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Marcos Efren Bolanos (Michigan State University), “Signal processing inspired graph theoretic methods for understanding functional connectivity of the brain”, Advisor: Prof. Selin Aviyente (2012)
Functional brain networks underlying cognitive control processes have been of central interest in neuroscience. A great deal of empirical and theoretical work now suggests that frontal networks in particular the medial prefrontal cortex (mPFC) and lateral prefrontal cortex (lPFC) are involved in cognitive control. Recently, researchers have adapted tools from graph theory. Graph theory can model a network by a set of vertices and edges upon which complex network analysis may be applied. In this thesis, existing graph measures and graph theoretic approaches are modified specifically for the analysis of the functional brain network. Concepts from signal processing are adapted to graphs to identify central vertices and anomalies. A new definition of entropy rate based on modeling the adjacency matrix of a graph as a Markov process is introduced to quantify the local complexity of a weighted graph. Finally, we introduce a hierarchical consensus clustering algorithm that uses the well-known Fiedler vector to reveal a hierarchical structure of the brain network across various modular resolutions.
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