Enhancement of synchronization in a hybrid neural circuit by spike timing dependent plasticity

Synchronization of neural activity is fundamental for many functions of the brain. We demonstrate that spike-timing dependent plasticity (STDP) enhances synchronization (entrainment) in a hybrid circuit composed of a spike generator, a dynamic clamp emulating an excitatory plastic synapse, and a chemically isolated neuron from the Aplysia abdominal ganglion. Fixed-phase entrainment of the Aplysia neuron to the spike generator is possible for a much wider range of frequency ratios and is more precise and more robust with the plastic synapse than with a nonplastic synapse of comparable strength. Further analysis in a computational model of HodgkinHuxley-type neurons reveals the mechanism behind this significant enhancement in synchronization. The experimentally observed STDP plasticity curve appears to be designed to adjust synaptic strength to a value suitable for stable entrainment of the postsynaptic neuron. One functional role of STDP might therefore be to facilitate synchronization or entrainment of nonidentical neurons

Nonlinear dynamics in one dimension: On a criterion for coarsening and its temporal law

We develop a general criterion about coarsening for a class of nonlinear evolution equations describing one dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process takes place and the one where the wavelength is fixed in the course of time. An intermediate scenario may occur, namely `interrupted coarsening'. The power of the criterion lies in the fact that the statement about the occurrence of coarsening, or selection of a length scale, can be made by only inspecting the behavior of the branch of steady state periodic solutions. The criterion states that coarsening occurs if lambda'(A)>0 while a length scale selection prevails if lambda'(A)<0, where $lambda$ is the wavelength of the pattern and A is the amplitude of the profile. This criterion is established thanks to the analysis of the phase diffusion equation of the pattern. We connect the phase diffusion coefficient D(lambda) (which carries a kinetic information) to lambda'(A), which refers to a pure steady state property. The relationship between kinetics and the behavior of the branch of steady state solutions is established fully analytically for several classes of equations. Another important and new result which emerges here is that the exploitation of the phase diffusion coefficient enables us to determine in a rather straightforward manner the dynamical coarsening exponent. Our calculation, based on the idea that |D(lambda)|=lambda^2/t, is exemplified on several nonlinear equations, showing that the exact exponent is captured. Some speculations about the extension of the present results to higher dimension are outlined.Comment: 16 pages. Only a few minor changes. Accepted for publication in Physical Review

Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n

Pattern formation without heating in an evaporative convection experiment

We present an evaporation experiment in a single fluid layer. When latent heat associated to the evaporation is large enough, the heat flow through the free surface of the layer generates temperature gradients that can destabilize the conductive motionless state giving rise to convective cellular structures without any external heating. The sequence of convective patterns obtained here without heating, is similar to that obtained in B\'enard-Marangoni convection. This work present the sequence of spatial bifurcations as a function of the layer depth. The transition between square to hexagonal pattern, known from non-evaporative experiments, is obtained here with a similar change in wavelength.Comment: Submitted to Europhysics Letter

Coarsening in potential and nonpotential models of oblique stripe patterns

We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic length scale growing in time as $t^{1/2}$. Further from onset, the characteristic lengths along the preferred directions $\hat{x}$ and $\hat{y}$ grow with different exponents, close to 1/3 and 1/2, respectively. In this regime, one-dimensional dynamical scaling relations hold. We draw an analogy between this problem and Model A in a stationary, modulated external field. For deep quenches, nonpotential effects produce a complicated dislocation dynamics that can lead to either arrested or faster-than-power-law growth, depending on the model considered. In the arrested case, small isolated domains shrink down to a finite size and fail to disappear. A comparison with available experimental results of electroconvection in nematics is presented.Comment: 13 pages, 13 figures. To appear in Phys. Rev.