Normalized entropy of rank distribution： a novel measure of heterogeneity of complex networks

Many unique properties of complex networks result from heterogeneity. The measure and analysis of heterogeneity are important and desirable to the research of the properties and functions of complex networks. In this paper, the rank distribution is proposed as a new statistic feature of complex networks. Based on the rank distribution, a novel measure of the heterogeneity called a normalized entropy of rank distribution （NERD） is proposed. The NERD accords with the normal meaning of heterogeneity within the context of complex networks compared with conventional measures. The heterogeneity of scale-free networks is studied using the NERD. It is shown that scale-free networks become more heterogeneous as the scaling exponent decreases and the NERD of scale-free networks is independent of the number of vertices, which indicates that the NERD is a suitable and effective measure of heterogeneity for networks with different sizes.

Assessment of the Elastic-Wave Well Treatment in Oil-Bearing Clastic and Carbonate Reservoirs

A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustically induced effects).In such a context,a new technique is proposed to predict the effectiveness of the elastic-wave well treatment using the rank distribution according to Zipf’s law.It is revealed that,when the results of elastic wave well treatments are analyzed,groups of wells exploiting various geological deposits can differ in terms of their slope coefficients and free members.As the slope coefficient increases,the average increase in the well oil production rate(after the well treatment)becomes larger.An equation is obtained accordingly for estimating the slope coefficient in the Zipf’s equation from the frequency of the elastic wave.The obtained results demonstrate the applicability of the Zipf’s law in the analysis of the technological efficiency of elastic-wave well treatment methods.

High-throughput metabarcoding of SAR11 assemblages from the southwest Atlantic shelf and arid Patagonia:richness and associated rank abundance distributions

Background:Massively parallel sequencing of environmental DNA allows microbiological studies to be performed in greater detail than was possible with first-generation sequencing.For example,it facilitates the use of approaches hitherto largely applied to flora and fauna,such as rank abundance distribution(RAD)analyses.Methods:Here,we set out to advance the knowledge on Ca.Pelagibacterales(SAR11)communities from southern South America using environmental sequences from the open ocean in the Argentine sea,the uncharted Engaño Bay,as well as a river and an oligohaline shallow lake from the Patagonian Steppe ecoregion.The structures of the SAR11 assemblages present in these ecosystems were dissected by direct and rarefaction-based estimates of species richness,and evaluations of the corresponding abundance distributions(ADs),which was addressed by RAD analyses.Results:Microbial community composition analyses revealed that the studied SAR11 assemblages coexist with 27 bacterial phyla.SAR11 richness was in general very high,but ADs turned out to be highly uneven.The results were compatible with prior knowledge,and similar to that derived from point estimates of diversity.However,our comprehensive dissection allowed for more detailed quantitative comparisons to be made between the environments surveyed,and revealed differences regarding both richness and the underlying ADs.Conclusions:Despite SAR11 assemblages being extremely rich,their ADs are very uneven.Richness and ADs can vary,not only between fresh and salt water,but also between oceanic and coastal marine environments.The obtained results provide insights on general topics such as adaptation and the contrast between marine and freshwater radiations.

Similarities and differences of city-size distributions in three main urban agglomerations of China from 1992 to 2015： A comparative study based on nighttime light data

Comparing the city-size distribution at the urban agglomeration（UA） scale is important for understanding the processes of urban development. However, comparative studies of city-size distribution among China＇s three largest UAs, the Beijing-Tianjin-Hebei agglomeration（BTHA）, the Yangtze River Delta agglomeration（YRDA）, and the Pearl River Delta agglomeration（PRDA）, remain inadequate due to the limitation of data availability. Therefore, using urban data derived from time-series nighttime light data, the common characteristics and distinctive features of city-size distribution among the three UAs from 1992 to 2015 were compared by the Pareto regression and the rank clock method. We identified two common features. First, the city-size distribution became more even. The Pareto exponents increased by 0.17, 0.12, and 0.01 in the YRDA, BTHA, and PRDA, respectively. Second, the average ranks of small cities ascended, being 0.55, 0.08 and 0.04 in the three UAs, respectively. However, the average ranks of large and medium cities in the three UAs experienced different trajectories, which are closely related to the similarities and differences in the driving forces for the development of UAs. Place-based measures are encouraged to promote a coordinated development among cities of differing sizes in the three UAs.