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Wulfram Gerstner

Publications and source records attributed to Wulfram Gerstner.

17 recordsLinked to original sources
PubMed2005

Transient information flow in a network of excitatory and inhibitory model neurons: role of noise and signal autocorrelation.

We investigate the performance of sparsely-connected networks of integrate-and-fire neurons for ultra-short term information processing. We exploit the fact that the population activity of networks with balanced excitation and inhibition can switch from an oscillatory firing regime to a state of asynchronous irregular firing or quiescence depending on the rate of external background spikes. We find that in terms of information buffering the network performs best for a moderate, non-zero, amount of noise. Analogous to the phenomenon of stochastic resonance the performance decreases for higher and lower noise levels. The optimal amount of noise corresponds to the transition zone between a quiescent state and a regime of stochastic dynamics. This provides a potential explanation of the role of non-oscillatory population activity in a simplified model of cortical micro-circuits.

Action Potentials↗
PubMed2005

Predicting spike times of a detailed conductance-based neuron model driven by stochastic spike arrival.

Reduced models of neuronal activity such as integrate-and-fire models allow a description of neuronal dynamics in simple, intuitive terms and are easy to simulate numerically. We present a method to fit an integrate-and-fire-type model of neuronal activity, namely a modified version of the spike response model, to a detailed Hodgkin-Huxley-type neuron model driven by stochastic spike arrival. In the Hogkin-Huxley model, spike arrival at the synapse is modeled by a change of synaptic conductance. For such conductance spike input, more than 70% of the postsynaptic action potentials can be predicted with the correct timing by the integrate-and-fire-type model. The modified spike response model is based upon a linearized theory of conductance-driven integrate-and-fire neurons.

Action Potentials↗
PubMed2005

Signal buffering in random networks of spiking neurons: microscopic versus macroscopic phenomena.

In randomly connected networks of pulse-coupled elements a time-dependent input signal can be buffered over a short time. We studied the signal buffering properties in simulated networks as a function of the networks' state, characterized by both the Lyapunov exponent of the microscopic dynamics and the macroscopic activity derived from mean-field theory. If all network elements receive the same signal, signal buffering over delays comparable to the intrinsic time constant of the network elements can be explained by macroscopic properties and works best at the phase transition to chaos. However, if only 20% of the network units receive a common time-dependent signal, signal buffering properties improve and can no longer be attributed to the macroscopic dynamics.

Action Potentials↗
PubMed2005

Robust self-localisation and navigation based on hippocampal place cells.

A computational model of the hippocampal function in spatial learning is presented. A spatial representation is incrementally acquired during exploration. Visual and self-motion information is fed into a network of rate-coded neurons. A consistent and stable place code emerges by unsupervised Hebbian learning between place- and head direction cells. Based on this representation, goal-oriented navigation is learnt by applying a reward-based learning mechanism between the hippocampus and nucleus accumbens. The model, validated on a real and simulated robot, successfully localises itself by recalibrating its path integrator using visual input. A navigation map is learnt after about 20 trials, comparable to rats in the water maze. In contrast to previous works, this system processes realistic visual input. No compass is needed for localisation and the reward-based learning mechanism extends discrete navigation models to continuous space. The model reproduces experimental findings and suggests several neurophysiological and behavioural predictions in the rat.

Animals↗
PubMed2005

Noise-enhanced computation in a model of a cortical column.

Varied sensory systems use noise in order to enhance detection of weak signals. It has been conjectured in the literature that this effect, known as stochastic resonance, may take place in central cognitive processes such as memory retrieval of arithmetical multiplication. We show, in a simplified model of cortical tissue, that complex arithmetical calculations can be carried out and are enhanced in the presence of a stochastic background. The performance is shown to be positively correlated to the susceptibility of the network, defined as its sensitivity to a variation of the mean of its inputs. For nontrivial arithmetic tasks such as multiplication, stochastic resonance is a collective property of the microcircuitry of the model network.

Cerebral Cortex↗
PubMed2005

Adaptive exponential integrate-and-fire model as an effective description of neuronal activity.

