Maurer-Cartan Elements and Cyclic Operads

First we argue that many BV and homotopy BV structures, including both familiar and new examples, arise from a common underlying construction. The input of this construction is a cyclic operad along with a cyclically invariant Maurer-Cartan element in an associated Lie algebra. Using this result we introduce and study the operad of cyclically invariant operations, with instances arising in cyclic cohomology and $S^1$ equivariant homology. We compute the homology of the cyclically invariant operations; the result being the homology operad of $\mathcal{M}_{0,n+1}$, the uncompactified moduli spaces of punctured Riemann spheres, which we call the gravity operad after Getzler. Motivated by the line of inquiry of Deligne's conjecture we construct `cyclic brace operations' inducing the gravity relations up-to-homotopy on the cochain level. Motivated by string topology, we show such a gravity-BV pair is related by a long exact sequence. Examples and implications are discussed in course.Comment: revised version to appear in the Journal of Noncommutative Geometr

Feynman Categories

In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs, modular operads, twisted (modular) operads, properads, hyperoperads, their colored versions, as well as algebras over operads and an abundance of other related structures, such as crossed simplicial groups, the augmented simplicial category or FI--modules. The usefulness of this approach is that it allows us to handle all the classical as well as more esoteric structures under a common framework and we can treat all the situations simultaneously. Many of the known constructions simply become Kan extensions. In this common framework, we also derive universal operations, such as those underlying Deligne's conjecture, construct Hopf algebras as well as perform resolutions, (co)bar transforms and Feynman transforms which are related to master equations. For these applications, we construct the relevant model category structures. This produces many new examples.Comment: Expanded version. New introduction, new arrangement of text, more details on several constructions. New figure

Forecasting Short Term Trends in Prices of U.S. Stock Market

This thesis explores a cubic model to forecast short term trends in stock prices. Specifically, this model recognizes the limited applicability of instantaneous rate of change indications from the current stock price of an individual corporation. Discussed first is the nature of share price as a data vector and derivations of linear and non-linear mathematical operators. A proposed methodology demonstrates market entry and exit techniques that comprise a trading system and prediction range is evaluated with emphasis on error analysis

April 18, 1989 Statement By Police Commissioner Benjamin Ward on the Final Report of C.C.R.B. on the Tompkins Square Park Incident

This statement by New York City Police Commissioner Benjamin Ward was made in response to the Civilian Complaint Review Board\u27s report concerning the Tompkins Square Park riot on August 6,1988. Attached to Ward\u27s statement is Operations Order No. 72 dated June 19, 1989 re: Issuance of New Department Helmets and Shield Number Decals. This document was included with the background memorandum on the Civilian Complaint Review Board

Fan Safety at Sports Facilities

Accidents involving fans occur at sports facilities around the globe. The purpose of this research was to discover the reactions of local facility managers and their customers to fan accidents at sports venues, recommendations to address safety concerns at their sports facilities, opinions of customers expressed to their facility managers regarding possible installation of additional safety measures as related to the fan experience at sports events, and opinions of facility managers to the possible elimination of the assumption of risk or “baseball” rule. Baseball is the sport with the most reported fan accidents at their stadiums but other sports have fan accidents and deaths as well. The results revealed the opinions of the facility managers. Several responded that when they hear about fan accidents their first thought is about preventing them at their facilities. Others felt fans should be more aware of their surroundings and the possible dangers related to the sport/event being played at the facility. Most facility managers are in favor of raising railing heights but are not in favor of installing netting throughout the facilities. Most also felt the assumption of risk rule would not be eliminated. Based on the results, facility managers are concerned about the safety of their customers but feel their customers/fans must also accept responsibility for their own safety

Understanding the effects of violent video games on violent crime

Psychological studies invariably find a positive relationship between violent video game play and aggression. However, these studies cannot account for either aggressive effects of alternative activities video game playing substitutes for or the possible selection of relatively violent people into playing violent video games. That is, they lack external validity. We investigate the relationship between the prevalence of violent video games and violent crimes. Our results are consistent with two opposing effects. First, they support the behavioral effects as in the psychological studies. Second, they suggest a larger voluntary incapacitation effect in which playing either violent or non-violent games decrease crimes. Overall, violent video games lead to decreases in violent crime. --Video Games,Violence,Crime