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133
The NEURON Simulation Environment
, 1997
"... This article describes the concepts and strategies that have guided the design and implementation of this simulator, with emphasis on those features that are particularly relevant to its most efficient use. 1.1 The problem domain ..."
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Cited by 146 (9 self)
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This article describes the concepts and strategies that have guided the design and implementation of this simulator, with emphasis on those features that are particularly relevant to its most efficient use. 1.1 The problem domain
Networks of Spiking Neurons: The Third Generation of Neural Network Models
 Neural Networks
, 1997
"... The computational power of formal models for networks of spiking neurons is compared with that of other neural network models based on McCulloch Pitts neurons (i.e. threshold gates) respectively sigmoidal gates. In particular it is shown that networks of spiking neurons are computationally more powe ..."
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Cited by 138 (12 self)
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The computational power of formal models for networks of spiking neurons is compared with that of other neural network models based on McCulloch Pitts neurons (i.e. threshold gates) respectively sigmoidal gates. In particular it is shown that networks of spiking neurons are computationally more powerful than these other neural network models. A concrete biologically relevant function is exhibited which can be computed by a single spiking neuron (for biologically reasonable values of its parameters), but which requires hundreds of hidden units on a sigmoidal neural net. This article does not assume prior knowledge about spiking neurons, and it contains an extensive list of references to the currently available literature on computations in networks of spiking neurons and relevant results from neurobiology. 1 Definitions and Motivations If one classifies neural network models according to their computational units, one can distinguish three different generations. The first generation i...
Chaotic Balanced State in a Model of Cortical Circuits
 NEURAL COMPUT
, 1998
"... The nature and origin of the temporal irregularity in the electrical activity of cortical neurons in vivo are still not well understood. We consider the hypothesis that this irregularity is due to a balance of excitatory and inhibitory currents into the cortical cells. We study a network model w ..."
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Cited by 83 (1 self)
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The nature and origin of the temporal irregularity in the electrical activity of cortical neurons in vivo are still not well understood. We consider the hypothesis that this irregularity is due to a balance of excitatory and inhibitory currents into the cortical cells. We study a network model with excitatory and inhibitory populations of simple binary units. The internal feedback is mediated by relatively large synaptic strengths, so that the magnitude of the total excitatory as well as inhibitory feedback is much larger than the neuronal threshold. The connectivity is random and sparse. The mean number of connections per unit is large but small compared to the total number of cells in the network. The network also receives a large, temporally regular input from external sources. An analytical solution of the meanfield theory of this model which is exact in the limit of large network size is presented. This theory reveals a new cooperative stationary state of large networks, which we term a balanced state. In this state, a balance between the excitatory and inhibitory inputs emerges dynamically for a wide range of parameters, resulting in a net input whose temporal fluctuations are of the same order as its mean. The internal synaptic inputs act as a strong negative feedback, which linearizes the population responses to the external drive despite the strong nonlinearity of the individual cells. This feedback also greatly stabilizes 1 the system's state and enables it to track a timedependent input on time scales much shorter than the time constant of a single cell. The spatiotemporal statistics of the balanced state is calculated. It is shown that the autocorrelations decay on a short time scale yielding an approximate Poissonian temporal s...
Probabilistic Interpretation of Population Codes
, 1998
"... We present a general encodingdecoding framework for interpreting the activity of a population of units. A standard population code interpretation method, the Poisson model, starts from a description as to how a single value of an underlying quantity can generate the activities of each unit in the p ..."
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Cited by 77 (14 self)
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We present a general encodingdecoding framework for interpreting the activity of a population of units. A standard population code interpretation method, the Poisson model, starts from a description as to how a single value of an underlying quantity can generate the activities of each unit in the population. In casting it in the encodingdecoding framework, we find that this model is too restrictive to describe fully the activities of units in population codes in higher processing areas, such as the medial temporal area. Under a more powerful model, the population activity can convey information not only about a single value of some quantity but also about its whole distribution, including its variance, and perhaps even the certainty the system has in the actual presence in the world of the entity generating this quantity. We propose a novel method for forming such probabilistic interpretations of population codes and compare it to the existing method.
Reduction of the HodgkinHuxley Equations to a SingleVariable Threshold Model
 NEURAL COMPUTATION
, 1997
"... It is generally believed that a neuron is a threshold element which fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the fourdimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximat ..."
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Cited by 67 (22 self)
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It is generally believed that a neuron is a threshold element which fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the fourdimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximated by a response kernel expansion in terms of a single variable, the membrane voltage. The firstorder term is linear in the input and has the typical form of an elementary postsynaptic potential. Higherorder kernels take care of nonlinear interactions between input spikes. In contrast to the standard Volterra expansion the kernels depend on the firing time of the most recent output spike. In particular, a zeroorder kernel which describes the shape of the spike and the typical afterpotential is included. Our model neuron fires, if the membrane voltage, given by the truncated response kernel expansion crosses a threshold. The threshold model is tested on a spike train generated by t...
Generalized IntegrateandFire Models of Neuronal Activity Approximate Spike Trains of a . . .
