{"title": "A Functional Architecture for Motion Pattern Processing in MSTd", "book": "Advances in Neural Information Processing Systems", "page_first": 1451, "page_last": 1458, "abstract": "", "full_text": "A Functional Architecture for Motion \n\nPattern Processing in MSTd \n\n \n \n \n \n \n \n\nScott A. Beardsley \n\nDept. of Biomedical Engineering \n\nBoston University \nBoston, MA 02215 \nsbeardsl@bu.edu \n\nAbstract \n\nLucia M. Vaina \n\nDept. of Biomedical Engineering  \n\nBoston University \nBoston, MA 02215 \n\nvaina@bu.edu \n\n \n\ntasks, \n\nto  elucidate \n\ntwo  motion  pattern \n\nPsychophysical  studies  suggest \nthe  existence  of  specialized \ndetectors  for  component  motion  patterns  (radial,  circular,  and \nspiral), that are consistent with the visual motion properties of cells \nin the dorsal medial superior temporal area (MSTd) of non-human \nprimates.  Here  we  use  a  biologically  constrained  model  of  visual \nmotion  processing  in  MSTd,  in  conjunction  with  psychophysical \nperformance  on \nthe \ncomputational mechanisms associated with the processing of wide-\nfield motion patterns encountered during self-motion. In both tasks \ndiscrimination  thresholds  varied  significantly  with  the  type  of \nmotion  pattern  presented,  suggesting  perceptual  correlates  to  the \npreferred  motion  bias  reported  in  MSTd.  Through  the  model  we \ndemonstrate  that  while  independently  responding  motion  pattern \nunits  are  capable  of  encoding  information  relevant  to  the  visual \nmotion  tasks,  equivalent  psychophysical  performance  can  only  be \nachieved \nthat \nsystematically  inhibit  non-responsive  units.  These  results  suggest \nthe cyclic trends in psychophysical performance may be mediated, \nin part, by recurrent connections within motion pattern responsive \nareas  whose  structure  is  a  function  of  the  similarity  in  preferred \nmotion patterns and receptive field locations between units. \n\ninterconnected \n\npopulations \n\nneural \n\nusing \n\n1  Introduction \n\nA major challenge in computational neuroscience is to elucidate the architecture of \nthe  cortical  circuits  for  sensory  processing  and  their  effective  role  in  mediating \nbehavior. In the visual motion system, biologically constrained models are playing \nan  increasingly  important  role  in  this  endeavor  by  providing  an  explanatory \nsubstrate linking perceptual performance and the visual properties of single cells.  \nSingle  cell  studies  indicate  the  presence  of  complex  interconnected  structures  in \nmiddle temporal and primary visual cortex whose most basic horizontal connections \ncan  impart  considerable  computational  power  to  the  underlying  neural  population \n[1, 2].  Combined  psychophysical  and  computational  studies  support  these  findings \n\n\f \n\n \n\n \nFigure  1:  a)  Schematic  of  the  graded  motion  pattern  (GMP)  task.  Discrimination \npairs of stimuli were created by perturbing the flow angle (\u03c6) of each 'test' motion \n(with  average  dot  speed,  vav),  by  \u00b1\u03c6p  in  the  stimulus  space  spanned  by  radial  and \ncircular  motions.  