Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. In this paper, we propose an extension to the independent cascade model that incorporates the emergence and propagation of negative opinions. The new model has an explicit parameter called quality factor to model the natural behavior of people turning negative to a product due to product defects. Our model incorporates negativity bias (negative opinions usually dominate over positive opinions) commonly acknowledged in the social psychology literature. The model maintains some nice properties such as submodularity, which allows a greedy approximation algorithm for maximizing positive influence within a ratio of 1 − 1/e. We define a quality sensitivity ratio (qs-ratio) of influence graphs and show a tight bound of Θ( n/k) on the qs-ratio, where n is the number of nodes in the network and k is the number of seeds selected, which indicates that seed selection is sensitive to the quality factor for general graphs. We design an efficient algorithm to com- * Author affiliations and emails: W. pute influence in tree structures, which is nontrivial due to the negativity bias in the model. We use this algorithm as the core to build a heuristic algorithm for influence maximization for general graphs. Through simulations, we show that our heuristic algorithm has matching influence with a standard greedy approximation algorithm while being orders of magnitude faster.

In this paper, we introduce a game-theoretic framework to address the community detection problem based on the structures of social networks. We formulate the dynamics of community formation as a strategic game called community formation game: Given an underlying social graph, we assume that each node is a selfish agent who selects communities to join or leave based on her own utility measurement. A community structure can be interpreted as an equilibrium of this game. We formulate the agents' utility by the combination of a gain function and a loss function. We allow each agent to select multiple communities, which naturally captures the concept of "overlapping communities". We propose a gain function based on the modularity concept introduced by Newman (Proc Natl Acad Sci 103(23): [8577][8578][8579][8580][8581][8582] 2006), and a simple loss function that reflects the intrinsic costs incurred when people join the communities. We conduct extensive experiments under this framework, and our results show that our algorithm is effective in identifying overlapping communities, and are often better then other algorithms we evaluated especially when many people Responsible editors:A game-theoretic framework 225 belong to multiple communities. To the best of our knowledge, this is the first time the community detection problem is addressed by a game-theoretic framework that considers community formation as the result of individual agents' rational behaviors.

We consider the problem of locating facilities in a metric space to serve a set of selfish agents. The cost of an agent is the distance between her own location and the nearest facility. The social cost is the total cost of the agents. We are interested in designing strategy-proof mechanisms without payment that have a small approximation ratio for social cost. A mechanism is a (possibly randomized) algorithm which maps the locations reported by the agents to the locations of the facilities. A mechanism is strategy-proof if no agent can benefit from misreporting her location in any configuration. This setting was first studied by Procaccia and Tennenholtz [21]. They focused on the facility game where agents and facilities are located on the real line. Alon et al. studied the mechanisms for the facility games in a general metric space [1]. However, they focused on the games with only one facility. In this paper, we study the two-facility game in a general metric space, which extends both previous models. We first prove an Ω(n) lower bound of the social cost approximation ratio for deterministic strategyproof mechanisms. Our lower bound even holds for the line metric space. This significantly improves the previous constant lower bounds [21, 17]. Notice that there is a matching linear upper bound in the line metric space [21]. Next, we provide the first randomized strategy-proof mechanism with a constant approximation ratio of 4. Our mechanism works in general metric spaces. For randomized strategy-proof mechanisms, the previous best upper bound is O(n) which works only in the line metric space.

We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let p be an arbitrary distribution over an interval I which is τ -close (in total variation distance) to an unknown probability distribution q that is defined by an unknown partition of I into t intervals and t unknown degree-d polynomials specifying q over each of the intervals. We give an algorithm that drawsÕ(t(d + 1)/ε 2 ) samples from p, runs in time poly(t, d, 1/ε), and with high probability outputs a piecewise polynomial hypothesis distribution h that is (O(τ ) + ε)-close (in total variation distance) to p. This sample complexity is essentially optimal; we show that even for τ = 0, any algorithm that learns an unknown t-piecewise degree-d probability distribution over I to accuracy ε must use Ω( t(d+1) poly(1+log(d+1)) · 1 ε 2 ) samples from the distribution, regardless of its running time. Our algorithm combines tools from approximation theory, uniform convergence, linear programming, and dynamic programming.We apply this general algorithm to obtain a wide range of results for many natural problems in density estimation over both continuous and discrete domains. These include state-of-theart results for learning mixtures of log-concave distributions; mixtures of t-modal distributions; mixtures of Monotone Hazard Rate distributions; mixtures of Poisson Binomial Distributions; mixtures of Gaussians; and mixtures of k-monotone densities. Our general technique yields computationally efficient algorithms for all these problems, in many cases with provably optimal sample complexities (up to logarithmic factors) in all parameters.

The detection of adulteration of high priced oils is a particular concern in food quality and safety. Therefore, it is necessary to develop authenticity detection method for protecting the health of customers. In this study, fatty acid profiles of five edible oils were established by gas chromatography coupled with mass spectrometry (GC/MS) in selected ion monitoring mode. Using mass spectral characteristics of selected ions and equivalent chain length (ECL), 28 fatty acids were identified and employed to classify five kinds of edible oils by using unsupervised (principal component analysis and hierarchical clustering analysis), supervised (random forests) multivariate statistical methods. The results indicated that fatty acid profiles of these edible oils could classify five kinds of edible vegetable oils into five groups and are therefore employed to authenticity assessment. Moreover, adulterated oils were simulated by Monte Carlo method to establish simultaneous adulteration detection model for five kinds of edible oils by random forests. As a result, this model could identify five kinds of edible oils and sensitively detect adulteration of edible oil with other vegetable oils about the level of 10%.