American-style football participation is associated with high risks to a spectrum of sports-related brain injury involving acute reactions and chronic manifestations. Traditional methods of identifying injury have proven ineffective at protecting athletes and mitigating risk as they rely on the presence and recognition of inconsistent symptom expression. This is, in part, due to the lack of an objective measure of quantifying exposure. Brain trauma profiling was defined to capture a spectrum of exposure by incorporating the primary characteristics that associate with risk of neurological injury. This profile includes strain magnitude associated with impact, frequency at which impacts are experienced, time interval between impacts, over the duration of exposure. Trauma profiling methods differentiated player field position in professional American-style football where three unique trauma profiles were identified based on similarities among the characteristics of trauma. Regional strain from common head impacts showed that distribution was independent of field position regardless of variation in impact conditions. Rather, brain regions vulnerable to strains were dictated by the frequency and magnitude that govern the position profile. The extent of tissue volume involved in common head impacts was field position dependent. Skill positions tended to experience impacts involving greater tissue volumes reaching deeper white matter structures, but were infrequent. Impacts common to line positions typically involved less brain tissue of predominately superficial cortical gray matter, but were experienced at high frequency counts. The primary findings from this research show that brain trauma profiling may be used as an objective measurement tool to define exposure. The results indicate that exposure is not uniform and that brain trauma and injury risk can be described using unique combinations of these characteristics. Regional areas vulnerable to strain are dictated by the frequency and magnitude of impact and therefore in order to effectively protect against brain injury, both characteristics need to be managed. Lastly, this research demonstrates that either few impacts involving high brain volume or frequent impacts with little brain volume involvement may both result in brain dysfunction. Brain trauma profiling methods has broad application in future research. This measurement tool will be useful in identifying how injury occurs in various sports, military units, and particularly important for vulnerable populations and the developing brain. This knowledge is instrumental in establishing risk prevention strategies and public health policies for specific environments.

No description available.

An option is a contract between two parties where the holder has the option to buy or sell some underlying asset after a predefined exercise time. Options where the holder only has the right to buy or sell at the exercise time is said to be of European-style, while options that can be exercised any time before the exercise time is said to be of American-style. Asian options are options where the payoff is determined by some average value of the underlying asset, e.g., the arithmetic or the geometric average. For arithmetic Asian options, there are no closed-form pricing formulas, and one must apply numerical methods. Several methods have been proposed and tested for Asian options. For example, the Monte Carlo method isslowforEuropean-styleAsianoptionsandnotapplicableforAmerican-styleAsian options. In contrast, the finite difference method have successfully been applied to price both European- and American-style Asian options. But from a financial point of view, one is also interested in different measures of sensitivity, called the Greeks, which are hard approximate with the finite difference method. For more accurate approximations of the Greeks, researchers have turned to the finite element method with promising results for European-style Asian options. However, the finite element method has never been applied to American-style Asian options, which still lack accurate approximations of the Greeks. Here we present a study of pricing European- and American-style Asian options using the finite element method. For European-style options, we consider two different pricing PDEs. The first equation we consider is a convection-dominated problem, which we solve by applying the so-called streamline-diffusion method. The second equation comes from modelling Asian options as options on a traded account, which we solve by using the so-called cG(1)cG(1) method. For American-style options, the model based on options on a traded account is not applicable. Therefore, we must consider the first convection-dominated problem. To handle American-style options, we study two different methods, a penalty method and the projected successive over-relaxation method. For European-style Asian options, both approaches give good results, but the model based on options on a traded account show more accurate results. For American-style Asian options, the penalty method give accurate results. Meanwhile, the projected successive over-relaxation method does not converge properly for the tested parameters. Our result is a first step towards an accurate and fast method to calculate the price and the Greeks of both European- and American-style Asian options. Because good estimations of the Greeks are crucial when hedging and trading of options, we anticipate that the ideas presented in this work can lead to new ways of trading with Asian options.

The purpose of this study is to investigate the relationships between effective school characteristics and norm referenced standardized test scores in American-style international schools. In contrast to schools in traditional effective schools research, international schools typically have middle to high SES families, and display average to above average achievement. Eleven effective school characteristics were identified and correlated with standardized test scores for grades 4, 6, and 8 and high school SAT scores. Data was gathered from an online teacher questionnaire designed for this study. All eleven characteristics were present in high performing international schools while frequent analysis of student progress, high academic expectations and positive school environment were more prominent. Positive school environment, high academic expectations, strong instructional leadership and cultural diversity were chosen as important characteristics of an effective international school. Learning time is maximized was the only characteristic that was significantly correlated with achievement and only in grades 4, 6 and 8. There was no statistically significant relationship found between norm referenced test scores and the aggregate effective school characteristics score.