Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

Executive control in bilinguals: a concise review on fMRI studies

The investigation of bilingualism and cognition has been enriched by recent developments in functional magnetic resonance imaging (fMRI). Extending how bilingual experience shapes cognition, this review examines recent fMRI studies adopting executive control tasks with minimal or no linguistic demands. Across a range of studies with divergent ages and language pairs spoken by bilinguals, brain regions supporting executive control significantly overlap with brain regions recruited for language control (Abutalebi & Green, this issue). Furthermore, limited but emerging studies on resting-state networks are addressed, which suggest more coherent spatially distributed functional connectivity in bilinguals. Given the dynamic nature of bilingual experience, it is essential to consider both task-related functional networks (externally-driven engagement), and resting-state networks, such as default mode network (internal control). Both types of networks are important elements of bilingual language control, which relies on domain-general executive control.