Characterization of Maximally Random Jammed Sphere Packings: II. Correlation Functions and Density Fluctuations

In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of correlation functions that can be rigorously related to effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, elastic moduli, and electromagnetic characteristics. First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings. We show analytically how the contacts between spheres in the MRJ packings translate into distinct functional behaviors of these two-point correlation functions that do not arise in the other two models examined here. Then, we show how the spectral density distinguishes the MRJ packings from the other disordered systems in that the spectral density vanishes in the limit of infinite wavelengths. These packings are hyperuniform, which means that density fluctuations on large length scales are anomalously suppressed. Moreover, we study and compute exclusion probabilities and pore size distributions as well as local density fluctuations. We conjecture that for general disordered hard-sphere packings, a central limit theorem holds for the number of points within an spherical observation window. Our analysis links problems of interest in material science, chemistry, physics, and mathematics. In the third paper, we will evaluate bounds and estimates of a host of different physical properties of the MRJ sphere packings based on the structural characteristics analyzed in this paper.Comment: 25 pages, 13 Figures; corrected typos, updated reference

Characterization of Maximally Random Jammed Sphere Packings. III. Transport and Electromagnetic Properties via Correlation Functions

In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here, we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.Comment: 19 pages, 16 Figure

Analysing Errors of Open Information Extraction Systems

We report results on benchmarking Open Information Extraction (OIE) systems using RelVis, a toolkit for benchmarking Open Information Extraction systems. Our comprehensive benchmark contains three data sets from the news domain and one data set from Wikipedia with overall 4522 labeled sentences and 11243 binary or n-ary OIE relations. In our analysis on these data sets we compared the performance of four popular OIE systems, ClausIE, OpenIE 4.2, Stanford OpenIE and PredPatt. In addition, we evaluated the impact of five common error classes on a subset of 749 n-ary tuples. From our deep analysis we unreveal important research directions for a next generation of OIE systems.Comment: Accepted at Building Linguistically Generalizable NLP Systems at EMNLP 201

A limited speech recognition system 2 Final report

Limited speech recognition system for computer voice lin

THE NATURAL HISTORY AND CAPTIVE HUSBANDRY OF THE SALT CREEK TIGER BEETLE, \u3ci\u3eCicindela (=Ellipsoptera) nevadica lincolniana\u3c/i\u3e (COLEOPTERA: CARABIDAE).

Tiger beetles have long been admired for their mix of beauty, speed, and ferocious hunting abilities (Pearson 2011). The tiger beetles are some of the fastest insects on the planet with the Australian species, Cicindela hudsoni being clocked at 2.5meters per second (Merrit 1999). The tiger beetles run so fast that they are temporarily blinded when they are engaged in the high speed pursuit of their prey (Friedlander 2014). However, despite their speed, and the joy they bring to many enthusiasts, tiger beetles are unable to outrun the destruction and degradation of their habitats by human activities, and an estimated 15 percent of the 255 described species and subspecies of North American tiger beetles are now threatened with extinction (Pearson 2011). Several species of tiger beetle are very niche specialized and will only inhabit certain areas where the conditions are just right for their survival (Pearson 2006). The saline wetlands of Lancaster and Saunders counties located in eastern Nebraska are home to one such beetle. An endemic subspecies of the Nevada Tiger Beetle, Cicindela (=Ellipsoptera) nevadica, calls these saline wetlands home. This beetle is aptly named the Salt Creek Tiger beetle, Cicindela (=Ellipsoptera) nevadica lincolniana, due to its presence only along Little Salt Creek and associated tributaries (Spomer, et al. 2007). The olive-colored, 5mm long beetles are dependent on the saline wetlands, and due to the rapid destruction of their habitat by farmers and developers, are now threatened with extinction (Spomer, et al.2007). The population numbers for the C. n. lincolniana range from 150-1000 adults a year, making this species one of the most endangered insects in North America (Higley & Spomer 2001). The following paper gives a brief overview of the natural history of the C. n. lincolniana and outlines the efforts of the Omaha’s Henry Doorly Zoo and Aquarium in its attempt to captive rear this species, and save Nebraska’s native tigers and the wetlands they call home

Kantorovich-Rubinstein Distance and Barycenter for Finitely Supported Measures: Foundations and Algorithms

The purpose of this paper is to provide a systematic discussion of a generalized barycenter based on a variant of unbalanced optimal transport (UOT) that defines a distance between general non-negative, finitely supported measures by allowing for mass creation and destruction modeled by some cost parameter. They are denoted as Kantorovich–Rubinstein (KR) barycenter and distance. In particular, we detail the influence of the cost parameter to structural properties of the KR barycenter and the KR distance. For the latter we highlight a closed form solution on ultra-metric trees. The support of such KR barycenters of finitely supported measures turns out to be finite in general and its structure to be explicitly specified by the support of the input measures. Additionally, we prove the existence of sparse KR barycenters and discuss potential computational approaches. The performance of the KR barycenter is compared to the OT barycenter on a multitude of synthetic datasets. We also consider barycenters based on the recently introduced Gaussian Hellinger–Kantorovich and Wasserstein–Fisher–Rao distances