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In this paper, we consider a space-time Riesz-Caputo fractional advection-diffusion equation. The equation is obtained from the standard advection-diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α ∈ (0, 1], the first-order and secondorder space derivatives by the Riesz fractional derivatives of order β 1 ∈ (0, 1) and β 2 ∈ (1, 2], respectively. We present an explicit difference approximation and an implicit difference approximation for the equation with initial and boundary conditions in a finite domain. Using mathematical induction, we prove that the implicit difference approximation is unconditionally stable and convergent, but the explicit difference approximation is conditionally stable and convergent. We also present two solution techniques: a Richardson extrapolation method is used to obtain higher order accuracy and the short-memory principle is used to investigate the effect of the amount of computations. A numerical example is given; the numerical results are in good agreement with theoretical analysis.

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Social interactions in multiplayer online games are an essential feature for a growing number of players worldwide. However, this interaction between the players might lead to the emergence of undesired and unintended behavior, particularly if the game is designed to be highly competitive. Communication channels might be abused to harass and verbally assault other players, which negates the very purpose of entertainment games by creating a toxic player-community. By using a novel natural language processing framework, we detect profanity in chat-logs of a popular Multiplayer Online Battle Arena (MOBA) game and develop a method to classify toxic remarks. We show how toxicity is non-trivially linked to game success.

The time fractional diffusion equation (tfde) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order in (0,1). In this work, an explicit finite-difference scheme for tfde is presented. Discrete models of a non-Markovian random walk are generated for simulating random processes whose spatial probability density evolves in time according to this fractional diffusion equation. We derive the scaling restriction of the stability and convergence of the discrete non-Markovian random

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Abstract-For many networked games, such as the Defense of the Ancients and StarCraft series, the unofficial leagues created by players themselves greatly enhance user-experience, and extend the success of each game. Understanding the social structure that players of these games implicitly form helps to create innovative gaming services to the benefit of both players and game operators. But how to extract and analyse the implicit social structure? We address this question by first proposing a formalism consisting of various ways to map interaction to social structure, and apply this to real-world data collected from three different game genres. We analyse the implications of these mappings for in-game and gaming-related services, ranging from network and socially-aware matchmaking of players, to an investigation of social network robustness against player departure.