Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems.
An adaptive label propagation algorithm (ALPA) is proposed to detect and monitor communities in dynamic networks. Unlike the traditional methods by re-computing the whole community decomposition after each modification of the network, ALPA takes into account the information of historical communities and updates its solution according to the network modifications via a local label propagation process, which generally affects only a small portion of the network. This makes it respond to network changes at low computational cost. The effectiveness of ALPA has been tested on both synthetic and real-world networks, which shows that it can successfully identify and track dynamic communities. Moreover, ALPA could detect communities with high quality and accuracy compared to other methods. Therefore, being low-complexity and parameter-free, ALPA is a scalable and promising solution for some real-world applications of community detection in dynamic networks.
Abstract. The label propagation algorithm (LPA) has been proved to be a fast and effective method for detecting communities in large complex networks. However, its performance is subject to the non-stable and trivial solutions of the problem. In this paper, we propose a modified label propagation algorithm LPAf to efficiently detect community structures in networks. Instead of the majority voting rule of the basic LPA, LPAf updates the label of a node by considering the compression of a description of random walks on a network. A multi-step greedy agglomerative strategy is employed to enable LPAf to escape the local optimum. Furthermore, an incomplete update condition is also adopted to speed up the convergence.Experimental results on both synthetic and real-world networks confirm the effectiveness of our algorithm.
PACS
The
main limitations on the power conversion efficiency (PCE) of
all-polymer solar cells (all-PSCs) are the weak absorption coefficients
of widely used naphthalene diimide (NDI)-based polymer acceptors and
the difficulty of morphology control. Herein, a 3,3′-difluoro-2,2′-bithiophene
(2FT) unit is introduced into the NDI-based polymer N2200 by random
copolymerization, creating three terpolymer acceptors PNDI-2FT-0.1,
PNDI-2FT-0.2, and PNDI-2FT-0.3. Incorporation of 2FT into the backbone
is found to significantly improve the absorption coefficients of terpolymers.
More importantly, it can be observed that random copolymerization
of 2FT into the backbone not only can reduce the strong aggregation
of the polymer but also can produce more flexible main chains to favor
closer contact and better miscibility with the crystalline donor PBDB-T
relative to the N2200 bipolymer. Under the optimal condition, a PBDB-T:PNDI-2FT-0.1-based
device achieves a notable PCE of 9.46% with a short-circuit current
(J
SC) of 16.62 mA cm–2. Note that both the PCE and J
SC are
the outstanding values in NDI-based all-PSCs. Moreover, the optimized
morphology of a bulk heterojunction induced by random terpolymers
enables an active layer that has good thickness tolerance. These results
demonstrate that the simultaneous regulation of light absorption and
miscibility between a donor and an acceptor by random copolymerization
is a promising strategy to realize high-performance all-PSCs.
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