"... We demonstrate that singlevariable integrateandfire models can quantitatively capture the dynamics of a physiologicallydetailed model for fastspiking cortical neurons. Through a systematic set of approximations, we reduce the conductance based model to two variants of integrateandfire mode ..."
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Cited by 58 (14 self)
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We demonstrate that singlevariable integrateandfire models can quantitatively capture the dynamics of a physiologicallydetailed model for fastspiking cortical neurons. Through a systematic set of approximations, we reduce the conductance based model to two variants of integrateandfire models. In the first variant (nonlinear integrateandfire 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). The direct reduction links features of the simple models to biophysical features of the full conductance based model. To quantitatively
Rate Coding Versus Temporal Order Coding: What the Retinal Ganglion Cells Tell the Visual Cortex
, 2001
"... It is often supposed that messages sent to the visual cortex by the... ..."
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Cited by 56 (13 self)
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It is often supposed that messages sent to the visual cortex by the...
Fast Sigmoidal Networks via Spiking Neurons
 Neural Computation
, 1997
"... We show that networks of relatively realistic mathematical models for biological neurons can in principle simulate arbitrary feedforward sigmoidal neural nets in a way which has previously not been considered. This new approach is based on temporal coding by single spikes (respectively by the timing ..."
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Cited by 52 (8 self)
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We show that networks of relatively realistic mathematical models for biological neurons can in principle simulate arbitrary feedforward sigmoidal neural nets in a way which has previously not been considered. This new approach is based on temporal coding by single spikes (respectively by the timing of synchronous firing in pools of neurons), rather than on the traditional interpretation of analog variables in terms of firing rates. The resulting new simulation is substantially faster and hence more consistent with experimental results about the maximal speed of information processing in cortical neural systems. As a consequence we can show that networks of noisy spiking neurons are "universal approximators" in the sense that they can approximate with regard to temporal coding any given continuous function of several variables. This result holds for a fairly large class of schemes for coding analog variables by firing times of spiking neurons. Our new proposal for the possible organiza...
Fluctuating synaptic conductances recreate in vivolike activity in neocortical neurons
 Neuroscience
, 2001
"... AbstractöTo investigate the basis of the £uctuating activity present in neocortical neurons in vivo, we have combined computational models with wholecell recordings using the dynamicclamp technique. A simpli¢ed `pointconductance' model was used to represent the currents generated by thousands of ..."
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Cited by 49 (22 self)
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AbstractöTo investigate the basis of the £uctuating activity present in neocortical neurons in vivo, we have combined computational models with wholecell recordings using the dynamicclamp technique. A simpli¢ed `pointconductance' model was used to represent the currents generated by thousands of stochastically releasing synapses. Synaptic activity was represented by two independent fast glutamatergic and GABAergic conductances described by stochastic randomwalk processes. An advantage of this approach is that all the model parameters can be determined from voltageclamp experiments. We show that the pointconductance model captures the amplitude and spectral characteristics of the synaptic conductances during background activity. To determine if it can recreate in vivolike activity, we injected this pointconductance model into a singlecompartment model, or in rat prefrontal cortical neurons in vitro using dynamic clamp. This procedure successfully recreated several properties of neurons intracellularly recorded in vivo, such as a depolarized membrane potential, the presence of highamplitude membrane potential £uctuations, a lowinput resistance and irregular spontaneous ¢ring activity. In addition, the pointconductance model could simulate the enhancement of responsiveness due to background activity. We conclude that many of the characteristics of cortical neurons in vivo can be explained by fast glutamatergic and
Spatiotemporal structure of cortical activity: Properties and behavioral relevance
 J. Neurophysiol
, 1998
"... mutal Slovin, and Moshe Abeles. Spatiotemporal structure of millisecond time scale. cortical activity: properties and behavioral relevance. J. Neuro The single neuron timedependent rate function was taken physiol. 79: 2857–2874, 1998. The study was designed to reveal by many as the coding paramete ..."
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Cited by 48 (2 self)
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mutal Slovin, and Moshe Abeles. Spatiotemporal structure of millisecond time scale. cortical activity: properties and behavioral relevance. J. Neuro The single neuron timedependent rate function was taken physiol. 79: 2857–2874, 1998. The study was designed to reveal by many as the coding parameter (e.g., Barlow 1972, 1992, occurrences of precise firing sequences (PFSs) in cortical activity and to test their behavioral relevance. Two monkeys were trained 1994; Newsome et al. 1989; Rolls 1991). Others suggested to perform a delayedresponse paradigm and to open puzzle boxes. a population coding, based on either the summed activity of Extracellular activity was recorded from neurons in premotor and neurons (Georgopoulos et al. 1986; Schwartz 1994), or the prefrontal areas with an array of six microelectrodes. An algorithm coherency in firing among cells (Eckhorn et al. 1988; Engel was developed to detect PFSs, defined as a set of three spikes and et al. 1991a–c; Gray and Singer 1992; Gray et al. 1989, two intervals with a precision of {1 ms repeating significantly 1992). Both views ignored the detailed temporal structure more than expected by chance. The expected level of repetition of cortical activity, assuming that precision is not compatible was computed based on the firing rate and the pairwise correlation with a noisy cortical environment. Despite this notion, sevof