Cells are able to function and survive due to a delicate orchestration of the expression of genes and their downstream products at the genetic, transcriptomic, proteomic, and metabolic levels. Since metabolites are ultimately the causative agents for physiological responses and responsible for much of the functionality of the organism, a comprehensive understanding of cellular functioning mandates deep insights into how metabolism works. Gaining these insights is impeded by the fact that the regulation and dynamics of metabolic networks are often too complex to allow intuitive predictions, which thus renders mathematical modeling necessary as a means for assessing and understanding metabolic systems. The most difficult step of the modeling process is the extraction of information regarding the structure and regulation of the system from experimental data. The work presented here addresses this "inverse" task with three new methods that are applied to models within Biochemical Systems Theory (BST). Alternating Regression (AR) dissects the nonlinear estimation task into iterative steps of linear regression by utilizing the fact that power-law functions are linear in logarithmic space. Eigenvector Optimization (EO) is an extension of AR that is particularly well suited for the identification of model structure. Dynamic Flux Estimation (DFE) is a more general approach that can involve AR and EO and resolves open issues of model validity and quality beyond residual data fitting errors. The necessity of fast solutions to biological inverse problems is discussed in the context of concept map modeling, which allows the conversion of hypothetical network diagrams into mathematical models.

abstract: Our ability to understand networks is important to many applications, from the analysis and modeling of biological networks to analyzing social networks. Unveiling network dynamics allows us to make predictions and decisions. Moreover, network dynamics models have inspired new ideas for computational methods involving multi-agent cooperation, offering effective solutions for optimization tasks. This dissertation presents new theoretical results on network inference and multi-agent optimization, split into two parts - The first part deals with modeling and identification of network dynamics. I study two types of network dynamics arising from social and gene networks. Based on the network dynamics, the proposed network identification method works like a `network RADAR', meaning that interaction strengths between agents are inferred by injecting `signal' into the network and observing the resultant reverberation. In social networks, this is accomplished by stubborn agents whose opinions do not change throughout a discussion. In gene networks, genes are suppressed to create desired perturbations. The steady-states under these perturbations are characterized. In contrast to the common assumption of full rank input, I take a laxer assumption where low-rank input is used, to better model the empirical network data. Importantly, a network is proven to be identifiable from low rank data of rank that grows proportional to the network's sparsity. The proposed method is applied to synthetic and empirical data, and is shown to offer superior performance compared to prior work. The second part is concerned with algorithms on networks. I develop three consensus-based algorithms for multi-agent optimization. The first method is a decentralized Frank-Wolfe (DeFW) algorithm. The main advantage of DeFW lies on its projection-free nature, where we can replace the costly projection step in traditional algorithms by a low-cost linear optimization step. I prove the convergence rates of DeFW for convex and non-convex problems. I also develop two consensus-based alternating optimization algorithms --- one for least square problems and one for non-convex problems. These algorithms exploit the problem structure for faster convergence and their efficacy is demonstrated by numerical simulations. I conclude this dissertation by describing future research directions. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2017