Principles of Information Processing in Neural Nets

PRINCIPLES OF INFORMATION PROCESSING IN NEURAL NETS (Printsipy pererabotki informatsii v nervnykh setyakh)

E. N. Sokolov, S. V. Fomill.and G. G. Vaitkyavichyus

1.

Direct measurement of the absorption spectra of individual cones in carp, monkeys, and man j7, 8 / has shown that there are three different pigments having respective absorption-maxima in the dark blue (cyanolab), green (chlorolab) and red (erythrolab) parts of the visual spectrum. Thus different electromagnetic vibrations within the visual spectrum are converted into different degrees of excitation of three types of cones.

~ntroduction

In analyzing information-transmission in actual nerve nets basic consideration is usually given to the classification of nerve impulses. The assump-' tion is made that the specific configuration of the spike potentials serves as a code for the external signals acting on the receptor. However, data are now available which indicate that in many cases signals from external sources are coded through the "channel number" /1/ (neurons responding selectively to a definite audio frequency /2, 3, 4/, the slope of a line /5/, speed of motion /6/).

The question arises as to how a system of three independent receivers with widely overlapping absorption spectra guarantees the perception of a great number of hues. Our aim is to describe a model for a neural net that provides the human eye with differentiated perception of hues.

In this paper we discuss the analysis of coding by "channel number" in color vision.

2.

Statement of the problem 3. Construction of the model

Any electromagnetic radiation that a human is capable of perceiving as light may be described by a function p (~), where ~ is the wavelength and p (oX) is the radiation energy corresponding to an interval (~, A + .c:. A). The totality of all such signals is therefore an infinite-dimensional function space. However, when the eye perceives a signal this space degenerates and the totality of different color sensations of the eye is at most a threedimensional space. Any of these color sensations may be obtained from a combination of three primary colors, which we call monochromatic radiations, of wavelengths 700, 540, and 550 TnJl.. In other words, the eye's color perception is an operator which transforms the infinite-dimensional space of color signals into a three-dimensional color space. Properly speaking, the theory of color vision is the investigation of this operator and the system it realizes.

Our model consists of two layers of formal neurons : a layer of receptors having different (though widely overlapping) characteristics, and a layer of color detectors. The receptor output signal, which is proportional to the logarithm of the number of light quanta absorbed /9/, is fed with a certain coefficient to a set of n elements in the second layer, the latter being formal neurons. The elements of the second layer are interconnected by lateral inhibition. Thus an external signal at the output of the receptors can be represented by a three-dimensional vector F (f ( ))) whose components indicate the level of excitation in the i-th receiver caused by the given spectral structure f ( )). If the components of vector A (j) define the connections from the receptors to the j-th element of the second layer, the level of the input signal to the j-th neuron will be a functional

It follows from the fact that the color space is three-dimensional that the eye contains three primary radiation-receivers whose excitation lev e ls are the components of a three-dimensional vector that describes the hues perceived by the eye.

220

avoid th is sltu" t ion, tftl' s:: 1gle-~ayer' model may Le rep l aced by:, m ult il3.yer structure. Lt't us f ix f(~)~ 1'1(1) ill (l) a nd reg ar d Ihe fun c tio nal as a funcl ion uf j; assuming for thE' mom ent th at j is a cont in u ous va t'ia lJl.." ; l' l us find a vector A (j) s u c h th a t the functiunal y (J, f (~) ) will hp a maximum for j = jo '

The derivative of fun c tion a l (1) with respect must vanish at j = jo, i. e.,

YJ' " (jJ \ (1)) = (F, A" 'Jo )~ Q ,',

to

j

(2 )

Moreover', it is nntural to add tht:' following restri~ ti on to condition (2):

, A (j) , = cons t

(3 )

It follows from (2) that th~ v ectol' A' J;" U) is o rthogonal to th~ vector F (f\ (1 )), and fr0111 (3) th a t th e vector A' J=J o is orthogonal t f) thp V('ctOl' _~ Uo); ill other words, as on(' of th e s<,jut io~s , vector A(jo) must be collinear \\' it.h v('C'wr F :rl ' ~ It follows from (3) and from IIw ra,'1 that \'l'l:t()r'~ A und F a re parallel that Ill<' \'(,l'I"'\ (j' is uniq uel y defined for any f ( ;), ; ;,,',d ,i .

