Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions

The geometric mean is shown to be an appropriate statistic for the scale of a heavy-tailed coupled Gaussian distribution or equivalently the Student's t distribution. The coupled Gaussian is a member of a family of distributions parameterized by the nonlinear statistical coupling which is the reciprocal of the degree of freedom and is proportional to fluctuations in the inverse scale of the Gaussian. Existing estimators of the scale of the coupled Gaussian have relied on estimates of the full distribution, and they suffer from problems related to outliers in heavy-tailed distributions. In this paper, the scale of a coupled Gaussian is proven to be equal to the product of the generalized mean and the square root of the coupling. From our numerical computations of the scales of coupled Gaussians using the generalized mean of random samples, it is indicated that only samples from a Cauchy distribution (with coupling parameter one) form an unbiased estimate with diminishing variance for large samples. Nevertheless, we also prove that the scale is a function of the geometric mean, the coupling term and a harmonic number. Numerical experiments show that this estimator is unbiased with diminishing variance for large samples for a broad range of coupling values.Comment: 17 pages, 5 figure

Bubble Raft Model for a Paraboloidal Crystal

We investigate crystalline order on a two-dimensional paraboloid of revolution by assembling a single layer of millimeter-sized soap bubbles on the surface of a rotating liquid, thus extending the classic work of Bragg and Nye on planar soap bubble rafts. Topological constraints require crystalline configurations to contain a certain minimum number of topological defects such as disclinations or grain boundary scars whose structure is analyzed as a function of the aspect ratio of the paraboloid. We find the defect structure to agree with theoretical predictions and propose a mechanism for scar nucleation in the presence of large Gaussian curvature.Comment: 4 pages, 4 figure

A Humanistic Approach to Understanding Child Consumer Socialization in US Homes

We present findings from a qualitative, multisite, multi-method, longitudinal study of parents and their preschool-aged children that explores the intersections of marketing influences in the home and in the larger outside world of children. Findings indicate that preschoolers represent complicated and nuanced “consumers in training” beyond predictions based on their “perceptual stage of development.” Specifically, our data revealed interesting ways in which marketing and consumer culture can foster a number of pro-social consumer outcomes (e.g., charity, gift-giving, financial literacy). We also noted an emerging understanding by preschoolers of the social meanings of goods for identity construction and product evaluation. Finally, through a presentation of an idiographic case, we show how consumer socialization cannot be attributed to one factor such as media but is based on multiple and concurrent factors—parents, siblings, peers, and home environment—that act to moderate, mediate, and provide meaning for marketing messages

An Economic Analysis of Carbon Sequestration for Wheat and Grain Sorghum Production in Kansas

This study examined the economic potential with and without carbon credit payments of two crop and tillage systems in South Central Kansas that could reduce carbon dioxide emissions and sequester carbon in the soil. Experiment station cropping practices, yield data, and soil carbon data for continuously cropped wheat and grain sorghum produced with conventional tillage and no-tillage from1986 to 1995 were used to determine soil carbon changes and to develop enterprise budgets to determine expected net returns for a typical dryland farm in South Central Kansas. No-till had lower net returns because of lower yields and higher overall costs. Both crops produced under no-till had higher annual soil C gains than under conventional tillage. Carbon credit payments may be critical to induce farm managers to use cropping practices, such as no-till, that sequester soil carbon. The carbon credit payments needed will be highly dependent on cropping system production costs, especially herbicide costs, which substitute for tillage as a means of weed control. The C values estimated in this study that would provide an incentive to adopt no-tillage range from $0 to$95.991ton/year, depending upon the assumption about herbicide costs. In addition, if producers were compensated for other environmental benefits associated with no-till, carbon credits could be reduced.carbon credit value, carbon sequestration, grain sorghum, no-tillage, wheat, Crop Production/Industries,

Stiffening thermal membranes by cutting

Two-dimensional crystalline membranes have recently been realized experimentally in such systems as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly affect the effective mechanical properties of properly thermalized membranes, renormalizing both bending rigidity and elastic moduli so that in particular they become stiffer to bending than their bare bending rigidity would suggest. We use molecular dynamics simulations to examine how the mechanical behavior of thermalized two-dimensional clamped ribbons (cantilevers) depends on their precise topology and geometry. We find that a simple slit smooths roughness as measured by the variance of height fluctuations. This counterintuitive effect may be due to the counter-posed coupling of the lips of the slit to twist in the intact regions of the ribbon.Comment: 7 page

Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary

We investigate the zero temperature structure of a crystalline monolayer constrained to lie on a two-dimensional Riemannian manifold with variable Gaussian curvature and boundary. A full analytical treatment is presented for the case of a paraboloid of revolution. Using the geometrical theory of topological defects in a continuum elastic background we find that the presence of a variable Gaussian curvature, combined with the additional constraint of a boundary, gives rise to a rich variety of phenomena beyond that known for spherical crystals. We also provide a numerical analysis of a system of classical particles interacting via a Coulomb potential on the surface of a paraboloid.Comment: 12 pages, 8 figure

Numerical Observation of a Tubular Phase in Anisotropic Membranes

We provide the first numerical evidence for the existence of a tubular phase, predicted by Radzihovsky and Toner (RT), for anisotropic tethered membranes without self-avoidance. Incorporating anisotropy into the bending rigidity of a simple model of a tethered membrane with free boundary conditions, we show that the model indeed has two phase transitions corresponding to the flat-to-tubular and tubular-to-crumpled transitions. For the tubular phase we measure the Flory exponent $\nu_F$ and the roughness exponent $\zeta$. We find $\nu_F=0.305(14)$ and $\zeta=0.895(60)$, which are in reasonable agreement with the theoretical predictions of RT --- $\nu_F=1/4$ and $\zeta=1$.Comment: 8 pages, LaTeX, REVTEX, final published versio

Electronic properties of disclinated flexible membrane beyond the inextensional limit: Application to graphene

Gauge-theory approach to describe Dirac fermions on a disclinated flexible membrane beyond the inextensional limit is formulated. The elastic membrane is considered as an embedding of 2D surface into R^3. The disclination is incorporated through an SO(2) gauge vortex located at the origin, which results in a metric with a conical singularity. A smoothing of the conical singularity is accounted for by replacing a disclinated rigid plane membrane with a hyperboloid of near-zero curvature pierced at the tip by the SO(2) vortex. The embedding parameters are chosen to match the solution to the von Karman equations. A homogeneous part of that solution is shown to stabilize the theory. The modification of the Landau states and density of electronic states of the graphene membrane due to elasticity is discussed.Comment: 15 pages, Journal of Physics:Condensed Matter in pres