Observations of Eros at the Opposition 1930-31

Jones, Harold Spencer

doi:10.1093/mnras/90.8.724

Monthly Notices of the Royal Astronomical Society

1930

DOI: 10.1093/mnras/90.8.724

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Observations of Eros at the Opposition 1930-31

Harold Spencer Jones

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1961

2011

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“…Most recently, the notions of "strongly" versus "weakly" discontinuous transitions have been introduced [16], with the model studied in [6] showing weakly discontinuous characteristics, while an idealized deterministic "most explosive" model [15,17] is strongly discontinuous. Here we analyze and extend a related model by Bohman, Frieze and Wormald (BFW) [1], which predates the more recent work, and show that surprisingly [18], multiple stable giant components can coexist and that the percolation transition is strongly discontinuous.The "most explosive" deterministic process [15][16][17] begins with n isolated nodes, with n set to a power of two for convenience. Edges that connect pairs of isolated nodes are added sequentially, creating components of size k = 2, until no isolated nodes remain.…”

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“…The existence of multiple stable macroscopic components is surprising and unanticipated [18], and has not been previously observed in stochastic percolation. A model of cluster aggregation where largest clusters are occasionally "frozen" and prevented from growing, does lead to multiple giant components [20], however the freezing is imposed on the system.…”

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Explosive Percolation with Multiple Giant Components

2011

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We generalize the random graph evolution process of Bohman, Frieze, and Wormald [T. Bohman, A. Frieze, and N. C. Wormald, Random Struct. Algorithms, 25, 432 (2004)]. Potential edges, sampled uniformly at random from the complete graph, are considered one at a time and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function asymptotically approaching the value α = 1/2. We show that multiple giant components appear simultaneously in a strongly discontinuous percolation transition and remain distinct. Furthermore, tuning the value of α determines the number of such components with smaller α leading to an increasingly delayed and more explosive transition. The location of the critical point and strongly discontinuous nature are not affected if only edges which span components are sampled. The percolation phase transition models the onset of large-scale connectivity in lattices or networks, in systems ranging from porous media, to resistor networks, to epidemic spreading [2][3][4][5]. Percolation was considered a robust second-order transition until a variant with a choice between edges was shown to result in a seemingly discontinuous transition [6]. Subsequent studies have shown similar results for scale-free networks [7,8], lattices [9, 10], local cluster aggregation models [11], singleedge addition models [12,13], and models which control only the largest component [14]. It seems a fundamental requirement that in the sub-critical regime the evolution mechanism produces many clusters which are relatively large, though sublinear, in size [11,12,15]. Most recently, the notions of "strongly" versus "weakly" discontinuous transitions have been introduced [16], with the model studied in [6] showing weakly discontinuous characteristics, while an idealized deterministic "most explosive" model [15,17] is strongly discontinuous. Here we analyze and extend a related model by Bohman, Frieze and Wormald (BFW) [1], which predates the more recent work, and show that surprisingly [18], multiple stable giant components can coexist and that the percolation transition is strongly discontinuous.The "most explosive" deterministic process [15][16][17] begins with n isolated nodes, with n set to a power of two for convenience. Edges that connect pairs of isolated nodes are added sequentially, creating components of size k = 2, until no isolated nodes remain. The cutoff k is then doubled and edges leading to components of size k = 4 are added sequentially, until all components have size k = 4. k is then doubled yet again and the process iterated. By the end of the phase k = n/2, only two components remain, each with size n/2. The addition of the next edge connects those two components during which the size of * Electronic address: chwei@ucdavis.edu † Electronic address: raissa@cse.ucdavis.edu the largest component jumps in value by n/2. Letting t denote the number of edges added to the graph, we define the critical t c as the single edge who's addition produces the l...

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Explosive Percolation with Multiple Giant Components

2011

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Harold Spencer Jones, 1890-1960

Woolley¹

1961

Biogr. Mems Fell. R. Soc.

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Harold Spencer Jones was the third child, and eldest son, of Henry Charles Jones, an accountant, and Sarah Ryland, who had been a schoolmistress. He was born in Kensington on 29 March 1890 and exhibited as a child a remarkable interest in mathematics. He was encouraged in his mathematical interests by his parents, and went to Latymer Upper School, from which he won a scholarship to Jesus College, Cambridge. He took a First Class in Part I of the Mathematical Tripos in 1909, and was a Wrangler in Part II of the Tripos in 1911. He then read Part II of the Natural Sciences Tripos, in Physics, and again secured a First. He was second Smith’s Prizeman in 1913 and Isaac Newton Student in 1912. In 1913 he was elected to a Fellowship in Jesus College. In 1913 he was appointed Chief Assistant at the Royal Observatory, which was then at Greenwich, where he remained for ten years, with some interruption occasioned by the 1914-1918 war. During Spencer Jones’s first period at Greenwich he went to Russia with C. R. Davidson to observe the eclipse of 1914. He wrote several papers on a subject which remained one of great interest to him, namely the variation of latitude, as observed by the Cookson floating telescope. He also made a determination of the photographic magnitude scale of the North Polar Sequence. In the midst of these activities, he was appointed to the office of H.M. Astronomer at the Cape of Good Hope, taking up office in 1923. He was, of course, a young man to be appointed to such a position, in which he was director of a large observatory.

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Observations of Eros at the Opposition 1930-31

Cited by 2 publications

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Explosive Percolation with Multiple Giant Components

Explosive Percolation with Multiple Giant Components

Harold Spencer Jones, 1890-1960

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