Visual motion computation in recurrent neural networks

Visual neuroscientists seek to answer two related questions. First, what does the visual system do? Second, how does it do it? While an answer to the second question is a description based on anatomy and biophysics, an answer to the first question is a description of computations performed on images. Important steps in providing this description were made with the publication of two classical studies on primary visual cortex by Movshon et al. (1978a,b). These studies have not aged in their readability, and do not require an interpretive key to be enjoyed by the contemporary reader. As an introduction, however, this Perspectives article briefly reviews the state of the art at the time of their appearance, their main findings, and their influence on three decades of subsequent investigations. The 1960s brought important advances in the understanding of the computations performed by the retina. An influential view emerged that described retinal ganglion cells as linear filters, i.e. as processes that compute a weighted sum of the intensities in the stimulus, with weights given by the receptive field (Enroth-Cugell & Robson, 1966). This simple 'linear model' applied to the majority of ganglion cells in the cat retina (those of the X type, corresponding to P cells in primates). It was quite powerful, as it promised to predict the responses of X ganglion cells to arbitrary stimuli, on the basis of the simple knowledge of the receptive field. This purely linear view was complemented by the discovery that another kind of ganglion cells, those of Y type (which correspond to M cells in primates), perform non-linear operations, suggesting that they sum the distorted output of subunits that in turn have linear receptive fields (Enroth-Cugell & Robson, 1966; Hochstein & Shapley, 1976). This arrangement confers position invariance: for stimuli of high spatial frequency, Y cells respond equally regardless of position within the receptive field. These advances suggested new ways of looking at simple and complex cells in primary visual cortex. Hubel & Wiesel (1962) had defined simple cells as having distinct antagonistic regions in their receptive fields, and had suggested that knowing those regions, one could predict 'the responses to any shape of stimulus, stationary or moving'. They had defined complex cells as any cell that was not simple, and had reported that complex cells achieved position invariance within their receptive field: they would respond to a stimulus of the appropriate orientation regardless of position within the receptive field. These attributes of simple and complex cells resembled those of X and Y ganglion cells. Some authors proposed that the correspondence could be anatomical, i.e. that it reflected predominance of X inputs to simple cells and of Y inputs to complex cells (Stone, 1972; Movshon, 1975), a suggestion that was not later confirmed. More generally, however, the linear and non-linear models and the stimulation procedures that had been so useful to analyse X and Y cells (Enroth-Cugell & Robson, 1966; Hochstein & Shapley, 1976) constituted promising starting points for a concise and precise characterization of simple and complex cells. In addition to the breakthroughs in retinal physiology, another force was pushing towards the use of quantitative engineering techniques in primary visual cortex: such techniques were proving successful to study human perception. In particular, the University of Cambridge – where Movshon, Thompson and Tolhurst operated – was a hotbed of research into the relations between single neuron responses and perceptual phenomena. These phenomena were investigated with rigorous psychophysical measures, and described with quantitative models based on image filtering (Graham, 1989; Wandell, 1995). Much of this research rested on the concept of 'channels', which are linear filters. Simple cells in the cortex seemed to be good candidates for such a role. Did they exhibit linear summation? The time had come to apply the power of linear systems analysis and related techniques to primary visual cortex. In their first article, Movshon et al. (1978a) applied linear systems analysis to the responses of simple cells. They measured responses of simple cells to gratings and bars, and asked if such responses were consistent with the output of a linear receptive field (Fig. 1A). The models of simple and complex cells proposed by Movshon, Thompson and Tolhurst ( Movshon et al. 1978a,b) A, linear model of simple cells. The first stage is linear filtering, i. e. aweighted sum of the image intensities, with weights given by the receptive field. The second stage isrectification: only the part of the responses that is larger than a threshold is seen in the firing rate response. B, subunit model of complex cells. The first stage is linear filtering by a number of receptive fields such asthose of simple cells (here we show four of them with spatial phases offset by 90 deg). The subsequent stages involve rectification, and then summation. Much as Enroth-Cugell & Robson (1966) had done for X retinal cells, they asked if the responses to drifting sinusoidal stimuli were sinusoidal, as one would expect from a linear filter. The results supported this view, provided that the responses were rectified by the spike threshold, which shows only the part of the responses that lie above threshold (Fig. 1A). The authors then asked how the responses depended on the spatial phase of a standing grating whose contrast oscillated sinusoidally in time. This test had been applied to X and Y retinal cells by Hochstein & Shapley (1976). Here the linear model was put to a quantitative test, and the fit was good, provided again that the output of the receptive field was passed through a rectification stage that thresholded it (Fig. 1A). Movshon, Thompson and Tolhurst were even able to suggest how high the threshold should be relative to rest. They expressed this threshold in the units of firing rate responses, spikes s−1. For example, for the cell in their Fig. 4, the estimated threshold was 8 spikes s−1 (if the receptive field were to output 12 spikes s−1, the neuron would output 4 spikes s−1). Finally, the authors asked a key question: was the selectivity of simple cells predictable on the basis of the receptive field alone, as had been suggested by Hubel and Wiesel, and as would be expected of a linear filter? To test this hypothesis, they turned again to the approach that had demonstrated the linearity of X retinal cells (Enroth-Cugell & Robson, 1966). First, they measured responses to drifting gratings of various spatial frequencies (Fig. 2A). Then, they measured responses to bars flashed at various positions, thus estimating the profile of the receptive field (Fig. 2B, histograms). According to the linear hypothesis, the first data set could be used to predict the second one. This was indeed the case for the cells (Fig. 2B, curve): just as predicted by the linear model, the selectivity of simple cells for spatial frequency could be predicted on the basis of the receptive field profile. Linearity of spatial summation in simple cells the experiment in Fig. 9 of the first 1978 article by Movshon, Thompson and Tolhurst ( Movshon et al. 1978a) Responses were simulated from a model simple cell with a linear spatial receptive field that summates strongly distorted thalamic inputs (Carandini et al. 2002). A, spatial frequency tuning of the simple cell. The ordinate marks the amplitude of the sinusoidal modulation caused by drifting sinusoidal gratings, whose spatial frequency is plotted on the abscissa. B, profile of the receptive field of the simple cell. The histogram shows the firing rate elicited by flashing bars in various spatial positions across the receptive field. Negative responses indicate responses elicited when withdrawing the bar. The curve shows the prediction based on linearity, obtained by Fourier transform of the data in A. For all its success in explaining responses of simple cells, the linear model (Fig. 1A) could not possibly work for complex cells. Complex cells are insensitive to the precise position of a bar within the receptive field, and respond both to the onset and to the offset of the bar. Neither of these properties could arise from a single linear receptive field. Hubel & Wiesel (1962) had therefore described complex cells as summing the output of a number of simple cells with similar orientation preference but different receptive field profiles. Borrowing from the subunit model proposed for Y ganglion cells by Hochstein & Shapley (1976), such a description could be made quantitative by postulating a number of linear receptive fields orientated in space (subunits), whose outputs are rectified by threshold, and integrated into a single response (Fig. 1B). In their second article, Movshon et al. (1978b) went on to propose such a subunit model for complex cells (Fig. 1B), and to justify each of its components. They started by performing the same three measures that they had performed in simple cells. First, the authors studied the modulation in firing rate caused by drifting sinusoidal gratings. Complex cells responded phasically only at the lowest spatial frequencies, but as soon as the frequency approached the optimal, the responses became constant in time. This was consistent with a subunit model (Fig. 1B). Each of the subunits would respond with a sinusoid, but the rectified sinusoids would be offset in time, and therefore they would sum to an approximately constant value. Second, they asked how complex cell responses depended on the spatial phase of a standing grating whose contrast reversed in time. Just as for Y ganglion cells (Hochstein & Shapley, 1976), the cells did not care for spatial phase, giving two responses for each cycle of the stimulus (once for each sign of contrast). These results again were consistent with the subunit model (Fig. 1B): each subunit would give positive responses only once in each cycle, and only at specific spatial phases, but the sum of the positive subunit responses would rise twice in each cycle, irrespective of spatial phase. Third, they asked whether the selectivity of complex cells was predictable on the basis of the receptive field alone. The answer was a resounding no: as predicted by the subunit model (Fig. 1B), receptive fields of complex cells don't have strong distinct subregions, so it is not possible to predict their selectivity from a receptive field profile. While all these results seemed consistent with a subunit model (Fig. 1B), a key attribute of that model remained to be verified: are the receptive fields of the subunits really linear? To test this hypothesis, the authors devised an elegant experiment, in which they measured the interaction of dark and light bars in different positions of the receptive field. To understand this experiment, consider a simplified model of complex cell that includes only four subunits (Fig. 1B), and imagine placing a bright bar over the central positive region in the receptive field of the first subunit. This subunit will give a strong positive response, and will thus operate well above threshold. Conversely, the third subunit, which has the opposite receptive field, will be