Research Interests

Zebrafish pfeffer mutant
  • Applied dynamical systems
  • Computational and mathematical biology
  • Data science
  • Dynamics of patterns and nonlinear waves
  • Numerical continuation

Nonlinear waves

Planar spiral wave

My group has studied the existence, stability, and bifurcations of nonlinear waves, ranging from one-dimensional travelling waves and source defects to planar spiral waves.

Computational biology

Dendrogram of significant genes

I am interested in applications of data science to problems in genomics. In collaboration with Sohini Ramachandran's lab, my group has shown that clustering algorithms can extract differential genetic architectures between immunological and metabolic phenotypes from gene-level association statistics.

Data science

fMRI inferred activity pattern

In collaboration with Xi Luo's lab, my lab have developed new statistical algorithms to simultaneously estimate brain activity and effective connectivity from large-scale fMRI data.

Mathematical biology

mRNA localization simulation zebrafish fin simulation

My lab has focused on modeling patterning and localization during the early development of organisms. With Kimberly Mowry's lab, we developed models to understand the role played by molecular motors and anchoring in mRNA localization in Xenopus oocytes based on experimental FRAP data. My lab also investigated robustness and redundancy of stripe patterning in the Danio zebrafish family using agent-based models.

Undergraduate research

REU Summer@ICERM 2016

I have organized several research experiences for undergraduates as part of NSF-funded REUs or Brown-funded UTRA projects. The photo is from Summer@ICERM 2016, where 26 undergraduate researchers worked with a team of graduate students, postdocs, and 3 faculty (including me).

AUTO and HOMCONT

AUTO bifurcation diagram

HOMCONT, jointly developed with Alan Champneys (University of Bristol) and Yuri A Kuznetsov (Utrecht University), is a numerical toolbox for homoclinic bifurcation analysis. It is designed for use with Auto07p written by Eusebius Doedel (Concordia University).