A retinomorphic chip with parallel pathways : encoding INCREASING, ON, DECREASING, and OFF visual signals

University of Pennsylvania ScholarlyCommons Departmental Papers (BE) Department of Bioengineering February 2001 A retinomorphic chip with parallel pathways : encoding INCREASING, ON, DECREASING, and OFF visual signals Kwabena A. Boahen University of Pennsylvania, boahen@seas.upenn.edu Follow this and additional works at: http://repository.upenn.edu/be_papers Recommended Citation Boahen, K. A. (2001). A retinomorphic chip with parallel pathways : encoding INCREASING, ON, DECREASING, and OFF visual signals. Retrieved from http://repository.upenn.edu/be_papers/7 Postprint version. Published in Analog Integrated Circuits and Signal Processing, Volume 30, Issue 2, February 2002, pages 121-135. Publisher URL: http://dx.doi.org/10.1023/a:1013751627357 This paper is posted at ScholarlyCommons. http://repository.upenn.edu/be_papers/7 For more information, please contact libraryrepository@pobox.upenn.edu.

A retinomorphic chip with parallel pathways : encoding INCREASING, ON, DECREASING, and OFF visual signals Abstract Retinomorphic chips may improve their spike-coding efficiency by emulating the primate retina's parallel pathways. To model the four predominant ganglion-cell types in the cat retina, I morphed outer and inner retina microcircuits into a silicon chip, Visio1. It has 104 x 96 photoreceptors, 4 x 52 x 48 ganglion-cells, a die size of 9.25 x 9.67 mm 2 in 1.2 µm 5V CMOS, and consumes 11.5 mw at 5 spikes/second/ganglion-cell. Visio1 includes novel subthreshold current-mode circuits that model horizontal-cell autofeedback, to decouple spatial filtering from local gain control, and model amacrine-cell loop-gain modulation, to adapt temporal filtering to motion. Different ganglion cells respond to motion in a quadrature sequence, making it possible to detect edges of one contrast or the other moving in one direction or the other. I present results from a multichip 2-D motion system, which implements Watson and Ahumada's model of human visualmotion sensing. Keywords neuromorphic systems, analog VLSI, mixed-mode design, CMOS imager, silicon retina, silicon neuron, spatiotemporal filtering, automatic gain control, contrast gain control, direction selectivity Comments Postprint version. Published in Analog Integrated Circuits and Signal Processing, Volume 30, Issue 2, February 2002, pages 121-135. Publisher URL: http://dx.doi.org/10.1023/a:1013751627357 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/be_papers/7

V i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskru et{bi$t yt{ sr't $t - { sr'tsti$pp z$rzsj 7$tsjR bsa ts BsY t _ tt $B t$t $t nn1( 78$Y Gsj, _Y$jsI j}ys _V dd(; 3 A Zs k d1 1((d VAR s{ i $tb8b }Y${ {Y$}R 8sk $8} B% Y $ R}$, T{BI$t ^{$ t{k Ak 8T Zjs$t Y } $8s $ts:r }s sjj j }sybskr qb 8BI j Y PBZ } IB8$tst stj$btt{ jj k} R $t Y {s $ts y 8B }Y I BZ sti $tt $ts 8${ B{$ {Z$R $tb s R$j${Bt {Y$} z$r$bd y YsR d(; E }YBB { }B R ; x1 ;M stj$btt { jjr s I$ R$9 BP 31x 3E88 1 $t d1 8 xz ]!7 sti {BtRZ8 R ddx8g s x R}$, R\R {BtI\stj$BtT{ jj z$r$bd $t{jzi R tb% j RZAY RYBjI {Z tt8bi {$ {Z$R Ys 8BI j YB $9BtsjT{ jj szbp IAs{, B I {BZ}j R}s$sj hj $t P B8 jb{sj s$t {Bt Bj sti 8BI j s8s{ $t T{ jj jbb}ts$t 8BIZjs$Bt B sis} 8}BT sj hj $t B 8B$Bt *$& t stj$bt { jjr R}BtI B 8B$Bt $t s JZsI sz R JZ t{ 8s,$t $ }BRR$Aj B I { I R BP Bt {Bt sr B Y BY 8B%$t $t Bt I$ {$Bt B Y BY y } R t RZjR P B8 s 8Zj${Y$} 1T* 8B$Bt RkR 8 by${y $8}j 8 tr GsRBt sti VYZ8sIs:R 8BI j BP YZ8st %$RZsjT8B$Bt R tr$t kbb IRU W Z B8B }Y${ 7kR 8R VtsjB zn7y $- ITBI * R$t ]!7 y8s 7$j${Bt i $ts 7$j${Bt W Z Bt 7}s$B 8}B sj 3$j $t VZB8s${ ps$t ]Bt Bj ]Bt sr ps$t ]Bt Bj *$ {$Bt 7 j {$%$k d _s sjj j _sybskr $t Y i $ts qy } R t{ BP %$RZsj }sybskr R} {$sj$9 I PB R}s$sj sti 8}B sj RBjZ$Btv{sjj I }s %B{ jjzjs sti 8stB{ jjzjs }sybskr $t } $8s Rv YsR A t {Bth 8 I ABY }YkR$BjB${sjjk sti stsb8${sjjk >1M 1; dh W Z BtR $t Y R }sybskr }BBj R$tsjR B% $Y R}s{ B $8 B s% s BZ JZstZ8 4Z{Zs$BtR 8s$ts$t$t Y Rs8 tb$r j % j sr Y k si }BB RBjZ$Bt $t Bt IB8s$t PB BBI RBjZ$Bt $t Y BY >dxh VR Y j$y $t tr$k I B}R }BBj$t B{{Z R B% js I$Rst{ R B jbt $8 R B 8s$ts$t Y R$tsjTBTtB$R s$b >EH qy $R s {Bt$tZZ8 BP R}s$sj sti 8}B sj RBjZ$BtR b$y$t s{y }sybsk YBb % IZ B Y %s $s$bt BP R}s$B 8}B sj {Ys s{ $R${R BP 8$I sti }s srbj $tsj stj$bt { jjr b$y {{ t ${$k >d;h qy k st P B8 R8sjj sti RZRs$t I $t Y PB% s by ht I s$jr BP st BA` { RsA$j$9 I Ak s{,$t s RBj% I B js sti str$ t $t Y } $}Y k by RZII t 8B$Bt $t Y RZ BZtI$tR $R {s}z I V s $% t {{ t ${$k }s srbjr wsjrb {sjj I { jjrd {B% bb B Y $8 R {s 1((d jzb V{sI 8${ _ZAj$RY R _ $t I $t Y W Y jstir }u}ƒ!0" g3]+3]3++g" gpu+3" }!g

1 bsa ts BsY t Cone Cone Gain Spat 1/λ Freq Horizontal Cell Ampl Ampl 0 Ampl 0 Ampl Bipolar Cell Amacrine Cell Gain Gain Temp Temp 1/τ 1/τ Freq Freq Gain Gain Temp 1/τ Temp 1/τ Freq Freq Ganglion Cell Freq Ampl Ganglion Cells On Off Inc. Dec. wsd wad wsd i $tsj 7 Z{Z U qy %$RZsj R$tsj $R jsk I P B8 Y }YBB { }B R w{sjj I {Bt RD B Y stj$bt { jjr wbybr s-btr PB 8 Y B}${ t % D Ak A$}Bjs { jjr b$y Rkts}${ $t s{$btr B{{Z $t b$y$t bb }j -$PB 8 jsk R <B $9Btsj { jjr 8 I$s js sj $t s{$btr $t Y h R wbz D }j -$PB 8 jsk by$j s8s{ $t { jjr 8 I$s js sj $t s{$btr $t Y R {BtI w$tt D }j -$PB 8 jsk Y R $t t ZT BtR s $ty$a$b k 3BZ k} R BP stj$bt { jjr by${y y {sjj Ct CPP 't{ sr't sti I { sr't t{bi Y $ts:r BZ}Z $t Y $ R}$, s$tr wad i $tsj 3Zt{$BtU qy %$RZsj R$tsj $R AstI}sRR hj I R}s$sjjk $t Y BZ $ts Y t jbb}srr sti Y$Y}sRR hj I 8}B sjjk $t Y $tt $ts qy R stsjb R$tsjR s h R YsjPTbs% {$h I sti Y t js t{bi I sr R}$, s$tr 7}s$sj hj R sis} B j$y $t tr$kvy $ s$t $R $t% R jk } B}B $Btsj q 8}B sj hj R sis} B R$8ZjZR R} IvY $ $8 T{BtRst $R $t% R jk } B}B $Btsj w$ + ) b" by $R Y bs% j ty R j { I Ak Y R}s$sj hj D VtI R}$,$t t Z BtR sis} B Y $ $t}z:r s BP {Yst vy $ h $t s $R j$t s jk } B}B $Btsj 3$Z d i $tsj ]$ {Z$R sti!} s$btr jbt I$Rst{ R sti R}BtI 8B str$ tjk Yst 8$I R wsjrb {sjj I # { jjrd >;n d;h yt 8R BP s{zsj tz8a R sti Rs8}j$t I tr$$ R 8$I R sti }s srbjr 8s, Z} (0 BP Y Bsj stj$bt { jj }B}Zjs$Bt sti B{{Z $t s s$b BP sabz Ud >nxh W$t $8 R P b }s srbjr s JZ$ I B $j Y $ts A {szr Y $ I ti $${ h jir s Y $8 R js qy 8s$t$t d(0 BP Y { jjr PB 8 s Y B t BZR BZ} sti } B` { 8s$tjk B Y 8$IA s$t >nxh }u}ƒ!0" g3]+3]3++g" gpu+3" }!3

