In the Genomic Signal Processing Lab, we are breaking new ground in mathematics, genetics, and at the interface between the two fields, since our highly cited1 invention of the "eigengene."2,3
At the interface, we pioneered both matrix4,5,6 and tensor7,8 modeling of large-scale molecular biological data, which, as we demonstrated, can be used to correctly predict previously unknown physical,9,10,11 cellular,12,13,14,15,16 and evolutionary17,18 mechanisms that govern the activity of DNA and RNA.19,20,21
In mathematics, we developed the only framework that can create a single coherent model from multiple two-dimensional datasets, by extending the generalized singular value decomposition (GSVD) from two to more than two matrices.22,23,24
In genetics, our recent GSVD and tensor GSVD comparisons of the genomes of tumor and normal cells from the same sets of glioblastoma and lower-grade astrocytoma brain25,26,27 and, separately, ovarian28,29,30,31,32,33,34 cancer patients uncovered patterns of DNA copy-number alterations, which, as we showed, are correlated with a patient's survival and response to chemotherapy. For three decades prior, the best predictor of ovarian cancer survival was the tumor's stage; more than a quarter of ovarian tumors are resistant to the platinum-based chemotherapy, the first-line treatment, yet no diagnostic existed to distinguish resistant from sensitive tumors before the treatment. For five decades prior, the best prognostic indicator of glioblastoma was the patient's age at diagnosis. The ovarian and brain cancer data were published, but the patterns remained unknown until we applied our mathematical frameworks.
Currently, our work is supported by a five-year, three million-dollar National Cancer Institute (NCI) Physical Sciences in Oncology U01 project grant.35,36 Additional support for our work comes from the Utah Science, Technology, and Research (USTAR) Initiative.