**Abstract**:

**Abstract**
**Due to the aperture problem, the initial direction of tracking responses to a translating bar is biased towards the direction orthogonal to the bar. This observation offers a powerful way to explore the interactions between retinal and extraretinal signals in controlling our actions. We conducted two experiments to probe these interactions by briefly (200 and 400 ms) blanking the moving target (45° or 135° tilted bar) during steady state (Experiment 1) and at different moments during the early phase of pursuit (Experiment 2). In Experiment 1, we found a marginal but statistically significant directional bias on target reappearance for all subjects in at least one blank condition (200 or 400 ms). In Experiment 2, no systematic significant directional bias was observed at target reappearance after a blank. These results suggest that the weighting of retinal and extraretinal signals is dynamically modulated during the different phases of pursuit. Based on our previous theoretical work on motion integration, we propose a new closed-loop two-stage recurrent Bayesian model where retinal and extraretinal signals are dynamically weighted based on their respective reliabilities and combined to compute the visuomotor drive. With a single free parameter, the model reproduces many aspects of smooth pursuit observed across subjects during and immediately after target blanking. It provides a new theoretical framework to understand how different signals are dynamically combined based on their relative reliability to adaptively control our actions. Overall, the model and behavioral results suggest that human subjects rely more strongly on prediction during the early phase than in the steady state phase of pursuit.**

*optimal cue combination*rule whereby each signal is weighted by a coefficient proportional to the inverse variance of the signal itself. The model is simulated for different levels of prediction (

*high*and

*low*) in both steady state and early pursuit blanking conditions. Importantly, with a single set of parameters, the model captures both the drop of horizontal velocity during blank and the transient component of vertical eye velocity at target reappearance. With the help of the model-based simulations, we confirm the observation that extraretinal signals must dominate retinal signals during blanking in the early phase of pursuit (consistent with a

*high-prediction*mode) and that retinal signals dominate during blanking in the steady state of pursuit (consistent with a

*low-prediction*mode). This study opens the door to a new way of thinking about the interactions between retinal and extraretinal signals for eye movements, within the framework of Bayesian inference and dynamic optimal cue integration.

*SD*7.06). Three of them were completely naive to the present study as well as to eye movement research in general. All subjects were healthy and had normal or corrected to normal vision and had no relevant medical and psychiatric history. The experiments were conducted in accordance with Centre National de la Recherche Scientifique (CNRS) ethical regulations for behavioral research. All subjects participated after having given an informed consent.

^{2}and that of the white stimulus was 68 cd/m

^{2}. The spatial resolution of the screen was set to 1280 (H) × 1024 (V) pixels.

*csaps*spline function in MATLAB with a spline coefficient of 0.0001. All the above-mentioned filtering and smoothing operations are equivalent to a Butterworth (acausal) filter of order two with cut-off frequency of about 40 Hz. During the visual inspection of single trials in MATLAB, we used an automatic conjoint acceleration and velocity threshold to detect and remove catch-up saccades (Krauzlis & Miles, 1996a). An objective method was used to compute the smooth pursuit latency in each trial and the method is based on the intersection between the two linear regression lines with a threshold criterion for slope increase (Krauzlis & Miles, 1996a; Masson & Castet, 2002). Oculomotor traces were aligned to stimulus onset. Outlier trials (less than 5%) were eliminated using an offline inspection. The outlier trials are those in which saccades could not be eliminated without excluding the majority of the trial or in which high levels of noise exist during fixation and persist during pursuit.

*ė*and

_{h}*ė*, respectively. Figure 1a shows the different parameters that were extracted from the horizontal velocity profile on each trial for quantitative analysis. δ

_{v}*t*

_{drop}corresponds to the duration for which eye velocity dropped, starting at ∼80 ms (mean latency of pursuit responses) after blank initiation and before reaching a

*plateau*velocity during the blank.

*V*

_{min}denotes the minimum eye velocity reached during the blanking period (the plateau).

*V*

_{80}is the velocity observed 80 ms after blank initiation and

*V*

_{ext}is the velocity measured 80 ms after the reappearance of the target (Figure 1a).

*δV*

_{drop}is the drop in the eye velocity because of the blank and is computed as the difference between

*V*

_{min}and

*V*

_{80}i.e., (

*V*

_{min}−

*V*

_{80}).

