Theses and Dissertations at Montana State University (MSU)
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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.Item Fault-diagnosis by inserting the minimum number of test points in system graphs(Montana State University - Bozeman, College of Engineering, 1974) Patel, MaheshItem A branch-and-bound algorithm for the crossing number of a graph(Montana State University - Bozeman, College of Engineering, 2000) Tan, ZhengItem An efficient implementation of a planarity testing and maximal planar subgraph algorithm(Montana State University - Bozeman, College of Engineering, 1996) Li, ZhongyuanItem Apriori approach to graph-based clustering of text documents(Montana State University - Bozeman, College of Engineering, 2008) Hossain, Mahmud Shahriar; Chairperson, Graduate Committee: Rafal A. AngrykThis thesis report introduces a new technique of document clustering based on frequent senses. The developed system, named GDClust (Graph-Based Document Clustering) [1], works with frequent senses rather than dealing with frequent keywords used in traditional text mining techniques. GDClust presents text documents as hierarchical document-graphs and uses an Apriori paradigm to find the frequent subgraphs, which reflect frequent senses. Discovered frequent subgraphs are then utilized to generate accurate sense-based document clusters. We propose a novel multilevel Gaussian minimum support strategy for candidate subgraph generation. Additionally, we introduce another novel mechanism called Subgraph-Extension mining that reduces the number of candidates and overhead imposed by the traditional Apriori-based candidate generation mechanism. GDClust utilizes an English language thesaurus (WordNet [2]) to construct document-graphs and exploits graph-based data mining techniques for sense discovery and clustering. It is an automated system and requires minimal human interaction for the clustering purpose.