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1 Brain Sciences Center, Veterans Affairs Medical Center 55417;; 2 Department of Neuroscience, University of Minnesota Medical School, Minneapolis, Minnesota 55455; 3 Department of Neurology, University of Minnesota Medical School, Minneapolis, Minnesota 55455; 4 Department of Psychiatry, University of Minnesota Medical School, Minneapolis, Minnesota 55455; 5 Cognitive Sciences Center, University of Minnesota, Minneapolis, Minnesota 55455
Submitted 4 April 2003; accepted in final form 21 April 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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;
Boussaoud et al. 1990;
Newsome et al. 1990) and
functional neuroimaging studies in human subjects
(Cheng et al. 1995;
Tootell et al. 1995;
Zeki et al. 1991) have
documented the involvement of several areas in stimulus motion processing,
including the middle temporal area (MT)
(Albright 1984;
Zeki 1974), medial superior
temporal area (MST) (Tanaka et al.
1986; Van Essen et al.
1981), superior temporal polysensory area
(Bruce et al. 1981;
Oram et al. 1993), area 7a
(Motter and Mountcastle 1981;
Siegel and Read 1997;
Merchant et al. 2001), and the
ventral intraparietal area (Colbi et al. 1993). More detailed analyses of the
neural mechanisms underlying visual motion processing have been performed in
animal experiments the results of which indicate that different areas relate
to different aspects of this processing. For example, cell responses in MT
relate mostly to rectilinear motion for which a columnar arrangement is
present (Zeki 1974). Indeed,
the coherent engagement of neuronal populations in area MT using intracortical
microstimulation has been found to bias the perception of stimulus motion in
the direction of the preferred direction of the columns stimulated (Salzman et
al. 1990,
1992). In addition to
responding to rectilinear motion, cells in MST and area 7a also respond to
optic-flow stimuli, including stimulus motion in depth
(Duffy and Wurtz 1991;
Merchant et al. 2001;
Siegel and Read 1997;
Tanaka and Saito 1989).
Finally, the population vector analysis has been successfully applied in
several studies to reconstruct the course of a moving visual stimulus from the
discharge of cell ensembles in MT (Kruse
et al. 2002), MST (Page and
Duffy 1999), and area 7a
(Steinmetz et al. 1987).
Optic flow corresponds to the changes in the optic array induced by the
relative motion between the subject and the environment. Information about
optic flow is indispensable for encoding direction of heading, orientation,
and visual navigation in three-dimensional space, controlling posture and
locomotion, and perception of moving objects and the selection of motor
actions that allow the appropriate interaction with them
(Koenderink 1986; Lee
1976,
1980). Neurons in area MST
respond selectively to expansion, rotation, and deformation but also to
mixtures of motions (plano-radial, -circular, etc.)
(Duffy and Wurtz 1991;
Lagae et al. 1994;
Tanaka and Saito 1989;
Tanaka et al. 1986). MST is
reciprocally connected with parietal area 7a (Andersen 1990;
Cavada and Goldman-Rakic 1989),
which in turn also contains neurons with optic-flow selectivity
(Merchant et al. 2001;
Siegel and Read 1997). Area 7a
not only elaborates on the processing of optic-flow information but also
integrates optic flow with gaze-position signals
(Read and Siegel 1997). In a
recent study, we described the responses of single cells in area 7a to eight
stimulus motions that covered all basic motions of optic-flow stimuli, namely
right-, left-, up-, and downward, expansion, contraction, clockwise,
counterclockwise stimulus motions
(Merchant et al. 2001). In the
present study, we investigated the functional organization of these responses
using tree clustering and multidimensional scaling (MDS). Specifically, we
sought to find out whether these responses in a neuronal ensemble are
clustered and, if so, to determine the superordinate dimensions underlying the
resulting clusters. In these analyses we followed R. N. Shepard's pioneering
approach in analyzing psychophysical measurements of similarity using tree
clustering and MDS (Shepard
1980).
