Date of Award


Document Type


Degree Name

Master of Science (MS)


Department of Mathematics

First Advisor

Olcay Akman


Genes are segments of DNA that provide a blueprint for cells and organisms to effectively control processes and regulations within individuals. There have been many attempts to quantify these processes, as a greater understanding of how genes operate could have large impacts on both personalized and precision medicine. Gene interactions are of particular interest, however, current biological methods can not easily reveal the details of these interactions. Therefore, we infer networks of interactions from gene expression data which we call a gene regulatory network, or GRN. Due to the robust behavior of genes and the inherent variability within interactions, models incorporating stochasticity are more realistic than those that are only deterministic. These methods are designed to bypass the need for large amounts of data and extensive knowledge about a network. In this work, we extend previous work investigating additional ways to incorporate stochasticity into gene regulatory networks. First, we use a transition function and investigate its inherent variation, then we use a statistical distribution for activating and degrading the states of genes,

and finally, we use a new method incorporating spectral density to incorporate stochasticity within a GRN.


Imported from Liesman_ilstu_0092N_11780.pdf


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