Artificial Spike Trains Research Articles

A general method to generate artificial spike train populations matching recorded neurons.

We developed a general method to generate populations of artificial spike trains (ASTs) that match the statistics of recorded neurons. The method is based on computing a Gaussian local rate function of the recorded spike trains, which results in rate templates from which ASTs are drawn as gamma distributed processes with a refractory period. Multiple instances of spike trains can be sampled from the same rate templates. Importantly, we can manipulate rate-covariances between spike trains by performing simple algorithmic transformations on the rate templates, such as filtering or amplifying specific frequency bands, and adding behavior related rate modulations. The method was examined for accuracy and limitations using surrogate data such as sine wave rate templates, and was then verified for recorded spike trains from cerebellum and cerebral cortex. We found that ASTs generated with this method can closely follow the firing rate and local as well as global spike time variance and power spectrum. The method is primarily intended to generate well-controlled spike train populations as inputs for dynamic clamp studies or biophysically realistic multicompartmental models. Such inputs are essential to study detailed properties of synaptic integration with well-controlled input patterns that mimic the in vivo situation while allowing manipulation of input rate covariances at different time scales.

Long-Term Depression Learning in Spinal Cord Networks.

Investigating learning in networks of spinal cord neurons can provide insight into the dynamics of connectivity in human spinal cords. It may also hold implications for developing neural prosthetics and neurocomputers. Culturing neural networks on microelectrode arrays (MEAs) allows for the repeated observation and stimulation of electrophysiological activity in vitro. Here we used MEAs to demonstrate learning in networks of spinal cord neurons. This was done by exposing E17 mouse spinal cord cultures to high frequency artificial spike trains, or tetanization. Unexpectedly, when comparing the networks' responses to low-frequency probing stimulations before and after tetanization, the cultures were found to demonstrate long-term depression (LTD). LTD was most significantly observed between 500-1000 ms after low-frequency probing. These results indicate that periodic high-frequency excitation of spinal cord networks can result in decreased synaptic efficacy.

Spike-contrast: A novel time scale independent and multivariate measure of spike train synchrony

BackgroundSynchrony within neuronal networks is thought to be a fundamental feature of neuronal networks. In order to quantify synchrony between spike trains, various synchrony measures were developed. Most of them are time scale dependent and thus require the setting of an appropriate time scale. Recently, alternative methods have been developed, such as the time scale independent SPIKE-distance by Kreuz et al. New methodIn this study, a novel time-scale independent spike train synchrony measure called Spike-contrast is proposed. The algorithm is based on the temporal “contrast” (activity vs. non-activity in certain temporal bins) and not only provides a single synchrony value, but also a synchrony curve as a function of the bin size. ResultsFor most test data sets synchrony values obtained with Spike-contrast are highly correlated with those of the SPIKE-distance (Spearman correlation value of 0.99). Correlation was lower for data containing multiple time scales (Spearman correlation value of 0.89). When analyzing large sets of data, Spike-contrast performed faster. Comparison of existing methodSpike-contrast is compared to the SPIKE-distance algorithm. The test data consisted of artificial spike trains with various levels of synchrony, including Poisson spike trains and bursts, spike trains from simulated neuronal Izhikevich networks, and bursts made of smaller bursts (sub-bursts). ConclusionsThe high correlation of Spike-contrast with the established SPIKE-distance for most test data, suggests the suitability of the proposed measure. Both measures are complementary as SPIKE-distance provides a synchrony profile over time, whereas Spike-contrast provides a synchrony curve over bin size.

Network-Wide Adaptive Burst Detection Depicts Neuronal Activity with Improved Accuracy.

