Planar cell polarity (PCP) signaling controls the polarization of cells within the plane of an epithelium. Two molecular modules composed of Fat(Ft)/Dachsous(Ds)/Four-jointed(Fj) and a ‘PCP-core’ including Frizzled(Fz) and Dishevelled(Dsh) contribute to polarization of individual cells. How polarity is globally coordinated with tissue axes is unresolved. Consistent with previous results, we find that the Ft/Ds/Fj-module has an effect on a MT-cytoskeleton. Here, we provide evidence for the model that the Ft/Ds/Fj-module provides directional information to the core-module through this MT organizing function. We show Ft/Ds/Fj-dependent initial polarization of the apical MT-cytoskeleton prior to global alignment of the core-module, reveal that the anchoring of apical non-centrosomal MTs at apical junctions is polarized, observe that directional trafficking of vesicles containing Dsh depends on Ft, and demonstrate the feasibility of this model by mathematical simulation. Together, these results support the hypothesis that Ft/Ds/Fj provides a signal to orient core PCP function via MT polarization.DOI: http://dx.doi.org/10.7554/eLife.02893.001

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Abstract-Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations such as package delivery, firefighting, and fast disaster response. As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously in the airspace, in order to ensure their liveness and safety requirements are met. Hamilton-Jacobi (HJ) reachability is a powerful framework for providing conditions under which these requirements can be met, and for synthesizing the optimal controller for meeting them. However, due to the curse of dimensionality, HJ reachability is only tractable for a small number of vehicles if their set of maneuvers is unrestricted. In this paper, we define a platoon to be a group of UAVs in a single-file formation. We model each vehicle as a hybrid system with modes corresponding to its role in the platoon, and specify the set of allowed maneuvers in each mode to make the analysis tractable. We propose several liveness controllers based on HJ reachability, and wrap a safety controller, also based on HJ reachability, around the liveness controllers. For a single altitude range, our approach guarantees safety for one safety breach; in the unlikely event of multiple safety breaches, safety can be guaranteed over multiple altitude ranges. We demonstrate the satisfaction of liveness and safety requirements through simulations of three common scenarios.

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Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations. As a result, unmanned aerial systems traffic management is needed to ensure the safety and goal satisfaction of potentially thousands of UAVs flying simultaneously. Currently, the analysis of large multi-agent systems cannot tractably provide these guarantees if the agents' set of maneuvers is unrestricted. In this paper, platoons of UAVs flying on air highways is proposed to impose an airspace structure that allows for tractable analysis. For the air highway placement problem, the fast marching method is used to produce a sequence of air highways that minimizes the cost of flying from an origin to any destination. The placement of air highways can be updated in real-time to accommodate sudden airspace changes. Within platoons traveling on air highways, each vehicle is modeled as a hybrid system. Using Hamilton-Jacobi reachability, safety and goal satisfaction are guaranteed for all mode transitions. For a single altitude range, the proposed approach guarantees safety for one safety breach per vehicle; in the unlikely event of multiple safety breaches, safety can be guaranteed over multiple altitude ranges. We demonstrate the platooning concept through simulations of three representative scenarios.