A simulation model for public bike-sharing systems

Urban areas are in need of efficient and sustainable mobility services. Public bicycle sharing systems stand out as a promising alternative and many cities have invested in their deployment. This has led to a continuous and fast implementation of these systems around the world, while at the same time, research works devoted to understand the system dynamics and deriving optimal designs are being developed. In spite of this, many promoting agencies have faced the impossibility of evaluating a system design in advance, increasing the uncertainty on its performance and the risks of failure. This paper describes the development of an agent-based simulation model to emulate a bike-sharing system. The goal is to obtain a tool to evaluate and compare different alternatives for the system design before their implementation. This tool will support the decision-making process in all the stages of implementation, from the strategical planning to the daily operation. The main behavioral patterns and schemes for all agents involved are designed and implemented into a Matlab programming code. The model is validated against real data compiled from the Barcelona’s Bicing system showing good accuracy.Postprint (published version

Resolvent estimates for the magnetic Schr\"odinger operator in dimension n≥2n \geq 2

It is well known that the resolvent of the free Schr\"odinger operator on weighted $L^2$ spaces has norm decaying like $\lambda^{-\frac{1}{2}}$ at energy $\lambda$. There are several works proving analogous high-frequency estimates for magnetic Schr\"odinger operators, with large long or short range potentials, in dimensions $n \geq 3$. We prove that the same estimates remain valid in all dimensions $n \geq 2$.Comment: 21 page

Fixed angle scattering: Recovery of singularities and its limitations

We prove that in dimension n ≥ 2 the main singularities of a complex potential q having a certain a priori regularity are contained in the Born approximation qθ constructed from fixed angle scattering data. Moreover, q-qθ can be up to one derivative more regular than q in the Sobolev scale. In fact, this result is optimal. We construct a family of compactly supported and radial potentials for which it is not possible to have more than one derivative gain. Also, these functions show that for n > 3, the maximum derivative gain can be very small for potentials in the Sobolev scale not having a certain a priori level of regularity which grows with the dimension.The author was supported by Spanish government predoctoral grant BES-2015- 074055 (project MTM2014-57769-C3-1-P

Simulation of left-right asymmetry in heart morphogenesis

There are several studies on the heart morphogenesis in the vertebrate embryo, and in particular on how during the development of the heart tube bilateral symmetry is broken leading to morphogenesis with left-right asymmetry. Despite clinical and experimental findings, it is still not entirely clear how left-right patterning drives asymmetric morphogenesis, as the focus has generally been on a simple description of the direction of the loop. One way to overcome the conundrums in clinical research is to use predictive computational models to help explore shape variations during heart development, depending on the congenital anomaly to be studied. Heterotaxy, as a set of pathologies affecting the spatial structure of the heart due to left-right asymmetry (among others), can lead to cardiovascular diseases, so it is of particular relevance to find the origin of this anomaly and the different configurations that can lead to its emergence. One of them is known as "Transposition of the great arteries (TGA)" and is suspected to be due to a twist of the outflow tract (OFT) during morphogenesis. For this study we aimed to predict, through computational simulations and using discretization and finite element meshing methods, the morphogenesis of a heart model developed after the heart tube loop when the OFT region does not grow, mainly using the quantification of the twist angle. The results provide an insight into the mechanism of the cardiac loop, where the flipping tendency is to the right leading to a re-organization of the ventricles as the first finding. This is relevant for congenital heart defects as well as for the estimation of the left-right pattern in the morphogenesis of the heart in order to get a better classification in the different classes of heterotaxy syndrome.Incomin