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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Two male monkeys (Macaca mulatta, 6 and 7 kg body wt) were used in this study. Animal care conformed to the principles outlined in The Guide for Care and Use of Laboratory Animals (National Institutes for Health Publication No. 85-23, revised 1985). Animal studies protocols were approved by the local institutional review boards.
Visual stimuli
Stimuli were presented on a 69 x 69-cm tangent screen placed 48.5 cm in front of the animal. Small square patches of random dots were presented successively at 25 different positions in a regular 5 x 5 grid. The dots could move in eight different motion conditions: the four cardinal directions of translation (rightward, leftward, upward, downward), expansion, contraction, clockwise (CW) rotation, and counterclockwise (CCW) rotation. Stimuli were back-projected on the screen using an LCD projector (NEC Multisync MT 820/1020) with a refresh rate of 60 Hz. The whole screen subtended 71° of visual angle (DVA), at eye level. The small square patches were 13.8 x 13.8 cm and subtended 16.2 DVA on a side at the center of the screen. Stimuli were presented within such a patch for 400 ms, one patch at a time, with an inter-patch presentation interval of 150 ms. The stimuli were composed of 30 white dots moving within a square on a black background. Each dot was a circle of 0.35 DVA in diameter and moved for a maximum lifetime of 400 ms, after which it was assigned to a new random location within a square patch. If a moving dot traveled outside the patch displayed, it was relocated to a new random location within the square. The dots were relocated asynchronously to avoid coherent flickering of the stimuli. This constant reshuffling essentially eliminated pattern and density artifacts because the pattern of dots was changing constantly and each region within the square had approximately the same number of points at any time. The linear (constant) speed in the four directions of translation (left-, right-, up-, and downward), and mean linear speed in the directions of expansion and contraction was 40 DVA/s; the angular speed in both directions of rotation was 430°/s.
Task
The monkeys (monkeys 1 and 2) were seated in a primate
chair with the left arm loosely restrained. In the visual stimulation task, a
yellow spot of 0.32 DVA diameter served as the fixation point (FP) and was
presented in the center of the translucent tangent screen. The monkeys were
trained to fixate this spot (within 2 DVA) for the duration of stimulus
presentation. During that time, monkey 1 maintained the right hand in
a relaxed position (monitored using a video camera), whereas monkey 2
maintained grasp of a vertical semi-isometric joystick with the right hand by
exerting a constant pulling force on the joystick of 
0.22 N. First, the
FP was turned on which the monkeys fixated; following attainment of fixation,
100–500 ms were allowed for monkey 2 to grasp the joystick.
Then stimuli were presented on the screen. A juice reward was delivered
randomly every 1.1–3.3 s while fixation was maintained; if fixation was
broken, the trial was aborted. The x-y eye position was monitored
using an oculometer (Dr. Bouis, Karlsruhe, Germany). Both the eye and the
joystick position were sampled at 200 Hz. The eight different motion
conditions were interleaved and presented in a pseudorandom order. The 25
different patch locations were nested within each stimulus motion condition
and were also presented pseudorandomly. A complete run consisted of the
presentation of all conditions in three repetitions.
Neural recordings
Impulse activity of single neurons was recorded extracellularly from area
7a (left hemisphere). The recording sites have been published elsewhere
(Merchant et al. 2001). All
isolated neuronal potentials were recorded regardless of their activity during
the task, and the recording sites changed from session to session.
General data analysis
We analyzed the activity of 587 neurons with a stable response to the
stimuli presented; details on the functional properties of these neurons are
given in Merchant et al.
(2001). A repeated-measures
ANOVA was used to assess the statistical significance of the motion condition
and location effects. The frequency of discharge (based on spike counts)
during the last 300 ms of the 400-ms-long visual stimulation period was the
dependent variable. The spike counts were square-root transformed to stabilize
the variance (Snedecor and Cochran
1989). The activity of 150/587 (25.5%) cells that showed a
significant main effect of motion condition and/or a significant effect of
motion condition x location interaction was analyzed further in the tree
clustering analyses in the following text.
