“Be Carefully Taught”: African Americans in Adams County in the 20th Century

Every year over a million visitors flood Adams County, Pennsylvania to tour the famous, or rather infamous, site of the Battle of Gettysburg. While most visitors primarily come to Gettysburg to learn about the battle, many leave with understandings of the unending impact of the Civil War on race relations. However, for a town that sparks such a progressive mentality in some, Adams County, and specifically Gettysburg, is often criticized for being ‘frozen in time,’ unwilling to keep up with progressive race relations after the battle ended. A panel entitled “Black Experiences in Adams County in the 19th & 20th Centuries” sponsored by the Adams County Historical Society and the Gettysburg College History and Africana Studies departments, addressed the importance of remembering this African American story. The panel included Gettysburg College Professor Scott Hancock, author Peter Levy, and Adams County residents Darryl Jones and Jane Nutter. [excerpt

Extreme Dependence Models

Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these events is of fundamental importance. For this purpose, probabilistic models and statistical methods are in high demand. There are several approaches to modelling multivariate extremes as described in Falk et al. (2011), linked to some extent. We describe an approach for deriving multivariate extreme value models and we illustrate the main features of some flexible extremal dependence models. We compare them by showing their utility with a real data application, in particular analyzing the extremal dependence among several pollutants recorded in the city of Leeds, UK.Comment: To appear in Extreme Value Modelling and Risk Analysis: Methods and Applications. Eds. D. Dey and J. Yan. Chapman & Hall/CRC Pres

An interface element based on the partition of unity

An alternative interface finite element is developed. By using the partition of unity property of finite element shape functions, discontinuous shape functions are added to the standard finite element basis. The interface behaviour is described by extra degrees of freedom at existing nodes, avoiding the need for ‘doubled nodes’. The element is kinematically equivalent to a conventional interface element but is more flexible because it allows the inclusion of interface surfaces within solid elements. In describing interface phenomena, the methodology proposed here makes possible the use of coarser meshes and it is completely insensitive to mesh topology. The new formulation is analysed throughly and comparisons are drawn with the conventional formulation

Discontinuous modelling of crack propagation in a gradient-enhanced continuum

A numerical model for the description of the combined continuous/discontinuous failure in a regularised strain-softening continuum is proposed. The continuum is regularised through the introduction of gradient terms into the constitutive equations. At the transition to discrete failure, the problem fields are enhanced through a discontinuous interpolation based on the partition of unity concept. The discretisation procedure is described in detail and numerical examples illustrate the performance of the combined continuous/discontinuous approach

A novel technique for modelling interfaces in reinforced brittle materials

A novel numerical technique for the modelling of interfaces is introduced for the analysis of reinforced brittle materials. The method exploits the partition of unity property of finite element shape functions. By considering finite element shape functions as partitions of unity, extra degrees of freedom are added to the nodes at the interface between the matrix and reinforcement. A gradient-enhanced damage model is used to simulate the continuum response. Numerical results for a three-point bending test and a pull-out test are presented. The numerical procedure proposed here is suitable for a great variety of applications ranging from discrete cracking and steel-concrete interaction in concrete to delamination processes in composite materials

Models for extremal dependence derived from skew-symmetric families

Skew-symmetric families of distributions such as the skew-normal and skew-$t$ represent supersets of the normal and $t$ distributions, and they exhibit richer classes of extremal behaviour. By defining a non-stationary skew-normal process, which allows the easy handling of positive definite, non-stationary covariance functions, we derive a new family of max-stable processes - the extremal-skew-$t$ process. This process is a superset of non-stationary processes that include the stationary extremal-$t$ processes. We provide the spectral representation and the resulting angular densities of the extremal-skew-$t$ process, and illustrate its practical implementation (Includes Supporting Information).Comment: To appear in Scandinavian Journal of Statistic

Likelihood-based inference for max-stable processes

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so likelihood-based methods remain far from providing a complete and flexible framework for inference. In this article we develop inferentially practical, likelihood-based methods for fitting max-stable processes derived from a composite-likelihood approach. The procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost. The utility of this methodology is examined via simulation, and illustrated by the analysis of U.S. precipitation extremes