This article is an addendum to the 2001 paper [1] which investigated an approach to hierarchical clustering based on the level sets of a density function induced on data points in a d-dimensional feature space. We ref...This article is an addendum to the 2001 paper [1] which investigated an approach to hierarchical clustering based on the level sets of a density function induced on data points in a d-dimensional feature space. We refer to this as the “level-sets approach” to hierarchical clustering. The density functions considered in [1] were those formed as the sum of identical radial basis functions centered at the data points, each radial basis function assumed to be continuous, monotone decreasing, convex on every ray, and rising to positive infinity at its center point. Such a framework can be investigated with respect to both the Euclidean (L2) and Manhattan (L1) metrics. The addendum here puts forth some observations and questions about the level-sets approach that go beyond those in [1]. In particular, we detail and ask the following questions. How does the level-sets approach compare with other related approaches? How is the resulting hierarchical clustering affected by the choice of radial basis function? What are the structural properties of a function formed as the sum of radial basis functions? Can the levels-sets approach be theoretically validated? Is there an efficient algorithm to implement the level-sets approach?展开更多
Ophiolites are fragments of oceanic lithosphere that are produced at spreading centers at ocean ridges,back arc basins,or forearcs during subduction initiation,and are key indicators of plate tectonics.Although it is ...Ophiolites are fragments of oceanic lithosphere that are produced at spreading centers at ocean ridges,back arc basins,or forearcs during subduction initiation,and are key indicators of plate tectonics.Although it is widely agreed that ophiolites are remnants of oceanic crust and associated depleted mantle preserved in orogens,the recognition of ophiolites and their tectonic significance is still a topic of discussion and disagreement.We propose that ophiolites can be recognized in the geologic record by some combination of genetically related pillow basalt,layered gabbro,sheeted dykes,podiform chromite,harzburgite or/and dunite.Mafic igneous rocks have either ocean-ridge basalt or immature oceanic arc basalt chemical compositions.Using a scoring system of 1–11 for ophiolite confidence level,scores of8 are considered confident,6–8 probable,and<6 questionable or unlikely ophiolites.Most ophiolites with scores6 are<900 Ma.The oldest confident ophiolite(score of 8)is the Zunhua ophiolite in eastern China at 2550 Ma,and the oldest well documented sheeted dykes occur in the Jormua and Purtuniq ophiolites at 2000–1950 Ma.Ophiolites do not become geographically widespread until after 900 Ma,and most ophiolites of all ages formed in a forearc(subduction initiation)tectonic setting.If ophiolite production requires plate tectonics,subduction must have begun at least locally by 2700 Ma but did not become widespread until after 2000 Ma.The abundance of ophiolites after 900 Ma may reflect better preservation of subduction-related ophiolites,or to an increasing global network of interconnected plates.Ophiolite frequency peaks in the geologic record partially reflect geographic regions where ophiolites have been extensively studied rather than monitoring the production rate of ophiolites,but the scarcity of>900 Ma ophiolites is probably real.展开更多
文摘This article is an addendum to the 2001 paper [1] which investigated an approach to hierarchical clustering based on the level sets of a density function induced on data points in a d-dimensional feature space. We refer to this as the “level-sets approach” to hierarchical clustering. The density functions considered in [1] were those formed as the sum of identical radial basis functions centered at the data points, each radial basis function assumed to be continuous, monotone decreasing, convex on every ray, and rising to positive infinity at its center point. Such a framework can be investigated with respect to both the Euclidean (L2) and Manhattan (L1) metrics. The addendum here puts forth some observations and questions about the level-sets approach that go beyond those in [1]. In particular, we detail and ask the following questions. How does the level-sets approach compare with other related approaches? How is the resulting hierarchical clustering affected by the choice of radial basis function? What are the structural properties of a function formed as the sum of radial basis functions? Can the levels-sets approach be theoretically validated? Is there an efficient algorithm to implement the level-sets approach?
文摘Ophiolites are fragments of oceanic lithosphere that are produced at spreading centers at ocean ridges,back arc basins,or forearcs during subduction initiation,and are key indicators of plate tectonics.Although it is widely agreed that ophiolites are remnants of oceanic crust and associated depleted mantle preserved in orogens,the recognition of ophiolites and their tectonic significance is still a topic of discussion and disagreement.We propose that ophiolites can be recognized in the geologic record by some combination of genetically related pillow basalt,layered gabbro,sheeted dykes,podiform chromite,harzburgite or/and dunite.Mafic igneous rocks have either ocean-ridge basalt or immature oceanic arc basalt chemical compositions.Using a scoring system of 1–11 for ophiolite confidence level,scores of8 are considered confident,6–8 probable,and<6 questionable or unlikely ophiolites.Most ophiolites with scores6 are<900 Ma.The oldest confident ophiolite(score of 8)is the Zunhua ophiolite in eastern China at 2550 Ma,and the oldest well documented sheeted dykes occur in the Jormua and Purtuniq ophiolites at 2000–1950 Ma.Ophiolites do not become geographically widespread until after 900 Ma,and most ophiolites of all ages formed in a forearc(subduction initiation)tectonic setting.If ophiolite production requires plate tectonics,subduction must have begun at least locally by 2700 Ma but did not become widespread until after 2000 Ma.The abundance of ophiolites after 900 Ma may reflect better preservation of subduction-related ophiolites,or to an increasing global network of interconnected plates.Ophiolite frequency peaks in the geologic record partially reflect geographic regions where ophiolites have been extensively studied rather than monitoring the production rate of ophiolites,but the scarcity of>900 Ma ophiolites is probably real.