We introduce a two-dimensional integrate-and-fire model that combines an exponential spike mechanism with an adaptation equation, based on recent theoretical findings. We describe a systematic method to estimate its parameters with simple electrophysiological protocols (current-clamp injection of pulses and ramps) and apply it to a detailed conductance-based model of a regular spiking neuron. Our simple model predicts correctly the timing of 96% of the spikes (+/-2 ms) of the detailed model in response to injection of noisy synaptic conductances. The model is especially reliable in high-conductance states, typical of cortical activity in vivo, in which intrinsic conductances were found to have a reduced role in shaping spike trains. These results are promising because this simple model has enough expressive power to reproduce qualitatively several electrophysiological classes described in vitro.

Action Potentials↗
PubMed2005

Generalized Bienenstock-Cooper-Munro rule for spiking neurons that maximizes information transmission.

Maximization of information transmission by a spiking-neuron model predicts changes of synaptic connections that depend on timing of pre- and postsynaptic spikes and on the postsynaptic membrane potential. Under the assumption of Poisson firing statistics, the synaptic update rule exhibits all of the features of the Bienenstock-Cooper-Munro rule, in particular, regimes of synaptic potentiation and depression separated by a sliding threshold. Moreover, the learning rule is also applicable to the more realistic case of neuron models with refractoriness, and is sensitive to correlations between input spikes, even in the absence of presynaptic rate modulation. The learning rule is found by maximizing the mutual information between presynaptic and postsynaptic spike trains under the constraint that the postsynaptic firing rate stays close to some target firing rate. An interpretation of the synaptic update rule in terms of homeostatic synaptic processes and spike-timing-dependent plasticity is discussed.

Action Potentials↗
PubMed2005

Short-term synaptic plasticity orchestrates the response of pyramidal cells and interneurons to population bursts.

The synaptic drive from neuronal populations varies considerably over short time scales. Such changes in the pre-synaptic rate trigger many temporal processes absent under steady-state conditions. This paper examines the differential impact of pyramidal cell population bursts on post-synaptic pyramidal cells receiving depressing synapses, and on a class of interneuron that receives facilitating synapses. In experiment a significant shift of the order of one hundred milliseconds is seen between the response of these two cell classes to the same population burst. It is demonstrated here that such a temporal differentiation of the response can be explained by the synaptic and membrane properties without recourse to elaborate cortical wiring schemes. Experimental data is first used to construct models of the two types of dynamic synaptic response. A population-based approach is then followed to examine analytically the temporal synaptic filtering effects of the population burst for the two post-synaptic targets. The peak-to-peak delays seen in experiment can be captured by the model for experimentally realistic parameter ranges. It is further shown that the temporal separation of the response is communicated in the outgoing action potentials of the two post-synaptic cells: pyramidal cells fire at the beginning of the burst and the class of interneuron receiving facilitating synapses fires at the end of the burst. The functional role of such delays in the temporal organisation of activity in the cortical microcircuit is discussed.

Action Potentials↗
PubMed2005

Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance.

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

Action Potentials↗
PubMed2005

A computational model of parallel navigation systems in rodents.

Several studies in rats support the idea of multiple neural systems competing to select the best action for reaching a goal or food location. Locale navigation strategies, necessary for reaching invisible goals, seem to be mediated by the hippocampus and the ventral and dorsomedial striatum whereas taxon strategies, applied for approaching goals in the visual field, are believed to involve the dorsolateral striatum. A computational model of action selection is presented, in which different experts, implementing locale and taxon strategies, compete in order to select the appropriate behavior for the current task. The model was tested in a simulated robot using an experimental paradigm that dissociates the use of cue and spatial information.

Animals↗
PubMed2004

Noninvasive brain-actuated control of a mobile robot by human EEG.

Brain activity recorded noninvasively is sufficient to control a mobile robot if advanced robotics is used in combination with asynchronous electroencephalogram (EEG) analysis and machine learning techniques. Until now brain-actuated control has mainly relied on implanted electrodes, since EEG-based systems have been considered too slow for controlling rapid and complex sequences of movements. We show that two human subjects successfully moved a robot between several rooms by mental control only, using an EEG-based brain-machine interface that recognized three mental states. Mental control was comparable to manual control on the same task with a performance ratio of 0.74.

Algorithms↗
PubMed2004

Cognitive navigation based on nonuniform Gabor space sampling, unsupervised growing networks, and reinforcement learning.