*δV*

_{ant}is the anticipatory rise in the eye velocity before target reappearance and is calculated as the difference between

*V*

_{ext}and

*V*

_{min}i.e., (

*V*

_{ext}−

*V*

_{min}) as shown in Figure 1a.

*δ*

*t*

_{drop},

*δV*

_{drop},

*δV*

_{ant}) measured from the horizontal eye velocity component with the blank starting time as the factor in both open loop and steady state blanking experiments. We conducted a paired

*t*test on the slide average vertical eye velocity component to measure the significance of its change upon target reappearance from the baseline during the blank.

*ė*) and vertical (

_{h}*ė*) eye velocity traces across different conditions are shown in Figure 2 for a naive subject (Subject 4) and a nonnaïve subject (Subject 2). The velocity traces in red are responses to a no blank condition. In all blanking conditions, the target disappeared at 600 ms (shown by the black dotted line). At ∼690 ms the horizontal component of eye velocity began decelerating for ∼180 ms and ∼280 ms (average across subjects) for blanking durations of 200 and 400 ms, respectively (Figure 3a). After the deceleration, horizontal eye velocity reached a stable value (

_{v}*V*

_{min}) for the 400 ms blank duration as seen in Figure 2a. Some subjects show a brief anticipatory acceleration starting before 80 ms of target reappearance (target reappearance indicated by solid colored vertical line) and later responding to the target reappearance with higher acceleration as seen in Figure 2a (green and black traces).

*ė*)

_{h}*δ*

*t*

_{drop}is plotted for different blank durations in Figure 3a. All subjects showed a similar increase in

*δ*

*t*

_{drop}with longer blank durations (

*p*< 0.001). In Figure 3b, the amplitude of the drop in the horizontal eye velocity (

*δV*

_{drop}) is plotted against blank durations. This drop was marginal but significantly higher for the longer blank duration (

*p*< 0.001). Subjects with larger pursuit experience (red and blue lines) showed a smaller drop.

*δV*

_{ant}and shown in Figure 3b for 200 and 400 ms blank durations. The anticipatory pursuit was higher with a 400 ms blank duration as compared to the 200 ms condition (

*p*< 0.001 for all subjects). This can be explained by the fact that expectation of target reappearance was higher for trials with long blank durations.

*ė*)

_{v}_{,}gray arrow in Figure 4a). This change (

*SE*) for each subject. An equivalent quantity for the change (

_{,}colored arrows in Figure 4a) was statistically different from the vertical eye velocity during the blank (

_{,}gray arrow in Figure 4a), we conducted a paired

*t*test between the two velocities (

*t*test revealed a significant change (

*p*< 0.05) in the slide average vertical component on target reappearance for all blanking conditions in three subjects (Subjects 2, 3, and 4). Subject 6 showed a significant change for all conditions except when the target reappeared with a bar rotation after a 400 ms blank. Subject 1 showed no significant change except when the target reappeared with same orientation after a 400 ms blank. Subject 5 showed a significant change only when target reappeared identical after 400 ms blanking and when it rotated after a 200 ms blank. A similar

*t*test was conducted in a no blank condition. Except for Subject 1, all the subjects showed no significant change. Overall, we found a change in the vertical bias following target reappearance across all conditions, with some variability across subjects and conditions, as expected from our previous study (Montagnini et al., 2006a).

*ė*) and vertical (

_{h}*ė*) eye velocity when target motion was blanked for 400 ms during the early phase of smooth pursuit, meaning with the blank onset within the first 100 ms of smooth pursuit. Figures 5a, b illustrates mean eye velocity profiles obtained with the same naive (Subject 4) and nonnaïve (Subject 2) participants already plotted in Figure 2. The no blank condition is plotted in red. Dotted lines indicate blank onset and solid lines indicate blank end, with different conditions distinguished by different colors. The initial increase in the vertical pursuit component was clipped off when the moving stimulus disappeared. This is evident when the moving line was blanked 140 ms after target motion onset or earlier. The horizontal component started to decrease down to a plateau and then re-accelerated before target reappearance. Given the latency of ∼80 ms for the bar stimulus, this brief phase of pursuit represents an anticipatory acceleration to catch up with the target at its expected reappearance. Panels c and e zoom on the vertical eye velocity profiles for two 300 ms epochs, starting 100 ms after stimulus onset. Panels d and f zoom on the vertical eye velocity profiles for two 300 ms epochs, starting 100 ms after target reappearance.