'; ,

With this choice of \h'tOI' ,\ (J) 1'0)' fixed f 1 (~), the func ti onal y (j, fl (~) ) uttuins its unique maximum at the j-th e lement. Thus, if the mput vector o f th e seco nd layer is = I1 y (1, f), , . '4 Y (n, f) ", then (see 10, 11 / ) the o utput vector Z- ,: zl' .. " z,,11 m:.ly b p defined by th e formula

y

Y = :\ Z

(4 )

wht"'p element ~ il :n tht' mal,'j" ,\= 11~,: ~ is thl' ,.\t'ight of I hp latej';) 1 i nh ib i to cy c'onnections fr'om dll' j-th to tht' i-t h C'~emelH <.If tilt' second layel'.

The elements 9'i J are c ho sen s uhj ect t o the co ndition th a t th e maximum fOl' th e fun c tiona l y (j, f 1 (~) ) be intensifi ed, i,e., tha t the functional z (j , f 1 (1)) must hav e a much sharper ma xim um than ~;(J , fl( ~)) ' (It is ass um e d that the perception of:1 c ertain hu e cOl'l'espo nds t o the preferential e:.;citation of one n euro n - th e j-th - o f th e second layec.) If th e functional y (j, f 1 (1)) n ttaillS its ma:-; im u:-n :11 1he Jo-th ne ur'on, then the coefficient 9' i , a is pl'o p ort ionn l to the d iffe l'enc (' het \\'('('n t he rh' I ' n ~,,' liZl'd function Y(J, f l (~)) and :i " "!'1:1i n 'll1,'l1t!l\' ~ Ci - jo i ). In con clusion it must be )'emarKed tha t if th(' funcl ional y (j, f l(~ )) does not ha v(' a cl ear -cut mClxim um, the inhibition fac t ors ut'e lal'ge, To

Tht.' above IT;ud('; for' colol' visio n has been si mulated by a special comput er-program. Th e s p ecial feature o f this pro gra m i s that it provides for co mputation of the c harac t erist ics of single formal ne u rons and their co mpariso n with the l'esponse of ceal neur ons involved in color perce ption, 1'h(, absorption spectra of the three primary pigments were stored i n the computer's memory (Figure 1); these spectra a r e in good agreement with data ob tained by Yust ova / 12 / (Figu re 1 a) fl'om :1nalysis of color blindne ss.

Tomita's data , 9 , were used to ensure that the lc,vd o f output response for each receiver be d: ,'('ct ly proportional to the logarithm of the :lumber of light quanta absorbed. Th r-L't' suitably weighted types of "cones" transmitted excitat ions to 129 second-layer" neurons", thes(' latt er being provided with lateral inhibitory f(' edback connections (Figure 2). Thi s exhausts the initial data for the model. Next , the c o mput er was u sed to select vectors A (j) a nd coefficie nts ~ iJ as d escr ibed above (see p , 4), i. e" to select the connection fa c tors for the linkups Df the " cone s" with the second-layer neurons and also fo :' the later:d inhib it ory connections , Funher l':.;p('riml'nts with thl' mo del wen' aiffied at compal' ison of a n umb er of psy c h ological and phys io'! ug:,:al ] .. \\'03 ,>\'i th the ['es u lts obtained on the model.

Shce these bws were not incor p ora t ed in the model in advance, the fa~ t that the model' '" response coi ncides with the laws of color visio n is a s ubstantia l indicat ion in favor o f its correc tness,

5 . ('ompal'is,:m o f the behoviol' of t he model with psvehophy siological data a. Th E' ld\\' of color mi:.;tur l' . It is l-::10\\'n from col<) r in1l' tI'Y that th e only p I'oper t ies L)f the colol' l'l'cei\'e l's - th e COI1L'S - that expla i:l all the laws ,)~' coIn I' ;1)i :-:tuI'''' 31'e th('il' pigment ch'1 racteristics. ,\ , Iht' l .. ;!sis uf th(, \Vd] known form ula

whl're ~r, ~~, and ~h al'(' t he p !'im:1 r~' coh)!'s, :.;nd b r ( ~ i \, h~t~i), :,l1d bh(~ i ) nre the 3l': lS itivitil's nf

,.

'/.

80 10

.,.

..

.. JO

•0

FIGURE 1. Pigment sensitivity curve according to Ma rks 13 / . Wavelengths a re set off along the abscissa, and number of quanta absorbed by the given pigment along the ordinate.

fIGURE 1 a. Pigment sensi tivity curve according to Yustova /1/,

T /I •

z;

•

•

h,;.• FIGURE 3. Color mixture curves: 1 - curve computed on the basis of the pigments indicated in figure 2; 2 - standard curve .

'IGURE 2. Block - diagram of model baving variable threshold. I - la'er of receptors each of which is connected to each element of the se:ond layer; II - layer of formal neurons with lat eral inhibitory connecions.

'Or---~---+----~--~--~--~--

__

1.2 -z. ~--~--~----~--~---+~L3~~ -JD.

-.0 --+----+i- - ii---t-- t - -t - t i -

- ,$'0 ~

o

- 60

L-.l.._ ~_.~ --l._---'_- - '

( ;J

fI GURE 4. Illustration of the Betzold - Brucke effect. The coordinates are the l evels of excitation for the corresponding receptors (for details see text).

Ioj~ ~

y~,:

!~ v

Jo lJ

l' ~ ~

:J-y J

b ; O m lJ

fIGURE 5. Betzold-Briicke effect . Abscissa s: ,,·avelengths. Ordinates: changes of ,,'avelength of monochro matic light required to obtain radiation of the same hue when the intensity is reduced ten- fOld. Solid curve - experimental curve; the circles indi cate the curve compu ted on the m,)del.

222

the color receivers for a given wave-length ~ i ' one can compute the mixture coeff icients r (~), g (~), and b (~), which indicate the proportions of the pr i m a ry colors requir ed for the perception of a co lor wi th wave-length ~.

ce rta in degree of acc.l'racy one ca n ass ume that all possible vectors F have their end-pOints on the surface ob tained by joining a ll pure-c olor points to the white poi nt 1 • Choose a vector GA and add l og a to all its coo rdina t es , which co rresponds to an a-fold i nc rease in light intensity.(This oper a tion is eq uiv a lent to addition of a cer tain quantity of ~it e light to the mono c hr o matic light defined by OA, s inc e it involves exc itation of all three r ece ivers t o th e same d egree .) As th e coordinates of vecto r OA are conti nu o usly increased in this way, it c uts the surface of cons tant intensity in th e line alA (in th e general case - along a plane c urv e). Th e vectors_GAl a nd OA 2 sti mul ate the sa ~e sensati on, i. e., OAI d e fine s th e sa m e color as OA 2 , but for th e i nitial intensity J o. L ater we ~hall de t er mine how the dir ection o f th e vector OA l co rr espond s to the color. The computer curve is given in Figure 5 together with the ex p e rim e ntally obt ai ned points.

°

Figure 3 illustrates standard color-m ix ture c urves and c urves computed for th e pigm ent c hara c teristi cs i ntr oduc e d in the mod e l for the primary co lors 435 , 545, a nd 700 TTlJ.l. It was assum e d that a mi xtur e o f the thre e pr imary co lors wa s equal t o a monoc hromatic radiati on if and only if the m axim um excit ation t ook place in one and the same e l e m ent o f th e second l ayer. This condi tion holds in th e optic systems of monkeys a nd s quirr els / 13,14,15 /. It must be emphasized th a t th e col o r-mixture c urves in the model were obtained independently of psychophysical data, on th e basis of the c h arac teristics of the pigm e nts an d the principl e of coding by neuron numb e r . The fai rly good ag re e ment of the results with the s tandard curves (in no case was the devi a tion mor e than 8.0%) indicates that the model co nfor m s to the b as ic principle of color vi sion. Th e source of the observed deviations is in th e initial c ha ra c t e ri s tics of th e pigments.

