Matrix Valued Spherical Functions Associated to the Complex Projective Plane

The main purpose of this paper is to compute all irreducible spherical functions on G=\SU(3) of arbitrary type $\delta\in \hat K$, where $K={\mathrm{S}}(\mathrm{U}(2)\times\mathrm{U}(1))\simeq\mathrm{U}(2)$. This is accomplished by associating to a spherical function $\Phi$ on $G$ a matrix valued function $H$ on the complex projective plane $P_2(\mathbb{C})=G/K$. It is well known that there is a fruitful connection between the hypergeometric function of Euler and Gauss and the spherical functions of trivial type associated to a rank one symmetric pair $(G,K)$. But the relation of spherical functions of types of dimension bigger than one with classical analysis, has not been worked out even in the case of an example of a rank one pair. The entries of $H$ are solutions of two systems of ordinary differential equations. There is no ready made approach to such a pair of systems, or even to a single system of this kind. In our case the situation is very favorable and the solution to this pair of systems can be exhibited explicitely in terms of a special class of generalized hypergeometric functions ${}_{p+1}F_p$.Comment: 70 pages, 1 figur

One-dimensional quantum walks with one defect

The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the case of the non negative integers. Using this method we classify, according to such localization properties, all the quantum walks with one defect at the origin, providing explicit expressions for the asymptotic return probabilities at the origin

Tetrachloroethylene (PCE, Perc) Levels in Residential Dry Cleaner Buildings in Diverse Communities in New York City

Fugitive tetrachloroethylene (PCE, perc) emissions from dry cleaners operating in apartment buildings can contaminate residential indoor air. In 1997, New York State and New York City adopted regulations to reduce and contain perc emissions from dry cleaners located in residential and other buildings. As part of a New York State Department of Health (NYSDOH) study, indoor air perc levels were determined in 65 apartments located in 24 buildings in New York City where dry cleaners used perc on site. Sampling occurred during 2001–2003, and sampled buildings were dispersed across minority and nonminority as well as low-income and higher income neighborhoods. For the entire study area, the mean apartment perc level was 34 μg/m(3), 10-fold lower than mean apartment levels of 340–360 μg/m(3) documented before 1997. The maximum detected perc level was 5,000 μg/m(3), 5-fold lower than the maximum of 25,000 μg/m(3) documented before 1997. Despite these accomplishments, perc levels in 17 sampled apartments still exceeded the NYSDOH residential air guideline of 100 μg/m(3), and perc levels in 4 sampled apartments exceeded 1,000 μg/m(3). Moreover, mean indoor air perc levels in minority neighborhoods (75 μg/m(3)) were four times higher than in nonminority households (19 μg/m(3)) and were > 10 times higher in low-income neighborhoods (256 μg/m(3)) than in higher income neighborhoods (23 μg/m(3)). Logistic regression suitable for clustered data (apartments within buildings) indicated that perc levels on floors 1–4 were significantly more likely to exceed 100 μg/m(3) in buildings located in minority neighborhoods (odds ratio = 6.7; 95% confidence interval, 1.5–30.5) than in nonminority neighborhoods. Factors that may be contributing to the elevated perc levels detected, especially in minority and low-income neighborhoods, are being explored

Repeatable texture sampling with interchangeable patches

Rendering textures in real-time environments is a key task in computer graphics. This paper presents a new parallel patch-based method which allows repeatable sampling without cache, and does not create visual repetitions. Interchangeable patches of arbitrary shape are prepared in a preprocessing step, such that patches may lie over the boundary of other patches in a repeating tile. This compresses the example texture into an infinite texture map with small memory requirements, suitable for GPU and ray-tracing applications. The quality of textures rendered with this method can be tuned in the offline preprocessing step, and they can then be rendered in times comparable to Wang tiles. Experimental results demonstrate combined benefits in speed, memory requirements, and quality of randomisation when compared to previous methods

