Limits and tradeoffs in the control of autocatalytic systems

Despite the complexity of biological networks, we find that certain common architectures govern network structures. These architectures impose fundamental constraints on system performance and create tradeoffs that the system must balance in the face of uncertainty in the environment. This means that while a system may be optimized for a specific function through evolution, the optimal achievable state must follow these constraints. One such constraining architecture is autocatalysis, as seen in many biological networks including glycolysis and ribosomal protein synthesis. Using a minimal model, we show that ATP autocatalysis in glycolysis imposes stability and performance constraints and that the experimentally well-studied glycolytic oscillations are in fact a consequence of a tradeoff between error minimization and stability. We also show that additional complexity in the network results in increased robustness. Ribosome synthesis is also autocatalytic where ribosomes must be used to make more ribosomal proteins. When ribosomes have higher protein content, the autocatalysis is increased. We show that this autocatalysis destabilizes the system, slows down response, and also constrains the system’s performance. On a larger scale, transcriptional regulation of whole organisms also follows architectural constraints and this can be seen in the differences between bacterial and yeast transcription networks. We show that the degree distributions of bacterial transcription network follow a power law distribution while the yeast network follows an exponential distribution. We then explored the evolutionary models that have previously been proposed and show that neither the preferential linking model nor the duplication-divergence model of network evolution generates the power-law, hierarchical structure found in bacteria. However, in real biological systems, the generation of new nodes occurs through both duplication and horizontal gene transfers, and we show that a biologically reasonable combination of the two mechanisms generates the desired network.

Distributed Control and Optimization for Communication and Power Systems

We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.

This thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.

Our second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.

Second, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.

A systems approach to cardiovascular health and disease with a focus on aortic wave dynamics

Cardiovascular diseases (CVDs) have reached an epidemic proportion in the US and worldwide with serious consequences in terms of human suffering and economic impact. More than one third of American adults are suffering from CVDs. The total direct and indirect costs of CVDs are more than $500 billion per year. Therefore, there is an urgent need to develop noninvasive diagnostics methods, to design minimally invasive assist devices, and to develop economical and easy-to-use monitoring systems for cardiovascular diseases. In order to achieve these goals, it is necessary to gain a better understanding of the subsystems that constitute the cardiovascular system. The aorta is one of these subsystems whose role in cardiovascular functioning has been underestimated. Traditionally, the aorta and its branches have been viewed as resistive conduits connected to an active pump (left ventricle of the heart). However, this perception fails to explain many observed physiological results. My goal in this thesis is to demonstrate the subtle but important role of the aorta as a system, with focus on the wave dynamics in the aorta.

The operation of a healthy heart is based on an optimized balance between its pumping characteristics and the hemodynamics of the aorta and vascular branches. The delicate balance between the aorta and heart can be impaired due to aging, smoking, or disease. The heart generates pulsatile flow that produces pressure and flow waves as it enters into the compliant aorta. These aortic waves propagate and reflect from reflection sites (bifurcations and tapering). They can act constructively and assist the blood circulation. However, they may act destructively, promoting diseases or initiating sudden cardiac death. These waves also carry information about the diseases of the heart, vascular disease, and coupling of heart and aorta. In order to elucidate the role of the aorta as a dynamic system, the interplay between the dominant wave dynamic parameters is investigated in this study. These parameters are heart rate, aortic compliance (wave speed), and locations of reflection sites. Both computational and experimental approaches have been used in this research. In some cases, the results are further explained using theoretical models.

The main findings of this study are as follows: (i) developing a physiologically realistic outflow boundary condition for blood flow modeling in a compliant vasculature; (ii) demonstrating that pulse pressure as a single index cannot predict the true level of pulsatile workload on the left ventricle; (iii) proving that there is an optimum heart rate in which the pulsatile workload of the heart is minimized and that the optimum heart rate shifts to a higher value as aortic rigidity increases; (iv) introducing a simple bio-inspired device for correction and optimization of aortic wave reflection that reduces the workload on the heart; (v) deriving a non-dimensional number that can predict the optimum wave dynamic state in a mammalian cardiovascular system; (vi) demonstrating that waves can create a pumping effect in the aorta; (vii) introducing a system parameter and a new medical index, Intrinsic Frequency, that can be used for noninvasive diagnosis of heart and vascular diseases; and (viii) proposing a new medical hypothesis for sudden cardiac death in young athletes.