Mean Shortest Path Length Research Articles

Network Pharmacology-Based Analysis on the Potential Biological Mechanisms of Sinisan Against Non-Alcoholic Fatty Liver Disease.

Non-alcoholic fatty liver disease (NAFLD) has become the most prevalent liver disease in China. Sinisan (SNS) is a traditional Chinese medicine formula that has been widely used in treating chronic liver diseases, including NAFLD. However, its underlying biological mechanisms are still unclear. In this study, we employed a network pharmacology approach consisting of overlapped terms- (genes or pathway terms-) based analysis, protein-protein interaction (PPI) network-based analysis, and PPI clusters identification. Unlike the previous network pharmacology study, we used the shortest path length-based network proximity algorithm to evaluate the efficacy of SNS against NAFLD. And we also used random walk with restart (RWR) algorithm and Community Cluster (Glay) algorithm to identify important targets and clusters. The screening results showed that the mean shortest path length between genes of SNS and NAFLD was significantly smaller than degree-matched random ones. Six PPI clusters were identified and ten hub targets were obtained, including STAT3, CTNNB1, MAPK1, MAPK3, AGT, NQO1, TOP2A, FDFT1, ALDH4A1, and KCNH2. The experimental study indicated that SNS reduced hyperlipidemia, liver steatosis, and inflammation. Most importantly, JAK2/STAT3 signal was inhibited by SNS treatment and was recognized as the most important signal considering the network pharmacology part. This study provides a systems perspective to study the relationship between Chinese medicines and diseases and helps to discover potential mechanisms by which SNS ameliorates NAFLD.

Functional Network Alterations as Markers for Predicting the Treatment Outcome of Cathodal Transcranial Direct Current Stimulation in Focal Epilepsy.

Background and PurposeTranscranial direct current stimulation (tDCS) is an emerging non-invasive neuromodulation technique for focal epilepsy. Because epilepsy is a disease affecting the brain network, our study was aimed to evaluate and predict the treatment outcome of cathodal tDCS (ctDCS) by analyzing the ctDCS-induced functional network alterations.MethodsEither the active 5-day, −1.0 mA, 20-min ctDCS or sham ctDCS targeting at the most active interictal epileptiform discharge regions was applied to 27 subjects suffering from focal epilepsy. The functional networks before and after ctDCS were compared employing graph theoretical analysis based on the functional magnetic resonance imaging (fMRI) data. A support vector machine (SVM) prediction model was built to predict the treatment outcome of ctDCS using the graph theoretical measures as markers.ResultsOur results revealed that the mean clustering coefficient and the global efficiency decreased significantly, as well as the characteristic path length and the mean shortest path length at the stimulation sites in the fMRI functional networks increased significantly after ctDCS only for the patients with response to the active ctDCS (at least 20% reduction rate of seizure frequency). Our prediction model achieved the mean prediction accuracy of 68.3% (mean sensitivity: 70.0%; mean specificity: 67.5%) after the nested cross validation. The mean area under the receiver operating curve was 0.75, which showed good prediction performance.ConclusionThe study demonstrated that the response to ctDCS was related to the topological alterations in the functional networks of epilepsy patients detected by fMRI. The graph theoretical measures were promising for clinical prediction of ctDCS treatment outcome.

Random walks on a tree with applications

The various dynamics of many complex systems, both natural and artificial, can be well described as random walks on a newly proposed yet powerful object known as a complex network. Here we consider random walks on a special kind of network, a tree. Using the methods of probability-generating functions, we derive a close connection between the widely studied parameters mean first-passage time M and mean shortest path length A on trees. This suggests that for a given tree, the analytic value for M can be easily obtained by calculating the value A when determining the latter is more convenient and vice versa. As a result, the well-known T graph is selected as one of various applications of our methods, and we then obtain an exact solution to its quantity M. On the one hand, the result addressed here is in perfect agreement with previous ones. On the other hand, our method is easier to manipulate than most preexisting ones, for instance, methods from spectral graph theory, since no complicated techniques are involved.

Cognitive function, disease burden and the structural connectome in systemic lupus erythematosus.

Objective To investigate brain structural connectivity in relation to cognitive abilities and systemic damage in systemic lupus erythematosus (SLE). Methods Structural and diffusion MRI data were acquired from 47 patients with SLE. Brains were segmented into 85 cortical and subcortical regions and combined with whole brain tractography to generate structural connectomes using graph theory. Global cognitive abilities were assessed using a composite variable g, derived from the first principal component of three common clinical screening tests of neurological function. SLE damage ( LD) was measured using a composite of a validated SLE damage score and disease duration. Relationships between network connectivity metrics, cognitive ability and systemic damage were investigated. Hub nodes were identified. Multiple linear regression, adjusting for covariates, was employed to model the outcomes g and LD as a function of network metrics. Results The network measures of density (standardised ß = 0.266, p = 0.025) and strength (standardised ß = 0.317, p = 0.022) were independently related to cognitive abilities. Strength (standardised ß = -0.330, p = 0.048), mean shortest path length (standardised ß = 0.401, p = 0.020), global efficiency (standardised ß = -0.355, p = 0.041) and clustering coefficient (standardised ß = -0.378, p = 0.030) were independently related to systemic damage. Network metrics were not related to current disease activity. Conclusion Better cognitive abilities and more SLE damage are related to brain topological network properties in this sample of SLE patients, even those without neuropsychiatric involvement and after correcting for important covariates. These data show that connectomics might be useful for understanding and monitoring cognitive function and white matter damage in SLE.