Thus the Betz old-Brii c k e e ff ec t is th e result of a loga rithm ic transform a t ion o f th e input signals in th e color-visio n system.

c.

Differential spectral sensitivity of the eye.

Th e minima l change in wavelength requir e d for a t est subject to discern a change in the hue of a color at constant int e nsity describes the eye's differen tial spectra sensitivity.

b. The Betzold-Brucke effect. In colorimetry a color is usually represented by a point on the chromaticity diagram, the point's coo rdinates being determined by three trichromatic coefficients which satisfy the relation x+ y+ z = 1. The disadvantage of this system lies in the strong depend ence of the color-characterizing point's coordinates on the choice of primary colors.

Th e differential spe c tral sensitivity of the eye is kn own from psyc hophysi cal tests. In our case th e c h a r ac teristic is fairly well approximatei by th e rate of change in th e direction of vec tor F (~) as a fun ctio n of ~ when the intensity of the ligh!..is cons t ant. It is easily seen that the vec tors A U) h ave no effect on this c harac teristic. The rat e of c hange in direction of F (~) may be determin e d from the formula

In certain c ases it seems more convenient to use natural coordinates, i.e., to set off the excitation levels of the three color re ce ptors - the numbers x" Xg, X h - on the coordinate axes of a three-dim ensional space. The color is then described by the direction of the vector F = Ilx" x8' xblland this dir ec tion depends neither on the choice of primary colors nor on the intensity of the light incident on the receptors.

cos j} = where Fjis the vect<2,!' in the color space for wa velength ~, and F j- I th e vector for wavelength ~ + 6. (6.= const. for all ~).

We shall demonstrate the advantages of this system by looking at the Betzold-Brticke effect, which is the phenomenon of increase in light intensity or of addition of white light to monochromatic light resulting not only in a change in saturation but also a change in hue. Thus an increase in brightness makes red more yellow and violet-blue becomes light blue.

This curve has been computed, and is shown in Figure 6 together with the experimental curve. The good fit (correlation coefficient = 0.85) again att e sts to the correctness of the model, since the differential sensitivity was determined independently.

Figure 4 illustrates the projections of the hodographs o'f the vectors F for light intensities J o and J (curves LI and Lz)' where J= 10 J o. With a

The observed deviations are apparently due to the fact tha t the differential spectral sensitivity depends not only on the rate of change in~ngle but also on the absolute value of the vector F.

723

,

u~-

?DD

400 FIGURE 6. Differential spectral sensitivity of the eye. Abscissas: wavelengths. Ordinates: Proportional m inimal variation in wavelength for which an observer can still perceive a change in radiation sensation. Solid curve experimentally obtained curve; dotted curve - that obtained from Tlodel.

600

700

FIGURE 7. Spectral sensitivity of LGN cells according to 1\, L. de Valois '14/. Ivavelengths are set off along the abscissa, and the average number of spike potentials by which the cell responds to stimulation of equal energy are marked along the ordinate axis.

DJ 0.2

I

,,~

,36f

0-0

A=b70 m p

b-
id ..... 0-0

~=

500 m p 600mp

),,~"'Omp

.26 t

o.i

Ht i to r l

1b

12 ~

", 0"

500

700 ~~~-r~~~-r'-'-"~~II 400

600

~

33 , ..mp _-), ,•• mp

mp

FIGURE g, Output responses of m "del "neurons" at fix ed \,avelength, Absc issas: number of the "neuro n" or of the corresponding wavelength fo r a monochromatic stimulator, Ordinates: res ponse of each element.

flGCRE 8. Spectral sensitivity of the model "neurons," (The light flux has a constant numbe r of quanta for any wavelength . )

