The telencephalic premotor nucleus HVC is situated at a critical point in the pattern-generating premotor circuitry of oscine songbirds. A striking feature of HVC's premotor activity is that its projection neurons burst extremely sparsely. Here we present a computational model of HVC embodying several central hypotheses: 1) sparse bursting is generated in bistable groups of recurrently connecte...

We study the emergence of polyrhythmic dynamics of motifs which are the building block for small inhibitory-excitatory networks, such as central pattern generators controlling various locomotive behaviors of animals. We discover that the pacemaker determining the specific rhythm of such a network composed of realistic Hodgkin-Huxley-type neurons is identified through the order parameter, which ...

The representation dimension was defined by M.Auslander in 1970 and is, due to spectacular recent progress, one of the most interesting homological invariants in representation theory. The precise value is not known in general, and is very hard to compute even for small examples. For group algebras, it is known in the case of cyclic Sylow subgroups, due to Auslander’s fundamental work. For some...

Modulatory projection neurons gate neuronal networks, such as those comprising motor central pattern generators; in turn, they receive feedback from the networks they gate. A recent study has shown that, in the crab stomatogastric ganglion, this feedback is also subject to modulation: the enhanced feedback feeds forward through the projection neurons to modify circuit output.

This has a unique solution v(x, t) = Ttf(x) in the sense of Hille and Phillips [14, p. 622] whenever Tt is a C0–semigroup on X with generator −A; one writes Tt = e−tA [14, p. 321]. In order to ensure that v(x, t) converges μ-almost everywhere to f(x) as t→ 0+, it is often necesary to impose further conditions on f . For any closed linear operator V in X, we recall that the domain of V is the Ba...