Random Recurrent Neural Networks Dynamics

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using an averaging principle. After a first introductory section, the section 1 reviews the various models from the points of view of the single neuron dynamics and of the global network dynamics. A summary of notations is presented, which is quite helpful for the sequel. In section 2, mean-field dynamics is developed. The probability distribution characterizing global dynamics is computed. In section 3, some applications of mean-field theory to the prediction of chaotic regime for Analog Formal Random Recurrent Neural Networks (AFRRNN) are displayed. The case of AFRRNN with an homogeneous population of neurons is studied in section 4. Then, a two-population model is studied in section 5. The occurrence of a cyclo-stationary chaos is displayed using the results of \cite{Dauce01}. In section 6, an insight of the application of mean-field theory to IF networks is given using the results of \cite{BrunelHakim99}.Comment: Review paper, 36 pages, 5 figure

Hierarchical model for the scale-dependent velocity of seismic waves

Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's principle of least time in a medium with random velocity fluctuations. Existing perturbation theories predict a linear increase of the velocity shift with increasing separation, and cannot describe the saturation of the velocity shift at large separations that is seen in computer simulations. Here we show that this long-standing problem in seismology can be solved using a model developed originally in the context of polymer physics. We find that the saturation velocity scales with the four-third power of the root-mean-square amplitude of the velocity fluctuations, in good agreement with the computer simulations.Comment: 7 pages including 3 figure

How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation

This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks ? and; (ii) what are the effects of synaptic plasticity on these statistics ? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure

A view of Neural Networks as dynamical systems

We consider neural networks from the point of view of dynamical systems theory. In this spirit we review recent results dealing with the following questions, adressed in the context of specific models. 1. Characterizing the collective dynamics; 2. Statistical analysis of spikes trains; 3. Interplay between dynamics and network structure; 4. Effects of synaptic plasticity.Comment: Review paper, 51 pages, 10 figures. submitte

MARSTRUCT benchmark study on nonlinear FE simulation of an experiment of an indenter impact with a ship side-shell structure

This paper presents a benchmark study on collision simulations that was initiated by the MARSTRUCT Virtual Institute. The objective was to compare assumptions, finite element models, modelling techniques and experiences between established researchers within the field. Fifteen research groups world-wide participated in the study. An experiment involving a rigid indenter penetrating a ship-like side structure was used as the case study. A description of how the experiment was performed, the geometry model of it, and material properties were distributed to the participants prior to their simulations. The paper presents the results obtained from the fifteen FE simulations and the experiment. It presents a comparison of, among other factors, the reaction force versus the indenter displacement, internal energy absorbed by the structure versus the indenter displacement, and analyses of the participants' ability to predict failure modes and events that were observed in the experiment. The outcome of the study is a discussion and recommendations regarding mesh size, failure criteria and damage models, interpretation of material data and how they are used in a constitutive material model, and finally, uncertainties in general

Random recurrent neural networks dynamics

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are varying according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using an averaging principle. After a first introductory section, the section 2 reviews the various models from the points of view of the single neuron dynamics and of the global network dynamics. A summary of notations is presented, which is quite helpful for the sequel. In section 3, mean-field dynamics is developed. The probability distribution characterizing global dynamics is computed. In section 4, some applications of mean-field theory to the prediction of chaotic regime for Analog Formal Random Recurrent Neural Networks (AFRRNN) are displayed. The case of AFRRNN with an homogeneous population of neurons is studied in section 4.1. Then, a two-population model is studied in section 4.2. The occurrence of a cyclo-stationary chaos is displayed using the results of [16]. In section 5, an insight of the application of mean-field theory to IF networks is given using the results of [9]