strongly suppressed, and will operate much below threshold. The second and fourth subunits, in turn, will barely respond, so they will operate (as normally) slightly below threshold. Adding a second bar to the stimulus therefore will mostly reveal the receptive field properties of the first subunit. Indeed, as shown in Fig. 8 of the original article, the interaction profiles between bars resemble receptive fields. If these receptive fields of the subunits operate linearly (and if all subunits are similar in spatial frequency preferences), then it should be possible to predict the spatial frequency selectivity of the neuron based on the receptive field profile of the subunits, just as for simple cells (Fig. 2). The results of this experiment, illustrated in Fig. 9 of the original article, confirm this prediction, providing strong support for the subunit model of complex cells (Fig. 1B). The results of the two articles therefore can be summarized by two models: the linear model of simple cells (Fig. 1A), and the subunit model of complex cells (Fig. 1B). These models share two key attributes: (1) all the image processing is performed by linear filters; (2) the non-linearities operate on the time-varying signals that are output by the filters. These models have formed the basis for much that has followed in the subsequent three decades. There is obviously no space here to cover this territory, for which we refer the reader to recent reviews (e.g. Carandini et al. 2005). What might be more useful would be to discuss those aspects that, with 100% hindsight, could have been analysed differently, and would arguably have led to slightly different conclusions. First, when comparing responses to gratings to the profiles of the receptive field (Fig. 2), whether for simple cells or for the subunits of complex cells, a free scaling factor was allowed to obtain a match. Such a scaling factor should not be necessary for the simple models shown in Fig. 1, but it is necessary for actual cells, whose responsiveness depends very much on the local distribution of contrast. To account for this dependence, the models were later extended to include a divisive stage that controls responsiveness on the basis of the distribution of local contrast (for reviews see Heeger, 1992; Carandini et al. 1999). Second, the authors were perhaps wise to concentrate on one spatial dimension, and thus to avoid the contentious issue of orientation selectivity. Orientation tuning curves were not measured in this study, arguably because rotating the stimulation device involved placing one's hand within centimetres of electrocution, something that was done only reluctantly, once for each cell (J. A. Movshon, personal communication). Had the authors measured 2-dimensional receptive field profiles they could have asked whether these profiles predicted orientation selectivity. This issue remained open for decades and is not entirely closed to this date (reviewed by Ferster & Miller, 2000). Finally, perhaps the greatest limitation of these studies is that they concentrated on the spatial domain, and did not test linearity in the temporal domain. On the one hand, as was shown in the subsequent decades, the concept of spatial receptive field can be fruitfully extended to 3-dimensional space–time, to account for phenomena of direction selectivity (in fact, the nascent signs of such an extension can be seen already in the second 1978 article). On the other hand, as demonstrated later by Tolhurst et al. (1980), in primary visual cortex temporal summation is far from linear: responses are much more transient than would be expected from the frequency selectivity curves. This non-linearity is puzzling: how could a receptive field be spatially linear and temporally non-linear? It is now thought that because a cortical cell sums inputs from a variety of spatially displaced thalamic neurons, even if the individual inputs are grossly distorted by saturating and threshold non-linearities, the overall spatial summation properties of the neuron will remain approximately linear (Carandini et al. 2002; Priebe & Ferster, 2006). Indeed, the simulations shown here (Fig. 2) resulted from a model cell that summates such strongly non-linear inputs. This model cell passes the test of spatial linearity devised by the 1978 papers (Fig. 2), yet it would fail any test of temporal linearity. If it took three decades to obtain this realization, it is possibly because these 1978 papers made such a compelling case for linearity, and the field took them as evidence that every step in the visual system up to the primary visual cortex had to be linear. The reasoning, partly explicit in these papers and implicit in much of the subsequent literature, was that there could be no non-linear stages from the cones to the cortex because those stages would have prevented the cortical cells from passing the linearity tests. These are modest limitations, and they are evident only with three decades of hindsight. Overall the impact of these papers on the field was forceful and positive. As is evident from glancing at any recent review (e.g. Carandini et al. 2005) much of what was done to this date to explain responses of primary visual cortex, e.g. to explain properties such as orientation selectivity, direction selectivity and binocular integration, rested on the results of these two classical papers. Moreover, these studies succeeded in providing a foundation for the models of pattern perception based on psychophysical channels (Graham, 1989). Our only hope is that similarly powerful quantitative studies will soon appear for areas beyond the primary visual cortex.

