We discuss the difficulties that background independent theories based on quantum geometry encounter in deriving general relativity as the low energy limit. We follow a geometrogenesis scenario of a phase transition from a pre-geometric theory to a geometric phase which suggests that a first step towards the low energy limit is searching for the effective collective excitations that will charac...

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable und...

If we look at Frobenius’s theorem, this suggests that we should focus on the subgroups of a fixed Sylow p-subgroup P , and all of the conjugation maps cg for the various g ∈ G between the subgroups of P . Often, if g ∈ G and Q 6 P , Q · cg = Q does not lie inside P , and so we simply ignore those maps, and only keep the ones where both the domain and the image are inside P . This leads us to de...

We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show ho...

With the unprecedented proliferation of high-speed communication services many people will have high-speed access to virtually unlimited amounts of information in many forms of media. A tremendous amount of research effort is being applied to the problems of how to provide these multi-media services to tens and hundreds of thousands of concurrent users. The I/O problems alone are significant an...