Exploring Winning Strategies for the Game of Cycles

This report details my adventures exploring the Game of Cycles in search of winning strategies. I started by studying combinatorial game theory with hopes to use the Sprague-Grundy Theorem and the structure of Nimbers to gain insight for the Game of Cycles. In the second semester, I pivoted to studying specific types of boards instead. In this thesis I show that variations of the mirror-reverse strategy developed by Alvarado et al. in the original Game of Cycles paper can be used to win on additional game boards with special structure, such as lollipops, steering wheel locks, and 3-spoke trees. Additionally I propose a new working conjecture that the player with the winning strategy is always determined by the parity of the number of markable edges on the board at the start of the game

Exercise and Diet Patterns as Factors in Forearm Trabecular and Cortical Bone Development in Pubertal Girls

PURPOSE: As peak bone mineral accrual velocity occurs at menarche, optimization of circum-menarcheal exercise and diet may reduce future fracture risk. We evaluated a 3-year non-dominant upper extremity bone loading index, and key nutrients, as circum-menarcheal factors in development of post-menarcheal bone properties at the distal radius – a common fragility fracture site. METHODS: A previously published circum-menarcheal bone loading index was evaluated as a predictor of indices of theoretical bone compressive and torsional strength for 48 original BLI study participants with post-menarcheal radius peripheral quantitative computed tomography (pQCT) scans. Mean intakes of lactose, zinc, total fat, magnesium, protein, calcium and potassium were tested as predictors of dual energy X-ray absorptiometry bone mineral content at comparable sites. SPSS v27 generated descriptive statistics and multiple linear regression models, with gynecological age, height and whole-body non-bone lean mass as covariates; backward stepwise regressions initially entered all predictors, plus diet factors. RESULTS: Gynecological age, height, lean mass and 3yrBLI all provided significant explanatory value in the 4% IBS model, but only lean mass and 3yrBLI were significant factors in the 33% SSI model; 3yrBLI explained substantial variance in both models (p\u3c0.002). For DXA models, total fat, lean mass and 3yrBLI were positive factors, whereas protein and calcium intakes were negative factors (p\u3c0.15). CONCLUSIONS: Over 3 circum-menarcheal years, greater forearm bone loading exercise was associated with higher post-menarcheal bone mass and strength indices. Future studies should evaluate interactions among fat, protein and calcium intakes in exercise studies of tissue-specific bone growth.https://orb.binghamton.edu/research_days_posters_2022/1074/thumbnail.jp

Improving the performance of a two-sided vibro-impact energy harvester with asymmetric restitution coefficients

We study the influence of asymmetric restitution coefficients in a model of a two-sided vibro-impact energy harvester (VI-EH), considering the dynamical behavior and the implications for energy output. In the VI-EH, a ball moves freely within a forced cylinder and collides with a compliant dielectric polymer on either end, thus converting the motion into output voltage. We develop (semi-)analytical results for 1:1 periodic solutions, with alternating impacts on either end, focusing on the case of asymmetric restitution coefficients on the top and bottom of the cylinder. New types of 1:1 periodic solutions are found, with energy output clearly different from the symmetric setting. The analysis covers non-intuitive results, including the non-monotonic dependencies of the energy output on the asymmetric restitution coefficients. We find unexpected parameter ranges with improved levels of energy output, as well as stability results indicating that this output is robust to parameter fluctuations or external perturbations. Furthermore, by identifying parameter combinations that limit performance through asymmetries, we show how asymmetric restitution coefficients can counteract these detrimental effects. The analysis is based on maps for the dynamics between impacts, leading to a series of conditions for stable 1:1 periodic solutions in terms of the system parameters. We compare stability and bifurcation structure obtained analytically and numerically. The analysis shows possible regions of bi-stability between different behaviors that may not be captured by numerical approaches.</p