I am generally interested in using analytical as well as statistical and computational approaches in order to understand biological systems, particularly those of neuroscience. I am also interested in fundamental questions of probability measure in infinite dimensional Banach spaces. My recent work as been on inverse problems relevant to biology as well as mathematical modeling of Cortical Spreading Depression and ectopic tissue calcification.
I am currently a postdoctoral fellow at the National Institutes of Health working primarily on a joint project with the social security administration in the goal of optimizing all aspects of the processing of disability benefits. From 2012-2015, I was an NSF postdoctoral fellow at the Mathematical Biosciences Institute (MBI). My postdoctoral mentors at MBI were Robert M. Miura (NJIT) and Kevin C. Brennan (UofU). I previously completed my Ph.D. in Biomathematics at UCLA, where my advisor was Tom Chou.
The primary tools that I use and study in my research include the path integral, stochastic differential equations, partial differential equations, homogenization, Gaussian processes, and convex optimization.
- Joshua C. Chang and Robert Miura. Regulation of biological tissue mineralization through post-nucleation shielding. [preprint] [arXiv:1501.02526] [CNP poster]
- Joshua C. Chang, Pak-Wing Fok, and Tom Chou. Bayesian Uncertainty Quantification for Bond Energies and Mobilities Using Path Integral Analysis, Biophysical Journal (2015), [doi:10.1016/j.bpj.2015.07.028] [arXiv:1502.06415] [DFS poster]
- Joshua C. Chang, Van Savage, and Tom Chou. A path-integral approach to Bayesian inference for inverse problems using the semiclassical approximation, Journal of Statistical Physics. [doi:10.1007/s10955-014-1059-y] [arXiv:1312.2974]
- Joshua C. Chang, K.C. Brennan, Dongdong He, H. Huang, R.M. Miura, Phillip L. Wilson, J.J. Wylie. A mathematical model of the metabolic and perfusion effects on cortical spreading depression. PLoS One, August 2013. [link] [arXiv preprint]
- Joshua C. Chang, and Tom Chou. Iterative graph cuts for image segmentation with a nonlinear statistical shape prior, Journal of Mathematical Imaging and Vision, Volume 49, Issue 1, pp 87-97, DOI:10.1007/s10851-013-0440-9. [arXiv preprint] [Springer]
See Research for a complete list of my publications.
Some of my current collaborators in no particular order:
- Robert Miura, NJIT Departments of Mathematical Sciences and Biomedical Engineering
- KC Brennan, University of Utah Department of Neurology
- Huaxiong Huang, York University Department of Mathematics and Statistics
- Jonathan Wylie, City University of Hong Kong Department of Mathematics
- Tom Chou, UCLA Departments of Biomathematics and Mathematics
- Leopold Matamba Messi, Mathematical Biosciences Institute
- Jorge Manuel Mendez, University of Utah Department of Neurology
- Pak-Wing Fok, University of Delaware Department of Mathematical Sciences
- José Otero, The Ohio State Univeristy Department of Pathology
- Patrick Gygli, The Ohio State University Department of Pathology
I am grateful for support from the following institutions and agencies: