William Goffman

Dispersion of papers among journals based on a mathematical analysis of two diverse medical literatures.

Two entire literatures relating to research in mast cells and schistosomiasis have been found to differ in almost every respect.

On relevance as a measure

Abstract Relevance is defined as a measure of information conveyed by a document relative to a query. It is shown that the relationship between the document and the query, though necessary, is not sufficient to determine relevance.

A searching procedure for information retrieval

Abstract A search procedure for an information retrieval system is developed whereby the answer to a question is obtained by maximizing an evaluation function of the systems output in terms of the probability of relevance. Necessary and sufficient conditions are given for a set to be an answer to a query. A partition of the file is made in such a way that all documents belonging to the answer are members of the same class. Hence the answer can be generated by one relevant document. In this manner a search of the total file is avoided.

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.

An indirect method of information retrieval

Abstract The information retrieval process, treated strictly as a matching procedure, has the defects that the whole file must be probed for each query, and that it overlooks the fact that the relevance of the information from one document depends upon what is already known about the subject, and in turn affects the relevance of other documents subsequently examined. A mathematical model of a search technique in which the defects of the direct method are taken into account is demonstrated by an experiment in which a given paper is treated as an enquiry and the references cited in the paper are treated as relevant answers. The results in two tests show much better results than those achieved by the direct method. No spurious material was retrieved by either method.

Communication and Epidemic Processes

It is pointed out that communication processes can be represented as epidemic processes. Consequently, epidemic theory can be applied to the study of any process in which information is transmitted within a population. The members of such populations need not be human beings but could be micro-organisms or even machines. The fundamental notion of stability of an epidemic process is introduced and a stability theorem is derived. A mechanism, called an information retrieval process, which instigates an epidemic process is defined, certain general properties of the mechanism are established and the means of controlling it are discussed. Pontryagin’s maximum principle is applied to the problem of achieving optimal control of an epidemic process and it is shown that stability of the process is equivalent to stability in the sense of Lyapunov. This result makes it possible to determine the conditions for stability without knowledge of the solution of the differential equations which represent the process.

A Mathematical Method for Analyzing the Growth of a Scientific Discipline

The spread of ideas within a scientific community and the spread of infectious disease are both special cases of a general communication process. Thus a general theory of epidemics can explain the growth of symbolic logic from 1847 to 1962. An epidemic model predicts the rise and fall of particular research areas within symbolic logic. A Markov chain model of individual movement between research areas indicates that once an individual leaves an area he is not expected to return.

A methodology for test and evaluation of information retrieval systems

Abstract : Information retrieval systems are discussed in terms of their purpose and function. The essential components of an information retrieval system are defined. A methodology for evaluating the comparative performance of systems is developed. Specific measures and methods of analysis of results are presented. (Author)

A mathematical model for describing the compatibility of infectious diseases

Abstract A mathematical model describing the conditions under which a set of infectious diseases will co-occur is developed. The underlying assumptions are that, given two diseases, either (1) they occur independently of each other, (2) one augments the other, or (3) one inhibits the other. It is further assumed that there exists a measure of effective contact between a susceptible and the infectious material transmitted by an infective and that there exists a threshold for a given susceptible with respect to a given disease. Based on these assumptions, necessary and sufficient conditions are established for the co-occurrence of a set of diseases independent of the sequence of exposure; and sufficient conditions are given for the co-occurrence of a set of diseases where the order of exposure is specified. A method of classifying diseases according to their likelihood of co-occurrence is also given.

Theoretical considerations in information retrieval systems

A method for automatic loading of library subroutines, which can be adapted to operate in conjunction with any conventional two-pass assembler is described. The method is specifically designed to cope with a nested library structure.