197,399 research outputs found
Effect of noise in a cortical neural model
No full textAbstract: Recently Segev et al. [Phys. Rev. E 64, 011920 (2001); Phys. Rev. Lett. 88, 118102 (2002)] made long-term observations of spontaneous activity of in-vitro cortical networks, which differ from predictions of current models in many features. In this paper we generalize the excitatory-inhibitory cortical model introduced in a previous paper [Scarpetta et al., Neural Comput. 14, 2371 (2002)], including intrinsic white noise and analyzing effects of noise on the spontaneous activity of the nonlinear system, in order to account for the experimental results of Segev et al. Analytically we can distinguish different regimes of activity, depending on the model parameters. Using analytical results as a guide line, we perform simulations of the nonlinear stochastic model in two different regimes, B and C. The power spectrum density (PSD) of the activity and the interevent-interval distributions are computed, and compared with experimental results. In regime B the network shows stochastic resonance phenomena and noise induces aperiodic, collective synchronous oscillations that mimics experimental observations at 0.5 mM Ca concentration. In regime C the model shows spontaneous synchronous periodic activity that mimics activity observed at 1 mM Ca concentration and the PSD shows two peaks at the first and second harmonics in agreement with experiments. at 1 mM Ca. Moreover (due to intrinsic noise and nonlinear activation function effects) the PSD shows a broad band peak at low frequency. This feature, observed experimentally, does not find explanation in the previous models. Besides we identify parametric changes (namely, increase of noise or decreasing of excitatory connect ions) that reproduces the fading of periodicity found experimentally at long times, and we identify a way to discriminate between those two possible effects measuring experimentally the low frequency PSD.
Accession Number: WOS:00022568950005
The multidimensional stationary-phase method for asymptotic estimate of edge effects in the multiple Kirchoff diffraction by curved surfaces
No full textEnergetic properties of the elastic half-space loaded by a periodic distribution of vibrating punches: the study of the phase shift influence
No full textWe develop an analytical approach to study the wave properties of an elastic half-space subjected to harmonic vibrations applied on its free surface by a periodic array of rigid punches. Contrary to previous investigation, it is assumed that any neighbouring pair
of these oscillates with a (common) phase shift, thus implying rather specific behaviours of the structure. Starting from integral equations for the contact stress and representation formulas for the wave field in both the anti-plane and in-plane problems, suitable mild approximations on the kernels allow analytical solution of some related (auxiliary) integral equations in a given range of (not too high) frequency. The explicit formulas thus obtained for the wave field are reflected through some figures and enable us to investigate the energetic properties of the structure with respect to different phase shifts. A direct numerical solution of the original integral equations confirms the precision of the analytical solution
Some Analytical results for Acoustic Scattering through a Periodic Array of Elastic Membranes
No full textIn the context of wave propagation through acoustic media, an analytical approach is developed to study the (normal) incidence of a pressure wave into a periodic array of (thin) elastic membranes. The frequency of this wave is assumed in a range implying the so-called one-mode (far field) propagation, so that mild approximations holding in this range can be employed. Thus, the problem is reduced to some integral equations based on the opening between adjacent membranes and independent on frequency. By means of the (analytical) solution of such equations, an explicit formula for the transmission coefficient is set up and reflected in some figures for concrete values of the various parameters involved. The peculiarities of the scattering structure are finally discussed
Dynamics of on-line learning in radial basis function neural networks
No full textWe present a method for analyzing the behavior of RBFs in an on-line scenario which provides a description of the learning dynamics without invoking the thermodynamic limit. Our analysis is based on a master equation that describes the dynamics of the weight space probability density for any value of the input space dimension. Because the transition probability appearing in the master equation cannot be written in closed form, some approximate form of the dynamics is developed. We assume a arbitrary small learning rate (small noise) and we derive in this limit the dynamic evolution of the means and the variances of the net weights. The analytic results are then confirmed by simulations
Wave properties of the elastic half-space loaded by a periodic distribution of vibrating punches: an analytical approach
No full textAn analytical approach is developed to study the wave properties
of an elastic half-space subjected to harmonic vibrations applied on its free surface by a periodic array of rigid punches. In the frequency range ensuring the so-called one-mode (far-field) propagation, both the antiplane and in-plane problems are reduced to integral equations which are solved analytically. The explicit formulas obtained for the wave field are reflected through some figures in order to discuss the peculiar physical properties of the structure
Encoding and Replay of Dynamic Attractors with Multiple Frequencies: Analysis of a STDP Based Learning Rule
No full textAfter learning, each encoded oscillatory spatio-temporal pattern who satisfy the stability condition forms a dynamical attractor, such that, when the state of the system falls in the basin of attraction of one such dynamical attractor, it is recovered with the same encoded phase relationship among units. Here we extend the analysis introduced in our previous work, to the case of distributed frequencies, and we study the relation between stability of multiple frequencies and the shape of the learning window. The stability of the dynamical attractors play a critical role. We show that imprinting into the network a spatio-temporal pattern with a new frequency of oscillation can destroy the stability of patterns encoded with different frequency of oscillation. The system is studied both with numerical simulations, and analytically in terms of order parameters when a finite number of dynamic attractors are encoded into the network in the thermodynamic limit
Spatiotemporal learning in analog neural networks using spike-timing-dependent synaptic plasticity
No full textIncorporating the spike-timing-dependent synaptic plasticity (STDP) into a learning rule, we study spatiotemporal learning in analog neural networks. First, we study learning of a finite number of periodic spatiotemporal patterns by deriving the dynamics of the order parameters. When a pattern is retrieved successfully, the order parameters exhibit periodic oscillation. Analyzing this oscillation of the order parameters, we elucidate the relation of the STDP time window to the properties of the retrieval state; the phase of the Fourier transform of the STDP time window determines the retrieval frequency and the time average of the STDP time window crucially affects the storage capacity. We also evaluate the stability of the order parameter oscillation and identify the retrieval state that is stable in single-pattern learning but unstable in multiple-pattern learning even when the retrieval state is independent of a pattern number. To examine the further applicability of the STDP-based learning rule, we also study learning of nonperiodic spatiotemporal Poisson patterns. Our numerical simulations demonstrate that the Poisson patterns are memorized successfully not only in analog neural networks but also in spiking neural networks
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