b)  Schematic  of  the  shifted  center-of-motion  (COM)  task. \nDiscrimination  pairs  of  stimuli  were  created  by  shifting  the  COM  of  the  \u2018test\u2019\nmotion to the left and right of a central fixation point. For each motion pattern the\nCOM was shifted within the illusory inner aperture and was never explicitly visible. \n       \nand  suggest  that  recurrent  connections may  play  a  significant  role  in  encoding the \nvisual motion properties associated with various psychophysical tasks [3, 4]. \nUsing  this  methodology  our  goal  is  to  elucidate  the  computational  mechanisms \nassociated  with  the  processing  of  wide-field  motion  patterns  encountered  during \nself-motion. In the human visual motion system, psychophysical studies suggest the \nexistence  of  specialized  detectors  for  the  motion  pattern  components  (i.e.,  radial, \ncircular and spiral motions) associated with self-motion [5, 6]. Neurophysiological \nstudies reporting neurons sensitive to motion patterns in the dorsal medial superior \ntemporal  area  (MSTd)  support  the  existence  of  such  mechanisms  [7-10],  and  in \nconjunction with psychophysical studies suggest a strong link between the patterns \nof neural activity and motion-based perceptual performance [11, 12].  \nThrough  the  combination  of  human  psychophysical  performance  and  biologically \nconstrained  modeling  we  investigate  the  computational  role  of  simple  recurrent \nconnections  within  a  population  of  MSTd-like  units.  Based  on  the  known  visual \nmotion properties within MSTd we ask what neural structures are computationally \nsufficient to encode psychophysical performance on a series of motion pattern tasks.   \n\n2  Motion pattern discrimination \n\nUsing  motion  pattern  stimuli  consistent  with  previous  studies  [5,  6],  we  have \ndeveloped  a  set  of  novel  psychophysical  tasks  designed  to  facilitate  a  more  direct \ncomparison  between  human  perceptual  performance  and \nthe  visual  motion \nproperties of cells in MSTd that have been found to underlie the discrimination of \nmotion patterns [11, 12]. The psychophysical tasks, referred to as the graded motion \npattern (GMP) and shifted center-of-motion (COM) tasks, are outlined in Fig. 1. \nUsing  a  temporal  two-alternative-forced-choice  task  we  measured  discrimination \nthresholds  to  global  changes  in  the  patterns  of  complex  motion  (GMP  task),  [13], \nand shifts in the center-of-motion (COM task). Stimuli were presented with central \nfixation  using  a  constant  stimulus  paradigm  and  consisted  of  dynamic  random  dot \ndisplays  presented  in  a  24o  annular  region  (central  4o  removed).  In  each  task,  the \nstimulus  duration  was  randomly  perturbed  across  presentations  (440\u00b140  msec)  to \ncontrol  for  timing-based  cues,  and  dots  moved  coherently  through  a  radial  speed\n\n\f \n\n \nFigure 2: a) GMP thresholds across 8 'test' motions at two mean dot speeds for two \nobservers. Performance varied continuously with thresholds for radial motions (\u03c6=0,\n180o)  significantly  lower  than  those  for  circular  motions  (\u03c6=90,270o),  (p<0.001;\nt(37)=3.39). b) COM thresholds at three mean dot speeds for two observers. As with \nthe GMP task, performance varied continuously with thresholds for radial motions \nsignificantly lower than those for circular motions, (p<0.001; t(37)=4.47).   \n \ngradient  in  directions  consistent  with  the  global  motion  pattern  presented. \nDiscrimination  thresholds  were  obtained  across  eight  \u2018test\u2019  motions  corresponding \nto  expansion,  contraction, CW  and  CCW  rotation,  and  the  four  intermediate  spiral \nmotions.  To  minimize  adaptation  to  specific  motion  patterns,  opposing  motions \n(e.g., expansion/ contraction) were interleaved across paired presentations.  \n\n2.1  Results \n\nDiscrimination thresholds are reported here from a subset of the observer population \nconsisting  of three  experienced  psychophysical  observers,  one  of which  was na\u00efve \nto  the  purpose  of  the  psychophysical  tasks.  