_{v}*ė*)

_{h}*t*

_{drop}) is shown in Figures 6a and 6c for 200 ms and 400 ms blank durations, respectively, across different blank onset times. A significant dependence upon the timing of stimulus blanking can be appreciated (

*p*< 0.001). When the moving target was blanked at either 100 or 180 ms for 200 ms, mean deceleration phases (across subjects) lasted ∼90 or ∼140 ms respectively. Similarly, blanking the moving target at either 100 or 180 ms for 400 ms resulted in mean deceleration phase (across subjects) that lasted for ∼160 or ∼250 ms, respectively. Thus, earlier target blanking resulted in shorter phases of horizontal pursuit deceleration.

*δV*

_{drop}) is plotted against timing of target disappearance in Figure 6b and 6d (solid lines) for 200 ms and 400 ms blank durations, respectively. An early blanking (starting at 100 ms after stimulus onset) for 200 ms duration resulted in a small reduction in eye velocity with a mean ±

*SE*across subjects of 0.55 ± 0.22°/s while a later blanking (starting at 180 ms after stimulus onset) resulted in a larger drop with a mean ±

*SE*across subjects of 2.3 ± 0.29°/s. Similarly, blanking at 100 ms with a 400 ms duration resulted in a small reduction in eye velocity with a mean ±

*SE*across subjects of 1.61 ± 0.35°/s while blanking at 180 ms resulted in a larger drop with a mean (±

*SE*) across subjects of 3.75 ± 0.31°/s. The drop in eye velocity increased with later blanking, as shown by the significant effect of the timing of target blanking upon

*δV*

_{drop}(

*p*< 0.001).

*SE*across subjects equal to 2.9 ± 0.13°/s and 2.76 ± 0.22°/s for blanking onset time of 100 and 120 ms, respectively, (Figure 6b) for the 200 ms blank. A similar trend is observed for 400 ms blank duration (Figure 6d) where anticipatory eye velocity was higher when compared to the same blanking onset timing but a duration of 200 ms. For a 200 ms blank, except for Subject 2 (blue line in Figure 6b) all subjects show a statistically significant (

*p*< 0.001) relationship between

*δV*

_{ant}and blanking onset timing. For 400 ms blanking duration, except for Subjects 1, 2, and 5 (red, blue, and magenta lines in Figure 6d) all the subjects show a statistically significant (

*p*< 0.001) dependence of

*δV*

_{ant}upon the time at which blanking starts.

*ė*)

_{v}*SE*across subjects) is shown in Figures 7b and 8b for 200 and 400 ms blank durations, respectively. An equivalent quantity for the change (

*t*test,

*p*< 0.05). When blanking started at 100 ms, only one subject (Subject 1) showed a significant change. When blanking started at 120 ms, only one subject (Subject 2) showed a significant change. When blanking started at 140 ms, three subjects (Subjects 2, 3, and 5) showed a significant change. For the other conditions, Subjects 2, 3, 4, and 5 showed a significant change. In a similar way, asterisks in Figure 8b indicate significant change in vertical eye velocity at target reappearance for the 400 ms blanking duration block. When blanking started 100 ms after pursuit onset, only two subjects (Subjects 3 and 6) showed a significant change. When blanking started at 140 ms, three subjects (Subjects 1, 3, and 6) showed a significant change. When blanking started at 160 ms, three subjects (Subjects 1, 2, and 3) showed a significant change. For the remaining two conditions, only one subject (Subject 3) showed a significant change. All the subjects show a significant reduction in the vertical eye velocity component in the no blank condition.

*oculomotor plant*that converts the target velocity estimate into eye velocity (Goldreich, Krauzlis, & Lisberger, 1992), the inference model produces smooth pursuit traces that are very similar to human smooth pursuit responses to a translating tilted bar (Bogadhi et al., 2011). For the sake of simplicity, our first model operated in open-loop conditions with no physical feedback from the moving eye to the retinal module encoding visual motion.

