Simulating global properties of electroencephalograms with minimal random neural networks

The human electroencephalogram (EEG) is globally characterized by a 1/f power spectrum superimposed with certain peaks, whereby the "alpha peak" in a frequency range of 8-14 Hz is the most prominent one for relaxed states of wakefulness. We present simulations of a minimal dynamical network model of leaky integrator neurons attached to the nodes of an evolving directed and weighted random graph (an Erdos-Renyi graph). We derive a model of the dendritic field potential (DFP) for the neurons leading to a simulated EEG that describes the global activity of the network. Depending on the network size, we find an oscillatory transition of the simulated EEG when the network reaches a critical connectivity. This transition, indicated by a suitably defined order parameter, is reflected by a sudden change of the network's topology when super-cycles are formed from merging isolated loops. After the oscillatory transition, the power spectra of simulated EEG time series exhibit a 1/f continuum superimposed with certain peaks. (c) 2007 Elsevier B.V. All rights reserved.

Stability criteria for the contextual emergence of macrostates in neural networks

More than thirty years ago, Amari and colleagues proposed a statistical framework for identifying structurally stable macrostates of neural networks from observations of their microstates. We compare their stochastic stability criterion with a deterministic stability criterion based on the ergodic theory of dynamical systems, recently proposed for the scheme of contextual emergence and applied to particular inter-level relations in neuroscience. Stochastic and deterministic stability criteria for macrostates rely on macro-level contexts, which make them sensitive to differences between different macro-levels.

An Efficient Parameterization of Dynamic Neural Networks for Nonlinear System Identification

Dynamic neural networks (DNNs), which are also known as recurrent neural networks, are often used for nonlinear system identification. The main contribution of this letter is the introduction of an efficient parameterization of a class of DNNs. Having to adjust less parameters simplifies the training problem and leads to more parsimonious models. The parameterization is based on approximation theory dealing with the ability of a class of DNNs to approximate finite trajectories of nonautonomous systems. The use of the proposed parameterization is illustrated through a numerical example, using data from a nonlinear model of a magnetic levitation system.

Cultured neural networks

This special section contains papers addressing various aspects associated with the issue Of Cultured neural networks. These are networks, that are formed through the monitored growth of biological neural tissue. In keeping with the aims of the International Journal of Adaptive Control and Signal Processing, the key focus of these papers is to took at particular aspects of signal processing in terms of both stimulating such a network and in assigning intent to signals collected as network outputs. Copyright (C) 2009 John Wiley & Sons, Ltd.

Global exponential periodicity of a class of neural networks with recent-history distributed delays

In this paper, we propose to study a class of neural networks with recent-history distributed delays. A sufficient condition is derived for the global exponential periodicity of the proposed neural networks, which has the advantage that it assumes neither the differentiability nor monotonicity of the activation function of each neuron nor the symmetry of the feedback matrix or delayed feedback matrix. Our criterion is shown to be valid by applying it to an illustrative system. (c) 2005 Elsevier Ltd. All rights reserved.

Prediction of Parkinson’s disease tremor onset using radial basis function neural networks

The possibility of using a radial basis function neural network (RBFNN) to accurately recognise and predict the onset of Parkinson’s disease tremors in human subjects is discussed in this paper. The data for training the RBFNN are obtained by means of deep brain electrodes implanted in a Parkinson disease patient’s brain. The effectiveness of a RBFNN is initially demonstrated by a real case study.

Neural networks for identification of nonlinear systems under random piecewise polynomial disturbances

The problem of identification of a nonlinear dynamic system is considered. A two-layer neural network is used for the solution of the problem. Systems disturbed with unmeasurable noise are considered, although it is known that the disturbance is a random piecewise polynomial process. Absorption polynomials and nonquadratic loss functions are used to reduce the effect of this disturbance on the estimates of the optimal memory of the neural-network model.

Input/output linearization using dynamic recurrent neural networks

This paper brings together two areas of research that have received considerable attention during the last years, namely feedback linearization and neural networks. A proposition that guarantees the Input/Output (I/O) linearization of nonlinear control affine systems with Dynamic Recurrent Neural Networks (DRNNs) is formulated and proved. The proposition and the linearization procedure are illustrated with the simulation of a single link manipulator.

Neural networks for linear control: an analysis

This paper considers the use of radial basis function and multi-layer perceptron networks for linear or linearizable, adaptive feedback control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parameterization. A comparison is made with standard, nonneural network algorithms, e.g. self-tuning control.