Average distance in a hierarchical scale-free network: an exact solution

Various real systems simultaneously exhibit scale-free and hierarchical structure. In this paper, we study analytically average distance in a deterministic scale-free network with hierarchical organization. Using a recursive method based on the network construction, we determine explicitly the average distance, obtaining an exact expression for it, which is confirmed by extensive numerical calculations. The obtained rigorous solution shows that the average distance grows logarithmically with the network order (number of nodes in the network). We exhibit the similarity and dissimilarity in average distance between the network under consideration and some previously studied networks, including random networks and other deterministic networks. On the basis of the comparison, we argue that the logarithmic scaling of average distance with network order could be a generic feature of deterministic scale-free networks.Comment: Definitive version published in Journal of Statistical Mechanic

Atrocalopteryx melli orohainani ssp. nov. on the Island of Hainan, China (Zygoptera: Calopterygidae)

The new sp. is described from the mountain core of Hainan, southern China, where it usually occurs at altitudes not lower than 300 m asl. It lives on the same type of small, shaded rivers as the nominate ssp. on the continent, and is distinguished by its larger size, slightly less enfumed wings, and a 2.6% difference in the sequence of the barcoding portion of the mitochodrial DNA-cytochrome c oxidase subunit I gene (COI). Holotype male: Diaoluoshan mountain, 6-VIII-2011; deposited in the Inst. Hydrobiol., Jinan Univ., Guanghou. It is argued that this geographically defined ssp. evolved because of persistent poor gene flow with continental populations, caused by the lowland "panhandle" between Hainan and the continent. This barrier was probably functioning equally well during interglacials (like at present) as during pleniglacials (when Hainan was connected to the mainland), because lack of suitable environments (small sized running waters), and dry and cold conditions continued to limit the contact with A. melli of the mainland

Experimental study on sinter pot test with added light burnt dolomite in sintering production

Reasonable matching structure of sintering flux has great effect on improving the sinter quality and reducing energy consumption. In this paper, the feasibility of replacing part or all of quick lime in sintering production with limestone, dolomite, light burnt magnesium powder and light burnt dolomite is studied by sinter pot test in the lab. The result shows that when with 5,47 % of light burnt dolomite replacing part of the quick lime, the results such as the weighted average of sinter granularity, the production yield, the utilization coefficient, the tumbler index and the reduction degree meet the actual production requirements

Exact solution of mean geodesic distance for Vicsek fractals

The Vicsek fractals are one of the most interesting classes of fractals and the study of their structural properties is important. In this paper, the exact formula for the mean geodesic distance of Vicsek fractals is found. The quantity is computed precisely through the recurrence relations derived from the self-similar structure of the fractals considered. The obtained exact solution exhibits that the mean geodesic distance approximately increases as an exponential function of the number of nodes, with the exponent equal to the reciprocal of the fractal dimension. The closed-form solution is confirmed by extensive numerical calculations.Comment: 4 pages, 3 figure

On the convergence of stochastic dual dynamic programming and related methods

We discuss the almost-sure convergence of a broad class of sampling algorithms for multi-stage stochastic linear programs. We provide a convergence proof based on the finiteness of the set of distinct cutcoefficients. This differs from existing published proofs in that it does not require a restrictive assumption