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1. Future Directions in Computational Mathematics, Algorithms, and Scientific Software. Report of the Panel.

Author

Society for Industrial and Applied Mathematics, Philadelphia, PA.

Abstract

The critical role of computers in scientific advancement is described in this panel report. With the growing range and complexity of problems that must be solved and with demands of new generations of computers and computer architecture, the importance of computational mathematics is increasing. Multidisciplinary teams are needed; these are found in most advanced and industrial laboratories, but rarely in universities. The existing educational opportunities are not producing the required personnel to meet substantial shortages. Therefore, the panel strongly recommends increased federal support for: (1) research in computational mathematics, methods, algorithms, and software for scientific computing; (2) the development of interdisciplinary research teams; (3) the establishment and continued operation of a suitable research infrastructure for the teams; (4) graduate and post-doctoral students directly involved in the research of some interdisciplinary team; and (5) young researchers and cross-disciplinary visitors. In the second section, research opportunities in a number of mathematical areas are described. New modes of research are discussed next, followed by comments on educational needs and a final section on funding considerations. Appendices contain a list of related reports, information on laboratory facilities for scientific computing, and letters and position papers. (MNS)

Published
1985

2. Knowledge Acquisition from Structural Descriptions.

Author

Rand Corp., Santa Monica, CA., Hayes-Roth, Frederick, and McDermott, John

Abstract

The learning machine described in this paper acquires concepts representable as conjunctive forms of the predicate calculus and behaviors representable as productions (antecedent-consequent pairs of such conjunctive forms): these concepts and behavior rules are inferred from sequentially presented pairs of examples by an algorithm that is probably effective for a wide variety of problems. A method for inducing knowledge by abstracting such representations from a sequence of training examples is described. The proposed learning method, interference matching, induces abstractions by finding regional properties common to two or more exemplars. Three tasks solved by a program that performs an interference matching algorithm are presented. Several problems concerning the relational representation of examples and the induction of knowledge by interference matching are also discussed. The similarities between this task and other computer science problems are indicated, and directions for future research are considered. (Author/JEG)

Published
1976

3. The Structure-Mapping Engine.

Author

Illinois Univ., Urbana. Dept. of Computer Science. and Falkenhainer, Brian

Abstract

This paper describes the Structure-Mapping Engine (SME), a cognitive simulation program for studying human analogical processing. SME is based on Gentner's Structure-Mapping theory of analogy, and provides a "tool kit" for constructing matching algorithms consistent with this theory. This flexibility enhances cognitive simulation studies by simplifying experimentation. Furthermore, SME is very efficient, making it a candidate component for machine learning systems as well. The Structure-Mapping theory is reviewed and the design of the engine described. Some examples of its operation are then demonstrated. Finally, plans for using SME in cognitive simulation studies are discussed. Appendices list detailed examples of definitions according to various analogies, as well as sample outputs. (Author/MNS)

Published
1986