*ν*

_{0}is the stimulus velocity, the likelihood function

*L*

_{1}for edge related information (1D) in the velocity space (

*v*,

_{x}*v*) is given by: where

_{y}*Z*is the partition function (the same symbol is used for all distributions),

*θ*is the orientation of the line relative to the vertical, taken as positive in anticlockwise direction, and

*σ*

_{1}is the standard deviation of the speed in the orthogonal direction to the line. The likelihood function

*L*

_{2}for the terminator related information in the velocity space (

*v*,

_{x}*v*) is given by: where

_{y}*σ*

_{2}is the standard deviation of the velocity of the image 2D cues. The overall likelihood function is the product of the two (1D and 2D) likelihoods since, they are both assumed to be independent:

*σ*

_{0}), the initial sensory prior distribution

*P*

_{0}can be written in the velocity space (

*v*,

_{x}*v*) as follows: The likelihood function (

_{y}*L*) is combined with the initial prior (

*P*

_{0}) using Bayes's rule to obtain the initial posterior distribution (

*Q*

_{0}) To obtain a read out of the distribution that can be used for the later stages, a decision rule called maximum a posteriori (MAP) is implemented as: The posterior distribution at every instant

*t*is used to dynamically update the prior (i.e., generating a recurrent Bayesian computation) used at the next iteration: Finally, at any time

*t*, the retinal Posterior can be expressed as: The square-root variance terms (or standard deviations)

*σ*

_{0}(2.87°/s),

*σ*

_{1}(1.38°/s), and

*σ*

_{2}(4.22°/s)

_{,}for the prior, 1D, and 2D likelihood, respectively, were estimated from an independent set of oculomotor data, applying Bayes's rule to pure 1D and pure 2D motion stimuli as described in detail in Montagnini et al. (2007). The delay in the retinal block

*δ*

_{ret}is estimated to be 65 ms based on the physiology literature (see Bogadhi et al., 2011).

*P*

_{ext}) is assumed to be Gaussian and centered on zero. For the sake of simplicity, the initial variance in the extraretinal prior is assumed to be same as the variance in the retinal prior (

*σ*=

_{ext}*σ*

_{0}in Equation 9). The extraretinal prior is combined with the probability of target velocity in space (

*P*, see below) and updated with the resultant posterior as shown in Figure 9. This recurrent operation changes the extraretinal prior before blank onset.

_{T}*P*

_{out}corresponds to the output of the sensory estimation

*Q*

_{0}and its weighted combination with the extraretinal prior distribution

*P*

_{ext}as well as its evolution in time is described in the next section.

*P*(

_{ext}*v*,

_{x}*v*) and the posterior from the retinal recurrent block

_{y}*Q*(

*v*,

_{x}*v*) are represented in the same velocity space and both have the same units. The extraretinal prior

_{y}*P*(

_{ext}*v*,

_{x}*v*) and the retinal posterior

_{y}*Q*(

*v*,

_{x}*v*) are weighted according to their respective reliabilities (i.e., they are inversely proportional to their variance) and combined linearly to form the dynamic post-sensory output (

_{y}*P*

_{out}in Equation 10 and Figure 9, see detailed description below) both during the blank and at target reappearance. The probability distribution of target velocity in space

*P*is obtained by the summation of the post-sensory output with the positive feedback (see Figure 9 and below). A copy of

_{T}*P*is given as an input to the extraretinal block (Freeman, Champion, & Warren, 2010) and its role here is analogous to that of the efference copy of the premotor drive. The resultant posterior is then used to update the extraretinal prior with a constant delay (

_{T}*δ*

_{ext}). Imposing a conditional update of the extraretinal (prediction) component similar to a Kalman filter is beyond the scope of this study. Instead, we decided that the extraretinal prior is updated only when the retinal weight (

*W*

_{ret}) is greater than 0.99 indicating that the extraretinal block stores a visuomotor drive triggered by reliable retinal motion information. This delayed update of prior with posterior can be viewed as a

*sample and hold*mechanism, with the prior storing the memory signal, equivalent to the indirect loop of the model described by Bennett and Barnes (2004). The delay

*δ*

_{ext}(∼97.5 ms) was arbitrarily set at 1.5 times the update delay in the retinal block

*δ*

_{ret}(∼65 ms). The MAP of the probability distribution of target velocity in space (i.e., the target velocity estimate) serves as an input to both the oculomotor plants and the positive feedback system.

