An Optimal Skorokhod Embedding for Diffusions

Given a Brownian motion $B_t$ and a general target law $\mu$ (not necessarily centered or even integrable) we show how to construct an embedding of $\mu$ in $B$. This embedding is an extension of an embedding due to Perkins, and is optimal in the sense that it simultaneously minimises the distribution of the maximum and maximises the distribution of the minimum among all embeddings of $\mu$. The embedding is then applied to regular diffusions, and used to characterise the target laws for which a $H^p$-embedding may be found.Comment: 22 pages, 4 figure

Agenda Control in the Bundestag, 1980-2002

We find strong evidence of monopoly legislative agenda control by government parties in the Bundestag. First, the government parties have near-zero roll rates, while the opposition parties are often rolled over half the time. Second, only opposition parties’ (and not government parties’) roll rates increase with the distances of each party from the floor median. Third, almost all policy moves are towards the government coalition (the only exceptions occur during periods of divided government). Fourth, roll rates for government parties sky- rocket when they fall into the opposition and roll rates for opposition parties plummet when they enter government, while policy movements go from being nearly 100 per cent rightward when there is a rightist government to 100 per cent leftward under a leftist government

Calculating the inherent visual structure of a landscape (inherent viewshed) using high-throughput computing

This paper describes a method of calculating the inherent visibility at all locations in a landscape (‘total viewshed’) by making use of redundant computer cycles. This approach uses a simplified viewshed program that is suitable for use within a distributed environment, in this case managed by the Condor system. Distributing the calculation in this way reduced the calculation time of our example from an estimated 34 days to slightly over 25 hours using a cluster of 43 workstations. Finally, we discuss the example ‘total viewshed’ raster for the Avebury region, and briefly highlight some of its implications

Discrete solitons in electromechanical resonators

We consider a parametrically driven Klein--Gordon system describing micro- and nano-devices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear Schrodinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright and dark discrete solitons admitted by the Klein--Gordon system through the discrete Schrodinger equation. We show that a parametric driving can not only destabilize onsite bright solitons, but also stabilize intersite bright discrete solitons and onsite and intersite dark solitons. Most importantly, we show that there is a range of values of the driving coefficient for which dark solitons are stable, for any value of the coupling constant, i.e. oscillatory instabilities are totally suppressed. Stability windows of all the fundamental solitons are presented and approximations to the onset of instability are derived using perturbation theory, with accompanying numerical results. Numerical integrations of the Klein--Gordon equation are performed, confirming the relevance of our analysis