Neuronal networks are often characterized by their spiking and bursting statistics. Previously, we introduced an adaptive burst analysis method which enhances the analysis power for neuronal networks with highly varying firing dynamics. The adaptation is based on single channels analyzing each element of a network separately. Such kind of analysis was adequate for the assessment of local behavior, where the analysis focuses on the neuronal activity in the vicinity of a single electrode. However, the assessment of the whole network may be hampered, if parts of the network are analyzed using different rules. Here, we test how using multiple channels and measurement time points affect adaptive burst detection. The main emphasis is, if network-wide adaptive burst detection can provide new insights into the assessment of network activity. Therefore, we propose a modification to the previously introduced inter-spike interval (ISI) histogram based cumulative moving average (CMA) algorithm to analyze multiple spike trains simultaneously. The network size can be freely defined, e.g., to include all the electrodes in a microelectrode array (MEA) recording. Additionally, the method can be applied on a series of measurements on the same network to pool the data for statistical analysis. Firstly, we apply both the original CMA-algorithm and our proposed network-wide CMA-algorithm on artificial spike trains to investigate how the modification changes the burst detection. Thereafter, we use the algorithms on MEA data of spontaneously active chemically manipulated in vitro rat cortical networks. Moreover, we compare the synchrony of the detected bursts introducing a new burst synchrony measure. Finally, we demonstrate how the bursting statistics can be used to classify networks by applying k-means clustering to the bursting statistics. The results show that the proposed network wide adaptive burst detection provides a method to unify the burst definition in the whole network and thus improves the assessment and classification of the neuronal activity, e.g., the effects of different pharmaceuticals. The results indicate that the novel method is adaptive enough to be usable on networks with different dynamics, and it is especially feasible when comparing the behavior of differently spiking networks, for example in developing networks.

Suppression of spontaneous activity before visual response in the primate V1 neurons during a visually guided saccade task.

Visually guided saccadic eye movements are thought to involve multiple stages of processing in diverse brain structures including the primary visual cortex (V1). The variability of neural activity in each of these structures may present ambiguities for downstream stages in identifying sensory and motor signals among spontaneous discharges. The response time of saccadic eye movements made toward a visual target is correlated with the time of the first spikes in V1 that are evoked by the target (Lee et al., 2010). This suggests that downstream neurons receiving the output of V1 are faced with a challenging task of discriminating first spikes of visual response against spontaneous discharge. Here we report a novel response property of the macaque V1 neurons. Immediately before neurons discharge a burst of activity to a visual saccade target, spontaneous discharges were transiently suppressed. This suppression was maximal ∼18 ms after target onset. Based on simulations of artificial spike trains, we propose that the transient suppression enhances temporal contrast for identifying the onset of visual response by increasing the reliability of detection of response onset by downstream neurons, thereby facilitating visually guided behavioral responses.

Use of Granger causality analysis and artificial spike trains to examine pause coding in Purkinje cell spike activity related to rhythmic licking

Cerebellar Purkinje cells in mice show strong activity modulation related to rhythmic licking behavior [1]. Here we examine whether this modulation may preferentially be related to long inter-spike intervals (ISIs), i.e. pauses in spike activity. A preferential use of spike pauses for event coding of Purkinje cells has previously been suggested [2,3]. We analyzed the lick modulation of Purkinje cell spike trains by several methods. First, we used peri-lick time histograms constructed separately by spikes initiating ISIs of different duration (Fig. ​(Fig.1B1B,​,1C).1C). We found that short and long ISIs showed lick modulation, but licks of intermediate duration did not. Next we conducted a wavelet-based frequency resolved Granger causality analysis [4] to determine whether ISIs of different duration were caused by licks and/or were causal in the control of lick timing. We found there was a peak at 6 Hz from lick to spike in 12 cells, and a smaller peak also at 6 Hz from spike to lick in 5 out of those 12 cells. The peaks for plots (scaled to a possible maximum of 1.0) ranged from 0.1 to 0.8 for lick to spike causality and from 0.1 to 0.3 for spike to lick causality. Again, we found that short (0-10 ms) and long (40 ms and above) were preferentially involved in lick coding. To better understand the ISI duration dependence of lick coding we constructed controlled artificial spike trains from gamma ISI distributions [5], each matching slow spontaneous and lick-triggered spike rate fluctuations. The surrogate data show the same results as the biological ones in terms of preferential short and long ISI involvement in lick modulation. However, causality from spike data to licks was not observed in the artificial data. From these results we infer that any relation between specific ISI durations and lick modulation is due to the statistical properties of rate modulated spike trains, and can be mimicked by a simple gamma - distributed process. We also found that even the spike of single Purkinje cells can be predictive of lick events, suggesting Purkinje cell activity is involved in the control of lick timing. Figure 1 Peri-lick spike histogram broken up by ISI duration. A) The schematic showing the regular lick occurrence with an average lickinterval around 160ms. B) Peri-lick spike histogram for a Purkinje cell recording. The time at which the tongue touches the lick ...