The directional selectivity of cells to the translating dots was determined
as follows. First, an ANOVA was performed, where the direction of translation
was used as a factor. Then the directional tuning of these cells was assessed
using bootstrap (Lurito et al.
1991) (P < 0.05).
Tree clustering analyses of stimulus motions
We performed tree clustering analyses to determine the pattern of grouping
of 8 different kinds of stimulus motion using the activity of the 150 neurons
in the preceding text. First, we defined the variables that served as the
basis for cluster formation as follows. For each cell, the mean discharge rate
for the eight motion conditions was calculated, by averaging the discharge
rate during the last 300 of the 400 ms of visual motion stimulation across
repetitions for those locations inside the receptive field mapped using a
double Gaussian regression (Merchant et
al. 2001). These values were standardized by re-expressing them as
z scores that corresponded to the discharge rate variation of each
motion condition around the mean of all motion conditions, expressed in SD
units. Thus the primary clustering variables consisted of 150-dimensional
vectors containing the z scores for each cell for every motion
condition. The squared Euclidean distance between the 150-dimensional vectors
of all possible pairs of motion conditions conformed an 8 x 8
dissimilarity matrix that was used in the tree clustering analyses described
in the following text.
Two different analyses were performed on the dissimilarity matrix, namely
an ultrametric and an additive tree analysis
(Corter 1976). An ultrametric
tree is a type of hierarchical clustering that can be fit by agglomerative
algorithms and in which the path-length distances between clustering variables
satisfy the following mathematical relationship for any three variables
a–c in the tree
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).
The functions DCDIST and DCLINK of the IMSL library (Digital Visual Fortran,
Professional Edition 1998) were used to execute the hierarchical tree
clustering analysis. In the resulting trees (or dendrograms) horizontal
distances represent estimated dissimilarities between motion conditions,
whereas vertical distances are arbitrary.
We also used an additive tree analysis on the dissimilarity matrix to test
for the robustness of clustering. An additive tree follows a basic
mathematical relationship characterizing distances in the tree called additive
inequality, and states that for any four variables in the tree that can be
labeled as x, y, u and v
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Consense analysis
A hierarchical ultrametric clustering analysis of the different visual stimuli was also performed for each individual neuron. The 150 dendrograms obtained were analyzed using the program CONSENSE (version 3.5c by J. Felsenstein, University of Washington 1986–1993). This analysis provides the frequency of occurrence of the branch combinations in the population of dendrograms analyzed.
Tree clustering by different number of neurons
The minimum number of neurons necessary to produce the clustering observed in the dendrogram shown in Fig. 1 was computed using bootstrapping as follows. First, a fixed number of neurons K was chosen randomly with replacement. Then a hierarchical ultrametric clustering analysis was performed on the dissimilarity matrix for this group of neurons and the dendrogram structure saved. This procedure was repeated 1,000 times. Finally, two analyses were carried out on these 1,000 dendrograms. First, we counted the number (and percentage) of dendrograms that showed the same clustering of stimulus motions as in Fig. 1. And second, we performed a consensus analysis to estimate the robustness of specific clusters when smaller Ks were used.
