Stable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral grids

In this paper, we first construct a nonconforming finite element pair for the incompressible Stokes problem on quadrilateral grids, and then construct a discrete Stokes complex associated with that finite element pair. The finite element spaces involved consist of piecewise polynomials only, and the divergence-free condition is imposed in a primal formulation. Combined with some existing results, these constructions can be generated onto grids that consist of both triangular and quadrilateral cells

Event Organization 101: Understanding Latent Factors of Event Popularity

The problem of understanding people's participation in real-world events has been a subject of active research and can offer valuable insights for human behavior analysis and event-related recommendation/advertisement. In this work, we study the latent factors for determining event popularity using large-scale datasets collected from the popular Meetup.com EBSN in three major cities around the world. We have conducted modeling analysis of four contextual factors (spatial, group, temporal, and semantic), and also developed a group-based social influence propagation network to model group-specific influences on events. By combining the Contextual features And Social Influence NetwOrk, our integrated prediction framework CASINO can capture the diverse influential factors of event participation and can be used by event organizers to predict/improve the popularity of their events. Evaluations demonstrate that our CASINO framework achieves high prediction accuracy with contributions from all the latent features we capture.Comment: International AAAI Conference on Web and Social Media (ICWSM) 2017 https://www.aaai.org/ocs/index.php/ICWSM/ICWSM17/paper/view/1557

Zero forcing sets and controllability of dynamical systems defined on graphs

In this paper, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established. To illustrate the proposed results, special cases including path, cycle, and complete graphs are discussed. Moreover, as shown for graphs with a tree structure, the proposed results of the present paper together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases