Kybemetik 10, 58-60 (1972) @ by Springer-Verlag 1972 Holographic Aspects of Temporal Memory and Optomotor Responses A. BORSELLINOand T. POGGIO* Istituto di Scienze Fisiche, Genova, Italy Laboratorio di Cibemetica e Biofisica del CNR, Camogli, Italy Received August 2, 1971 Abstract. A mathematical analogy between the holographic models of temporal memory and Reichardt's optomotor theory is stressed. It is pointed out that the sequence of operations which is essential to any holographic model of brain function. ing is actually carried out by a nervous structure in the opto- motor behaviour. Some implications in both the optomotor theory and the hypothesis of neural holographic processes are further sug- gested. The optomotor response of insects (their evoked response to movement relative to themselves in their visual surroundings) allows, through a quantitative system analysis, the specification of some fundamental functional principles of the central nervous system (Reichardt, 1969). It is not necessary for our purpose to specify all the experimental and theoretical details, otherwise well known (see for example Reichardt, 1957). Highly reproducible experiments lead to undoubtable, con- clusions about the existence of physiological mecha- nisms able to connect sensory input and motor output in a well defined manner. A model, devised by Reichardt, accounts for the functional properties of the neurophysiological system. The model is a network of linear illters, the weighting functions of which are fitted by analyzing the experi- mental data. It allows a very accurate prediction of insect's responses to previously untested stimulus patterns. The model (Fig. 1) envisages two cross.connected information channels from two input units A and B (the elementary event which evokes an optomotor response consists of a sequence of two light stimuli impinging on two adjacent receptors). The two input elements transform the light stimulus into the time functions LA and LB which are determined by the structure and speed of the pattern. The functions L.A and LB are further transformed by a succession of components that carry out linear transformations, multiplication and time averaging. If we designate with WDF and WDH the weighting functions on the channels and with WGGthe auto- correlation function of the light-flux fluctuation G(t), then we obtain-according to the model and on the basis of all the experimental conclusions-the following expression for the optomotor response 00 00 R(L1t) = J WDP(n) dn JWDH(~) WGG(n-~ -L1t) d~ 0 0 (1) 00 00 - J WDH('Y})dn J WDP(~) WGG('Y} -~ -,1 t) d~ 0 0 the equivalent of which in the frequency domain is 00 R(At) = ! f YDYl (YpYIl- YJ Yu) 8(w) eiwdldO). (2) -00 * Present address: Max-Planck-Institut fUr Biologische Kybernetik, Tiibingen, Germany YD, Yp, Yu are transfer functions of the illters and 8(w) is the spectral density of G(t), related to WGG through the Wiener's theorem. It does not matter if G(t) is a periodic stimulus or a random distribution of light points:. in both cases the predictions fit perfectly the experimental findings (Reichardt, 1969). The exact localization of the anatomical structures underlying the optomotor behaviour is still an un- solved problem. Many aspects however are now quite clear. Some histological sections of the first optic gan- glion -the lamina -have sometimes been considered as an indication that the pattern of fibers from retina to lamina may be isomorphic to the information flow diagram of Fig. 1. As a matter of fact the projection of fibers from neighboring ommatidia in one element of the lamina (cartridge) is well compatible with the Reichardt's scheme. Braitenberg (1967) and Kirsch- feld (1967) demonstrated that this localization cannot be upheld any more. While it is true that fibers from different ommatidia come together in one cartridge, Moving intensity pattern A Y LA $ B Y La E;J Linear filters Ommatidia L* A L* a Linear filters )lH' ~H~ ~ ~ L'AF' Lt!H L"BF. L\H $ $ Multipliers Low - pass filters L'AF' L'SH L'BF' L'AH L'AF . L~H - L:'!3F. L1H Subtraction units +R Fig. 1. Reichardt's model describing stimulus-reaction rela- tions of optomotor responses (from Reichardt, 1969)