BRS Operators and Covariant Derivatives in Loop Space for P-Branes Coupled to Yang-Mills

Canonical forms are given for the nilpotent BRS operator \d and the covariant `loop space' derivative {\cal D}_{\m} for the p-brane fields for all odd p. The defining characteristic of {\cal D}_{\m} is that it is a functional derivative operator which generalizes the ordinary functional derivative and also commutes with \d. Methods of construction for the canonical forms are discussed.Comment: 21 pages, CTP-TAMU-50/9

Octonion X,Y-Product G2G_{2} Variants

The automorphism group $G_{2}$ of the octonions changes when octonion X,Y-product variants are used. I present here a general solution for how to go from $G_{2}$ to its X,Y-product variant.Comment: 5 pages, latex, no figure

An Extended Laplace Approximation Method for Bayesian Inference of Self-Exciting Spatial-Temporal Models of Count Data

Self-Exciting models are statistical models of count data where the probability of an event occurring is influenced by the history of the process. In particular, self-exciting spatio-temporal models allow for spatial dependence as well as temporal self-excitation. For large spatial or temporal regions, however, the model leads to an intractable likelihood. An increasingly common method for dealing with large spatio-temporal models is by using Laplace approximations (LA). This method is convenient as it can easily be applied and is quickly implemented. However, as we will demonstrate in this manuscript, when applied to self-exciting Poisson spatial-temporal models, Laplace Approximations result in a significant bias in estimating some parameters. Due to this bias, we propose using up to sixth-order corrections to the LA for fitting these models. We will demonstrate how to do this in a Bayesian setting for Self-Exciting Spatio-Temporal models. We will further show there is a limited parameter space where the extended LA method still has bias. In these uncommon instances we will demonstrate how a more computationally intensive fully Bayesian approach using the Stan software program is possible in those rare instances. The performance of the extended LA method is illustrated with both simulation and real-world data

Modeling and Estimation for Self-Exciting Spatio-Temporal Models of Terrorist Activity

Spatio-temporal hierarchical modeling is an extremely attractive way to model the spread of crime or terrorism data over a given region, especially when the observations are counts and must be modeled discretely. The spatio-temporal diffusion is placed, as a matter of convenience, in the process model allowing for straightforward estimation of the diffusion parameters through Bayesian techniques. However, this method of modeling does not allow for the existence of self-excitation, or a temporal data model dependency, that has been shown to exist in criminal and terrorism data. In this manuscript we will use existing theories on how violence spreads to create models that allow for both spatio-temporal diffusion in the process model as well as temporal diffusion, or self-excitation, in the data model. We will further demonstrate how Laplace approximations similar to their use in Integrated Nested Laplace Approximation can be used to quickly and accurately conduct inference of self-exciting spatio-temporal models allowing practitioners a new way of fitting and comparing multiple process models. We will illustrate this approach by fitting a self-exciting spatio-temporal model to terrorism data in Iraq and demonstrate how choice of process model leads to differing conclusions on the existence of self-excitation in the data and differing conclusions on how violence is spreading spatio-temporally

Spouse Abuse

The term spouse abuse is commonly used to refer to Aggressive, violent and/or controlling behaviours that take place between two people involved in an intimate Relationship. Spouse abuse is a high frequency crime resulting in victims from all social classes, ethnicities, genders and educational backgrounds. Preventative methods at societal and community levels are required in addition to more traditional intervention approaches in order to adequately address this problem. This entry will provide an evidence based description of spouse abuse, considering its definition, terminology, prevalence, victims and Perpetrators and issues related to the treatment and prevention of this problem

Bearing Witness

Dixon, Jennifer. Bearing Witness. Library Journal 11 Sep. 2019: n. pag. Online