A common situation in science, engineering, industry and defense is where a large amount of data is available from a system that is fundamentally newtworked, and one wishes to infer the intrinsic topology and interaction patterns of the unknown network from the available data. Despite tremendous progress in network science and engineering in the past decade, this inverse problem of predicting complex networks has received relatively little attention, mainly due to the extremely challenging nature of the problem. This proposal presents a comprehensive research plan, based on extensive preliminary studies, to investigate the problem of obtaining knowledge about network from data, with a particular eye toward significant applications such as systems biology. The particular research aims are, as follows. Firstly, we will address the issue of predicting hub nodes and full topology of the unknown network of interest under the influence of noise, a typical real-world situation. A rigorous theoretical framework will be derived to demonstrate that the dynamical-correlation matrix, which can be computed efficiently and solely from data, determines the topology of the network, and the diagonal elements of the matrix reveal the hub nodes in the network. Extensive computations will be performed to test the validity of the theory, leading to efficient and transformative algorithms that can be readily adopted to a variety of problems in data-based acquisition of knowledge about the complex network. Secondly, we will develop a compressivesensing approach to predicting the underlying dynamical processes on unknown network, based on timeseries measurements. Besides theoretical analysis and computations, we will pay particular attention to algorithmic development and practical issues that will affect the transformative potential of the algorithms. Finally, we will address a significant application in systems biology: prediction and characterization of gene regulatory networks based on spatiotemporal dynamics. In particular, we propose to study the regulatory networks governing animal development at the systems level by leveraging our prior research results and devising novel approaches. The PI (Lai) has expertise in nonlinear dynamical systems and complex networks. The co-PI (Ye) has extensive experience in computer science and systems biology. Their combined expertise will make the proposed research successful and highly productive. Intellectual Merit and Transformative Potential: The anticipated outcome of the proposed research is a comprehensive theoretical paradigm for predicting complex dynamical systems and networks, and a number of computationally efficient algorithms that can be implemented directly in real time in practical applications. The proposed research is interdisciplinary as it requires analytic and computational tools from random signal processing, nonlinear dynamics, statistical physics, applied mathematics, control theory, systems biology, computer science and engineering. Methods resulted from the proposed research are expected to be directly transformable to fields such as biomedical science and engineering, communication networks, and defense and homeland security. Broader Impacts: The proposed activity can find applications not only in physical and biological sciences, engineering, computer and social sciences, but also in problems of significant societal concern, especially those related with defense and homeland security due to the ubiquity and extreme importance of complex networks to the modern infrastructure in the US.We anticipate that the proposed research will help create an exciting environment for graduate and undergraduate students with respect to interdisciplinary awareness and skills. The nature of the proposed research renders it interesting to the general public as well.
|Effective start/end date||9/15/10 → 8/31/14|
- National Science Foundation (NSF): $539,779.00
Nonlinear dynamical systems