On the biophysics of vision

A photochemical system is considered which is similar to that of S. Hecht but which includes an intermediate substance between visual purple and visual white. This intermediate is assumed to change the embrane voltage of the photoreceptors. A simple model is presented from which one may calculate the frequency of the impulses resulting from the application of light. It is found that this physicochemicai model enables one to account for a considerable number of physiological phenomena of vision. Among these are the light and dark adaptation phenomena. By introducing a simple assumption regarding spatial interaction one can account for some psychological phenomena such as the effect of intensity, light-dark ratio, shape, and area on the critical flicker frequency. A number of other phenomena are discussed in terms of the model. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 18(600)-1454. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

Note on the fusion frequency for stimuli of alternating duration

The case of alternating stimulus patterns of moderately high intensity is considered in terms of the model previously discussed (Landahl, 1957,Bull. Math. Biophysics,19, 157–62). If both of the alternating patterns have the same light-dark ratio, then the relation between the period of the longer and the period of the shorter pattern at the critical flicker frequency is independent of the light-dark ratio and is given by a dimensionless expression which is roughly in agreement with data in which the light-dark ratio is one (C. R. Brown and D. M. Forsyth, 1959,Science,129, 390–91). This research was supported in whole or in part by the U. S. Air Force under Contract AF 49(638)-414 monitored by the Air Force Office of Scientific Research.     

On some distribution functions for non-linear switching elements with finite dead time

Summary The output distribution function of a non-linear switching element with a Poissonian sequence of impulses at the input is calculated by a straightforward method. The dead time of the element is taken into account. Some limiting properties of this distribution and its mean value are studied.The present research has been sponsored in part by the Air Force Avionics Lab., Research and Technology Div., Wright-Patterson Air Force, Air Force System Command — U.S.A.F. — Government of United States of America, Contract no. AF 33(615)-2786.     

The transfer function of a photoreceptor organ

summary The dynamic response of a simple ganglionic photoreceptor has been studied. It exemplifies the general processes of sensory reception and transmission of sensory information in the form of trains of nerve impulses. The experimental basis of the defining linear transfer function is presented. This transfer function is composed of a second order lag and a transport delay. The ventral nerve cord conduction time does not contribute to the transport delay. Nonlinear discrepancies from the linear model are evaluated and discussed.This research is supported in part by the Air Force (AF-33(616)-7282); the Office of Naval Research [Nonr-609(39)]: the Army Chemical Corp. (Da-18-108-405-Cml-942); and the U.S. Public Health Service (B-3055, B-3090).     

A model for conditioning and the effect of spaced trials in learning

A mechanism is suggested in which a postulated substance can enter a synaptic region only during the simultaneous action of a conditioned and an unconditioned stimulus. If this substance remains and produces a physico-chemical change, then a consequence is that the degree of learning will depend on the spacing of conditioning trials and the time constant of the process will be related to the rate of diffusion or transport of the substance along the axon. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Contract No. AF 49(638)-414.     

A neural net model for escape learning

An escape learning situation is discussed in terms of a neural model in which a stimulus can result in a conditioned excitement and a specific conditioned response. By using the simplest relations between the strengths of conditioning and the number of reinforcements and by introducing a distribution of fluctuations occurring regularly in time, one can calculate the probabilities of various responses, as well as the various latencies, in successive trials. The results are in moderately satisfactory agreement with the data of R. L. Solomon and L. C. Wynne (Psychol. Monogr.,67, No. 4, 1953). Consequences of the model for various experimental situations are discussed. This research was supported in part by the United States Public Health Service Grant RCA GM K6 18,420 and in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Grant No. AF AFOSR 370-64.     

On the interpretation of the effect of area on the critical flicker frequency

The effects of area and intensity on the critical flicker frequency, threshold, and reaction time are considered in terms of neural net theory. An attempt is made to develop a mechanism which can account for the phenomena associated with the empirically observed laws of Ricco, Granit, Talbot, and Ferry-Porter as well as observations on reaction time and threshold. A simple model gives results which are substantially in agreement with observation except for a few apparent discrepancies. Experimental procedures are suggested which can determine whether these are apparent or real. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18(600)-1454. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

Mathematical biophysics of color vision: III. Color constancy

A mechanism is presented which can account for certain aspects of the phenomena of color constancy. The mechanism involves interaction between a given region and the remaining field. Each region is represented by a color center having the structure previously introduced (Landahl, 1952,Bull. Math. Biophysics,14, 317–25) to account for a number of phenomena of color vision. The trichromatic, symmetric mechanism is introduced for simplicity. The interaction is such that collaterals from each of the primaries representing the background send elements to each of the centers corresponding to the primaries representing the spot. However, the collaterals impinging upon unlike centers are excitatory while the collaterals impinging on like centers, corresponding to the same primary colors, are inhibitory. With proper choice of coefficients, the result is that for small changes in illumination, the resulting apparent color is unchanged. However, for greater changes in the color of the illumination, there results a distortion of the apparent color. A number of examples are illustrated numerically. This research was supported in whole or in part by the U. S. Air Force under Contract AF 49(638)-414 monitored by the Air Force Office of Scientific Research.     