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr n V{$%$k $t s{y }sybsk $R t{bi I Ak s }s$ BP {B8}j 8 ts k {Ystt jr R % I Ak CtT sti CPPT8$I R B Ak CtT sti CPPT}s srbjr qy Ct {Ystt j R$tsjR $t{ sr R $t s8}j$zi Ak $t{ sr$t % R${j T j sr B R}$, TI$R{Ys s R Y CPP {Ystt j R$tsjR I { sr R $t s8}j$zi $t s R$8$js PsRY$Bt >1H ]B8}j 8 ts k R$tsj$t B% {B8 R Y RYB {B8$tR BP ZR$t s R$tj {Ystt j B str8$ ABY $t{ sr R sti I { sr R 8 srz I js$% B s AsR j$t U d ej %s I R}$, TI$R{Ys s R sti % R${j T j sr s R 8ZR A 8s$ts$t I $t Y JZ$ R{ t Rs * { sr R s str8$ I b$y jbb hi j$k A {szr JZstZ8 4Z{Zs$BtR w$ RYB tb$r D I { sr Btjk sr Y RJZs BB BP Y 8 st s * { sr R s str8$ I b$y jbb R} I A {szr JZsts s $tp JZ t sti 8 8A st }Bjs $9s$Bt sti str8$ 8B%sj s }srr$% e-{ } } $B B Y % k h R Rkts}R R PBZtI $t BI sti {Bt 8$tsjR {B8}j 8 ts k R$tsj$t $R ZR I Y BZYBZ Y $ts B str8$ $tpb 8s$Bt ^{$ tjk ZR$t % R${j R B R}$, R yt sii$$bt B IZ{$t JZ$ R{ t h $t s R Ak ZR$t {B8}j 8 tt s k {Ystt jr y }BRZjs Ys PZ Y Rs%$tR $t R}$, R sti % R${j R s s{y$ % I Ak sis}$t Y AsR j$t vaby s Y stj$btt{ jj j % j sti s Y t bb,tj % j V Y stj$btt{ jj j % j Y AsR j$t $R R Ak {sj{$z8ti } ti t }BsRR$Z8 {Ystt jr by${y RYZt Y $t}z {Z t > H V Y t bb,tj % j $ $R R Ak } Rkts}${ $ty$a$$bt P B8 s8s{ $t { jjr by${y 8$ts % R${j j sr s Ct sti CPP A$}Bjs T{ jj 8$tsjR >ndh Ys%$t j$, j s,k $t sb R Y R AsR j$t TR $t s8s{ $t { jjr PBjjBb Y R$tsj:R 8}B sj s% s qb trz R$tsj 4Z{Zs$BtR s tb 8sR, I Ak s Ikts8${ AsR j$t s jbt $8 TR{sj s% s 8ZR A {B8}Z I by t {Yst $R RjBb VtI B trz Y R$tsj { BRR R Y AsR j$t by t $R I $%s$% {Yst R R$t s RYB $8 TR{sj s% s 8ZR A {B8}Z I by t {Yst $R s}$i qyzr R}$, R sti % R${j R s {BtR % I sr P JZ t JZsts } BIZ{ I Ak PsR R$tsjR s I$R{Ys I PB RYB IZ s$btr by$j $tp JZ t JZsts } BIZ{ I Ak RjBb R$tsjR s I$R{Ys I PB jbt IZ s$btr i $tb8b }Y${ {Y$}R by${y } PB 8 sis}$% }$- jt}s sjj j JZst$T 9s$Bt > H 8sk $8} B% Y $ R}$, T{BI$t ^{$ t{k Ak 8Zjs$t }s sjj j }sybskr $t Y $ts qb Y$R ti y Ys% { s I $tsj d qy BI }sybsk IB R ht b$y s R$tj {Ystt j A {szr $R 8 st s{$%$k $R %$ Zsjjk 9 B }u}ƒ!0" g3]+3]3++g" gpu+3" }!p

; bsa ts BsY t Cone Outer Segments I I c V cq I' I c ' V cq Cone Terminals Horizontal Cells Excitation Inhibition wsd Conduction Modulation wsd W Z sj ${ B{$ {Z$ ku ]Bt 8$tsjR w]qd { $% s }YBB{Z t { Ys $R } B}B $Btsj B $t{$i t j$y $t tr$k P B8 Y $ BZ R 8 tr w]!d qb {Bt Bj ]! B ]q s tzs$bt b$ybz {Yst$t Y {Bt Tt bb,:r R}s{ T{BtRst Y YB $9Btsj { jj w<]d 8BIZjs R ABY ]q s} `Zt{$BtR sti 8 8A st {BtIZ{T st{ R ]Bt T -{$s$bt 8BIZjs$Bt $R sj$9 I Ak pv V szbt { }B R $t Y <] 8 8A st by${y PB 8 s }BR$$% P IAs{, jbb} wad ]!7 ]$ {Z$U V }!7 str$rb b$y $R RBZ { $ I B ~ { sti $R s $ I B ~ Y } BIZ{ R s {Z t } B}B $Btsj B Y } BIZ{ BP Y ]q sti <] s{$%$$ R by${y s } R t I Ak Y {Z tr { { sti { Y qy$r {Z t $R RZt, P B8 Y ]q tbi ~ { B8BI j <] RYZt$t $ty$a$$bt sti IZ8} I Bt Y <] tbi ~ Y B 8BI j ]q -{$s$bt sti <] szbp IAs{, ~ {J R R Y 8 st j % j BP Y {Bt {Z t { { 3$Z 1 B }Y$t Y!Z i $ts V c V h Vss1 I h V hh V c ' V h ' wad Vss1 I h ' V hh 8${ B{$ {Z$R R %$t Y 8stB{ jjzjs sti }s %B{ jjzjs }sybskr $t s {Y$} z$r$bd Ys 8BI jr Y PBZ } IB8$tst stj$bt { jj k} R z$r$bd } PB 8R Y B} s$btr RYBbt $t 3$Z d s Y }$- jtj % j VtsB8${sjjk $I t$h I t Z sj 8${ B{$ {Z$R Ys } PB 8 Y R B} st $BtR sti Y $ ]!7 t Z B8B }YR s I R{ $A I $t Y 7 {$BtR 1 sti n qy R {Z tt8bi {$ {Z$R B} s $t Y RZAY RYBjI T $Bt >n1h by R8sjjTR$tsj {BtIZ{st{ R sti str{btiz{st{ R s } B}B $Btsj B Y {Z t j % j >1H {Z ttr} si$t I$&ZRB t T bb,r s j$t s >d1 ;1 ;H sti Y t sj$9 I strj$t s } $t{$}j YBjIR >xh z$r$bd:r I R$t sti } PB 8st{ s I R{ $A I $t 7 {$Bt ; sti $R s}}j${s$bt $t s 8Zj${Y$} sjt$8 1T* 8B$BtTR tr$t RkR 8 $R I R{ $A I $t 7 {$Bt x 7 {$Bt E {Bt{jZI R Y }s} 1!Z i $ts BI j qy BZ $ts } PB 8R R}s$B 8}B sj AstI}sRR hj $t sti sis}r $R s$t jb{sjjkvaby s Y { }B j % j >de n(h sti s Y t bb, j % j _ %$BZR s 8}R B 8s, Y R bb PZt{$BtR {B -$R $t Bt }u}ƒ!0" g3]+3]3++g" gpu+3" }!<

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr x t bb, } BIZ{ I ZtI R$ saj R$I T & {R >d1 nh yt }s ${Zjs Y {$ {Z$ Rs R $t$t $P kbz s tzs IZtIst jbbtp JZ t{k 8}BT sj sti R}s$sj R$tsjR Ak $t{ sr$t Y t s$% TP IAs{, jbb}:r s$t VtI Y { }$% h ji -}stir sjs 8$tjk $P kbz IZ{ }YBB{Z t R tr$$%$k Ak $t{ sr$t Y {Bt ubu{bt {BtIZ{st{ qb B% {B8 Y Y$YTs$t t s$% TP IAs{, BZ $ts {$ {Z$ 8BI j:r RYB {B8$tR y R s {Y I Y t Z BA$BjBk j$ sz PB s $T tsj 8 {Yst$R8 Ys {BZjI I {BZ}j R}s$B 8}B sj hj $t jb{sj s$t {Bt Bj sti 8}B sj RsA$j$k <B $9BtsjT{ jj szbp IAs{, by${y bsr I 8BtR s I Ak s8 8stR sti G Aj$t s P b k s R sb $t Y $ Rsjs8stI >1nH {st s{y$ % Y$R <B $9Btsj { jjr w<]d by${y s,tbbt B ZR Y $ty$a$b k t Z B str8$ pv V sjrb -} RR pv VTs I ]jt{ystt jr qy R {Ystt jr Ys% s % Rsj }B t$sj BP T1(8z sti Y PB I }Bjs $9 Y { jj by t Y k s B} t I PB 8$t s }BR$$% TP IAs{, jbb} s8 8stR sti G Aj$t RYBb I Ys Y$R szbp IAs{, jbb} s{{bzt I PB Y - 8 jk RjBb Ikts8${R BP <]R $t{ sr$t Y $ $8 {BtRst P B8 Ex8R B x((8r k stsjkr$r BP Y si B&R $t%bj% I $t BZ T $ts I R$t YsR k$ ji I bb t b Yk}BY R R sabz Y Bj BP szbp IAs{, >MH <] szbp IAs{, {st $8} B% 8}B sj RsA$j$k Ak s8}j$pk$t Y {Bt R$tsj sjjbb$t ZR B I { sr Y R ty BP Y {Bt ubu<] Rkts}R qyzr b {st s tzs jbbtp JZ t{k R$tsjR by$j 8s$ts$tT $t 8}B sj RsA$j$k V jbb {Bt ubu<] Rkts}${ str{btiz{st{ - tir Y {Bt :R Ikts8${ st sr b jj VZBP IAs{, {st sjrb 8s, { }$% Th ji R$9 $ti } ti t BP R tr$$%$k Ak 8BIZjs$t Y & {T $% R ty BP Y {Bt ubu<] Rkts}R B <] s{$%$k } B%$I R s js ABBR B Rkts}${ $t}z P B8 {Bt R qy PB $P <] s{$%$k $R } B}B $Btsj B $t tr$k Y t Y {Bt ubu<] Rkts}${ R ty A {B8 R } B}B $Btsj B $t tr$k sr b jj {B8} trs$t PB Y I T { sr $t {Bt R tr$$%$k b$y $t{ sr$t $t tr$k by t jb{sj szb8s${ s$t {Bt Bj $R $t & { V t Z sj 8${ B{$ {Z$ PB Y BZ $ts Ys $t{jzi R <] szbp IAs{, $R RYBbt $t 3$Z 1s V RkR 8Tj % j stsjkr$r BP szbp IAs{, b$y Y s$i BP Y AjB{, I$s s8 RYBbt $t 3$Z ns % sjr Ys w W \ 7{B 7 Y{ ) wf 1 {' 1 LdDwf 1 Y '1 LdDL\b4 w f 1 Y 7 { ) '1 Ld wf 1 { '1 LdDwf 1 Y '1 LdDL\b4 4 W 7{B 4, by 4 $R Y s tzs$bt P B8 Y {Bt BZ R 8 t w]!d B Y {Bt 8$tsj w]qd sti \ $R Y s8}j$h{s$bt P B8 ]q B Y <] qyzr <] jbb}srrthj R Y ]! R$tsj by$j ]q AstI}sRRThj R $ }u}ƒ!0" g3]+3]3++g" gpu+3" }!x