Root polytopes and abelian ideals

We study the root polytope $\mathcal P_\Phi$ of a finite irreducible crystallographic root system $\Phi$ using its relation with the abelian ideals of a Borel subalgebra of a simple Lie algebra with root system $\Phi$. We determine the hyperplane arrangement corresponding to the faces of codimension 2 of $\mathcal P_\Phi$ and analyze its relation with the facets of $\mathcal P_\Phi$. For $\Phi$ of type $A_n$ or $C_n$, we show that the orbits of some special subsets of abelian ideals under the action of the Weyl group parametrize a triangulation of $\mathcal P_\Phi$. We show that this triangulation restricts to a triangulation of the positive root polytope $\mathcal P_\Phi^+$.Comment: 41 pages, revised version, accepted for publication in Journal of Algebraic Combinatoric

Multi-scale Inference of Interaction Rules in Animal Groups Using Bayesian Model Selection

Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis). We show that these exhibit a stereotypical ‘phase transition’, whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have ‘memory’ of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture fine scale rules of interaction, which are primarily mediated by physical contact. Conversely, the Markovian self-propelled particle model captures the fine scale rules of interaction but fails to reproduce global dynamics. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects

Substance use and dietary practices among students attending alternative high schools: results from a pilot study

<p>Abstract</p> <p>Background</p> <p>Substance use and poor dietary practices are prevalent among adolescents. The purpose of this study was to examine frequency of substance use and associations between cigarette, alcohol and marijuana use and selected dietary practices, such as sugar-sweetened beverages, high-fat foods, fruits and vegetables, and frequency of fast food restaurant use among alternative high school students. Associations between multi-substance use and the same dietary practices were also examined.</p> <p>Methods</p> <p>A convenience sample of adolescents (n = 145; 61% minority, 52% male) attending six alternative high schools in the St Paul/Minneapolis metropolitan area completed baseline surveys. Students were participants in the Team COOL (Controlling Overweight and Obesity for Life) pilot study, a group randomized obesity prevention pilot trial. Mixed model multivariate analyses procedures were used to assess associations of interest.</p> <p>Results</p> <p>Daily cigarette smoking was reported by 36% of students. Cigarette smoking was positively associated with consumption of regular soda (p = 0.019), high-fat foods (p = 0.037), and fast food restaurant use (p = 0.002). Alcohol (p = 0.005) and marijuana use (p = 0.035) were positively associated with high-fat food intake. With increasing numbers of substances, a positive trend was observed in high-fat food intake (p = 0.0003). There were no significant associations between substance use and fruit and vegetable intake.</p> <p>Conclusions</p> <p>Alternative high school students who use individual substances as well as multiple substances may be at high risk of unhealthful dietary practices. Comprehensive health interventions in alternative high schools have the potential of reducing health-compromising behaviors that are prevalent among this group of students. This study adds to the limited research examining substance use and diet among at-risk youth.</p> <p>Trial registration number</p> <p>ClinicalTrials.gov: <a href="http://www.clinicaltrials.gov/ct2/show/NCT01315743">NCT01315743</a></p

Quantifying the interplay between environmental and social effects on aggregated-fish dynamics

Demonstrating and quantifying the respective roles of social interactions and external stimuli governing fish dynamics is key to understanding fish spatial distribution. If seminal studies have contributed to our understanding of fish spatial organization in schools, little experimental information is available on fish in their natural environment, where aggregations often occur in the presence of spatial heterogeneities. Here, we applied novel modeling approaches coupled to accurate acoustic tracking for studying the dynamics of a group of gregarious fish in a heterogeneous environment. To this purpose, we acoustically tracked with submeter resolution the positions of twelve small pelagic fish (Selar crumenophthalmus) in the presence of an anchored floating object, constituting a point of attraction for several fish species. We constructed a field-based model for aggregated-fish dynamics, deriving effective interactions for both social and external stimuli from experiments. We tuned the model parameters that best fit the experimental data and quantified the importance of social interactions in the aggregation, providing an explanation for the spatial structure of fish aggregations found around floating objects. Our results can be generalized to other gregarious species and contexts as long as it is possible to observe the fine-scale movements of a subset of individuals.Comment: 10 pages, 5 figures and 4 supplementary figure