A Bose-Einstein Approach to the Random Partitioning of an Integer

Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of connected components. Questions such as the evaluation of the probability of random covering and parking configurations, number and length of the gaps are addressed. They are the discrete versions of similar problems raised in the continuum. For each value of k, asymptotic results are presented when n,N both go to infinity according to two different regimes. This model may equivalently be viewed as a random partitioning problem of N items into n recipients. A grand-canonical balls in boxes approach is also supplied, giving some insight into the multiplicities of the box filling amounts or spacings. The latter model is a k-nearest neighbor random graph with N vertices and kn edges. We shall also briefly consider the covering problem in the context of a random graph model with N vertices and n (out-degree 1) edges whose endpoints are no more bound to be neighbors

Evaluation of the Impact of Bus Rapid Transit on Air Pollution

Mexico City’s bus rapid transit (BRT) network, Metrobus, was introduced in an attempt to reduce congestion, increase city transport efficiency and cut air polluting emissions. In June 2005, the first BRT line in the metropolitan area began service. We use differences-in-differences and quantile regression techniques in undertaking the first quantitative policy impact assessment of the BRT system on air polluting emissions. The air pollutants considered are carbon monoxide (CO), nitrogen oxides (NOX), particulate matter of less than 2.5 μm (PM 2.5), particulate matter of less than 10 μm (PM10), and sulfur dioxide (SO2). The ex-post analysis uses real field data from air quality monitoring stations for periods before and after BRT implementation. Results show that BRT constitutes an effective environmental policy, reducing emissions of CO, NOX, PM2.5 and PM10

Evaluation of the impact of Bus Rapid Transit on air pollution in Mexico City

Mexico City's bus rapid transit (BRT) network, Metrobus, was introduced in an attempt to reduce congestion, increase city transport efficiency and cut air polluting emissions. In June 2005, the first BRT line in the metropolitan area began service. We use the differences-in-differences technique to make the first quantitative assessment of the policy impact of a BRT system on air polluting emissions. The air pollutants considered are carbon monoxide (CO), nitrogen oxides (NOX), particulate matter of less than 10 µm (PM10), and sulfur dioxide (SO2). The ex-post analysis uses real field data from air quality monitoring stations for periods before and after BRT implementation. Results show that BRT constitutes an effective environmental policy, reducing emissions of CO, NOX, and PM10

Numerical Bifurcation Analysis of Conformal Formulations of the Einstein Constraints

The Einstein constraint equations have been the subject of study for more than fifty years. The introduction of the conformal method in the 1970's as a parameterization of initial data for the Einstein equations led to increased interest in the development of a complete solution theory for the constraints, with the theory for constant mean curvature (CMC) spatial slices and closed manifolds completely developed by 1995. The first general non-CMC existence result was establish by Holst et al. in 2008, with extensions to rough data by Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC theory remains mostly open; moreover, recent work of Maxwell on specific symmetry models sheds light on fundamental non-uniqueness problems with the conformal method as a parameterization in non-CMC settings. In parallel with these mathematical developments, computational physicists have uncovered surprising behavior in numerical solutions to the extended conformal thin sandwich formulation of the Einstein constraints. In particular, numerical evidence suggests the existence of multiple solutions with a quadratic fold, and a recent analysis of a simplified model supports this conclusion. In this article, we examine this apparent bifurcation phenomena in a methodical way, using modern techniques in bifurcation theory and in numerical homotopy methods. We first review the evidence for the presence of bifurcation in the Hamiltonian constraint in the time-symmetric case. We give a brief introduction to the mathematical framework for analyzing bifurcation phenomena, and then develop the main ideas behind the construction of numerical homotopy, or path-following, methods in the analysis of bifurcation phenomena. We then apply the continuation software package AUTO to this problem, and verify the presence of the fold with homotopy-based numerical methods.Comment: 13 pages, 4 figures. Final revision for publication, added material on physical implication