Pairings of automorphic distributions

We present a pairing of automorphic distributions that applies in situations where a Lie group acts with an open orbit on a product of generalized flag varieties. The pairing gives meaning to an integral of products of automorphic distributions on these varieties. This generalizes classical integral representations or "Rankin-Selberg integrals" of L-functions, and gives new constructions and analytic continuations of automorphic L-functions. Keywords: Automorphic forms, invariant pairings, automorphic distributions, L-functions, analytic continuation, rapid decay.Comment: 19 pages, to appear in Mathematische Annale

Subluminal OPERA Neutrinos

The OPERA collaboration has announced to have observed superluminal neutrinos with a mean energy 17.5 GeV, but afterward the superluminal interpretation of the OPERA results has been refuted theoretically by Cherenkov-like radiation and pion decay. In a recent work, we have proposed a kinematical resolution to this problem. A key idea in our resolution is that the OPERA neutrinos are not superluminal but subluminal since they travel faster than the observed speed of light in vacuum on the earth while they do slower than the true speed of light in vacuum determining the causal structure of events. In this article, we dwell upon our ideas and present some concrete models, which realize our ideas, based on spin 0, 1 and 2 bosonic fields. We also discuss that the principle of invariant speed of light in special relativity can be replaced with the principle of a universal limiting speed.Comment: 17 page

Advertisements’ Perpetuation of Rape Culture: A look at how images containing objectification and victimization impact consumers

The research I have conducted explores connections between images shown in advertisements and the perpetuation of rape culture and gendered stereotypes in society. It was guided by the Cultivation Theory which looks at how media, such as advertisements, can shape our reality. After an extensive literature review, data was gathered via an experimental design utilizing surveys. Within these surveys, respondents were randomly shown an advertisement I created containing the variables to be tested (i.e. images with objectification and victimization). After viewing the ad, they answered questions regarding their attitude toward the brand/product depicted, purchase intentions, a rape myth acceptance scale (Burt, 1980), and a sex role stereotyping scale (Burt, 1980). Both of these scales are widely accepted and were previously tested. Data was then analyzed to uncover any statistically significant interactions between the variables in order to gain a better understanding of how the images viewed in advertisements impact consumers’ beliefs and perceptions. Analysis revealed that while there is a model effect, meaning advertisers should use models in their ads, there isn’t any statistically significant positive difference for using images containing objectification or victimization. Using images with these variables can actually have a negative impact on the viewer’s attitude toward the ad and the brand. Additionally, analysis showed that viewing images with these variables increased the viewer’s acceptance of rape myths

Reducing the standard deviation in multiple-assay experiments where the variation matters but the absolute value does not

You measure the value of a quantity x for a number of systems (cells, molecules, people, chunks of metal, DNA vectors, etc.). You repeat the whole set of measures in different occasions or assays, which you try to design as equal to one another as possible. Despite the effort, you find that the results are too different from one assay to another. As a consequence, some systems' averages present standard deviations that are too large to render the results statistically significant. In this work, we present a novel correction method of very low mathematical and numerical complexity that can reduce the standard deviation in your results and increase their statistical significance as long as two conditions are met: inter-system variations of x matter to you but its absolute value does not, and the different assays display a similar tendency in the values of x; in other words, the results corresponding to different assays present high linear correlation. We demonstrate the improvement that this method brings about on a real cell biology experiment, but the method can be applied to any problem that conforms to the described structure and requirements, in any quantitative scientific field that has to deal with data subject to uncertainty.Comment: Supplementary material at http://bit.ly/14I718

A historical perspective on Modified Newtonian Dynamics

I review the history and development of Modified Newtonian Dynamics (MOND) beginning with the phenomenological basis as it existed in the early 1980s. I consider Milgrom's papers of 1983 introducing the idea and its consequences for galaxies and galaxy groups, as well as the initial reactions, both negative and positive. The early criticisms were primarily on matters of principle, such as the absence of conservation laws and perceived cosmological problems; an important step in addressing these issues was the development of the Lagrangian-based non-relativistic theory of Bekenstein and Milgrom. This theory led to the development of a tentative relativistic theory that formed the basis for later multi-field theories of gravity. On an empirical level the predictive success of the idea with respect to the phenomenology of galaxies presents considerable challenges for cold dark matter. For MOND the essential challenge remains the absence of a generally accepted theoretical underpinning of the idea and, thus, cosmological predictions. I briefly review recent progress in this direction. Finally I discuss the role and sociology of unconventional ideas in astronomy in the presence of a strongly entrenched standard paradigm.Comment: 25 pages, 9 figures, previous uploaded file was out of date, Canadian Journal of Physic

GRBs as standard candles: There is no "circularity problem" (and there never was)

The 2002 discovery of the "Amati Relation" of GRB spectra created the possibility that this and other correlations of GRB phenomenology might be used to make GRBs into standard candles. One recurring apparent difficulty with this program has been that some of the primary observational quantities to be fit as "data" - the isotropic-equivalent prompt energy $E_{iso}$ and the collimation-corrected "total" prompt energy energy $E_{\gamma}$ - depend for their construction on the very cosmological models that they are supposed to help constrain. This is the so-called "circularity problem" of standard candle GRBs. This paper is intended to point out that the circularity problem is not in fact a problem at all, except to the extent that it amounts to a self-inflicted wound. It arises essentially because of an unfortunate choice of data variables, such as $E_{iso}$, which are unnecessarily model-dependent. If, instead, the empirical correlations of GRB phenomenology which are formulated in source-variables are {\it mapped to the primitive observational variables} (such as fluence) and compared to the observations in that space, then all circularity disappears. I also indicate here a set of procedures for encoding high-dimensional empirical correlations in a "Gaussian Tube" smeared model that includes both the correlation and its intrinsic scatter, and how that source-variable model may easily be mapped to the space of primitive observables and fashioned into a likelihood. I discuss the projections of such Gaussian tubes into sub-spaces, which may be used to incorporate data from GRB events that may lack some element of the data (for example, GRBs without ascertained jet-break times). In this way, a large set of inhomogeneously observed GRBs may be assimilated into a single analysis, so long as each possesses at least two correlated data attributes.Comment: 10 pages, to appear in New Astronom