Please note the earlier than usual start-time!
We investigate the behaviour of free-surface waves on time-varying potential flow in the limit as the Froude number becomes small. These waves are exponentially small in the Froude number, and are therefore inaccessible to ordinary asymptotic methods. As such, we demonstrate how exponential asymptotic techniques may be applied to the complexified free surface in order to extract information about the wave behaviour on the free surface, using a Lagrangian form of the potential flow equations. We consider the specific case of time-varying flow over a step, and demonstrate that the results are consistent with the steady state case.
We
explore two different threading approaches on a graphics processing
unit (GPU) exploiting two different characteristics of the current GPU
architecture. The fat thread approach tries to minimise data access time
by relying on shared memory and registers potentially sacrificing
parallelism. The thin thread approach maximises parallelism and tries to
hide access latencies. We apply these two approaches to the parallel
stochastic simulation of chemical reaction systems using the stochastic
simulation algorithm (SSA) by Gillespie. In these cases, the proposed
thin thread approach shows comparable performance while eliminating the
limitation of the reaction system's size.
Link to paper:
This talk highlights the role of Gaussian Process models in sequential
data analysis. Issues of active data selection, global optimisation,
sensor selection and prediction in the presence of changepoints are
discussed.
An agent is presented with an N Bandit (Fruit) machines. It is assumed that each machine produces successes or failures according to some fixed, but unknown Bernoulli distribution. If the agent plays for ever, how can he/she choose a strategy that ensures the average successes observed tend to the parameter of the "best" arm?
Alternatively suppose that the agent recieves a reward of a^n at the nth button press for a success, and 0 for a failure; now how can the agent choose a strategy to optimise his/her total expected rewards over all time? These are two examples of classic Bandit Problems.
We analyse the behaviour of two strategies, the Narendra Algorithm and the Gittins Index Strategy. The Narendra Algorithm is a "learning"
strategy, in that it answers the first question in the above paragraph, and we demonstrate this remains true when the sequences of success and failures observed on the machines are no longer i.i.d., but merely satisfy an ergodic condition. The Gittins Index Strategy optimises the reward stream given above. We demonstrate that this strategy does not "learn" and give some new explicit bounds on the Gittins Indices themselves.
We solve the problem of static hedging of (upper) barrier options (we concentrate on up-and-out put, but show how the other cases follow from this one) in models where the underlying is given by a time-homogeneous diffusion process with, possibly, independent stochastic time-change.
The main result of the paper includes analytic expression for the payoff of a (single) European-type contingent claim (which pays a certain function of the underlying value at maturity, without any pathdependence),
such that it has the same price as the barrier option up until hitting the barrier. We then consider some examples, including the Black-Scholes, CEV and zero-correlation SABR models, and investigate an approximation of the exact static hedge with two vanilla (call and put) options.