In a social network, adoption probability refers to the probability that a social entity will adopt a product, service, or opinion in the foreseeable future. Such probabilities are central to fundamental issues in social network analysis, including the influence maximization problem. In practice, adoption probabilities have significant implications for applications ranging from social network-based target marketing to political campaigns; yet, predicting adoption probabilities has not received sufficient research attention. Building on relevant social network theories, we identify and operationalize key factors that affect adoption decisions: social influence, structural equivalence, entity similarity, and confounding factors. We then develop the locally-weighted expectation-maximization method for Naïve Bayesian learning to predict adoption probabilities on the basis of these factors. The principal challenge addressed in this study is how to predict adoption probabilities in the presence of confounding factors that are generally unobserved. Using data from two large-scale social networks, we demonstrate the effectiveness of the proposed method. The empirical results also suggest that cascade methods primarily using social influence to predict adoption probabilities offer limited predictive power, and that confounding factors are critical to adoption probability predictions.

A large number of studies have investigated the transaction log of general‐purpose search engines such as Excite and AltaVista, but few studies have reported on the analysis of search logs for search engines that are limited to particular Web sites, namely, Web site search engines. In this article, we report our research on analyzing the search logs of the search engine of the Utah state government Web site. Our results show that some statistics, such as the number of search terms per query, of Web users are the same for general‐purpose search engines and Web site search engines, but others, such as the search topics and the terms used, are considerably different. Possible reasons for the differences include the focused domain of Web site search engines and users' different information needs. The findings are useful for Web site developers to improve the performance of their services provided on the Web and for researchers to conduct further research in this area. The analysis also can be applied in e‐government research by investigating how information should be delivered to users in government Web sites.

Introduction of a continuous hydrogen-bonding network suppressed the conformational flexibility of an oligomeric backbone. Cyclization of a rigidified, suitably sized oligomer led to a circular aromatic pentamer. Its crystal structure determined by X-ray crystallography reveals a pseudo five-fold symmetric planarity in the solid state, which is quite unusual among all the previously described shape-persistent macrocycles and synthetic foldamers with biased conformations enforced by noncovalent forces.

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Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second-or higher-order derivatives. For a class of multivariate limiting distributions, we use Bismut's formula in Malliavin calculus to control the derivatives of the Stein equation solutions by the first derivative of the test function. Combined with Stein's exchangeable pair approach, we obtain a general theorem for multivariate approximations with near optimal error bounds on the Wasserstein distance. We apply the theorem to the unadjusted Langevin algorithm.

Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also applied to a combinatorial central limit theorem, a general system of binary codes, the anti-voter model on a complete graph, and the Curie-Weiss model. A general moderate deviation result for independent random variables is also proved.Comment: Published in at http://dx.doi.org/10.1214/12-AOP746 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Under the sublinear expectation [·] := sup θ∈Θ E θ [·] for a given set of linear expectations {E θ : θ ∈ Θ}, we establish a new law of large numbers and a new central limit theorem with rate of convergence. We present some interesting special cases and discuss a related statistical inference problem. We also give an approximation and a representation of the G-normal distribution, which was used as the limit in Peng (2007)'s central limit theorem, in a probability space.