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MDS analysis
The data for this analysis were the pairwise distances among the various clusters in the tree shown in Fig. 1. As mentioned in the preceding text, the distance between two clusters is the sum of the intervening horizontal distances; for example, the distance between the "horizontal" and "vertical" cluster is: 9.8 + 78.9 + 38.8 = 127.5 (arbitrary units) and so on for other pairs. The resulting dissimilarity matrix was analyzed by metric MDS, employing two dimensions and an interval scale (ALSCAL procedure, SPSS 10.1 for Windows, SPSS, Chicago, IL). The success of the MDS analysis was evaluated by computing Kruskal's stress formula 1 and the R2. The latter is the proportion of variance of the scaled data (disparities) in the data which is accounted for by their corresponding distances. In addition, a plot of derived stimulus (i.e., tree clusters) configuration and a scatterplot of linear fit were generated.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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for
details), it did not, by itself, reveal any underlying orderly pattern of
variation of neuronal activity with respect to the stimulus parameters. This
issue was investigated in this study using tree clustering and MDS. Tree-clustering analyses
Hierarchical (ultrametric) and an additive tree analyses were used to determine the clustering pattern of stimulus motions based on cell responses. The ultrametric dendrogram obtained is shown in Fig. 1. It can be seen that the two directions of horizontal motion (rightward and leftward), the two directions of vertical motion (upward and downward), and the two directions of rotatory motion (CW and CCW) were clustered in three separate branches (horizontal, vertical, and rotatory motion, respectively). In contrast, no such clustering was observed for the radial aspect of stimulus motion (expansion, contraction). In fact, contraction and expansion were in separate branches, and expansion was in its own branch by itself. It is worth mentioning that the same tree configuration was observed using additive tree analysis (R2 = 0.96).
Tree clustering is a multivariate analysis that does not assign a probability value to the occurrence of different groupings. For that purpose, we used bootstrapping to compute the probability of obtaining by chance the entire population clustering (Fig. 1) and each of the major clusters. In this analysis, the z scores of the eight conditions were randomly permuted for every cell, and a hierarchical tree clustering analysis performed on 150 bootstrapped cells. The results showed that the stimulus motion clustering of Fig. 1 was never observed on the total number of bootstraps (n = 104; hence P < 10–4).
The clustering in Fig. 1 was
not observed in the dendrogram derived from the population of those cells that
did not show a significant stimulus motion effect in the ANOVA (n =
217; Fig. 2A) nor in
the dendrogram produced from a population of cells recorded in motor cortex
(n = 108; Fig.
2B) under identical stimulation conditions
(Merchant et al. 2001). In
addition, the clustering of opposite horizontal, vertical, and rotatory
motions was not observed at the single cell level. An example from a single
cell is shown in Fig. 3, A and
B. Figure
3C shows that frequency of occurrence of each cluster or
branch observed in the single cell analysis was >10% in most of the
clusters.
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Next we investigated the relation between the number K of neurons
in the population and the probability of obtaining the clustering in the
dendrogram observed. The results are shown in
Fig. 4C, where is
evident that the probability of obtaining the dendrogram observed
(Fig. 1) increases with
K, and essentially plateaus at K 
130 cells.
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Robustness of branch clustering
It would be of interest to know the robustness of the clustering shown in Fig. 1. We assessed this issue by constructing consensus dendrograms generated by bootstrapping the actual data at different K values. Figure 4A shows examples of such dendrograms and B summarizes the outcome of this analysis as a plot of the probability of a cluster occurrence (left-right, up-down, CW-CCW, expansion alone), irrespective of other clusters, against K. It can be seen that this probability decreased with lower K values (as expected) for all clusters above. However, the rate of this decrease was smaller for the expansion alone and the right-left cluster than for the CW-CCW and up-down cluster. Therefore the former two groupings were more robust than the latter two.