E bsa ts BsY t CO + - HC 1 2 2 l h ρ +1 HC 1 2 2 l c ρ +1 Response HC CT wsd CT Spatial Frequency wsd 7kR 8TN % j ]Bt{ }U z$rzsj R$tsjR s% j P B8 Y {Bt BZ TR 8 t w]!d B Y {Bt 8$tsj w]qd sti Bt B Y YB $9Btsj { jj w<]d by${y {jbr R Y t s$% P IAs{, jbb} qb sj$9 jb{sj szb8s${ s$t {Bt Bj <] 8BIZjs R Y s tzs$bt P B8 ]! B ]q VtI B, } Y jbb}ts$t {BtRst <] sjrb 8BIZjs R Y R$tsj $ { $% R P B8 ]q $%$t $R B s }BR$$% TP IAs{, jbb} qy$r {B8} trs$bt, }R R}s$sj hj $t $t%s $st by$j <] s{$%$k s{,r Y jb{sj s% s $t tr$k { {B X sti ]q s{$%$k A {B8 R } B}B $Btsj B {Bt sr { {B b{ {B X wad 3 JZ t{k i R}BtR RU BY <] sti ]q s{ sr jbb}srr hj R AZ <] YsR s jbt R}s{ {BtRst w$ f Y kf { D qyzr <] $ty$a$$bt j$8$ts R jbb P JZ t{k R$tsjR RZj$t $t AstI}sRR R}BtR $t ]q qy$r AstI}sRR {Ys T s{ $R${ {B R}BtIR B st $8}ZjR R}BtR w$ { }$% h jid b$y s R8sjj { t sj -{$sb k $Bt sti s js RZ BZtI$t $ty$a$b k $Bt 3$Z n!z i $ts 7}s$sj 3$j $t wad sr RYBbt $t 3$Z na qy R hj R Ys% Y Rs8 {B t P JZ t{k by${y $R $t% R jk } B}B $Btsj B Y {jbr I jbb} R}s{ T{BtRst f \ ) w4b\d db;$ f { f Y by f { sti f Y s Y R}s{ T{BtRstR BP Y {Bt sti YB $9BtsjT{ jj t bb,r qy PB R}s$sj hj $t $R $t%s $st $P b 8s, \ } B}B $Btsj B 4 by${y 8s, R <] s{$%$k s{, Y jb{sj s% s $t tr$k < t{ ]q s{$%$k A {B8 R } B}B $Btsj B {Bt sr $P b R \ ) 4 ) 7 Y{ V tb% j {Z tt8bi ]!7 {$ {Z$ Ys ZR R <] szbp IAs{, B I {BZ}j R}s$B 8}B sj hj $t jb{sj s$t {Bt Bj sti 8}B sj RsT A$j$k $R RYBbt $t 3$Z 1A y $8}j 8 t ]q s tzs$bt Ak 8BIZjs$t Y {BtIZ{st{ R BP ABY Y {Bt :R 8 8A st sti $R s} `Zt{$BtRv Y BZY <] RYZt$t $ty$a$$btvby${y j s% R Y {Bt Tt bb,:r R}s{ {BtRst Zt{Yst I ]Z tr } R t R$tsjR $tr si BP %Bjs R sr Y$R $R s {Z tt8bi {$ {Z$ y ZR Y RZAR{ $}R { sti Y B I tb {Bt sti YB $9BtsjT{ jj s }s$ BP j R I tb R {BZ}j$t A b t { jjr B B BZtI by${y $R I tb I Ak ( VtI y ZR Z}} {sr Rk8ABjR w }u}ƒ!0" g3]+3]3++g" gpu+3" }!E

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr qsaj y W s$% % RZR _BR$$% 3 IAs{, V tzs$bt *s8}$tt3s{b 7}s{ T]BtRst 7 tr$$%$k $ { { { Y 6 h W {+ { { d {+ { {L Y+ { Y < y { {L{ Y b< y U y{ db; Y \ y{ db; Y _BR ( < y U y \ y { { { { $R Y 8 st {Bt s{$%$k { Y $R Y 8 st YB $9Btsj { jj s{$%$k by${y $R } B}B $Btsj B j$y $t tr$k sti 6 e # J q b~ e $R Y s$b A b t Y Y 8sj %Bjs sti Y es jk %Bjs yi sjjk Y s tzs$bt s 8 srz BP jbbtp JZ t{k R$tsjR: js$% s8}j$zi RYBZjI A 9 B Y Is8}$tTPs{B < y ) 0 {( b Y( s 8 srz BP 8}B sj RsA$j$k RYBZjI A j RR Yst Bt Y R}s{ {BtRst U y )w YY {{ D db; s 8 srz BP { }$% h ji R$9 RYBZjI A $ti } ti t BP { Y sti Y R tr$$%$k \ y )wub {{ D{ d s 8 srz BP }YBBR$tsj s8}j$h{s$bt Y RYBZjI A $t% R jk } B}B $Btsj B { Y { Y D B } R t Y 8 st w$ *]D R$tsj %sjz by$j jbb {sr Bt R w 7 Y D } R t R8sjj $trstst BZR I %$s$btr P B8 Y 8 st yt Y {Bt$tZZ8 j$8$ Y BZ $ts {$ {Z$:R R8sjjTR$tsj w$ j$t s D A Ys%$B {st A I R{ $A I $t 8R BP Y {Bt sr R$tsjR # 7 { b{ { sti _ # 7 Y b{ Y sr PBjjBbRU 7 ( _ L {{ n 1 ) {(J x Q { Y { Y Q0 L, L YY n 1 _ ) Y(J x Q_ { Y Q0, by n 1 # ( 1 b(? 1 L ( 1 b(r 1 3 qy sarbjz R$tsj j % jr s $R A {szr Y str$rb R: R8sjjTR$tsj {BtIZ{st{ R sti str{btiz{st{ R Ys 8BI j 8 8A st {BtIZ{st{ R s} `Zt{$BtR sti {Y 8${sj Rkts}R R s j$t s jk } B}B $Btsj B Y *] {Z t j % j $t Y RZAY RYBjI $Bt {{ sti YY s I 8$t I Ak Y js$% R$9 BP Y str$rb R {BZ}j$t Y {Bt tbi R B Y sti Y A$sR %Bjs s}}j$ I B Y str$rb R {BZ}j$t Y YB $9BtsjT{ jj tbi R B Y >d1h J x # >xbr $R Y Y 8sj %Bjs WB${ Ys Y A Ys%$B $R t$ jk j$t s $t Y {Bt sr R$tsjR sti _ s}s P B8 Y $t}z s tzs$bt sti Y $8 T{BtRstR by${y s {Bt Bjj I Ak { Y <Bb % Y $8 T{BtRstR s{, s{y BY 8s,$t $ srk B 8s$ts$t 8}B sj RsA$j$k yt {Bt sr 8k s j$ I R$t >d1 nh by${y j$ I Bt Y$YTs$t t s$% P IAs{, $R I R{ $A I Ak Y JZs$BtRU 7 ( { Y _ L {{ { { { Y n 1 ) {(J x { Y Q Q0 L 6 e L YY { Y { { n 1 _ ) Y(J x { { Q_ Q0 L 6 e_, }u}ƒ!0" g3]+3]3++g" gpu+3" }!

M bsa ts BsY t Bipolar Cell Amacrine Cell V wa I bt+ I bt- V tq V tq V t+ V t- V tq V tq Ganglion Cell I bt V na I na Excitation Inhibition wsd Conduction Modulation I c Vss1 wad Vss1 wsd W Z sj ${ B{$ {Z$U qy 8 {Yst$R8 PB 8BIZjs$t } Rkts}${ $ty$a$$bt s Y A$}Bjs 8$tsj w qd $R tb,tbbtv8k 8BI j srr$tr Y$R Bj B s b$i Th ji s8s{ $t { jj 3ZjjTbs% {$h{s$bt $R sj$9 I Ak {Bt% t{ BP Ct sti CPP }sybskr 3B 8B%$t R$8Zj$ Y s}t`zt{$bt {BZ}j I GVR BAs$t R$tsj t k Ak R}s$sj $t s$bt wad $}Bjs Tq 8$tsj 7ZA{$ {Z$U =tj$, Y t Z sj {$ {Z$ {B8}j 8 ts k R$tsj$t $R tb ZR I PB ]R sti WVR sti 8BIZjs$Bt B{{Z R A PB jbb}srr hj $t qy WV R$tsj { ts $R RZA s{ I P B8 Y Zt {$h I {Bt R$tsj { { B BAs$t Y q R$tsj { A V PBZ T str$rb {$h } BIZ{ R Ct sti CPP q R$tsjR w{ AÈ D VtI s PBZ T str$rb RZA s{b s, R Y I$& t{ A b t { AL sti { A sti RZ}}j$ R $ B Y WV tbi w~ ts Dv~ bs 8BIZjs R Y {Z t j % j $t Y RZA s{b 3$Z ; B }Y$t Y ytt i $ts y by 6 e # J x b~ e $R Y s$b A b t Y Y 8sj %Bjs w1x8z s BB8 8} sz D sti Y es jk %Bjs wk}${sjjk sabz 1xzD yt {B8}s $RBt Y <]ubu{bt Rkts}${ s$t \ {Y # QbQ_ $R s YBZRstI w$ db6 e D $8 R R8sjj $t Y t b {$ {Z$ by$j Y {Bt ubu<] Rkts}${ s$t \ Y{ # Q_bQ $R $tht$ vpb 9 B 8}B sj sti R}s$sj P JZ t{$ R w$ *]DvIZ B d((0 }BR$$% P IAs{, 1 qy$r }BR$$% P IAs{, s st 8 t bsr } %$BZRjk ZR I B sj$9 s PsR {Z tt s8}j$h sti AZ& Rs >;(H 3B tbt9 B P JZ t{$ R Y {Bt ubu<] Rkts}${ s$t $R } B}B $Btsj B { Y wsti Y t{ B j$y $t tr$kd $t Y t b {$ {Z$ IZ B Y 8BIZjsB k & { BP YB $9BtsjT{ jj szbp IT As{, qy $t tr$kti } ti t{$ R BP Y {Ys s{ $R${R BP Y R bb {$ {Z$R s {B8}s I $t qsaj y 1 qy R Rkts}${ s$tr s BAs$t I Ak R $t Y 8}B sj sti R}s$sj I $%st $% R JZsj B 9 B sti I$& t$s$t Y h R sti R {BtI JZs$Bt R} {$% jk }u}ƒ!0" g3]+3]3++g" gpu+3" }!L

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr n ytt i $ts BI j qy $tt $ts } PB 8R jbb}srr sti Y$Y}sRR 8}B sj hj $t sti sis}r $R Ikts8${R jb{sjjk $I sti }s srbj stj$bt { jjr { $% Rkts}${ $t}zr P B8 ABY A$}Bjs sti s8s{ $t { jjr AZ }s srbj { jjr { $% 8B s8s{ $t $t}z w$ P IPB bs I $ty$a$$btd >1d dn 1EH by${y s{{bztr PB Y $ 8B str$ t R}BtR _s srbjr sjrb Ys% js I ti $${ h jir sti s I $% t Ak A$}Bjs { jjr b$y js I tt I $${ sti s-btsj h jir Yst YBR Ys I $% Y 8$I R >n; nxh by${y s{{bztr PB Y $ js { }$% h jir _ RZ8sAjk ABY 8$I sti }s srbj A$}Bjs { jjr { $% } Rkts}${ s8s{ $t $t}z w$ P IAs{, $ty$a$$btd s Y $ 8$tsjR y Yk}BY R$9 Ys s {Yst $t {jbr ITjBB} s$t } BIZ{ R 8}B sj sis}s$bt sti Ys Y$R s$t $R {Bt Bjj I Ak 8BIZjs$t Y R ty BP P IAs{, $ty$a$$bt 3$Z ;s $jjzr s R Y$R $tsj 8 {Yst$R8 PB sis}$t 8}B sj Ikts8${R V b$i Th ji s8s{ $t { jj wgvd 8BIT Zjs R Y R ty BP P IAs{, w$ } Rkts}${D $ty$a$$bt s Y A$}Bjs 8$tsjR w qd GV $R -{$ I Ak Ct sti CPP A$}Bjs R sti $ty$a$ I Ak Ct sti CPP ts BbTh ji s8s{ $t { jjr wwvd Vjj Y R Rkts}${ $t s{$btr Ys% A t PBZtI $t st stsb8${sjjk $I t$h I s8s{ $t { jj k} {sjj I Vd >1xH qy R { jjr Ys% Y${, I ti $ R s js s-bi ti $${ h ji sti s {BZ}j I B Y Ak s} `Zt{$BtR < t{ Y k {st $t s sti I$R $AZ R$tsjR s}$ijk B% s js s s k $tt T $ts {$ {Z$ 8BI j by${y bsr 8B$%s I Ak 8}B sj sis}s$bt sjrb s{{bztr PB {Bt srts$t {Bt Bj $t Y $ts qy {jsrr${ RZj $R Ys stj$bt { jj R}BtR R {B8} RR $t s8}j$zi sti $8 by t Y k s I $% t b$y js sti js R } {Yst R $t $t tt R$k >ne nh z${b sti 7Ys}j k s{{bzt I PB ABY BP Y R tbtj$t s & {R Ak 8BI j$t Y $tt $ts b$y s Y$Y}sRR 8}B sj hj bybr $8 T{BtRst I { sr R b$y {Bt sr >;dh V Y PZt{$Btsj j % j Y 8BI j y } B}BR Y $R RR t$sjjk $I t${sj B Y $ R k {Bt $AZ$Bt $R B 4 RY BZ Y t Z sj 8 {Yst$R8R Ak by${y {Bt sr $R 8 srz I sti Y $8 T{BtRst $R si`zr I yt Y } B{ RR y srr$t R} {$h{ Bj R B stsb8${sjjk $I t$h I $tsj { jjr sti Y $ Rkts}${ {Btt {$BtR V RkR 8Tj % j stsjkr$r BP jbb}ts$t 8BIZjs$Bt b$y Y s$i BP Y AjB{, I$s s8 RYBbt $t 3$Z xs sti Y Ns}js{ strpb 8 % sjr Ys 7 ts ) 6 + \ X Ld 7 A{, 7 A ) + \X L 6 + \ X Ld 7 A{, 7 { ) + \X + \ X Ld 7 A{ wdd }u}ƒ!0" g3]+3]3++g" gpu+3" }!