For  each  condition,  performance  is \nreported as the mean and standard error averaged across 8-12 thresholds. \nAcross  observers  and  dot  speeds  GMP  thresholds  followed  a  distinct  trend  in  the \nstimulus space [13], with radial motions (expansion/contraction) significantly lower \nthan circular motions (CW/CCW rotation), (p<0.001; t(37)=3.39), (Fig. 2a). While \nthresholds for the intermediate spiral motions were not significantly different from \ncircular motions (p=0.223, t(60)=0.74), the trends across 'test' motions were well fit \nwithin the stimulus space (SB: r>0.82, SC: r>0.77) by sinusoids whose period and \nphase were 196 \u00b1 10o and -72 \u00b1 20o respectively (Fig. 1a). \nWhen the radial speed gradient was removed by randomizing the spatial distribution \nof  dot  speeds,  threshold  performance  increased  significantly  across  observers \n(p<0.05; t(17)=1.91), particularly for circular motions (p<0.005; t(25)=3.31), (data \nnot  shown).  Such  performance  suggests  a  perceptual  contribution  associated  with \nthe presence of the speed gradient and is particularly interesting given the fact that \nthe  speed  gradient  did  not  contribute  computationally  relevant  information  to  the \ntask. However, the speed gradient did convey information regarding the integrative \nstructure  of  the  global  motion  field  and  as  such  suggests  a  preference  of  the \nunderlying motion mechanisms for spatially structured speed information. \nSimilar trends in performance were observed in the COM task across observers and \ndot speeds. Discrimination thresholds varied continuously as a function of the 'test' \n\n\f \n\nmotion with thresholds for radial motions significantly lower than those for circular \nmotions, (p<0.001; t(37)=4.47) and could be well fit by a sinusoidal trend line (e.g. \nSB at 3 deg/s: r>0.91, period = 178 \u00b1 10o and phase = -70 \u00b1 25o), (Fig. 2b).  \n\n2.2  A local or global task? \n\nThe consistency of the cyclic threshold profile in stimuli that restricted the temporal \nintegration  of  individual  dot  motions  [13],  and  simultaneously  contained  all \ndirections  of  motion,  generally  argues  against  a  primary  role  for  local  motion \nmechanisms  in  the  psychophysical  tasks.  While  the  psychophysical  literature  has \nreported  a  wide  variety  of  \u201clocal\u201d  motion  direction  anisotropies  whose  properties \nare reminiscent of the results observed here, e.g. [14], all would predict equivalent \nthresholds for radial and circular motions for a set of uniformly distributed and/or \nspatially  restricted  motion  direction  mechanisms.  Together  with  the  computational \nimpact of the speed gradient and psychophysical studies supporting the existence of \nwide-field motion pattern mechanisms [5, 6], these results suggest that the threshold \ndifferences across the GMP and COM tasks may be associated with variations in the \ncomputational properties across a series of specialized motion pattern mechanisms.     \n\n3  A computational model \n\nThe  similarities  between  the  motion  pattern  stimuli  used  to  quantify  human \nperception  and  the  visual  motion  properties  of  cells  in  MSTd  suggests  that  MSTd \nmay  play  a  computational  role  in  the  psychophysical  tasks.  To  examine  this \nhypothesis,  we  constructed  a  population  of  MSTd-like  units  whose  visual  motion \nproperties were consistent with the reported neurophysiology (see [13] for details). \nAcross the population, the distribution of receptive field centers was uniform across \npolar  angle  and  followed  a  gamma  distribution  \u0393(5,6)  across  eccenticity  [7].  