Kui Ren |
Research |

I am a faculty member in the Department of Mathematics and the Institute for Computational Engineering and Sciences (ICES) in the University of Texas at Austin. I received my PhD from Columbia University in 2006 and spent a year in The University of Chicago as a L. E. Dickson instructor in Applied Mathematics before joining UT Austin in Fall 2008.

I am interested in applied and computational mathematics. My recent research topics include: inverse problems, mathematical imaging, fast algorithms, kinetic modeling, and complex networks. Here are some recent preprint/publications (most of which can be found on arXiv or Google Scholar):

·
An implicit
boundary integral method for computing electric potential of macromolecules in
solvent (with R. Tsai and Y. Zhong), *Preprint, *2017.
[pdf].

·
Surface
effects in dense random graphs with sharp edge constraint (with C. Radin and L. Sadun), *Preprint,
*2017. [pdf].

·
Quantitative
photo-acoustic imaging of two-photon absorption, (with P. Bardsley
and R. Zhang), *Submitted*, 2017. [pdf].

·
A global
stability estimate for the photo-acoustic inverse problem in layered media,
(with F. Triki), *Submitted*, 2017. [pdf].

·
The phases of
large networks with edge and triangle constraints, (with R. Kenyon, C. Radin and L. Sadun), *J. Phys.
A: Math. Theor.*, 50, 435001, 2017. [pdf].

·
Nonlinear
quantitative photoacoustic tomography with two-photon absorption (with R.
Zhang), *SIAM J. Appl. Math.*, In Press, 2017. [pdf].

·
A fast
algorithm for radiative transport in isotropic media (with R. Zhang and Y. Zhong), *Submitted*, 2016. [pdf].

·
A symmetry
breaking transition in the edge/triangle network model (with C. Radin and L. Sadun), *Submitted*,
2016. [pdf].

·
Numerical
algorithms based on Galerkin methods for the modeling
of reactive interfaces in photoelectrochemical (PEC)
solar cells (with M. Harmon and I. M. Gamba), *J. Comput. Phys.*, 327, 140-167, 2016. [pdf
].

·
Inverse
transport problems in quantitative PAT for molecular imaging (with R. Zhang and
Y. Zhong), *Inverse Problems,* 31, 125012, 2015. [pdf].

·
Bipodal structure in
oversaturated random graphs (with R. Kenyon, C. Radin
and L. Sadun), *Int. Math. Res. Notices*, 2016,
1-36, 2016. [pdf].

·
A one-step
reconstruction algorithm for quantitative photoacoustic imaging (with T. Ding
and S. Vallelian), *Inverse Problems,* 31, 095005, 2015. [pdf]. This paper was selected as by Inverse
Problems as one of the papers in its collection: Highlight
of 2015

·
Multipodal Structure
and Phase Transitions in Large Constrained Graphs (with R. Kenyon, C. Radin and L. Sadun), *J. Stat.
Phys., *168, 233-258, 2017. [pdf].

·
The Asymtotics of Large Constrained Graphs (with C. Radin and L. Sadun), *J. Phys. A: Math. Theor.*
47**,** 175001*, *2014. [pdf]. One figure in the paper appears on the cover of the
journal.

·
Quantitative
photoacoustic imaging in the radiative transport regime (with A. Mamonov), *Commun**. Math.
Sci*, 12, 201-234, 2014. [pdf].

·
Inverse
transport calculations in optical imaging with subspace optimization algorithms
(with T. Ding), *J. Comput. Phys., *273,
212-226, 2014 [pdf]

·
Quantitative
fluorescence photoacoustic tomography
(with H. Zhao), *SIAM J Imag. Sci.*, 6,
2404-2429, 2013. [pdf]

·
A hybrid
reconstruction method for quantitative PAT (with H. Gao and H. Zhao), *SIAM
J. Imag. Sci.*, 6, 32-55, 2013. [pdf]

·
On the
modeling and simulation of reaction-transfer dynamics in
semiconductor-electrolyte solar cells (with Y. He, I. M. Gamba
and H. Lee), *SIAM J. Appl. Math.,* 75,
2515-2539, 2015. [pdf].

·
On
multi-spectral quantitative photoacoustic tomography (with G. Bal), *Inverse Problems*, 28, 025010,
2012. [pdf]. This paper was selected as a featured article by
Inverse Problems and then chosen to be
included in its collection Highlight
of 2012

·
Quantitative
Thermo-acoustics and related problems (with
G. Bal, G. Uhlmann and T. Zhou), *Inverse Problems*,
27, 055007, 2011. [pdf].

·
Multiple-source
quantitative photoacoustic tomography (with
G. Bal), *Inverse Problems*, 27, 075003, 2011. [pdf]. Read the news about
this paper from Inverse Problems.

·
Non-uniqueness
result for a hybrid inverse problem (with
G. Bal), *Contemporary Mathematics*, 2011. [pdf].

·
Recovering
doping profiles in semiconductor devices with the Boltzmann-Poisson model (with
Y. Cheng and I. M. Gamba), *J. Comput.
Phys.,* 230, 3391-3412, 2011*.*
[pdf].

·
Recent
development in numerical techniques for transport-based medical imaging
methods, *Commun**. Comput.
Phys., *8, 1-50, 2010*.* [pdf].

·
Parametric
image reconstruction using the discrete cosine transform for optical tomography
(with X. Gu, J. Masciotti and A. H. Hilescher), *J.
Biomed. Opt., *14, 064003, 2009*.* [pdf].

·
Physics-based models
for measurement correlations. Application to an inverse Sturm-Liouville problem (with
G. Bal), *Inverse Problems, *25, 055006, 2009*.* [pdf].

·
Transport-based
imaging in random media (with G. Bal),
*SIAM Applied Math., *68, 1738-1762, 2008 *.*
[pdf].

·
Experimental
validation of a transport-based imaging method in highly scattering
environments (with G. Bal, L. Carin and D. Liu), *Inverse Problems, *23, 2527-2539,
2007*. * [pdf].

·
Transport- and
diffusion-based optical tomography in small domain: A comparative study (with G. Bal and A. H. Hilescher),
*Applied Optics, *46, 6669-6679, 2007*.* [pdf].

· Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer (with X. Gu and A. Hielscher), Appl. Optics, 46, 1624-1632, 2007. [pdf].

·
Frequency
domain optical tomography based on the equation of radiative transfer (with G.
Bal and A. H. Hielscher), *SIAM J. Sci. Comput., *28, 1463-1489, 2006*.* [pdf].

·
Reconstruction
of singular surfaces by shape sensitivity analysis and level set method (with G. Bal), Math. Models Methods Appl. Sci.
(M3AS)*, *16, 1347-1373, 2006*.* [pdf].

·
Optical
tomographic imaging as a PDE-constrained optimization problem (with G. Abdoulaev and A.
H. Hielscher), *Inverse Problems, *21,
1507-1530, 2005. [pdf].

·
Atmospheric
concentration profile reconstructions from radiation measurements (with G. Bal), *Inverse Problems, *21, 153-168,
2005. [pdf].

·
Algorithm for solving the equation of radiative transfer in the
frequency domain (G. S. Abdoulaev, G. Bal and A. H. Hilescher),
*Optics Lett., *29, 578-580, 2004*.* [pdf].

·
Generalized
diffusion model in optical tomography with clear layers (with G. Bal), *J. Opt. Soc. Am. A, *20,
2355-2364, 2003*.* [pdf].

If you are interested, a full list of publications can be found here.

My Erdös number is 4 according to MathSciNet of American Mathematical Society.

If you have a PhD in mathematics but forget
already who your thesis advisor was, you can probably figure it out here.

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