Colouring the Triangles Determined by a Point Set

Let P be a set of n points in general position in the plane. We study the chromatic number of the intersection graph of the open triangles determined by P. It is known that this chromatic number is at least n^3/27+O(n^2), and if P is in convex position, the answer is n^3/24+O(n^2). We prove that for arbitrary P, the chromatic number is at most n^3/19.259+O(n^2)

Searching for a Solution to Program Verification=Equation Solving in CCS

International audienceUnder non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for equilibrium stopping policies, formulated as fixed points of an operator. Under appropriate conditions, fixed-point iterations converge to equilibrium stopping policies. This iterative approach corresponds to the hierarchy of strategic reasoning in game theory and provides “agent-specific” results: it assigns one specific equilibrium stopping policy to each agent according to her initial behavior. In particular, it leads to a precise mathematical connection between the naive behavior and the sophisticated one. Our theory is illustrated in a real options model

Environmental sensitivity of n-i-n and undoped single GaN nanowire photodetectors

In this work, we compare the photodetector performance of single defect-free undoped and n-in GaN nanowires (NWs). In vacuum, undoped NWs present a responsivity increment, nonlinearities and persistent photoconductivity effects (~ 100 s). Their unpinned Fermi level at the m-plane NW sidewalls enhances the surface states role in the photodetection dynamics. Air adsorbed oxygen accelerates the carrier dynamics at the price of reducing the photoresponse. In contrast, in n-i-n NWs, the Fermi level pinning at the contact regions limits the photoinduced sweep of the surface band bending, and hence reduces the environment sensitivity and prevents persistent effects even in vacuum