The use of evolutionary programming to train a neural network is addressed by examining a simple classification problem involving two populations of interest. The first follows a Gaussian distribution having zero means and unit variance; the second is also Gaussian, but with a mean of one and unit variance. Ten independent samples are drawn from either one of the populations with the objective being to properly identify the appropriate underlying distribution. A network consisting of 10 input nodes, a single hidden layer of 10 nodes, and a final classifying node was constructed. To train the network, evolutionary programming was used to minimize the sum of the squared differences between each target output and the actual network output. A population of 10 parent vectors representing the 121 weights and biases of the network was maintained, and the limit of evolution was chosen to be 1000 generations. A training set of 100 patterns, 50 from each population, was determined randomly and then fixed for the extent of the evolution. The results indicate that evolutionary programming is useful for discovering the optimal set of weights in a neural network

It is the unique decision-making ability which makes the human operator particularly suited to accomplish flight control computation. His decisions range from the simplest repetitive determination of control actions, each intended to minimize the error, to complex problems of the sequential reprogramming of all the lower levels of decision which, in totality, comprise his information transduction process. The human sensory-input and motor-output channels must be properly used in order to insure maximum efficiency of the over-all human computer. The perceived noise can only be separated from the signal after the decision-making operation to be performed has been clearly identified. Human noise filter and information handling rate characteristics may be enhanced through the utilization of inherent qualities of the various input and output channels. A brief summary is made of the considerable effort which has been devoted toward the development of mathematical models for human tracking. It is emphasized that the human decision-making ability must be incorporated into the model before a realistic representation can be attained. A stochastic model is considered which is constructed in a heuristic manner, incorporating the decision-making ability. Specific direction is indicated which may yield the most fruitful approach to the mathematical analysis of human flight control computation. This future model would be of great value as a link between the related work in the fields of neurophysiology, biophysics, and psychology. Most important, it should provide a cockpit synthesis technique which will aid the design of future manned aircraft.

The sampling theorem is recognized as an interpolation formula. Starting from the Lagrange Polynomial, this theorem is developed under conditions which are of broader applicability than those usually stated. Such a view point indicates the essential unity of temporal and frequency domain application. It will also be shown that the theorem is applicable as an exact interpolation formula throughout the complex plane. The basic theorem is extended to include sampling of the first derivative of the function. The concept of band-limited functions is introduced through use of Fourier-Stieltjes representations. This is then shown to be subsumed under the general class of functions which is considered in connection with the interpolation theorems developed. This approach, as presented, readily leads to the establishment of many sampling theorems. It is hoped that this paper will aid the formulation of particularly applicable sampling theorems for specific problems.

The human operator often perceives rate as well as amplitude information in sampling various displayed continuous parameters. It is therefore necessary to extend the Sampling Theorem to allow the analysis of certain man-machine relations. The result is stated and the required mathematics included in the Appendix. Certain distinct problem areas where this extension can be employed fruitfully are indicated.