Persistence DNA, protein and RNA analysis
The key ideas recently developed by Dr. Nguyen using his expertise in algebraic topology are to represent DNA sequences using mathematical or graphical representations based on which one can associate each DNA sequence with topological objects such as persistent barcodes or persistent diagrams. These topological objects explore and detect the hidden features or patterns of DNA sequences using tools from algebraic topology. The similarities of the DNA sequences will be mirrored by similarities of their topological counterparts. Under our proposed topological framework one can easily compare differences between DNA sequences from different diseases, cancer types or subtypes by comparing their topological representations. The approaches have wide and fundamental application such as in clustering diseases and phylogenetic inference. Such approaches can be applied to analyzing RNA sequences and proteins. Our approaches have appealing visualization features.