MDS analysis
The MDS analysis was successfully applied on the tree-cluster dissimilarity matrix; the stress value was 0.026 and the R2 was 0.998. The derived tree-cluster configuration plot and linear fit are shown in Fig. 5, A and B, respectively. It can be seen in Fig. 5A that the most important dimension (abscissa) separated expansion from all other stimulus motions, whereas the second dimension (ordinate) separated planar motions from motion in depth. The linear fit between the disparities (monotonically transformed data) versus the obtained distances is showed in Fig. 5B. This scatter plot represents the fit of the derived distances to the data, which is the fit that is being optimized by the MDS procedure. It is obvious that there is an almost perfect linear relation between these two measures, which was reflected in the high R2 and the low stress value obtained.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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;
Page and Duffy 1999;
Steinmetz et al. 1987). The
second consideration stems from behavioral aspects, namely the prominence of
expansion in daily life due to locomotion. Locomotion is a common, if not the
most common, activity of an organism, and during this activity, the dominant
optic flow consists of expansion. Accordingly, we were interested in the
possibility that expansion may be represented in a privileged way, so to
speak, compared with the other kinds of visual motion. Finally, Shepard's
instrumental work on deriving hidden principles of organization from proximity
(i.e., similarity or dissimilarity) judgments using tree clustering and MDS
(Shepard 1980) led us to the
use of the very same methods to analyze neural response data for the purpose
of uncovering latent organizational principles in the visual motion domain. In
fact, our application of these analyses followed closely that of Shepard's in
using both of the afore-mentioned methods to gain complementary insights into
this organization. Indeed, both analyses provided excellent fit to the data
(R2 = 0.96 and 0.998 for the additive tree clustering and
MDS, respectively) and their results are discussed separately in the following
text.
The tree-clustering analysis revealed a grouping of opposite basic
directions of motion into superordinate units. Thus left-/rightward stimuli
were grouped together, as well as up-/downward and CW/CCW. The interpretation
of these superordinate units is obvious as they signify horizontal, vertical,
and rotatory motions, respectively. This clustering of opposite directions may
appear to be counter intuitive from the viewpoint of cell tuning to stimulus
direction. For example, if cells were tuned to the direction of dot
translation, one would expect the resulting dendrogram configuration to be
such that opposite directions (i.e., the preferred and its opposite) would be
in separate branches, but this was not observed in our study. We believe that
this is due to the fact that only 29 of the150 cells (19.3%) included in the
hierarchical tree-clustering analysis were significantly tuned to rectilinear
stimulus motion. Although the horizontal, vertical, and rotatory motions were
represented individually at the single cell level, the simultaneous grouping
of these three motion classes apparently is an emergent property
(Johnson 2000) of the neuronal
ensemble because it was not observed at the single-cell level. This
higher-order organization of functional cell properties complements previous
observations on area 7a cellular responses to moving stimuli in general
(Motter and Mountcastle 1981;
Sakata et al. 1994;
Steinmetz et al. 1987) as well
as to optic-flow stimuli in particular
(Read and Siegel 1997;
Siegel and Read 1997). It
should be mentioned that the tree-clustering analyses aim to identify groups
in a multivariate set of data (Shepard
1980). These analyses are based on similarities (or
dissimilarities) between the objects, and no assumptions are made concerning
the number of groups or group structure that can be obtained
(Johnson and Wichern 1998).
Thus the fact that the horizontal, vertical, and rotation types of stimulus
motion were grouped together in the present results was not due to a priori
considerations in the analyses. Therefore this dendrogram configuration
depends on the multivariate relationships between the firing rates of the
population of area 7a neurons during the presentation of the different types
of stimulus motion. Finally, it should be noted that in this study, stimuli
were delivered in patches of the visual field; possible responses to full-flow
stimulation were not investigated.
The findings in the preceding text do not necessarily follow from the
existence of a selectivity of single-cell discharge to optic flow. This is
evidenced by the fact that such selectivity was also observed in the motor
cortex (Merchant et al. 2001)
but no clustering was found in that area
(Fig. 2B). The
clustering in the preceding text does not necessarily follows from the
existence of a selectivity of single-cell discharge to optic flow because such
selectivity was also observed in the motor cortex
(Merchant et al. 2001) but no
clustering was found in that area (Fig.
2B). Therefore the clustering observed in area 7a seems
to rely on specific constraints among cell responses to the different kinds of
optic-flow stimuli. Apparently, such constraints are absent in the motor
cortex, and there may or may be not present in other areas, such as MST.
Although the nature of these putative constraints is not known, one could
speculate on the substrate that would be necessary for them to operate on.