STD-Dependent and Independent Encoding of Input Irregularity as Spike Rate in a Computational Model of a Cerebellar Nucleus Neuron

Neurons in the cerebellar nuclei (CN) receive inhibitory inputs from Purkinje cells in the cerebellar cortex and provide the major output from the cerebellum, but their computational function is not well understood. It has recently been shown that the spike activity of Purkinje cells is more regular than previously assumed and that this regularity can affect motor behaviour. We use a conductance-based model of a CN neuron to study the effect of the regularity of Purkinje cell spiking on CN neuron activity. We find that increasing the irregularity of Purkinje cell activity accelerates the CN neuron spike rate and that the mechanism of this recoding of input irregularity as output spike rate depends on the number of Purkinje cells converging onto a CN neuron. For high convergence ratios, the irregularity induced spike rate acceleration depends on short-term depression (STD) at the Purkinje cell synapses. At low convergence ratios, or for synchronised Purkinje cell input, the firing rate increase is independent of STD. The transformation of input irregularity into output spike rate occurs in response to artificial input spike trains as well as to spike trains recorded from Purkinje cells in tottering mice, which show highly irregular spiking patterns. Our results suggest that STD may contribute to the accelerated CN spike rate in tottering mice and they raise the possibility that the deficits in motor control in these mutants partly result as a pathological consequence of this natural form of plasticity.Electronic supplementary materialThe online version of this article (doi:10.1007/s12311-011-0295-9) contains supplementary material, which is available to authorized users.

On the Number of Preganglionic Neurons Driving Human Postganglionic Sympathetic Neurons: A Comparison of Modeling and Empirical Data

Postganglionic sympathetic axons in awake healthy human subjects, regardless of their identity as muscle vasoconstrictor, cutaneous vasoconstrictor, or sudomotor neurons, discharge with a low firing probability (∼30%), generate low firing rates (∼0.5 Hz) and typically fire only once per cardiac interval. The purpose of the present study was to use modeling of spike trains in an attempt to define the number of preganglionic neurons that drive an individual postganglionic neuron. Artificial spike trains were generated in 1–3 preganglionic neurons converging onto a single postganglionic neuron. Each preganglionic input fired with a mean interval distribution of either 1000, 1500, 2000, 2500, or 3000 ms and the SD varied between 0.5×, 1.0×, and 2.0× the mean interval; the discharge frequency of each preganglionic neuron exhibited positive skewness and kurtosis. Of the 45 patterns examined, the mean discharge properties of the postganglionic neuron could only be explained by it being driven by, on average, two preganglionic neurons firing with a mean interspike interval of 2500 ms and SD of 5000 ms. The mean firing rate resulting from this pattern was 0.22 Hz, comparable to that of spontaneously active muscle vasoconstrictor neurons in healthy subjects (0.40 Hz). Likewise, the distribution of the number of spikes per cardiac interval was similar between the modeled and actual data: 0 spikes (69.5 vs 66.6%), 1 spike (25.6 vs 21.2%), 2 spikes (4.3 vs 6.4%), 3 spikes (0.5 vs 1.7%), and 4 spikes (0.1 vs 0.7%). Although some features of the firing patterns could be explained by the postganglionic neuron being driven by a single preganglionic neuron, none of the emulated firing patterns generated by the firing of three preganglionic neurons matched the discharge of the real neurons. These modeling data indicate that, on average, human postganglionic sympathetic neurons are driven by two preganglionic inputs.