224

l\] ,)f'COVL'r, thc se nsitivity a lso depends on the intens ity, sincc whe n th e latter is Increased the ;i()l id :Ingll' \\' ithin which v('et cH' F is sit u Jted b ,",'OllH':-; sm ~,llt ' I', ~d1J vic,' VCI ' sa , H O'.I'cver', the d lClngl'" ;n th,' n lll ,kl ' s cl i ff'"l"'nti:lt'ng ":lp:;" ity '.\h id ; Iw ('ompal;y ilil 'I'l':l s ing intl'rlslty :,1'<" not the: same thr'oughout th,' spec trum - i>eIng g J'C' J\('!' Ijl po in t s \\' hpr',' the BC'tzold - I)I'uCKl' effl'ct is s tt' ongu',

d , (,olor-blindness, Th e most widely st ud ied forms of d ic hromatism at present a r e pI'otanopia , deuter'anopia, a nd tritanopia, T1 1(' 1:1 ;<1. for': )' u t' co:o ,' blindness ha s aroust'd co n sid e r' ~liJle con tr ove r sy, and we s hall thpI'('forl' nu t c<)ns i dl'~' it, In pI'otanopia p('rcl'ption of the long"wave end o f th e s p ectr um is s h ortcned and th el'c is an achromatic n('utr' a l z one i n th e rcgion of 4 9 0 tl1j..L, In deuteranopia th e long - wave end of the s pe c trum is not shortened, a nd the neut ra l zo n e i s observed in the regi on of 500 m /-l , All these phcnom ena m ay be expla in ed by th e model, if WE' rep la c e the ery th rolab b y chlorolab (in protanopia) and conv(~rsel:, (in de ut eranopia) , Th e mod e l wi ll then " see yellow" in (hp lorrg " \I' aVE' section of the spectrum and achromatically where the sensi ti vi t y c u rves of th e t WO rem a in ing pigment s int e t' sec t. A c h arac t er'is t ic feature of thest' forms of dichl'o matism is that th e second-layer neut'('ns' r eg ion o f max i m a l excita t ion for all possible f (~) narrows, i , e " certain neurons ar'e in effect not exci t ed a t all , while o thers ( "y ellow" col or neurons), e,g" i n the long-wavp spc tion of thp spectr u m, an' excited con t in u ally for any ~ ,

5, ReSpO!) Sl' of the l'll'mt'nts of the model to ligh t uf \'~1I'i,)us \\'ave]engths :-\s d e scrihl:. d :1hpv f' , n ut.. nlt1dt:'1 \\.·a~ C \ )r1 Slr' u c t p d i n th (' fonn () f " rlt.' Ut':tl net, mIlking il pnssiblv III i so l a tr' the c h ;"1r '-l l. . tl'1' i st i\ ' s o f i 1S t'lt.'r. l l· ~1tS ~1 !1l~

c o nlpar'p th e nl '.~: i th tht' :'f.'spn !1 s e :s o f !'(' ::: ! ~ (,Ui · \ ' :IS. To co mp:l t'c' the !'eSp"'lsl'S o f the TT'"d,,} "" tll t he resp o nses of c]c (' trophysiolog icall y " c,,'<,, " d pd re: l: '1e u l'ons ,It \'ar' io us le\'cls of tlw o pt ~c SYSll'tn, :hf' ()utput [,PSPO:1SC" ,)f thf' s('('ond-]a:-'l'!' :H' U!',)ns \\' e:' c cl etel'mi:1f'cl, 11 is kno '.\'n that

~ !l

the Ilpt:C S:;Sll';1:

~ht ~ : '(' sp()n~ l'

of : :1d i v id u a l c e ;; s t u : :ght ()f , Lffl' I'C' tl t ','",\ l-: l" ' !2 t !' :' fr' om the bipo lar c ells t o the !leUl'l)t1S of the btct'~ rl geniculate body, displays a clea l' :llllag o ,l:st ic charac t e r ; in other' \\'or'ds, t he- c ells :ll'c' ex c itcd a t cer t ain waveleng th s a nd inhib ited at (lt h et's 13,14,15,15,17,18,1 9 , Th e reSp"11 Sl' o f tIll'S,'

cells (after R, L. De Valoi s / 13 , 14 . ) is illustrated in Figur e 'j , Figur'e 8 shows thl' cor r e spo ndi ng response on the Thl' sa me ,lntagoni,stic (' h:'ir ~,cter is a pp are nt - the neuron s a!'e: ('xcitcd by sume: sec t ions o f th e sp e c trum and in hib i t e d by o th ers, iJ ~ir t of th e' "ncu r o:1s " of th e m ode L

