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Title: From graph structure to network function: Using spectral graph theory to predict and control dynamics Authors:  Rosemary Braun - Northwestern University (United States) [presenting]
Phan Nguyen - Lawrence Livermore National Laboratory (United States)
Abstract: The structure of networked system governs the dynamics of processes taking place on the graph (such as the flow of current, information, etc.) Spectral decomposition of the graph Laplacian provides a means to summarize the network structure and make predictions about those dynamics. Spectral graph theory (SGT) has been used extensively to analyze networked systems, cluster data, and perform dimension reduction. However, much the underlying theory was developed in the context of unsigned, undirected graphs; in contrast, real networks are often directed/asymmetric, and have both positive ("activating") and negative ("inhibitory") valences. I will discuss our recent efforts to extend spectral graph theory to directed, signed networks. I will also describe a new SGT-based approach for analyzing gene regulatory networks, predicting gene expression dynamics, and identifying network elements that can be targeted to control those dynamics. Finally, I will discuss how these methods might be exploited to restore the spectral (and hence the dynamical) properties of a "damaged" network, even when the original graph topology cannot be recovered.