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IEEE Transactions on Automatic Control, 1981
We consider the problem of root clustering of a real matrix in an algebraic region of the complex plane. It is shown that a criterion (previously obtained) based on an n^{2} \times n^{2} matrix reduces to a criterion based on an \frac{1}{2}n(n-1) \times \frac{1}{2}n(n-1) matrix.
S. Gutman, G. Shwartz
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We consider the problem of root clustering of a real matrix in an algebraic region of the complex plane. It is shown that a criterion (previously obtained) based on an n^{2} \times n^{2} matrix reduces to a criterion based on an \frac{1}{2}n(n-1) \times \frac{1}{2}n(n-1) matrix.
S. Gutman, G. Shwartz
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Igor: Crash Deduplication Through Root-Cause Clustering
Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security, 2021Fuzzing has emerged as the most effective bug-finding technique. The output of a fuzzer is a set of proof-of-concept (PoC) test cases for all observed "unique'' crashes. It costs developers substantial efforts to analyze each crashing test case. This, mostly manual, process has lead to the number of reported crashes out-pacing the number of bug fixes ...
Jiang, Zhiyuan +5 more
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Clustering Rooted Ordered Trees
2007 IEEE Symposium on Computational Intelligence and Data Mining, 2007Tree structures have gained popularity for storing data from different domains such as XML documents, bio informatics and so on. Clustering these data can facilitate different operations. In this paper, we propose TreeCluster, a novel and heuristic algorithm for clustering tree structured data.
Mostafa Haghir Chehreghani +3 more
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Cluster roots: A curiosity in context
Plant and Soil, 2005Cluster roots are an adaptation for nutrient acquisition from nutrient-poor soils. They develop on root systems of a range of species belonging to a number of different families (e.g., Proteaceae, Casuarinaceae, Fabaceae and Myricaceae) and are also found on root systems of some crop species (e.g., Lupinus albus, Macadamia integrifolia and Cucurbita ...
Michael W. Shane, Hans Lambers
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Regions of polynomial root clustering
Journal of the Franklin Institute, 1977Abstract A criterion for root exclusion from a region composed as a union of elemental regions—discs and halfplanes—is established. Associated with each elemental region is a derived polynomial which must be by the criterion a strictly Hurwitz polynomial.
Bickart, T. A., Jury, E. I.
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Admissible Regions for Root Clustering
IMA Journal of Mathematical Control and Information, 1986Given \(A\in {\mathbb{C}}^{n\times n}\) and an algebraic region R, we find necessary and sufficient conditions for the inclusion \(\sigma\) (A)\(\subset R\), where \(\sigma\) (A) is the spectrum of A. We present a general test based on the composite matrix approach.
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Freezing rooted cluster morphisms and pro-cluster algebras
2022We provide a new tool for studying cluster algebras by introducing a new category fClus of rooted cluster algebras. We characterize isomorphisms in our new category and show that it is neither complete nor cocomplete. We give a recipe for constructing morphisms in fClus with an interesting geometric interpretation and study the corresponding inverse ...
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RAIRO - Theoretical Informatics and Applications, 2014
Six kinds of both of primitivity and periodicity of words, introduced by Ito and Lischke [M. Ito and G. Lischke, Math. Log. Quart. 53 (2007) 91–106; Corrigendum in Math. Log. Quart. 53 (2007) 642–643], give rise to defining six kinds of roots of a nonempty word.
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Six kinds of both of primitivity and periodicity of words, introduced by Ito and Lischke [M. Ito and G. Lischke, Math. Log. Quart. 53 (2007) 91–106; Corrigendum in Math. Log. Quart. 53 (2007) 642–643], give rise to defining six kinds of roots of a nonempty word.
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An Existence Test for Root Clusters and Multiple Roots
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1988Let f be analytic in the interior of the disk \(K(\tilde z;r)\) with center \(\tilde z\) and radius r, and let ...
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Distribution and Function of Proteoid Roots and other Root Clusters
Botanica Acta, 1995AbstractProteoid roots are bottlebrush‐like clusters of rootlets which form along lateral roots. They are characteristic of most species of the Proteaceae, which are mainly distributed in Australia and South Africa. Homologous root clusters are present in species of the Casuarinaceae, Mimosaceae, Fabaceae, Myricaceae and Moraceae.
Barbara Dinkelaker +2 more
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