Optimal regularity of minimal graphs in the hyperbolic space

We discuss the global regularity of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space when the boundary of the domain $\Omega\subset\mathbb R^n$ has a nonnegative mean curvature and prove an optimal regularity $f\in C^{\frac{1}{n+1}}(\bar{\Omega})$. We can improve the H\"older exponent for $f$ if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.Comment: Accepted by Calc. Var. Partial Differential Equation

Benchmarking the Privacy-Preserving People Search

People search is an important topic in information retrieval. Many previous studies on this topic employed social networks to boost search performance by incorporating either local network features (e.g. the common connections between the querying user and candidates in social networks), or global network features (e.g. the PageRank), or both. However, the available social network information can be restricted because of the privacy settings of involved users, which in turn would affect the performance of people search. Therefore, in this paper, we focus on the privacy issues in people search. We propose simulating different privacy settings with a public social network due to the unavailability of privacy-concerned networks. Our study examines the influences of privacy concerns on the local and global network features, and their impacts on the performance of people search. Our results show that: 1) the privacy concerns of different people in the networks have different influences. People with higher association (i.e. higher degree in a network) have much greater impacts on the performance of people search; 2) local network features are more sensitive to the privacy concerns, especially when such concerns come from high association peoples in the network who are also related to the querying user. As the first study on this topic, we hope to generate further discussions on these issues.Comment: 4 pages, 5 figure

Gravitational waves with dark matter minispikes: the combined effect

It was shown that the dark matter(DM) minihalo around an intermediate mass black hole(IMBH) can be redistributed into a cusp, called the DM minispike. We consider an intermediate-mass-ratio inspiral consisting of an IMBH harbored in a DM minispike with nonannihilating DM particles and a small black hole(BH) orbiting around it. We investigate gravitational waves(GWs) produced by this system and analyze the waveforms with the comprehensive consideration of gravitational pull, dynamical friction and accretion of the minispike and calculate the time difference and phase difference caused by it. We find that for a certain range of frequency, the inspiralling time of the system is dramatically reduced for smaller central IMBH and large density of DM. For the central IMBH with $10^5M_\odot$, the time of merger is ahead, which can be distinguished by LISA, Taiji and Tianqin. We focus on the effect of accretion and compare it with that of gravitational pull and friction. We find that the accretion mass is a small quantity compared to the initial mass of the small BH and the accretion effect is inconspicuous compared with friction. However, the accumulated phase shift caused by accretion is large enough to be detected by LISA, Taiji and Tianqin, which indicate that the accretion effect can not be ignored in the detection of GWs.Comment: 10 pages, 14 figure

Coauthor prediction for junior researchers

Research collaboration can bring in different perspectives and generate more productive results. However, finding an appropriate collaborator can be difficult due to the lacking of sufficient information. Link prediction is a related technique for collaborator discovery; but its focus has been mostly on the core authors who have relatively more publications. We argue that junior researchers actually need more help in finding collaborators. Thus, in this paper, we focus on coauthor prediction for junior researchers. Most of the previous works on coauthor prediction considered global network feature and local network feature separately, or tried to combine local network feature and content feature. But we found a significant improvement by simply combing local network feature and global network feature. We further developed a regularization based approach to incorporate multiple features simultaneously. Experimental results demonstrated that this approach outperformed the simple linear combination of multiple features. We further showed that content features, which were proved to be useful in link prediction, can be easily integrated into our regularization approach. © 2013 Springer-Verlag

Laboratory studies on the temperature-phased anaerobic digestion of mixtures of primary and waste activated sludge

The temperature-phased anaerobic digestion (TPAD) involves the operation of two reactors in series, the first maintained at a thermophilic temperature (commonly 55° C) and the second maintained at a mesophilic temperature (commonly 35° C).;The purpose of the research was to compare the performance of the temperature-phased system with the conventional single-stage mesophilic system for treating mixtures of primary sludge (PS) and waste activated sludge (WAS). The TPAD systems used in the study consisted of two, completely-mixed reactors operated in series. The first and the second stages were operated at 55° C and 35° C, respectively. The single-stage system was operated at 35° C.;The reactors were fed 50-50 volumetric mixtures of PS and WAS. The WAS had an approximate total solids (TS) content of four percent. The TS content of the PS varied in a range from 3 to 5%, but was adjusted to 4% by either dewatering or dilution. The systems were operated as completely-mixed reactors over a range of solids retention times (SRT) from 11 to 40 days. The minimum and maximum SRTs in the thermophilic first-stage was one to eight days, respectively;The single-stage mesophilic unit achieved volatile solids (VS) destructions ranging from 32% at the 24-day SRT to 47% at the 40-day SRT. VS destruction for two-stage System A varied from 45% at the 14-day SRT to 50% at the 28-day SRT. For two-stage system B, VS destruction varied from 34% at the 11-day SRT to 45% at the 24-day SRT;For the same VS removal, the SRT required for the two-stage system was only 40% of that require for the single-stage system. In other words, the capacity was more than doubled by using the TPAD system without any deterioration in VS destruction. The increased capacity of the TPAD system was due to the much higher reaction rate achieved at the higher temperature in the first thermophilic stage. The biogas production per unit volume of the TPAD system was higher in proportion to the increased VS destruction in the TPAD system, as compared with the single-stage mesophilic system;The TPAD systems greatly outperformed the single-stage system in terms of both total and fecal coliform destruction. The single-stage mesophilic system achieved only a one log or less reduction in fecal coliforms. In contrast, the TPAD system achieved an average six log reduction in fecal coliforms. The effluent fecal coliform content was always far below 1000 MPN/g TS. Serious foaming in the single-stage was observed in an SRT range from 24 to 34 days. Nearly no foaming existed in both TPAD systems at all SRTs studied;It is concluded that the TPAD system for sludge digestion combines the advantages of thermophilic digestion (higher rates of VS destruction, high coliform destruction, and reduced foaming) with the advantages of mesophilic digestion (lower volatile fatty acids and a less odorous digested sludge) while eliminating the disadvantages of both the thermophilic and mesophilic anaerobic digestion

Social Data Offloading in D2D-Enhanced Cellular Networks by Network Formation Games

Recently, cellular networks are severely overloaded by social-based services, such as YouTube, Facebook and Twitter, in which thousands of clients subscribe a common content provider (e.g., a popular singer) and download his/her content updates all the time. Offloading such traffic through complementary networks, such as a delay tolerant network formed by device-to-device (D2D) communications between mobile subscribers, is a promising solution to reduce the cellular burdens. In the existing solutions, mobile users are assumed to be volunteers who selfishlessly deliver the content to every other user in proximity while moving. However, practical users are selfish and they will evaluate their individual payoffs in the D2D sharing process, which may highly influence the network performance compared to the case of selfishless users. In this paper, we take user selfishness into consideration and propose a network formation game to capture the dynamic characteristics of selfish behaviors. In the proposed game, we provide the utility function of each user and specify the conditions under which the subscribers are guaranteed to converge to a stable network. Then, we propose a practical network formation algorithm in which the users can decide their D2D sharing strategies based on their historical records. Simulation results show that user selfishness can highly degrade the efficiency of data offloading, compared with ideal volunteer users. Also, the decrease caused by user selfishness can be highly affected by the cost ratio between the cellular transmission and D2D transmission, the access delays, and mobility patterns