d( bsa ts BsY t BC BT + - + - + - WA 1 τ na s+1 NA GC Excited Inhbited NFA BT WFA Temporal Frequency wsd wad wsd 7kR 8TN % j ]Bt{ }U z$rzsj R$tsjR s jsk I P B8 {Bt 8$tsj B stt j$bt { jj wp]d Ak Y A$}Bjs { jj w ]D qy k s sjrb P I B s ts BbTh ji s8s{ $t { jj wwvd by${y PB 8R ABY t s$% TP IAs{, sti t s$% TP IPB bs I jbb}r 3 IAs{, R ty $R 8BIZjs I Ak s b$i Th ji s8s{ $t { jj wgvd Ys {B8}Z R Y I$& t{ A b t PZjjTbs% {$h I wibzaj s BbRD q sti WV R$tsjR wad 3 JZ t{k i R}BtR RU WV $ty$a$$bt j$8$ts R jbb P JZ t{$ R T RZj$t $t s Y$Y}sRR R}BtR $t q Ys YsR Y Rs8 {B t P JZ t{k sr Y jbb}srr WV R}BtR 3B P JZ t{$ R sab% Y$R {B t P JZ t{k q -{$s$bt IB8$ts R sti Y t{ GV s{$%$k $R R sti $ ABBRR WV $ty$a$$bt 3B P JZ tt {$ R A jbb Y {B t P JZ t{k Bt Y BY YstI WV $ty$a$$bt IB8$ts R sti Y t{ GV s{$%$k PsjjR sti $ Y Bj R WV $ty$a$$bt 3$Z x ytt i $ts q 8}B sj 3$j $t PB WV q sti Y }s srbj stj$bt { jj wp]d R} {$% jk by + \ # 6+ ts,6# dbwd L { bs b{ bs( D3 w1d + ts $R Y $8 T{BtRst BP WV sti { bs b{ bs( $R Y 8BIZjs$Bt BP $R R}BtR Ak GV bybr R}BtR $R { bs( PB 9 B P JZ t{k w$ Rs${ $t}zd qyzr WV jbb}srrthj R Y ] R$tsj by$j q Y$Y}sRRT hj R $vy R hj R Ys% Y Rs8 {B t P JZ t{k by${y $R $t% R jk } B}B $Btsj B Y {jbr I jbb} $8 T{BtRst + \ qy BZY Y I } tt I t{ BP + \ Bt Y 8BIZjs$Bt j % j Y {B t P JZ t{k A {B8 R } B}B $Btsj B GV s{$%$k sr RYBbt $t 3$Z xa 3 IPB bs I $ty$a$$bt } BIZ{ R s }Z jk str$ t R}BtR $t }s st RBj { jjr by sr 8$I R by${y IB tb { $% P IPB bs I $ty$a$$bt Ys% s RZRs$t I {B8}Bt t qy$r R$IZsj s{$%$k 67 A $t{ sr R sr Y jbb} s$t $R IZ{ I B jbb Y {B t P JZ t{kvsti YZR Y q R}BtR srk8}b${sjjk s}} Bs{Y R st sjj}srr hj <Bb % WV:R R$IZsj BbR $t Y Rs8 bsk sti {st{ jr BZ q:r R$IZsj $t Y }s srbj stj$bt { jj $ R} {$% BP Y s$t R $t qyzr s }Z jk Y$Y}sRR R}BtR $R s{y$ % IvY$R $R $8}BRR$Aj b$y s ht$ Ts$t t s$% P IAs{, jbb} }u}ƒ!0" g3]+3]3++g" gpu+3" }!g+

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr dd qy b$i Th ji s8s{ $t { jj { t R Y {B t P JZ t{$ R BP Y Y$Y}sRR sti jbb}srr hj R Bt Y $t}z R} { Z8 G$Y qubugv sti WVuBuGV Rkts}R R BP JZsj R ty GV:R s{$%$k $R $% t Ak bb n 1 7 bs L ^7 A ^ { bs ^7 ts ^ ) ( wnd { bs( by bb $R Y {BZ}j$t R ty A b t GVRvtB 8sj$9 I Ak Y Rkts}${ R tyvsti ^7^ $R Y PZjjTbs% u {$h I % R$Bt BP 7yYs% t j { I GV:R j s,s {BtIZ{st{ WB${ Ys GV 8BIZjs R Y $ty$a$$bt $ { $% R P B8 WV PB 8$t st szbp IAs{, jbb} stsjbbzr B Ys PBZtI $t <]R 3B jbb R}s$sj P JZ t{$ R w$ Bt s% s D Y Ns}js{$st $R {jbr B 9 B sti b Ys% { bs ^7 A ^X { bs( ^7 ts ^X ) /7 A/ /7 ts / ) 0 + ts 1 1 Ld, by 7X $R Y jb{sj R}s$sj s% s BP 7 WB${ Ys { bs ) { bs( by t ) ( Y t{ Y jbb}ts$t $R Zt$k s *] sti 7 A ) 7 ts ) 7 A{ b13 7ZAR$Z$t Y$R -} RR$Bt $tb ejzs$bt 1 k$ jiru + \ ) + ts dl 0 + 1 ts 1 Ld F +ts b1 U db+ ts db ( db+ ts 3 < t{ Y {B t P JZ t{k db+ \ s{,r Y $t}z P JZ t{k $P $ $R Y$Y Yst WV:R $t $tr${ {ZTB& P JZ t{k db+ ts 7Z{Y 8}B sj sis}s$bt {BZjI s{{bzt PB Y %s $s$bt BP stt j$bt { jjr: 8}B sj Ikts8${R b$y {{ t ${$k W Z BA$BjB$RR Ys% BAR % I Ys ABY 8$I R sti }s srbjr A {B8 8B str$ t b$y $t{ sr$t {{ t ${$k sti Y 8$I :R RZRs$t I {B8}Bt t I { sr R >;n d;h p$% t Ys Y $t}z R} { Z8 RY$PR B Y$Y 8}B sj P T JZ t{$ R b$y $t{ sr$t {{ t ${$k >dmh Y$R %s $s$bt $t 8}B sj {Ys s{ $R${R b$y {{ t ${$k {st A } BIZ{ I Ak s 8}B sj sis}t s$bt 8 {Yst$R8 j$, Y Bt } B}BR I Y q 8}B sj sis}s$bt $t 8k $tt T $ts {$ {Z$ 8BI j sjrb RZjR $t s8}j$zi {B8} RR$Bt B RBT{sjj I {Bt srts$t {Bt Bj qy$r {B8T } RR$Bt $R %$I t $P b strpb 8 Y RTIB8s$t JZs$BtR PB 7 A sti 7 ts wejzs$bt dd $tb Y $8 TIB8s$tU + ts dlj + ts dlj Q7 A Q0 L 7 A ) + ts dlj Q7 ts L 7 ts ) 7 A{ Q0 dlj Q7 A{ Q0 L 7 A{ dlj, by j # { bs b{ bs( 3B s Zt$PB 8 $t tr$k B% s js s s b$y 7 A{ ) { ( 7 ts ) 7 A ) { ( b1sti{ bs ) { bs( y88 I$s jk sp Y $t tt R$k $R R }} I B { d b Ys% 7 ts ) { ( b1sti7 A ) { d { ( b1 7ZAR$Z$t w;d wxd }u}ƒ!0" g3]+3]3++g" gpu+3" }!gg

d1 bsa ts BsY t I na- I na+ I na V sq V n- V n+ I cq Vss1 Vss1 V cq I na- Ina+ V wa I bt+ I bt- Vaa V sq Vss1 wsd V t+ V t- V n- V n+ wsd Ws BbT3$ ji V8s{ $t 7ZA{$ {Z$U V P t{ {Z t { {J by${y 8s{Y R Y {Bt {Z t:r 8 st j % j $R RZA s{ I P B8 s {B}k BP { ts } BIZ{ I Ak Y A$}Bjs T 8$tsj w qd {$ {Z$ wrybbt $t 3$Z ;AD sti Y I$& t{ $R {$h I B BAs$t Ct sti CPP ts BbTh ji s8s{ $t wwvd R$tsjR w{ tsè D wad G$I T 3$ ji V8s{ $t 7ZA{$ {Z$U ]B}$ R BP Y Ct sti CPP qw{ AÈ D sti WV w{ tsè D R$tsjR BAs$t I P B8 Y q sti WV {$ {Z$R Ak {Btt {$t s R {BtI str$rb $t }s sjj j s RZt, P B8 B 8$ B I BtB Y GV tbi w~ bs D B -{$ B $ty$a$ $ R} {$% jk W $YAB $t GV tbi R s {Btt { I B Y Ak str$rb R B 8BI j Y $ s} `Zt{$BtR 3$Z E B }Y$t Y ytt i $ts yy Y R %sjz R $t ejzs$bt n k$ jir { bs b{ bs( )w{ d { ( b1dbw{ ( b1d by${y JZsjR 1Ld by # w{ d { ( Db{ ( $R Y {Bt sr y Ys% srrz8 I Ys Y BZ T $ts:r 8}B sj hj $t $R $tht$ jk PsR sti $R $t tr$k sis}s$bt $R $tht$ jk RjBb PB R$8}j${$k i }js{$t 7 A{ b$y wdld{ ( $R I $%s$% b$y { ( &w0d sti j b$y 1 L d $t Y JZs$Bt PB 7 A sab% k$ jir d + ts 1 dl Q7 A Q0 L 7 A ) { w ( dl 1 wad + W ts dl &w0d 3 y $R %$I t P B8 Y$R RZj Ys Y $8 T{BtRst RYB tr sti Y I $%$t PB { {B8} RR R sr {Bt sr $t{ sr R yt 8k 8BI j Y$R & { B{{Z R s Y A$}Bjs 8$tsj by${y }srr R $ Bt B ABY RZRs$t I w8$i T B Tj$, D sti str$ t w}s srbjt B OTj$, D stj$bt { jjr z${b sti 7Ys }j k I$I BAR % {Bt srts$t {Bt Bj $t ABY sti O stj$bt { jjr $t Y $ -} $8 tr b$y {sr >nh V {Z tt8bi ]!7 {$ {Z$ y I R$t I B $8}j 8 t $tt $ts 8}B sj sis}s$bt $R RYBbt $t 3$Z ;A y IB R tb $t{jzi P IPB T }u}ƒ!0" g3]+3]3++g" gpu+3" }!g3