Obviously, this should be a substrate of diverse responses by single cells to
a variety of optic-flow stimuli. It is noteworthy that this clustering was
present in small cell ensembles (Fig.
4), which indicates that the underlying conditions for the
clustering are widely distributed in the population.
The clustering of vertical and horizontal axis by cells in area 7a could
relate to different aspects of depth perception, including perception of
motion in depth, perception of change in the size of an object, and the visual
guidance of locomotion. The results of psychophysical experiments
(Beverly and Regan 1979;
Regan and Gray 2000) have
suggested that the presence of one-dimensional relative motion subsystems is
necessary to perceive motion in depth or the change in size of an object;
these subsystems integrate the input from opposing directionally selective
neurons, the output of which signals the speed and sign of relative motion of
the object along a given retinal meridian. Our results suggest that cells in
area 7a could be the part of this relative motion subsystem. In contrast to
the clustering of planar motions, radial motions were split: expansion was all
by itself, whereas contraction was alone but within a larger cluster
comprising the planar motions (Fig.
1). This finding suggests that radial motion, and, within it,
expansion and contraction, are represented quite differently in the ensemble.
Specifically, the fact that expansion was in a branch stemming directly off
the root of the dendrogram indicates a fundamental difference between
expansion and all other stimulus motions. This special place of expansion may
stem from the fact that it is perhaps the most frequently generated kind of
stimulus motion in species with forward locomotion: its high frequency of
occurrence in daily life may account for its uniqueness in the population
coding of stimulus motion but also for its high prevalence as a major effect
on the activity of cells in various cortical areas
(Anderson and Siegel 1999;
Duffy and Wurtz 1991;
Schaafsma and Duysens 1996;
Siegel and Read 1997). It is
possible that the planar optic flow that accompanies locomotion may be
principally relevant to maintaining dynamic stability while locomoting and
accordingly is located on the other main branch of the hierarchy in the
observed clustering (Fig.
1).
These considerations and interpretations of the tree-clustering results were further supported by the results of the MDS analysis. We used MDS as a second stage of analysis to gain an insight into the dimensions along which the tree clusters varied; therefore the data used as input to the MDS analysis were the derived inter-cluster distances (Fig. 1). The results obtained indicated two dimensions in operation (Fig. 5A). The first dimension separated expansion from all other stimuli; this underscores the uniqueness of this kind stimulus motion and probably signifies its importance for locomotion. This dimension could have been inferred from the tree-clustering analysis as evidenced by the placement of the expansion and all other stimulus motions combined in two separate clusters. Now, the second dimension in MDS obviously separated planar from radial motions, a finding not apparent in the tree-clustering analysis. A possible interpretation of the grouping of up-down, left-right, and CW/CCW motions is that all of them correspond to rotations with respect to the three cardinal axes of rotation. For example, to a good approximation, the up-down motions could come from rotation of the eyes or head-plus-eyes about a pitch axis through the head, the left-right motion could come from rotation of the eyes or head-plus-eyes about a yaw axis through the head, and the CW/CCW rotation could come from rotation of the eyes or head-plus-eyes about a roll axis through the head. In addition, the up-down and left-right motions could also come from up-down and left-right translatory movement of the head, respectively. In contrast to these considerations, radial motions can only come from translation in depth, which, in turn, typically comes about from moving in space, a very common activity. We believe that it is this last feature that is captured by the second dimension in the MDS plot (Fig. 5A). Thus radial motion in general, and expansion in particular, seem to hold a special place in the ensemble processing of visual motion in area 7a, reflecting, most probably, behavioral considerations.
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DISCLOSURES |
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FOOTNOTES |
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Address for reprint requests: Corresponding author: Apostolos P. Georgopoulos, Brain Sciences Center, One Veterans Drive, Minneapolis, MN, 55417. Tel: 612-725-2282, Fax: 612-725-2291, E-mail: omega{at}umn.edu
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