Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy

This paper is a continuation of math.DG/0408005. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of S^n by looking at the conormal bundle of appropriate submanifolds of S^n. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey-Lawson for submanifolds in R^n in their pioneering paper. We also construct calibrated submanifolds in complete metrics with special holonomy G_2 and Spin(7) discovered by Bryant and Salamon on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds in a compact manifold with special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some paragraphs rewritten for improved clarit

Motivating Entrepreneurial Activity in the MENA Region: Do Human Capital and Corruption Matter?

Since the time of Schumpeter, entrepreneurship has been strongly associated with positive economic development. His primary contribution stems from his core theory that ‘entrepreneurship is the engine of national economic growth’. But not all entrepreneurship creates a positive impact on the economy. Thus, it is important to develop a deep understanding of the business climate that leads entrepreneurial activity to foster economic growth. This article delves into the role of human capital (HC) and corruption (CPI) in developing the type of entrepreneurial climate that leads to economic growth. Using data gathered from the Global Entrepreneurship Monitor (GEM), the World Bank and various NGO data sites, this article conducts an empirical investigation of the impact of human capital (HC) and corruption (CPI) on the overall level of the total entrepreneurial activity (TEA) and follows this by further studying the impact of these antecedent factors on the disaggregated levels of total entrepreneurial activity; opportunity-motivated entrepreneurial activity (OME) and necessity-motivated entrepreneurial activity (NME)

The importance of regional variation in the analysis of urbanization-agriculture interactions

La recherche géographique sur l'agriculture dans les régions métropolitaines a été orientée vers l'étude des changements agricoles influencés par l'urbanisation. D'autres processus d'évolution et les facteurs liés aux variations de l'environnement régional ont été négligés. Certaines recherches récentes faisant apparaître l'importance de l'environnement régional à des échelles géographiques différentes sont décrites. Premièrement, une typologie de régions basées sur les régions métropolitaines de recensement du Canada est présentée. Certains groupes de la typologie ont connu des changements agricoles importants qui ne s'expliquent pas par les pressions du développement métropolitain. Des différences régionales dans l'environnement agricole apportent des explications partielles. Deuxièmement, pour la région de Montréal des variables agricoles (de 1961 à 1971) sont analysées avec une analyse factorielle. Les résultats sont interprétés en termes a) de l'urbanisation et b) des variations dans l'environnement à l'intérieur de la région. En dernier lieu, pour une municipalité située près de Toronto, une analyse est faite de la répartition géographique du morcellement des parcelles cadastrales. Une fois encore, des liens sont apparents avec certaines caractéristiques de l'environnement. La conclusion est que les changements agricoles ne sont pas homogènes, soit entre régions, soit à l'intérieur d'une même région, et que l'explication devrait être formulée aussi bien en termes de la variation de l'environnement régional qu'en termes des influences métropolitaines.Research into agriculture in metropolitan regions has concentrated on urban-induced agricultural land use changes. Other processes of change and factors related to variations in the regional environment have been neglected. Some recent research is reported here which points to the importance of the regional environment at a variety of scale levels. First, a typology of regions based on Census Metropolitan Areas in Canada is developed. Some groups of regions experienced significant agricultural changes quite unrelated to metropolitan development pressures. Regional differences in the agricultural environment are suggested as partial explanations. Second, for the Montréal region, a series of agricultural variables (1961 to 1971) are analysed using factor analysis. Results are interpreted in the light of a) urbanisation forces and b) internal variation in the regional environment. Finally, for a township near Toronto, an investigation is made of the distribution of severances. Once more, relationships appear with certain physical characteristics. The paper concludes that agricultural change is not uniform either between regions or within regions, and that part of the variation is related to differences in the "regional" environment and part to metropolitan forces

Word-level Symbolic Trajectory Evaluation

Symbolic trajectory evaluation (STE) is a model checking technique that has been successfully used to verify industrial designs. Existing implementations of STE, however, reason at the level of bits, allowing signals to take values in {0, 1, X}. This limits the amount of abstraction that can be achieved, and presents inherent limitations to scaling. The main contribution of this paper is to show how much more abstract lattices can be derived automatically from RTL descriptions, and how a model checker for the general theory of STE instantiated with such abstract lattices can be implemented in practice. This gives us the first practical word-level STE engine, called STEWord. Experiments on a set of designs similar to those used in industry show that STEWord scales better than word-level BMC and also bit-level STE.Comment: 19 pages, 3 figures, 2 tables, full version of paper in International Conference on Computer-Aided Verification (CAV) 201