For \neach unit, visual motion responses followed a gaussian tuning profile as a function \nof the stimulus flow angle G(\u03c6), (\u03c3i=60\u00b130o; [10]), and the distance of the stimulus \nCOM from the unit\u2019s receptive field center Gsat(xi, yi, \u03c3s=19o), Eq. 1, such that its \npreferred  motion  response  was  position  invariant  to  small  shifts  in  the  COM  [10] \nand degraded continuously for large shifts [9].  \nWithin  the  model,  simulations  were  categorized  according  to  the  distribution  of \npreferred  motions  represented  across  the  population  (one  reported  in  MSTd  and  a \nuniform  control).  The  first  distribution  simulated  an  expansion  bias  in  which  the \ndensity  of  preferred  motions  decreased  symmetrically  from  expansions  to  con-\ntraction [10]. The second distribution simulated a uniform preference for all motions \nand  was  used  as  a  control  to  quantify  the  effects  of  an  expansion  bias  on \npsychophysical  performance.  Throughout  the  paper  we  refer  to  simulations \ncontaining these distributions as \u2018Expansion-biased\u2019 and \u2018Uniform\u2019 respectively. \n\n3.1  Extracting perceptual estimates from the neural code \n\nFor each stimulus presentation, the ith unit\u2019s response was calculated as the average \nfiring rate, Ri, from the product of its motion pattern and spatial tuning profiles, \n     \n\n        (1) \n\n         \n\nG\n\nR\n\nR\n\nP\n\n+\n\n=\n\n,yy,xx\n\u2212\ni\n\n\u2212\n\ni\n\n\u03c3\ns\n\n(\n=\n\u03bb\n\n)12\n\n(\nmin\n\n[\n\u03c3\u03c6\u03c6\nt\n\n\u2212\n\n]\n\n,\n\ni\n\ni\n\n)\nG\n\n(\n\nsat\ni\n\ni\n\nmax\n\n)\n\nwhere Rmax is the maximum preferred stimulus response (spikes/s), min[ ] refers to \nthe  minimum  angular  distance  between  the  stimulus  flow  angle \u03c6  and  the  unit\u2019s \npreferred  motion  \u03c6i,  Gsat  is  the  unit\u2019s  spatial  tuning  profile  saturated  within  the \ncentral 5\u00b13o, \u03c3ti and \u03c3s are the standard deviations of the unit\u2019s motion pattern and \n\n\f \n\n^ \n\n \n \nFigure  3:  Model  vs.  psychophysical  performance  for  independently  responding \nunits. Model thresholds are reported as the average (\u00b11 S.E.) across five simulated \npopulations. a) GMP thresholds were highest for contracting motions and lowest for \nexpanding  motions  across  all  Expansion-biased  populations.  b)  Comparable  trends \nin  performance  were  observed  for  COM  thresholds.  Comparison  with  the  Uniform \ncontrol simulations in both tasks (2000 units shown here) indicates that thresholds \nclosely followed the distribution of preferred motions simulated within the model.  \n \nspatial  tuning  profiles  respectively,  (xi,yi)  is  the  spatial  location  of  the  unit\u2019s \nreceptive  field  center,  (x,y)  is  the  spatial  location  of  the  stimulus  COM,  and  \nP(\u03bb=12) is the background activity simulated as an uncorrelated Poisson process.  \nThe  psychophysical  tasks  were  simulated  using  a  modified  center-of-gravity \napproach  to  decode  estimates  of  the  stimulus  properties,  i.e.  flow  angle  ( )\u03c6   and \nCOM location in the visual field  (\n)yx \u02c6,\u02c6\nRx\n\uf8eb\n\u2211\ni\ni\n\uf8ec\ni\n\uf8ec\nR\n\u2211\n\uf8ec\ni\n\uf8ed\ni\n\n                                  (\n\n, from the neural population     \n\n)\n\u02c6,\u02c6,\u02c6\nyx\n\u03c6\n\nRy\ni\ni\nR\ni\n\n        (2) \n\nv\n\u03c6\ni\n\nR\ni\n\n,\n\n\u2211\ni\n\n\u2211\ni\n\n,\n\n\u2211\ni\n\n   \n\n\uf8f6\n\uf8f7\n\uf8f7\n\uf8f7\n\uf8f8\n\n=\n\n       \n\ni\u03c6v   is  the  unit  vector  in  the  stimulus  space  (Fig.  1a)  corresponding  to  the \nwhere \nunit\u2019s  preferred  motion.  