Research

Computational Complexity of Biological Networks

The study of biological networks is a fast growing field with a tremendous potential. Our team, which consists of expertise in mathematics (Y. Rong), bio-physics (G. Wang and C. Zeng), and computer science (R. Simha), has already made breakthroughs on the Reverse Engineering Problem which asks for network structure given information on its dynamics. The previous methods, based on exhaustive enumeration, were possible only for networks with up to four or five nodes. We have found a fast algorithm that can handle networks with any realistic size such as thousands of nodes. Furthermore, we have proved that the problem of determining a minimal network solution is NP-hard[1]. More recently, we have been discussing with Valerie Hu to see if some of our ideas can be applied to her research on autism, a complex neurodevelopmental disorder in which her group has shown that hundreds to thousands of genes are disrupted, depending on the severity or phenotype of autism. Our work has now led to a $1.2 million NSF CDI (Cyber-enabled Discovery and Innovation) award – a highly competitive NSF five-year initiative aimed to “create revolutionary science and engineering research outcomes made possible by innovations and advances in computational thinking.”

Statistical Analysis of Microarray Data

Yinglei Lai has been working on the co-expression based analysis methods for microarray data for many years. Supported by his several NIH grants, he has published various statistical methods for analyzing large-scale gene expression data. The related computer software has also been implemented and distributed freely through the Internet. The co-expression based analysis is closely related to the biological network models. Recently, Lai has been discussing some statistical issues in the biological network models with Rong, Simha, and Zeng. This effort will be continued in the near future. Yinglei Lai has also been collaborating with Valerie Hu on the analysis of gene expression data for autism studies. With NIH and Autism Speaks funding, Valerie has now published six studies on the genomics and epigenetics of autism spectrum disorders, with Yinglei Lai as a coauthor on the large-scale study of unrelated case-controls in which circadian rhythm dysfunction was observed specifically in autistic individuals with severe language impairment. We anticipate that future collaborative studies will include computational modeling of pathway disruption caused by a specific environmental or biologic factor.

Mathematical Tools in Medical Imaging

Our new faculty member Svetlana Roudenko has worked on applications of analysis and differential equation methods in medical imaging and in biology topics such as population and disease dynamics. She is bringing her expertise in how (i)fundamental mathematical concepts are used in modern medical imaging such as MRI, PET and CT modalities, (ii) in disease dynamics, (iii) educational experience on how to combine mathematical concepts in biology and medicine in current undergraduate curriculum. She has been funded by various granting agencies, current funding including: (1) NSF-FRG grant (30%co-PI for the amount $818K) towards investigation of mathematical methods in medical imaging, (2) NSF-DUI (CCLI) grant (sole PI, $75K) in which she has introduced a new undergraduate course which combines differential equations and analysis curriculum with studying modern medical imaging techniques, under this grant she has also creates a manuscript which is now considered for publication at one of the AMS series; (3) NSF-DMS Analysis program ($107K) for studying partial differential equations and their application to fluid and air dynamics. In the past she had funding from other institutions such as Los Alamos National Lab and European grant agencies. As part of the proposed activities, besides collaborating with the core faculty of GWIMS, she will establish collaboration with the Department of Electrical and Computer Engineering (Murray Loew, director of the biomedical engineering program, on research topics in medical imaging and signal processing) and faculty and practitioners at the GWU Medical Center. She has previously worked with bioengineers and radiologists at the St. Joseph Hospital in Phoenix.