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Most previous analysis of Twitter user behavior has focused on individual information cascades and the social followers graph, in which the nodes for two users are connected if one follows the other. We instead study aggregate user behavior and the retweet graph with a focus on quantitative descriptions. We find that the lifetime tweet distribution is a type-II discrete Weibull stemming from a power law hazard function, that the tweet rate distribution, although asymptotically power law, exhibits a lognormal cutoff over finite sample intervals, and that the inter-tweet interval distribution is a power law with exponential cutoff. The retweet graph is small-world and scale-free, like the social graph, but less disassortative and has much stronger clustering. These differences are consistent with it better capturing the real-world social relationships of and trust between users than the social graph. Beyond just understanding and modeling human communication patterns and social networks, applications for alternative, decentralized microblogging systems-both predicting real-word performance and detecting spam-are discussed.

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Hybrid Na‐ion capacitors (NICs) are receiving considerable interest because they combine the merits of both batteries and supercapacitors and because of the low‐cost of sodium resources. However, further large‐scale deployment of NICs is impeded by the sluggish diffusion of Na+ in the anode. To achieve rapid redox kinetics, herein the controlled fabrication of mesoporous orthorhombic‐Nb2O5 (T‐Nb2O5)/carbon nanofiber (CNF) networks is demonstrated via in situ SiO2‐etching. The as‐obtained mesoporous T‐Nb2O5 (m‐Nb2O5)/CNF membranes are mechanically flexible without using any additives, binders, or current collectors. The in situ formed mesopores can efficiently increase Na+‐storage performances of the m‐Nb2O5/CNF electrode, such as excellent rate capability (up to 150 C) and outstanding cyclability (94% retention after 10 000 cycles at 100 C). A flexible NIC device based on the m‐Nb2O5/CNF anode and the graphene framework (GF)/mesoporous carbon nanofiber (mCNF) cathode, is further constructed, and delivers an ultrahigh power density of 60 kW kg−1 at 55 Wh kg−1 (based on the total weight of m‐Nb2O5/CNF and GF/mCNF). More importantly, owing to the free‐standing flexible electrode configuration, the m‐Nb2O5/CNF//GF/mCNF NIC exhibits high volumetric energy and power densities (11.2 mWh cm−3, 5.4 W cm−3) based on the full device, which holds great promise in a wide variety of flexible electronics.

Hard carbon (HC) is a promising anode material for K+-storage due to its randomly oriented turbostratic structure. However, most reported HC anodes exhibit low initial Coulombic efficiency (ICE) and no...

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