Joe A Guthrie

Lexical disambiguation using simulated annealing

The resolution of lexical ambiguity is important for most natural language processing tasks, and a range of computational techniques have been proposed for its solution. None of these has yet proven effective on a large scale. In this paper, we describe a method for lexical disambiguation of text using the definitions in a machine-readable dictionary together with the technique of simulated annealing. The method operates on complete sentences and attempts to select the optimal combinations of word senses for all the words in the sentence simultaneously. The words in the sentences may be any of the 28,000 headwords in Longmans Dictionary of Contemporary English (LDOCE) and are disambiguated relative to the senses given in LDOCE. Our initial results on a sample set of 50 sentences are comparable to those of other researchers, and the fully automatic method requires no hand-coding of lexical entries, or hand-tagging of text.

A characterization of ℵ0-spaces

A new characterization is given for the ℵ0-spaces of E. Michael. It is known that if X and Y are ℵ0-spaces, then the space of maps from X to I, with the compact-open topology, is also an ℵ0-space. The characterization of ℵ0-spaces is used to show that there is a topology, called the cs-open topology, coarser than the compact-open topology even in the special case of the real functions on the unit interval, in which the mapping space from an ℵ0-space to an ℵ0-space is again an ℵ0-space. Other basic properties of the cs-open topology are given.

Document classification by machine: theory and practice

In this note, we present results concerning the theory and practice of determining for a given document which of several categories it best fits. We describe a mathematical model of classification schemes and the one scheme which can be proved optimal among all those based on word frequencies. Finally, we report the results of an experiment which illustrates the efficacy of this classification method.

Maximal connected expansions of the reals

The question of whether there exist nontrivial maximal connected Hausdorff spaces is settled in the affirmative by showing that there is a maximal connected topology for the reals which is finer than the Eucidean topology.

Pseudocompactness and invariance of continuity

Abstract Given a space ( X , ˕) and a class Σ of spaces, we study the topologies comparable to ˕ which determine the same continuous functions into all spaces of Σ, which we call the Σ-invariant expansions and compressions of ˕. We extend results of E. Kocela relating pseudo-compactness and real-invariant expansions to obtain characterizations of minimal perfectly Hausdorff and perfectly Hausdorff-closed spaces. We solve by a counterexample the problem posed by Kocela of whether his necessary conditions for a real-invariant expansion of the unit interval are sufficient. Nontrivial examples of maximal real-invariant expansions are given.

Expansions of k-spaces

Abstract Simple expansions and expansions by point finite and locally finite collections are studied for particular classes of k -spaces. All such expansions of Frechet spaces are shown to be Frechet, and sufficient conditions for the preservation of property P ϵ { k 1 , sequential, k } under simple and locally finite expansions are established.

Document Classification and Routing

A document classification and routing system is described which uses a probabilistic approach to determine the “flavor” of a text. The necessary probabilities are determined from the relevant training documents. Development, refinement, and testing of the system’s ability to route 120,000 documents into 50 topics are discussed as well as the mathematical model on which it is based.

Characterizing topological properties by real functions

This chapter discusses what completely regular space ( X ) can be characterized by the fact that some, or all, of the members of C(X) (collection of all continuous real-valued mappings defined on X) satisfy a given property. The requirement that X be completely regular is included to assure the existence of nonconstant members in C(X) . It is well known that some of the most interesting classes of spaces will provide answers to this question as it is true that (1) X is compact if each f ∈ C(X) is perfect; (2) X is countably compact if each f ∈ C(X) is closed and a priori; and (c) X is pseudocompact if each f ∈ C(X) is bounded. The chapter shows that this list can be extended to include the first countable spaces, locally compact spaces, and the spaces of point-countable type, which are a common generalization of both.

Uncommon Connections with Common Numerators

Abstract Undergraduate students who are pre-service teachers need to make connections between the college mathematics they are learning and the pre-college mathematics they will be teaching. Spanning a broad range of undergraduate curricula, this article describes useful lesser-known connections, explorations, and original proofs involving fractions. In particular, we use standard tools of number theory to investigate when an integer results from , an expression that arises from the not uncommon situation of adding fractions with a common numerator.