Cognitive abilities, brain white matter hyperintensity volume, and structural network connectivity in older age.

ObjectiveTo assess brain structural connectivity in relation to cognitive abilities in healthy ageing, and the mediating effects of white matter hyper‐intensity (WMH) volume.MethodsMRI data were analysed in 558 members of the Lothian Birth Cohort 1936. Brains were segmented into 85 regions and combined with tractography to generate structural connectomes. WMH volume was quantified. Relationships between whole‐brain connectivity, assessed using graph theory metrics, and four major domains of cognitive ability (visuospatial reasoning, verbal memory, information processing speed and crystallized ability) were investigated, as was the mediating effects of WMH volume on these relationships.ResultsVisuospatial reasoning was associated with network strength, mean shortest path length, and global efficiency. Memory was not associated with any network connectivity metric. Information processing speed and crystallized ability were associated with all network measures. Some relationships were lost when adjusted for mean network FA. WMH volume mediated 11%–15% of the relationships between most network measures and information processing speed, even after adjusting for mean network FA.ConclusionBrain structural connectivity relates to visuospatial reasoning, information processing speed and crystallized ability, but not memory, in this relatively healthy age‐homogeneous cohort of 73 year olds. When adjusted for mean FA across the network, most relationships are lost, except with information processing speed suggesting that the underlying topological network structure is related to this cognitive domain. Moreover, the connectome‐processing speed relationship is partly mediated by WMH volume in this cohort. Hum Brain Mapp 39:622–632, 2018. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Research on effects of low-frequency repetitive transcranial magnetic stimulation over primary motor cortex on functional connectivity of brain

Repetitive transcranial magnetic stimulation (rTMS) can influence the stimulated brain regions and other distal brain regions connecting to them. The purpose of the study is to investigate the effects of low-frequency rTMS over primary motor cortex on brain by analyzing the brain functional connectivity and coordination between brain regions. 10 healthy subjects were recruited. 1 Hz rTMS was used to stimulate primary motor cortex for 20 min. 1 min resting state electroencephalography (EEG) was collected before and after the stimulation respectively. By performing phase synchronization analysis between the EEG electrodes, the brain functional network and its properties were calculated. Signed-rank test was used for statistical analysis. The result demonstrated that the global phase synchronization in alpha frequency band was decreased significantly after low-frequency rTMS ( P<0.05). The phase synchronization was down-regulated between motor cortex and ipsilateral frontal/parietal cortex, and also between contralateral parietal cortex and bilateral frontal cortex. The mean degree and global efficiency of brain functional networks in alpha frequency band were significantly decreased ( P<0.05), and the mean shortest path length were significantly increased ( P<0.05), which suggested the information transmission of the brain networks and its efficiency was reduced after low-frequency rTMS. This study verified the inhibition function of the low-frequency rTMS to brain activities, and demonstrated that low-frequency rTMS stimulation could affect both stimulating brain regions and distal brain regions connected to them. The findings in this study could be of guidance to clinical application of low-frequency rTMS.

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. First, we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures-thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore, we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length, and network diameter are highly sensitive to the interior crisis captured in this particular data set.

Association of Structural Global Brain Network Properties with Intelligence in Normal Aging

Higher general intelligence attenuates age-associated cognitive decline and the risk of dementia. Thus, intelligence has been associated with cognitive reserve or resilience in normal aging. Neurophysiologically, intelligence is considered as a complex capacity that is dependent on a global cognitive network rather than isolated brain areas. An association of structural as well as functional brain network characteristics with intelligence has already been reported in young adults. We investigated the relationship between global structural brain network properties, general intelligence and age in a group of 43 cognitively healthy elderly, age 60–85 years. Individuals were assessed cross-sectionally using Wechsler Adult Intelligence Scale-Revised (WAIS-R) and diffusion-tensor imaging. Structural brain networks were reconstructed individually using deterministic tractography, global network properties (global efficiency, mean shortest path length, and clustering coefficient) were determined by graph theory and correlated to intelligence scores within both age groups. Network properties were significantly correlated to age, whereas no significant correlation to WAIS-R was observed. However, in a subgroup of 15 individuals aged 75 and above, the network properties were significantly correlated to WAIS-R. Our findings suggest that general intelligence and global properties of structural brain networks may not be generally associated in cognitively healthy elderly. However, we provide first evidence of an association between global structural brain network properties and general intelligence in advanced elderly. Intelligence might be affected by age-associated network deterioration only if a certain threshold of structural degeneration is exceeded. Thus, age-associated brain structural changes seem to be partially compensated by the network and the range of this compensation might be a surrogate of cognitive reserve or brain resilience.

Research on the Structure of Peer-to-Peer Overlay Based on the Complex Network Theory

Relationship between nodes in peer-to-peer overlay, currently becomes a hot topic in the field of complex network. In this paper a model of peer-to-peer overlay was purposed. And then the paper focused on figuring out the mean-shortest path length (MSPL), clustering coefficient (CC) and the degree of every node which allowed us to discover the degree distribution. The results show that the degree distribution function follows approximately power law distribution and the network possesses notable clustering and small-world properties.