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr dn Photoreceptors 142λ = 85.2µm C H WA Convergence Phototransistor Neuron Outer Retina 153λ = 91.8µm Bipolar Cells 1/4 Inner Retina Divergence Current- Mirror Integrator NA Ganglion Cells wsd wad wsd y8s V sk V {Y$ {Z U $}Bjs { jjr by${y {Btt { }YBB { }B R B ; stj$bt { jjr wbt BP s{y k} D RZARs8}j Y $8s Ak s Ps{B BP ; V { }B $Y RZ}}j$ R $R bb $I t${sj BZ}Z {Z tr B Bt A$}Bjs { jj B B bb t $YAB $t { jjr 7s $t b$y st ] ] { }B s sk b ti Z} b$y ; ]b1 ]b1 stj$btt{ jj s skr wad _$- j NskBZU qy }$- j YsR n!7 str$rb RU M $t Y BZ $ts E $t Y $tt $ts sti de $t Y t Z Btv}jZR str$rb R $t Y I jstr Z{Z R wb$y s {B88Bt qtrys} I s D Ys {Btt { { }B w]d YB $9BtsjT{ jj w<d sti b$i Th jits8s{ $t { jj wgvd tbi R B Y $ R$- t s R t $YAB R =tj$, Y R{Y 8s${ $t 3$Z 1A Y }YBB str$rb :R {Z t $R 8$ B I h R qy $tt T $ts {$ {Z$ $R R} si s{ BRR PBZ }$- jr b$y E str$rb R $t bb BP Y 8 sti x $t Y BY bb PB s Bsj BP 11 qy RZA{$ {Z$ RYBbt Y } BIZ{ R Y BtTRZRs$t I BZ}Z w$ { tsl $t 3$Z EsD yt bb BP Y }$- jr s }BjkdT}Bjk1 {s}s{$b vss{y I B Y ts BbTh ji s8s{ $t tbi wwvdv }js{ R Y b jjt str$rb sab% Y {Z tt8$ B $t sb _$- jr s $j I Y -sbtsjjk Ak 4$}}$t YBR $t % k BY {BjZ8t % ${sjjk 3$Z z$r$bd ]Y$} * R$t bs I WV $ty$a$$bt BtB str$ t p]r W % Y j RR j$, Y $ts $ } BIZ{ R s Y$Y}sRR R}BtR Ak }js{$t s jbb}srr hj $t s t s$% P IAs{, jbb} qyzr {B t P JZ t{$ R BP Y Y$Y}sRR sti jbb}srr R}BtR R s szb8s${sjjk 8s{Y I qb {B8}s Y t $ R BP Y Y$Y}sRRT sti jbb}srrthj I R$tsjR $ PZjjTbs% {$h R Y 8 s, R }u}ƒ!0" g3]+3]3++g" gpu+3" }!gp

d; bsa ts BsY t Y I$& t{ sti $t s R $ B% R}s{ ZR$t sii$$btsj {$ {Z$ k RYBbt $t 3$Z E yt {Bt sr s R$8$js $8 T{BtRst sis}s$bt R{Y 8 } B}BR I Ak N$Z ZR R R }s s Y$Y}sRR sti jbb}srr hj R $t s R Y I$& T t{ A b t Y $ } s, R}BtR R B% $8 sti si`zrr Y $ $8 T {BtRstR I$ {jk Ak {Yst$t Y s8}j$h R: A$sR {Z tr >1H qy$r R{Y 8 v$8}j 8 t I b$y s %Bjs T8BI {$ {Z$v JZ$ R Y s8}j$t h R: str{btiz{st{ R B A 8s{Y I sti sis}r B% R % sj {k{j R 7$t{ Y I 8B% R Bt sp s R$tj R}BtR {k{j $ $R $8} st $% Ys sis}s$bt B{{Z $trstst BZRjk sti Y$R $tpb 8s$Bt } B}T ss JZ${,jk B t $YAB $t { jjr BY BA` {$% R s s{y$ % I Ak 8k $tb8b }Y${ {$ {Z$ k $tt T $ts {$ {Z$ 8BI j {B8}Z R R$tsj t k s}$ijk Ak ZR$t R}s$sj $t s$bt R$t{ PB s 8B%$t R$8ZjZR sjj }YsR R BP Y R}BtR s s%s$jsaj s I$& t jb{s$btr s Y Rs8 $trst VtI $ ZR R Y Rs8 s% s$t t bb, B I$R $AZ Y RZjR JZ${,jk qy$r {Bjj {$% {B8}Zs$Bt sjrb 8s, R Y $tb8b }Y${ s}} Bs{Y 8B BAZR {B8}s I B } s,ti {$Bt =tpb Zts jk $R ]!7 $8}j 8 ts$bt $t z$r$bd YsR s jbbtp JZ t{k 8}B sj $trsa$j$kv B Y b$y BY RYB {B8$tRvYs bsr I$R{B% I IZ $t R$t ; ]Y$} * R$t sti q R$t y I R$t I sti PsA ${s I s ; x1 ;M stj$btt{ jj {Y$} {sjj I z$r$bd $t s d1 8 w ) (3E 8D IBZAj }Bjk IBZAj 8 sj ttb jj ]!7 } B{ RR $R I$ R$9 $R 31x 3E88 1 z$r$bd:r s {Y$ {Z sti }$- j jskbz s I R{ $A I $t 3$Z es{y }$- j $t{jzi R st sis}$% R$j${Bt t Z Bt Ys t s R R}$, R >H by${y s si BZ Ak st srkt{y BtBZR sii RRT % t str8$ $t Ps{ >ddh pstj$btt{ jj k} $R I T 8$t I Ak I {BI$t Y N7 :R BP Bb sti {BjZ8t sii RR R z$r$bd bsr ZR I $t s sjt$8 8B$Bt } B{ RR$t s}}j${s$bt sr I R{ $A I $t 7 {$Bt x yt sii$$bt B YB $9BtsjT{ jj szbp IAs{, $t Y BZ $ts sti s8s{ $t T{ jj jbb}ts$t 8BIZjs$Bt $t Y $tt $ts z$r$bd 8BI jr {Bt ubua$}bjs {Bt% t{ by${y 8s, R Y { }$% Th ji { t 8B pszrr$sttj$, >nmh V{{B I$t B 8k R$8Zjs$BtR Y R } P T JZ t{k BjjTB& Ys RZjR } BIZ{ R E(I s tzs$bt s nx $8 R Y } s, R}s$sj P JZ t{kv{b8}s I B n1 $8 R Y } s, b$ybz {Bt% t{ <$Y R}s$sj P JZ t{$ R 8ZR A j$8$ts I B } R % Y R$tsjuButB$R s$b sp Y$Y}sRR 8}B sj hj $t sr Y R {B8T }Bt tr } BIZ{ } B}B $Bts jk Y$Y 8}B sj P JZ t{$ R by t Y R$8ZjZR 8B% R 3Z Y R$tsjuButB$R tyst{ 8 t 8sk A sj$9 I }u}ƒ!0" g3]+3]3++g" gpu+3" }!g<

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr dx wsd wsd N$Y R}B Rs$Bts k wjb{s I by Y R$tj s{$% yt{ sr't { jj $RDU $t { jjr }${, Z} Y $t{ sr I R$tsj s Y R}B:R jb{s$bt by$j $PP { jjr }${, Z} Y I { sr I R$tsj $t RZ BZtI$t $Bt IZ B js sj $ty$a$$bt 3$- IT}s t tb$r IZ B str$rb 8$R8s{Y $R sjrb %$I t wad N$Y R}B 8B%$t Z} sti B Y $YU yt{ sr't { jjr }${, Z} Y $t{ sr R s Y -{$sb k { t :R j si$t I sti s Y $ty$a$b k RZ BZtI:R s$j$t I by$j - { sr't { jjr }${, Z} Y I { sr R s Y $ty$a$b k RZ BZtI:R j si$t I sti -{$sb k { t :R s$j$t I qy 8 st R}$, s bsr x R}$, R\t Z Bt\R { 3$Z M i R}BtR BP i $tb8b }Y${ ]Y$} B N$Y 7}B wad Ak {Bt% t{ s Y stj$btt{ jj j % j by${y y s8 k B $t{jzi v$ bbzji sjrb } BIZ{ Y }s srbj { jjr: js { }$% h jir z$r$bd IB R tb $t{jzi Rkts}${ $t s{$btr s Y stj$btt{ jj j % j Y R b$jj A sii I $t Y t - % R$Bt =tj$, $t 3$Z ds $R Ct sti CPP stj$bt { jjr s I $% t Ak ts BbTh ji s8s{ $t wwvd R$tsjR w{ tsè $t 3$Z EsD by$j $R yt{ sr't sti - { sr't stj$bt { jjr s I $% t Ak A$}Bjs T 8$tsj w qd R$tsjR w{ AÈ $t 3$T Z ;AD * $%$t sjj PBZ stj$bt { jj k} R b$y q R$tsjR sti sii$t P IPB bs I WV $ty$a$$bt BtB Y str$ t { jjr j$, Y $ts IB R b$jj 8s, Y $ R}BtR R 8B str$ t qyzr Y R stj$btt{ jj j % j Rkts}${ $t s{$btr RZj $t s 8B ^{$ t t{bi$t sr Y k 8B% IZtIst jbbtp JZ t{k R$tsjR z$r$bd:r j$ytr}b R}BtR R s RYBbt $t 3$Z M Y R 8 srz T 8 tr I 8BtR s Y & {R BP YB $9BtsjT{ jj w<]d sti s8s{ $t T{ jj $ty$a$$bt <]R $ty$a$ t $YAB $t R}s$sj jb{s$btr $%$t $R B Y $ty$a$b k RZ BZtI by${y $R %$I t $t Y $PP R}BtR GY$j WVR $ty$a$ PB{sjjk AZ b$y s I jsk 8$ts$t Y R}BtR $t Y yt{ sr't sti - { sr't { jjr <Bb % Y R}B R{s} R Y$R 8}B sj js sj $ty$a$$bt by t $ 8B% R $%$t $R B yt{ srt }u}ƒ!0" g3]+3]3++g" gpu+3" }!gx

