Characterization of maximally random jammed sphere packings: Voronoi correlation functions

We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a central sphere contacts 12 neighbors) in the MRJ packings, a preliminary Voronoi topology analysis indicates the presence of strongly distorted icosahedra.Comment: 13 pages, 10 figure

Multilevel Bayesian framework for modeling the production, propagation and detection of ultra-high energy cosmic rays

Ultra-high energy cosmic rays (UHECRs) are atomic nuclei with energies over ten million times energies accessible to human-made particle accelerators. Evidence suggests that they originate from relatively nearby extragalactic sources, but the nature of the sources is unknown. We develop a multilevel Bayesian framework for assessing association of UHECRs and candidate source populations, and Markov chain Monte Carlo algorithms for estimating model parameters and comparing models by computing, via Chib's method, marginal likelihoods and Bayes factors. We demonstrate the framework by analyzing measurements of 69 UHECRs observed by the Pierre Auger Observatory (PAO) from 2004-2009, using a volume-complete catalog of 17 local active galactic nuclei (AGN) out to 15 megaparsecs as candidate sources. An early portion of the data ("period 1," with 14 events) was used by PAO to set an energy cut maximizing the anisotropy in period 1; the 69 measurements include this "tuned" subset, and subsequent "untuned" events with energies above the same cutoff. Also, measurement errors are approximately summarized. These factors are problematic for independent analyses of PAO data. Within the context of "standard candle" source models (i.e., with a common isotropic emission rate), and considering only the 55 untuned events, there is no significant evidence favoring association of UHECRs with local AGN vs. an isotropic background. The highest-probability associations are with the two nearest, adjacent AGN, Centaurus A and NGC 4945. If the association model is adopted, the fraction of UHECRs that may be associated is likely nonzero but is well below 50%. Our framework enables estimation of the angular scale for deflection of cosmic rays by cosmic magnetic fields; relatively modest scales of $\approx\!3^{\circ}$ to $30^{\circ}$ are favored. Models that assign a large fraction of UHECRs to a single nearby source (e.g., Centaurus A) are ruled out unless very large deflection scales are specified a priori, and even then they are disfavored. However, including the period 1 data alters the conclusions significantly, and a simulation study supports the idea that the period 1 data are anomalous, presumably due to the tuning. Accurate and optimal analysis of future data will likely require more complete disclosure of the data.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS654 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Development and Evaluation of the Nebraska Assessment of Computing Knowledge

One way to increase the quality of computing education research is to increase the quality of the measurement tools that are available to researchers, especially measures of students’ knowledge and skills. This paper represents a step toward increasing the number of available thoroughly-evaluated tests that can be used in computing education research by evaluating the psychometric properties of a multiple-choice test designed to differentiate undergraduate students in terms of their mastery of foundational computing concepts. Classical test theory and item response theory analyses are reported and indicate that the test is a reliable, psychometrically-sound instrument suitable for research with undergraduate students. Limitations and the importance of using standardized measures of learning in education research are discussed