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The interdiction problem arises in a variety of areas including military logistics, infectious disease control, and counter-terrorism. In the typical formulation of network interdiction, the task of the interdictor is to find a set of edges in a weighted network such that the removal of those edges would maximally increase the cost to an evader of traveling… (More)

Complex socioeconomic networks such as transportation networks, information systems and even underground organizations are often designed for resilience-to be able to function even if some of the nodes (e.g. hubs, routers, operatives etc.) are compromised by a human or natural adversary. In many cases the adversary threatens to cause a cascade where the… (More)

Terrorist organizations change over time because of processes such as recruitment and training as well as counter-terrorism (CT) measures, but the effects of these processes are typically studied qualitatively and in separation from each other. Seeking a more quantitative and integrated understanding, we constructed a simple dynamic model where equations… (More)

Complex socioeconomic networks such as information, finance and even terrorist networks need resilience to cascades--to prevent the failure of a single node from causing a far-reaching domino effect. We show that terrorist and guerrilla networks are uniquely cascade-resilient while maintaining high efficiency, but they become more vulnerable beyond a… (More)

Major revolts have recently erupted in parts of the Middle East with substantial international repercussions. Predicting, coping with and winning those revolts have become a grave problem for many regimes and for world powers. We propose a new model of such revolts that describes their evolution by building on the classic Lanchester theory of combat. The… (More)

Networks are widely used in science and technology to represent relationships between entities , such as social or ecological links between organisms, enzymatic interactions in metabolic systems, or computer infrastructure. Statistical analyses of networks can provide critical insights into the structure, function, dynamics, and evolution of those systems.… (More)

In network interdiction problems, evaders (e.g., hostile agents or data packets) may be moving through a network towards targets and we wish to choose locations for sensors in order to intercept the evaders before they reach their destinations. The evaders might follow deter-ministic routes or Markov chains, or they may be reactive, i.e., able to change… (More)

Shortest path network interdiction is a combinatorial optimization problem on an activity network arising in a number of important security-related applications. It is classically formulated as a bilevel maximin problem representing an " interdictor " and an " evader ". The evader tries to move from a source node to the target node along a path of the least… (More)

Mathematical research of terrorism has the potential to inform both scholars and policy-makers. This thesis presents several projects in this emerging area: (1) an ordinary-differential equations model of a terrorist organization focused on evaluating various counter-terrorism measures and predicting the evolution of terrorist conflicts; (2) a model of… (More)

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract The following thesis is a project in mathematical biology building upon the so-called " error… (More)