Desynchronizing effect of high-frequency stimulation in a generic cortical network model

Transcranial Electrical Stimulation (TCES) and Deep Brain Stimulation (DBS) are two different applications of electrical current to the brain used in different areas of medicine. Both have a similar frequency dependence of their efficiency, with the most pronounced effects around 100Hz. We apply superthreshold electrical stimulation, specifically depolarizing DC current, interrupted at different frequencies, to a simple model of a population of cortical neurons which uses phenomenological descriptions of neurons by Izhikevich and synaptic connections on a similar level of sophistication. With this model, we are able to reproduce the optimal desynchronization around 100Hz, as well as to predict the full frequency dependence of the efficiency of desynchronization, and thereby to give a possible explanation for the action mechanism of TCES.Comment: 9 pages, figs included. Accepted for publication in Cognitive Neurodynamic

Random walk on disordered networks

Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The effects of disorder and space-curvature on the diffusion phenomena are investigated. In disordered systems the mean square displacement displays an enhancement at short time and a lowering at long ones, with respect to the ordered case. The asymptotic expression for the diffusion equation on hyperbolic cellular systems relates random walk on curved lattices to hyperbolic Brownian motion.Comment: 10 Pages, 3 Postscript figure

Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is Brownian for the rest of the nodes. Transport within a supernode is affected by the finite size effects vanishing as $N\to\infty.$ For the even dimensions of space, $d=2,4,6,...$, the finite size effects break down the perturbation theory at small scales and can be regularized by using the heat-kernel expansion.Comment: 21 pages, 2 figures include

Fe and N self-diffusion in amorphous FeN: A SIMS and neutron reflectivity study

Simultaneous measurement of self-diffusion of iron and nitrogen in amorphous iron nitride (Fe86N14) using secondary ion mass spectroscopy (SIMS) technique has been done. In addition neutron reflectivity (NR) technique was employed to study the Fe diffusion in the same compound. The broadening of a tracer layer of 57Fe8615N14 sandwiched between Fe86N14 layers was observed after isothermal vacuum annealing of the films at different temperatures in SIMS measurements. And a decay of the Bragg peak intensity after isothermal annealing was observed in [Fe86N14/57Fe86N14]10 multilayers in NR. Strong structural relaxation of diffusion coefficient was observed below the crystallization temperature of the amorphous phase in both measurements. It was observed from the SIMS measurements that Fe diffusion was about 2 orders of magnitude smaller compared to nitrogen at a given temperature. The NR measurements reveal that the mechanism of Fe self-diffusion is very similar to that in metal-metal type metallic glasses. The structural relaxation time for Fe and N diffusion was found comparable indicating that the obtained relaxation time essentially pertain to the structural relaxation of the amorphous phase.Comment: 10 pages 12 figure