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Controlling the efficiency of trapping in a scale-free small-world network.

ABSTRACT: Designing appropriate techniques to effectively control the trapping process in complex systems towards desirable efficiency is of paramount importance in the study of trapping problem. In this paper, we present three different methods guiding trapping process in a scale-free small-world network with a deep trap positioned at an initial node. All the proposed approaches dominate the trapping process by varying the transition probability of random walks. In the first two techniques, the transition probability is modified by an introduced weight parameter and a stochastic parameter, respectively. And the third scheme is a combination of the first two approaches, controlled by both parameters synchronously. For all the three control strategies, we derive both analytically and numerically the average trapping time (ATT) as the measure of the trapping efficiency, with the obtained explicit expressions being in good agreement with their corresponding exact numerical solutions. Our results indicate that the weight parameter changes simultaneously the dominating scaling of ATT and its prefactor. Different from the weight parameter, the stochastic parameter only modifies the prefactor, keeping the leading scaling unchanged. Finally, compared with the first two manners, the third strategy is a fine control, possessing the advantages of the first two ones. This work deepens the understanding of controlling trapping process in complex systems.

SUBMITTER: Lin Y

PROVIDER: S-EPMC4158604 | biostudies-other | 2014

REPOSITORIES: biostudies-other

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Project description:Hepatic encephalopathy (HE) is a complex neuropsychiatric syndrome and a major complication of liver cirrhosis. Dysmetabolism of the brain, related to elevated ammonia levels, interferes with intercortical connectivity and cognitive function. For evaluation of network efficiency, a 'small-world' network model can quantify the effectiveness of information transfer within brain networks. This study aimed to use small-world topology to investigate abnormalities of neuronal connectivity among widely distributed brain regions in patients with liver cirrhosis using resting-state functional magnetic resonance imaging (rs-fMRI). Seventeen cirrhotic patients without HE, 9 with minimal HE, 9 with overt HE, and 35 healthy controls were compared. The interregional correlation matrix was obtained by averaging the rs-fMRI time series over all voxels in each of the 90 regions using the automated anatomical labeling model. Cost and correlation threshold values were then applied to construct the functional brain network. The absolute and relative network efficiencies were calculated; quantifying distinct aspects of the local and global topological network organization. Correlations between network topology parameters, ammonia levels, and the severity of HE were determined using linear regression and ANOVA. The local and global topological efficiencies of the functional connectivity network were significantly disrupted in HE patients; showing abnormal small-world properties. Alterations in regional characteristics, including nodal efficiency and nodal strength, occurred predominantly in the association, primary, and limbic/paralimbic regions. The degree of network organization disruption depended on the severity of HE. Ammonia levels were also significantly associated with the alterations in local network properties. Results indicated that alterations in the rs-fMRI network topology of the brain were associated with HE grade; and that focal or diffuse lesions disturbed the functional network to further alter the global topology and efficiency of the whole brain network. These findings provide insights into the functional changes in the human brain in HE.

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Controlling the efficiency of trapping in a scale-free small-world network.

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