Chapter III: Part 3

Figure 10 is largely self-explanatory. Item a is our schematic symbol for a single NPO with n₀ = 1. Items b, d (including larger feedback loops), and f are typical of artificial intelligence networks. Item c is employed to effect the level changing required in order to apply the three channels in cascade algorithm to the solution of one-dimensional coding problems. Observe that items c and e are the only configurations requiring the γ output. Item d may be used as a limiter by making T⁻¹ high compared to the highest frequency present in the signal. Observe that item e is the only application of NPO’s that requires either the ξ₂ or β outputs. Item f serves the purpose of handling higher power levels into and out of what effectively is a single (larger) NPO.

CONCLUSION

The definition of self-organizing behavior suitably represented has permitted the use of Information Theoretic techniques to synthesize a (mathematical) mechanism for a self-organizing machine. Physical mechanization in the form of an NPO has been accomplished and has introduced the experimental phase of the program. From among the many items deserving of further study we may mention: more economical physical mechanization through introduction of modern technology; identification of networks of NPO’s with their group theoretic descriptions; analysis of the dimensionality of tasks which a SOM might be called on to simulate, and prototype SOM applications to related tasks. It is hoped that progress along these lines can be reported in the future.

REFERENCES

1. Ścibor-Marchocki, Romuald I.,
“A Topological Foundation for Self-Organization,”
Anaheim, California:Northrop Nortronics, NSS Report 2828,
November 14, 1963

2. It is true that our definition is very similar to that proposed
by Hawkins (reference 5). Compare for example his definition of
learning machines (page 31 of reference 5). But the subsequent
developments reviewed therein are different from the one we have
followed.

3. Ashby, W. R.,
“The Set Theory of Mechanism and Homeostasis,”
Technical Report 7, University of Illinois, September 1962

4. Ashby, W. R.,
“Systems and Information,”
_Transactions PTGME_ =MIL-7=:94-97 (April-July, 1963)

5. Hawkins, J. K.,
“Self-Organizing Systems—A Review and Commentary,”
_Proc. IRE_. =49=:31-48 (January 1961)

6. Mesarovic, M. D.,
“On Self Organizational Systems,”
Spartan Books, pp. 9-36, 1962

7. Braverman, D.,
“Learning Filters for Optimum Pattern Recognition,”
_PGIT_ =IT-8=:280-285 (July 1962)

8. We make the latter statement despite the fact that we employ a
statistical treatment of self-organization. We may predict the
performance of, for example, the NPO by using a statistical
description, but it does not necessarily follow that the NPO
computes statistics.

9. McCulloch, W. S., and Pitts, W.,
“A Logical Calculus of the Ideas Imminent in Nervous Activity,”
_Bull-Math. Biophys_ =5=:115 (1943)

10. Newell, A., Shaw, J. C., and Simon, H. A.,
“Empirical Explorations of the Logic Theory Machine:
A Case Study in Heuristic,”
_Proc. WJCC_, pp. 218-230, 1957

10a. The spaces W, X, Y, and Z are stochastic spaces; that is,
each space is defined as the ordered pair (X,p(X)) where
p(X) = {p(x) ∋ x ∈ X}, p(x) ≥ 0, x ∈ X and ∫x p(x)dx = 1.
Such spaces possess a metrizable topology.

11. We use the following convention for probability distributions:
if the arguments of p( ) are different, they are different
functions, thus: p(x) ≠ p(y) even if y = x.

12. One can prove the existence of a metric directly but in order
to perform the metrization the space has to be decomposed first.
But decomposing a space without having a metric calls for a neat
trick, accomplished (as far as we know) only by the method used
by the SOM.

12a. In this example we use a hemisphere; in general, it would be
a spherical cap.

A Topological Foundation for Self-Organization

R. I. ŚCIBOR-MARCHOCKI

_Northrop Nortronics_
_Systems Support Department_
_Anaheim, California_

It is shown that by the use of Information
Theory, any metrizable topology may be metrized
as an orthogonal Euclidean space (with a random
Gaussian probability distribution) times
a denumerable random cartesian product of
irreducible (wrt direct product) denumerable
groups. The necessary algorithm to accomplish
this metrization from a statistical basis is
presented. If such a basis is unavailable,
a certain nilpotent projection operator has
to be used instead, as is shown in detail in
the companion paper. This operator possesses
self-organizing features.

INTRODUCTION

In the companion article[8] we will define a self-organizing system as one which, after observing the input and output of an unknown phenomenon (transfer relation), organizes itself into a simulation of the unknown phenomenon.