de bsa ts BsY t Motion Speed, ν Speed, ν Spike Raster All cells in Column 25 Spatial Bandpass λ Space λ Space Temporal Highpass & Lowpass λ/4 Space λ/4 Space Spike Histogram 20ms bins Time Halfwave Rectification Space wsd Space 0.3s Time OFF-Sus (--) ON-Sus (++) ON-Trans (-+) OFF-Trans (+-) wsd e-} { I i R}BtR RU sti}srr R}s$sj hj $t }srr R s }s ${Zjs bs% j ty sti ` {R Y BY R <$Y}sRR sti jbb}srr 8}B sj hj $t strjs R Y R}BtR $t R}s{ Ak b; <sjptbs% {$h{s$bt } BIZ{ R s R JZ t{ BP PBZ R}BtR R Ys } s, b; s}s {B$t{$I$t b$y Y yt{ sr't wk jjbbd Ct w td I { sr't wajz D sti CPP w ID }s R BP Y {k{j i % R$t Y I$ {$Bt % R R Y 8}B sj {Bt sr $t {Yst$t Y k jjbb sti AjZ T R}BtR R wad!ar % I i R}BtR RU 7}$, s$tr } BIZ{ I $t R}BtR B % ${sj As R 8B%$t s d1 H \R w JZsjR n1 }$- jr\rd b {B I I P B8 ; ;x t Z BtR $t Y Rs8 {BjZ8t *Z $t Y$R 1ExR {B I$t s{y t Z Bt h I dn R}$, R Bt s% s qy Y$RB s8 by${y {B8A$t R sjj Y R}$, s$tr P B8 Y$R R$tj T $sj 8Zj$}j Tt Z Bt {B I$t {Bth 8R Ys Y PBZ stj$bt { jj k} R } B%$I s JZsI sz } R ts$bt 3$Z 7}$, isr R sti <$RB s8r PB B%$t ei R wad 't sti - { sr't R}BtR R s Y j si$t sti s$j$t I R BP Y -{$sb k { t sti Y $ty$a$b k RZ BZtI qy $R {BtR$I T saj %s $sa$j$kv R} {$sjjk s8bt Y RZRs$t I { jjrviz B str$rt B 8$R8s{Y by${y bsr RkR 8s${ } BIZ{$t R $s$btr B $ t I s sabz n( I R P B8 % ${sj j$, YBR I R{ $A I $t >nnh V sr }jb BP R}$, s$tr {B I I P B8 t Z BtR $t s R$tj {BjZ8t $R RYBbt $t 3$Z A =tpb Zts jk { BRRsj, ti I B 8s, sjj Y t Z BtR h by t s { s$t s{$%$k j % j bsr -{ I I RB y YsI B, } Y $ 8 st h $t s R A jbb d(<9vr % sj $8 j RR Yst $t Y sj $ts W % Y j RR Y R JZ t{ $t by${y Y PBZ k} R h $R sr } I${ I $t 3$Z s q str$ t { jjr s 8B Rkt{Y Bt$9 I }u}ƒ!0" g3]+3]3++g" gpu+3" }!ge

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr d Yst RZRs$t I Bt R $ti${s$t Ys Y $ $t}zr s js v 8}B sj sis}s$bt IB R tb s}} s B A bb,$t sr -} { I VjRB Y R {BtI YsjP BP Y R}BtR R JZ t{ $R I jsk Iv$tI${s$t $Y s P s{b k } $BI wztj$, jkd B AjZ $t $t Y BZ $ts by${y B{{Z R by t $R 8}B sj AstIb$IY $R -{ I I y -} { I B ZR Y %s $saj {Z tts$t A b t Y {$h sti Y RZA s{b $t 8k $tt $ts {$ {Z$ wr 3$Z ;AD B 8BIZjs Y jbb}ts$t AZ Ys } B% I PZ$j qy {Z tr $t Y RZA s{b s \ bs { AÈ b$y\ bs # w~}tl~j~bsdbj x by ~ }t s{{bztr PB Zt JZsj }3eq sti t3eq {Z tr by t ~ J ) ~ bs IZ B I$& t{ R $t ABIkT & { sti 9 BTA$sR {Z tr }$t $t 8$tI Ys Y I s$t {BtIZ{st{ / I BP Y RZA s{b :R BZ}Z str$rb R $R } B}B $Btsj B Y $ {Z t j % jr b hti Ys Y %Bjs {Yst 8 ts } BIZ{ I s tbi ~ ts PB s $% t {Z t I$& t{ 7 A # { AL { A $RU 8 ts ) \ bs7 A / I ) \ bs 7 A \ bs w{ AL L { A Db~ e ) 7 A { AL L { A ~ e 3 y $R $ti } ti t BP Y {Z tts$t \ bs 7Z } $R$tjk %s k$t ~ bs IB R tb I$ {jk $t4z t{ Y js$btry$} A b t Y ts BbTh ji s8s{ $t sti A$}Bjs 8$tsj R$tsjR $t 8k {$ {Z$ ytps{ 7 ts ) / 8 8 ts ) ~ e J x { ts { AL L { A 7 A, by / 8 ) y ts bj q $R Y P IAs{, I %${ :R str{btiz{st{ < t{ B 8BIZjs Y jbb} s$t b 8ZR {Yst $Y { ts B { AÈ # { AL L { A { ts Y ts BbTh ji s8{ $t {Z t:r 8 st j % j $R R Ak { {J Y 8 st {Bt {Z t j % j by${y $R {BtRst wr Ak ~ {J $t 3$Z 1D <Bb % b {st $t{ sr Y 8 st A$}Bjs 8$tsj R$tsj j % jr { AÈ Ak $t{ sr$t ~ bs sti Y Ak IZ{ Y jbb}ts$t qy$r I T } ti t{ s $R R A {szr Y {$h :R A Ys%$B $R I R{ $A I Ak Y PBjjBb$t {$ {Z$ JZs$BtR >xhu { AL { A ) { 1 AJ { AL { A ) { { { ts, by { AJ ) { ( ~bsb1j x 3{ AÈ b$jj Ys% B A R % sj YZtI I $8 R js Yst { ts B s{y$ % s jbb}ts$t BP Zt$k IZ B Y js s$b A b t Y RZAY RYBjI!7 str$rb :R str{btiz{st{ sti $R I s$t {BtIZ{st{ w$ ~ o bj x D Z BP {BZ R Y 8 st {Z tr Y 8R j% R sjrb {Bt $AZ B b$i Th ji s8s{ $t -{$s$bt < t{ }u}ƒ!0" g3]+3]3++g" gpu+3" }!g

dm bsa ts BsY t Response (mv) 450 400 350 300 Response (mv) 450 400 350 300 250 0.5 1 1.5 2 2.5 Speed (rps) Speed 0.5 1 1.5 2 2.5 (rps) 160 Photoreceptors Response (mv) vs 300 Orientation 200 100 40 Ganglion Cells 1 DS Cell -200-100 100 200 300 i $tsj B} s$btrvasti}srr R}s$sj hj $t sti Y$Y}sRR 8}B sj hj $tv {B8}Z Y si$ t $t R}s{ $8 srrz8$t Y AstI}sRR }srr R Btjk Y bs% j ty sti Y jbb}srr 8}B sj hj {B8} trs R PB Y Y$Y}sRR: RsT Z s$bt sab% db+ wz}} Tj P }st jd qy s8}j$zi BP Y si$ t:r } B` {$Bt BtB Y % {B w, +D $R BAs$t I Ak RZ88$t R$tsjR P B8 PBZ k} R BP stj$bt { jjr b; s}s vbb }js{ R sbsk $t BZ {sr wjbb Tj PD qy R R}s$sj JZsI sz }YsR TRY$PR 8s{Y Y stj$bt { jjr: 8}B sj JZsI sz }YsR TRY$PR by t s Ajs{,ubY$ I 8B% R $t Y I$ {$Bt RYBbt sti Y t{ sjj PBZ R}BtR R } s, R$8Zjst BZRjk srz 8 tr % sj s {j s } P t{ PB {Bt sr }Bjs $k sti 8B$Bt I$ {$Bt $t s s { jj b$y Y$R { }$% h ji PB R} IR P B8 ; B ;( H \Rv JZ$%sj t B d( B d( }$- jr\r wz}} $YD V Y A R R} I $R I$ {$BtTZt$t $R A BsI sti { t I s BZtI E( H wjbb $YD 3$Z d( *$ {$BtT7 j {$% W Z BtR -100-200 }u}ƒ!0" g3]+3]3++g" gpu+3" }!gl

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr d Y s$b { ts bw{ AL L { A D 8ZR 8s$t {jbr B Zt$k by${y 8 str Ys Y s$t RskR js qy b$i Th ji s8s{ $t t bb, {sttb s{y JZ$j$A $Z8 s *] $P Y jbb}ts$t $R Y$Y A {szr Y A$}Bjs T 8$tsj R$tsj $R s tzs I Ak Y jbb} s$t V{{B I$t B Y Y B k 7 A ) 7 ts ) 7 A{ bwd L jd s *] by j $R Y 8BIZjs$Bt Z Y b$i Th ji s8s{ $t $R -{$ I Ak 7 A sti $ty$a$ I Ak j7 ts < t{ s *] -{$s$bt sti $ty$a$$bt s Asjst{ I by t j )dgy tj $R js GV $R $ty$a$ I by t % Y {Bt {Z t I %$s R R$t$h{stjk P B8 Y 8 st R$t{ /7 ts //{ { { {J / sti /7 AL /( VtI Y t{ ~ bs $t{ sr R IZ{$t {Z t j % jr $t Y RZA s{b by${y % tzsjjk I B} A jbb Y j s,s {Z tr NBbTP JZ t{k BR{$jjs$BtR s $R by t Y RZA s{b :R {Z t s B% by j8 I Ak j s,s {Z tr VRRZ8$t j s,s P B8 ~ II B ~ ts IB8$ts R $ {Ys R Y {s}s{$b IZ{$t { ts yp{ ts ) { { k{ {J $t$$sjjk $ty$a$$bt I { sr R by$j -{$s$bt $t{ sr R ]BtR JZ tjk ~ bs % tzsjjk }Bjs $9 R RB $t {Z t j % jr $t Y RZA s{b by${y I$R{Ys R ~ bs sti $t$$s R stby {k{j ejr $P { ts ) { { c{ {J ABY -{$s$bt sti $ty$a$$bt $t{ sr AZ $ty$a$$bt 8s$tR IB8$T tst < t{ ~ bs t % }Bjs $9 R VRRZ8$t j s,s B BZtI IB8T $ts R Bt Y BY YstI ~ bs R$jj $Y BR{$jjs R B $R } 8st tjk $ty$a$ Iv$ $R `ZR Ys Y $t JZsj$$ R PB { { s % R I 3B tbtrs${ $8s R b bbzji -} { Y $trsa$j$k B I$Rs}} s v $ I$I tb RYBb Z} $t R$8Zjs$BtR qy$r bsr $ti I Y {sr qb I T 8$t YBb Y jbb}ts$t sti Y $8 T{BtRst {Yst j ZR Rs b$y Y ]N JZs$Bt PB tbi ~ ts U g Q8 ts L / I 8 ts ) \ bs 7 A 3 Q0 7ZAR$Z$t 8 ts ) 7 ts b/ 8 sti / 8 ) { ts bj q $% R gj x Q{ ts L \ bsw{ AL L { A D J x 7 ts ) \ bs 7 A 3 { ts Q0 { ts ~ e VR Y {$h trz R Ys 7 A ) 7 { 7 ts b BAs$t Y PBjjBb$t I$& t$sj JZs$BtR PB 7 ts sti 7 A U + ts Q7 ts LwdL6D7 ts ) 7 {, \ bs Q0 + ts Q7 A \ bs Q0 L 7 A ) + ts Q7 { \ bs Q0 L 67 {, by + ts # gj x b{ ts sti 6 # wj x b~ e Dww{ AL L { A Db{ ts D U d qy I$& t$sj JZs$Bt PB 7 A bsr BAs$t I Ak RZAR$Z$t 7 ts ) 7 { 7 A $tb Y 7 ts JZs$Bt }u}ƒ!0" g3]+3]3++g" gpu+3" }!g

