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The article provides information on the upcoming symposiums related to the computer engineering in 1966. A one-day symposium will be sponsored by ACM, SIAM and Florida State University on March 14 on "The Recommended Impact of Computer Applications on the Undergraduate Mathematics Curriculum." The four New York Metropolitan Area chapters will hold a one-day symposium in New York City on March 18. A session of invited papers will be devoted to "The Application of Computers to the Problems of a Metropolitan Society." In addition, a session of contributed papers on any topics in the computer field is now in the process of being organized . Automatic Data Processing exhibits and workshops headline the Federal Government Accountants Association 15th National Symposium, in Minneapolis, June 15-17. Topics include "Case Studies in ADP," "Programming: The Modern Budget Officer's Tool," and "The Future of Computers in the Federal Government." The Instrument Society of America (ISA) has invited papers for presentation at the 21st Annual ISA Conference and Exhibit, to be conducted October 24-27 in New York City. Theme of the meeting is "Instrumentation for an Urban Society."

The article reports on finding all subgraphs of an undirected graph [H]. A maximal complete subgraph is also called clique which refers to a complete subgraph that is not included in any other complete subgraph. According to the authors, a research paper was released wherein descriptions of techniques to find maximal complete subgraphs are provided. The authors discussed two algorithms using a branch-and-bound technique so that there will be no clique. The first algorithm produces cliques in lexicographic order while the second is derived from the first algorithm.

The article presents a list of upcoming symposiums on computer science and technology in the U.S. Texas A&M Instrumentation Symposium for the Process Industries will be held in Texas University on January 19-21, 1966. The American Mathematical Society Annual Meeting, cosponsored by the Mathematics Association of America, will be held in Chicago, Illinois, on January 24-28, 1966. The 1966 Annual Symposium on Reliability will be held at the Sheraton-Palace Hotel, San Francisco, California, on January 25-27, 1966. The International Symposium on Information Theory will be held at the University of California, Los Angeles, on January 31-February 3, 1966. The 6th Annual Computing Center Conference, ACM-SIAM-FSU Symposium will held on March 12-19, 1966 at Florida State University, Tallahassee. The Symposium on Simulation Languages will be held on March 17-18, 1966, at the University of Pennsylvania, Philadelphia. The 4th International ISA Aerospace Instrumentation Symposium will be held at the College of Aeronautics, Cranfield, England, on March 21-25, 1966.

A list of a number of natural developments for the field of algebraic manipulation is given. Then the prospects for a general theory of functions defined by ordinary differential equations are discussed. The claim is made that recent developments in mathematics indicate that it should be possible to algorithmically generate many properties of solutions to differential equations. Such a theory is preferable to a less general effort to make algebraic manipulation systems knowledgeable about the usual special functions (e g exponential, hyper geometric) [ABSTRACT FROM AUTHOR]

Numerical mathematics is viewed as the analysis of continuous algorithms. Four of the components of numerical mathematics are discussed. These are: foundations (finite precision number systems, computational complexity), synthesis and analysis of algorithms, analysis of error, programs and program libraries. [ABSTRACT FROM AUTHOR]

Investigates how the special structure of matrices can be described and utilized for mathematical programming. Symbol manipulation of matrix expressions; Extension of matrix operators to sequence operators and cumulative operators.

The purpose of this note is to report computational experience additional to that recently summarized by Gue et al., with two algorithms for the zero-one linear programming problem. An error in Gue's paper is corrected. The utility of one of the algorithms as a suboptimizer is indicated. [ABSTRACT FROM AUTHOR]

The article presents abstracts of some of the papers that were published in the "Journal of the Association for Computing Machinery." A number of observations and comments are directed toward suggesting that more than the usual engineering flavor be given to computer science. The engineering aspect is important because most present difficulties in this field do not involve the theoretical question of whether certain things can be done, bat rather the practical question of how can they be accomplished well and simply. The teaching of computer science could be made more effective by various alterations, for example, the inclusion of a laboratory course in programming, the requirement for a strong minor in something other than mathematics, and more practical coding and less abstract theory, as well as more seriousness and less game playing. Recursive formulas for the numerical evaluation of the real convolution integral are derived for the case in which the impulse response is given analytically. These formulas require considerably less computation time and memory space than the general time series formulas and can be effectively applied for digital simulation of continuous physical systems.

This article presents news briefs related to the Association for Computing Machinery (ACM). J.F. Traub was appointed as the chairman of SIGNUM. Traub had been chairman of SICNUM. Traub then announced that professor C.W. Gear will serve as liaison between national SIGNUM and local chapters. Professor Gear will assist existing special interest committees on numerical mathematics at the chapter level, and will endeavor to help new ones get started. The ACM Council has approved the establishment of a Special Interest Committee for File Description and Translation (SICFIDET). One of SICFIDET's initial tasks will be to compile a glossary for terminology and practice in the areas of data management and information and file description, since there is at present a great divergence as well as variety in the use of identifiers in these areas. Plans are already under way for publication of a "SICFIDET Bulletin." The publication will include discussions of problems in the correspondences between logical and physical data forms, the evolution of a file description notation, the development of techniques for automatic generation of descriptions, and the information requirements for translation among different logical and physical forms.

