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

Escaping from cycles through a glass transition

A random walk is performed over a disordered media composed of $N$ sites random and uniformly distributed inside a $d$-dimensional hypercube. The walker cannot remain in the same site and hops to one of its $n$ neighboring sites with a transition probability that depends on the distance $D$ between sites according to a cost function $E(D)$. The stochasticity level is parametrized by a formal temperature $T$. In the case $T = 0$, the walk is deterministic and ergodicity is broken: the phase space is divided in a ${\cal O}(N)$ number of attractor basins of two-cycles that trap the walker. For $d = 1$, analytic results indicate the existence of a glass transition at $T_1 = 1/2$ as $N \to \infty$. Below $T_1$, the average trapping time in two-cycles diverges and out-of-equilibrium behavior appears. Similar glass transitions occur in higher dimensions choosing a proper cost function. We also present some results for the statistics of distances for Poisson spatial point processes.Comment: 11 pages, 4 figure

Molecular dynamics study of vacancy-like defects in a model glass : static behaviour

The possibility of defining vacancy-like defects in a Lennard-Jones glass is searched for in a systematic manner. Considering different relaxation levels of the same system, as well as different external pressures, we use a Molecular Dynamics simulation method, to study at constant volume or external pressure, the relaxation of a “piece” of glass, after the sudden removal of an atom. Three typical kinds of behaviour can be observed: the persistence of the empty volume left by the missing atom, its migration by clearly identifiable atomic jumps and the dissipation “on the spot”. A careful analysis of the probabilities of these three kinds of behaviour shows that a meaningful definition of vacancy-like defects can be given in a Lennard-Jones glass.Dans cet article, nous nous penchons de façon systématique sur la possibilité de définir des défauts de type lacunaire dans un verre de Lennard-Jones, à différents niveaux de relaxation et de pression, par une méthode de simulation numérique en dynamique moléculaire à volume ou à pression constants. Le défaut est créé en supprimant un atome et en suivant la réponse du système. Nous observons trois comportements typiques : la persistance sur place du “trou” laissé par l'atome supprimé, sa migration par des sauts atomiques clairement identifiés et enfin sa dissipation sur place. Une analyse détaillée de ces trois comportements montre qu'il est possible dans un verre de Lennard-Jones de définir des défauts de type lacunaire

Catalytic dehydrogenation of ethane over mononuclear Cr(III) surface sites on silica. part I. C - H activation by σ-bond metathesis

Mononuclear Cr(III)-silica models have been studied by quantum chemical methods with respect to catalytic activity toward dehydrogenation of ethane. Both cluster and slab models have been developed and used to explore the conceptual model of mononuclear Cr(III) with three covalent ligands that coordinate through oxygen. The study focuses on a reaction mechanism consisting of three main reaction steps: (1) C - H activation of ethane according to -bond metathesis and accompanied by the formation of O - H and Cr - C bonds, (2) -H transfer to chromium with subsequent loss of ethene and (3) regeneration of the chromium site under evolution of H2. An alternative mechanism is also explored, in which C - H activation takes place at a reactive hydridochromium complex. Stationary points pertaining to these reactions have been optimized, and free energy calculations are used to identify the rate-determining steps. The influence of the local structure of the chromium surface sites is explored by means of a number of idealized surface models and electronic energy profiles for the reactions.Peer Reviewe

Reactive phase formation at interfaces and diffusion processes

Proceedings of the International Meeting on Reactive Phase Formation at Interfaces and Diffusion Processesheld in Aussois, France, May 1993