This approach by Strehl and Ghosh introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. They discuss three approaches towards solving this problem to obtain high quality consensus functions. Their techniques have low computational costs and this makes it feasible to evaluate each of the techniques discussed below and arrive at the best solution by comparing the results against the objective function.
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Despite the many partitionings, Campos Novos is still one of the biggest municipality of Santa Catarina regarding the surface area. From 1869 until 1881, Campos Novos was under control of Curitibanos. Then it became an independent municipality, according to provincial law nº 923, of March 30, 1881.
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Extensive modifications have been made to the spatial arrangement of the interior of the ground floor, with partitionings of studwork and masonry, which effectively mirror the changes made to the interior over what is now more than twenty years of adaption. The upper level has been less modified.
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Sommerville used geometry to describe the voting theory of a preferential ballot.D. Sommerville (1928) "Certain hyperspatial partitionings connected with preferential voting", Proceedings of the London Mathematical Society 28(1):368 to 82 He addressed Nanson's method where n candidates are ordered by voters into a sequence of preferences. Sommerville shows that the outcomes lie in n ! simplexes that cover the surface of an n − 2 dimensional spherical space.
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Box Butte County was formed as part of a series of partitionings of the Nebraska Panhandle. In 1883, the Nebraska legislature divided the Panhandle into two counties, Sioux and Cheyenne. In 1885 the original Sioux County was divided into three counties: Sioux, Dawes, and Sheridan. Because of the distance to the county seat of Chadron, residents of southern Dawes County asked that it be split off; in 1886, the legislature created Box Butte County.
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Every member of the empty set is a nonempty set (that is vacuously true), and their union is the empty set. Therefore, the empty set is the only partition of itself. As suggested by the set notation above, we consider neither the order of the partitions nor the order of elements within each partition. This means that the following partitionings are all considered identical: :{ {b}, {a, c} } :{ {a, c}, {b} } :{ {b}, {c, a} } :{ {c, a}, {b} }.
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1913: King Abdulaziz Al Saud conquers Al-Ahsa Oasis, annexing it into his Kingdom of Najd. (This is recognised in the Treaty of Sèvres signed in 1920 with the other official partitionings of the Ottoman Empire.) 1932: Al-Ahsa becomes part of the Kingdom of Saudi Arabia, under the King Abdulaziz. 1930s: Huge petroleum deposits are discovered near Dammam, resulting in rapid modernization for the region. Jabal Qara is located 16 km (9.9 mi) east of Hofuf City Early 1960s: The oil fields in Al-Ahsa reach the production level of 1 million barrels per day.
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2.5D datasets can be conveniently represented on a framework of boxels, which are axis-aligned non- intersecting boxes that can be used to directly represent objects in the scene or as bounding volumes. Leonidas J. Guibas and Yuan Yao's work showed that axis- aligned disjoint rectangles in the plane can be ordered into four total orders so that any ray meets them in one of the four orders. This work has been proven to also be applicable to boxels in this context, and it is shown that there exist four different partitionings of the boxels into ordered sequences of disjoint sets, called antichains, so that boxels in one antichain can act as occluders of the boxels in subsequent antichains. The expected runtime for the antichain partitioning is O(n log n), where n is the number of boxels.
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