Higher order numerical methods for solving fractional differential equations

The final publication is available at Springer via http://dx.doi.org/10.1007/s10543-013-0443-3In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 0. The order of convergence of the numerical method is O(h^3) for α ≥ 1 and O(h^(1+2α)) for 0 < α ≤ 1 for sufficiently smooth solutions. Numerical examples are given to show that the numerical results are consistent with the theoretical results

Does congenital deafness affect the structural and functional architecture of primary visual cortex?

Deafness results in greater reliance on the remaining senses. It is unknown whether the cortical architecture of the intact senses is optimized to compensate for lost input. Here we performed widefield population receptive field (pRF) mapping of primary visual cortex (V1) with functional magnetic resonance imaging (fMRI) in hearing and congenitally deaf participants, all of whom had learnt sign language after the age of 10 years. We found larger pRFs encoding the peripheral visual field of deaf compared to hearing participants. This was likely driven by larger facilitatory center zones of the pRF profile concentrated in the near and far periphery in the deaf group. pRF density was comparable between groups, indicating pRFs overlapped more in the deaf group. This could suggest that a coarse coding strategy underlies enhanced peripheral visual skills in deaf people. Cortical thickness was also decreased in V1 in the deaf group. These findings suggest deafness causes structural and functional plasticity at the earliest stages of visual cortex