For  each  set  of  paired  stimuli,  psychophysical  judgments \nwere  made  by  comparing  the  estimated  stimulus  properties  according  to  the \ndiscrimination  criteria,  specified \nthe \npsychophysical experiments, discrimination thresholds were computed using a least-\nsquares fit to percent correct performance across constant stimulus levels. \n\nthe  psychophysical \n\ntasks.  As  with \n\nin \n\n3.2  Simulation 1: Independent neural responses \n\nIn the first series of simulations, GMP and COM thresholds were quantified across \nthree populations (500, 1000, and 2000 units) of independently responding units for \neach  simulated  distribution  (Expansion-biased  and  Uniform).  Across  simulations, \nboth  the  range  in  thresholds  and  their  trends  across  \u2018test\u2019  motions  were  compared \nwith  human  psychophysical  performance  to  quantify  the  effects  of  population  size \nand an expansion biased preferred motion distribution on model performance. \nOver the psychophysical range of interest (\u03c6p \u00b1 7o), GMP thresholds for contracting \nmotions  were  at  chance  across  all  Expansion-biased  populations,  (Fig.  3a).  While \nthresholds  for  expanding  motions  were  generally  consistent  with  those  for  human \nobservers,  those  for  circular  motions  remained  significantly  higher  for  all  but  the \nlargest populations. Similar trends in performance were observed for the COM task, \n(Fig.  3b).  Here  the  range  of  COM  thresholds  was  well  matched  with  human \nperformance  for  simulations  containing  1000  units,  however,  the  trends  across \nmotion patterns remained inconsistent even for the largest populations. \n\n\f \n\n \n \nFigure  4:  Proposed  recurrent  connection  profile  between  motion  pattern  units.  a)\nAcross  the  motion  pattern  space  connection  strength  followed  an  inverse  gaussian \nprofile such that the ith unit (with preferred motion \u03c6i) systematically inhibited units \nwith anti-preferred motions centered at 180+\u03c6i. b) Across the visual field connection \nstrength  followed  a  difference-of-gaussians  profile  as  a  function  of  the  relative \ndistance between receptive field centers such that spatially local units are mutually\nexcitatory (\u03c3Re=10o) and more distant units were mutually inhibitory (\u03c3Ri=80o).  \n \nFor  simulations  containing  a  uniform  distribution  of  preferred  motions,  the \nthreshold range was consistent with human performance on both tasks, however, the \ntrend across motion patterns was generally flat. What variability did occur was due \nprimarily to the discrete sampling of preferred motions across the population.  \nComparison of the discrimination thresholds for the Expansion-biased and Uniform \npopulations  indicates  that  the  trend  across  thresholds  was  closely  matched  to  the \nunderlying distributions of preferred motions. This result in due in part to the near-\nequal  weighting  of  independently  responding  units  and  can  be  explained  to  a  first \napproximation  by  the  proportional  increase  in  the  signal-to-noise  ratio  across  the \npopulation as a function of the density of units responsive to a given 'test' motion.   \n\n3.3  Simulation 2: An interconnected neural structure \n\nIn a second series of simulations, we examined the computational effect of adding \nrecurrent  connections  between  units.  If  the  distribution  of  preferred  motions  in \nMSTd  is  in  fact  biased  towards  expansions,  as  the  neurophysiology  suggests,  it \nseems  unlikely  that  independent  estimates  of  the  visual  motion  information  would \nbe sufficient to yield the threshold profiles observed in the psychophysical tasks.  \nWe  hypothesize  that  a  simple  fixed  architecture  of  excitatory  and/or  inhibitory \nconnections  is  sufficient  to  account  for  the  cyclic  trends  in  discrimination \nthresholds.  Specifically,  we  propose  that  a  recurrent  connection  profile  whose \nstrength varies as a function of (a) the similarity between preferred motion patterns \nand (b) the distance between receptive field centers, is computationally sufficient to \nrecover the trends in GMP/COM performance (Fig. 4), \n\nx(\ni\n\n\u2212\n\n\u2212\n\n2\ny(\n)x\n+\ni\nj\n2\n2\n\u03c3\neR\n\n\u2212\n\n2\n)y\nj\n\n   \n\nw\nij\n\n=\n\neS\nR\n\n\u2212\n\n\u2212\n\ne\n\nS\nR\n2\n\nx(\ni\n\n\u2212\n\n2\ny(\n)x\n+\ni\nj\n2\n2\n\u03c3\nRi\n\n\u2212\n\n2\n)y\nj\n\n2\n\n])\n\n(min[\n\u03c6\u03c6\n\u2212\n\u2212\ni\nj\n2\n2\n\u03c3\nI\n\n     (3) \n\n\u2212\n\neS\n\u03c6\n\n\f \n\n \n \nFigure  5:  Model  vs.  psychophysical  performance  for  populations  containing \nrecurrent  connections  (\u03c3I=80o).  As  the  number  of  units  increased  for  Expansion-\nbiased  populations,  discrimination  thresholds  decreased  to  psychophysical  levels\nand the sinusoidal trend in thresholds emerged for both the (a) GMP and (b) COM\ntasks. Sinusoidal trends were established for as few as 1000 units and were well fit \n(r>0.9) by sinusoids whose periods and phases were (193.8 \u00b1 11.7o, -70.0 \u00b1 22.6o) \nand (168.2 \u00b1 13.7o, -118.8 \u00b1 31.8o) for the GMP and COM tasks respectively.  \n \nwhere wij is the strength of the recurrent connection between ith and jth units, (xi,yi) \nand (xj,yj) denote the spatial locations of their receptive field centers, \u03c3Re (=10o) and \n\u03c3Ri (=80o) together define the spatial extent of a difference-of-gaussians interaction \nbetween  receptive  field  centers,  and  SR  and  S\u03c6  scale  the  connection  strength.  To \nexamine  the  effects  of  the  spread  of  motion  pattern-specific  inhibition  and \nconnection strength in the model, \u03c3I, S\u03c6, and SR were considered free parameters. \nWithin the parameter space used to define recurrent connections (i.e., \u03c3I, S\u03c6 and SR), \nMonte  Carlo  simulations  of  Expansion-biased  model  performance  (1000  units) \nyielded regions of high correlation on both tasks (with respect to the psychophysical \nthresholds, r>0.7) that were consistent across independently simulated populations. \nTypically  these  regions  were  well  defined  over  a  broad  range  such  that  there  was \nsignificant  overlap  between  tasks  (e.g.,  for  the  GMP  task  (SR=0.03),  \u03c3I=[45,120o], \nS\u03c6=[0.03,0.3] and for the COM task (\u03c3I=80o), S\u03c6 = [0.03,0.08], SR = [0.005, 0.04]). \nFig. 5 shows averaged threshold performance for simulations of interconnected units \ndrawn  from  the  highly  correlated  regions  of  the  (\u03c3I,  S\u03c6,  SR)  parameter  space.  For \npopulations  not  explicitly  examined  in  the  Monte  Carlo  simulations  connection \nstrengths  (S\u03c6,  SR)  were  scaled  inversely  with  population  size  to  maintain  an \nequivalent \nincorporation  of  recurrent \nconnections,  the  sinusoidal  trend  in  GMP  and  COM  thresholds  emerged  for \nExpansion-biased  populations  as  the  number  of  units  increased.  In  both  tasks  the \ncyclic threshold profiles were established for 1000 units and were well fit (r>0.9) by \nsinusoids whose periods and phases were consistent with human performance. \nUnlike \nthe  Expansion-biased  populations,  Uniform  populations  were  not \nsignificantly  affected  by  the  presence  of  recurrent  connections  (Fig.  5).  