title: Developing structural constraints on connectivity for biologically embedded neural networks.
abstract: In this article, we analyse under which conditions an abstract model of connectivity could actually be embedded geometrically in a mammalian brain. To this end, we adopt and extend a method from circuit design called Rent's Rule to the highly branching structure of cortical connections. Adding on recent approaches, we introduce the concept of a limiting Rent characteristic that captures the geometrical constraints of a cortical substrate on connectivity. We derive this limit for the mammalian neocortex, finding that it is independent of the species qualitatively as well as quantitatively. In consequence, this method can be used as a universal descriptor for the geometrical restrictions of cortical connectivity. We investigate two widely used generic network models: uniform random and localized connectivity, and show how they are constrained by the limiting Rent characteristic. Finally, we discuss consequences of these restrictions on the development of cortex-size models.
authors.affiliation: Highly Parallel VLSI Systems and Neuromorphic Circuits, Institute of Circuits and Systems, Faculty of Electrical Engineering and Information Technology, Technische Universität Dresden, Dresden, Germany, partzsch@iee.et.tu-dresden.de.
authors.forename: Johannes
authors.initials: J
authors.lastname: Partzsch
authors.forename: René
authors.initials: R
authors.lastname: Schüffny
mesh_terms: D009415:Nerve Net; D016571:Neural Networks, Computer