inference. We also establish a relationship between the optimal regularization parameter and p/N, allowing for straightforward overfitting corrections in time-to-event analysis

Near Horizon Extremal Geometry Perturbations: Dynamical Field Perturbations vs. Parametric Variations

In arXiv:1310.3727 we formulated and derived the three universal laws governing Near Horizon Extremal Geometries (NHEG). In this work we focus on the Entropy Perturbation Law (EPL) which, similarly to the first law of black hole thermodynamics, relates perturbations of the charges labeling perturbations around a given NHEG to the corresponding entropy perturbation. We show that field perturbations governed by the linearized equations of motion and symmetry conditions which we carefully specify, satisfy the EPL. We also show that these perturbations are limited to those coming from difference of two NHEG solutions (i.e. variations on the NHEG solution parameter space). Our analysis and discussions shed light on the "no-dynamics" statements of arXiv:0906.2380 and arXiv:0906.2376.Comment: 38 page