Using SVG as the Rendering Model for Structured and Graphically Complex Web Material

This paper reports some experiments in using SVG (Scalable Vector Graphics), rather than the browser default of (X)HTML/CSS, as a potential Web-based rendering technology, in an attempt to create an approach that integrates the structural and display aspects of a Web document in a single XML-compliant envelope. Although the syntax of SVG is XML based, the semantics of the primitive graphic operations more closely resemble those of page description languages such as PostScript or PDF. The principal usage of SVG, so far, is for inserting complex graphic material into Web pages that are predominantly controlled via (X)HTML and CSS. The conversion of structured and unstructured PDF into SVG is discussed. It is found that unstructured PDF converts into pages of SVG with few problems, but difficulties arise when one attempts to map the structural components of a Tagged PDF into an XML skeleton underlying the corresponding SVG. These difficulties are not fundamentally syntactic; they arise largely because browsers are innately bound to (X)HTML/CSS as their default rendering model. Some suggestions are made for ways in which SVG could be more totally integrated into browser functionality, with the possibility that future browsers might be able to use SVG as their default rendering paradigm.

Mode locking in a spatially extended neuron model: active soma and compartmental tree

Understanding the mode-locked response of excitable systems to periodic forcing has important applications in neuroscience. For example it is known that spatially extended place cells in the hippocampus are driven by the theta rhythm to generate a code conveying information about spatial location. Thus it is important to explore the role of neuronal dendrites in generating the response to periodic current injection. In this paper we pursue this using a compartmental model, with linear dynamics for each compartment, coupled to an active soma model that generates action potentials. By working with the piece-wise linear McKean model for the soma we show how the response of the whole neuron model (soma and dendrites) can be written in closed form. We exploit this to construct a stroboscopic map describing the response of the spatially extended model to periodic forcing. A linear stability analysis of this map, together with a careful treatment of the non-differentiability of the soma model, allows us to construct the Arnol'd tongue structure for 1:q states (one action potential for q cycles of forcing). Importantly we show how the presence of quasi-active membrane in the dendrites can influence the shape of tongues. Direct numerical simulations confirm our theory and further indicate that resonant dendritic membrane can enlarge the windows in parameter space for chaotic behavior. These simulations also show that the spatially extended neuron model responds differently to global as opposed to point forcing. In the former case spatio-temporal patterns of activity within an Arnol'd tongue are standing waves, whilst in the latter they are traveling waves.