[8] Kleyn, P. A., “Conceptual Design of Self-Organizing Machines,” Anaheim, California:Northrop Nortronics, NSS Report 2832, Nov. 14, 1963.

Within the mathematical model, the aforementioned phenomenon may be represented as a topological space thus omitting for the moment the (arbitrary) designation of input and output which, as will be shown, bears on the question of uniqueness. Hence, for the purpose of this paper, which emphasizes the mathematical foundation, an intelligent device is taken as one which carries out the task of studying a space and describing it.

In keeping with the policy that one should not ask someone (or something) else to do a task that he could not do himself (at least in principle), let us consider how we would approach such a problem.

In the first place, we have to select the space in which the problem is to be set. The most general space that we feel capable of tackling is a metrizable topology. On the other hand, anything less general would be unnecessarily restrictive. Thus, we choose a metrizable topological space.

As soon as we have made this choice, we regret it. In order to improve the situation somewhat, we show that there is no (additional) loss of generality in using an orthogonal Euclidean space times[9] a denumerable random cartesian product of irreducible (wrt direct product) denumerable groups.

This paper provides a survey of the problem and a method for solving it which is conceptually clear but not very practical. The companion paper[10] provides a practical method for solving this problem by means of the successive use of a certain nilpotent projection operator.

[9] Random cartesian product.

[10] Kleyn, P. A., “Conceptual Design of Self-Organizing Machines,” Anaheim, California:Northrop Nortronics, NSS Report 2832, Nov. 14, 1963.

METRIZATION

We start with a metrizable topological space. There are many equivalent axiomatizations of a metrizable topology; _e.g._, see Kelley. Perhaps the easiest way to visualize a metrizable topology is to consider that one was given a metric space but that he lost his notes in which the exact form of the metric was written down. Thus one knows that he can do everything that he could in a metric space, if only he can figure out how.

The “figuring out how” is by no means trivial. Here, it will be assumed that a cumulative probability distribution has been obtained on the space by one of the standard methods; bird in cage,[11] Munroe I,[12] Munroe II,[13] ordering (see Halmos[14] or Kelley[15]). This cumulative probability distribution is a function on X onto the interval [0,1] of real numbers. The inverse of this function, which exists by the Radon Nikodym theorem, provides a mapping from the real interval onto the non-trivial portion of X. This mapping induces all of the pleasant properties of the real numbers on the space X: topological, metric, and ordering.

Actually, it turns out that, especially if the dimensionality of the space is greater than one, the foregoing procedure not only provides one metrization, but many. Indeed, this lack of uniqueness is what makes the procedure exceedingly difficult. Only by imposing some additional conditions that result in the existence of a unique solution, does the problem become tractable.

We choose to impose the additional condition that the resulting metric space be a Euclidean geometry with a rectangular coordinate system.

[11] Harman, W. W., “Principles of the Statistical Theory of Communication,” New York, New York:McGraw-Hill, 1963.

[12] Munroe, M. E., “Introduction to Measure and Integration,” Cambridge, Mass.:Addison-Wesley, 1953.

[13] Munroe, M. E., “Introduction to Measure and Integration,” Cambridge, Mass.:Addison-Wesley, 1953.

[14] Halmos, P. R., “Measure Theory,” Princeton, New Jersey:D. Van Nostrand Co., Inc., 1950.

[15] Kelley, J. L., “General Topology,” Princeton, New Jersey:D. Van Nostrand Co., Inc., 1955.

Even this always does not yield uniqueness, but we will show the additional restriction that will guarantee uniqueness after the necessary language is developed. Since all metrizations of a given metrizable topology are isomorphic, in the quotient class the orthogonal Euclidean geometry serves the purpose of being a convenient representative of the unique element resulting from a given metrizable topology.

Furthermore, the same comment applies to the use of a Gaussian distribution as the probability distribution on this orthogonal Euclidean geometry. Namely, the random Gaussian distribution on an orthogonal Euclidean geometry is a convenient representative member of the equivalence class which maps into one element (stochastic space) of the quotient class.

Information Theory

Now, we will show that Information Theory provides the language necessary to describe the metrization procedure in detail.

