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Wulfram Gerstner

Publications and source records attributed to Wulfram Gerstner.

At least 19 recordsLinked to original sources
PubMed2006

Triplets of spikes in a model of spike timing-dependent plasticity.

Classical experiments on spike timing-dependent plasticity (STDP) use a protocol based on pairs of presynaptic and postsynaptic spikes repeated at a given frequency to induce synaptic potentiation or depression. Therefore, standard STDP models have expressed the weight change as a function of pairs of presynaptic and postsynaptic spike. Unfortunately, those paired-based STDP models cannot account for the dependence on the repetition frequency of the pairs of spike. Moreover, those STDP models cannot reproduce recent triplet and quadruplet experiments. Here, we examine a triplet rule (i.e., a rule which considers sets of three spikes, i.e., two pre and one post or one pre and two post) and compare it to classical pair-based STDP learning rules. With such a triplet rule, it is possible to fit experimental data from visual cortical slices as well as from hippocampal cultures. Moreover, when assuming stochastic spike trains, the triplet learning rule can be mapped to a Bienenstock-Cooper-Munro learning rule.

Action Potentials↗
PubMed2006

From spiking neurons to rate models: a cascade model as an approximation to spiking neuron models with refractoriness.

A neuron that is stimulated repeatedly by the same time-dependent stimulus exhibits slightly different spike timing at each trial. We compared the exact solution of the time-dependent firing rate for a stochastically spiking neuron model with refractoriness (spike response model) with that of an inhomogeneous Poisson process subject to the same stimulus. To arrive at a mapping between the two models we used alternatively (i) a systematic parameter-free Volterra expansion of the exact solution or (ii) a linear filter combined with nonlinear Poisson rate model (linear-nonlinear Poisson cascade model) with a single free parameter. Both the cascade model and the second-order Volterra model showed excellent agreement with the exact rate dynamics of the spiking neuron model with refractoriness even for strong and rapidly changing input. Cascade rate models are widely used in systems neuroscience. Our method could help to connect experimental rate measurements to the theory of spiking neurons.

Action Potentials↗
PubMed2006

Predicting spike timing of neocortical pyramidal neurons by simple threshold models.

Neurons generate spikes reliably with millisecond precision if driven by a fluctuating current--is it then possible to predict the spike timing knowing the input? We determined parameters of an adapting threshold model using data recorded in vitro from 24 layer 5 pyramidal neurons from rat somatosensory cortex, stimulated intracellularly by a fluctuating current simulating synaptic bombardment in vivo. The model generates output spikes whenever the membrane voltage (a filtered version of the input current) reaches a dynamic threshold. We find that for input currents with large fluctuation amplitude, up to 75% of the spike times can be predicted with a precision of +/-2 ms. Some of the intrinsic neuronal unreliability can be accounted for by a noisy threshold mechanism. Our results suggest that, under random current injection into the soma, (i) neuronal behavior in the subthreshold regime can be well approximated by a simple linear filter; and (ii) most of the nonlinearities are captured by a simple threshold process.

Action Potentials↗
PubMed2006

Statistics of subthreshold neuronal voltage fluctuations due to conductance-based synaptic shot noise.

Neurons in the central nervous system, and in the cortex in particular, are subject to a barrage of pulses from their presynaptic populations. These synaptic pulses are mediated by conductance changes and therefore lead to increases or decreases of the neuronal membrane potential with amplitudes that are dependent on the voltage: synaptic noise is multiplicative. The statistics of the membrane potential are of experimental interest because the measurement of a single subthreshold voltage can be used to probe the activity occurring across the presynaptic population. Though the interpulse interval is not always significantly smaller than the characteristic decay time of the pulses, and so the fluctuations have the nature of shot noise, the majority of results available in the literature have been calculated in the diffusion limit, which is valid for high-rate pulses. Here the effects that multiplicative conductance noise and shot noise have on the voltage fluctuations are examined. It is shown that both these aspects of synaptic drive sculpt high-order features of the subthreshold voltage distribution, such as the skew. It is further shown that the diffusion approximation can only capture the effects arising from the multiplicative conductance noise, predicting a negative voltage skew for excitatory drive. Exact results for the full dynamics are derived from a master-equation approach, predicting positively skewed distributions with long tails in voltage ranges typical for action potential generation. It is argued that, although the skew is a high-order feature of subthreshold voltage distributions, the increased probability of reaching firing threshold suggests a potential role for shot noise in shaping the neuronal transfer function.

Action Potentials↗
PubMed2006

Optimal spike-timing-dependent plasticity for precise action potential firing in supervised learning.

In timing-based neural codes, neurons have to emit action potentials at precise moments in time. We use a supervised learning paradigm to derive a synaptic update rule that optimizes by gradient ascent the likelihood of postsynaptic firing at one or several desired firing times. We find that the optimal strategy of up- and downregulating synaptic efficacies depends on the relative timing between presynaptic spike arrival and desired postsynaptic firing. If the presynaptic spike arrives before the desired postsynaptic spike timing, our optimal learning rule predicts that the synapse should become potentiated. The dependence of the potentiation on spike timing directly reflects the time course of an excitatory postsynaptic potential. However, our approach gives no unique reason for synaptic depression under reversed spike timing. In fact, the presence and amplitude of depression of synaptic efficacies for reversed spike timing depend on how constraints are implemented in the optimization problem. Two different constraints, control of postsynaptic rates and control of temporal locality, are studied. The relation of our results to spike-timing-dependent plasticity and reinforcement learning is discussed.

Action Potentials↗
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↗