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Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 907 (36 self)
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. Two principal problems of matrix perturbation theory are the following. Given a matrix E, pr...
Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
, 1990
"... Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of ..."
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Cited by 626 (14 self)
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, that of preferential relations, turns out to have been studied by E. Adams in [2]. The pr...
Estimating the number of clusters in a dataset via the Gap statistic
, 2000
"... We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference ..."
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Cited by 502 (1 self)
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We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference
e pr w
"... tio Updatefunctionalization) [1], subdivision of ancestral functions (subfunctionalization) [3], or a combination of the two [4]. Surprisingly, however, several studies in yeast and nematode have found many duplicate gene pairs with negative epistasis [5–9], meaning that deleting both gene copies pr ..."
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tio Updatefunctionalization) [1], subdivision of ancestral functions (subfunctionalization) [3], or a combination of the two [4]. Surprisingly, however, several studies in yeast and nematode have found many duplicate gene pairs with negative epistasis [5–9], meaning that deleting both gene copies produces a significantly larger defect than expected from the effects of individual deletions. Negative epistasis is caused by functional redundancy [10]. Whereas one might think that most of these negatively epistatic gene pairs are young duplicates that have not had sufficient time to diverge in function, this is not the case [7–9]. In fact, many of them are quite old [7–9] and some originated as early as a billion years ago [7]. The longtermmaintenance activity of the duplicate genes [3], expression reduction after gene duplication is a type of subfunctionalization in the joint levels rather than patterns of activity. So, all previous theoretical results on subfunctionalization should apply to our model. Note, however, that subfunctionalization in the joint patterns of activity cannot explain the long retention of genetic redundancy because negative epistasis is not expected if the two daughter genes have nonoverlapping protein functions or tissue/ condition expressions. Substantial expression reduction after gene duplication in yeasts To test if the expression levels of duplicate genes are indeed decreased compared to their progenitor genes we examined gene expression levels measured by the
Practical Graph Isomorphism
, 1981
"... We develop an improved algorithm for canonically labelling a graph and finding generators for its automorph.ism grou.p. The emphasis i, on th.e power of the algorithm for,01 fling pr4ctical problem.t, rather than on the theoretical n,icetiu of tJu algo rith.m. Th.e nsult is a.n implementa.tion wh.ic ..."
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Cited by 337 (7 self)
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We develop an improved algorithm for canonically labelling a graph and finding generators for its automorph.ism grou.p. The emphasis i, on th.e power of the algorithm for,01 fling pr4ctical problem.t, rather than on the theoretical n,icetiu of tJu algo rith.m. Th.e nsult is a.n implementa.tion wh
Results 1  10
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