Computing with infinite networks

For neural networks with a wide class of weight-priors, it can be shown that in the limit of an infinite number of hidden units the prior over functions tends to a Gaussian process. In this paper analytic forms are derived for the covariance function of the Gaussian processes corresponding to networks with sigmoidal and Gaussian hidden units. This allows predictions to be made efficiently using networks with an infinite number of hidden units, and shows that, somewhat paradoxically, it may be easier to compute with infinite networks than finite ones.

Inequality, fiscal capacity and the political regime: lessons from the post-communist transition

Using panel data for twenty-seven post-communist economies between 1987-2003, we examine the nexus of relationships between inequality, fiscal capacity (defined as the ability to raise taxes efficiently) and the political regime. Investigating the impact of political reform we find that full political freedom is associated with lower levels of income inequality. Under more oligarchic (authoritarian) regimes, the level of inequality is conditioned by the state’s fiscal capacity. Specifically, oligarchic regimes with more developed fiscal systems are able to defend the prevailing vested interests at a lower cost in terms of social injustice. This empirical finding is consistent with the model developed by Acemoglu (2006). We also find that transition countries undertaking early macroeconomic stabilisation now enjoy lower levels of inequality; we confirm that education fosters equality and the suggestion of Commander et al (1999) that larger countries are prone to higher levels of inequality.

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.