A search for distant radio galaxies from SUMSS and NVSS: III. radio spectral energy distributions and the z-alpha correlation

This is the third in a series of papers that present observations and results for a sample of 76 ultra-steep-spectrum radio sources designed to find galaxies at high redshift. Here we present multi-frequency radio observations, from the Australia Telescope Compact Array, for a subset of 37 galaxies from the sample. Matched resolution observations at 2.3, 4.8 and 6.2GHz are presented for all galaxies, with the z<2 galaxies additionally observed at 8.6 and 18GHz. New angular size constraints are reported for 19 sources based on high resolution 4.8 and 6.2GHz observations. Functional forms for the rest-frame spectral energy distributions are derived: 89% of the sample is well characterised by a single power law, whilst the remaining 11% show some flattening toward higher frequencies: not one source shows any evidence for high frequency steepening. We discuss the implications of this result in light of the empirical correlation between redshift and spectral index seen in flux limited samples of radio galaxies. Finally, a new physical mechanism to explain the redshift -- spectral index correlation is posited: extremely steep spectrum radio galaxies in the local universe usually reside at the centres of rich galaxy clusters. We argue that if a higher fraction of radio galaxies, as a function of redshift, are located in environments with densities similar to nearby rich clusters, then this could be a natural interpretation for the correlation. We briefly outline our plans to pursue this line of investigation.Comment: MNRAS in pres

Z2SAL: a translation-based model checker for Z

Despite being widely known and accepted in industry, the Z formal specification language has not so far been well supported by automated verification tools, mostly because of the challenges in handling the abstraction of the language. In this paper we discuss a novel approach to building a model-checker for Z, which involves implementing a translation from Z into SAL, the input language for the Symbolic Analysis Laboratory, a toolset which includes a number of model-checkers and a simulator. The Z2SAL translation deals with a number of important issues, including: mapping unbounded, abstract specifications into bounded, finite models amenable to a BDD-based symbolic checker; converting a non-constructive and piecemeal style of functional specification into a deterministic, automaton-based style of specification; and supporting the rich set-based vocabulary of the Z mathematical toolkit. This paper discusses progress made towards implementing as complete and faithful a translation as possible, while highlighting certain assumptions, respecting certain limitations and making use of available optimisations. The translation is illustrated throughout with examples; and a complete working example is presented, together with performance data

The G_2 sphere over a 4-manifold

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by the study of the most basic properties of our construction. The structure is co-calibrated if, and only if, M is an Einstein manifold. The fibres are always associative. In fact, the associated 3-form results from a linear combination of three other volume 3-forms, one of which is the volume of the fibres. We also give new examples of co-calibrated structures on well known spaces. We hope this contributes both to the knowledge of special geometries and to the study of 4-manifolds.Comment: 13 page

Numerical Linked-Cluster Approach to Quantum Lattice Models

We present a novel algorithm that allows one to obtain temperature dependent properties of quantum lattice models in the thermodynamic limit from exact diagonalization of small clusters. Our Numerical Linked Cluster (NLC) approach provides a systematic framework to assess finite-size effects and is valid for any quantum lattice model. Unlike high temperature expansions (HTE), which have a finite radius of convergence in inverse temperature, these calculations are accurate at all temperatures provided the range of correlations is finite. We illustrate the power of our approach studying spin models on {\it kagom\'e}, triangular, and square lattices.Comment: 4 pages, 5 figures, published versio

Size, shape and surface chemistry of nano-gold dictate its cellular interactions, uptake and toxicity

Colloidal gold is undoubtedly one of the most extensively studied nanomaterials, with 1000s of different protocols currently available to synthesise gold nanoparticles (AuNPs). While developments in the synthesis of AuNPs have progressed rapidly in recent years, our understanding of their biological impact, with particular respect to the effect of shape, size, surface characteristics and aggregation states, has struggled to keep pace. It is generally agreed that when AuNPs are exposed to biological systems, these parameters directly influence their pharmacokinetic and pharmacodynamic properties by influencing AuNPs distribution, circulation time, metabolism and excretion in biological systems. However, the rules governing these properties, and the science behind them, are poorly understood. Therefore, a systematic understanding of the implications of these variables at the nano-bio interface has recently become a topic of major interest. This Review Article attempts to ignite a discussion around the influence of different physico-chemical parameters on biological activity of AuNPs, while focussing on critical aspects of cellular interactions, uptake and cytotoxicity. The review also discusses emerging trends in AuNP uptake and toxicity that are leading to technological advances through AuNP-based therapy, diagnostics and imaging