Barriers for women in athletics administration have been examined by researchers to understand such barriers through a multi-level approach (Cunningham, 2010; Taylor & Wells, 2017). Research suggests barriers exist at a macro-level with gender discrimination (Schull, Shaw, & Kihl, 2013), homologous reproduction and hegemony (Knoppers, 1989; Regan & Cunningham, 2012). Examples of occupational segregation (Whiteside & Hardin, 2010) define barriers at the meso-level, and variables, such as self-efficacy, exist at the micro-level for women in male-dominated fields (Marra, Rodgers, Shen, & Bogue, 2009). The purpose of this study was to examine the relationship between self-limiting behavior and the intent to pursue the athletics director position, as well as the relationship between motivational persistence and the intent to pursue the athletics director position. The potentially mediated relationship of self-efficacy between these relationships was also investigated. The target population was female senior-level administrators at FBS and FCS institutions. Additionally, the aim was to understand if race moderates the relationship among self-efficacy, self-limiting behavior, and motivational persistence for female senior-level athletics administrators at FBS institutions. Lastly, the research sought to understand the differences between African American and White female senior-level administrators and their perceptions of self-efficacy, self-limiting behavior, and motivational persistence and intentions to pursue the athletics director position. Ninety-seven female senior-level athletic administrators were surveyed with 11 of those participants completing an in-depth interview. Seventy-five percent of the women surveyed do not plan on becoming a director of athletics at an FBS institution; however, 44% indicated they would pursue an NCAA Division I FCS or Division I - AAA athletics director position at some point. In other words, there is more of an interest to pursue the athletics director position at a less powerful institution. The data also suggested African American women in senior-level administration positions report higher self-limiting behaviors and higher self-efficacy than White women. Moreover, race was found to be a moderator between self-efficacy and intention to pursue the FBS athletics director position. Qualitative interviews from 11 women were conducted for analysis of experiences. Four major themes emerged from the data: Assets, resources, micro-level challenges, and macro-level challenges. Limitations including small sample size as well as unreliable measures for self-limiting behavior were discussed. The current study suggests that self-efficacy is important when it comes to intentions to pursue the athletics director position. It is also important to note the racial differences between groups as it relates to self-efficacy and intentions. Keywords: athletic administration, self-efficacy, racial differences, women, career intentions / Kinesiology

<p>Computer programs keep finding their ways into new safety-critical applications, while at the same time growing more complex. This calls for new and better methods to verify the correctness of software. We focus on one approach to verifying systems, namely that of <i>model checking</i>. At first, we investigate two categories of problems related to model checking: <i>games</i> and <i>stochastic infinite-state systems</i>. In the end, we join these two lines of research, by studying <i>stochastic infinite-state games</i>.</p><p>Game theory has been used in verification for a long time. We focus on finite-state 2-player parity and limit-average (mean payoff) games. These problems have applications in model checking for the <i>μ</i>-calculus, one of the most expressive logics for programs. We give a simplified proof of memoryless determinacy. The proof applies <i>both</i> to parity and limit-average games. Moreover, we suggest a strategy improvement algorithm for limit-average games. The algorithm is discrete and strongly subexponential.</p><p>We also consider probabilistic infinite-state systems (Markov chains) induced by three types of models. <i>Lossy channel systems (LCS)</i> have been used to model processes that communicate over an unreliable medium. <i>Petri nets</i> model systems with unboundedly many parallel processes. <i>Noisy Turing machines</i> can model computers where the memory may be corrupted in a stochastic manner. We introduce the notion of <i>eagerness</i> and prove that all these systems are eager. We give a scheme to approximate the value of a reward function defined on paths. Eagerness allows us to prove that the scheme terminates. For probabilistic LCS, we also give an algorithm that approximates the limit-average reward. This quantity describes the long-run behavior of the system.</p><p>Finally, we investigate Büchi games on probabilistic LCS. Such games can be used to model a malicious cracker trying to break a network protocol. We give an algorithm to solve these games.</p>

Computer programs keep finding their ways into new safety-critical applications, while at the same time growing more complex. This calls for new and better methods to verify the correctness of software. We focus on one approach to verifying systems, namely that of model checking. At first, we investigate two categories of problems related to model checking: games and stochastic infinite-state systems. In the end, we join these two lines of research, by studying stochastic infinite-state games. Game theory has been used in verification for a long time. We focus on finite-state 2-player parity and limit-average (mean payoff) games. These problems have applications in model checking for the μ-calculus, one of the most expressive logics for programs. We give a simplified proof of memoryless determinacy. The proof applies both to parity and limit-average games. Moreover, we suggest a strategy improvement algorithm for limit-average games. The algorithm is discrete and strongly subexponential. We also consider probabilistic infinite-state systems (Markov chains) induced by three types of models. Lossy channel systems (LCS) have been used to model processes that communicate over an unreliable medium. Petri nets model systems with unboundedly many parallel processes. Noisy Turing machines can model computers where the memory may be corrupted in a stochastic manner. We introduce the notion of eagerness and prove that all these systems are eager. We give a scheme to approximate the value of a reward function defined on paths. Eagerness allows us to prove that the scheme terminates. For probabilistic LCS, we also give an algorithm that approximates the limit-average reward. This quantity describes the long-run behavior of the system. Finally, we investigate Büchi games on probabilistic LCS. Such games can be used to model a malicious cracker trying to break a network protocol. We give an algorithm to solve these games.