*P*

_{out}) only when the physical negative feedback is functional. The horizontal (

*v*) and vertical (

_{x}*v*) components of the MAP are delayed by

_{y}*δ*

_{p}and passed through low-pass filters with gain,

*K*= (

*K*,

_{x}*K*), and cut-off frequencies,

_{y}*ω*= (

*ω*,

_{x}*ω*), as shown in Figure 9. For simplicity, both horizontal and vertical components of the positive feedback system are shown as one single entity in Figure 9. The delay

_{y}*δ*

_{p}and the filter parameters were kept constant for both

*v*and

_{x}*v*across all conditions,

_{y}*δ*

_{p}= 110 ms;

*K*

_{x}= 3 (9.54 dB);

*ω*

_{x}= 1 Hz;

*K*

_{y}= 2 (6 dB);

*ω*

_{y}= 1 Hz. The values of the positive feedback system were set to compensate for the combined dynamics of the horizontal and vertical oculomotor plants in generating retinal slip, along with the retinal recurrent Bayesian block in processing the retinal slip to estimate (

*P*

_{out}). The parameters of the retinal recurrent Bayesian network as well the oculomotor plant (

*K*

_{d},

*K*

_{p}) were taken from our previous study (see table 2 in Bogadhi et al., 2011).

*Q*(

_{t}*v*,

_{x}*v*), and the extraretinal prior,

_{y}*P*(

_{ext}*v*,

_{x}*v*), are weighted and combined to give the resultant post-sensory output,

_{y}*P*

_{0}(

*v*,

_{x}*v*), as described here. Following the idea proposed by recent models for sensory cue combination (Ernst & Banks, 2002; Kersten, Mamassian, & Yuille, 2004; Oshiro, Angelaki, & DeAngelis, 2011), the retinal and extraretinal weights were modeled as a function of their respective reliabilities (i.e., the inverse of their variance) as shown in Equation 10: and where

_{y}*W*

_{ret}and

*W*

_{ext}are dynamical retinal and extraretinal weights, respectively, and the symbols (

*Q*(

_{t}*v*,

_{x}*v*), and extraretinal prior,

_{y}*P*(

_{ext}*v*,

_{x}*v*).

_{y}*μ*) and the mean of the extraretinal prior (

_{ret}*μ*) are linearly weighted and summed to give the mean of the post sensory output (

_{ext}*c*is kept constant across all conditions (

*c*= 1). For the extraretinal variance increase during the blank, the value of

*c*determines the strength of prediction: where

*t*is the blanking onset time,

_{b}*c*is the constant determining the rate at which variance increases, and

*initial*variance of the prior. Note that the particular functional dependence (hyperbolic) of the prior variance on

*t*we have chosen here is coherent with the natural time course of the prior variance in a simple Bayesian recurrent model as the one described by Equation 8 (See also equations 9 and 10 in Montagnini et al., 2007). However, the constant

*c*depends on mechanisms (e.g., the resetting of the prior) that we cannot really model in detail at this stage and thus we will keep it as a free parameter.

*t*

_{ext}∼ 97.5 ms, the variance of the extraretinal signal starts decreasing as a result of the Bayesian computation in the extraretinal network. When the blank is introduced, both retinal and extraretinal variances increase gradually back to their initial value (see Equation 12). The dynamics of increase in the retinal variance is constant in both low- and high-prediction cases. What determines if the prediction is low or high is the dynamics of increase in extraretinal variance, determined by the constant

*c*in Equation 12. In the high-prediction case (

*c*= 10,000 for the example in the left panels of Figure 10), the extraretinal variance stays low during the blank (Figure 10e) and hence higher weight is given to extraretinal signals whereas in the low-prediction case (

*c*= 50 for the example in the right panels of Figure 10), the extraretinal variance increases to a higher value during the blank (Figure 10f) and hence relatively lower weight is attributed to the extraretinal signals. The

*c*values were chosen such that model pursuit responses capture the low- and high-prediction categories qualitatively. At the end of the blanking period, when the target reappears, the retinal variance starts decreasing again as a result of Bayesian computation in the retinal block whereas the extraretinal variance remains constant for some more time since our model assumes that the extraretinal signal is updated only when retinal information is reliable (i.e.,

*W*

_{ret}≥ 0.99).

*c*. When the stimulus is blanked during the early phase of pursuit, the extraretinal variance changes little during the blank and the retinal variance increases towards its initial value (Figure 10e). Therefore the extraretinal weight is high during the blank resulting in a small drop in the horizontal eye velocity. At the end of the blank, once the target reappears the extraretinal weight decreases and the retinal weight increases. Since the extraretinal weight is still higher than the retinal weight at the time of reappearance, no bias is seen in the vertical eye velocity (Figure 10h). A similar pattern of dynamics of the weights and the resulting pursuit responses can be seen for the steady state blanking condition shown in Figures 10a, c, e (black line). Note that, in the high-prediction case we had to decrease the gain of the positive feedback (

*K*

_{x}= 1.8) to avoid motor behavior instability in the steady state blanking condition only. For all other blanking conditions, we kept this parameter identical (

*K*

_{x}= 3).

