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Artificial Intelligence and Machine Learning

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Research and Advances Jan 1 1964

GIT—a heuristic program for testing pairs of directed line graphs for isomorphism

Given a pair of directed line graphs, the problem of ascertaining whether or not they are isomorphic is one for which no efficient algorithmic solution is known. Since a straightforward enumerative algorithm might require 40 years of running time on a very high speed computer in order to compare two 15-node graphs, a more sophisticated approach seems called for. The situation is similar to that prevailing in areas such as game-playing and theorem-proving, where practical algorithms are unknown (for the interesting cases), but where various practical though only partially successful techniques are available. GIT—Graph Isomorphism Tester—incorporates a variety of processes that attempt to narrow down the search for an isomorphism, or to demonstrate that none exists. No one scheme is relied upon exclusively for a solution, and the program is designed to avoid excessive computation along fruitless lines. GIT has been written in the COMIT language and successfully tested on the IBM 7090.
Research and Advances Jan 1 1964

An efficient composite formula for multidimensional quadrature

A (2s+1)-point, second-degree quadrature formula for integration over an s-dimensional hyper-rectangle is presented. All but one of the points lie on the surface with weights of opposite sign attached to points on opposite faces. When a large volume is subdivided into congruent rectangular subdivisions, only one point is required in each interior subdivision to achieve second-degree accuracy.
Research and Advances Jan 1 1964

On the numerical solution of boundary value problems for linear ordinary differential equations

A numerical method is presented for the solution of boundary value problems involving linear ordinary differential equations. The method described is noniterative and makes use of any one-step numerical integration scheme to reduce the problem from one of boundary values to one of initial values. Comments are made concerning some numerical results of applying the method to a specific problem. In addition an extension of the algorithm described to more general problems is discussed.
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Research and Advances Dec 1 1961

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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Research and Advances Jun 1 1961

On a class of iteration formulas and some historical notes

The class of iteration formulas obtainable by rational approximations of “Euler's formula” is derived with the corresponding error estimates. Some historical notes on iterative procedures are followed by a derivation of Euler's formula with the associated error estimate in a new notation which simplifies the error estimate and suggests generalizations. The final section considers the Padé approximants to the “Euler polynomial” and shows how a number of known formulas may be derived from this unified approach. There is a short discussion of the “best” formula.
Research and Advances May 1 1961

Automatic abstracting and indexing—survey and recommendations

In preparation for the widespread use of automatic scanners which will read documents and transmit their contents to other machines for analysis, this report presents a new concept in automatic analysis: the relative-frequency approach to measuring the significance of words, word groups, and sentences. The relative-frequency approach is discussed in detail, as is its application to problems of automatic indexing and automatic abstracting. Included in the report is a summary of automatic analysis studies published as of the date of writing. Conclusions are drawn that point toward more sophisticated mathematical and linguistic techniques for the solution of problems of automatic analysis.
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Research and Advances Feb 1 1961

Two subroutines for symbol manipulation with an algebraic compiler

The current University of North Carolina version of the IT Compiler [1, 2], as well as the GAT Compiler of Arden and Graham of the University of Michigan [3], have special “alphabetic read” and “alphabetic type” statements. On the UNIVAC 1105 these features allow the direct input or output of six-symbol words, each symbol being either an alphanumeric or special character. Internally, each symbol is represented by a six-bit binary coded decimal code. On the IBM 650, five-symbol words are processed, with each symbol represented internally by a two-digit decimal code.
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Research and Advances Feb 1 1961

Comment on a paper on parallel processing

The article by Lynn Yarbrough on Parallel Processing in the October Communications is interesting since it attracts attention to a subject which needs to be given increased consideration. His indictment of manufacturers for failing to provide what he feels is minimal to realizing the advantages of multi-programming is not applicable to STRETCH, however. It may be recalled that his specific complaint concerns the lack of protection of any program or monitor from the unpredictable actions of any other program. On page 15 of the STRETCH Data Processing System Reference Manual, we read: Address monitoring facilities are provided … The upper and lower boundaries of the storage area to be defined are placed in two address boundary registers. An alarm will be given when an address falls either inside or outside the defined area, whichever is desired. Storing in protected areas is normally suppressed.
Research and Advances Feb 1 1961

The BKS system for the Philco-2000

The BKS System is a program sequencing system designed for the Philco-2000 computer to meet operational requirements of the Bettis and Knolls Atomic Power Laboratories. The Philco-2000 on which this system is being used has a 32,768-word memory, 16 tape transports on-line, and an electric typewriter on-line. The card-to-tape, card-to-printer, tape-to-card, tape-to-printer, and routine tape-to-tape operations are performed with off-line equipment.

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