The optimum capacity of a cache memory with given access time is determined analytically based upon a model of linear storage hierarchies wherein both the hit ratio function and the device technology-cost function are assumed to be power functions. Explicit formulas for the capacities and access times of the storage levels in the matching hierarchy of required capacity and allowable cost are derived. The optimal number of storage levels in a hierarchy is shown to increase linearly with the logarithm of the ratio of the required hierarchy capacity and the cache capacity.

A method is developed for the reconstruction of a two-dimensional convex symmetric object from two orthogonal projections. To reconstruct a three-dimensional object, the object is divided into thin slices and the slices are individually reconstructed. An experimental result of the reconstruction of a clay model from its X-ray pictures is described. Applicability of this technique to cardiac cineangiography is discussed.

We demonstrate in this correspondence that the procedure introduced by Chow and Liu for estimating tree-dependent probability distributions is consistent.

The performance of a pattern recognition system is characterized by its error and reject tradeoff. This paper describes an optimum rejection rule and presents a general relation between the error and reject probabilities and some simple properties of the tradeoff in the optimum recognition system. The error rate can be directly evaluated from the reject function. Some practical implications of the results are discussed. Examples in normal distributions and uniform distributions are given.

A method is presented to approximate optimally ann-dimensional discrete probability distribution by a product of second-order distributions, or the distribution of the first-order tree dependence. The problem is to find an optimum set ofn - 1first order dependence relationship among thenvariables. It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information. It is further shown that when this procedure is applied to empirical observations from an unknown distribution of tree dependence, the procedure is the maximum-likelihood estimate of the distribution.

The memory we describe here is a logical and practical outgrowth of the content addressable distributed logic memory of Lee and Paull.1 However, there are several significant differences: the inclusion of a "match" flip-flop and a "control" flip-flop in each cell of the memory, the addition of a "Mark" line to activate many cells simultaneously, and the control of the propagation of the marking signal. As a consequence of these, the memory has some novel capabilities, among which are the ability to simultaneously shift the contents of a large group of cells, thus opening or closing a gap in the memory, and the ability to simultaneously mark strings of interest in separate parts of the memory.

Within the framework of an early paper1 which considers character recognition as a statistical decision problem, the detailed structure of a recognition system can be systematically derived from the functional form of probability distributions. A binary matrix representation of signal is used in this paper. A nearest-neighbor dependence method is obtained by going beyond the usual assumption of statistical independence. The recognition network consists of three levels-a layer of AND gates, a set of linear summing networks in parallel, and a maximum selection circuit. Formulas for weights or recognition parameters are also derived, as logarithms of ratios of conditional probabilities. These formulas lead to a straightforward procedure of estimating weights from sample characters, which are then used in subsequent recognition. Simulation of the recognition method is performed on a digital computer. The program consists of two main operations-estimation of parameters from sample characters, and recognition using these estimated values. The experimental results indicate that the effect of neighbor dependence upon recognition performance is significant. On the basis of a rather small sample of 50 sets of hand-printed alphanumeric characters, the recognition performance of the nearest-neighbor method compares favorably with other recognition schemes.

The character recognition problem, usually resulting from characters being corrupted by printing deterioration and/or inherent noise of the devices, is considered from the viewpoint of statistical decision theory. The optimization consists of minimizing the expected risk for a weight function which is preassigned to measure the consequences of system decisions As an alternative minimization of the error rate for a given rejection rate is used as the critenon. The optimum recogition is thus obtained. The optimum system consists of a conditional-probability densisities computer; character channels, one for each character; a rejection channel; and a comparison network. Its precise structure and and ultimate performance depend essentially upon the signals and noise structure. Explicit examples for an additive Gaussian noise and a ``cosine'' noise are presented. Finally, an error-free recognition system and a possible criterion to measure the character style and deteriortation are presented.