A Decomposition Algorithm to Solve the Multi-Hop Peer-to-Peer Ride-Matching Problem

In this paper, we mathematically model the multi-hop Peer-to-Peer (P2P) ride-matching problem as a binary program. We formulate this problem as a many-to-many problem in which a rider can travel by transferring between multiple drivers, and a driver can carry multiple riders. We propose a pre-processing procedure to reduce the size of the problem, and devise a decomposition algorithm to solve the original ride-matching problem to optimality by means of solving multiple smaller problems. We conduct extensive numerical experiments to demonstrate the computational efficiency of the proposed algorithm and show its practical applicability to reasonably-sized dynamic ride-matching contexts. Finally, in the interest of even lower solution times, we propose heuristic solution methods, and investigate the trade-offs between solution time and accuracy

Computer Generation of Metal Components by Simultaneous Deposition of Mould, Cores and Part

A new solid freeforming method based on co-delivery of mould powder materials and part powder materials using vibration-controlled, dry powder valves is presented in this paper. Thin layers of stainless steel powder are delivered to the forming area according to the cross-section of the CAD file to produce the component. Mould powder which has low sinterability is delivered to the non-forming areas of the same layer. All powders are delivered by computer-controlled, acoustic powder valves. The flow rate and switching of the valves provides the composition and shape control during fabrication. The stacked layers of loose powder are then sintered in a conventional furnace. The mould materials are removed after sintering. This method avoids the high thermal stress problem in selective laser sintering, avoids high capitalisation, makes use of conventional furnaces and allows for the incorporation of three dimensional function gradients. Test pieces including step wedge and Spierpinski’s cube were fabricated. Advantages, limitations and problems are discussed.Mechanical Engineerin

Extremal Charged Rotating Black Holes in Odd Dimensions

Employing higher order perturbation theory, we obtain charged rotating black holes in odd dimensions, where the Einstein-Maxwell Lagrangian may be supplemented with a Chern-Simons term. Starting from the Myers-Perry solutions, we use the electric charge as the perturbative parameter, and focus on extremal black holes with equal-magnitude angular momenta. For Einstein-Maxwell-Chern-Simons theory with arbitrary Chern-Simons coupling constant, we perform the perturbations up to third order for any odd dimension. We discuss the physical properties of these black holes and study their dependence on the charge. In particular, we show that the gyromagnetic ratio $g$ of Einstein-Maxwell black holes differs from the lowest order perturbative value $D-2$, and that the first correction term to $g/(D-2)$ is universal.Comment: 24 pages, 3 figure

Log-Euclidean Bag of Words for Human Action Recognition

Representing videos by densely extracted local space-time features has recently become a popular approach for analysing actions. In this paper, we tackle the problem of categorising human actions by devising Bag of Words (BoW) models based on covariance matrices of spatio-temporal features, with the features formed from histograms of optical flow. Since covariance matrices form a special type of Riemannian manifold, the space of Symmetric Positive Definite (SPD) matrices, non-Euclidean geometry should be taken into account while discriminating between covariance matrices. To this end, we propose to embed SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW approach to its Riemannian version. The proposed BoW approach takes into account the manifold geometry of SPD matrices during the generation of the codebook and histograms. Experiments on challenging human action datasets show that the proposed method obtains notable improvements in discrimination accuracy, in comparison to several state-of-the-art methods