A Generalized Spatial Measure for Resilience of Microbial Systems

The emergent property of resilience is the ability of a system to return to an original state after a disturbance. Resilience may be used as an early warning system for significant or irreversible community transition; that is, a community with diminishing or low resilience may be close to catastrophic shift in function or an irreversible collapse. Typically, resilience is quantified using recovery time, which may be difficult or impossible to directly measure in microbial systems. A recent study in the literature showed that under certain conditions, a set of spatial-based metrics termed recovery length, can be correlated to recovery time, and thus may be a reasonable alternative measure of resilience. However, this spatial metric of resilience is limited to use for step-change perturbations. Building upon the concept of recovery length, we propose a more general form of the spatial metric of resilience that can be applied to any shape of perturbation profiles (for example, either sharp or smooth gradients). We termed this new spatial measure “perturbation-adjusted spatial metric of resilience” (PASMORE). We demonstrate the applicability of the proposed metric using a mathematical model of a microbial mat

Urban Atlas, land use modelling and spatial metric techniques

Recently, through the GMES program of ESA the Urban Atlas dataset was released. The Urban Atlas is providing pan-European comparable land use and land cover data for Large Urban Zones with more than 100.000 inhabitants as defined by the Urban Audit. The production of the various datasets started in 2009 and is expected to be completed by the end of 2011. At presently datasets for more than 150 urban areas have been released. Most importantly the datasets can be freely downloaded and distributed. The availability of such a huge dataset produced with the same standards will have a major impact on the development of urban transportation models and the comparative analysis of the urban areas across Europe. Combined with the data sets that will be developed from the various Census of population it could become the basis for the application of various models in the next ten years. In this paper two major themes are discussed. First, how the current state of art in urban modeling (behavioral, cellular automata and statistical) can use these models, what type of additional data might be needed and how these datasets can be combined with other data for developing land use transportation models. Second, spatial metric techniques are used to define indicators for the landscape that could be used for comparing the structure and the form of the various cities. In the last ten years there has been an increasing interest in applying spatial metric techniques analysis of urban environments, to examine unique spatial components of intra-and inter-city urban structure, as well as, the dynamics of change. The landscape perspective assumes abrupt transitions between individual patches that result in distinct edges. These measures provide a link between the detailed spatial structures that result from urban change processes. The spatial metric indicators were developed for several cities and are then used for a comparative study of city typologies and urban fabric characteristics.

Post-Newtonian Freely Specifiable Initial Data for Binary Black Holes in Numerical Relativity

Construction of astrophysically realistic initial data remains a central problem when modelling the merger and eventual coalescence of binary black holes in numerical relativity. The objective of this paper is to provide astrophysically realistic freely specifiable initial data for binary black hole systems in numerical relativity, which are in agreement with post-Newtonian results. Following the approach taken by Blanchet, we propose a particular solution to the time-asymmetric constraint equations, which represent a system of two moving black holes, in the form of the standard conformal decomposition of the spatial metric and the extrinsic curvature. The solution for the spatial metric is given in symmetric tracefree form, as well as in Dirac coordinates. We show that the solution differs from the usual post-Newtonian metric up to the 2PN order by a coordinate transformation. In addition, the solutions, defined at every point of space, differ at second post-Newtonian order from the exact, conformally flat, Bowen-York solution of the constraints.Comment: 41 pages, no figures, accepted for publication in Phys. Rev. D, significant revision in presentation (including added references and corrected typos

Latticing quantum gravity

I discuss some aspects of a lattice approach to canonical quantum gravity in a connection formulation, discuss how it differs from the continuum construction, and compare the spectra of geometric operators - encoding information about components of the spatial metric - for some simple lattice quantum states.Comment: 7 pages, TeX, 1 figure (epsf); contribution to Santa Margherita Conference on Constrained Dynamics and Quantum Gravit

Classically Integrable Cosmological Models with a Scalar Field

New classes of classically integrable models in the cosmological theories with a scalar field are obtained by using freedoms of defining time and fields. In particular, some models with the sum of exponential potentials in the flat spatial metric are shown to be integrable. The model with the Sine-Gordon potential can be solved in terms of analytic continuation of the non-periodic Toda field theory.Comment: 10 pages, Late

The densitized lapse ("Taub function") and the Taub time gauge in cosmology

The role of the Taub time gauge in cosmology is linked to the use of the densitized lapse function instead of the lapse function in the variational principle approach to the Einstein equations. The spatial metric variational equations then become the Ricci evolution equations, which are then supplemented by the Einstein constraints which result from the variation with respect to the densitized lapse and the usual shift vector field. In those spatially homogeneous cases where the least disconnect occurs between the general theory and the restricted symmetry scenario, the recent adjustment of the conformal approach to solving the initial value problem resulting from densitized lapse considerations is seen to be inherent in the use of symmetry-adapted metric variables. The minimal distortion shift vector field is a natural vector potential for the new York thin sandwich initial data approach to the constraints, which in this case corresponds to the diagonal spatial metric gauge. For generic spacetimes, the new approach suggests defining a new minimal distortion shift gauge which agrees with the old gauge in the Taub time gauge, but which also makes its defining differential equation agree with the vector potential equation for solving the supermomentum constraint in any time gauge.Comment: 22 pages, Latex article style, no figure