A contribution to the study of diffusion of neutral particles through pores

Diffusion through a flat pore into a large open region is proportional to the linear dimension of the pore and not to its area. This was first explained by Brown and Escombe (1900) for a circular pore and is here generalized, by means of a dimensional argument, to include any type of regular opening. The problem is further generalized to include diffusion through pores of finite thickness, finite distance apart, and into finite regions. Since this problem cannot be solved exactly, an approximation method is introduced. Reasons for the credibility of the approximation are presented. It is then shown, by means of the approximation method, that the diffusive flow through a pore is equal to the total concentration difference divided by the resistance of the system. The resistance, in turn, is the sum of the resistances of all portions of the system, each of which is calculated. The result is compared with results which have been calculated exactly for limiting cases and found to agree very well. The results are then applied to a standard method of computing pore size in membranes, and it is shown that the correction factor is negligible. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 49(638)-414. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

Oscillations and multiple steady states in a cyclic gene model with repression

In this paper we study the cyclic gene model with repression considered by H. T. Banks and J. M. Mahaffy. Roughly, the model describes a biochemical feedback loop consisting of an integer number G of single gene reaction sequences in series. The model leads to a system of functional differential equations. We show that there is a qualitative difference in the dynamics between even and odd G if the feedback repression is sufficiently large. For even G, multiple stable steady states can coexist while for odd G, periodic orbits exist.This research was supported in part by the Air Force Office of Scientific Research under Contract #AFOSR-84-0376 and by the US Army Research Office under Contract #DAAG29-84-K-0082     

An avoidance learning situation. A neural net model

A simple avoidance situation is considered in terms of a neural net learning model. Data for the control situation can be represented by an expression having three parameters which determine the initial and the steady state activities together with the transient aspects. The introduction of a learning parameter then allows one to calculate satisfactorily the results obtained in the experimental situation in which shock is applied. This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Grant No. AF AFOSR 370-63 and in part by the United States Public Health Service Grant RCA GM K6 18,420.     

Brain and physics of many-body problems

Summary On the basis of a recent physical theory of many-body problems developped in our Institute, a model of the brain is formulated, and it is shown how some of its typical features, such as learning and memory processes, find therein a natural and simple explanation. In the Appendix a short surview of the necessary mathematical formalism is finally given.A brief outline of the model presented in this paper was unformally given by one of the authors (L.M.R.) at the I.S.P. Neurosciences Research Program; Boulder Colorado, in July 1966.This work has been sponsored in part by: Air Force Avionics Lab., Research and Technology Div., Wright Patterson Air Force, Air Force System Commend-U.S.A.F.-Government of United States of America. Contract No. AF 33(615)-2786.     

On visual adaptation: II. The electroretinogram and the bipolar cells

First a model for theb-wave of the electroretinogram is given. The essential part of the model is the diffusion into the rod-bipolar synapse of a transmitter substance, followed by the induction of an inhibitor. Making use of this model, adaptation to an illumination too weak to cause of significant decrease in the concentration of visual pigment is interpreted as due to a decreased effectiveness of the rod impulse in exciting the bipolar cell. The disparity between threshold changes for very small test spots and for relatively large spots is explained simply, without invoking any additional physiological mechanisms. This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Contract No. AF(638)-414 and in part by the United States Public Health Service Training Grant 2G-833.     

Neuromuscular junctions in the buccal mass of Aplysia: Fine structure and electrophysiology of excitatory transmission

The lower extrinsic protractor muscle in the buccal mass of Aplysia consists of bundles of muscle fibers 4–12 m̈ in diameter, containing thick and thin filaments that are not arranged in a transversely striated pattern. Individual fibers come close to one another and form specialized junctional regions. Electrophysiological evidence indicates that the muscle fibers form an electrical syncytium. Muscle bundles are innervated by more than one excitatory axon at a number of points along their length. The presynaptic terminals contain spherical electron-lucent vesicles and a few larger electron-dense vesicles. There are no obvious structural postsynaptic specializations. Graded contraction can result from summation of excitatory junctional potentials in separate axons or from summation and facilitation of junctional potentials from a single axon. The buildup of facilitation during a train of stimuli results from the linear summation of facilitation remaining from preceding impulses.     

