A Dynamic, Scalable Algorithm to Optimize the Allocation of Athletics Scholarships

When a high school student athlete makes the decision to swim collegiately, one of the leading factors in choosing a university is the amount of the scholarship award. These awards are determined by the equivalency category in the National Collegiate Athletic Association (NCAA) Divisions I and II and the National Association of Intercollegiate Athletics (NAIA). Rules govern financial aid and the number of scholarships allowed by a member institution. The exact financial distribution among athletes, however, is mostly the coaches’ responsibility and there is scarcity in the literature on how these scholarships are distributed among athletes in a college/ university, which is why it’s important for Athletics Departments within these colleges and universities to have a model to help distribute the scholarship amounts in an optimal manner that promotes transparency and ethical leadership. This paper provides a model to aid coaches in the distribution of financial award/ scholarships in a women’s swimming in a major urban university; however, the model can be applied and adjusted for financial award distribution for any collegiate sport following any institute specific policies and preferences

What’s in a Coefficient? The “Not so Simple” Interpretation of R2, for Relatively Small Sample Sizes

There are several misconceptions when interpreting the values of the coefficient of determination, R2, in simple linear regression. R2 is heavily dependent on sample size n and the type of data being analyzed but becomes insignificant when working with very large sample sizes. In this paper, we comment on these observations and develop a relationship between R2, n, and the level of significance α, for relatively small sample sizes. In addition, this paper provides a simplified version of the relationship between R2 and n, by comparing the standard deviation of the dependent variable, Sy, to the standard error of the estimate, Se. This relationship will serve as a safe lower bound to the values of R2. Computational experiments are performed to confirm the results from both models. Even though the focus of the paper is on simple linear regression, we present the groundwork for expanding our two models to the multiple regression case

Elastic modulus varies along the bovine femur

Bone is a heterogeneous material and its mechanical properties vary within the body. Variations in the mechanical response of different bone samples taken from the body cannot be fully explained by only looking at local compositional information at the tissue level. Due to different states of the stress within bones, one might expect that mechanical properties change over the length of a bone; this has not been a matter of systematic research in previous studies. In this study, the distribution of the tissue elastic modulus along the bovine femur is investigated using three-point bending tests. Two bovine femora were split to seven and eight blocks from proximal to distal metaphysis, respectively and twenty beam shaped bone samples were extracted and tested from each block. Based on our findings, the longitudinal elastic modulus follows a gradient pattern along the bovine femur as it increases along the bone from the proximal metaphysis to mid-diaphysis and then decreases toward the distal metaphysis again. Considering long bones to be subjected to bending loads, this mechanism alters the bone structure to support load in the regions where it is needed; similar as outlined by Wolff's law. In another part of this study, microfocus X-ray computed tomography (μCT) was found unable to predict the same trend of changes for the elastic modulus via image-based or density-based elastic moduli calculations. This is insofar important as conventional finite element models of bone are often directly shaped from μCT data. Based on our findings, it seems that current computed tomography based finite element models generated in this manner may not adequately capture the local variation of material behavior of bone tissue, but this may be improved by considering the changes of the elastic modulus along the femur.</p