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Full-Text Articles in Engineering
The Sensitivity Of A Laplacian Family Of Ranking Methods, Claire S. Chang
The Sensitivity Of A Laplacian Family Of Ranking Methods, Claire S. Chang
HMC Senior Theses
Ranking from pairwise comparisons is a particularly rich subset of ranking problems. In this work, we focus on a family of ranking methods for pairwise comparisons which encompasses the well-known Massey, Colley, and Markov methods. We will accomplish two objectives to deepen our understanding of this family. First, we will consider its network diffusion interpretation. Second, we will analyze its sensitivity by studying the "maximal upset" where the direction of an arc between the highest and lowest ranked alternatives is flipped. Through these analyses, we will build intuition to answer the question "What are the characteristics of robust ranking methods?" …
Characterizing Forced Communication In Networks, Samuel C. Gutekunst
Characterizing Forced Communication In Networks, Samuel C. Gutekunst
HMC Senior Theses
This thesis studies a problem that has been proposed as a novel way to disrupt communication networks: the load maximization problem. The load on a member of a network represents the amount of communication that the member is forced to be involved in. By maximizing the load on an important member of the network, we hope to increase that member's visibility and susceptibility to capture. In this thesis we characterize load as a combinatorial property of graphs and expose possible connections between load and spectral graph theory. We specifically describe the load and how it changes in several canonical classes …
A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance, Sorathan Chaturapruek
A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance, Sorathan Chaturapruek
HMC Senior Theses
The obstacle avoidance navigation problem for Unmanned Aerial Vehicles (UAVs) is a very challenging problem. It lies at the intersection of many fields such as probability, differential geometry, optimal control, and robotics. We build a mathematical framework to solve this problem for quadrotors using both a theoretical approach through a Hamiltonian system and a machine learning approach that learns from human sub-experts' multiple demonstrations in obstacle avoidance. Prior research on the machine learning approach uses an algorithm that does not incorporate geometry. We have developed tools to solve and test the obstacle avoidance problem through mathematics.