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We consider a generalisation of the birthday problem that arises in the analysis of algorithms for certain variants of the discrete logarithm problem in groups. More precisely, we consider sampling coloured balls and placing them in urns, such that the distribution of assigning balls to urns depends on the colour of the ball. We determine the expected(More)
This paper addresses the problem of designing stabilizing controllers that minimize the 7-l ~ norm of a certain closed-loop transfer function while maintaining the C1 norm of a different transfer function below a prespecified level. This problem arises in the context of rejecting both stochastic as well as bounded persistent disturbances. Alternatively, in(More)
We demonstrate triggered single photon emission at room temperature from a site-controlled III-nitride quantum dot embedded in a nanowire. Moreover, we reveal a remarkable temperature insensitivity of the single photon statistics, and a g((2))[0] value at 300 K of just 0.13. The combination of using high-quality, small, site-controlled quantum dots with a(More)
The paper presents a transient analysis technique for point contact elastohydrodynamic (EHL) lubrication problems using coupled elastic and hydrodynamic equations. Full coupling is made possible by use of a novel differential de¯ection formulation. The way in which the differential de¯ection is incorporated into the overall solution method for a point(More)
We use the lace expansion to analyse networks of mutually-avoiding self-avoiding walks, having the topology of a graph. The networks are defined in terms of spread-out self-avoiding walks that are permitted to take large steps. We study the asymptotic behaviour of networks in the limit of widely separated network branch points, and prove Gaussian behaviour(More)