Transcranial Direct Current Stimulation (tDCS) Improves Performance on Spelling and Word Detection Tasks

Deficits in written language involving spelling can have negative effects on a person’s education and occupation. Conventional spelling therapy is a time consuming and cost-prohibitive option, if even available, highlighting the need for improved methods for remediation. One possible way to address this need may be through the use of transcranial direct current stimulation (tDCS). This study sought to examine the effects of tDCS on performance during spelling, word detection, and facial recognition tasks. Active or sham tDCS was randomly assigned to typically functioning adults. The anode electrode was placed over Broca’s area (F7 in the 10/20 EEG system) and the cathode was positioned over the upper right arm. Outcome was assessed before, during, immediately after tDCS, and again 3-5 days after tDCS. Data was analyzed using analysis of variance (ANOVA) to examine if group differences existed. Significant differences were found between active and sham tDCS on both the spelling and word-search tests. There was no significant difference between active and sham tDCS on either of the facial recognition tasks

On the construction of minimum information bivariate copula families

Copulas have become very popular as modelling tools in probability applications. Given a finite number of expectation constraints for functions defined on the unit square, the minimum information copula is that copula which has minimum information (Kullback-Leibler divergence) from the uniform copula. This can be considered the most ``independent'' copula satisfying the constraints. We demonstrate the existence and uniqueness of such copulas, rigorously establish the relation with discrete approximations, and prove an unexpected relationship between constraint expectation values and the copula density formula

Approximate uncertainty modeling in risk analysis with vine copulas

Many applications of risk analysis require us to jointly model multiple uncertain quantities. Bayesian networks and copulas are two common approaches to modelling joint uncertainties with probability distributions. This paper focuses on new methodologies for copulas by developing work of Cooke, Bedford, Kurowica and others on vines as a way of constructing higher dimensional distributions which do not suffer from some of the restrictions of alternatives such as the multivariate Gaussian copula. The paper provides a fundamental approximation result, demonstrating that we can approximate any density as closely as we like using vines. It further operationalizes this result by showing how minimum information copulas can be used to provide parametric classes of copulas which have such good levels of approximation. We extend previous approaches using vines by considering non-constant conditional dependencies which are particularly relevant in financial risk modelling. We discuss how such models may be quantified, in terms of expert judgement or by fitting data, and illustrate the approach by modelling two financial datasets

Effects of State Sales Tax on GDP Per Capita: A Statewide Study for the United States

Economists have viewed the relationship between the impact of taxes on the GDP, however research dealing with the sales tax rate and the GDP have yet to be analyzed to the extent that income taxes have been investigated. In an effort to fill this void, we examine how the state sales tax rate across all fifty states within the United States impact the corresponding state’s real GDP per capita. There will be a simple regression model along with additional multiple regressions to analyze the impact of the state sales tax rate on the state’s economy. As a result of this investigation, the R-squared value increased dramatically from the initial simple regression to the last multiple regression model, as well as the statistical significance of certain explanatory variables, including the state sales tax rate

Velocity-sensitised Magnetic Resonance Imaging of foams

Although flowing foams are used in a variety of technologies, foam rheology is still incompletely understood. In this paper we demonstrate the use of a velocity-sensitised magnetic resonance imaging (MRI) sequence for the study of flowing foam. We employ a constant-time (pure phase encode) imaging technique, SPRITE, which is immune to geometrical distortions caused by the foam-induced magnetic field inhomogeneity. The sample magnetisation is prepared before the SPRITE imaging with the Cotts 13-interval motion-sensitisation sequence, which is also insensitive to the effects of the foam heterogeneity. We measure the development of a power-law velocity profile in the foam downstream of a Venturi constriction (in which the cross-section of the tube decreases by 89% in area) in a vertical, cylindrical pipe