Slowly adapting pulmonary stretch receptor spike patterns carry lung distension information

Slowly adapting pulmonary stretch receptors (SARs) provide the respiratory and cardiovascular control systems with information regarding the rate and depth of breathing. Previous information theoretical analysis demonstrated that SAR spike count provides a reliable representation of lung distension. This study examines whether SAR spike patterns may also provide information about lung distension. To investigate this, artificial spike trains were generated with the same number of spikes (but randomized intervals) as those recorded from SARs in response to three different lung inflation volumes in urethane-anesthetized rabbits. Three different spike train classification methods were applied to estimate which stimulus evoked them, and the accuracy with which artificial spike trains were classified was compared to that of real SAR spike trains using the same methods. Because real SAR spike trains were classified with higher accuracies than artificial ones containing the same number of spikes, we conclude that SAR spike patterns, in addition to spike counts, contain information concerning the amplitude of lung distension.

Data driven generation of Purkinje cell spike train correlations to study input output relations in deep cerebellar nuclei neurons

Cerebellar output generation in the deep cerebellar nuclei (DCN) presents a fundamental but poorly understood component of cerebellar function. Experimental data obtained in vitro and in anesthetized animals as well as modeling studies have shown that correlations between Purkinje cell inputs are important in determining the spike rate and spike pattern of DCN output. How a DCN neuron process the synaptic inputs from hundreds of presynaptic Purkinje cells in an awake behaving animal, and the importance of the correlation structure between those inputs, remain unknown, however. We aim to quantitatively assess the correlation structure of Purkinje cells from data recorded in awake mice, and to determine how such correlations interact with the intrinsic DCN physiological properties. It is experimentally impossible to record all the inputs that are reaching a single DCN neuron in an awake animal. Therefore methods need to be developed that can extrapolate the correlations found in a small number of simultaneous recordings to an ensemble of several hundred artificial spike trains with the same correlation structure. Several analytical methods have been developed to generate sets of spike trains with specific correlations in spike times as well as spike rates [1-4]. On the other hand, experimental evidence from Purkinje cell recordings in anesthetized animals point to specific correlation features such as shared pauses [5], synchronous single spikes [6], and synchronous climbing fiber bursts [7]. We will analyze the spike train data obtained from multi-electrode recordings in awake behaving mice to determine the presence of correlation features as well as spike rate correlations. We will derive artificial spike trains using a method based on previous algorithms [1-4]. We will also introduce feature based specific correlations in our constructed artificial spike trains present in our recordings. We will optimize this process so that artificial spike trains show the same inter-spike interval statistics, rate correlations, and feature based correlations seen in recorded spike trains. These data will allow us to drive am ulticompartmental DCN model neuron to study synaptic integration in the awake condition. Because large sets of correlated spike trains are required for all single neuron model explorations of signal processing in awake animals we expect that the generation of realistic input correlations will become an important topic as the field of simulating neural properties in vitro matures to simulating the awake condition.

Estimating the amount of information carried by a neuronal population

Although all brain functions require coordinated activity of many neurons, it has been difficult to estimate the amount of information carried by a population of spiking neurons. We present here a Fourier-based method for estimating the information delivery rate from a population of neurons, which allows us to measure the redundancy of information within and between functional neuronal classes. We illustrate the use of the method on some artificial spike trains and on simultaneous recordings from a small population of neurons from the lateral geniculate nucleus of an anesthetized macaque monkey.

Network-State Modulation of Power-Law Frequency-Scaling in Visual Cortical Neurons

Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of Vm activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the Vm reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the “effective” connectivity responsible for the dynamical signature of the population signals measured at different integration levels, from Vm to LFP, EEG and fMRI.

Generating Spike Trains with Specified Correlation Coefficients

Spike trains recorded from populations of neurons can exhibit substantial pairwise correlations between neurons and rich temporal structure. Thus, for the realistic simulation and analysis of neural systems, it is essential to have efficient methods for generating artificial spike trains with specified correlation structure. Here we show how correlated binary spike trains can be simulated by means of a latent multivariate gaussian model. Sampling from the model is computationally very efficient and, in particular, feasible even for large populations of neurons. The entropy of the model is close to the theoretical maximum for a wide range of parameters. In addition, this framework naturally extends to correlations over time and offers an elegant way to model correlated neural spike counts with arbitrary marginal distributions.

