Aiming to expand the frontiers of research on living systems and to reveal quantitative mechanisms underlying biological phenomena, such as arising from neural systems, cardiovascular systems, tumor growth, and evolution. The research of the center focuses on mathematical modeling of biological processes in living systems, systemic analysis of large-scale data from biological and medical observations, development of new efficient computational methods for simulation of biological models, and exploration of new mathematical structures in biological and medical sciences.
The group led by Prof. Dan Hu has broad interests in understanding properties of biological systems by modeling, simulation, and analysis. Currently, the main interests of the group focus on 1) designing principles of biological transport networks such as circulation systems and leaf venation, namely, the function and properties of their network structures and physiological processes to form particular network structures; 2) propagation of blood pulse waves and signal decoding of blood pressure waveforms; 3) numerical methods for interaction between blood flow and blood vessels; and 4) numerical methods for free energy calculation of molecular systems and study of function and dynamics of membrane-peptide structures.
Jinglai Li’s mathematical interests lie on the interface between statistical science and scientific computing. From a practical perspective, he is interested in modeling and simulation of physical or engineered systems with uncertainty. Many of these systems are subject to various sources of uncertainty: parameters, initial conditions, and boundary conditions, which may be poorly characterized; computational models may contain incomplete or underresolved representations of the underlying physical processes, and systems may be perturbed by stochastic external forcing. These uncertainties have profound influence on the system characteristics and must be carefully quantified in modeling and simulation of the systems. The central theme of his research is uncertainty quantification (UQ). Specifically, he has been working on two classes of UQ problems: (1) Bayesian inferences for inverse problems, (2) rare event simulations and reliability analysis.
Weidong Liu’s research is focused on high-dimensional statistical inference. One of main targets in this area is to analyze mathematical/statistical models arising from biology and medical science. Particularly, Weidong Liu has developed several statistical tools to estimate graphical structures of dependency between genes in microarray data. Weidong Liu has also developed multiple testing procedures to control the false positive/negative ratio in the selection of important features among noisy data.
The research group of Prof. Min Tang is interested in the areas of numerical computation and applied analysis in mathematical biology and physics. Their work is motivated by understanding deterministic PDE models at different scales and their connections. Currently the research of the group focuses on 1) Chemotaxis - in order to understand the dependence of population behaviors on signal pathways of each cell - various macroscopic models can be derived from a transport system whose turning operator takes into account the dynamical intracellular pathway, 2) Establishing connections between different types of models that characterize cancerous cells multiplication; 3) Uniformly convergent multi-scale schemes for radiative transport equation, anisotropic diffusion equation and fluid equations, etc.
The group of Professor Zhenli Xu has general interests in modeling and scientific computing for problems from biophysical and biological systems. Their research group has been working on electrostatic solvation models of biomolecules and ion transport within ion channels, with attempt to construct appropriate continuum descriptions of ion correlations and to develop numerical techniques to address computational difficulties stemming from continuum modeling, such as of dielectric interfaces.
Dr. Wenjun Ying’s current research is focused on numerical algorithms for differential and integral equations from applications in mathematical biology, such as blood flow in the heart and vesicles transportation in the vessels. Dr. Ying has successfully developed a novel Cartesian grid method for modelling cardiac electrical wave propagation in the virtual heart(s) and potential distribution around biological cells and molecules. Dr. Ying is now working on application and further development of the method for a larger variety of (free boundary, moving interface and fluid-structure interaction) problems in mathematical biology.
Professor Lei Zhang’s research focuses on the multi-scale modeling, analysis and simulation, as well as applications in materials science and biology. He has applied novel numerical homogenization techniques to coarse graining of polymer self-assembly systems. Recently, he has been working on the modeling, analysis and simulation of cell motility models.
The research group led by Prof. Xiaoqun Zhang has broad interests in developing mathematical modeling and algorithms in imaging and data sciences and their application in biomedical engineering, medicine and other related interdisciplinary fields. The current research interests focus on 1) High dimensional image processing and analysis, including image restoration, segmentation, dynamic imaging reconstruction, multi-modality imaging, information fusion and multi/hyperspectral imaging etc. 2) Large scale optimization algorithms and high performance computing for imaging and data sciences. 3) Regularization methods in linear and nonlinear inverse problems. 4) High dimensional data analysis and machine learning.
Dongzhuo Zhou’s lab is interested in mathematical modeling and scientific computing for important problems in biophysical and biological sciences. In particular, it focuses on understanding of the relation between structures and functions of biological neuronal network dynamics, development of new efficient computational methods for modeling large-scale cortical networks, exploration of potential mechanisms underlying information processing in the brain, investigation of new mathematical frameworks embedded in biological processes and design of quantitative tools to extract useful information from neurophysiological data measured in experiment.