We study spatial learning and navigation for autonomous agents. A state space representation is constructed by unsupervised Hebbian learning during exploration. As a result of learning, a representation of the continuous two-dimensional (2-D) manifold in the high-dimensional input space is found. The representation consists of a population of localized overlapping place fields covering the 2-D space densely and uniformly. This space coding is comparable to the representation provided by hippocampal place cells in rats. Place fields are learned by extracting spatio-temporal properties of the environment from sensory inputs. The visual scene is modeled using the responses of modified Gabor filters placed at the nodes of a sparse Log-polar graph. Visual sensory aliasing is eliminated by taking into account self-motion signals via path integration. This solves the hidden state problem and provides a suitable representation for applying reinforcement learning in continuous space for action selection. A temporal-difference prediction scheme is used to learn sensorimotor mappings to perform goal-oriented navigation. Population vector coding is employed to interpret ensemble neural activity. The model is validated on a mobile Khepera miniature robot.

Cognition↗
PubMed2004

Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy.

We demonstrate that single-variable integrate-and-fire models can quantitatively capture the dynamics of a physiologically detailed model for fast-spiking cortical neurons. Through a systematic set of approximations, we reduce the conductance-based model to 2 variants of integrate-and-fire models. In the first variant (nonlinear integrate-and-fire model), parameters depend on the instantaneous membrane potential, whereas in the second variant, they depend on the time elapsed since the last spike [Spike Response Model (SRM)]. The direct reduction links features of the simple models to biophysical features of the full conductance-based model. To quantitatively test the predictive power of the SRM and of the nonlinear integrate-and-fire model, we compare spike trains in the simple models to those in the full conductance-based model when the models are subjected to identical randomly fluctuating input. For random current input, the simple models reproduce 70-80 percent of the spikes in the full model (with temporal precision of +/-2 ms) over a wide range of firing frequencies. For random conductance injection, up to 73 percent of spikes are coincident. We also present a technique for numerically optimizing parameters in the SRM and the nonlinear integrate-and-fire model based on spike trains in the full conductance-based model. This technique can be used to tune simple models to reproduce spike trains of real neurons.

Action Potentials↗
PubMed2003

Piecewise linear differential equations and integrate-and-fire neurons: insights from two-dimensional membrane models.

We derive and study two-dimensional generalizations of integrate-and-fire models which can be found from a piecewise linear idealization of the FitzHugh-Nagumo or Morris-Lecar model. These models give rise to new properties not present in one-dimensional integrate-and-fire models. A detailed analytical study of the models is presented. In particular, (i) for the piecewise linear FitzHugh-Nagumo model, we determine analytically the bistability regime between stationary solutions and oscillations, that is, typical for class-II models. (ii) In the piecewise Morris-Lecar model, we find a noncanonical class-I transition from a stationary state to oscillations with logarithmic dependence similar to that found for leaky integrate-and-fire models. (iii) Furthermore, we establish a relation to the recently proposed resonate-and-fire model and show that a short input current pulse can trigger several spikes.

Journal Article↗
PubMed2002

Mathematical formulations of Hebbian learning.

Several formulations of correlation-based Hebbian learning are reviewed. On the presynaptic side, activity is described either by a firing rate or by presynaptic spike arrival. The state of the postsynaptic neuron can be described by its membrane potential, its firing rate, or the timing of backpropagating action potentials (BPAPs). It is shown that all of the above formulations can be derived from the point of view of an expansion. In the absence of BPAPs, it is natural to correlate presynaptic spikes with the postsynaptic membrane potential. Time windows of spike-time-dependent plasticity arise naturally if the timing of postsynaptic spikes is available at the site of the synapse, as is the case in the presence of BPAPs. With an appropriate choice of parameters, Hebbian synaptic plasticity has intrinsic normalization properties that stabilizes postsynaptic firing rates and leads to subtractive weight normalization.

Action Potentials↗
PubMed2002

Stable propagation of activity pulses in populations of spiking neurons.

We investigate the propagation of pulses of spike activity in a neuronal network with feedforward couplings. The neurons are of the spike-response type with a firing probability that depends linearly on the membrane potential. After firing, neurons enter a phase of refractoriness. Spike packets are described in terms of the moments of the firing-time distribution so as to allow for an analytical treatment of the evolution of the spike packet as it propagates from one layer to the next. Analytical results and simulations show that depending on the synaptic coupling strength, a stable propagation of the packet with constant waveform is possible. Crucial for this observation is neither the existence of a firing threshold nor a sigmoidal gain function--both are absent in our model--but the refractory behavior of the neurons.

Action Potentials↗