It is possible to introduce Information Theory axiomatically by a suitable generalization of the axioms[16] in Feinstein.[17] But to simplify the discussion here, we will use the less elegant but equivalent method of defining certain definite integrals. The probability density distribution p is defined from the cumulative probability distribution P by

P(X′) = ∫X′_{measurable ⊂ X} p(x)dx. (1)

Then the information rate H is defined as

H(X) = -∫ₓp(x) ln κ p(x)dx (2)

where kappa has (carries) the units of X. Finally,
the channel rate R is defined as

R(⨀Xᵢ) = ΣH(Xᵢ) - H(X), (3)
I I

where X is the denumerable[18] cartesian product space

X = ⨂Xᵢ. (4)
I

[16] Feinstein uses his axioms only in finite space X; _i.e._, card(X) < K₀.

[17] Feinstein, A., “Foundations of Information Theory,” New York, New York: McGraw-Hill, 1958.

[18] If I is infinite, certain precautions have to be exercised.

Next, we define the angle Θ

|Θ(⨀Xᵢ)| = sin⁻¹_e_^{-R(⨀Xᵢ)} (5)
I
and the norm

|X| = κ(2π_e_)⁻¹ᐟ² _e_^{(HX)}. (6)

Now, if[19] a statistically independent basis; _i.e._, one for which
κ
R(⨀Xᵢ) ≡ constant, (7)
I

can be provided in terms of one-dimensional components; _i.e._, none of them can be decomposed further, then it is just the usual problem of diagonalization of a symmetric matrix by means of a congruence transformation to provide an orthogonal coordinate system. Furthermore, for uniqueness, we arrange the spectrum in decreasing order. Then, by means of the Radon Nikodym theorem applied to each of these one-dimensional axes, the probability distribution may be made; _e.g._, Gaussian, if desired. Thus, we obtain the promised orthogonal Euclidean space.

[19] This “if” is the catch that makes all methods of metrization of a space of dimensionality higher than one impractical, except the method of successive projections upon unit spheres centered at the center of gravity. The method of using that nilpotent projection operator is described in the companion paper(see footnote page 65).

Channel

At this time we can state the remaining additional condition required that a decomposition be unique. The index space I has to be partitioned into exactly two parts, say I′ and I″; _i.e._,

I′ ∪ I″ = I (8)

I′ ∩ I″ = φ,

such that

dim(X′) = dim(X″), (9)

where

X′ = ⨂Xᵢ (10)
I′

X″ = ⨂Xᵢ.
I″

(If dim (X) is odd, then we have to cheat a little by putting in an extra random dummy dimension.) And then the decomposition of the space

X = ⨂Xᵢ (11) I

has to be carried out so that this partitioning is preserved. Since this partitioning is arbitrary (as far as the mathematics is concerned), it is obvious that a space which is not partitioned will have many (equivalent) decompositions. On the other hand, if the partitioning is into more than two parts, then the existence of a decomposition is not guaranteed.

A slight penalty has to be paid for the use of this partitioning, namely: instead of eventually obtaining a random cartesian product of one-dimensional spaces, we obtain an extended channel (with random input) of single-dimensional channels. It is obvious that if we were to drop the partitioning temporarily, each such single-dimensional channel would be further decomposed into two random components. This decomposition is not unique. But one of these equivalent decompositions is particularly convenient; namely, that decomposition where we take the component out of the original X′ and that which is random to it, say V. This V (as well as the cartesian product of all such V’s, which of necessity are random) is called the linearly additive noise. The name “linearly additive” is justified because it is just the statistical concept isomorphic to the linear addition of vectors in orthogonal Euclidean geometry. (The proof of this last statement is not completed as yet.)

Denumerable Space

The procedure for this decomposition was worded to de-emphasize the possible presence of a denumerable (component of the) space. Such a component may be given outright; otherwise, it results if the space was not simply connected. Any denumerable space is zero dimensional, as may be verified easily from the full information theoretic definition of dimensionality.

The obvious way of disposing of a denumerable space is to use the conventional mapping that converts a Stieltjes to a Lebesque integral, using fixed length segments. (It can be shown that H is invariant under such a mapping.) Unfortunately, while this mapping followed by a repetition of the preceding procedure will always solve a given problem (no new[20] denumerable component _need_ be generated on the second pass), little insight is provided into the structure of the resulting space. On the other hand, because channels under cascading constitute a group, any such denumerable space is a representation of a denumerable group.

[20] Only non-cyclic irreducible (wrt direct product) denumerable group components of the old denumerable space will remain.

SUMMARY

In summary, the original metrizable topological space was decomposed into an orthogonal Euclidean space times[21] a denumerable random cartesian product of irreducible (wrt direct product) denumerable groups. Thus, since any individual component of a random cartesian product may be studied independently of the others, all that one needs to study is: (1) a Gaussian distribution on a single real axis and (2) the irreducible denumerable groups.

[21] Random cartesian product.

Finally, it should be emphasized that there are only these two ways of decomposing a metrizable topology; (1) if a (statistical) basis is given, use the diagonalization of a symmetric matrix algorithm described earlier (and given in detail in the three channels in cascade problem), and (2) otherwise use a suitable network of the NPO’s with n₀=1. Of course, any hybrid of these two methods may be employed as well.

On Functional Neuron Modeling

C. E. HENDRIX

_Space-General Corporation_
_El Monte, California_

There are two very compelling reasons why mathematical and physical models of the neuron should be built. Model building, while widely used in the physical sciences, has been largely neglected in biology. However, there can be little doubt that building neuron models will increase our understanding of the function of real neurons, if experience in the physical sciences is any guide. Secondly, neuron models are extremely interesting in their own right as new technological devices. Hence, the interest in, and the reason for symposia on self-organizing systems.

We should turn our attention to the properties of real neurons, and see which of them are the most important ones for us to imitate. Obviously, we cannot hope to imitate _all_ the properties of a living neuron, since that would require a complete simulation of a living, metabolizing cell, and a highly specialized one at that; but we can select those functional properties which we feel are the most important, and then try to simulate those.

The most dramatic aspect of neuron function is, of course, the axon discharge. It is this which gives the neuron its “all-or-nothing” character, and it is this which provides it with a means for propagating its output pulses over a distance. Hodgkin and Huxley (1) have developed a very complete description of this action. Their model is certainly without peer in describing the nature of the real neuron.

On the technological side, Cranes’ “neuristors” (2) represent a class of devices which imitate the axonal discharge in a gross sort of way, without all the subtle nuances of the Hodgkin-Huxley model. Crane has shown that neuristors can be combined to yield the various Boolean functions needed in a computer.

However, interesting as such models of the axon are, there is some question as to their importance in the development of self-organizing systems. The pulse generation, “all-or-nothing” part of the axon behavior could just as well be simulated by a “one-shot” trigger circuit. The transmission characteristic of the axon is, after all, only Nature’s way of sending a signal from here to there. It is an admirable solution to the problem, when one considers that it evolved, and still works, in a bath of salt water. There seems little point, however, in a hardware designer limiting himself in this way, especially if he has an adequate supply of insulated copper wire.

If the transmission characteristic of the axon is deleted, the properties of the neuron which seem to be the most important in the synthesis of self-organizing systems are:

a. The neuron responds to a stimulus with an electrical
pulse of standard size and shape. If the stimulus
continues, the pulses occur at regular intervals
with the rate of occurrence dependent on the
intensity of stimulation.

b. There is a threshold of stimulation. If the
intensity of the stimulus is below this threshold,
the neuron does not fire.

c. The neuron is capable of temporal and spatial
integration. Many subthreshold stimuli arriving at
the neuron from different sources, or at slightly
different times, can add up to a sufficient level to
fire the neuron.

d. Some inputs are excitatory, some are inhibitory.

e. There is a refractory period. Once fired, there is
a subsequent period during which the neuron cannot
be fired again, no matter how large the stimulus.
This places an upper limit on the pulse rate of any
particular neuron.

f. The neuron can learn. This property is conjectural
in living neurons, since it appears that at
the present time learning has not been clearly
demonstrated in isolated living neurons.
However, the learning property is basic to all
self-organizing models.

Neuron models with the above characteristics have been built, although none seem to have incorporated _all_ of them in a single model. Harman (3) at Bell Labs has built neuron models which have the characteristics (a) through (e), with which he has built extremely interesting devices which simulate portions of the peripheral neuron system.

Various attempts at learning elements have been made, perhaps best exemplified by those of Widrow (4). These devices are capable of “learning,” but are static, and lack all the temporal characteristics listed in (a) through (e). Such devices can be used to deal with temporal patterns only by a mapping technique, in which a temporal pattern is converted to a spatial one.

Having listed which seem to be the important properties of a neuron, it is possible to synthesize a simple model which has all of them.

A number of input stimuli are fed to the neuron through a resistive summing network which establishes the threshold and accomplishes spatial integration. The voltage at the summing junction triggers a “one-shot” circuit, which, by its very nature, accomplishes pulse generation and exhibits temporal integration and a refractory period. The polarity of an individual input determines whether it shall be excitatory or inhibitory. This much of the circuitry is very similar to Harmon’s model.

