Online-offline activities and game-playing behaviors of avatars in a massive multiplayer online role-playing game

Massive multiplayer online role-playing games (MMORPGs) are very popular in China, which provides a potential platform for scientific research. We study the online-offline activities of avatars in an MMORPG to understand their game-playing behavior. The statistical analysis unveils that the active avatars can be classified into three types. The avatars of the first type are owned by game cheaters who go online and offline in preset time intervals with the online duration distributions dominated by pulses. The second type of avatars is characterized by a Weibull distribution in the online durations, which is confirmed by statistical tests. The distributions of online durations of the remaining individual avatars differ from the above two types and cannot be described by a simple form. These findings have potential applications in the game industry.Comment: 6 EPL pages including 10 eps figure

Linear extension of the Erdos-Heilbronn conjecture

The famous Erdos-Heilbronn conjecture plays an important role in the development of additive combinatorics. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erdos-Heilbronn conjecture): For any finite subset A of a field F and nonzero elements $a_1,...,a_n$ of F, the set {a_1x_1+...+a_nx_n: x_1,....,x_n are distinct elements of A} has cardinality at least min{p(F)-delta, n(|A|-n)+1}, where the additive order p(F) of the multiplicative identity of F is different from n+1, and delta=0,1 takes the value 1 if and only if n=2 and $a_1+a_2=0$. In this paper we prove this conjecture of Sun when $p(F)\geq n(3n-5)/2$. We also obtain a sharp lower bound for the cardinality of the restricted sumset {x_1+...+x_n: x_1\in A_1,...,x_n\in A_n, and P(x_1,...,x_n)\not=0}, where $A_1,...,A_n$ are finite subsets of a field F and $P(x_1,...,x_n)$ is a general polynomial over F

Clinical Features and Genetic Analysis of 20 Chinese Patients with X-Linked Hyper-IgM Syndrome

X-linked hyper-IgM syndrome (XHIGM) is one type of primary immunodeficiency diseases, resulting from defects in the CD40 ligand/CD40 signaling pathways. We retrospectively analyzed the clinical and molecular features of 20 Chinese patients diagnosed and followed up in hospitals affiliated to Shanghai Jiao Tong University School of Medicine from 1999 to 2013. The median onset age of these patients was 8.5 months (range: 20 days–21 months). Half of them had positive family histories, with a shorter diagnosis lag. The most common symptoms were recurrent sinopulmonary infections (18 patients, 90%), neutropenia (14 patients, 70%), oral ulcer (13 patients, 65%), and protracted diarrhea (13 patients, 65%). Six patients had BCGitis. Six patients received hematopoietic stem cell transplantations and four of them had immune reconstructions and clinical remissions. Eighteen unique mutations in CD40L gene were identified in these 20 patients from 19 unrelated families, with 12 novel mutations. We compared with reported mutation results and used bioinformatics software to predict the effects of mutations on the target protein. These mutations reflected the heterogeneity of CD40L gene and expanded our understanding of XHIGM