Generalized Convolution Roots of Positive Definite Kernels on Complex Spheres

Convolution is an important tool in the construction of positive definite kernels on a manifold. This contribution provides conditions on an $L^2$-positive definite and zonal kernel on the unit sphere of $\mathbb{C}^q$ in order that the kernel can be recovered as a generalized convolution root of an equally positive definite and zonal kernel

A logic for n-dimensional hierarchical refinement

Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high level states into inner sub-states, and of their transitions into inner sub-transitions is common refinement procedure adopted in a number of specification formalisms. This paper introduces a hybrid modal logic for k-layered transition systems, its first-order standard translation, a notion of bisimulation, and a modal invariance result. Layered and hierarchical notions of refinement are also discussed in this setting.Comment: In Proceedings Refine'15, arXiv:1606.0134

Dominant feedback : concepts, algorithms and convergence

Imperial Users onl

The solar siblings in the Gaia era

We perform realistic simulations of the Sun's birth cluster in order to predict the current distribution of solar siblings in the Galaxy. We study the possibility of finding the solar siblings in the Gaia catalogue by using only positional and kinematic information. We find that the number of solar siblings predicted to be observed by Gaia will be around 100 in the most optimistic case, and that a phase space only search in the Gaia catalogue will be extremely difficult. It is therefore mandatory to combine the chemical tagging technique with phase space selection criteria in order to have any hope of finding the solar siblings.Comment: To be published in the proceedings of the GREAT-ITN conference "The Milky Way Unravelled by Gaia: GREAT Science from the Gaia Data Releases", 1-5 December 2014, University of Barcelona, Spain, EAS Publications Series, eds Nicholas Walton, Francesca Figueras, and Caroline Soubira