2,051 research outputs found
A unified view on weakly correlated recurrent networks
The diversity of neuron models used in contemporary theoretical neuroscience
to investigate specific properties of covariances raises the question how these
models relate to each other. In particular it is hard to distinguish between
generic properties and peculiarities due to the abstracted model. Here we
present a unified view on pairwise covariances in recurrent networks in the
irregular regime. We consider the binary neuron model, the leaky
integrate-and-fire model, and the Hawkes process. We show that linear
approximation maps each of these models to either of two classes of linear rate
models, including the Ornstein-Uhlenbeck process as a special case. The classes
differ in the location of additive noise in the rate dynamics, which is on the
output side for spiking models and on the input side for the binary model. Both
classes allow closed form solutions for the covariance. For output noise it
separates into an echo term and a term due to correlated input. The unified
framework enables us to transfer results between models. For example, we
generalize the binary model and the Hawkes process to the presence of
conduction delays and simplify derivations for established results. Our
approach is applicable to general network structures and suitable for
population averages. The derived averages are exact for fixed out-degree
network architectures and approximate for fixed in-degree. We demonstrate how
taking into account fluctuations in the linearization procedure increases the
accuracy of the effective theory and we explain the class dependent differences
between covariances in the time and the frequency domain. Finally we show that
the oscillatory instability emerging in networks of integrate-and-fire models
with delayed inhibitory feedback is a model-invariant feature: the same
structure of poles in the complex frequency plane determines the population
power spectra
Multiple firing coherence resonances in excitatory and inhibitory coupled neurons
The impact of inhibitory and excitatory synapses in delay-coupled
Hodgkin--Huxley neurons that are driven by noise is studied. If both synaptic
types are used for coupling, appropriately tuned delays in the inhibition
feedback induce multiple firing coherence resonances at sufficiently strong
coupling strengths, thus giving rise to tongues of coherency in the
corresponding delay-strength parameter plane. If only inhibitory synapses are
used, however, appropriately tuned delays also give rise to multiresonant
responses, yet the successive delays warranting an optimal coherence of
excitations obey different relations with regards to the inherent time scales
of neuronal dynamics. This leads to denser coherence resonance patterns in the
delay-strength parameter plane. The robustness of these findings to the
introduction of delay in the excitatory feedback, to noise, and to the number
of coupled neurons is determined. Mechanisms underlying our observations are
revealed, and it is suggested that the regularity of spiking across neuronal
networks can be optimized in an unexpectedly rich variety of ways, depending on
the type of coupling and the duration of delays.Comment: 7 two-column pages, 6 figures; accepted for publication in
Communications in Nonlinear Science and Numerical Simulatio
The Spatial Structure of Stimuli Shapes the Timescale of Correlations in Population Spiking Activity
Throughout the central nervous system, the timescale over which pairs of neural spike trains are correlated is shaped by stimulus structure and behavioral context. Such shaping is thought to underlie important changes in the neural code, but the neural circuitry responsible is largely unknown. In this study, we investigate a stimulus-induced shaping of pairwise spike train correlations in the electrosensory system of weakly electric fish. Simultaneous single unit recordings of principal electrosensory cells show that an increase in the spatial extent of stimuli increases correlations at short (~10 ms) timescales while simultaneously reducing correlations at long (~100 ms) timescales. A spiking network model of the first two stages of electrosensory processing replicates this correlation shaping, under the assumptions that spatially broad stimuli both saturate feedforward afferent input and recruit an open-loop inhibitory feedback pathway. Our model predictions are experimentally verified using both the natural heterogeneity of the electrosensory system and pharmacological blockade of descending feedback projections. For weak stimuli, linear response analysis of the spiking network shows that the reduction of long timescale correlation for spatially broad stimuli is similar to correlation cancellation mechanisms previously suggested to be operative in mammalian cortex. The mechanism for correlation shaping supports population-level filtering of irrelevant distractor stimuli, thereby enhancing the population response to relevant prey and conspecific communication inputs. © 2012 Litwin-Kumar et al
Neural oscillations as a signature of efficient coding in the presence of synaptic delays
Cortical networks exhibit ‘global oscillations’, in which neural spike times are entrained to an underlying oscillatory rhythm, but where individual neurons fire irregularly, on only a fraction of cycles. While the network dynamics underlying global oscillations have been well characterised, their function is debated. Here, we show that such global oscillations are a direct consequence of optimal efficient coding in spiking networks with synaptic delays and noise. To avoid firing unnecessary spikes, neurons need to share information about the network state. Ideally, membrane potentials should be strongly correlated and reflect a ‘prediction error’ while the spikes themselves are uncorrelated and occur rarely. We show that the most efficient representation is when: (i) spike times are entrained to a global Gamma rhythm (implying a consistent representation of the error); but (ii) few neurons fire on each cycle (implying high efficiency), while (iii) excitation and inhibition are tightly balanced. This suggests that cortical networks exhibiting such dynamics are tuned to achieve a maximally efficient population code
Locking of correlated neural activity to ongoing oscillations
Population-wide oscillations are ubiquitously observed in mesoscopic signals
of cortical activity. In these network states a global oscillatory cycle
modulates the propensity of neurons to fire. Synchronous activation of neurons
has been hypothesized to be a separate channel of signal processing information
in the brain. A salient question is therefore if and how oscillations interact
with spike synchrony and in how far these channels can be considered separate.
