Theses and Dissertations at Montana State University (MSU)
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/733
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Item An adaptive genetic algorithm for fitting DeGroot opinion diffusion models on social networks(Montana State University - Bozeman, College of Letters & Science, 2022) Johnson, Kara Layne; Chairperson, Graduate Committee: John J. BorkowskiWhile a variety of options are available for modeling opinion diffusion--the process through which opinions change and spread through a social network--current methods focus on modeling the process on online social networks where large quantities of opinion data are readily available. For in-person networks, where data are more difficult to collect, models that predict the opinions of the individuals in the network require that the structure of social influence--who is influenced by whom and to what degree--is specified by the researcher instead of informed by data. In order to fit data-driven opinion diffusion models on small networks with limited data, we developed a genetic algorithm for fitting the DeGroot opinion diffusion model. We detail the algorithm and present simulation studies to assess the algorithm's performance. We find the algorithm is able to recover model parameters across a variety of network and data set conditions, it continues to perform well under the assumption violations expected in practical applications, and the algorithm performance is robust to most choices of hyperparameters. Finally, we present an analysis of data from the study that motivated the methodological development.Item The emergence of collective behavior on social and biological networks(Montana State University - Bozeman, College of Letters & Science, 2018) Wilander, Adam Troy Charles; Chairperson, Graduate Committee: Scott McCallla; Dissertation contains an article of which Adam Troy Charles Wilander is not the main author.In this thesis, we broadly examine collective behaviors in various social and biological contexts. Aggregation, for instance, is a natural phenomenon that occurs in a variety of contexts; it is observed in schools of fish, flocks of birds, and colonies of bacteria, among others. This behavior can be found in some agent-based models, where it is typically assumed every pair of individuals interact according to a simple set of rules. In the first half of this thesis, we study a particular, well-understood aggregation model upon relaxation of the assumption that every individual interacts with every other. We review prior results on this topic -- when the underlying structure of interactions is an Erdos-Renyi graph. Seeking to incorporate community structure into the network, we establish the analogous problem under a class of networks called stochastic block graphs; a particular aspect of the system's metastable dynamics is explored upon varying the graph's connection densities. Finally, we evaluate the potential to leverage this system's dynamics in order to recover community structure (given a known graph as input). In the second half of this thesis, we similarly explore the aggregate behaviors of synchronization and desynchronization, appearing in diverse settings such as the study of metabolic oscillations and cell behaviors over time, respectively. Previous studies have leveraged a model in which repressilator entities are connected by a diffusive quorum sensing mechanism; these have shown (numerically) that the complex composition of observable behaviors depends upon the insertion point of the upregulating protein in the feedback loop. We rigorously prove a version of this; for negative feedback, negative signaling (Nf-Ns) systems we find only a unique stable equilibrium or a stable oscillation is possible. Additionally, we observe (numerically) the complex multistable dynamics that arise when a positive signal is included in the feedback loop and characterize this shift as a saddle node bifurcation of a cubic curve.