Topic

# Congruence (geometry)

About: Congruence (geometry) is a research topic. Over the lifetime, 524 publications have been published within this topic receiving 12860 citations. The topic is also known as: congruent to.

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TL;DR: The paper demonstrates, for a sequence of simple languages expressing finite behaviors, that in each case observation congruence can be axiomatized algebraically and the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties.

Abstract: Since a nondeterministic and concurrent program may, in general, communicate repeatedly with its environment, its meaning cannot be presented naturally as an input/output function (as is often done in the denotational approach to semantics). In this paper, an alternative is put forth. First, a definition is given of what it is for two programs or program parts to be equivalent for all observers; then two program parts are said to be observation congruent if they are, in all program contexts, equivalent. The behavior of a program part, that is, its meaning, is defined to be its observation congruence class.The paper demonstrates, for a sequence of simple languages expressing finite (terminating) behaviors, that in each case observation congruence can be axiomatized algebraically. Moreover, with the addition of recursion and another simple extension, the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties.

1,486 citations

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TL;DR: The authors summarizes problems with congruence indices, presents an alternative approach that overcomes these problems, and illustrates this approach using data from two samples, and recommends the use and further development of this approach.

1,116 citations

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01 Sep 2006-Methodology: European Journal of Research Methods for The Behavioral and Social Sciences

TL;DR: In this article, the authors used Tucker's congruence coefficient to assess the similarity of factor interpretations and found that a value in the range.85-94 corresponds to a fair similarity, while a value higher than.95 implies that the two factors or components compared can be considered equal.

Abstract: When Tucker's congruence coefficient is used to assess the similarity of factor interpretations, it is desirable to have a critical congruence level less than unity that can be regarded as indicative of identity of the factors. The literature only reports rules of thumb. The present article repeats and broadens the approach used in the study by Haven and ten Berge (1977). It aims to find a critical congruence level on the basis of judgments of factor similarity by practitioners of factor analysis. Our results suggest that a value in the range .85-.94 corresponds to a fair similarity, while a value higher than .95 implies that the two factors or components compared can be considered equal.

895 citations

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TL;DR: The extent to which four cultures (clan, adhocracy, hierarchy, or market cultures) were dominant on campus was examined in this article, based on questionnaire responses by 3,406 administrators, faculty department heads, and trustees from 334 colleges and universities.

Abstract: Organizational effectiveness was studied, based on questionnaire responses by 3,406 administrators, faculty department heads, and trustees from 334 colleges and universities. The extent to which four cultures (clan, adhocracy, hierarchy, or market cultures) were dominant on campus was examined. (ERIC ED 627, 52 PP, MF $.97, PC $7.14).

671 citations

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TL;DR: In this paper, the authors study efficient Bayes-Nash incentive compatible mechanisms in a social choice setting that allows for informational and allocative externalities, and show that such mechanisms exist only if a congruence condition relating private and social rates of information substitution is satisfied.

Abstract: We study efficient, Bayes-Nash incentive compatible mechanisms in a social choice setting that allows for informational and allocative externalities. We show that such mechanisms exist only if a congruence condition relating private and social rates of information substitution is satisfied. If signals are multi-dimensional, the congruence condition is determined by an integrability constraint, and it can hold only in nongeneric cases where values are private or a certain symmetry assumption holds. If signals are one-dimensional, the congruence condition reduces to a monotonicity constraint and it can be generically satisfied. We apply the results to the study of multi-object auctions, and we discuss why such auctions cannot be reduced to one-dimensional models without loss of generality.

493 citations