Reverse mathematics and infinite traceable graphs

This paper falls within the general program of investigating the proof theoretic strength (in terms of reverse mathematics) of combinatorial principals which follow from versions of Ramsey's theorem. We examine two statements in graph theory and one statement in lattice theory proved by Galvin, Rival and Sands \cite{GRS:82} using Ramsey's theorem for 4-tuples. Our main results are that the statements concerning graph theory are equivalent to Ramsey's theorem for 4-tuples over \RCA while the statement concerning lattices is provable in \RCA. Revised 12/2010. To appear in Archive for Mathematical Logi

A \Gamma-structure on Lagrangian Grassmannians

For n odd the Lagrangian Grassmannian of \R^{2n} is a \Gamma-manifold.Comment: 6 pages; v2: new coauthor, nicer proo

Characterising the role of GABA and its metabolism in the wheat pathogen Stagonospora nodorum

A reverse genetics approach was used to investigate the role of γ-aminobutyric acid metabolism in the wheat pathogenic fungus Stagonospora nodorum. The creation of mutants lacking Sdh1, the gene encoding succinic semialdehyde dehydrogenase, resulted in strains that grew poorly on γ-aminobutyric acid as a nitrogen source. The sdh1 mutants were more susceptible to reactive oxygen stress but were less affected by increased growth temperatures. Pathogenicity assays revealed that the metabolism of γ-aminobutyric acid is required for complete pathogenicity. Growth assays of the wild-type and mutant strains showed that the inclusion of γ-aminobutyric acid as a supplement in minimal media (i.e., not as a nitrogen or carbon source) resulted in restricted growth but increased sporulation. The addition of glutamate, the precursor to GABA, had no effect on either growth or sporulation. The γ-aminobutyric acid effect on sporulation was found to be dose dependent and not restricted to Stagonospora nodorum with a similar effect observed in the dothideomycete Botryosphaeria sp. The positive effect on sporulation was assayed using isomers of γ-aminobutyric acid and other metabolites known to influence asexual development in Stagonospora nodorum but no effect was observed. These data demonstrate that γ-aminobutyric acid plays an important role in Stagonospora nodorum in responding to environmental stresses while also having a positive effect on asexual development.The work was supported by Australian Research Council and Grains Research and Development Corporation

Arrangements in unitary and orthogonal geometry over finite fields

AbstractLet V be an n-dimensional vector space over Fq. Let Φ be a Hermitian form with respect to an automorphism σ with σ2 = 1. If σ = 1 assume that q is odd. Let A be the arrangement of hyperplanes of V which are non-isotropic with respect to Φ, and let L be the intersection lattice of A. We prove that the characteristic polynomial of L has n − v roots 1, q,…, qn − v− 1 where v is the Witt index of Φ

Langevin processes, agent models and socio-economic systems

We review some approaches to the understanding of fluctuations in some models used to describe socio and economic systems. Our approach builds on the development of a simple Langevin equation that characterises stochastic processes. This provides a unifying approach that allows first a straightforward description of the early approaches of Bachelier. We generalise the approach to stochastic equations that model interacting agents. Using a simple change of variable, we show that the peer pressure model of Marsilli and the wealth dynamics model of Solomon are closely related. The methods are further shown to be consistent with a global free energy functional that invokes an entropy term based on the Boltzmann formula. A more recent approach by Michael and Johnson maximised a Tsallis entropy function subject to simple constraints. We show how this approach can be developed from an agent model where the simple Langevin process is now conditioned by local rather than global noise. The approach yields a BBGKY type hierarchy of equations for the system correlation functions. Of especial interest is that the results can be obtained from a new free energy functional similar to that mentioned above except that a Tsallis like entropy term replaces the Boltzmann entropy term. A mean field approximation yields the results of Michael and Johnson. We show how personal income data for Brazil, the US, Germany and the UK, analysed recently by Borgas can be qualitatively understood by this approach.Comment: 1 figur