The perfect integrator driven by Poisson input and its approximation in the diffusion limit

In this note we consider the perfect integrator driven by Poisson process input. We derive its equilibrium and response properties and contrast them to the approximations obtained by applying the diffusion approximation. In particular, the probability density in the vicinity of the threshold differs, which leads to altered response properties of the system in equilibrium.Comment: 7 pages, 3 figures, v2: corrected authors in referenc

Higher class field theory and the connected component

Abstract. In this note we present a new self-contained approach to the class field theory of arithmetic schemes in the sense of Wiesend. Along the way we prove new results on space filling curves on arithmetic schemes and on the class field theory of local rings. We show how one can deduce the more classical version of higher global class field theory due to Kato and Saito from Wiesend’s version. One of our new result says that the connected component of the identity element in Wiesend’s class group is divisible if some obstruction is absent