Higgsed Gauge-flation

We study a variant of Gauge-flation where the gauge symmetry is spontaneously broken by a Higgs sector. We work in the Stueckelberg limit and demonstrate that the dynamics remain (catastrophically) unstable for cases where the gauge field masses satisfy $\gamma < 2$, where $\gamma = g^2\psi^2/H^2$, $g$ is the gauge coupling, $\psi$ is the gauge field vacuum expectation value, and $H$ is the Hubble rate. We compute the spectrum of density fluctuations and gravitational waves, and show that the model can produce observationally viable spectra. The background gauge field texture violates parity, resulting in a chiral gravitational wave spectrum. This arises due to an exponential enhancement of one polarization of the spin-2 fluctuation of the gauge field. Higgsed Gauge-flation can produce observable gravitational waves at inflationary energy scales well below the GUT scale.Comment: 52 pages, 14 figure

On the Invalidity of Fourier Series Expansions of Fractional Order

The purpose of this short paper is to show the invalidity of a Fourier series expansion of fractional order as derived by G. Jumarie in a series of papers. In his work the exponential functions $e^{in\omega x}$ are replaced by the Mittag-Leffler functions $E_\alpha \left (i (n\omega x)^\alpha\right) ,$ over the interval $[0, M_\alpha/ \omega]$ where $0< \omega<\infty$ and $M_\alpha$ is the period of the function $E_\alpha \left( ix^\alpha\right),$ i.e., $E_\alpha \left( ix^\alpha\right)=E_\alpha \left( i(x+M_\alpha)^\alpha\right).

Exploration vs. Exploitation in the Information Filtering Problem

We consider information filtering, in which we face a stream of items too voluminous to process by hand (e.g., scientific articles, blog posts, emails), and must rely on a computer system to automatically filter out irrelevant items. Such systems face the exploration vs. exploitation tradeoff, in which it may be beneficial to present an item despite a low probability of relevance, just to learn about future items with similar content. We present a Bayesian sequential decision-making model of this problem, show how it may be solved to optimality using a decomposition to a collection of two-armed bandit problems, and show structural results for the optimal policy. We show that the resulting method is especially useful when facing the cold start problem, i.e., when filtering items for new users without a long history of past interactions. We then present an application of this information filtering method to a historical dataset from the arXiv.org repository of scientific articles.Comment: 36 pages, 5 figure

A new species of the basal araneomorph spider genus Ectatosticta (Araneae, Hypochilidae) from China

The hypochilid spider Ectatosticta davidi (Simon) is redescribed on the basis of adults from Mt. Taibaishan in Shaanxi Province, China; the specimens from Qinghai Province previously identified as E. davidi by most modern authors belong to a new species described as E. deltshevi. Keywords: Araneae, Araneomorphae, Hypochilidae, Ectatosticta, Chin