A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

Book Review "Selling sex: a hidden history of prostitution", R. Frances, UNSW Press, Sydney, 2007

In the opening pages of Selling Sex we are introduced to 'Joy', a statue of a young female sex worker which stood in East Sydney for eighteen months during 1995- 1997. Following complaints by local residents, the statue was removed from public view and returned to its owner. Evidently, Joy was considered a reminder of the community's 'bad old days', when it was better known for prostitution than restaurants. In a nation in which almost every sizable community has proudly erected monuments to military men, the removal of Joy reveals much about labour and gender relations in Australia. For Frances, the removal of Joy is symbolic, our historical treatment of sex workers having parallels with our treatment of the convicts. This work sets out to give these women (male prostitutes do not figure in this history) a voice and break with the stereotypes of 'abandoned whores' or 'sad victims'. It also sets out to place the sex industry in the broader national and international context in which it has historically operated...