*c*= 50). Under these conditions, when the stimulus is blanked during the early phase of pursuit, the extraretinal variance increases more dramatically (Figure 10e) while the retinal variance increases towards its initial value (Figure 10f). As a result, the extraretinal weight is lower during the blank and hence a larger drop in eye velocity is seen during target occlusion. Once the target reappears, the extraretinal weight decreases and conversely, the retinal weight increases. Note that the weight given to retinal signal is much higher at target reappearance, as compared to the high-prediction setting (Figure 10c). This results in a significant bias in the vertical eye velocity since now the pursuit behavior carries the signature of the aperture problem affecting the visual motion computation (Figure 10j). Similar dynamics of the weights and the resulting pursuit responses can be seen for the steady state blanking condition shown in Figures 10b, d, f (black line).

*c*and thus the strength of the prediction. This variability and its dependence on the prediction level can be appreciated by comparing the black curves in Figure 2a and 2b with the corresponding black curves in Figure 10b and 10a, respectively.

*c*, the model predicts that a larger drop of horizontal velocity (higher retinal slip) during blank is accompanied by a higher vertical bias at target reappearance, as inferred from Figures 10b, d, and j, and this irrespective of whether the target is blanked in steady state or during early pursuit. We estimated the correlation between the observed horizontal eye velocity drop (absolute value) during blank and the observed aperture bias on target reappearance when the stimulus is blanked during steady state for either 200 ms or 400 ms blanking durations. Figure 11 plots the mean horizontal eye velocity drop during the blank against the mean percentage change in vertical bias at target reappearance for each subject and for two blanking durations. The line with the positive slope in Figure 11 is the line of best fit in a least squares sense. We tested the correlation in the steady state blanking conditions since this condition showed a significant aperture bias after the blank. Absolute eye velocity drop and the aperture bias were indeed positively correlated (Pearson correlation,

*r*= 0.74;

*p*< 0.01). Because the inclusion in the dataset of different blanking durations might have added some spurious covariance in the data, we also estimated the partial correlation between absolute velocity drop and vertical bias controlling for the variable blanking duration: also in this case the Pearson correlation turns out to be significant and with a similar correlation coefficient (Pearson correlation,

*r*= 0.75;

*p*< 0.01). Overall, this observation from data suggests that the level of prediction (reflected in the dynamics of cue interaction) largely determines the dynamics of pursuit during the blank and the aperture bias on target reappearance as predicted by the model.

*W*

_{ret}≥ 0.99). On the contrary, if the extraretinal block was to be functional when the retinal weight is much less than one, like for instance during the blanking period, the eye velocity memory would be updated with the zero velocity information during the blank and this would lead to a rapid degradation of the target velocity information. In the current version of the model, the extraretinal information is indeed somehow degraded, as expressed by the increase of the extraretinal prior variance, but it is not biased toward zero. Finally, we assumed an ad hoc fast dynamic transient for resetting both retinal and extraretinal prior variances after the blank onset. Although such assumption is neither derived from some general properties of the Bayesian framework nor from the physiological literature, this reset is a biologically plausible feature of the model. Clearly, each of these specific assumptions needs to be specifically addressed in future studies.

*β*) depending upon expectation about target reappearance. If such a switching mechanism were true, we should have observed a significant vertical bias at target reappearance in the early blanking conditions, very similar to the bias observed in the steady state blanking conditions for all subjects. This was clearly not the case. Our results suggest that the transfer of weights from retinal to extraretinal signals during blanking is not regulated by an ad hoc, instantaneous switching process but rather follows a well-defined, dynamical change.

*c*in Equation 12. Our model does not predict the full pattern of eye movements for each subject, in particular the anticipatory velocity at the end of blank in the early blanking conditions and the relative difference observed for the post-blank bias in vertical velocity between the early and late blanking conditions. Nonetheless, this model provides a more complete theoretical framework for smooth pursuit, which is fully dynamical and can incorporate some interindividual differences, as well as the constraints imposed by both retinal and extraretinal inputs to the premotor drive.

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