The analytic index for a family of Dirac-Ramond operators

We derive a cohomological formula for the analytic index of the Dirac-Ramond operator and we exhibit its modular properties.Comment: 6 page

Surface holonomy and gauge 2-group

Just as point objects are parallel transported along curves, giving holonomies, string-like objects are parallel transported along surfaces, giving surface holonomies. Composition of these surfaces correspond to products in a category theoretic generalization of the gauge group, called a 2-group. I consider two different ways of constructing surface holonomies, one by using a pair of one and two form connections, and another by using a pair of one-form connections. Both procedures result in the structure of a 2-group.Comment: 8pp, RevTeX4, Submitted upon invitation to IJGMM

An update on transcriptional and post-translational regulation of brain voltage-gated sodium channels

Voltage-gated sodium channels are essential proteins in brain physiology, as they generate the sodium currents that initiate neuronal action potentials. Voltage-gated sodium channels expression, localisation and function are regulated by a range of transcriptional and post-translational mechanisms. Here, we review our understanding of regulation of brain voltage-gated sodium channels, in particular SCN1A (Naᵥ1.1), SCN2A (Naᵥ1.2), SCN3A (Naᵥ1.3) and SCN8A (Naᵥ1.6), by transcription factors, by alternative splicing, and by post-translational modifications. Our focus is strongly centred on recent research lines, and newly generated knowledge