December 1961 - Vol. 4 No. 12

Features

Research and Advances

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.
Research and Advances

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.
Research and Advances

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.
Research and Advances

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).

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