Probabilistic measures of edge criticality in graphs: a study in water distribution networks

AbstractThe issue of vulnerability and robustness in networks have been addressed by several methods. The goal is to identify which are the critical components (i.e., nodes/edges) whose failure impairs the functioning of the network and how much this impacts the ensuing increase in vulnerability. In this paper we consider the drop in the network robustness as measured by the increase in vulnerability of the perturbed network and compare it with the original one. Traditional robustness metrics are based on centrality measures, the loss of efficiency and spectral analysis. The approach proposed in this paper sees the graph as a set of probability distributions and computes, specifically the probability distribution of its node to node distances and computes an index of vulnerability through the distance between the node-to-node distributions associated to original network and the one obtained by the removal of nodes and edges. Two such distances are proposed for this analysis: Jensen–Shannon and Wasserstein, based respectively on information theory and optimal transport theory, which are shown to offer a different characterization of vulnerability. Extensive computational results, including two real-world water distribution networks, are reported comparing the new approach to the traditional metrics. This modelling and algorithmic framework can also support the analysis of other networked infrastructures among which power grids, gas distribution and transit networks

Maturation trajectories of cortical resting-state networks depend on the mediating frequency band

The functional significance of resting state networks and their abnormal manifestations in psychiatric disorders are firmly established, as is the importance of the cortical rhythms in mediating these networks. Resting state networks are known to undergo substantial reorganization from childhood to adulthood, but whether distinct cortical rhythms, which are generated by separable neural mechanisms and are often manifested abnormally in psychiatric conditions, mediate maturation differentially, remains unknown. Using magnetoencephalography (MEG) to map frequency band specific maturation of resting state networks from age 7 to 29 in 162 participants (31 independent), we found significant changes with age in networks mediated by the beta (13–30 Hz) and gamma (31–80 Hz) bands. More specifically, gamma band mediated networks followed an expected asymptotic trajectory, but beta band mediated networks followed a linear trajectory. Network integration increased with age in gamma band mediated networks, while local segregation increased with age in beta band mediated networks. Spatially, the hubs that changed in importance with age in the beta band mediated networks had relatively little overlap with those that showed the greatest changes in the gamma band mediated networks. These findings are relevant for our understanding of the neural mechanisms of cortical maturation, in both typical and atypical development.This work was supported by grants from the Nancy Lurie Marks Family Foundation (TK, SK, MGK), Autism Speaks (TK), The Simons Foundation (SFARI 239395, TK), The National Institute of Child Health and Development (R01HD073254, TK), National Institute for Biomedical Imaging and Bioengineering (P41EB015896, 5R01EB009048, MSH), and the Cognitive Rhythms Collaborative: A Discovery Network (NFS 1042134, MSH). (Nancy Lurie Marks Family Foundation; Autism Speaks; SFARI 239395 - Simons Foundation; R01HD073254 - National Institute of Child Health and Development; P41EB015896 - National Institute for Biomedical Imaging and Bioengineering; 5R01EB009048 - National Institute for Biomedical Imaging and Bioengineering; NFS 1042134 - Cognitive Rhythms Collaborative: A Discovery Network

Analysis Of Grapevine Gene Expression Data Using Node-based Resilience Clustering

Powdery mildew is the most economically important disease of cultivated grapevines worldwide. In the agricultural community, there is a great need for better understanding of the complex genetic basis of powdery mildew (PM) resistance by delineating possible gene biomarkers associated with the plants\u27 defense mechanisms. Machine learning techniques can be applied to analysis of gene expression data to aid knowledge discovery of disease fighting genes. In this work, we apply a data-driven computational model, utilizing a graph-based clustering algorithm - Node-Based Resilience Clustering (NBRClust), to analyze grapevine gene expression data to identify possible gene biomarkers associated with powdery mildew disease defense mechanisms. We investigated two graph representations (geometric and kNN) on the mean differences of PM inoculated vs. mock inoculated gene expression values of Cabernet and Norton (PM disease resistant) species across 6 time points. By applying the contrarian approach, we hypothesized that smaller sized clusters will contain genes that do not follow general patterns, hence, could display distinct expression patterns of PMinduced transcripts across the time points that may insinuate biological relevance. We compared the smaller clusters obtained in Norton in contrast with the ones from Cabernet in terms of the genes that clustered in common between both (intersection of sets) as well as the differences of the sets. The results obtained demonstrate the usefulness of the geometric graphs for this domain application in contrast to the kNN graphs. Some genes that belong to biologically relevant pathways were identified that displayed differences in patterns across the time points between Norton and Cabernet species