A high-efficiency model indicating the role of inhibition in the resilience of neuronal networks to damage resulting from traumatic injury.

Recent investigations of traumatic brain injuries have shown that these injuries can result in conformational changes at the level of individual neurons in the cerebral cortex. Focal axonal swelling is one consequence of such injuries and leads to a variable width along the cell axon. Simulations of the electrical properties of axons impacted in such a way show that this damage may have a nonlinear deleterious effect on spike-encoded signal transmission. The computational cost of these simulations complicates the investigation of the effects of such damage at a network level. We have developed an efficient algorithm that faithfully reproduces the spike train filtering properties seen in physical simulations. We use this algorithm to explore the impact of focal axonal swelling on small networks of integrate and fire neurons. We explore also the effects of architecture modifications to networks impacted in this manner. In all tested networks, our results indicate that the addition of presynaptic inhibitory neurons either increases or leaves unchanged the fidelity, in terms of bandwidth, of the network's processing properties with respect to this damage.

Wave Generation in Unidirectional Chains of Idealized Neural Oscillators.

We investigate the dynamics of unidirectional semi-infinite chains of type-I oscillators that are periodically forced at their root node, as an archetype of wave generation in neural networks. In previous studies, numerical simulations based on uniform forcing have revealed that trajectories approach a traveling wave in the far-downstream, large time limit. While this phenomenon seems typical, it is hardly anticipated because the system does not exhibit any of the crucial properties employed in available proofs of existence of traveling waves in lattice dynamical systems. Here, we give a full mathematical proof of generation under uniform forcing in a simple piecewise affine setting for which the dynamics can be solved explicitly. In particular, our analysis proves existence, global stability, and robustness with respect to perturbations of the forcing, of families of waves with arbitrary period/wave number in some range, for every value of the parameters in the system.

Self-organization in predominantly feedforward oscillator chains.

Results on the dynamics of certain predominantly feedforward networks of phase oscillators are presented. We start with a purely feedforward chain and show numerically that in certain parameter ranges, independent of the length of the chain, there is a global attractor that is effectively a two-dimensional torus. Specifically, we find that after the system has reached its steady state, the phases of all the oscillators in the chain at any one moment in time are determined entirely by the phases of the first two oscillators. In the cases tested this phenomenon is found to persist with the addition of feedback couplings whose strengths may be up to a significant fraction of the feedforward strengths.