1( bsa ts BsY t qy R {$ {Z$ JZs$BtR I$& P B8 Y 8BI j JZs$BtR wejzs$btr ; sti xdv Y {$ {Z$:R {Bt {Z t 7 { by${y $R Y stsjb BP Y 8BI j:r A$}BT js { jj {Z t 7 A{ $R tb 8BIZjs I!tjk Y $8 T{BtRstR s 8BIZjs IvIZ B Y {Yst$t I s$tt{btiz{st{ v8z{y sr $t N$Z:R s}} Bs{Y >1H 7 $t \ bs ) + ts JZsj$9 R Y I $%$t PB { R PB Y R bb JZs$BtR by t Y 8}B sj P JZ t{k $R 8s,$t Y s8}j$zi R BP 7 A sti 7 ts Y Rs8 x * {$t B$Bt *$ {$Bt qy PBZ stj$btt{ jj k} R R}BtI B s 8B%$t I $t R Bk} I R JZ t{ R by${y 8s, $ }BRR$Aj B I$R$tZ$RY I R BP Bt {Bt sr B Y BY 8B%$t $t Bt I$ {$Bt B Y BY Vt -s8}j $R RYBbt $t 3$Z vrbs}}$t I sti t B k jjbb sti AjZ } BIZ{ R Y BY Y R JZ t{ R =R$t z$r$bd sr s P Bt ti I$ {$BtTR j {$% w*7d { jjr {st A AZ$j R$8}jk Ak b$ $t Z} Y R PBZ I$R$t{ { }T $% h jir ZR$t %$ Zsj {Btt {$BtR >d(h sr RYBbt $t 3$Z d( GYs -s{jk IB RZ{Y *7 { jjr {B8}Z 2 VtI bys $R Y & { BP 8}B sj sis}s$bt2 qb {B8}Z I$ {$Bt BP 8B$Bt b {st } B` { Y si$ t $t R}s{ $8 n{w?, 0D # w({b(?, ({b(0d BtB Y % {B w, +D by Y?Ts-$R $R } } ti${zjs B Y I by${y 8B% R $t Y }BR$$%? I$ {$Bt b$y % jb{$k " # w({b(0dbw({b(?d qys $R w, +D Nn{w?, 0D ) ({ (? L + ({ (0 )w L +"D ({ (? 3 < t{ by t sti " Ys% Y Rs8 R$t wy } P I I$ {$BtD Y } B` {$Bt:R s8}j$zi $R js VtI by t sti " Ys% B}}BR$ R$tR wy tzjj I$ {$BtD Y } B` {$Bt:R s8}j$zi $R R8sjj G {st 8s-$8$9 Y } B` {$Bt Ak sis}$t $Y Y j ty {BtT Rst B Y $8 T{BtRst + B 8s, w, +D }B$t sjbt Y si$ t qb IB Y$R b 8ZR JZsj$9 Y R}s$sj sti 8}B sj {B8}Bt tr BP Y } B` {$BtU ({ e eee e (? e ) + ({ e eee (0 e 3 + ) ({b(0 ({b(? e # "3 yt RB IB$t b BAs$t s R}BtR BP 1 w({b(?d $t Y } P I I$ {$Btv $ti } ti t BP R} IvstI Y R}BtR $t Y tzjjti$ {$Bt I$Rs}T } s R qy $8 T{BtRst sis}s$bt % R$Bt BP Y$R R s k $R s{{b8t }j$ry I Ak 8k $tt $ts 8}B sj sis}s$bt 8 {Yst$R8 by${y s{r B JZsj$9 Y$Y}sRR sti jbb}srr R}BtR R wr 3$Z ;sd }u}ƒ!0" g3]+3]3++g" gpu+3" }!3+

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr 1d q strjs$t Y AstI}sRRThj I $8s Ow?, 0D Ak b; $t Y t T s$%? I$ {$Bt k$ jir Y R}s$sj I $%s$% vr{sj I Ak b1$ qb BAs$t Y$R s}} B-$8s RZj srrz8 Ys Y R}s$sj hj }srr R Y P JZ t{k 1$b vsti ` {R sjj BY P JZ t{$ R yt Ys {sr Y I $%s$% $R (O (? ) ( (? R$t w 1$? "0 W ) 1$ w W 1$? {BR "0 ) 1$ Ow? b;,0d3 <$Y}sRR 8}B sj hj $t k$ jir st $8s Y} w?, 0D Ys $R Y 8}B sj I $%s$% BP s jbb}srr hj I % R$Bt j} w?, 0D BP Y B $$tsj $8s vr{sj I Ak +b1$ qb BAs$t Y$R s}} B-$8s RZj srrz8 Ys Y Y$Y}sRR sti jbb}srr hj R Ys% Y Rs8 {B t P JZ t{k 1$b+ yt Ys {sr 8s,$t ZR BP Y Ns}js{ strpb 8 Y I $%s$% $R F ( j} k R ) XI j} wxdow?, XD ) 1$ (0 + I Y}wXDOw?, XD ) 1$ + R\ Y}w?, 0Di R$t{ Y hj R: strp PZt{$BtR s js I Ak I Y} wxd )+XI j} wxdb1$ $P Y P JZ t{k $R $t <9 < t{ b BAs$t st -s{ 8}B sj I $%s$% $P b }js{ Y B $$tsj $8s b$y Y jbb}srr hj I Bt qy PB B BAs$t Y } B` {$Bt BP Y R}s{ $8 si$ t n{w?, 0D BtB w, +D }srr Y strjs I AstI}sRRTR}s$sjThj I $8s Y BZY s jbb}srr 8}B sj hj sti Y Zt strjs I $8s Y BZY s Y$YT }srr 8}B sj hj sti RZ8 Y $ BZ}ZR B Y wr 3$Z d(d VtI 8s-$8$9 Y } B` {$Bt Ak JZsj$9$t Y BZ}Z s8}j$zi R BP Y R bb hj R Y BZY 8}B sj sis}s$bt qy$r sis}s$bt 8s, R Y $ts -JZ$R$ jk R tr$$% B 8B$Bt Ak 8s{Y$t Y $tt $ts:r I jsk B Y $8 TBPT4$Y s{ BRR BZ T $ts { }$% h jir y $8}j T 8 t I Y$R sjb $Y8 Ak b$ $t Z} z$r$bd:r stj$bt { jjr B R$j${Bt t Z BtR Bt s R {BtI t Z B8B }Y${ {Y$} >H sr RYBbt $t 3$Z d( y 8 srz I {j s } P t{ R PB {Bt sr }Bjs $k sti 8B$Bt I$ {$Bt PB R} IR R}stt$t Bt I {si % t YBZY 8}B sj sis}s$bt bsr tb bb,$t {B {jk qy$r $tb8b }Y${ 8B$Bt sjb $Y8 $R s } s{${sj % R$Bt BP GsT RBt sti VYZ8sIs:R <$ja T strpb 8TAsR I 8BI j BP YZ8st %$RZsjT 8B$Bt R tr$t >;;H yt Y $ 8BI j Y R}s$sjjk sti 8}B sjjk AstIT }srr hj I $8s $R <$ja T strpb 8 I R}s$sjjk sti 8}B sjjk sti RZ88 I b$y $R jp V <$ja strpb 8 }YsR TRY$PR s{y P JZ t{k {B8}Bt t Ak ( H v$r s8}j$zi 8s$tR Zt{Yst I y s}} B-$8s s R}s$sj <$ja strpb 8 Ak strjs$t Ak b;vs }YsR I$& t{ BP -s{jk ( H PB Y } s, P JZ t{k VtI y s}} B-$8s s 8}BT sj <$ja strpb 8 Ak JZsj$9$t Y Y$Y}sRR sti jbb}srr BZ}Z s8}j$zi RvbY${Y Ys% s }YsR I$& t{ BP -s{jk ( H e$ tt T ]Z88$tR sj:r $8}j 8 ts$bt BP VI jrbt sti t:r >dh {jbr jkt }u}ƒ!0" g3]+3]3++g" gpu+3" }!3g

11 bsa ts BsY t js I R}s$B 8}B sj t k 8BI j $R JZ$ R$8$js >1( dhvaz $ js{,r Y sis}$% 8}B sj Ikts8${R } B%$I I Ak Y <$ja strt PB 8 E ]Bt{jZR$BtR y % R T t$t I BZ sti $tt $ts 8${ B{$ {Z$R sti 8B }Y I Y 8 $tb ]!7 {$ {Z$R B $8}j 8 t }s sjj j %$RZsj }sybskr Bt s R$j${Bt {Y$} qy R 8${ B}Bb {Z tt8bi $tb8b }Y${ {$ {Z$R s Ps$ jk {B8}s{ sjjbb$t R % sj j % jr BP } B{ RR$t B A } PB 8 I s Y PB{sj }jst k B$t s R } PZ Y Yst } %$BZR $tb8b }Y${ {Y$}R > H sti $t{jzi$t $tt T $ts } B{ RR$t y 8BI j I Y PBZ } IB8$tst stj$btt{ jj k} R $t Y } $8s $ts yt sii$$bt B $8} B%$t R}$, T{BI$t ^{$ t{k Y R R} {$sj$9 I %$RZsj {Ystt jr } B%$I 8B BAZR } $8$$% R PB {B8}Z$t B}${sj 4Bb Yst I$& t$s$bt sti I$%$R$Bt by${y 8BR si$ ttasr I sjt B $Y8R {sjj PB >11 nh VIs}$% $tt T $ts 8}B sj Ikts8${R - ti Y Ikts8${ st PB 8B$Btv`ZR j$, sis}$% BZ T $ts s8}j$h{s$bt - tir Y Ikts8${ st PB $t tr$k =tpb Zts jk 8k } R t I R$t Ps$j I B 8BIZjs Y jbb}ts$t y s8 I R$t$t $ B {$Pk Y$R W % Y j RR sti I R}$ - 8 jk j$8$ I 8 st h $t s R BP x<9 y I 8BtR s I I$ {$BtTR j {$%$k B% Bt I {si BP R} I V{,tBbj I 8 tr y bsr s IB{B sj RZI t s ]sj {Y $t ]s % si:r jsa by t y A Zt Y$R } B` { by $ bsr PZtI I Ak!Wi *Vi_V sti W73:R ei] _ B s8 y $R {Z tjk PZtI I Ak Rs TZ} PZtIR P B8 =t$% R$k BP _ ttrkj%st$s:r et$t $t sti I${sj 7{YBBjR wy BZY Y ytr$z BP I${$t sti et$t $td sti Y GY$s, 3BZtIs$Bt y Yst, srsy$i WB8Z s eizs IB ibr z$isj sti izht zstizjj t PB Y $ Y j} $t } B s88$t Y } B` {$% Th ji } B{ RRB ABs I B $8}j 8 t *7 { }$% h jir s Y dm q jjz $I W Z B8B }Y${ et$t $t GB,RYB} i P t{ R d VI jrbt e < sti F i tu dmx 7}s$B 8}B sj et k BI jr BP Y _ { }$Bt BP B$Bt: F!}7B{V81w1D 1M;u1 }u}ƒ!0" g3]+3]3++g" gpu+3" }!33

