Borcherds-Kac-Moody Symmetry of N=4 Dyons

We consider compactifications of heterotic string theory to four dimensions on CHL orbifolds of the type T^6 /Z_N with 16 supersymmetries. The exact partition functions of the quarter-BPS dyons in these models are given in terms of genus-two Siegel modular forms. Only the N=1,2,3 models satisfy a certain finiteness condition, and in these cases one can identify a Borcherds-Kac-Moody superalgebra underlying the symmetry structure of the dyon spectrum. We identify the real roots, and find that the corresponding Cartan matrices exhaust a known classification. We show that the Siegel modular form satisfies the Weyl denominator identity of the algebra, which enables the determination of all root multiplicities. Furthermore, the Weyl group determines the structure of wall-crossings and the attractor flows of the theory. For N> 4, no such interpretation appears to be possible.Comment: 44 pages, 1 figur

Efficacy of Electrical Stimulation Intervention in Treating Adults with Dysphagia: A Systematic Review

Purpose: Dysphagia is a term used for a swallowing disorder resulting from problems with the oral cavity, pharynx, esophagus, or gastroesophageal junction. Dysphagia can have significant impacts on an individual’s quality of life and statistics suggest that nearly 15 million adults in the United States present with swallowing disorders. Common medical complications associated with dysphagia are malnutrition, dehydration, aspiration pneumonia, and even death. Traditional dysphagia treatment (TDT) for adults currently consists of diet modification, compensatory strategies involving postural adjustments, and swallowing exercises to strengthen musculature. The objective of this systematic review is to determine whether electrical stimulation (ES) improves swallowing function in adults with dysphagia. Methodology: Four indexed databases were searched to obtain studies pertaining to the use of ES in dysphagia treatment and its success. Application of inclusionary and exclusionary criteria narrowed the results and relevant studies were selected for this systematic review. Studies were also hand-selected and appraised for validity to ensure minimal bias. Results: Results of the selected studies revealed varying statistically significant effects of ES as a treatment for adults with dysphagia. However, many studies suggest ES is most effective in producing positive outcomes when coupled with TDT. Conclusion: The results of the systematic review suggest efficacy of ES is highest when it is used in conjunction with TDT. Studies with statistically significant results reported on only a minor improvement with ES. None of the studies reported negative outcomes related to ES. Additional research is needed to determine overall efficacy of ES as an evidence-based intervention for adults with dysphagia resulting from various etiologies.https://scholarworks.uvm.edu/csdms/1005/thumbnail.jp

Using fractals and power laws to predict the location of mineral deposits

Around the world the mineral exploration industry is interested in getting that small increase in probability measure on the earth's surface of where the next large undiscovered deposit might be found. In particular WMC Resources Ltd has operations world wide looking for just that edge in the detection of very large deposits of, for example, gold. Since the pioneering work of Mandelbrot, geologists have been familiar with the concept of fractals and self similarity over a few orders of magnitude for geological features. This includes the location and size of deposits within a particular mineral province. Fractal dimensions have been computed for such provinces and similarities of these aggregated measures between provinces have been noted. This paper explores the possibility of making use of known information to attempt the inverse process. That is, from lesser dimensional measures of a mineral province, for example, fractal dimension or more generally multi-fractal measures, is it possible to infer, even with small increase in probability, where the unknown (preferably large) deposits might be located

Collective Quartics and Dangerous Singlets in Little Higgs

Any extension of the standard model that aims to describe TeV-scale physics without fine-tuning must have a radiatively-stable Higgs potential. In little Higgs theories, radiative stability is achieved through so-called collective symmetry breaking. In this letter, we focus on the necessary conditions for a little Higgs to have a collective Higgs quartic coupling. In one-Higgs doublet models, a collective quartic requires an electroweak triplet scalar. In two-Higgs doublet models, a collective quartic requires a triplet or singlet scalar. As a corollary of this study, we show that some little Higgs theories have dangerous singlets, a pathology where collective symmetry breaking does not suppress quadratically-divergent corrections to the Higgs mass.Comment: 4 pages; v2: clarified the existing literature; v3: version to appear in JHE