# December 1961 - Vol. 4 No. 12

## Features

What is proprietary in mathematical programming?— impressions of a panel discussion

A panel discussion on “What is Proprietary in Mathematical Programming?” was sponsored by the Special Interest Committee on Mathematical Programming of the ACM during a Hall of Discussion/on September 7th at the 16TH National ACM meeting in Los Angeles. This note consists solely of the impressions garnered by the moderator of the panel and does not necessarily represent the position of any of the panelists or other participants in the discussion.

n-dimensional codes for detecting and correcting multiple errors0

The paper introduces a new family of codes for detecting and correcting multiple errors in a binary-coded message. The message itself is arranged (conceptually) into a multidimensional rectangular array. The processes of encoding and error detection are based upon parity evaluations along prescribed dimensions of the array. Effectiveness of the codes is increased by introducing a “system check bit”, which is essentially a parity check on the other parity bits. Only three-dimensional codes are discussed in this paper, with parity evaluations along the horizontal, the vertical, and one main diagonal. However, the family of codes is not restricted to three dimensions, as evidenced by the discussion by Minnick and Ashenhurst on a similar multidimensional single-bit selection plan used for another purpose [6]. A four-dimensional code, correcting three and detecting four errors, has been developed; the extension to higher-dimensional codes with greater correction power is straightforward.

Notes on geometric weighted check digit verfication

This note describes a method for utilizing geometric weight modulus 11 checking digits on a computer which does not have either multiplication or division. In addition some attempt has been made to show some limitations of this system.

Machine calculation of moments of a probability distribution

A method is presented for the calculation on a machine of the moments of a probability distribution, necessitating little more than n additions and n references to memory for each moment, instead of the minimum of n multiplication, 2n additions, and 2n references to memory required by the most straightforward method (where n is the number of entries in the probability distribution). The method is directly applicable when a tabulated distribution exists, as when it has been computed by repeated convolution; but in this case it conserves both time and accuracy.

Inefficiency of the use of Boolean functions for information retrieval systems

In this note we attempt to point out why boolean functions are, in general, not applicable in information retrieval systems.

Simulation and analysis of biochemical systems: I. representation of chemical kinetics

In the study of problems in chemical kinetics in ordinary solution, reactions which may be represented by chemical equations of the form3 A + B = C + D (1) are represented kinetically by the differential equations d(C)/dt = d(D/dt = -d(A)/dt = - d(B)/dt = k(A)(B) (2) where (A), (B), (C), ··· , are the concentrations of A, B, C, ··· , and k is the kinetic constant for the reaction (assuming it to be occurring in ordinary solution).

Soviet cybernetics and computer sciences, 1960

This article records observations on Soviet research and technology in cybernetics and computer science, made by the author during a visit to the Soviet Union as a delegate to the IFAC Congress on Automatic Control held in Moscow in the summer of 1960.