Periodic solutions to a mean-field model for electrocortical activity

We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic inputs. The coupling of these components is represented by sigmoidal and quadratic nonlinearities. We consider these equations on a square domain with periodic boundary conditions, in the vicinity of the primary transition from a stable equilibrium to time-periodic motion through an equivariant Hopf bifurcation. We compute part of a family of standing wave solutions, emanating from this point.Comment: 9 pages, 5 figure

Cantorian Infinity and Philosophical Concepts of God

It is often alleged that Cantor’s views about how the set theoretic universe as a whole should be considered are fundamentally unclear. In this article we argue that Cantor’s views on this subject, at least up until around 1896, are relatively clear, coherent, and interesting. We then go on to argue that Cantor’s views about the set theoretic universe as a whole have implications for theology that have hitherto not been sufficiently recognised. However, the theological implications in question, at least as articulated here, would not have satisfied Cantor himself

How inter-firm networks influence the development of agglomerations

Non-market interactions are increasingly regarded as key explanations for spatial concentration. Consistently, both innovation and local knowledge spillovers play a central role in recent theories of agglomeration. According to these theories, exchange of localised knowledge gives firms an innovative advantage which results in better economic performance. However, it has turned out to be difficult to open the black box of economies of scale using empirical tests.\ud Since interactions get considerable attention in recent agglomeration theory, social network methods and theory are promising approaches to research spatial agglomerations. Even more so because simultaneously, there is an increasing emphasis on interfirm ties in the network field.\ud The goal of our research is to explore how interfirm networks influence the development of agglomerations. Firstly we provide a review on network and innovation literature in the field of spatial clusters. Secondly, we discuss measurement issues related to networks and innovation and ways to overcome them. Finally, we present preliminary results of our network study among high tech firms in the Dutch region of Twente