Solving Time Dependent Shortest Path Problems on Airway Networks Using Super-Optimal Wind

We study the Flight Planning Problem for a single aircraft, which deals with finding a path of minimal travel time in an airway network. Flight time along arcs is affected by wind speed and direction, which are functions of time. We consider three variants of the problem, which can be modeled as, respectively, a classical shortest path problem in a metric space, a time-dependent shortest path problem with piecewise linear travel time functions, and a time-dependent shortest path problem with piecewise differentiable travel time functions. The shortest path problem and its time-dependent variant have been extensively studied, in particular, for road networks. Airway networks, however, have different characteristics: the average node degree is higher and shortest paths usually have only few arcs. We propose A* algorithms for each of the problem variants. In particular, for the third problem, we introduce an application-specific "super-optimal wind" potential function that overestimates optimal wind conditions on each arc, and establish a linear error bound. We compare the performance of our methods with the standard Dijkstra algorithm and the Contraction Hierarchies (CHs) algorithm. Our computational results on real world instances show that CHs do not perform as well as on road networks. On the other hand, A* guided by our potentials yields very good results. In particular, for the case of piecewise linear travel time functions, we achieve query times about 15 times shorter than CHs

Guidelines for the diagnosis and management of cystathionine beta-synthase deficiency

Cystathionine beta-synthase (CBS) deficiency is a rare inherited disorder in the methionine catabolic pathway, in which the impaired synthesis of cystathionine leads to accumulation of homocysteine. Patients can present to many different specialists and diagnosis is often delayed. Severely affected patients usually present in childhood with ectopia lentis, learning difficulties and skeletal abnormalities. These patients generally require treatment with a low-methionine diet and/or betaine. In contrast, mildly affected patients are likely to present as adults with thromboembolism and to respond to treatment with pyridoxine. In this article, we present recommendations for the diagnosis and management of CBS deficiency, based on a systematic review of the literature. Unfortunately, the quality of the evidence is poor, as it often is for rare diseases. We strongly recommend measuring the plasma total homocysteine concentrations in any patient whose clinical features suggest the diagnosis. Our recommendations may help to standardise testing for pyridoxine responsiveness. Current evidence suggests that patients are unlikely to develop complications if the plasma total homocysteine concentration is maintained below 120 μmol/L. Nevertheless, we recommend keeping the concentration below 100 μmol/L because levels fluctuate and the complications associated with high levels are so serious