A Mean-Field Approximation of SIR Epidemics on an Erdös-Rényi Network Model.

The stochastic nature of epidemic dynamics on a network makes their direct study very challenging. One avenue to reduce the complexity is a mean-field approximation (or mean-field equation) of the dynamics; however, the classic mean-field equation has been shown to perform sub-optimally in many applications. Here, we adapt a recently developed mean-field equation for SIR epidemics on a network in continuous time to the discrete time case. With this new discrete mean-field approximation, this proof-of-concept study shows that, given the density of the network, there is a strong correspondence between the epidemics on an Erdös-Rényi network and a system of discrete equations. Through this connection, we developed a parameter fitting procedure that allowed us to use synthetic daily SIR data to approximate the underlying SIR epidemic parameters on the network. This procedure has improved accuracy in the estimation of the network epidemic parameters as the network density increases, and is extremely cheap computationally.

Variability of Betweenness Centrality and Its Effect on Identifying Essential Genes.

This paper begins to build a theoretical framework that would enable the pharmaceutical industry to use network complexity measures as a way to identify drug targets. The variability of a betweenness measure for a network node is examined through different methods of network perturbation. Our results indicate a robustness of betweenness centrality in the identification of target genes.

Heatmap centrality: A new measure to identify super-spreader nodes in scale-free networks.

The identification of potential super-spreader nodes within a network is a critical part of the study and analysis of real-world networks. Motivated by a new interpretation of the "shortest path" between two nodes, this paper explores the properties of the heatmap centrality by comparing the farness of a node with the average sum of farness of its adjacent nodes in order to identify influential nodes within the network. As many real-world networks are often claimed to be scale-free, numerical experiments based upon both simulated and real-world undirected and unweighted scale-free networks are used to illustrate the effectiveness of the proposed "shortest path" based measure with regards to its CPU run time and ranking of influential nodes.

Graph complexity analysis identifies an ETV5 tumor-specific network in human and murine low-grade glioma.

Conventional differential expression analyses have been successfully employed to identify genes whose levels change across experimental conditions. One limitation of this approach is the inability to discover central regulators that control gene expression networks. In addition, while methods for identifying central nodes in a network are widely implemented, the bioinformatics validation process and the theoretical error estimates that reflect the uncertainty in each step of the analysis are rarely considered. Using the betweenness centrality measure, we identified Etv5 as a potential tissue-level regulator in murine neurofibromatosis type 1 (Nf1) low-grade brain tumors (optic gliomas). As such, the expression of Etv5 and Etv5 target genes were increased in multiple independently-generated mouse optic glioma models relative to non-neoplastic (normal healthy) optic nerves, as well as in the cognate human tumors (pilocytic astrocytoma) relative to normal human brain. Importantly, differential Etv5 and Etv5 network expression was not directly the result of Nf1 gene dysfunction in specific cell types, but rather reflects a property of the tumor as an aggregate tissue. Moreover, this differential Etv5 expression was independently validated at the RNA and protein levels. Taken together, the combined use of network analysis, differential RNA expression findings, and experimental validation highlights the potential of the computational network approach to provide new insights into tumor biology.