Adaptive Gibbs samplers

We consider various versions of adaptive Gibbs and Metropolis- within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run, by learning as they go in an attempt to optimise the algorithm. We present a cautionary example of how even a simple-seeming adaptive Gibbs sampler may fail to converge. We then present various positive results guaranteeing convergence of adaptive Gibbs samplers under certain conditions

Comments Concerning Proposed United States-Andean Free Trade Agreement

Vogt presents two cases of US multinational corporations that benefit from violence against unionists in Colombia. He argues that a trade agreement with Colombia would normalize the violence instead of fight against it

Conformal invariants measuring the best constants for Gagliardo-Nirenberg-Sobolev inequalities

We introduce a family of conformal invariants associated to a smooth metric measure space which generalize the relationship between the Yamabe constant and the best constant for the Sobolev inequality to the best constants for Gagliardo-Nirenberg-Sobolev inequalities $\|w\r|_q \leq C\|\nabla w\|_2^\theta \|w\|_p^{1-\theta}$. These invariants are constructed via a minimization procedure for the weighted scalar curvature functional in the conformal class of a smooth metric measure space. We then describe critical points which are also critical points for variations in the metric or the measure. When the measure is assumed to take a special form --- for example, as the volume element of an Einstein metric --- we use this description to show that minimizers of our invariants are only critical for certain values of $p$ and $q$. In particular, on Euclidean space our result states that either $p=2(q-1)$ or $q=2(p-1)$, giving a new characterization of the GNS inequalities whose sharp constants were computed by Del Pino and Dolbeault.Comment: 20 page

Constructing an Explicit AdS/CFT Correspondence with Cartan Geometry

An explicit AdS/CFT correspondence is shown for the Lie group $SO(4,2)$. The Lie symmetry structures allow for the construction of two physical theories through the tools of Cartan geometry. One is a gravitational theory that has anti-de Sitter symmetry. The other is also a gravitational theory but is conformally symmetric and lives on 8-dimensional biconformal space. These "extra" four dimensions have the degrees of freedom used to construct a Yang-Mills theory. The two theories, based on AdS or conformal symmetry, have a natural correspondence in the context of their Lie algebras alone where neither SUSY, nor holography, is necessary.Comment: 13 pages, 1 Tabl

An Evaluation of Herbicides for Control of Wild Oats in Barley: Efficacy, Phytotoxicity, and Barley Variety Susceptibility Studies

The control of wild oats (Avena Jatua L.) in Alaskan spring-planted barley was investigated in a series of experiments conducted from 1981-1984. Rates and times of applications of triallate (a preemergence, soil-incorporated herbicide), diclofop, barban, and difenzoquat (postemergence herbicides) were investigated in relation to control of wild oats and barley yield in 1981-1982. Because of very high wild oats populations. none of the herbicides controlled wild oats to the point of· allowing a barley harvest. Generally, wild oats were best controlled when herbicides were applied at an early growth stage and at the highest application rates. Control of wild oats with triallate was the same whether incorporated using parallel or perpendicular passes of a spike-tooth harrow. In 1983-84 both single herbicide treatments and combinations of herbicides were studied. Barban, diclofop, and difenzoquat were applied alone or with triallate applied in the fall or spring in emulsifiable concentrate or granular formulation. Wild oats population levels were lower in these 2 years, and applications of even single herbicides provided good wild oats control. Of the individual herbicides, diclofop provided the best control of wild oats. In general, when triallate was applied in conjunction with diclofop, barban, or difenzoquat, control of wild oats was better and higher barley yields were obtained than when a single wild oats herbicide was applied. When triallate was applied in the fall, the granular formulation provided better control of wild oats than the emulsifiable formulation. In a study of the response of eight barley varieties ('Eero', 'Paavo', 'Galt', 'Otra', 'Otal', 'Datal', 'Udal', 'Weal') to high rates and late times of application of the four herbicides, none of the varieties were differentially susceptible. Diclofop decreased heights of all varieties and decreased test weights