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We have collected and cleaned two network data sets: Coauthorship and Citation networks for statisticians. The data sets are based on all research papers published in four of the top journals in statistics from 2003 to the first half of 2003 . We analyze the data sets from many different perspectives, focusing on (a) productivity, patterns and trends,(b) centrality and (c) community structures.

It has been an open question whether the family of merit functions $\psi _p\(p> 1) $, the generalized Fischer-Burmeister (FB) merit function, associated to the second-order cone is smooth or not. In this paper we answer it partly, and show that \psi _p is smooth for \psi _p , and we provide the condition for its coerciveness. Numerical results are reported to illustrate the influence of \psi _p on the performance of the merit function method based on \psi _p .

Opinions and sentiments are essential to human activities and have a wide variety of applications. As many decision makers turn to social media due to large volume of opinion data available, efficient and accurate sentiment analysis is necessary to extract those data. Hence, text sentiment analysis has recently become a popular field and has attracted many researchers. However, extracting sentiments from audio speech remains a challenge. This project explored the possibility of applying supervised Machine Learning in recognizing sentiments in English utterances on a sentence level. In addition, the project also aimed to examine the effect of combining acoustic and linguistic features on classification accuracy. Six audio tracks were randomly selected to be training data from 40 YouTube videos (monologue) with strong presence of sentiments. Speakers expressed sentiments towards products, films, or political events. These sentiments were manually labelled as negative and positive based on independent judgement of 3 experimenters. A wide range of acoustic and linguistic features were then analyzed and extracted using sound editing and text mining tools respectively. A novel approach was proposed, which used a simplified sentiment score to integrate linguistic features and estimate sentiment valence. This approach improved negation analysis and hence increased overall accuracy. Results showed that when both linguistic and acoustic features were used, accuracy of sentiment recognition improved significantly, and that excellent prediction was achieved when the four classifiers were trained respectively, namely kNN, SVM, Neural Network, and Naïve Bayes. Possible sources of error and inherent challenges of audio sentiment analysis were discussed to provide potential directions for future research.

Almost toric manifolds form a class of singular Lagrangian fibered symplectic manifolds that include both toric manifolds and the K3 surface. We classify closed almost toric four-manifolds up to diffeomorphism and indicate precisely the structure of all almost toric fibrations of closed symplectic four-manifolds. A key step in the proof is a geometric classification of the singular integral affine structures that can occur on the base of an almost toric fibration of a closed four-manifold. As a byproduct we provide a geometric explanation for why a generic Lagrangian fibration over the two-sphere must have 24 singular fibers.