Aspects of open-flavour mesons in a comprehensive DSBSE study

Open-flavour meson studies are the necessary completion to any comprehensive investigation of quarkonia. We extend recent studies of quarkonia in the Dyson-Schwinger-Bethe-Salpeter-equation approach to explore their results for all possible flavour combinations. Within the inherent limitations of the setup, we present the most comprehensive results for meson masses and leptonic decay constants currently available and put them in perspective with respect to experiment and other approaches.Comment: 38 pages, 26 figures, 2 tables, revised according to reviewer comment

Optimal Wind Farm Cabling

Wind farm cable length has a direct impact on the project cost, reliability and electrical losses. The optimum cable layout results in a lower unit cost of generating electricity offshore. This paper explores three cabling structures: the string structure, ring structures and multi-loop structure on a 3D seabed. The newly proposed multi-loop structure increases reliability and proves to be most economic when the failure rate and mean time to repair (MTTR) of cables are relatively high. Particle swarm optimization (PSO) is used to find the optimal substation location that minimizes the overall cable distance

Hessian barrier algorithms for linearly constrained optimization problems

In this paper, we propose an interior-point method for linearly constrained optimization problems (possibly nonconvex). The method - which we call the Hessian barrier algorithm (HBA) - combines a forward Euler discretization of Hessian Riemannian gradient flows with an Armijo backtracking step-size policy. In this way, HBA can be seen as an alternative to mirror descent (MD), and contains as special cases the affine scaling algorithm, regularized Newton processes, and several other iterative solution methods. Our main result is that, modulo a non-degeneracy condition, the algorithm converges to the problem's set of critical points; hence, in the convex case, the algorithm converges globally to the problem's minimum set. In the case of linearly constrained quadratic programs (not necessarily convex), we also show that the method's convergence rate is $\mathcal{O}(1/k^\rho)$ for some $\rho\in(0,1]$ that depends only on the choice of kernel function (i.e., not on the problem's primitives). These theoretical results are validated by numerical experiments in standard non-convex test functions and large-scale traffic assignment problems.Comment: 27 pages, 6 figure

Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations

This paper introduces a new mobile sensor scheduling problem, involving a single robot tasked with monitoring several events of interest that occur at different locations. Of particular interest is the monitoring of transient events that can not be easily forecast. Application areas range from natural phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano using a ground robot) to urban activities ({\em e.g.}, monitoring early formations of traffic congestion using an aerial robot). Motivated by those and many other examples, this paper focuses on problems in which the precise occurrence times of the events are unknown {\em a priori}, but statistics for their inter-arrival times are available. The robot's task is to monitor the events to optimize the following two objectives: {\em (i)} maximize the number of events observed and {\em (ii)} minimize the delay between two consecutive observations of events occurring at the same location. The paper considers the case when a robot is tasked with optimizing the event observations in a balanced manner, following a cyclic patrolling route. First, assuming the cyclic ordering of stations is known, we prove the existence and uniqueness of the optimal solution, and show that the optimal solution has desirable convergence and robustness properties. Our constructive proof also produces an efficient algorithm for computing the unique optimal solution with $O(n)$ time complexity, in which $n$ is the number of stations, with $O(\log n)$ time complexity for incrementally adding or removing stations. Except for the algorithm, most of the analysis remains valid when the cyclic order is unknown. We then provide a polynomial-time approximation scheme that gives a $(1+\epsilon)$-optimal solution for this more general, NP-hard problem

Automated Design of a High-Velocity Channel

Engineering design is a decision-making process. Optimization techniques can be used to insure that better decisions are made. One design of great interest to engineers is that of high-velocity channels used for routing floodwater out of urban areas. In the design of these channels it is very important to avoid such hydraulic phenomena as standing waves, hydraulic jumps, and shocks. These will require higher wall heights and more expense. These channels can be modeled with physical models, but they are expensive and time consuming. To minimize the cost of building and changing the physical models and the time required to perform the study, an automated numerical model can be used to test a range of designs before construction of the physical model. The resulting design can be used as an initial design, which is close to the desired design requiring fewer changes to the physical model, saving time and money