Phase sensitivity of complex cells in primary visual cortex

Simple cells in primary visual cortex were famously found to respond to low-level image components such as edges. Sparse coding and independent component analysis (ICA) emerged as the standard computational models for simple cell coding because they linked their receptive fields to the statistics of visual stimuli. However, a salient feature of image statistics, occlusions of image components, is not considered by these models. Here we ask if occlusions have an effect on the predicted shapes of simple cell receptive fields. We use a comparative approach to answer this question and investigate two models for simple cells: a standard linear model and an occlusive model. For both models we simultaneously estimate optimal receptive fields, sparsity and stimulus noise. The two models are identical except for their component superposition assumption. We find the image encoding and receptive fields predicted by the models to differ significantly. While both models predict many Gabor-like fields, the occlusive model predicts a much sparser encoding and high percentages of ‘globular’ receptive fields. This relatively new center-surround type of simple cell response is observed since reverse correlation is used in experimental studies. While high percentages of ‘globular’ fields can be obtained using specific choices of sparsity and overcompleteness in linear sparse coding, no or only low proportions are reported in the vast majority of studies on linear models (including all ICA models). Likewise, for the here investigated linear model and optimal sparsity, only low proportions of ‘globular’ fields are observed. In comparison, the occlusive model robustly infers high proportions and can match the experimentally observed high proportions of ‘globular’ fields well. Our computational study, therefore, suggests that ‘globular’ fields may be evidence for an optimal encoding of visual occlusions in primary visual cortex.

The effects of acute alcohol exposure on the response properties of neurons in visual cortex area 17 of cats

Edge is an important feature and edge detection matters a lot to image processing and pattern recognition. In consideration of high properties of human visual system in image perception, a brain-inspired edge detection model based on primary visual pathway was raised. According to the mechanism of lateral geniculate nucleus (LGN) cells and simple cells in primary visual cortex (V1), first, the difference of Gaussian function was adopted to model the concentric receptive field (RF) of a LGN cell; then, cell groups were created by the union of LGN cells with same property; next, RFs of simple cells with a certain preferred orientation were created by combining those of cell groups; finally, the responses of all V1 simple cells were gained by integrating the responses of different simple cells. The proposed model reflects orientation selectivity of simple cells. Results on the USF database indicate that it has better anti-noise performance and robustness in edge detection compared with the previous methods. It effectively combines brain-inspired intelligence with computer vision.

Effects of unexpected changes in visual scenes on the human acoustic startle response and prepulse inhibition

