Normal approximation under local dependence

We establish both uniform and nonuniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper than many existing ones in the literature. The proofs couple Stein's method with the concentration inequality approach.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000045

The Higgs as a Portal to Plasmon-like Unparticle Excitations

A renormalizable coupling between the Higgs and a scalar unparticle operator O_U of non-integer dimension d_U<2 triggers, after electroweak symmetry breaking, an infrared divergent vacuum expectation value for O_U. Such IR divergence should be tamed before any phenomenological implications of the Higgs-unparticle interplay can be drawn. In this paper we present a novel mechanism to cure that IR divergence through (scale-invariant) unparticle self-interactions, which has properties qualitatively different from the mechanism considered previously. Besides finding a mass gap in the unparticle continuum we also find an unparticle pole reminiscent of a plasmon resonance. Such unparticle features could be explored experimentally through their mixing with the Higgs boson.Comment: 12 LaTeX pages, 2 figure

Super edge-magic deficiency of join-product graphs

A graph $G$ is called \textit{super edge-magic} if there exists a bijective function $f$ from $V(G) \cup E(G)$ to $\{1, 2, \ldots, |V(G) \cup E(G)|\}$ such that $f(V(G)) = \{1, 2, \ldots, |V(G)|\}$ and $f(x) + f(xy) + f(y)$ is a constant $k$ for every edge $xy$ of $G$. Furthermore, the \textit{super edge-magic deficiency} of a graph $G$ is either the minimum nonnegative integer $n$ such that $G \cup nK_1$ is super edge-magic or $+\infty$ if there exists no such integer. \emph{Join product} of two graphs is their graph union with additional edges that connect all vertices of the first graph to each vertex of the second graph. In this paper, we study the super edge-magic deficiencies of a wheel minus an edge and join products of a path, a star, and a cycle, respectively, with isolated vertices.Comment: 11 page

A Note on Unparticle Decays

The coupling of an unparticle operator O_U to Standard Model particles opens up the possibility of unparticle decays into standard model fields. We study this issue by analyzing the pole structure (and spectral function) of the unparticle propagator, corrected to account for one-loop polarization effects from virtual SM particles. We find that the propagator of a scalar unparticle (of scaling dimension 1 < d_U < 2) with a mass gap m_g develops an isolated pole, m_p^2-i m_p Gamma_p, with m_p^2 < m_g^2 below the unparticle continuum that extends above m_g (showing that the theory would be unstable without a mass gap). If that pole lies below the threshold for decay into two standard model particles the pole corresponds to a stable unparticle state (and its width Gamma_p is zero). For m_p^2 above threshold the width is non zero and related to the unparticle decay rate into Standard Model particles. This picture is valid for any value of d_U in the considered range.Comment: 11 pages, 4 figure

Variational calculations on the hydrogen molecular ion

We present high-precision non-relativistic variational calculations of bound vibrational-rotational state energies for the $H_2^+$ and $D_2^+$ molecular ions in each of the lowest electronic states of $\Sigma_g$, $\Sigma_u$, and $\Pi_u$ symmetry. The calculations are carried out including coupling between $\Sigma$ and $\Pi$ states but without using the Born-Oppenheimer or any adiabatic approximation. Convergence studies are presented which indicate that the resulting energies for low-lying levels are accurate to about $10^{-13}$. Our procedure accounts naturally for the lambda-doubling of the $\Pi_u$ state.Comment: 23 pp., RevTeX, epsf.sty, 5 figs. Enhanced data in Table II, dropped 3 figs. from previous versio

A Hierarchical Emotion Regulated Sensorimotor Model: Case Studies

Inspired by the hierarchical cognitive architecture and the perception-action model (PAM), we propose that the internal status acts as a kind of common-coding representation which affects, mediates and even regulates the sensorimotor behaviours. These regulation can be depicted in the Bayesian framework, that is why cognitive agents are able to generate behaviours with subtle differences according to their emotion or recognize the emotion by perception. A novel recurrent neural network called recurrent neural network with parametric bias units (RNNPB) runs in three modes, constructing a two-level emotion regulated learning model, was further applied to testify this theory in two different cases.Comment: Accepted at The 5th International Conference on Data-Driven Control and Learning Systems. 201

Nigeria-Ghana Relations from 1960 to 2010: Roots of Convergence and Points of Departure

Over the years, relationship between Nigeria and Ghana has faced dramatictwists and turns. In a restless manner the interactions between the twocountries has oscillated between co-operation and mutual suspicion. Eventhough the two countries have so many things in common, their interactionshave defied the logic of simple prediction. The paper attempts to give reasonsfor this trend. Concentrating on a period that covers from Nigeria&rsquo;sindependence to 2010, the paper discusses that relations between the twocountries demonstrate the characteristic dynamism of the study ofinternational relations. It also shows how far the ruling elite can shape thedisposition of one country toward another, and concludes by demonstratinghow the unstable nature of African government can affect their relations, andstresses the need for collaboration between the two countries

The survival of witchcraft prosecutions and witch belief in South West Scotland

During the era of the Scottish witch-hunts, Dumfries and Galloway was one of the last regions to initiate witch prosecutions, but it was also one of the most reluctant to completely surrender all belief in witches until a comparatively late date. In the late seventeeth and early eighteenth centuries south-west Scotland, better known for the persecution of covenanters, took the practice of witchcraft and charming very seriously indeed, and for perhaps longer than other parts of Scotland, though the area has received surprisingly little scholarly investigation. The trial evidence is not incompatible with that found elsewhere though there is less demonic content. Accusations of witchcraft in this region were mostly concerned with the troubles of everyday life, agricultural problems, family tensions and disagreements between neighbours. From 1670 to about 1740, the very decades that were giving birth to the Scottish Enlightenment, learned interest in the supernatural was actually on the increase and the topic received an unprecedented level of questioning, investigation, and scrutiny. Ironically, the ‘superstitions’ that both church and state had been attempting to eradicate for some two hundred years were now being used to defend religion against the growing threat of atheism. The zeal of the ministers does seem to have contributed to the endurance of witch beliefs in the South West, as elsewhere. Against this backdrop, the survival of witch belief and the continued prosecution of witches in southwest Scotland is examined, thus contributing to our understanding of the individualistic nature of witch persecution and the various dynamics at play within the Scottish witch-hunting experience