Learning is postulated to take place in the following way: when the neuron fires, an outside influence (the environment, or a “trainer”) determines whether or not the result of firing was desirable or not. If it was desirable, the threshold of the neuron is lowered, making it easier to fire the next time. If the result was not desirable, the threshold is raised, making it more difficult for the neuron to fire the next time.

In a self-organizing system, many model neurons would be interconnected. A “punish-reward” (P-R) signal would be connected to all neurons in common. However, means would be provided for only those which have recently fired to be susceptible to the effects of the P-R signal. Therefore, only those which had taken part in a recent response are modified. This idea is due to Stewart (5), who applies it to his electrochemical devices instead of to an electronic device.

The mechanization of the circuitry is rather straight-forward. A portion of the output of the pulse generator is routed through a “pulse-stretcher” or short-term memory which temporarily records the fact that the neuron has recently fired. The pulse-stretcher output controls a gate, which either accepts or rejects the P-R signal. The P-R signal can take on only three values, a positive level, zero, or a negative level, depending on whether the signal is “punish,” “no action,” or “reward.” Finally, the gate output controls a variable resistor, which is part of the resistive summing network. Figure 1 is a block diagram of the complete model.

Note that this device differs from the usual “Perceptron” configuration in that the threshold resistor is the only variable element, instead of having each input resistor a variable weighting element. This simplification could lead to a situation where, to prepare a specified task, more single-variable neurons would be required than would multivariable ones. This possible disadvantage is partially, at least, offset by the very simple control algorithm which is contained in the design of the model, and is not the matter of great concern which it seems to be for most multivariable models.

Hand simulations of the action of this type of model suggest that a certain amount of randomness would be desirable. It appears that a self-organizing system built of these elements, and of sufficient complexity to be interesting, would have a fair number of recirculating loops, so that spontaneous activity would be maintained in the absence of input stimulus. If this is the case, then randomness could easily be introduced by adding a small amount of noise from a random noise generator to the signal on the P-R bus. Thus, any neurons which spontaneously fire would be continually having their thresholds modified.

The mechanization of the model is not particularly complex, and can be estimated as follows: The one-shot pulse generator would require two transistors, the pulse stretcher one more. The bi-directional gate would require a transistor and at least two diodes.

Several candidates for the electrically-controllable variable resistor are available (6). Particularly good candidates appear to be the “Memistor” or plating cell developed by Widrow (7), the solid state version of it by Vendelin (8), and the “solion” (9). All are electrochemical devices in which the resistance between two terminals is controlled by the net charge flow through a third terminal. All are adaptable to this particular circuit.

Of the three, however, the solion appears at first glance to have the most promise in that its resistance is of the order of a few thousand ohms (rather than the few ohms of the plating cells) which is more compatible with ordinary solid-state circuitry. Solions have the disadvantage that they can stand only very low voltages (less than 1 volt) and in their present form require extra bias potentials. If these difficulties can be overcome, they offer considerable promise.

In summary, it appears that a rather simple neuron model can be built which can mimic most of the important functions of real neurons. A system built of these could be punished or rewarded by an observer, so that it could be trained to give specified responses to specified stimuli. In some cases, the observer could be simply the environment, so that the system would learn directly from experience, and would be therefore a self-organizing system.

REFERENCES

1. Hodgkin, A. L., and Huxley, A. L.,
“A Quantitative Description of Membrane Current and its
Application to Conduction and Excitation in Nerve,”
_J. Physiol._ =117=:500-544 (August 1952)

2. Crane, H. D.,
“Neuristor—A Novel Device and System Concept,”
_Proc. IRE_ =50=:2048-2060 (Oct. 1962)

3. Harmon, L. D., Levinson, J., and Van Bergeijk, W. A.,
“Analog Models of Neural Mechanism,”
_IRE Trans. on Information Theory_ =IT-8=:107-112
(Feb. 1962)

4. Widrow, B., and Hoff, M. E.,
“Adaptive Switching Circuits,”
Stanford Electronics Lab Tech Report 1553-1, June 1960

5. Stewart, R. M.,
“Electrochemical Wave Interactions and Extensive Field Effects
in Excitable Cellular Structures,”
First Pasadena Invitational Symposium on Self-Organizing Systems,
Calif. Institute of Technology, Pasadena, Calif., 14 Nov. 1963