Background The formation of amblyopia is closely associated with glutamate receptors of visual cortex, and researches determined that the expression of metabolic glutamate receptor 1 (mGluR1) in the visual cortex of amblyopic rats is down-regulated.However, the effect of mGluR1 on synaptic transmission of neurons in the visual cortex is unclear. Objective This study was to investigate the role of mGluR1 in the synaptic transmission efficiency of neurons in the primary visual cortex of monocular form-deprivated rats. Methods Sixteen 14-day-old SD rats were randomly divided into normal control group and form-deprivation group, with 8 rats in each group.The eyelids of the left eyes were sutured to establish the monocular form-deprivation models in the rats of the form-deprivation group, and the visual cortex slices were prepared until 31 days after modeling and incubated in artificial cerebrospinal fluid with 3, 5-dihydroxyphenylglycine (DHPG), LY367385+ DHPG, 2-methyl-6-(phenyl acetylene) pyridine hydrochloride(MPEP)+ DHPG and LY367385+ MPEP+ DHPG, respectively.The field excitatory postsynaptic potential (fEPSP) of neurons in the visual cortex of V1 area was detected by extracellular microelectrode recording.The use and care of the animals followed the statement for the Use of Animals in Ophthalmic and Vision Research. Results The slope value before drug treatment was set as 100%, the fEPSP-slopes of the normal control group and the form-deprivation group were increased to (136.4±17.3)% and (120.7±12.8)% after DHPG induction with significant difference between the two groups (t=2.280; P<0.05). The fEPSP-slopes of the normal control group were (114.9±9.3)% and (112.6±15.3)% after LY367385 and MPEP treatment, and those of the form-deprivation group were (107.3±6.0)% and (110.1±4.1)%, which were significantly lower than those after DHPG induction (normal control group: t=2.641, 2.915; both at P<0.05; form-deprivation group: t=2.410, 2.372; both at P<0.05). The fEPSP-slopes of the normal control group and the form-deprivation group were (104.5±2.2)% and (102.8±14.9)% after LY367385+ MPEP treatment, which were lower than that after DHPG induction (t=3.080, 2.306; both at P<0.05). Conclusions The effect of mGluR1 on the synaptic transmission of neurons in the visual cortex weakens after monocular form-deprivation in rats.Both mGluR1 and mGluR5 participate in the neuronic synaptic transmission on visual cortex area and appear to be equivalent contribution. Key words: Electrophysiology; Excitatory amino acid agonists/pharmacology; Excitatory amino acid antagonists/pharmacology; Phenylacetates/pharmacology; Receptors, metabotropic glutamate/physiology; Visual cortex/growth & development; Neuronic synaptic transmission/drug effect; Form deprivation; Rats, SD

Primary visual cortex neurons that contribute to resolve the aperture problem

Calretinin-immunoreactive neurons in the primary visual cortex of dolphin and human brains

Numerous studies have demonstrated that observers often fail to notice large changes in visual scenes, a phenomenon known as change blindness. Some experiments have suggested that phenomenological experience in change blindness experiments is more diverse than the common distinction between change detection and change blindness allows to resolve. Recently, it has been debated whether changes in visual scenes can be detected ("sensed") without a corresponding perception of the changing object ("seeing") and whether these phenomena build on fundamentally different perceptual processes. The present study investigated whether phenomenologically different perceptual processes such as sensing and seeing rely on different or similar neural processes. We studied ERP effects of visual change processing (as compared to change blindness) when observers merely detected the presence of a change ("sensing") and when they identified the changing object in addition to detection ("seeing"). Although the visual awareness negativity (VAN)/selection negativity was similar for detection with and without identification, a change-related positivity and the N2pc contralateral to changes were found exclusively when the change was fully identified. This finding indicates that change identification requires perceptual and neural processes that are not involved in mere detection. In a second experiment, we demonstrated that the VAN and N2pc effects are similar to effects of selective attention in a visual search task. By contrast, the change-related positivity was specific for conscious processing of visual changes. The results suggest that changes can be detected ("sensed") without perception of the changing object. Furthermore, sensing and seeing seem to rely on different neural processes and seem to constitute different types of visual perception. These findings bear implications for how different categories of visual awareness are related to different stages in visual processing.

Extracellular spikes recorded in the visual cortex (Area 17/18, V1) are commonly classified into either regular-spiking (RS) or fast-spiking (FS). Using multi-electrode arrays positioned in cat V1 and a broadband stimulus, we show that there is also a distinct class with positive-spiking (PS) waveforms. PS units were associated mainly with non-oriented receptive fields while RS and FS units had orientation-selective receptive fields. We suggest that PS units are recordings of axons originating from the thalamus. This conclusion was reinforced by our finding that we could record PS units after cortical silencing, but not record RS and FS units. The importance of our findings is that we were able to correlate spike shapes with receptive field characteristics with high precision using multi-electrode extracellular recording techniques. This allows considerable increases in the amount of information that can be extracted from future cortical experiments. Extracellular spike waveforms from recordings in the visual cortex have been classified into either regular-spiking (RS) or fast-spiking (FS) units. While both these types of spike waveforms are negative-dominant, we show that there are also distinct classes of spike waveforms in visual Area 17/18 (V1) of anaesthetised cats with positive-dominant waveforms, which are not regularly reported. The spatial receptive fields (RFs) of these different spike waveform types were estimated, which objectively revealed the existence of oriented and non-oriented RFs. We found that units with positive-dominant spikes, which have been associated with recordings from axons in the literature, had mostly non-oriented RFs (84%), which are similar to the centre-surround RFs observed in the dorsal lateral geniculate nucleus (dLGN). Thus, we hypothesise that these positive-dominant waveforms may be recordings from dLGN afferents. We recorded from V1 before and after the application of muscimol (a cortical silencer) and found that the positive-dominant spikes (PS) remained while the RS and FS cells did not. We also noted that the PS units had spiking characteristics normally associated with dLGN units (i.e. higher response spike rates, lower response latencies and higher proportion of burst spikes). Our findings show quantitatively that it is possible to correlate the RF properties of cortical neurons with particular spike waveforms. This has implications for how extracellular recordings should be interpreted and complex experiments can now be contemplated that would have been very challenging previously, such as assessing the feedforward connectivity between brain areas in the same location of cortical tissue.

