Dynamical Symmetry Breaking in Planar QED

We investigate (2+1)-dimensional QED coupled with Dirac fermions both at zero and finite temperature. We discuss in details two-components (P-odd) and four-components (P-even) fermion fields. We focus on P-odd and P-even Dirac fermions in presence of an external constant magnetic field. In the spontaneous generation of the magnetic condensate survives even at infinite temperature. We also discuss the spontaneous generation of fermion mass in presence of an external magnetic field.Comment: 34 pages, 8 postscript figures, final version to appear on J. Phys.

A cross-border deforestation index to understand underlying drivers of deforestation

This paper considers a preliminary investigation involving the development of a Cross-Border Deforestation Index (CBDI), which is an attempt to quantify the differences in deforestation between two countries or potentially any two administrative units. In this study, the focus was on countries. For each pair of bordering countries, a 50km buffer zone was drawn and the average value of the Vegetation Continuous Field (VCF) was calculated for each country in the pair. The ratio of these two averages is the CBDI. Values of 1 indicate similar levels of forest cover but values greater than 1 point towards dissimilar land use policies within countries and/or sub-national administrative levels. This index was calculated for all pairs of bordering tropical countries in South and Central America, Asia and Africa. In addition, a visual analysis of the spatial variation of the VCF was undertaken to show how this can complement the CBDI. The results showed that countries such as Argentina, Brazil, Chile, El Salvador, Laos, Thailand and DR Congo, in combination with different neighbouring countries, all have CBDI values differing from 1. These areas are worth examining in greater detail in order to understand what types of drivers are behind these outlying CBDI values. These drivers could include land use policy, population pressure, accessibility, etc. Future work will i nclude the addition of environmental factors. By computing the CBDI for so called Homogeneous Response Units (HRU: areas of similar or identical environmental conditions in terms of soil, altitude and slope), we will be able to examine the changing effect on the CBDI. This work is still ongoing and will be expanded to consider HRU for all country pairs. In addition, regression of the CBDI with different drivers of deforestation will be attempted in order to help identify these underlying causes

Network synchronization: Optimal and Pessimal Scale-Free Topologies

By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree correlations and observe a generic tendency towards disassortativity. Still, we show that there is not a one-to-one correspondence between synchronizability and disassortativity. On the other hand, we study the nature of optimally un-synchronizable networks, that is, networks whose topology minimizes the range of stability of the synchronous state. The resulting ``pessimal networks'' turn out to have a highly assortative string-like structure. We also derive a rigorous lower bound for the Laplacian eigenvalue ratio controlling synchronizability, which helps understanding the impact of degree correlations on network synchronizability.Comment: 11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex Networks 2007

Microscopic Black Hole Pairs in Highly-Excited States

We consider the quantum mechanics of a system consisting of two identical, Planck-size Schwarzschild black holes revolving around their common center of mass. We find that even in a very highly-excited state such a system has very sharp, discrete energy eigenstates, and the system performs very rapid transitions from a one stationary state to another. For instance, when the system is in the 100th excited state, the life times of the energy eigenstates are of the order of $10^{-30}$ s, and the energies of gravitons released in transitions between nearby states are of the order of $10^{22}$ eV.Comment: 22 pages, 3 figures, uses RevTe

Cosmic censorship and spherical gravitational collapse with tangential pressure

We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state. It turns out that the Einstein equations can be reduced to the solution of an integral for the evolution of the area radius. We show that for positive pressure there is a finite region near the center which necessarily expands outwards, if collapse begins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity - any such singularity will necessarily be covered by a horizon. For negative pressure the entire object collapses inwards, but any singularities that could arise are not naked. Thus the nature of the evolution is very different from that of dust, even when the ratio of pressure to density is infinitesimally small.Comment: 16 pages, Latex file, two figures, uses epsf.st

An Exploration of Some Pitfalls of Thematic Map Assessment Using the New Map Tools Resource

A variety of metrics are commonly employed by map producers and users to assess and compare thematic maps’ quality, but their use and interpretation is inconsistent. This problem is exacerbated by a shortage of tools to allow easy calculation and comparison of metrics from different maps or as a map’s legend is changed. In this paper, we introduce a new website and a collection of R functions to facilitate map assessment. We apply these tools to illustrate some pitfalls of error metrics and point out existing and newly developed solutions to them. Some of these problems have been previously noted, but all of them are under-appreciated and persist in published literature. We show that binary and categorical metrics, including information about true-negative classifications, are inflated for rare categories, and more robust alternatives should be chosen. Most metrics are useful to compare maps only if their legends are identical. We also demonstrate that combining land-cover classes has the often-neglected consequence of apparent improvement, particularly if the combined classes are easily confused (e.g., different forest types). However, we show that the average mutual information (AMI) of a map is relatively robust to combining classes, and reflects the information that is lost in this process; we also introduce a modified AMI metric that credits only correct classifications. Finally, we introduce a method of evaluating statistical differences in the information content of competing maps, and show that this method is an improvement over other methods in more common use. We end with a series of recommendations for the meaningful use of accuracy metrics by map users and producer

Dynamical generalization of a solvable family of two-electron model atoms with general interparticle repulsion

Holas, Howard and March [Phys. Lett. A {\bf 310}, 451 (2003)] have obtained analytic solutions for ground-state properties of a whole family of two-electron spin-compensated harmonically confined model atoms whose different members are characterized by a specific interparticle potential energy u($r_{12}$). Here, we make a start on the dynamic generalization of the harmonic external potential, the motivation being the serious criticism levelled recently against the foundations of time-dependent density-functional theory (e.g. [J. Schirmer and A. Dreuw, Phys. Rev. A {\bf 75}, 022513 (2007)]). In this context, we derive a simplified expression for the time-dependent electron density for arbitrary interparticle interaction, which is fully determined by an one-dimensional non-interacting Hamiltonian. Moreover, a closed solution for the momentum space density in the Moshinsky model is obtained.Comment: 5 pages, submitted to J. Phys.