Directed mixed membership stochastic blockmodel

Mixed membership problem for undirected network has been well studied in network analysis recent years. However, the more general case of mixed membership for directed network remains a challenge. Here, we propose an interpretable and identifiable model: directed mixed membership stochastic blockmodel (DiMMSB for short) for directed mixed membership networks. DiMMSB allows that row nodes and column nodes of the adjacency matrix can be different and these nodes may have distinct community structure in a directed network. We also develop an efficient spectral algorithm called DiSP designed based on simplex structures inherent in the left and right singular vectors of the population adjacency matrix to estimate the mixed memberships for both row nodes and column nodes in a directed network. We show that DiSP is asymptotically consistent under mild conditions by providing error bounds for the inferred membership vectors of each row node and each column node using delicate spectral analysis. We demonstrate the advantages of DiSP with applications to simulated directed mixed membership network, the directed Political blogs network and the Papers Citation network.Comment: 35 pages, 6 figures, 2 table

Consistency of spectral clustering for directed network community detection

Directed networks appear in various areas, such as biology, sociology, physiology and computer science. In this paper, we construct a spectral clustering method based on the singular decomposition of the adjacency matrix to detect community in directed stochastic block model (DiSBM). By considering a sparsity parameter, under mild conditions, we show the proposed approach can consistently recover hidden row and column communities for different scaling of degrees. By considering the degree heterogeneity of both row and column nodes, we further modify the proposed method and establish a theoretical framework for directed degree corrected stochastic block model (DiDCSBM), and also show the consistency of the modified method for this case. Our theoretical results under DiSBM and DiDCSBM provide some innovations on some special directed networks, such as directed network with balanced clusters, directed network with nodes enjoying similar degrees, and the directed Erd\"os-R\'enyi graph. Furthermore, the theoretical results under DiDCSBM are consistent with those under DiSBM.Comment: 20 pages, comments are welcom

Analysis of Renewable Energy Research Hotspots and Trends Based on Bibliometric and Patent Survey

In recent years, renewable energy has taken on an increasingly important role as a result of the depletion of traditional fossil fuels and the pressure of climate change. Due to the advantages of clean energy production and wide availability, research on renewable energy has increased worldwide. We collected data from the Web of Science and the Derwent Innovations Index to analyze research trends in the field of renewable energy. It was found that the number of research achievements in this field has developed rapidly worldwide since 2005. The United States ranks first in the quantity and quality of literature and fourth in the number of authorized patents. China ranks second and first regarding the quantity of literature and authorized patents, respectively. Biomass energy, wind energy, and solar energy are trending research topics in various stages of development. China has maintained close cooperation with the United States, the United Kingdom, Australia, and other countries

Regulation of blood pressure during long-term ouabain infusion in Long-Evans rats

We tested whether ouabain, an inhibitor of the sodium pump, can lead to chronic hypertension in Long-Evans rats using sensitive 24-h measurements of blood pressure. After a control week of vehicle isotonic saline infusion (14.4 mL/day), ouabain was infused intravenously at 30 μg/kg/day in intact (2K) and uninephrectomized (1K) Long-Evans rats for a total of 4 weeks. Although plasma ouabain concentration rose to 0.97 ± 0.15 nmol/L with ouabain infusion, mean arterial pressure did not change in either 2K (Δ = −0.6 ± 1.3 mm Hg) or 1K (Δ = −1.2 ± 0.7 mm Hg) rats. These data suggest that Long-Evans rats are insensitive to the hypertensive effects of ouabain. Am J Hypertens 1999;12:423-426 © 1999 American Journal of Hypertension, Lt

Reliability modeling and evaluation of MMCs under different redundancy schemes

Due to the demand for high reliability, modular multilevel converters (MMCs) are designed with redundant submodules. Redundant submodules can be integrated into the converter by employing different redundancy schemes: The conventional active scheme, the load-sharing active scheme, and the passive scheme. Different schemes have different impacts on the improvement of converter reliability. The contributions of this paper include that an analytical method is proposed to evaluate the reliability of MMCs under different redundancy schemes and the factors' influence on the converter reliability is analyzed to determine the proper redundancy scheme. Reliability models of MMCs under different redundancy schemes are built using Markov chains and the iteration method. Based on the proposed models, the effects of redundant schemes are evaluated in terms of the converter reliability. A case study is conducted to validate the feasibility and robustness of proposed models and to specify the conditions in the favor of each redundancy scheme. The benefits of sharing redundancy among arms are also explored from the reliability point of view. If insulated-gate bipolar transistors (IGBTs) and capacitors are dominant components in a submodule in terms of failure rates, the load-sharing active scheme performs better; otherwise, setting the redundant submodules in an idle state is more effective. It is also found that the number of required redundant submodules is greatly reduced by sharing redundancy among arms