Real-time cooperative editing systems allow multiple users to view and edit the same text/graphic/image/multimedia document at the same time from multiple sites connected by communication networks. Consistency maintenance is one of the most significant challenges in designing and implementing real-time cooperative editing systems. In this article, a consistency model, with properties of convergence, causality preservation, and intention preservation, is proposed as a framework for consistency maintenance in real-time cooperative editing systems. Moreover, an integrated set of schemes and algorithms, which support the proposed consistency model, are devised and discussed in detail. In particular, we have contributed (1) a novel generic operation transformation control algorithm for achieving intention preservation in combination with schemes for achieving convergence and causality preservation and (2) a pair of reversible inclusion and exclusion transformation algorithms for stringwise operations for text editing. An Internet-based prototype system has been built to test the feasibility of the proposed schemes and algorithms.

The bianisotropic susceptibility Generalized Sheet Transition Conditions (GSTCs) synthesis method is extended from planar to spherical metasurfaces. Properties specific to the non-zero intrinsic curvature of the spherical shape are highlighted and different types of corresponding transformations are described. Finally, the susceptibility-GSTC method and exotic properties of spherical metasurfaces are validated and illustrated with three examples: illusion transformation, ring focusing and birefringence.

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Abstract-Mathematical modeling is an important approach to study information diffusion in online social networks. Prior studies have focused on the modeling of the temporal aspect of information diffusion. A recent effort introduced the spatiotemporal diffusion problem and addressed the problem with a theoretical framework built on the similarity between information propagation in online social networks and biological invasion in ecology [1]. This paper examines the spatio-temporal characteristics in further depth and reveals that there exist regularities in information diffusion in temporal and spatial dimensions. Furthermore, we propose a simpler linear partial differential equation that takes account of the influence of spatial population density and temporal decay of user interests in the information. We validate the proposed linear model with Digg news stories which received more than 3000 votes during June 2009, and show that the model can describe nearly 60% of the news stories with over 80% accuracy. We also use the most popular news story as a case study and find that the linear diffusive model can achieve an accuracy as high as 97.41% for this news story. Finally, we discuss the potential applications of this model towards finding super spreaders and classifying news story into groups.

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