6. Nagy, G.,
“A Survey of Analog Memory Devices,”
_IEEE Trans. on Electronic Cmptrs._ EC-12:388-393 (Aug. 1963)

7. Widrow, B.,
“An Adaptive Adaline Neuron Using Chemical Memistors,”
Stanford Electronics Lab Tech Report 1553-2, Oct. 1960

8. Vendelin, G. D.,
“A Solid State Adaptive Component,”
Stanford Electronics Lab Tech Report 1853-1, Jan. 1963

9. “Solion Principles of Electrochemistry and Low-Power
Electrochemical Devices,”
Dept. of Comm., Office of Tech. Serv. =PB= 131931
(U. S. Naval Ord. Lab., Silver Spring, Md., Aug. 1958)

Selection of Parameters for Neural Net Simulations[22]

R. K. OVERTON

_Autonetics Research Center_
_Anaheim, California_

Research of high quality has been presented at this Symposium. Of particular interest to me were the reports of the Aeronutronic group and the Librascope group. The Aeronutronic group was commendably systematic in its investigations of different arrangements of linear threshold elements, and the Librascope data, presenting the effects of attaching different values to the parameters of simulated neurons, are both systematic and interesting.

Unfortunately, however, interest in such research can obscure a more fundamental question which seems to merit study. That question concerns the parameters, or attributes, which describe the simulated neuron. Specifically, which parameters or attributes should be selected for simulation? (For example, should a period of supernormal sensitivity be simulated following an absolutely refractory period?)

Some selection obviously has to be made. Librascope, which is trying to simulate neurons more or less faithfully, plans to build a net of ten simulated neurons. In contrast, General Dynamics/Fort Worth, with roughly the same degree of effort, is working with 3900 unfaithfully-simulated neurons. This comparison is not a criticism of either group; the Librascope team has simply selected many more parameters for simulation than has the General Dynamics group. Each can make the selections it prefers, because the parameters of real neurons which are necessary and sufficient for learning have not been exhaustively identified.

From the point of view of one whose interests include real neurons, this lack of identification is unfortunate. I once wrote a book which included some guesses about the essential attributes of neurons. Since that time, many neuron simulation programs have been written. But these programs, although interesting and worthwhile in their own right, have done little to answer the question of the necessary parameters. That is, they do not make much better guesses possible. And yet better guesses would also make for more “intelligent” machines.

[22] This paper, submitted after the Symposium, represents a more detailed presentation of some of the issues raised in the discussion sessions at the Symposium and hence, constitutes a worthwhile addition to the Proceedings.

INDEX OF INVITED PARTICIPANTS

MICHAEL ARBIB Massachusetts Institute of Technology
ROBERT H. ASENDORF Hughes Research Laboratories/ Malibu
J. A. DALY Astropower/Newport Beach
GEORGE DeFLORIO System Development Corp./Santa Monica
DEREK H. FENDER California Institute of Technology
LEONARD FRIEDMAN Space Technology Labs./Redondo Beach
JAMES EMMETT GARVEY ONR/Pasadena
THOMAS L. GRETTENBERG California Institute of Technology
HAROLD HAMILTON Librascope/Glendale
JOSEPH HAWKINS Aeronutronic/Newport Beach
CHARLES HENDRIX Space-General Corp./El Monte
R. D. JOSEPH Astropower/Newport Beach
PETER A. KLEYN Nortronics/Anaheim
JOHN KUHN Space-General Corp./El Monte
FRANK LEHAN Space-General Corp./El Monte
EDWIN LEWIS Librascope/Glendale
PETER C. LOCKEMANN California Institute of Technology
GILBERT D. McCANN California Institute of Technology
C. J. MUNCIE Aeronutronic/Newport Beach
C. OVERMIER Nortronics/Anaheim
RICHARD K. OVERTON Autonetics/Anaheim
DIANE RAMSEY Astropower/Newport Beach
RICHARD REISS Librascope/Glendale
R. I. ŚCIBOR-MARCHOCKI Nortronics/Anaheim
JAMES J. SPILKER Philco/Palo Alto
ROBERT M. STEWART Space-General Corp./El Monte
HENNIG STIEVE California Institute of Technology
RICHARD TEW Space-General Corp./El Monte
JOHN THORSEN University of California/Los Angeles
RICHARD VINETZ Librascope/Glendale
CHRISTOPH von CAMPENHAUSEN California Institute of Technology
DAVID VOWLES California Institute of Technology
HORST WOLF Astropower/Newport Beach

U.S. GOVERNMENT PRINTING OFFICE: 1966 O—205-502