We show that, for points along the moment curve, the bar-and-joint rigidity matroid and the hyperconnectivity matroid coincide, and that both coincide with the \(C^{d-2}_{d-1}\)-cofactor rigidity of points along any (non-degenerate) conic in the plane. For hyperconnectivity in dimension two, having the points in the moment curve is no loss of generality. We also show that, restricted to bipartite graphs, the bar-and-joint rigidity matroid is freer than the hyperconnectivity matroid.

Mathematics Subject Classifications: 52C25, 52B40

Keywords: Rigidity, hyperconnectivity, moment curve, cofactor rigidity

Currency Warfare defined as the use of weaponized monetary or military force again an adversary’s currency during armed conflicts is common fixture of armed conflicts. However, the puzzle of why currency warfare is implemented in some armed conflicts but not others remains largely unexplored. This dissertation addresses this question by providing a theory of currency warfare implementation and argues that currency warfare occur when three necessary variables come together: (1) a threat to national security; (2) a strategy of subversion; and (3) that the costs (measured in political, economic, military and ethical terms) are lower than the benefits of implementing currency warfare. I further argue that what links these three variables together in a causal chain are the perception held by those decision-makers empowered to make the decision of whether to implement currency warfare or to refrain from doing so.

I test my hypothesis by applying process-tracing to within-case analysis of positive and negative cases of currency warfare. I examine eight positive and negative cases from the American Revolution (1775-1783), Napoleon Bonaparte’s war against Austria in 1809, The American decision to counterfeit Japanese currencies but not the German Reichsmark during the Second World War (1939-1945), The Suez War (1956) and the Middle East Crisis of 1958, the Persian Gulf War (1990-1991) and the ongoing ISIS War (2014-Present). The evidence indicates support for my proposed theory of currency warfare implementation providing for the first time a systematic framework by which to explain when and why currency warfare is implemented in some armed conflicts but not others.

Background: The increasing rates of physical inactivity and sedentary behaviors in youth (ages 6-17 years) are a significant public health concern. Physical activity (PA) levels decline with age starting in preadolescence, with marked disparities among underserved (racial/ethnic minority, low-income) youth, particularly girls. Factors within the social and physical environments appear to influence youth PA, but few studies have investigated their potential impact on accelerometer-measured activity of underserved youth. Purpose: This study examines how multi-level factors (individual: age, sex, BMI; social: transportation support; environmental: neighborhood characteristics) interact to influence a continuum of accelerometer-measured youth activity behaviors. Methods: Participants wore an accelerometer for 7 days. PA levels were classified as sedentary (<50 mg), light (50-150 mg), moderate (>150-500 mg), vigorous (>500mg), and MVPA (>=150 mg). Average daily minutes spent in PA and sedentary behaviors during waking time, the prevalence of meeting MVPA guidelines, and PA volume were estimated from accelerometer data. Three-way between-groups multivariate analysis of variance examined adjusted differences between age, sex, and weight status groups across activity outcomes. Main moderation analyses explored the effects of parent-perceived neighborhood environment and child BMI percentile in the relationship between transportation support and total child PA. Results: Participants (N=68, Mage= 9.2 years) spent an average of 103 minutes/day in MVPA and 50% of participants met MVPA guidelines. Youth engaged in more overall PA (p< .001) on weekdays than weekends. Participants were also highly sedentary, spending 65% of their waking time at a sedentary level. Older participants spent significantly more time in sedentary behavior (p <.01) and had lower PA volume (p <.01) than younger participants. Girls spent significantly more time in bouted MVPA (p <.01) and had higher PA volume (p= .01) than boys. Parent-perceived neighborhood environment (p= .02), not transportation support (p= .91), influenced total PA. The relationship between transportation support and total PA was not moderated by neighborhood environment nor child BMI. Conclusions: This study adds to the limited literature available on raw accelerometer data of underserved youth in the U.S. More research is needed to understand the underlying causes of PA and sedentary behavior patterns found in this study.