Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z...Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z） the number of particles in the n-th generation in the model for each z ∈ Z. We derive the exact convergence rate in the local limit theorem for Zn（z） assuming a condition like ＂EN（logN）1＋λ 〈 ∞＂ for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice.展开更多
We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a ...We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking walks on the directed edges. We prove a weighted version of Ihara’s Theorem which relates the transition probability matrix of a non-backtracking walk to the transition matrix for the usual random walk. This allows us to determine the spectrum of the transition probability matrix of a non-backtracking random walk in the case of regular graphs and biregular graphs. As a corollary, we obtain a result of Alon et al. in [1] that in most cases, a non-backtracking random walk on a regular graph has a faster mixing rate than the usual random walk. In addition, we obtain an analogous result for biregular graphs.展开更多
为了提高推荐算法评分预测的准确度,该文在Trust Walker模型的基础上,提出了一个改进的基于信任网络和随机游走策略的评分预测模型——Referential User Walker模型。该模型通过随机游走策略,利用信任网络中的信任朋友对目标物品或与目...为了提高推荐算法评分预测的准确度,该文在Trust Walker模型的基础上,提出了一个改进的基于信任网络和随机游走策略的评分预测模型——Referential User Walker模型。该模型通过随机游走策略,利用信任网络中的信任朋友对目标物品或与目标物品相似的物品的评分进行评分预测,并在信任网络中找到最可信的Top N评分参考用户,同时引入信任度权重,降低了噪声数据的影响。实验结果表明,与Trust Walker模型相比,Referential User Walker模型的评分预测准确度有所提高。展开更多
文摘Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z） the number of particles in the n-th generation in the model for each z ∈ Z. We derive the exact convergence rate in the local limit theorem for Zn（z） assuming a condition like ＂EN（logN）1＋λ 〈 ∞＂ for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice.
文摘We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking walks on the directed edges. We prove a weighted version of Ihara’s Theorem which relates the transition probability matrix of a non-backtracking walk to the transition matrix for the usual random walk. This allows us to determine the spectrum of the transition probability matrix of a non-backtracking random walk in the case of regular graphs and biregular graphs. As a corollary, we obtain a result of Alon et al. in [1] that in most cases, a non-backtracking random walk on a regular graph has a faster mixing rate than the usual random walk. In addition, we obtain an analogous result for biregular graphs.
文摘为了提高推荐算法评分预测的准确度,该文在Trust Walker模型的基础上,提出了一个改进的基于信任网络和随机游走策略的评分预测模型——Referential User Walker模型。该模型通过随机游走策略,利用信任网络中的信任朋友对目标物品或与目标物品相似的物品的评分进行评分预测,并在信任网络中找到最可信的Top N评分参考用户,同时引入信任度权重,降低了噪声数据的影响。实验结果表明,与Trust Walker模型相比,Referential User Walker模型的评分预测准确度有所提高。
