A Riccati type PDE for light-front higher helicity vertices

This paper is based on a curious observation about an equation related to the tracelessness constraints of higher spin gauge fields. The equation also occurs in the theory of continuous spin representations of the Poincar\'e group. Expressed in an oscillator basis for the higher spin fields, the equation becomes a non-linear partial differential operator of the Riccati type acting on the vertex functions. The consequences of the equation for the cubic vertex is investigated in the light-front formulation of higher spin theory. The classical vertex is completely fixed but there is room for off-shell quantum corrections.Comment: 27 pages. Updated to published versio

Microarray image analysis: background estimation using quantile and morphological filters

BACKGROUND: In a microarray experiment the difference in expression between genes on the same slide is up to 10(3 )fold or more. At low expression, even a small error in the estimate will have great influence on the final test and reference ratios. In addition to the true spot intensity the scanned signal consists of different kinds of noise referred to as background. In order to assess the true spot intensity background must be subtracted. The standard approach to estimate background intensities is to assume they are equal to the intensity levels between spots. In the literature, morphological opening is suggested to be one of the best methods for estimating background this way. RESULTS: This paper examines fundamental properties of rank and quantile filters, which include morphological filters at the extremes, with focus on their ability to estimate between-spot intensity levels. The bias and variance of these filter estimates are driven by the number of background pixels used and their distributions. A new rank-filter algorithm is implemented and compared to methods available in Spot by CSIRO and GenePix Pro by Axon Instruments. Spot's morphological opening has a mean bias between -47 and -248 compared to a bias between 2 and -2 for the rank filter and the variability of the morphological opening estimate is 3 times higher than for the rank filter. The mean bias of Spot's second method, morph.close.open, is between -5 and -16 and the variability is approximately the same as for morphological opening. The variability of GenePix Pro's region-based estimate is more than ten times higher than the variability of the rank-filter estimate and with slightly more bias. The large variability is because the size of the background window changes with spot size. To overcome this, a non-adaptive region-based method is implemented. Its bias and variability are comparable to that of the rank filter. CONCLUSION: The performance of more advanced rank filters is equal to the best region-based methods. However, in order to get unbiased estimates these filters have to be implemented with great care. The performance of morphological opening is in general poor with a substantial spatial-dependent bias

Consumers and Mixed-Brands: On the Polysemy of Brand Meaning

Brands have become one of the most discussed phenomena of marketing research in recent years. They are ubiquitous in the marketplace and virtually impossible for consumers to avoid. The corporate obsession with brands is likely to continue since the wealth of “how-to-do-branding” strategy handbooks suggest that brands are the magical panacea for creating superior business performance. In short, we live in a branded world, where companies seek to win and dominate markets by imposing brand meanings on consumers. This dissertation focuses on consumers’ use of brands in their everyday lives and examines how consumers develop and negotiate meanings for mixed-brands. The practice of mixing brands, also commonly referred to as co-branding, is a brand strategy gaining favor in the marketplace, where two or more brands are used as co-endorsers for a product. As brands become linked to each other through such co-endorsements, there is a possibility that consumers develop and negotiate a variety of symbolic meanings for the brand couple. This dissertation will illustrate how consumers deal with these symbolic meanings and how they interpret this particular brand strategy

Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Symmetry in Gravity

In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincare invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N=8 Supergravity should work.Comment: 26 pages, references added, published versio

Towards Unifying Structures in Higher Spin Gauge Symmetry

This article is expository in nature, outlining some of the many still incompletely understood features of higher spin field theory. We are mainly considering higher spin gauge fields in their own right as free-standing theoretical constructs and not circumstances where they occur as part of another system. Considering the problem of introducing interactions among higher spin gauge fields, there has historically been two broad avenues of approach. One approach entails gauging a non-Abelian global symmetry algebra, in the process making it local. The other approach entails deforming an already local but Abelian gauge algebra, in the process making it non-Abelian. In cases where both avenues have been explored, such as for spin 1 and 2 gauge fields, the results agree (barring conceptual and technical issues) with Yang-Mills theory and Einstein gravity. In the case of an infinite tower of higher spin gauge fields, the first approach has been thoroughly developed and explored by M. Vasiliev, whereas the second approach, after having lain dormant for a long time, has received new attention by several authors lately. In the present paper we briefly review some aspects of the history of higher spin gauge fields as a backdrop to an attempt at comparing the gauging vs. deforming approaches. A common unifying structure of strongly homotopy Lie algebras underlying both approaches will be discussed. The modern deformation approach, using BRST-BV methods, will be described as far as it is developed at the present time. The first steps of a formulation in the categorical language of operads will be outlined. A few aspects of the subject that seems not to have been thoroughly investigated are pointed out.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Liberal Arts Inspired Mathematics: A Report OR How to bring cultural and humanistic aspects of mathematics to the classroom as effective teaching and learning tools

This is the report of a project on ways of teaching university-level mathematics in a humanistic way. The main part of the project recounted here involved a journey to the United States during the fall term of 2012 to visit several liberal arts colleges in order to study and discuss mathematics teaching. Several themes that came up during my conversations at these colleges are discussed in the text: the invisibility of mathematics in everyday life, the role of calculus in American mathematics curricula, the is algebra necessary?\u27\u27 discussion, teaching mathematics as a language, the transfer problem in learning, and the relationship between humanistic mathematics and mathematics as taught in liberal arts contexts