Because of the complexity of the application and the large amount of data, the problem cannot be solved by using a single method. The solution we propose is to build multimodules NN architectures where several NN cooperate together. Such system suffer from generic problem for whom we propose solutions. They allow to reach accurate performances for multi-valued function approximations and probability estimations. The results are compared with six other methods which have been used for this problem. We show that the methodology we have developed is general and can be used for a large variety of applications.

Because eye muscles never cocontract and do not deal with external loads, one can write an equation that relates motoneuron firing rate to eye position and velocity - a very uncommon situation in the CNS. The semicircular canals transduce head velocity in a linear manner by using a high background discharge rate, imparting linearity to the premotor circuits that generate eye movements. This has allowed deducing some of the signal processing involved, including a neural network that integrates. These ideas are often summarized by block diagrams. Unfortunately, they are of little value in describing the behavior of single neurons - a fmding supported by neural network models.

The two well known learning algorithms of recurrent neural networks are the back-propagation (Rumelhart & el al., Werbos) and the forward propagation (Williams and Zipser). The main drawback of back-propagation is its off-line backward path in time for error cumulation. This violates the online requirement in many practical applications. Although the forward propagation algorithm can be used in an online manner, the annoying drawback is the heavy computation load required to update the high dimensional sensitivity matrix (0( fir) operations for each time step). Therefore, to develop a fast forward algorithm is a challenging task.

An important issue in neural computation is the dynamic range of weights in the neural networks. Many experimental results on learning indicate that the weights in the networks can grow prohibitively large with the size of the inputs. Here we address this issue by studying the tradeoffs between the depth and the size of weights in polynomial-size networks of linear threshold elements (LTEs). We show that there is an efficient way of simulating a network of LTEs with large weights by a network of LTEs with small weights. To prove these results, we use tools from harmonic analysis of Boolean functions.

Feedforward networks composed of units which compute a sigmoidal function of a weighted sum of their inputs have been much investigated. We tested the approximation and estimation capabilities of networks using functions more complex than sigmoids. Three classes of functions were tested: polynomials, rational functions, and flexible Fourier series. Unlike sigmoids, these classes can fit nonmonotonic functions. They were compared on three problems: prediction of Boston housing prices, the sunspot count, and robot arm inverse dynamics. The complex units attained clearly superior performance on the robot arm problem, which is a highly nonmonotonic, pure approximation problem. On the noisy and only mildly nonlinear Boston housing and sunspot problems, differences among the complex units were revealed; polynomials did poorly, whereas rationals and flexible Fourier series were comparable to sigmoids. 1 Introduction

Ion channels are the dynamical systems of the nervous system. Their distribution within the membrane governs not only communication of information between neurons, but also how that information is integrated within the cell. Here, an argument is presented for an'anti-Hebbian' rule for changing the distribution of voltage-dependent ion channels in order to flatten voltage curvatures in dendrites. Simulations show that this rule can account for the self-organisation of dynamical receptive field properties such as resonance and direction selectivity. It also creates the conditions for the faithful conduction within the cell of signals to which the cell has been exposed. Various possible cellular implementations of such a learning rule are proposed, including activity-dependent migration of channel proteins in the plane of the membrane.

THE MODEL; STOCHASTIC RESONANCE The reduced neuron model consists of a single Hopfield-type computational element, which may be modeled as a R-C circuit with nonlinear feedback provided by an operational amplifier having a sigmoid transfer function.

Recently synchronization phenomena in neural networks have attracted considerable attention. Gray et al. (1989, 1990) as well as Eckhorn et al. (1988) provided electrophysiological evidence that neurons in the visual cortex of cats discharge in a semi-synchronous, oscillatory manner in the 40 Hz range and that the firing activity of neurons up to 10 mm away is phase-locked with a mean phase-shift of less than 3 msec. It has been proposed that this phase synchronization can solve the binding problem for figure-ground segregation (von der Malsburg and Schneider, 1986) and underly visual attention and awareness (Crick and Koch, 1990). A number of theoretical explanations based on coupled (relaxation) oscillator mod-117 118 Schuster and Koch els have been proposed for burst synchronization (Sompolinsky et al., 1990). The crucial issue of phase synchronization has also recently been addressed by Bush and Douglas (1991), who simulated the dynamics of a network consisting of bursty, layer V pyramidal cells coupled to a common pool of basket cells inhibiting all pyramidal cells.

A network model with temporal sequencing and state-dependent modulatory features is described. The model is motivated by neurocognitive data characterizing different states of waking and sleeping. Computer studies demonstrate how unique states of sequencing can exist within the same network under different aminergic and cholinergic modulatory influences. Relationships between state-dependent modulation, memory, sequencing and learning are discussed.

The cold spot consisted of a high density of a Ca-activated K channel.