A Structural Property of Trees with an Application to Vertex-Arboricity

We provide a structural property of trees, which is applied to show that if a plane graph G contains two edge-disjoint spanning trees, then its dual graph G⁎ has the vertex-arboricity at most 2. We also show that every maximal plane graph of order at least 4 contains two edge-disjoint spanning trees

Evolution properties of the community members for dynamic networks

The collective behaviors of community members for dynamic social networks are significant for understanding evolution features of communities. In this Letter, we empirically investigate the evolution properties of the new community members for dynamic networks. Firstly, we separate data sets into different slices, and analyze the statistical properties of new members as well as communities they joined in for these data sets. Then we introduce a parameter φ to describe community evolution between different slices and investigate the dynamic community properties of the new community members. The empirical analyses for the Facebook, APS, Enron and Wiki data sets indicate that both the number of new members and joint communities increase, the ratio declines rapidly and then becomes stable over time, and most of the new members will join in the small size communities that is s≤10s≤10. Furthermore, the proportion of new members in existed communities decreases firstly and then becomes stable and relatively small for these data sets. Our work may be helpful for deeply understanding the evolution properties of community members for social networks

Identifying online user reputation of user–object bipartite networks

Identifying online user reputation based on the rating information of the user–object bipartite networks is important for understanding online user collective behaviors. Based on the Bayesian analysis, we present a parameter-free algorithm for ranking online user reputation, where the user reputation is calculated based on the probability that their ratings are consistent with the main part of all user opinions. The experimental results show that the AUC values of the presented algorithm could reach 0.8929 and 0.8483 for the MovieLens and Netflix data sets, respectively, which is better than the results generated by the CR and IARR methods. Furthermore, the experimental results for different user groups indicate that the presented algorithm outperforms the iterative ranking methods in both ranking accuracy and computation complexity. Moreover, the results for the synthetic networks show that the computation complexity of the presented algorithm is a linear function of the network size, which suggests that the presented algorithm is very effective and efficient for the large scale dynamic online systems

Anticipation of pain enhances the nociceptive transmission and functional connectivity within pain network in rats

<p>Abstract</p> <p>Background</p> <p>Expectation is a very potent pain modulator in both humans and animals. There is evidence that pain transmission neurons are modulated by expectation preceding painful stimuli. Nonetheless, few studies have examined the influence of pain expectation on the pain-related neuronal activity and the functional connectivity within the central nociceptive network.</p> <p>Results</p> <p>This study used a tone-laser conditioning paradigm to establish the pain expectation in rats, and simultaneously recorded the anterior cingulate cortex (ACC), the medial dorsal thalamus (MD), and the primary somatosensory cortex (SI) to investigate the effect of pain expectation on laser-induced neuronal responses. Cross-correlation and partial directed coherence analysis were used to determine the functional interactions within and between the recorded areas during nociceptive transmission. The results showed that under anticipation condition, the neuronal activity to the auditory cue was significantly increased in the ACC area, whereas those to actual noxious stimuli were enhanced in all the recorded areas. Furthermore, neuronal correlations within and between these areas were significantly increased under conditions of expectation compared to those under non-expectation conditions, indicating an enhanced synchronization of neural activity within the pain network. In addition, information flow from the medial (ACC and MD) to the lateral (SI cortex) pain pathway increased, suggesting that the emotion-related neural circuits may modulate the neuronal activity in the somatosensory pathway during nociceptive transmission.</p> <p>Conclusion</p> <p>These results demonstrate that the nociceptive processing in both medial and lateral pain systems is modulated by the expectation of pain.</p