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), *J. Comput. Phys.,
*2018. [pdf].

· Image
reconstruction in quantitative PAT with the simplified P_{2}
model (with C.
Frederick and S. Vallelian), *Submitted,
*2018. [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), *J.
Biomed. Opt.*, 23, 016002, 2018.
[pdf].

·
A global stability estimate for the
photo-acoustic inverse problem in layered media, (with F. Triki),
*European J. Appl. Math., *In
Press, 2018. [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.*, 78, 479-503, 2018.
[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), *AIHP-D*,
In Press, 2018. [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.

This webpage has been visited times since 2008. |