Distance statistics in large toroidal maps

We compute a number of distance-dependent universal scaling functions characterizing the distance statistics of large maps of genus one. In particular, we obtain explicitly the probability distribution for the length of the shortest non-contractible loop passing via a random point in the map, and that for the distance between two random points. Our results are derived in the context of bipartite toroidal quadrangulations, using their coding by well-labeled 1-trees, which are maps of genus one with a single face and appropriate integer vertex labels. Within this framework, the distributions above are simply obtained as scaling limits of appropriate generating functions for well-labeled 1-trees, all expressible in terms of a small number of basic scaling functions for well-labeled plane trees.Comment: 24 pages, 9 figures, minor corrections, new added reference

Distance statistics in quadrangulations with a boundary, or with a self-avoiding loop

We consider quadrangulations with a boundary and derive explicit expressions for the generating functions of these maps with either a marked vertex at a prescribed distance from the boundary, or two boundary vertices at a prescribed mutual distance in the map. For large maps, this yields explicit formulas for the bulk-boundary and boundary-boundary correlators in the various encountered scaling regimes: a small boundary, a dense boundary and a critical boundary regime. The critical boundary regime is characterized by a one-parameter family of scaling functions interpolating between the Brownian map and the Brownian Continuum Random Tree. We discuss the cases of both generic and self-avoiding boundaries, which are shown to share the same universal scaling limit. We finally address the question of the bulk-loop distance statistics in the context of planar quadrangulations equipped with a self-avoiding loop. Here again, a new family of scaling functions describing critical loops is discovered.Comment: 55 pages, 14 figures, final version with minor correction

Some photometer results obtained on the NASA 1969 Airborne Auroral Expedition

The spectral features measured by a photometer onboard the Convair 990 Galileo, during the Auroral Expedition are given in tables. The measurements given cover flights 3 to 15

Supersonic flutter of a thermally stressed flat panel with uniform edge loads

Supersonic flutter of thermally stressed flat panel with uniform edge load

A Spatial Panel Simultaneous-Equations Model of Business Growth, Migration Behavior, Local Public Services and Household Income in Appalachia

In this paper we develop a spatial panel simultaneous-equations model of business growth, migration behavior, local public services and median household income in a partial lag-adjustment growth-equilibrium framework and utilizing a one-way error component model for the disturbances. This model is an extension of the jobs follow people or people follow jobs literature and it improved previous models in the growth-equilibrium tradition by: (1) explicitly modeling local government and regional income in the growth process; (2) explicitly modeling gross in-migration and gross out-migration separately in order to spell out the differential effects, which used to be glossed over under net population change in previous studies; (3) explicitly incorporating both spatially lagged dependent variables and spatially lagged error terms to account for spatial spillover effects in the data set; and (4) extending and generalizing the modeling and estimation of simultaneous systems of spatially interrelated cross sectional equations into a panel data setting. To estimate the model, we develop a five-step new estimation strategy by generalizing the Generalized Spatial Three-Stage Least Squares (GS3SLS) approach outlined in Kelejian and Prucha (2004) into a panel data setting. The empirical implementation of the model uses county-level data from the 418 Appalachian counties for 1980-2000. Generally, the results from these model estimations are consistent with the theoretical expectations and empirical findings in the equilibrium growth literature and provide support to the basic hypotheses of this study. First, the estimates show the existence of feedback simultaneities among the endogenous variables of the model. Second, the results also show the existence of conditional convergence with respect to the respective endogenous variable of each equation of the model and the speed of adjustment parameters are generally comparable to those in literature. Third, the results from the parameter estimation of the model indicate the existence of spatial autoregressive lag effects and spatial cross-regressive lag effects with respect to the endogenous variables of the model. One of the key conclusions is that sector specific policies should be integrated and harmonized in order to give the desirable outcome. Besides, regionally focusing resources for development policy may yield greater returns than treating all locations the same.Community/Rural/Urban Development,

Combinatorics of bicubic maps with hard particles

We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by use of a bijection with a particular class of blossom trees with particles, obtained by an appropriate cutting of the maps. Although these trees have no simple local characterization, we prove that their enumeration may be performed upon introducing a larger class of "admissible" trees with possibly doubly-occupied edges and summing them with appropriate signed weights. The proof relies on an extension of the cutting procedure allowing for the presence on the maps of special non-sectile edges. The admissible trees are characterized by simple local rules, allowing eventually for an exact enumeration of planar bicubic maps with hard particles. We also discuss generalizations for maps with particles subject to more general exclusion rules and show how to re-derive the enumeration of quartic maps with Ising spins in the present framework of admissible trees. We finally comment on a possible interpretation in terms of branching processes.Comment: 41 pages, 19 figures, tex, lanlmac, hyperbasics, epsf. Introduction and discussion/conclusion extended, minor corrections, references adde

Analysis of the Copenhagen Accord pledges and its global climatic impacts‚ a snapshot of dissonant ambitions

This analysis of the Copenhagen Accord evaluates emission reduction pledges by individual countries against the Accord's climate-related objectives. Probabilistic estimates of the climatic consequences for a set of resulting multi-gas scenarios over the 21st century are calculated with a reduced complexity climate model, yielding global temperature increase and atmospheric CO2 and CO2-equivalent concentrations. Provisions for banked surplus emission allowances and credits from land use, land-use change and forestry are assessed and are shown to have the potential to lead to significant deterioration of the ambition levels implied by the pledges in 2020. This analysis demonstrates that the Copenhagen Accord and the pledges made under it represent a set of dissonant ambitions. The ambition level of the current pledges for 2020 and the lack of commonly agreed goals for 2050 place in peril the Accord's own ambition: to limit global warming to below 2 °C, and even more so for 1.5 °C, which is referenced in the Accord in association with potentially strengthening the long-term temperature goal in 2015. Due to the limited level of ambition by 2020, the ability to limit emissions afterwards to pathways consistent with either the 2 or 1.5 °C goal is likely to become less feasibl