From Contagion to Stability: Insights into Network Dynamics, Resilience and Stability
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The resilience of interconnected systems, such as financial networks, supply chains, software systems, and social networks, is a critical concern in today's highly connected world. While interconnectedness enables efficient economic transactions, rapid social learning, and adaptability to shocks, it also increases vulnerability to systemic risks, where localized disruptions can propagate and cause widespread failures. This thesis addresses this fundamental challenge by examining how to reason about and reinforce the resilience of complex networks through theoretical and applied tools, including probability, statistics, algorithms, and network science, whereas we rely on centralized and decentralized decision-making to design interventions that mitigate cascading failures and bolster network stability. First, the thesis focuses on optimizing resource allocation in networks undergoing contagion, developing novel resilience metrics for supply chains, and creating efficient algorithms to prevent cascading failures. Secondly, this thesis studies models of contagion and gives a formalized definition of resilience. Then, this thesis explores decentralized privacy-aware decision-making to reconcile privacy with efficient social learning in risk-prone environments to ensure resilience. Finally, the thesis studies models of network formation and also suggest modern ways to view complex interconnected systems through the lens of LLMs.