temporal relations requires the joint evaluation of responses from more than one neuron, only experiments that permit simultaneous measurements of responses 60528 Frankfurt from multiple units are considered. These include multi-Federal Republic of Germany electrode recordings from multiple individual cells, but also measurements of local field potentials (LFPs) and electroencephalographic (EEG) or magnetoencephalo-Most of our knowledge about the functional organization of neuronal systems is based on the analysis of the firing patterns of individual neurons that have been recorded one by one in succession. This approach permits as-sessment of event-related variations in discharge rate, but it precludes detection of any covariations in the amplitude or timing of distributed responses if these graphic (MEG) recordings. The signals of these latter

Abstract. We describe a set of preliminary experiments to evolve spiking neural controllers for a vision-based mobile robot. All the evolutionary experiments are carried out on physical robots without human intervention. After discussing how to implement and interface these neurons with a physical robot, we show that evolution finds relatively quickly functional spiking controllers capable of navigating in irregularly textured environments without hitting obstacles using a very simple genetic encoding and fitness function. Neuroethological analysis of the network activity let us understand the functioning of evolved controllers and tell the relative importance of single neurons independently of their observed firing rate. Finally, a number of systematic lesion experiments indicate that evolved spiking controllers are very robust to synaptic strength decay that typically occurs in hardware implementations of spiking circuits. 1 Spiking Neural Circuits The great majority of biological neurons communicate by sending pulses along

We analyze the effect of noise in integrate-and-fire neurons driven by timedependent input, and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for time-dependent sub-threshold input, diffusive noise can be replaced by escape noise with a hazard function that has a Gaussian dependence upon the distance between the (noise-free) membrane voltage and threshold. The approximation is improved if we add to the hazard function a probability current proportional to the derivative of the voltage. Stochastic resonance in response to periodic input occurs in both noise models and exhibits similar characteristics.

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We describe a model and implementation of evolutionary spiking neurons for embedded microcontrollers with few bytes of memory and very low power consumption. The approach is tested with an autonomous microrobot of less than 1 in 3 that evolves the ability to move in a small maze without human intervention and external computers. Considering the very large diffusion, small size, and low cost of embedded microcontrollers, the approach described here could find its way in several intelligent devices with sensors and/or actuators, as well as in smart credit cards. Artificial Spiking Circuits Most biological neurons communicate by sending pulses across connections to other neurons. The pulse is also known as “spike ” to indicate its short and transient nature. Neurons are affected by incoming spikes and generate a spike when their membrane potential becomes larger than a threshold. Spike generation is followed by a short “refractory period ” during which the neuron cannot generate another spike. Computational models of spiking neurons are attracting increasing interest in engineering and computer science (Maas & Bishop 1999). On the one hand, computer simulations of spiking networks can help to address specific questions in neuroscience, such as how biological neurons communicate with each other (Koenig, Engel, & Singer 1996; Rieke et al. 1997). On the other hand, a better understanding of spiking neurons is leading to the development of new neuromorphic devices (Horiuchi 2001), some of which may replace lesioned fibers or sensory organs. In addition, we argue that networks of spiking neurons represent suitable control systems for autonomous behavioral systems, 1 such as situated autonomous robots, because temporal patterns of sensory-motor events may be captured and exploited more efficiently (i.e., with fewer neurons or with higher probability) by the intrinsic time-dependent dynamics of spiking neurons than by 1 They certainly showed to be excellent control systems for biological organisms! other connectionist models (Rumelhart, McClelland, &

What is the 'meaning' of a single spike? Spike-triggered averaging ('reverse correlations') yields the typical input just before a spike. Similarly, cross-correlations describe the probability of firing an output spike given (one additional) presynaptic input spike. In this paper, we analytically calculate reverse and cross-correlations for a spiking neuron model with escape noise. The influence of neuronal parameters (such as the membrane time constant, the noise level, and the mean firing rate) on the form of the correlation function is illustrated. The calculation is done in the framework of a population theory that is reviewed. The relation of the population activity equations to population density methods is discussed. Finally, we indicate the role of cross-correlations in spike-time dependent Hebbian plasticity. 2001 Elsevier Science Ltd. All rights reserved.

In standard neural network models neurons are described in terms of mean firing rates, viz., an analog signal. Most real neurons, however, communicate by pulses, called action potentials or simply `spikes'. In this chapter the main di#erences between spike coding and rate coding are described. The integrate-and-fire model is studied as a simple model of a spiking neuron. Fast transients, synchrony, and coincidence detection are discussed as examples where spike coding is relevant. A description by spikes rather than rates has implications for learning rules. We show the relation of a spike-time dependent learning rule to standard Hebbian learning. Finally, learning rule and temporal coding are illustrated using the example of a coincidence detecting neuron in the barn owl auditory system. Keywords: temporal coding, coincidence detection, spikes, spiking neurons, integrateand -fire neurons, auditory system, Hebbian learning, spike-time dependent plasticity 1. SPIKES AND RATES In mos...

A number of models have been produced recently to explain the high variability of natural spike trains [Softky and Koch, 1993, J. Neurosci. 13 (1) 334-530]. These models use a range of different biological mechanisms including partial somatic reset, concurrent inhibition and excitation, correlated inputs and network dynamics effects. In this paper we examine which model is more likely to reflect the mechanisms used in the brain and we evaluate the ability of each model to reproduce the experimental Coefficient of Variation (CV) vs Mean ISI curves (CV = standard deviation/mean ISI). The results show that the partial somatic reset mechanism is the most likely candidate to reflect the mechanism used in the brain for reproducing irregular firing.

Most biological neurons communicate by short electrical pulses, called action potentials or spikes. In contrast to the standard neuron model used in artificial neural networks, integrate-and-fire neurons do not rely on a temporal average over the pulses. In integrate-and-fire and similar spiking neuron models, the pulsed nature of the neuronal signal is taken into account and considered as potentially relevant for coding and information processing. In contrast to more detailed neuron models, integrate-and-fire models do not describe explicitly the form of an action potential. Pulses are treated as formal events. This is no real drawback, since, in a biological spike train, all action potentials of a neuron have roughly the same form. The time course of an action potential does therefore not carry any information. Integrate-and-fire and similar spiking neuron models are phenomenological descriptions on an intermediate level of detail. Compared to other SINGLE-CELL MODELS,