Showing papers on "Equivalence class published in 1987"

The structure of equivalence classes.

Abstract: THE STRUCTURE OF EQUIVALENCE CLASSES CAN BE COMPLETELY DESCRIBED BY FOUR PARAMETERS: class size, number of nodes, the distribution of "singles" among nodes, and directionality of training. Class size refers to the number of stimuli in a class. Nodes are stimuli linked by training to at least two other stimuli. Singles are stimuli linked by training to only one other stimulus. The distribution of singles refers to the number of singles linked by training to each node. Directionality of training refers to the use of stimuli as samples and as comparison stimuli in training. These four parameters define the different ways in which the stimuli in a class can be organized, and thus provide a basis for systematically characterizing the properties of stimuli in a given equivalence class. The four parameters can also be used to account for the development of individual differences that are commonly characterized in terms of "understanding" and connotative meaning.Methods are described for generating all possible combinations of parameter values, and a formula is introduced which specifies all of the parameter values for an equivalence class. Its utility for interrelating experimental procedures is demonstrated by analyzing a number of representative experiments that have addressed equivalence-class formation.

Expansive dynamics on zero-dimensional groups

Abstract: If X is a compact, zero-dimensional group and T is an expansive, transitive automorphism then (X, T) is shown to be topologically conjugate to a full shift on finitely many symbols.The problem of classifying such automorphisms up to simultaneous algebraic isomorphism and topological conjugacy is discussed but not solved. It is proved that for any entropy there are only finitely many such equivalence classes. When the entropy is log p for a prime p, there is only one equivalence class. All are then equivalent to

The stable rationality of quotient spaces for simply connected groups

Abstract: Stable rationality of quotient varieties V/G is proved for representations V of simply connected groups G that have a trivial stabilizer of a generic point.Bibliography: 7 titles.

Restructuring Aspect Graphs into Aspect- and Cell-Equivalence Classes for Use in Computer Vision

Abstract: A potential disadvantage of using aspect graphs as object models in a computer vision system is their large size. The upper bound on the number of nodes in the aspect graph of an N-face convex object is O(N⋆⋆3). In this paper we introduce the concepts of "aspect-equivalence" and "cell-equivalence" and present a method of using them to restructure a data base of aspect graphs. This process identifies an interconnected set of equivalence classes which we use to form an Equivalence Class Graph (ECG).

A conceptual clustering program for rule generation

Abstract: We present an Interesting Situation Generator (ISG) that assists in the synthesis of interpretation rules from basic domain knowledge. The ISG is a hierarchical clustering program that discovers equivalence classes of situations (e.g. types of geological formations) that give rise to qualitatively distinct manifestations (e.g. different patterns of geophysical measurements corresponding to types of geological formations). The equivalence classes can be used by a rule generator to construct an initial set of interpretation rules of the form manifestation ⇒ situation.

A genealogical description of the infinitely-many neutral alleles model

Abstract: Kingman [8], [9] introduced the coalescent as a means of describing the genealogy of samples taken from a large evolving haploid population. The coalescent partitions a sample of genes into equivalence classes with respect to an ancestral population some time t into the past; genes in the same equivalence class in the sample have the same ancestors. As t increases the equivalence classes coalesce until, sufficiently far in the past, all individuals in the sample are equivalent, being descended from a common ancestor.

On the σ-Fields Which are Larger than a Sufficient One

Abstract: One of the most peculiar features of the set of sufficient σ-fields in a statistical space (Ω, A, P) is that it may happen that a σ-field which is larger than a sufficient one does not remain to be sufficient. In [4] there is a sufficient condition to avoid this pathological nature. According to [4] if the Boolean algebra A/N (P) is complete and F⊂A is a sufficient σ-field, then every σ-field G⊃F for which G/N (P) is a complete subalgebra of A/N (P) is sufficient. In this paper we give a necessary and sufficient condition for that any σ-field containing a fixed sufficient σ-field should be sufficient.

Quotient of manifolds by discrete groups

Abstract: The quotient of manifolds by discrete subgroups of their isometry group are considered. In particular, symmetry breaking due to the quotient structure, topological properties, and harmonic analysis of the resultant manifolds are discussed and illustrated by two‐dimensional examples. New solutions of d=11 supergravity and the d=6 Einstein–Yang–Mills theory are thus obtained, for which alterations in their spectrum and symmetry breaking are discussed.