A Legendrian knot atlas for knots of arc index 10

We expand the atlas of Legendrian knots in standard contact three-space to knots of arc index 10.Comment: 152 pages, including 145 pages of table

An Analysis of the Impact of Team Payroll on Regular Season and Postseason Success in Major League Baseball

Major League Baseball, like other American professional sports, has become a multibillion dollar industry. The institution of free agency has led to the escalation of payrolls and altered the make-up of rosters by dramatically reducing owners’ monopsony power. The ability of large market clubs such as the New York Yankees to compete continually for the game’s greatest prize illustrates the power of the dollar. This paper examines four distinct periods from 1977 to 2008 in order to assess the influence of pecuniary advantages on regular season and postseason outcomes. Payroll exerts great influence in the regular season, but not in the playoffs. A time series graph of slope coefficients from regression analyses indicates that an additional ten million 2008 dollars produces between one and three wins depending on the season. In addition, we test several other potential indicators of postseason success and find that October baseball is a truly random event

A Model of Rapid Radicalization Behavior Using Agent-Based Modeling and Quorum Sensing

Understanding the dynamics of radicalization, especially rapid radicalization, has become increasingly important to US policy in the past several years. Traditionally, radicalization is considered a slow process, but recent social and political events demonstrate that the process can occur quickly. Examining this rapid process, in real time, is impossible. However, recreating an event using modeling and simulation (M&S) allows researchers to study some of the complex dynamics associated with rapid radicalization. We propose to adapt the biological mechanism of quorum sensing as a tool to explore, or possibly explain, rapid radicalization. Due to the complex nature of quorum sensing, M&S allows us to examine events that we could not otherwise examine in real time. For this study, we employ Agent Based Modeling (ABM), an M&S paradigm suited to modeling group behavior. The result of this study was the successful creation of rapid radicalization using quorum sensing. The Battle of Mogadishu was the inspiration for this model and provided the testing conditions used to explore quorum sensing and the ideas behind rapid radicalization. The final product has wider applicability however, using quorum sensing as a possible tool for examining other catalytic rapid radicalization events

Energy conditions outside a dielectric ball

We show analytically that the vacuum electromagnetic stress-energy tensor outside a ball with constant dielectric constant and permeability always obeys the weak, null, dominant, and strong energy conditions. There are still no known examples in quantum field theory in which the averaged null energy condition in flat spacetime is violated.Comment: 12 pages, RevTex

Modern Warfare: An M and S Examination of the Dynamic Impact of Warlords and Insurgents on State Stability

9/11 changed the world as we knew it. Part of this change was to redirect the military of the United States away from focusing primarily on conventional conflict to a primary focus on unconventional or irregular conflict. This change required a tremendous learning effort by the military and their supporting research and development community. This learning effort included relearning of old but largely forgotten lessons as well as acquiring newly discovered knowledge. During the process of our immediate 9/11 response, we identified that we were engaged in Iraq and Afghanistan in an insurgency. Subsequently, our focus converged upon the description of insurgencies and the requirements for counterinsurgency. This paper argues that emerging conditions now allow the re-evaluation of the type of conflict occurring today and into the foreseeable future: that we, including the modeling and simulation world, emerge from a singular focus on orthodox insurgencies and start to consider the consequences and opportunities of the complexity of current conflicts. As an example of complexity, this paper will use the relatively common phenomenon of the Warlord or Warlordism. The paper will provide a definition of this phenomenon and then describe the implications for modelers. The paper will conclude by demonstrating the impact of incorporating this one rather prosaic complexity into an insurgency model, using agent based modeling (ABM)