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

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field