Reliability and Representational Bandwidth in the Auditory Cortex

To study and compare responses of different types of cortical neurons in the primary visual cortex in cats to grating stimuli before and during brief elevation of intraocular pressure (IOP). Single-unit electrophysiological recordings were performed in anesthetized and paralyzed cats. The IOP was elevated by injecting saline into the anterior chamber of the cat's eyes through a syringe needle. The IOP was elevated to a level at which the retinal perfusion pressure (arterial pressure minus IOP) was maintained at approximately 30 mmHg for a period of 4 minutes. The responses of simple and complex cells in the primary visual cortex to visually drifting sinusoidal gratings were measured before and during the elevation of IOP. The response amplitude of all the cortical cells in the primary visual cortex declined during a brief elevation of IOP. The decrease in the response of simple cells was always more significant than that of complex cells. The differential decrease between the two major types of cells was independent of the cell's receptive field location and cortical depth. There was a mild tendency for cells with higher preferred spatial frequencies to be more sensitive than those with lower frequencies. The preferred orientation and direction of most cortical cells remained roughly unchanged though their orientation and direction biases decreased. An increase in the animal's blood pressure, which returned the retinal perfusion pressure to a normal level, compensated for the decreased response induced by the elevation of IOP. The differential effects of a brief elevation of IOP on the response of simple and complex cells in the visual cortex are general and may originate from the retina through the lateral geniculate nucleus (LGN), where different effects of elevation of IOP are exerted on X- and Y-type retinal ganglion cells. The results may suggest differential behavior of neurons tin the parvo and magno pathways of the primate.

One way to characterize neural feature selectivity is to model the response probability as a nonlinear function of the output of a set of linear filters applied to incoming signals. Traditionally these linear filters are measured by probing neurons with correlated Gaussian noise ensembles and calculating correlation functions between incoming signals and neural responses. It is also important to derive these filters in response to natural stimuli, which have been shown to have strongly non-Gaussian spatiotemporal correlations. An information-theoretic method has been proposed recently for reconstructing neural filters using natural stimuli in which one looks for filters whose convolution with the stimulus ensemble accounts for the maximal possible part of the overall information carried the sequence of neural responses. Here we give a first-time demonstration of this method on real neural data, and compare responses of neurons in cat primary visual cortex driven with natural stimuli, noise ensembles, and moving gratings. We show that the information-theoretic method achieves the same quality of filter reconstruction for natural stimuli as that of well-established white-noise methods. Major parameters of neural filters derived from noise ensembles and natural stimuli, as well as from moving gratings are consistent with one another. We find that application of the reverse correlation method to natural stimuli ensembles leads to significant distortions in filters for a majority of studied cells with non-zero reverse-correlation filter.

Neurons in the primary visual cortex spontaneously spike even when there are no visual stimuli. It is unknown whether the spiking evoked by visual stimuli is just a modification of the spontaneous ongoing cortical spiking dynamics or whether the spontaneous spiking state disappears and is replaced by evoked spiking. This study of laminar recordings of spontaneous spiking and visually evoked spiking of neurons in the ferret primary visual cortex shows that the spiking dynamics does not change: the spontaneous spiking as well as evoked spiking is controlled by a stable and persisting fixed point attractor. Its existence guarantees that evoked spiking return to the spontaneous state. However, the spontaneous ongoing spiking state and the visual evoked spiking states are qualitatively different and are separated by a threshold (separatrix). The functional advantage of this organization is that it avoids the need for a system reorganization following visual stimulation, and impedes the transition of spontaneous spiking to evoked spiking and the propagation of spontaneous spiking from layer 4 to layers 2–3.