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr 1n 1 VtI BZ V p sti V BsY tu dm 7ktY ${ W Z sj ]$ {Z$R ZR$t ]Z tt*b8s$t 7$tsj i } R ts$btr: W Z sj ]B8}Zs$Bt d ;Mux(d n VtI BZ V p sti V BsY tu d;s V ;M((( }$- j x(((( str$rb R$j${Bt $ts $t {Z tt8bi RZAY RYBjI ]!7: ytu _ B{ ny $Ib R 7k8}BR$Z8 Bt ]$ { sti 7kR NsPsk NBZ$R$sts }} ud(1 ; VtI BZ V p sti V BsY tu d;a W Z sj ytpb 8s$Bt _ B{ RR$t wyyd: ytu yr8s$j sti q 3$ 9 w IRDU VtsjB zn7y 7$tsj sti ytpb 8s$Bt _ B{ RR$t {p sbt<$jj ]Ys} M x VtI BZ V p sti V BsY tu de q strj$t s ]$ {Z$R $t 7ZAY RYBjI E!7: F VtsjB yt s I ]$ { 7$ _ B{ d;dudee V${, F sti W i Ij${YU d1 GYs IB R Y $ts,tbb sabz tsz sj R{ t : W Z sj ]B8}Zs$Bt ;w1d deu1d( BsY t VU des i $tb8b }Y${ z$r$bt 7kR 8R: ytu ${ Bt Z B:EU 3$PY yt ]BtP W Z sj W bb,r sti 3Z99k 7kR 8R NBR Vjs8$BR ]V M BsY t VU dea i $tb8b }Y${ z$r$bt 7kR 8RU i % R et$t $t Y z A s i $ts: _Y* Y R$R ]sj$pb t$s ytr$z BP q {YtBjBk _srsi ts ]V BsY t VU d qy i $tb8b }Y${ V}} Bs{YU _$- jt_s sjj j VIs}$% V8}j$h{s$Bt 3$j $t sti +Zst$9s$Bt: VtsjB yt ]$ { sti 7$ _ B{ dn xnuem d( BsY t VU ds srr$% ]Btt {$%$k b t W Z B8B }Y${ ]Y$}R =R$t VII RRTe% tr: yt } }s s$bt dd BsY t VU da V qy BZY}ZT!tT* 8stI VII RRTe% t q str8$ PB W Z B8B }Y${ ]Y$}R: ytu ]BtP t{ Bt VI%st{ I i R s {Y $t zn7y NBR Vjs8$BR ]V d1 BsY t V sti V VtI BZU dd V {Bt srtr tr$$% $ts b$y {$} BT {sj Rkts}R R: ytu F e BBIk w IDU VI%st{ R $t t Z sj $tpb 8s$Bt } B{ RR$t ; zbj ; 7st s B ]V dn d; dx de d dm d ]BY t e sti _ 7 j$tu dd ${ B{$ {Z$ k js I B Y { }$% h ji { t BP Y BtTA s stj$bt { jj: F W Z B}YkR$Bj Exw1D nx1u ] Bt N F sti e s}jstu dx i { }$% h jir BP _ sti stj$bt { jjr s{ BRR Y } $8s $ts: z$r$bt i R nxwdd u1; ] Bt N F _Z }Z s sti sju dm; i R}BtR %s $sa$j$k $t $tsj stj$bt { jjr BP } $8s R: _ B{ Wsj V{sI 7{$ = 7 V (wdd Md1Mun( * ja Z{, q sti ] V siu d; _YBB { }B ]$ {Z$ b$y G$I *kts8${ ist : ytu _ B{ I$tR BP Y yt ts$btsj ]$ {Z$R sti 7kR 8R $t * $tbt V sti _ N tt$ U dm; 7}s$sj sti 8}B sj {Bt sr R tr$t $%$$ R BP t Z Bt R $t js sj t${zjs tz{j ZR BP 8s{sJZ : F _YkR$Bj wnbtid nx 1du;( e{, _ sti p Z{YRAsZ8U dn e^{$ t {BI$t BP tsz sj $8 T %s k$t $8s R $t Y s jk %$RZsj RkR 8: _Y$j q str ibksj 7B{ NBtI $Bj nnwd1(d nmxunx e$ tt T]Z88$tR i F zst I 7}$ j sti _ Z jj U d <s Ibs $8}j 8 ts$bt BP s %$RZsjT8B$Bt }$- j ZR$t B $ t I R}s$B 8}B sj t Z sj hj R: yeee q strs{$btr Bt ]$ {Z$R m 7kR 8R yytvtsjb m *$$sj 7$tsj _ B{ RR$t ;EwD dd1dune 1( e$ tt T]Z88$tR i F %st I 7}$ j _ Z jj sti sju d zn7y y8}j 8 ts$bt BP ]B ${sj z$rzsj B$Bt * {$Bt ZR$t st VtsjB W Z sj ]B8}Z : ytu * qbz 9,k w IDU VI%st{ R $t W Z sj ytpb 8s$Bt _ B{ RR$t 7kR 8R zbj 7st s B ]V }u}ƒ!0" g3]+3]3++g" gpu+3" }!3p

1; bsa ts BsY t 1d 3 I V sti _ 7 j$tu dmm qy!wtsj}ys stj$bt { jj BP Y {s $ts sti $R } Rkts}${ { jj k} R: F W Z BR{$ MwD 1n(nu1( 11 <B t _ sti p 7{YZt{,U dmd * 8$t$t B}${sj 4Bb: V $P 1n yt jj d dmxu1(; s8 8stR sti 3 G Aj$tU d1 pv VT8 I$s I }BR$$% szbp IAs{, jbb} {Bt BjR YB $9Btsj { jj,$t ${R $t $ Rsjs8stI $ts: F W Z BR{$ d1wd 1;xduEn 1; s}jst e sti i 7Ys}j ku dm1 sti O { jjr $t Y js sj t${zjs tz{j ZR BP 8s{sJZ 8Bt, kr: F _YkR$Bj wnbtid nn( d1xu;n 1x BjA < sti i W jrbtu dmx 3Zt{$Btsj W Z B{$ {Z$ k BP V8s{ $t { jjr $t Y ]s i $ts: ytu V psjj B sti _ pbz sr w IRDU W Z B{$ {Z$ k BP Y i $tsu V ]s`sj 8B $sj ejr %$ W b OB, }} 1dxu1n1 1E 1 1M 1 n( nd n1 nn n; nx ne n nm n ;( BjA < sti i W jrbtu dn!33tsj}ys sti!33ta s stj$bt { jjr $t {s $tsu yy W Z sj {$ {Z$ k sr % sj I Ak j { Bt 8${ BR{B}k BP <i_ Rs$tR: F ]B8} W Z Bj n1wdd Mxudd( Z/ 7 GU dxn *$R{Ys _s tr sti 3Zt{$Btsj! st$9s$bt BP s88sj$st i $ts: F W Z B}YkR$Bj de nuem N % tysj V p sti i G ibi$ {,U dmd i $tsj stj$bt { jj {jsrr R $t Y!jI GB ji 8Bt, ku 8B }YBjBk sti { t sj } B` {$BtR: 7{$ t{ 1dnw;xd1D ddnu;1 N$Z 7U de 7$j${Bt BI j BP B$Bt VIs}s$Bt $t Y 3jk: ytu n I =]7*T ]sj {Y 7k8}BR$Z8 Bt W Z sj ]B8}Zs$Bt N$Z 7U dm 7$j${Bt i $ts b$y VIs}$% 3$j $t _ B} $ R: ytu VI%st{ R $t W Z sj ytpb 8s$Bt _ B{ RR$t 7kR 8R 7st s B ]V sz$ p _ NZ,sR$ b${9 sti sju dm V8s{ $t { jj $t s{$btr ZtT I jk$t Y R}BtR B {Yst $t Y $ Rsjs8stI $ts: F W Z BR{$ w1d 1Eunx si ] VU dm VtsjB zn7y sti W Z sj 7kR 8R i si$t VU VII$RBt G Rj k _s%srb%$?{ V V p VtI BZ sti ] i G Rs U d; ]Ys s{ $9s$Bt BP 7ZAY RYBjI!7 $R8s{Y $t q str$rb R PB zn7y 7kR 8R: F VtsjB yt s I ]$ { m 7$ _ B{ E xum; _Bjks, F NU d;d qy i $ts ]Y${sB ynu ]Y${sB _ RR ibi$ {, i GU dmm qy _ $8s i $ts: ]B8} _ $8s $Bj ; 1(nu1M 7Ys}j k i sti F * z${b U d WBtj$t s 7}s$sj 7Z88s$Bt sti Y ]Bt sr ps$t ]Bt Bj BP ]s i $tsj pstj$bt ] jjr: F _YkR$Bj 1( d;du ded 7Ys}j k i sti F * z${b U dmd <Bb ]Bt sr ps$t ]Bt Bj BI$h R Y 3 JZ t{k i R}BtR R BP ]s i $tsj pstj$bt ] jjr: F _YkR$Bj ndm dedud 78$Y i pu dx 7$8Zjs$Bt BP st stsb8${sjjk I ht jb{sj {$ {Z$ v qy {Bt TYB $9Btsj { jj t bb, $t {s $ts: z$rzsj W Z BR{$ d1wnd x;xuxed qstt F sti ] siu dm!}${sj B$Bt 7 trb : ytu VtsjB zn7y sti W Z sj 7kR 8R i si$t VU VII$RBtTG Rj k ]Ys} d; }} 11u1xx q 8 R p ] sti G < $U dm 3sR ]!7 ]Z t V8}j$h sti Z& 7s : ej { Bt${R N R 1nwdnD ;d z${b F *U dm qy *kts8${r BP Y ]s i $tsj ] jj ] t : F _YkR$Bj nme 1du1;E ;1 z$b9 e sti V Z$U dn N$t s t bb,r AsR I Bt str$rb R: ej { Bt${R N R 1 1u1 ;n GsstsA sti i G ibi$ {,U dm _s srbj sti 8$I stj$bt { jjr BP Y } $8s $ts: F ]B8} W Z Bj 1MwnD ;n;ux; }u}ƒ!0" g3]+3]3++g" gpu+3" }!3<

i $tb8b }Y${ ]Y$} b$y _s sjj j _sybskr 1x ;; GsRBt V sti V F VYZ8sIs F U dmx BI j BP <Z8st z$rzsjtb$bt 7 tr$t: F!} 7B{ V8 1w1D n11un;1 }u}ƒ!0" g3]+3]3++g" gpu+3" }!3x

}u}ƒ!0" g3]+3]3++g" gpu+3" }!3E