Optimization of Green-Times at an Isolated Urban Crossroads

We propose a model for the intersection of two urban streets. The traffic status of the crossroads is controlled by a set of traffic lights which periodically switch to red and green with a total period of T. Two different types of crossroads are discussed. The first one describes the intersection of two one-way streets, while the second type models the intersection of a two-way street with an one-way street. We assume that the vehicles approach the crossroads with constant rates in time which are taken as the model parameters. We optimize the traffic flow at the crossroads by minimizing the total waiting time of the vehicles per cycle of the traffic light. This leads to the determination of the optimum green-time allocated to each phase.Comment: 8 pages, 6 eps figures, more explanation added. To appear in EPJ

Asymptotics of Randomly Weighted u- and v-statistics: Application to Bootstrap

This paper is mainly concerned with asymptotic studies of weighted bootstrap for u- and v-statistics. We derive the consistency of the weighted bootstrap u- and v-statistics, based on i.i.d. and non i.i.d. observations, from some more general results which we first establish for sums of randomly weighted arrays of random variables. Some of the results in this paper significantly extend some well-known results on consistency of u-statistics and also consistency of sums of arrays of random variables. We also employ a new approach to conditioning to derive a conditional CLT for weighted bootstrap u- and v-statistics, assuming the same conditions as the classical central limit theorems for regular u- and v-statistics

Minimising the heat dissipation of quantum information erasure

Quantum state engineering and quantum computation rely on information erasure procedures that, up to some fidelity, prepare a quantum object in a pure state. Such processes occur within Landauer's framework if they rely on an interaction between the object and a thermal reservoir. Landauer's principle dictates that this must dissipate a minimum quantity of heat, proportional to the entropy reduction that is incurred by the object, to the thermal reservoir. However, this lower bound is only reachable for some specific physical situations, and it is not necessarily achievable for any given reservoir. The main task of our work can be stated as the minimisation of heat dissipation given probabilistic information erasure, i.e., minimising the amount of energy transferred to the thermal reservoir as heat if we require that the probability of preparing the object in a specific pure state $|\varphi_1\rangle$ be no smaller than $p_{\varphi_1}^{\max}-\delta$. Here $p_{\varphi_1}^{\max}$ is the maximum probability of information erasure that is permissible by the physical context, and $\delta\geqslant 0$ the error. To determine the achievable minimal heat dissipation of quantum information erasure within a given physical context, we explicitly optimise over all possible unitary operators that act on the composite system of object and reservoir. Specifically, we characterise the equivalence class of such optimal unitary operators, using tools from majorisation theory, when we are restricted to finite-dimensional Hilbert spaces. Furthermore, we discuss how pure state preparation processes could be achieved with a smaller heat cost than Landauer's limit, by operating outside of Landauer's framework