Existence and wandering of bumps in a spiking neural network model

We study spatially localized states of a spiking neuronal network populated by a pulse coupled phase oscillator known as the lighthouse model. We show that in the limit of slow synaptic interactions in the continuum limit the dynamics reduce to those of the standard Amari model. For non-slow synaptic connections we are able to go beyond the standard firing rate analysis of localized solutions allowing us to explicitly construct a family of co-existing one-bump solutions, and then track bump width and firing pattern as a function of system parameters. We also present an analysis of the model on a discrete lattice. We show that multiple width bump states can co-exist and uncover a mechanism for bump wandering linked to the speed of synaptic processing. Moreover, beyond a wandering transition point we show that the bump undergoes an effective random walk with a diffusion coefficient that scales exponentially with the rate of synaptic processing and linearly with the lattice spacing.

Enhancing composite Digital Documents Using XML-based Standoff Markup

Document representations can rapidly become unwieldy if they try to encapsulate all possible document properties, ranging from abstract structure to detailed rendering and layout. We present a composite document approach wherein an XMLbased document representation is linked via a shadow tree of bi-directional pointers to a PDF representation of the same document. Using a two-window viewer any material selected in the PDF can be related back to the corresponding material in the XML, and vice versa. In this way the treatment of specialist material such as mathematics, music or chemistry (e.g. via read aloud or play aloud ) can be activated via standard tools working within the XML representation, rather than requiring that application-specific structures be embedded in the PDF itself. The problems of textual recognition and tree pattern matching between the two representations are discussed in detail. Comparisons are drawn between our use of a shadow tree of pointers to map between document representations and the use of a code-replacement shadow tree in technologies such as XBL.