Gauss's law for networks directly reveals community boundaries.

The study of network topology provides insight into the function and behavior of physical, social, and biological systems. A natural step towards discovering the organizing principles of these complex topologies is to identify a reduced network representation using cohesive subgroups or communities. This procedure often uncovers the underlying mechanisms governing the functional assembly of complex networks. A community is usually defined as a subgraph or a set of nodes that has more edges than would be expected from a simple, null distribution of edges over the graph. This view drives objective such as modularity. Another perspective, corresponding to objectives like conductance or density, is that communities are groups of nodes that have extremal properties with respect to the number of internal edges and cut edges. Here we show that identifying community boundaries rather than communities results in a more accurate decomposition of the network into informative components. We derive a network analog of Gauss's law that relates a measure of flux through a subgraph's boundary to the connectivity among the subgraph's nodes. Our Gauss's law for networks naturally characterizes a community as a subgraph with high flux through its boundary. Aggregating flux over these boundaries gives rise to a Laplacian and forms the basis of our "Laplacian modularity" quality function for community detection that is applicable to general network types. This technique allows us to determine communities that are both overlapping and hierarchically organized.

Severe asthma in humans and mouse model suggests a CXCL10 signature underlies corticosteroid-resistant Th1 bias.

We previously showed that Th1/type 1 inflammation marked by increased IFN-γ levels in the airways can be appreciated in 50% of patients with severe asthma, despite high dose corticosteroid (CS) treatment. We hypothesized that a downstream target of IFN-γ, CXCL10, which recruits Th1 cells via the cognate receptor CXCR3, is an important contributor to Th1high asthma and CS unresponsiveness. We show high levels of CXCL10 mRNA closely associated with IFNG levels in the BAL cells of 50% of severe asthmatics and also in the airways of mice subjected to a severe asthma model, both in the context of high-dose CS treatment. The inability of CS to dampen IFNG or CXCL10 expression was not because of impaired nuclear translocation of the glucocorticoid receptor (GR) or its transactivational functions. Rather, in the presence of CS and IFN-γ, STAT1 and GR were recruited on critical regulatory elements in the endogenous CXCL10 promoter in monocytes, albeit without any abatement of CXCL10 gene expression. High CXCL10 gene expression was also associated with a mast cell signature in both humans and mice, CXCR3 being also expressed by mast cells. These findings suggest that the IFN-γ-CXCL10 axis plays a central role in persistent type 1 inflammation that may be facilitated by CS therapy through GR-STAT1 cooperation converging on the CXCL10 promoter.