title: Flexible memory networks.
abstract: Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks having the maximal number of flexible memory patterns, given a constraint graph on the network's connectivity matrix. Modulo a mild topological condition, we find a close connection between maximally flexible networks and rank 1 matrices. The topological condition is H                         (1)(X;ℤ)=0, where X is the clique complex associated to the network's constraint graph; this condition is generically satisfied for large random networks that are not overly sparse. In order to prove our main results, we develop some matrix-theoretic tools and present them in a self-contained section independent of the neuroscience context.
authors.affiliation: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, USA. ccurto2@math.unl.edu
authors.forename: Carina
authors.initials: C
authors.lastname: Curto
authors.forename: Anda
authors.initials: A
authors.lastname: Degeratu
authors.forename: Vladimir
authors.initials: V
authors.lastname: Itskov
mesh_terms: D006801:Humans; D007858:Learning / Q000502:physiology; D008568:Memory / Q000502:physiology*; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology