In the Genomic Signal Processing Lab, we invented the
"eigengene,"^{1,2,3}
and pioneered the
matrix^{4,5,6}
and
tensor^{7,8,9,10,11,12}
modeling of large-scale molecular biological data, which, as we demonstrated, can be used to correctly predict previously unknown
physical,^{13,14,15}
cellular,^{16,17,18,19,20}
and evolutionary^{21,22}
mechanisms.^{23,24,25}

Now, supported by a five-year, three million-dollar National Cancer Institute (NCI) Physical Sciences in Oncology U01 project grant,^{26,27} we
develop novel, multi-tensor generalizations of the singular value decomposition, and use them in the comparisons of
brain,^{28,29,30,31}
lung,^{32},
ovarian,
^{33,34,35,36,37,38,39}
and uterine cancer and normal genomes, to uncover patterns of DNA copy-number alterations that predict survival and response to treatment, statistically better than, and independent of, the best indicators in clinical use and existing laboratory tests. Recurring alterations have been recognized as a hallmark of cancer for over a century, and observed in these cancers' genomes for decades; however, copy-number subtypes predictive of patients' outcomes were not identified before. The data had been publicly available, but the patterns remained unknown until the data were modeled by using the multi-tensor decompositions, illustrating the universal ability of these decompositions — generalizations of the frameworks that underlie the theoretical description of the physical world — to find what other methods miss.

- April 15, 2015. New method increases accuracy of ovarian cancer prognosis and diagnosis: Mathematical technique reveals predictive DNA patterns that other methods missed.

- November 25, 2013. On mathematics and brain cancer: A new approach for discovery from data opens a new way of studying cancer.

- January 23, 2012. Mathematical modeling of patient-matched genomic profiles predicts brain cancer survival and drug targets.

- December 22, 2011. A novel mathematical framework for discovery from comparison of large-scale datasets.

- April 29, 2011. Novel mathematical modeling of ribosomal RNA sequence data suggests a new way of looking at evolution.

- October 13, 2009. Mathematical modeling correctly predicts previously unknown biological mechanism of regulation.