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In this study, we present methods of network analysis from both statistical and
topological points of view to enhance our understanding of the robustness of the networks
and the gene – gene interactions they exhibit. Using different strategies, networks were
learned from a single cell dataset in which expression values were collected during various
stages of cell development. The bnlearn algorithm was used to construct directed and acyclic
Bayesian networks for statistical analysis which revealed greater homogeneity of activating
interactions than that of inhibiting interactions. Because topological data analysis relies of
cycles formed by edges in the network which are – by construction – not present in the
Bayesian networks, new networks were learned by computing entropy, mutual information,
and distances manually. Performance of persistence homology with the TDA algorithm
revealed topological features which rendered the networks topologically distinct.
Liebling, Marjorie C. Topological Approaches to Understanding Genetic Networks Presented to the S. Daniel Abraham Honors Program in Partial Fulfillment of the Requirements for Completion of the Program. Ma7 7, 2019.
*This is contructed from limited avaiable data and may be imprecise.