Both  the \nrange in thresholds and the flat trend across motion patterns were well matched to \nthose  in  Section  3.2.  Together  these  results  suggest  that  the  sinusoidal  trends  in \nGMP and COM performance may be mediated by the combined contribution of the \nrecurrent interconnections and the bias in preferred motions across the population. \n\nlevel  of  recurrent  activity.  With \n\nthe \n\n4  Discussion \n\nUsing  a  biologically  constrained  computational  model  in  conjunction  with  human \npsychophysical  performance  on  two  motion  pattern  tasks  we  have  shown  that  the \nvisual  motion  information  encoded  across  an  interconnected  population  of  cells \n\n\f \n\nresponsive to motion patterns, such as those in MSTd, is computationally sufficient \nto extract perceptual estimates consistent with human performance. Specifically, we \nhave  shown  that  the  cyclic  trend  in  psychophysical  performance  observed  across \ntasks, (a) cannot be reproduced using populations of independently responding units \nand  (b)  is  dependent,  in  part,  on  the  presence  of  an  expanding  motion  bias  in  the \ndistribution of preferred motions across the neural population.  \nThe  model\u2019s  performance  suggests  the  presence  of  specific  recurrent  structures \nwithin  motion  pattern  responsive  areas,  such  as  MSTd,  whose  strength  varies  as  a \nfunction  of  the  similarity  between  preferred  motion  patterns  and  the  distance \nbetween  receptive  field  centers.  While  such  structures  have  not  been  explicitly \nexamined in MSTd and other higher visual motion areas there is anecdotal support \nfor  the  presence  of  inhibitory  connections  [8].  Together,  these  results  suggest  that \nrobust processing of the motion patterns associated with self-motion and optic flow \nmay be mediated, in part, by recurrent structures in extrastriate visual motion areas \nwhose distributions of preferred motions are biased strongly in favor of expanding \nmotions. \n\nAcknowledgments \nThis work was supported by National Institutes of Health grant EY-2R01-07861-13 \nto L.M.V. \n\nReferences \n[1]  Malach,  R.,  Schirman,  T.,  Harel,  M.,  Tootell,  R.,  &  Malonek,  D.,  (1997), \n\nCerebral Cortex, 7(4): 386-393. \n\n[2]  Gilbert, C. D., (1992), Neuron, 9: 1-13. \n[3]  Koechlin, E., Anton, J., & Burnod, Y., (1999), Biological Cybernetics, 80: 25-\n\n44. \n\n[4]  Stemmler, M., Usher, M., & Niebur, E., (1995), Science, 269: 1877-1880. \n[5]  Burr, D. C., Morrone, M. C., & Vaina, L. M., (1998), Vision Research, 38(12): \n\n1731-1743. \n\n[6]  Meese, T. S. & Harris, S. J., (2002), Vision Research, 42: 1073-1080. \n[7]  Tanaka, K. & Saito, H. A., (1989), Journal of Neurophysiology, 62(3): 626-641. \n[8]  Duffy, C. J. & Wurtz, R. H., (1991), Journal of Neurophysiology, 65(6): 1346-\n\n1359. \n\n[9]  Duffy, C. J. & Wurtz, R. H., (1995), Journal of Neuroscience, 15(7): 5192-5208. \n[10]  Graziano,  M.  S.,  Anderson,  R.  A.,  &  Snowden,  R.,  (1994),  Journal  of \n\nNeuroscience, 14(1): 54-67. \n\n[11]  Celebrini,  S.  &  Newsome,  W.,  (1994),  Journal  of  Neuroscience,  14(7):  4109-\n\n4124. \n\n[12]  Celebrini,  S.  &  Newsome,  W.  T.,  (1995),  Journal  of  Neurophysiology,  73(2): \n\n437-448. \n\n[13]  Beardsley,  S.  A.  &  Vaina,  L.  M.,  (2001),  Journal  of  Computational  Neuro-\n\nscience, 10: 255-280. \n\n[14]  Matthews, N. & Qian, N., (1999), Vision Research, 39: 2205-2211. \n\n\f", "award": [], "sourceid": 2475, "authors": [{"given_name": "Scott", "family_name": "Beardsley", "institution": null}, {"given_name": "Lucia", "family_name": "Vaina", "institution": null}]}