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I am interested in characterizing the physical and logical constraints placed upon evolutionary processes in a manner that can be used to make predictions about the impact of these constraints on the architectural features of gene regulatory networks. I have combined ideas from machine learning, information geometry, and abstract algebra to study the spaces of correlations capable of being achieved by different gene regulatory network architectures when gene regulation is itself modeled as a stochastic process. The relationships between these spaces determine the capacity for natural selection to act upon and distinguish different network architectures. Understanding these relationships is thus crucial in the attempt to predict which network architectures are more likely to result from long-term evolutionary processes and thus which network architectures we can expect to find enriched in attempts to empirically reconstruct network architecture from gene expression data.