Book•
Mathematical foundations of information theory
01 Jan 1957-
About: The article was published on 1957-01-01 and is currently open access. It has received 1349 citations till now. The article focuses on the topics: Information diagram.
Citations
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TL;DR: In this paper, a measure of semantic similarity in an IS-A taxonomy based on the notion of shared information content is presented, and experimental evaluation against a benchmark set of human similarity judgments demonstrates that the measure performs better than the traditional edge counting approach.
Abstract: This article presents a measure of semantic similarity in an IS-A taxonomy based on the notion of shared information content. Experimental evaluation against a benchmark set of human similarity judgments demonstrates that the measure performs better than the traditional edge-counting approach. The article presents algorithms that take advantage of taxonomic similarity in resolving syntactic and semantic ambiguity, along with experimental results demonstrating their effectiveness.
2,190 citations
TL;DR: It is proposed that the species composition of communities utilizing different resource states may be used to develop weighting factors with which each state may be weighted in proportion to its degree of distinctness.
Abstract: Measures of niche breadth and overlap that depend on the distribution of individual among resource states (ecological categories) should be independent of the relative abundance of the species and of the number of resource states considered. Such measures should also take into account the degree of distinctness of the resource states from the point of view of the organisms concerned. An ecoassay of the distinctness of resource states may well be easier and more meaningful than measurements of physical and chemical factors. We propose that the species composition of communities utilizing different resource states may be used to develop weighting factors with which each state may be weighted in proportion to its degree of distinctness. The weighting factors are used in the development of indices of niche breadth and overlap that correct for variation in the range and distinctness of resource states and that suffer less from human subjectivity than do the measures used to date. The use of such indices and the relationship of niche overlap to competition are discussed.
1,369 citations
01 Jan 2006
TL;DR: In this article, the space of isospectral 0Hermitian matrices is shown to be the space in which the number 6) and 7) occur twice in the figure, and the discussion between eqs.(5.14) and (5.15) is incorrect.
Abstract: a ) p. 131 The discussion between eqs. (5.14) and (5.15) is incorrect (dA should be made as large as possible!). b ) p. 256 In the figure, the numbers 6) and 7) occur twice. c ) p. 292 At the end of section 12.5, it should be the space of isospectral 0Hermitian matrices. d ) p. 306 A ”Tr” is missing in eq. (13.43). e ) p. 327, Eq. (14.64b) is 〈Trρ〉B = N(14N+10) (5N+1)(N+3) should be 〈Trρ〉B = 8N+7 (N+2)(N+4)
1,089 citations
TL;DR: It was found that the natural thinning resulting from competition among the trees caused an increase in pattern-diversity, in young dense communities of forest trees, which is a measurable property of any collection of organisms containing more than one species.
908 citations
DOI•
01 May 2006
TL;DR: In this article, the space of isospectral 0Hermitian matrices is shown to be the space in which the number 6) and 7) occur twice in the figure, and the discussion between eqs.(5.14) and (5.15) is incorrect.
Abstract: a ) p. 131 The discussion between eqs. (5.14) and (5.15) is incorrect (dA should be made as large as possible!). b ) p. 256 In the figure, the numbers 6) and 7) occur twice. c ) p. 292 At the end of section 12.5, it should be the space of isospectral 0Hermitian matrices. d ) p. 306 A ”Tr” is missing in eq. (13.43). e ) p. 327, Eq. (14.64b) is 〈Trρ〉B = N(14N+10) (5N+1)(N+3) should be 〈Trρ〉B = 8N+7 (N+2)(N+4)
835 citations
References
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Journal Article•
TL;DR: The Mathematical Theory of Communication (MTOC) as discussed by the authors was originally published as a paper on communication theory more than fifty years ago and has since gone through four hardcover and sixteen paperback printings.
Abstract: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
15,525 citations
01 Jan 1922-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, the authors define the center of location as the abscissa of a frequency curve for which the sampling errors of optimum location are uncorrelated with those of optimum scaling.
Abstract: Centre of Location. That abscissa of a frequency curve for which the sampling errors of optimum location are uncorrelated with those of optimum scaling. (9.)
3,392 citations
01 Jul 1925
TL;DR: It has been pointed out to me that some of the statistical ideas employed in the following investigation have never received a strictly logical definition and analysis, and it is desirable to set out for criticism the manner in which the logical foundations of these ideas may be established.
Abstract: It has been pointed out to me that some of the statistical ideas employed in the following investigation have never received a strictly logical definition and analysis The idea of a frequency curve, for example, evidently implies an infinite hypothetical population distributed in a definite manner; but equally evidently the idea of an infinite hypothetical population requires a more precise logical specification than is contained in that phrase The same may be said of the intimately connected idea of random sampling These ideas have grown up in the minds of practical statisticians and lie at the basis especially of recent work; there can be no question of their pragmatic value It was no part of my original intention to deal with the logical bases of these ideas, but some comments which Dr Burnside has kindly made have convinced me that it may be desirable to set out for criticism the manner in which I believe the logical foundations of these ideas may be established
2,464 citations
TL;DR: It is shown that a certain differential form depending on the values of the parameters in a law of chance is invariant for all transformations of the parameter when the law is differentiable with regard to all parameters.
Abstract: It is shown that a certain differential form depending on the values of the parameters in a law of chance is invariant for all transformations of the parameters when the law is differentiable with regard to all parameters. For laws containing a location and a scale parameter a form with a somewhat restricted type of invariance is found even when the law is not everywhere differentiable with regard to the parameters. This form has the properties required to give a general rule for stating the prior probability in a large class of estimation problems.
2,292 citations