A Hamiltonian Formulation of the BKL Conjecture

The Belinskii, Khalatnikov and Lifshitz conjecture \cite{bkl1} posits that on approach to a space-like singularity in general relativity the dynamics are well approximated by `ignoring spatial derivatives in favor of time derivatives.' In \cite{ahs1} we examined this idea from within a Hamiltonian framework and provided a new formulation of the conjecture in terms of variables well suited to loop quantum gravity. We now present the details of the analytical part of that investigation. While our motivation came from quantum considerations, thanks to some of its new features, our formulation should be useful also for future analytical and numerical investigations within general relativity.Comment: 26 pages, 3 figures. Two references added. Minor typos corrected. To appear in PR

Ivory Tower Versus Corporate Lab: An Empirical Study of Basic Research and Appropriability

We explore the use of patent citations to measure the "basicness" and appropriability of inventions. We propose that the basicness of research underlying an invention can be characterized by the nature of the previous patents cited by an invention; that the basicness of research outcomes relates to the subsequent patents that cite an invention; and that the fraction of citing patents that are assigned to the same organization as the original invention is a measure of appropriabiity. We test the validity of these presumptions by comparing the value of our measures for university and corporate patents, and find that many of the measures do conform to our a priori belief that university research and research outcomes are more basic and harder to appropriate than those of corporations. We also find some evidence that basicness of outcomes is correlated with basicness of research, and that appropriability is lower for basic outcomes.

Measuring Economic Growth from Outer Space

GDP growth is often measured poorly for countries and rarely measured at all for cities. We propose a readily available proxy: satellite data on lights at night. Our statistical framework uses light growth to supplement existing income growth measures. The framework is applied to countries with the lowest quality income data, resulting in estimates of growth that differ substantially from established estimates. We then consider a longstanding debate: do increases in local agricultural productivity increase city incomes? For African cities, we find that exogenous agricultural productivity shocks (high rainfall years) have substantial effects on local urban economic activity.economic growth; remote sensing; urbanization; income measurement

Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I

We analyze the issue of anomaly-free representations of the constraint algebra in Loop Quantum Gravity (LQG) in the context of a diffeomorphism-invariant gauge theory in three spacetime dimensions. We construct a Hamiltonian constraint operator whose commutator matches with a quantization of the classical Poisson bracket involving structure functions. Our quantization scheme is based on a geometric interpretation of the Hamiltonian constraint as a generator of phase space-dependent diffeomorphisms. The resulting Hamiltonian constraint at finite triangulation has a conceptual similarity with the "mu-bar"-scheme in loop quantum cosmology and highly intricate action on the spin-network states of the theory. We construct a subspace of non-normalizable states (distributions) on which the continuum Hamiltonian constraint is defined which leads to an anomaly-free representation of the Poisson bracket of two Hamiltonian constraints in loop quantized framework.Comment: 60 pages, 6 figure

“Inspiring Imps”: programme evaluation of a football intervention targeting mentally ill health services users through a professional football club

The Active People survey (2010) shows that only 6.5% of disabled individuals participate in sport and exercise 3 times per week, compared with 16.5% of able bodied adults in the UK. Individuals with recognised disabilities have long been excluded from mainstream society. Particularly in sport, disability athletes can be afforded minority status and are treated as such (Nixon, 2000: In Handbook of Sports Studies, edited by J. Coakley and E. Dunning. London: Sage). This stigmatisation can be particularly acute among participants with diagnosed mental or psychological disabilities. Previous research concluded that sport can have positive psychological and social benefits, including improved well-being, motivation and social confidence (Crone and Guy, 2008: International Journal of Mental Health Nursing. 17, 197-207.). The aim of the present study was to investigate the feasibility of a 6 week exercise programme targeting mental ill health service users aged 16+. A weekly 2 hour session of football was introduced to promote health and wellbeing in the target group. Partners included county Football Association and a professional football club. The project enhanced local partnerships and partnerships with other professional football clubs. The key remaining aim is to ensure a sustainable “legacy” is achieved to ensure the continuation delivery of the project. The feasibility of the present study will be assessed using programme evaluation. Programme evaluation uses programme theory to produce a structured framework for assessment of the project (Rossi et al 2004; Evaluation: A systematic Approach. London, Sage). This allows a clear and logical progression from planning to implementation. Participant attrition rates and attendance records will be collected. These data will be supplemented with semi-structured interviews with participants and project stakeholders to assess programme development. The expected overall project outcome is to produce shared learning practice on similar interventions nationwide

Vertex Expansion for the Bianchi I model

A perturbative expansion of Loop Quantum Cosmological transitions amplitudes of Bianchi I models is performed. Following the procedure outlined in [1,2] for isotropic models, it is shown that the resulting expansion can be written in the form of a series of amplitudes each with a fixed number of transitions mimicking a spin foam expansion. This analogy is more complete than in the isotropic case, since there are now the additional anisotropic degrees of freedom which play the role of `colouring' of the spin foams. Furthermore, the isotropic expansion is recovered by integrating out the anisotropies.Comment: 15 pages, 2 figure