Figure 9 shows the re sponse of the entin' populat ion of model neurons for the fixed wavelengths 410,500,600, and 670 m /-l , It is clear fr om the form of th ese c urves that ne u rons whose maximal l'xcitation is for blue lig h t produ ce th e gr'eatest inh ibi t ory effect on neurons whose maximal l'xcitation occ urs for yellow ligh t, and vice versa , Th ese effects h ave a l so been observed by many a uthors i n real nerve nets 113, 14, 1 5 I and resemble th e antagonistic p r ocesses in various phas e -theor ie s based on H e ring's theory of opponent c ol ors , Her i ng's theory is usually considered to con fl ict wi th the three- c om ponent theory , In o ur model, h owe ver, Hering's lall' is a result o f the properties of a neural net exe mpl ifying th e three-component theory by m ea ns of color-co ding by n e u ron number.

6,

Ph eno m e no n of t he after-imag e

V/h cn a colo r A is c ut o ff, the o bs erH' r receives a sen s a ti on of a colo r B clos e to the colul' c o mpl e mentary to :\ (i,e " the color th a t i n c ombination wit h /\. pr'o duces wh i te ), It seems t o us th a t the lrtf' c h:ltlism of the a fter-im a g e involve s the e ffe c t of r'enewed activ i ty o n the p ar t o f th e second -layer' ne u rons a s a result o f the first c olor being c ut \)ff (assuming spo m aneo us ac t i v ity on th e pa rt of th e- tll' ut' o ns). Thus l h e greatest inCl'P ,lSf' in a ni ',: ;ty ; s o hsen'ec! in th e most inhib;ted l~ e ur ons, thi:" i s ;JPt'cl' j\'pd :IS a sens: n ion of t he ,' 0 ]01' l") r"t'PSp (l ~ l(!:ng 11) the l1umht'r o f th e llPurOl1 whose :!1h ih i t io l1 h . IS 1)(, e'11 dis c ontinu ed , This < : .. ,,-jOt, :! :U:"tl'., tl 'd 'I: ! ' igu l'l: 9, On bl u e i ight !W::lg c u t " ft', 11; (' g;" ':l tl' St ~ncrese In ac t :\-ity is obsel'ved i n ye :;,) '.':

!1 E'U!"()!1S,

~1 nd \ 'iC f' \ 'er-S 3 .

s :tu:llion :s llilsen'cc fOl' r cd a tlC

T l:c' ,: :e:

d .fl ~'(, l'r ~~ t ":', i "t ' i ·.''' t~ e: l :"' L:.i' !",: H ) d c:'!3

,li,'

\ ' :S : tli : -

" " s' ,' : :",'::',

, , !'

.-\ sin1ila r

g:'Cf'11

l ight,

pel"!'CQ'n1anCe

tl:t' PS,\' Cb,P!;YS:":' o f color

\I: ~;: , ': ~ : . • ,',;-" : : ~! ~ : '; 11 1

t

C' t:::

p:: 'e \-: I'Iusly inc0r -

pn r :ltP C : 11 tl;l" r.ll ' d ,, : - :'tlte:3ts [ 0 'ts ,'lllseness t o t hp :\,' 1 U:L p~'" ,'t'S:"t' S "r ,'0101' \':S ; OI1 , Co mp a r iSP :l n f l !~ t · p t 't · i ·l '\; ·:-: 1:~ : 1 .. 'V l,f the nl ode:' s c']elne nts i l ) th~!l 1 ' 1' , !;(L\ -:d u~ :~ :'t:\ ~ t1 neur'ons i n the color \' i si l '~1 .,\ 'ste m ;J.Isll I't' ve al s :, l'emarkable

similarity. These are important arguments for the claim that the structure of the connections in the model approximates that in the nervous system.

5.

Hubel, D. H. and T. N. Wiesel. Receptive Fields and Functional Architecture in Two Nonstriate Visual Areas of the Cat. - J. Neurophysiol., Vol. 28, p. 229. 1965.

Since the basic principle of the model is that of color-coding by channel number, it seems probable that this is indeed the principle utilized in c olor vision.