A description is given of a program for computing the solution to a small number of standard numerical analysis problems to any specified accuracy, up to a limit of 2000 correct decimal places. Each computed number is bounded in an interval with a multiple precision midpoint. Arithmetic operations involving these numbers are executed according to interval arithmetic concepts, with non-significant digits automatically discarded. Details are supplied of problem specification and problem computation. [ABSTRACT FROM AUTHOR]

Presents a note on author C.J. Cheney's paper 'Nonrecursive List-Compacting Algorithm,' which appeared in the November 1970 issue of the periodical 'Communications of the ACM.' Effect of circular list consisting exclusively of non-items on the flow of the list-compacting algorithm; Structural meaning of the list-compacting algorithm.

The article announces various appointments made at the Association for Computing Machinery's Special Interest Group for Mathematical Programming, including the appointment of M.A. Efroymson as the chairman, the appointment of A. Orden as the vice-chairman, and the appointment of T. Glans as the secretary.

The article presents information on the Stochastic Linear Programming workshop held at Princeton, New Jersey, on December 2-3, 1965. The workshop was sponsored by the Special Interest Group for Mathematical Programming. The workshop was aimed at bringing active workers in the field to report on theoretical advances, new applications, and existing computer codes. Participants also shared their perspectives on new research works in the field of computer science.

The early origins of mathematics are discussed, emphasizing those aspects which seem to be of greatest interest from the standpoint of computer science. A number of old Babylonian tablets, many of which have never before been translated into English, are quoted. Discusses the early origins of mathematics, particularly aspects of great interest from the standpoint of computer science. Introduction to Babylonian mathematics; Large number of clay tablets unearthed during expeditions in the Middle East which contain mathematical calculations; Clues about the life of early computer scientists. [ABSTRACT FROM AUTHOR]

A brief history of integer and continuous nonlinear programming is presented as well as the current obstacles to practical use of these mathematical programming techniques It is forecast that the useful contributions to nonlinear programming actualls made in the next few years are more likely to he consolidations than theoretical breakthroughs These contributions are likely to be the documentation of standard test problems, construction of user oriented software, and comparisons of currently known algorithms to demonstrate which techniques are best for specific problems. [ABSTRACT FROM AUTHOR]

A computer language and a set of programs within that language are described which allow the formulating and solving of a class of space planning problems. The language is an extension of Algol and includes means to represent spaces and objects, to manipulate them, and to test the resulting arrangements according to a variety of constraints. The algorithms used to solve problems expressed in this language rely on heuristic programming. Both the language and the search algorithms are detailed. [ABSTRACT FROM AUTHOR]

A quadratic programming algorithm is described for use with the magnified diagonal method of nonlinear regression with linear constraints. The regression method is published in JACM, July 1970. [ABSTRACT FROM AUTHOR]

There are situations in the natural sciences and medicine (e.g. in electron microscopy and X-ray photography in which it is desirable to estimate the gray levels of a digital picture at the individual points from the sums of the gray levels along straight tines (projections) at a Few angles. Usually, in such situations, the picture is far from determined and the problem is to find the "most representative" picture. Three algorithms are described (all using Monte Carlo methods which were designed to solve this problem. The algorithms are applicable in a large and varied number of fields. The most important uses may he the reconstruction of possibly asymmetric particles from electron micrographs and three-dimensional X-ray analysis. [ABSTRACT FROM AUTHOR]

A method for extracting a smooth polygonal contour from a digitized image is illustrated. The ordered sequence of contour points and the connection graph of the image are first obtained by a modified Ledley algorithm in one image scan. A minimal perimeter polygon subjected to specified constraints is then chosen as the approximating contour. The determination of the minimal polygon can be reduced to a nonlinear programming problem, solved by an algorithm which takes into account the weak bonds between variables. Some examples are presented, and the corresponding computing times are listed. [ABSTRACT FROM AUTHOR]

A fast method is presented for finding a fundamental set of cycles for an undirected finite graph. A spanning tree is grown and the vertices examined in turn, unexamined vertices being stored in a pushdown list to await examination. One stage in the process is to take the top element v of the pushdown list and examine it, i.e. inspect all those edges (v, z) of the graph for which z has not yet been examined. If z is already in the tree, a fundamental cycle is added; if not, the edge (v, z) is placed in the tree. There is exactly one such stage for each of the n vertices of the graph. For large n, the store required increases as n2 and the time as γ where γ depends on the type of graph involved. γ is bounded below by 2 and above by 3, and it is shown thaT both bounds are attained. In terms of storage our algorithm is similar to that of Gotlieb and Corneil and superior to that of Welch; in terms of speed it is similar to that of Welch and superior to that of Gotlieb and Corneil. Tests show our algorithm to be remarkably efficient (γ = 2) on random graphs. [ABSTRACT FROM AUTHOR]

Describes a translation approach allowing syntax and semantic extension using syntax macro. Discussion on the type of macros; Uses of macros; Description on conditional generation of macros; Examples of this programming language strategy in use; Discussion of the methods flexibility.

