A Formally Kahler structure on a knot space of a G<sub>2</sub>-manifold
A knot space in a manifold M is a space of oriented immersions S1 ↪ M up to Diff(S 1). J.-L. Brylinski has shown that a knot space of a Riemannian threefold is formally Kähler. We prove that a space of knots in a holonomy G 2 manifold is formally Kähler.
We prove the existence of a rank-one pseudotoric structure on an arbitrary smooth toric symplectic manifold. As a consequence, we propose a method for constructing Chekanov-type nonstandard Lagrangian tori on arbitrary toric manifolds.
We prove that any compact Kahler 3-dimensional manifold which has no nontrivial complex subvarieties is a torus. This is a very special case of a general conjecture on the structure of so-called simple manifolds, central in the bimeromorphic classication of compact Kahler manifolds. The proof follows from the Brunella pseudo-eectivity theorem, combined with fundamental results of Siu and of the second author on the Le- long numbers of closed positive (1;1)-currents, and with a version of the hard Lefschetz theorem for pseudo-eective line bundles, due to Takegoshi and Demailly-Peternell- Schneider. In a similar vein, we show that a normal compact and Kahler 3-dimensional analytic space with terminal singularities and nef canonical bundle is a cyclic quotient of a simple nonprojective torus if it carries no eective divisor. This is a crucial step towards completing the bimeromorphic classication of compact Kahler threefolds.
A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.