Primordial magnetic seed field amplification by gravitational waves: comment on gr-qc/0503006

We consider the amplification of cosmological magnetic fields by gravitational waves as it was recently presented in [gr-qc/0503006]. That study confined to infinitely conductive environments, arguing that on spatially flat Friedmann backgrounds the gravito-magnetic interaction proceeds always as if the universe were a perfect conductor. We explain why this claim is not correct and then re-examine the Maxwell-Weyl coupling at the limit of ideal magnetohydrodynamics. We find that the scales of the main results of [gr-qc/0503006] were not properly assessed and that the incorrect scale assessment has compromised both the physical and the numerical results of the paper. This comment aims to clarify these issues on the one hand, while on the other it takes a closer look at the gauge-invariance and the nonlinearity of [gr-qc/0503006].Comment: Revised version, to appear in PR

Optimal Routing of Energy-aware Vehicles in Networks with Inhomogeneous Charging Nodes

We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed time for vehicles to reach their destinations considering both traveling and recharging times at nodes when the vehicles do not have adequate energy for the entire journey. We study two versions of the problem. In the single vehicle routing problem, we formulate a mixed-integer nonlinear programming (MINLP) problem and show that it can be reduced to a lower dimensionality problem by exploiting properties of an optimal solution. We also obtain a Linear Programming (LP) formulation allowing us to decompose it into two simpler problems yielding near-optimal solutions. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into "subflows". We also provide an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss in accuracy. Numerical results are included to illustrate these approaches.Comment: To appear in proceeding of 22nd Mediterranean Conference on Control and Automation, MED'1

Generalised Entropy MDPs and Minimax Regret

Bayesian methods suffer from the problem of how to specify prior beliefs. One interesting idea is to consider worst-case priors. This requires solving a stochastic zero-sum game. In this paper, we extend well-known results from bandit theory in order to discover minimax-Bayes policies and discuss when they are practical.Comment: 7 pages, NIPS workshop "From bad models to good policies