Mathematics
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Dynamics, Networks, and Information: Methods for Nonlinear Interactions in Biological Systems
(2021)In this dissertation, we investigate complex, non-linear interactions in biological systems.This work is presented as two independent projects. The mathematics and biology in each differ, yet there is a unity in that both ... -
ANALYZING SEMI-LOCAL LINK COHESION TO DETECT COMMUNITIES AND ANOMALIES IN COMPLEX NETWORKS
(2021)Link cohesion is a new type of metric used to assess how supported an edge is relativeto other edges, accounting for nearby alternate paths and associated vertex degrees. A deterministic, scalable, and parallelizable link ... -
Emergent behaviors in adaptive dynamical networks with applications to biological and social systems
(2021)In this thesis, we consider three network-based systems, focusing on emergent behaviors resulting from adaptive dynamical features. In our first investigation, we create a model for gene regulatory networks in which the ... -
Closed Affine Manifolds with an Invariant Line
(2021)Radiant manifolds are affine manifolds whose holonomy preserves a point. Here we discuss certain properties of closed affine manifolds whose holonomy preserves an affine line. Particular attention is given to the case ... -
HOMOTOPY CONTINUATION METHODS FOR PHASE RETRIEVAL
(2021)In this dissertation, we discuss the problem of recovering a signal from a set of phaseless measurements. This type of problem shows up in numerous applications and is known for its numerical difficulty. It finds use in ...