Decision equation for binary systems. Application to neuronal behavior

Summary The exact mathematical treatment is given for a non linear equation describing the delayed yes-or-no response to a binary system to external stimulations, in some typical cases of interest. Comparison is made with neurophysiological data on the frequency rate of firings of stimulated neurons; the same equation, however, can be conceivably applied to a vast variety of phenomena. The procedures followed to solve the problems that arise in connection with this equation could be extended to more general types of non linear equations.The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research under Contract no. AF EOAR 65-44 through the European Office of Aerospace Research, OAR, United States Air Force.     

On visual adaptation: I. Photochemistry

Quantitative aspects of the photochemistry of visual adaptation are considered. A simplied model is given that fits data on changes of rhodopsin concentration during and following strong illumination. A variation on Wald’s compartment hypothesis is shown to fit the quasilinear dependence of log threshold upon pigment concentration. Finally, there is a brief review of pertinent data on cone pigments. This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Contract No. AF(638)-414, and in part by the United States Public Health Service Training Grant 2G-833.     

Environmental objections to the PAVE PAWS radar system: a scientific review

As part of our continental defense system, the United States Air Force has operated a radar system, known generally by the label PAVE PAWS, off of Cape Cod, MA since 1978. Some populated areas in the vicinity of the system are subject to a low level of background radiofrequency radiation from the system, and local citizens' groups have expressed concern that this radiofrequency radiation may affect their health. These concerns have been fueled by presentations and letters by Dr. R. A. Albanese, an applied mathematician at the Air Force Research Laboratory, who has proposed standards by which that PAVE PAWS radiofrequency radiation which is incident on populations should be judged. I discuss those standards that are sufficiently well defined to be subject to analysis and show that they are not based on sound quantitative reasoning.     

Koinzidenzfilter mit kurzen Impulsen

Summary Coincidence filters consist of one or more threshold elements (e.g. neurons or monostable multivibrators, extended by multiple input gates). They permit the propagation of an impulse train applied to the input only if its repetition rate does not exceed an upper and a lower boundary value. The difference between the upper and the lower boundary value may be defined as the functional bandwidth of the coincidence filter. The functional bandwidth is one of the most interesting characteristic figures of a coincidence filter. By means of this definition, the coincidence filter may be described as a device selecting quickly those impulse trains the repetition rates of which lie within the functional bandwidthThe functional bandwidth depends on the parameters of the impulse trains and of the coincidence filter. This gives rise to the question, which minimal bandwidth could be realized by coincidence filters.On the initiation by Tischner the properties of coincidence filters operated by rectangular impulses have been investigated by Schie f and by Kosel. Rectangular impulses have the advantage, that moderate variations of the amplitudes do not disturb the coincidence. In this case however very small impulse durations are required for the realization of small bandwidth.In the present paper the operation of coincidence filters by non rectangular impulses has been considered. Having the shape of an excitatory post-synaptic potential of motoneurons, the impulses are completely determined by the rising phase and the falling phase. These impulses have been termed short impulses in contrast to the rectangular impulses, which are long, compared to the duration of their rising and falling phases. The width of the short impulses decreases with increasing measuring level. Close to the amplitude the width becomes very small, which theoretically provides a very small functional bandwidth. The practical realization of very small functional bandwidth is heavily limited by the big variations which will be caused by minute alterations of the amplitudes as introduced by noise. The variation of the functional bandwidth caused by 1% alteration of the amplitude has been termed the error factor. In the present paper some relationships between the following four quantities have been worked out: realizable functional bandwidth, tolerable variation of functional bandwidth, error factor, and given variation of the amplitudes and thresholds (noise).The short impulses have been piecewise approximated by analytical functions (parabolic and hyperbolic) which in general permits an analytical treatment of the problems.     

Contributions to the theory of active transport: II. The gate type non-carrier mechanism and generalizations concerning tracer flow,efficiency, and measurement of energy expenditure

The gate type non-carrier mechanism, an active transport model, is discussed. In this mechanism, the actively transported particle passes through the gate itself by means of a series of reorganizations of the active transport mechanism. The net rate of transport, the rate of transport in either direction, and the efficiency of this model are analyzed. It is shown that on the basis of these analyses alone, this mechanism cannot be distinguished from a carrier mechanism. Three generalizations which apply to many individual type active transport models are then discussed. These pertain to (1) the dependency of the flow in one direction on the cencentration of the particles on the opposite side of the membrane, (2) the possibility of very high efficiencies for these models independent of the rate of the active transport, and (3) the methods whereby the energy expended in the active transport may be experimentally found. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18(600)-1454. Reproduction in whole or in part is permitted for any purpose of the United States Government.