New results in rho^0 meson physics

We compare the predictions of a range of existing models based on the Vector Meson Dominance hypothesis with data on e^+ e^- -> pi^+ pi^$ and e^+ e^- -> mu^+ mu^- cross-sections and the phase and near-threshold behavior of the timelike pion form factor, with the aim of determining which (if any) of these models is capable of providing an accurate representation of the full range of experimental data. We find that, of the models considered, only that proposed by Bando et al. is able to consistently account for all information, provided one allows its parameter "a" to vary from the usual value of 2 to 2.4. Our fit with this model gives a point-like coupling (gamma pi^+ \pi^-) of magnitude ~ -e/6, while the common formulation of VMD excludes such a term. The resulting values for the rho mass and pi^+ pi^- and e^+e^- partial widths as well as the branching ratio for the decay omega -> pi^+ pi^- obtained within the context of this model are consistent with previous results.Comment: 34 pages with 7 figures. Published version also available at http://link.springer.de/link/service/journals/10052/tocs/t8002002.ht

Generalized Shortest Path Kernel on Graphs

We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification problem, we consider the task of classifying random graphs from two well-known families, by the number of clusters they contain. We verify empirically that the generalized shortest path kernel outperforms the original shortest path kernel on a number of datasets. We give a theoretical analysis for explaining our experimental results. In particular, we estimate distributions of the expected feature vectors for the shortest path kernel and the generalized shortest path kernel, and we show some evidence explaining why our graph kernel outperforms the shortest path kernel for our graph classification problem.Comment: Short version presented at Discovery Science 2015 in Banf

Non-meanfield deterministic limits in chemical reaction kinetics far from equilibrium

A general mechanism is proposed by which small intrinsic fluctuations in a system far from equilibrium can result in nearly deterministic dynamical behaviors which are markedly distinct from those realized in the meanfield limit. The mechanism is demonstrated for the kinetic Monte-Carlo version of the Schnakenberg reaction where we identified a scaling limit in which the global deterministic bifurcation picture is fundamentally altered by fluctuations. Numerical simulations of the model are found to be in quantitative agreement with theoretical predictions.Comment: 4 pages, 4 figures (submitted to Phys. Rev. Lett.

Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 large-theory mathematical problems is constructed,extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE state-of-the-art system for automated reasoning in large theories.Comment: 26 page

Largeness and SQ-universality of cyclically presented groups

Largeness, SQ-universality, and the existence of free subgroups of rank 2 are measures of the complexity of a finitely presented group. We obtain conditions under which a cyclically presented group possesses one or more of these properties. We apply our results to a class of groups introduced by Prishchepov which contains, amongst others, the various generalizations of Fibonacci groups introduced by Campbell and Robertson

Higher Partial Waves in p+p->p+p+eta near Threshold

Exclusive measurements of the production of eta mesons in the p+p->p+p+eta reaction have been carried out at excess energies of 16 and 37 MeV above threshold. The deviations from phase space are dominated by the proton-proton final state interaction and this influences particularly the energy distribution of the eta meson. However, evidence is also presented at the higher energy for the existence of an anisotropy in the angular distributions of the eta meson and also of the final proton-proton pair, probably to be associated with D-waves in this system interfering with the dominant S-wave term. The sign of the eta angular anisotropy suggests that rho-exchange is important for this reaction.Comment: 16 pages, LaTeX2e, 3 EPS Figures, Updated version, Accepted for publication in Phys. Lett.