Experiments indeed showed that correlated spiking co-modulates with the static
firing rate and is also tightly locked to the phase of beta-oscillations. While
the dependence of correlations on the mean rate is well understood in
feed-forward networks, it remains unclear why and by which mechanisms
correlations tightly lock to an oscillatory cycle. We here demonstrate that
such correlated activation of pairs of neurons is qualitatively explained by
periodically-driven random networks. We identify the mechanisms by which
covariances depend on a driving periodic stimulus. Mean-field theory combined
with linear response theory yields closed-form expressions for the
cyclostationary mean activities and pairwise zero-time-lag covariances of
binary recurrent random networks. Two distinct mechanisms cause time-dependent
covariances: the modulation of the susceptibility of single neurons (via the
external input and network feedback) and the time-varying variances of single
unit activities. For some parameters, the effectively inhibitory recurrent
feedback leads to resonant covariances even if mean activities show
non-resonant behavior. Our analytical results open the question of
time-modulated synchronous activity to a quantitative analysis.Comment: 57 pages, 12 figures, published versio
Integration of continuous-time dynamics in a spiking neural network simulator
Contemporary modeling approaches to the dynamics of neural networks consider
two main classes of models: biologically grounded spiking neurons and
functionally inspired rate-based units. The unified simulation framework
presented here supports the combination of the two for multi-scale modeling
approaches, the quantitative validation of mean-field approaches by spiking
network simulations, and an increase in reliability by usage of the same
simulation code and the same network model specifications for both model
classes. While most efficient spiking simulations rely on the communication of
discrete events, rate models require time-continuous interactions between
neurons. Exploiting the conceptual similarity to the inclusion of gap junctions
in spiking network simulations, we arrive at a reference implementation of
instantaneous and delayed interactions between rate-based models in a spiking
network simulator. The separation of rate dynamics from the general connection
and communication infrastructure ensures flexibility of the framework. We
further demonstrate the broad applicability of the framework by considering
various examples from the literature ranging from random networks to neural
field models. The study provides the prerequisite for interactions between
rate-based and spiking models in a joint simulation
Decorrelation of neural-network activity by inhibitory feedback
Correlations in spike-train ensembles can seriously impair the encoding of
information by their spatio-temporal structure. An inevitable source of
correlation in finite neural networks is common presynaptic input to pairs of
neurons. Recent theoretical and experimental studies demonstrate that spike
correlations in recurrent neural networks are considerably smaller than
expected based on the amount of shared presynaptic input. By means of a linear
network model and simulations of networks of leaky integrate-and-fire neurons,
we show that shared-input correlations are efficiently suppressed by inhibitory
feedback. To elucidate the effect of feedback, we compare the responses of the
intact recurrent network and systems where the statistics of the feedback
channel is perturbed. The suppression of spike-train correlations and
population-rate fluctuations by inhibitory feedback can be observed both in
purely inhibitory and in excitatory-inhibitory networks. The effect is fully
understood by a linear theory and becomes already apparent at the macroscopic
level of the population averaged activity. At the microscopic level,
shared-input correlations are suppressed by spike-train correlations: In purely
inhibitory networks, they are canceled by negative spike-train correlations. In
excitatory-inhibitory networks, spike-train correlations are typically
positive. Here, the suppression of input correlations is not a result of the
mere existence of correlations between excitatory (E) and inhibitory (I)
neurons, but a consequence of a particular structure of correlations among the
three possible pairings (EE, EI, II)
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