Courant Institute and NYUAD Institute
New York University
October 28, 2014
A Novel Characterization of Amalgamated Networks in Natural Systems Using Sparse and Low-Rank Optimization
Densely-connected networks are prominent among natural systems, exhibiting topological characteristics often optimized for biological function. To reveal such features in highly-connected networks, we introduce a new network characterization determined by a decomposition of network-connectivity into low-rank and sparse components. Based on these components, we discover a new class of networks we define as amalgamated networks, which exhibit large functional groups and dense connectivity. Analyzing recent experimental findings on brain, food-web, and gene regulatory networks, we establish the unique importance of amalgamated networks in fostering biologically advantageous properties, including rapid communication both within and between functional groups as well as structural stability under attacks. We observe that our network characterization is scalable with network size and connectivity, thereby identifying topological structures significant to diverse physical systems, which are typically undetectable by conventional characterizations of connectivity. In other biological systems, we illustrate similar optimization techniques may be applied via compressive sensing of natural signals. We demonstrate further that the incorporation of localized random sampling, akin to receptive fields, may improve signal processing beyond conventional compressive sensing theory.