We regard each diffusion item as a distribution of these topics.
Topic-aware independent cascade (TIC) model [16] is an extension of the IC model to incorporate topic mixtures in any diffusion item.
One can still apply topic-oblivious influence maximization algorithms in online processing of every diffusion item, but it may not be efficient when there are a large number of items with different topic mixtures or real-time responses are required.
For further work, we are considering how to make the nonlinear p-Laplace diffusion item play a positive role in the stability criteria, which still remains an open and challenging problem.
Thus, we focus on preprocessing individual topic influence such that when a diffusion item with certain topic mixture comes, the online processing of finding the seed set is fast.
Recently, Barbieri et al. [16] propose the topic-aware independent cascade (TIC) and linear threshold (TLT) models, in which a diffusion item is a mixture of topics and influence parameters for each item are also mixtures of parameters for individual topics.
In the TIC model, the influence probability function p for any diffusion item (I=(lambda _1,lambda _2,dots,lambda _{d})) is defined as (p u,v) = sum _{i in [d]} lambda _i {p_i} u,v)), for all ( u,v in V) (or simply (p = sum _{i in [d]} lambda _i {p_i})).
In fact, when p = 2, 2-Laplace is the linear Laplace, and there are many papers (see, e.g., [9, 10, 19 21]) in which the Laplace diffusion item plays its role in their stability criteria for the linear Laplace PDEs can be considered in the special Hilbert space H 1 that can be orthogonally decomposed into the direct sum of infinitely many eigenfunction spaces.
In fact, when p = 2, 2-Laplace is the linear Laplace, and there are many papers (see, e.g., [10 13]) in which the Laplace diffusion item plays its role in their stability criteria, for the linear Laplace PDEs can be considered in the special Hilbert space H 1 that can be orthogonally decomposed into the direct sum of infinitely many eigenfunction spaces.
The diffusion of pressure is obtained by taking the divergence operation on both sides of equation (5), and combined with equation (6): (7) 0 = ∇ 2 p + (n - λ a ) χ Ω V - λ N χ Ω N p | ∂ Ω = 0 In the implementation, the finite element method is used to solve PDEs with diffusion item ∇ 2 [ 28].