Unbiased estimation of precise temporal correlations between spike trains

A key issue in systems neuroscience is the contribution of precise temporal inter-neuronal interactions to information processing in the brain, and the main analytical tool used for studying pair-wise interactions is the cross-correlation histogram (CCH). Although simple to generate, a CCH is influenced by multiple factors in addition to precise temporal correlations between two spike trains, thus complicating its interpretation. A Monte-Carlo-based technique, the jittering method, has been suggested to isolate the contribution of precise temporal interactions to neural information processing. Here, we show that jittering spike trains is equivalent to convolving the CCH derived from the original trains with a finite window and using a Poisson distribution to estimate probabilities. Both procedures over-fit the original spike trains and therefore the resulting statistical tests are biased and have low power. We devise an alternative method, based on convolving the CCH with a partially hollowed window, and illustrate its utility using artificial and real spike trains. The modified convolution method is unbiased, has high power, and is computationally fast. We recommend caution in the use of the jittering method and in the interpretation of results based on it, and suggest using the modified convolution method for detecting precise temporal correlations between spike trains.

Stimulus size dependence of information transfer from retina to thalamus

Relay cells in the mammalian lateral geniculate nucleus (LGN) are driven primarily by single retinal ganglion cells (RGCs). However, an LGN cell responds typically to less than half of the spikes it receives from the RGC that drives it, and without retinal drive the LGN is silent (Kaplan and Shapley, 1984). Recent studies, which used stimuli restricted to the receptive field (RF) center, show that despite the great loss of spikes, more than half of the information carried by the RGC discharge is typically preserved in the LGN discharge (Sincich et al., 2009), suggesting that the retinal spikes that are deleted by the LGN carry less information than those that are transmitted to the cortex. To determine how LGN relay neurons decide which retinal spikes to respond to, we recorded extracellularly from the cat LGN relay cell spikes together with the slow synaptic (‘S’) potentials that signal the firing of retinal spikes. We investigated the influence of the inhibitory surround of the LGN RF by stimulating the eyes with spots of various sizes, the largest of which covered the center and surround of the LGN relay cell's RF. We found that for stimuli that activated mostly the RF center, each LGN spike delivered more information than the retinal spike, but this difference was reduced as stimulus size increased to cover the RF surround. To evaluate the optimality of the LGN editing of retinal spikes, we created artificial spike trains from the retinal ones by various deletion schemes. We found that single LGN cells transmitted less information than an optimal detector could.

Spike Train Probability Models for Stimulus-Driven Leaky Integrate-and-Fire Neurons

Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike train data in important ways, but they are not very easy to apply to the analysis of spike train data. Instead, statistical methods based on point process models of spike trains provide a wide range of data-analytical techniques. Two simplified point process models have been introduced in the literature: the time-rescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (m-IMI) model. In this letter we investigate the extent to which the TRRP and m-IMI models are able to fit spike trains produced by stimulus-driven leaky integrate-and-fire (LIF) neurons. With a constant stimulus, the LIF spike train is a renewal process, and the m-IMI and TRRP models will describe accurately the LIF spike train variability. With a time-varying stimulus, the probability of spiking under all three of these models depends on both the experimental clock time relative to the stimulus and the time since the previous spike, but it does so differently for the LIF, m-IMI, and TRRP models. We assessed the distance between the LIF model and each of the two empirical models in the presence of a time-varying stimulus. We found that while lack of fit of a Poisson model to LIF spike train data can be evident even in small samples, the m-IMI and TRRP models tend to fit well, and much larger samples are required before there is statistical evidence of lack of fit of the m-IMI or TRRP models. We also found that when the mean of the stimulus varies across time, the m-IMI model provides a better fit to the LIF data than the TRRP, and when the variance of the stimulus varies across time, the TRRP provides the better fit.

