There are various dynamic networks around us. Many researchers have investigated the fitness, i.e. ability to get edges from other nodes, and popularity effects on network growth. The fitness-popularity dynamic network (FPDN) model was introduced recently. In the FPDN model, the fitness of a node is assumed invariant for a given period of time. In many real networks, however, the fitness may change over time in various ways. Herein, we propose a varying fitness-popularity dynamic network (V-FPDN) model by allowing variable fitness. Through the V-FPDN model, we can estimate the strength of fitness and popularity effects and show how the fitness of the nodes changes. The magnitude of these effects and fitness values are estimated simultaneously using the expectation-maximization (EM) algorithm combined with the Markov chain Monte Carlo (MCMC) method. We apply the FPDN and V-FPDN model to the Facebook wallpost network and compare the results. The YouTube subscription network is investigated using the V-FPDN model in various categories. We explain the superiority of the proposed model with remarkable interpretations.
The degree distribution has attracted considerable attention from network scientists in the last few decades to have knowledge of the topological structure of networks. It is widely acknowledged that many real networks have power-law degree distributions. However, the deviation from such a behavior often appears when the range of degrees is small. Even worse, the conventional employment of the continuous power-law distribution usually causes an inaccurate inference as the degree should be discrete-valued. To remedy these obstacles, we propose a finite mixture model of truncated zeta distributions for a broad range of degrees that disobeys a power-law behavior in the range of small degrees while maintaining the scale-free behavior. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. The validity of the suggested algorithm is evidenced by Monte Carlo simulations. We apply our method to five disciplines of scientific collaboration networks with remarkable interpretations. The proposed model outperforms the other alternatives in terms of the goodness-of-fit.
In this paper, we consider the problem of estimating the time-dependent ability of workers participating in distributed matrix-vector multiplication over heterogeneous clusters. Specifically, we model the workers’ ability as a latent variable and introduce a log-normally distributed working rate as a function of the latent variable with parameters so that the working rate increases as the latent ability of workers increases, and takes positive values only. This modeling is motivated by the need to reflect the impact of time-dependent external factors on the workers’ performance. We estimate the latent variable and parameters using the expectation-maximization (EM) algorithm combined with the particle method. The proposed estimation and inference on the working rates are used to allocate tasks to the workers to reduce expected latency. From simulations, we observe that our estimation and inference on the working rates are effective in reducing expected latency.
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