Computing the Least-core and Nucleolus for Threshold Cardinality Matching Games

Cooperative games provide a framework for fair and stable profit allocation in multi-agent systems. \emph{Core}, \emph{least-core} and \emph{nucleolus} are such solution concepts that characterize stability of cooperation. In this paper, we study the algorithmic issues on the least-core and nucleolus of threshold cardinality matching games (TCMG). A TCMG is defined on a graph $G=(V,E)$ and a threshold $T$, in which the player set is $V$ and the profit of a coalition $S\subseteq V$ is 1 if the size of a maximum matching in $G[S]$ meets or exceeds $T$, and 0 otherwise. We first show that for a TCMG, the problems of computing least-core value, finding and verifying least-core payoff are all polynomial time solvable. We also provide a general characterization of the least core for a large class of TCMG. Next, based on Gallai-Edmonds Decomposition in matching theory, we give a concise formulation of the nucleolus for a typical case of TCMG which the threshold $T$ equals $1$. When the threshold $T$ is relevant to the input size, we prove that the nucleolus can be obtained in polynomial time in bipartite graphs and graphs with a perfect matching

Tripartite Graph Clustering for Dynamic Sentiment Analysis on Social Media

The growing popularity of social media (e.g, Twitter) allows users to easily share information with each other and influence others by expressing their own sentiments on various subjects. In this work, we propose an unsupervised \emph{tri-clustering} framework, which analyzes both user-level and tweet-level sentiments through co-clustering of a tripartite graph. A compelling feature of the proposed framework is that the quality of sentiment clustering of tweets, users, and features can be mutually improved by joint clustering. We further investigate the evolution of user-level sentiments and latent feature vectors in an online framework and devise an efficient online algorithm to sequentially update the clustering of tweets, users and features with newly arrived data. The online framework not only provides better quality of both dynamic user-level and tweet-level sentiment analysis, but also improves the computational and storage efficiency. We verified the effectiveness and efficiency of the proposed approaches on the November 2012 California ballot Twitter data.Comment: A short version is in Proceeding of the 2014 ACM SIGMOD International Conference on Management of dat

Electronic Structure and Lattice dynamics of NaFeAs

The similarity of the electronic structures of NaFeAs and other Fe pnictides has been demonstrated on the basis of first-principle calculations. The global double-degeneracy of electronic bands along X-M and R-A direction indicates the instability of Fe pnictides and is explained on the basis of a tight-binding model. The de Haas-van Alphen parameters for the Fermi surface (FS) of NaFeAs have been calculated. A $\mathbf{Q}_{M}=(1/2,1/2,0)$ spin density wave (SDW) instead of a charge density wave (CDW) ground state is predicted based on the calculated generalized susceptibility $\chi(\mathbf{q})$ and a criterion derived from a restricted Hatree-Fock model. The strongest electron-phonon (e-p) coupling has been found to involve only As, Na z-direction vibration with linear-response calculations. A possible enhancement mechanism for e-p coupling due to correlation is suggested

Experimental study on solidification/stabilization of Cr in stainless steel pickling sludge by high temperature roasting process

For stainless steel pickling sludge (SSPS) produced in a stainless steel factory in southeast China, Fly ash (FA) and waste glass (WG) were used as solidification/stabilization (S/S) agents to conduct high-temperature roasting experiments on S/S of Cr in SSPS, respectively. The effects of roasting temperature and S/S agent dosage on the S/S of Cr were studied. The results show that both FA and WG can take positive way to S/S. By adding 25 % of FA to SSPS at roasting temperature of 1 500 °C, the Cr leaching concentration of S/S products can decrease to 0,63 ppm. As for WG as S/S agent, the Cr leaching concentration of the product can be reduced to 0,45ppm when the dosage is 20 % and the roasting temperature is 1 400 °C,. Considering the dosage and roasting temperature, WG is suggested as a better S/S agent

Study on distribution of sulfur element in blast furnace (BF) process with different pellet proportions

In this study, a series of BF smelting industrial tests were conducted with different proportions of pellet in ironbearing materials in a 450 m3 BF in Hebei, China. The results showed that with increasing proportion of pellet, total sulfur(S) input amount of the raw materials in BF iron-making process decreased after a slight increase. The sulfur input of pellets increased while that of sinter, coke and coal tended to decrease. On the other hand, the quantity and proportion of sulfur element in BF gas had a small rise while those in BF slag did not change much, and the quantity of sulfur in BF dust and iron remained relatively stable. The result revealed that increasing the pellet proportion will not affect the quality of pig iron (PI), but also can reduce the sulfur load of BF