AM with Multiple Merlins

We introduce and study a new model of interactive proofs: AM(k), or Arthur-Merlin with k non-communicating Merlins. Unlike with the better-known MIP, here the assumption is that each Merlin receives an independent random challenge from Arthur. One motivation for this model (which we explore in detail) comes from the close analogies between it and the quantum complexity class QMA(k), but the AM(k) model is also natural in its own right. We illustrate the power of multiple Merlins by giving an AM(2) protocol for 3SAT, in which the Merlins' challenges and responses consist of only n^{1/2+o(1)} bits each. Our protocol has the consequence that, assuming the Exponential Time Hypothesis (ETH), any algorithm for approximating a dense CSP with a polynomial-size alphabet must take n^{(log n)^{1-o(1)}} time. Algorithms nearly matching this lower bound are known, but their running times had never been previously explained. Brandao and Harrow have also recently used our 3SAT protocol to show quasipolynomial hardness for approximating the values of certain entangled games. In the other direction, we give a simple quasipolynomial-time approximation algorithm for free games, and use it to prove that, assuming the ETH, our 3SAT protocol is essentially optimal. More generally, we show that multiple Merlins never provide more than a polynomial advantage over one: that is, AM(k)=AM for all k=poly(n). The key to this result is a subsampling theorem for free games, which follows from powerful results by Alon et al. and Barak et al. on subsampling dense CSPs, and which says that the value of any free game can be closely approximated by the value of a logarithmic-sized random subgame.Comment: 48 page

Motion Hub, the implementation of an integrated end-to-end journey planner

© AET 2018 and contributorsThe term “eMobility” and been brought into use partly to encourage use of electric vehicles but more especially to focus on the transformation from electric vehicles as products to electrified personal transport as a service. Under the wider umbrella of Mobility-as-a-Service (MaaS) this has accompanied the growth of car clubs in general. The Motion Hub project has taken this concept a step further to include not just the car journey but the end-to-end journey. The booking of multifaceted journeys is well established in the leisure and business travel industries, where flights, car hire and hotels are regularly booked with a single transaction on a website. To complete an end-to-end scenario Motion Hub provides integration of public transport with electric vehicle and electric bike use. Building on a previous InnovateUK funded project that reviewed the feasibility of an integrated journey management system, the Motion Hub project has brought together a Car Club, a University, and EV infrastructure company, a bicycle hire company with electric bicycle capabilities and a municipality to implement a scheme and test it on the ground. At the heart of the project has been the development of a website that integrates the public transport booking with the hire of electric vehicles or bicycles. Taking the implementation to a fully working system accessible to members of the public presents a number of significant challenges. This paper identifies those challenges, details the progress and success of the Motion Hub and sets out the lessons learnt about end-to-end travel. The project was fortunate to have as its municipal partner the Council of a sizeable South East England town, Southend-on-Sea. With a population of 174,800 residents with good road, rail and air links there is considerable traffic in and out of the town. The Council has already shown its commitment to sustainable transport. In the previous six years it had installed a number of electric vehicle charging points for use by the public and latterly had trialled car club activity. An early challenge in the project was the location of physical infrastructure in an already crowded municipal space in order to provide the local ‘spokes’ of the system. In addition to its existing charging points, Southend now has four locations where electric cars can be hired, five where electric bikes are available and the local resources to maintain these assets. Combining a number of web-based services and amalgamating their financial transactions is relatively straightforward. However, introducing the potential for public transport ticketing as well raises additional security, scale and financial constraints. The project has engaged with major players and regulators across the public transport industry.Peer reviewe

Varying the Abundance of O Antigen in \u3cem\u3eRhizobium etli\u3c/em\u3e and Its Effect on Symbiosis with \u3cem\u3ePhaseolus vulgaris\u3c/em\u3e

Judged by migration of its lipopolysaccharide (LPS) in gel electrophoresis, the O antigen of Rhizobium etli mutant strain CE166 was apparently of normal size. However, its LPS sugar composition and staining of the LPS bands after electrophoresis indicated that the proportion of its LPS molecules that possessed O antigen was only 40% of the wild-type value. Its LPS also differed from the wild type by lacking quinovosamine (2-amino-2,6-dideoxyglucose). Both of these defects were due to a single genetic locus carrying a Tn5 insertion. The deficiency in O-antigen amount, but not the absence of quinovosamine, was suppressed by transferring into this strain recombinant plasmids that shared a 7.8-kb stretch of the R. etli CE3 lps genetic region α, even though this suppressing DNA did not carry the genetic region mutated in strain CE166. Strain CE166 gave rise to pseudonodules on legume host Phaseolus vulgaris, whereas the mutant suppressed by DNA from lps region α elicited nitrogen-fixing nodules. However, the nodules in the latter case developed slowly and were widely dispersed. Two other R. etli mutants that had one-half or less of the normal amount of O antigen also gave rise to pseudonodules on P. vulgaris. The latter strains were mutated in lps region α and could be restored to normal LPS content and normal symbiosis by complementation with wild-type DNA from this region. Hence, the symbiotic role of LPS requires near-normal abundance of O antigen and may require a structural feature conferred by quinovosamin