Several letters to the editor are presented in response to articles in the previous issues including "A Comparison of the Primal-Simplex and Primal-Dual Algorithms for Linear Programming," by R.K. Mueller and L. Cooper, "Algorithm and Formula," by T. Wangsness and J. Franklin, and a letter which further expounded the terms algorithm and program.

The article reports on several algorithms with their specific computational dynamics. A specific algorithm with its corresponding formula which provides for the procedure for deriving a certain value is provided. The algorithms include, among others, algorithm 290 for linear equations, algorithm 291 for logarithm of gamma functions, and algorithm 178 for direct search. Moreover, the algorithms are written in the ALGOL 60 Reference Language, Standard FORTRAN, and Basic FORTRAN. Specific instructions on how to submit algorithms are also included.

The elimination procedure as described by Williams has been coded in LISP and FORMAC and used in solving systems of polynomial equations. It is found that the method is very effective in the case of small systems, where it yields all solutions without the need for initial estimates. The method, by itself, appears inappropriate, however, in the solution of large systems of equations due to the explosive growth in the intermediate equations and the hazards which arise when the coefficients are truncated. A comparison is made with difficulties found in other problems in non-numerical mathematics such as symbolic integration and simplification. [ABSTRACT FROM AUTHOR]

An algorithm for finding the symbolic factors of multivariate polynomial with integer coefficients is presented. The algorithm is an extension of a technique used by Kronecker in a proof that the prime factoring of any polynomial may be found in a finite number of steps. The algorithm consists of factoring single-variable instances of the given polynomial by Kronecker's method and introducing the remaining variables by interpolation. Techniques for implementing the algorithm and several examples are discussed. The algorithm promises sufficient power to be used efficiently in an online system for symbolic mathematics. [ABSTRACT FROM AUTHOR]

As an investigation in artificial intelligence, computer experiments on deductive question-answering were run with a LISP program called DEDUCOM, an acronym for DEDUctive COMmunicator. When given 68 facts, DEDUCOM answered 10 questions answerable from the facts. A fact tells DEDUCOM either some specific information or a method of answering a general kind of question. Some conclusions drawn in the article ore: (1) DEDUCOM can answer a wide variety of questions. (2) A human can increase the deductive power of DEDUCOM by telling it more facts. (3) DEDUCOM can write very simple programs (it is hoped that this ability is the forerunner of an ability to self-program, which is a way to learn). (4) DEDUCOM is very slow in answering questions. (5) DEDUCOM's search procedure at present has two bad defects: some questions answerable from the given facts cannot be answered and some other answerable questions can be answered only if the relevant fads ore given in the "right" order. (6) At present, DEDUCOM's method of making logical deductions in predicate calculus has two bad defects: some facts have to be changed to logically equivalent ones before being given to DEDUCOM, and some redundant facts have to be given to DEDUCOM. [ABSTRACT FROM AUTHOR]

From the inequality 108 < 227, we are likely to conclude that we can represent 8-digit decimal floating-point numbers accurately by 27-bit floating-point numbers. However, we need 28 significant bits to represent some 8-digit numbers accurately. In general, we can show that if 10p < 2q-1, then q significant bits are always enough for p-digit decimal accuracy. Finally, we can define a compact 27-bit floating-point representation that will give 28 significant bits, for numbers of practical importance. [ABSTRACT FROM AUTHOR]

This article presents information on several articles related to computer science. In the article "Application of LISP to Sequence Prediction," by Paul W. Abrahams, a LISP program that analyzes sequences of letters and numbers is described. The program takes as input a sequence such as A C E G I and so on and produces as output the next element of the sequence, in this ease K. The program does this by creating a LISP program that will generate the nth element of the sequence, given n, and then executing this program with the length of the given sequence plus one as argument. In the article "Models for Mathematical Systems," by Alfred H. Morris, a program, written for the IBM 7090, which defines a model for a finite collection of associative algebras for the computer, is described and illustrated. The program contains a structure broad enough in scope to allow one to perform operations on such diverse mathematical concepts as differential equations, infinite series and differential forms in a simple yet comprehensive manner, while also serving in a foundation upon which a variety of higher level symbol manipulation languages can be developed.