Real time decoding of hand grasping signals from macaque premotor and parietal cortex

Real time decoding of hand grasping signals from macaque premotor and parietal cortex

Contribution of Individual Retinal Ganglion Cell Responses to Velocity and Acceleration Encoding

We investigate the capability of turtle retinal ganglion cell (RGC) ensembles to simultaneously encode multiple aspects of visual motion: speed, direction, and acceleration of moving patterns. Bayesian stimulus reconstruction reveals that the instantaneous firing rates of RGCs contain information about all of these stimulus properties. Stimulus velocity is mainly encoded by steady-state firing rates, whereas acceleration can be reconstructed from transient components in RGC activity induced by abrupt velocity changes. Therefore neurons in higher brain areas may in principle extract information about changing velocity from the instantaneous firing activity of RGCs, without the need to compare responses to present velocities to previous ones. However, reconstruction requires the estimation of a combined acceleration and velocity signal, indicating that RGC ensembles signal both properties simultaneously. In accordance with this conclusion, combined velocity/acceleration sensitivity enhances the similarity of artificial spike trains to experimental data by 50% compared with the case of pure velocity tuning. Decoding of motion direction in addition to speed and acceleration requires direction-sensitive cells, which generate higher firing rates for one of the motion directions and therefore show asymmetric velocity tuning. By dividing the entire ensemble of simultaneously recorded cells into one group of direction-sensitive cells and one group with symmetric tuning, we demonstrate that the population of direction-sensitive cells encodes a combination of motion speed, acceleration, and direction. However, estimation of velocity and acceleration is improved by including the larger group of RGC responses that are sensitive to speed but not to motion direction.

See globally, spike locally: oscillations in a retinal model encode large visual features

We show that coherent oscillations among neighboring ganglion cells in a retinal model encode global topological properties, such as size, that cannot be deduced unambiguously from their local, time-averaged firing rates. Whereas ganglion cells may fire similar numbers of spikes in response to both small and large spots, only large spots evoke coherent high frequency oscillations, potentially allowing downstream neurons to infer global stimulus properties from their local afferents. To determine whether such information might be extracted over physiologically realistic spatial and temporal scales, we analyzed artificial spike trains whose oscillatory correlations were similar to those measured experimentally. Oscillatory power in the upper gamma band, extracted on single-trials from multi-unit spike trains, supported good to excellent size discrimination between small and large spots, with performance improving as the number of cells and/or duration of the analysis window was increased. By using Poisson distributed spikes to normalize the firing rate across stimulus conditions, we further found that coincidence detection, or synchrony, yielded substantially poorer performance on identical size discrimination tasks. To determine whether size encoding depended on contiguity independent of object shape, we examined the total oscillatory activity across the entire model retina in response to random binary images. As the ON-pixel probability crossed the percolation threshold, which marks the sudden emergence of large connected clusters, the total gamma-band activity exhibited a sharp transition, a phenomena that may be experimentally observable. Finally, a reanalysis of previously published oscillatory responses from cat ganglion cells revealed size encoding consistent with that predicted by the retinal model.

Correlated firing improves stimulus discrimination in a retinal model.

Synchronous firing limits the amount of information that can be extracted by averaging the firing rates of similarly tuned neurons. Here, we show that the loss of such rate-coded information due to synchronous oscillations between retinal ganglion cells can be overcome by exploiting the information encoded by the correlations themselves. Two very different models, one based on axon-mediated inhibitory feedback and the other on oscillatory common input, were used to generate artificial spike trains whose synchronous oscillations were similar to those measured experimentally. Pooled spike trains were summed into a threshold detector whose output was classified using Bayesian discrimination. For a threshold detector with short summation times, realistic oscillatory input yielded superior discrimination of stimulus intensity compared to rate-matched Poisson controls. Even for summation times too long to resolve synchronous inputs, gamma band oscillations still contributed to improved discrimination by reducing the total spike count variability, or Fano factor. In separate experiments in which neurons were synchronized in a stimulus-dependent manner without attendant oscillations, the Fano factor increased markedly with stimulus intensity, implying that stimulus-dependent oscillations can offset the increased variability due to synchrony alone.