6.

Bar low, H. B. and R. M. Hill. Retinal Ganglian Cells Responding Selectively to Direction and Speed of Image Motion in the Rabbit. - J. Physiol. (England), Vol. 173, No. 3, pp. 377 -407. 1964.

8.

7.

Wa 1 d, G. The Receptors of Human Col or Vision.- Science, Vol.145, pp . 1007-1017. 1964.

Summary

1. We have proposed a model for color vision based on the principle of the coding of external signals by neuron number and the separation of three receivers.

8 . Marks,W.B., W.H.Dobell and E . F. M a c Ni c h 0 1. Visual Pigments of Single Pr i mate Cones . - Science, Vol. 143, pp . 1181 1183. 1964 .

2. The model was simulated on a computer and subjected to "psychophysiological" experiments, the results being then compared to known facts of color vision.

9.

3. The processes taking place in the model turned out to be similar to those envisaged by Hering's opponent-colors theory, and the response of the individual "neurons" of the model was very close to that of neurons in real nervous systems. 4. The model provides explanations for the actually observed differential spectral sensitivity of the eye, the Betzold-Brucke effect, the afterimage, and various facts of color-blindness.

10.

Ha r t 1 in e, H. K. Receptor Mechanisms and the Integration of Sensory Information in th e Eye. - Rev. Mod. Physics, 31,515. 1959

11.

Rei c h a r d t, W. and G. M a c Gin i tie . Zur Theorie der lateralen Inhibition. - Kybernetik, Vol. 1, No. 4, pp. 155 -165. 1962.

12.

Nyuberg,N.Ya. andE.N.Yustova. Issledovanie tsvetnogo zreniya dikhromatov (Investigation of the Color Vision of Dichromatic Subjects). - Trudy GOl, 24 (143), pp.33-93. 1955 .

13.

De Valois,R.L., J.Abramov a nd W.R. M e ad. Single Cell Anate Nucleus in the i\l a c a que. - J . Neu rophys i ol. , Vol. 30, No.3. 1967.

14.

De Valois,R . L.,J.Abramov,andG.H. J a cob s. Analysis of Response Patterns of LGN Cells. - J . Opt. Soc. America, 56, No. 7, pp.966-977. 1966 .

15.

Michael, Ch. R. Receptive Fields of Opponent Color Units in the Optic Nerve of the Ground Squirrel. - Science, Vol. 152, pp. 1092 -1097. 1967.

16.

Mac Nichol, E. F . Jr. Retinal Processing of Visu a l Data. - Proc . Nat. Acad. of Scien., Vol. 55, No. 6, pp. 1331 -1341. 1966.

BIBLIOGRAPHY 1.

2.

3.

4.

So k 0 10 v, E. N. Orientovochnyi refleks i vnimanie (The Orientating Reflex and P e rc e ption ). - X \'III Int e rn o.tion o. l Congr e ss on Psychology, Symposium 5, p. 25. Moskva. 1966. Tun t u ri, A . R. A Difference in the Representation of Auditory Signals for the Left and Right Ears i n the Iso-Frequency Contours of Right Middle Ectosyl vian Auditory Cortex of the Dog. - Amer . J . Physiol., 168, pp. 712 -727. 1952. Kat s u k i, Ya. Nervnye mekhanizmy slukhovogo analiza (Nerve Mechanisms in Auditory Analysis). - In Sbornik : Teoriya svyazi v sensornykh sistemakh, pp . 288 - 306. Mir , Moskva [?). 1964

Gershuni, G.V. O me k ha n i z m akhslukh a (On Auditory Mechanisms). - In Sborni k : Mekhanizmy slukha,pp.3-31. Nauka . Leningrad. 1967.

226

Tom ita, T, A. K an e ko, M. Mu r a k a m and E. L. P aut 1 er. Spectral Response Curves of Single Cones in the Carp. - Vision Research, Vol. 7, pp. 519 -532. 1967.

17. S v a et i chi n, G. Spectral Response from Single Cones. - Acta Physiol. Scand., Suppl., 39 134,pp.17-46 . 1956.