### Employment

• 2017 – present Assistant Professor, Auburn University Montgomery.
• 2016 – 2017 Lecturer, Auburn University Montgomery.
• 2012 – 2016 Research Instructor, Michigan State University.
• 2006 – 2012 Research and Teaching Assistant, Michigan State University.
• 2003 – 2005 Research Assistant, Western Connecticut State University.

### Education

• 2012 Ph.D. Applied Mathematics, Michigan State University, (MI USA).
• 2005 B.A. Computer Science, Western Connecticut State University, (CT USA).

### Honors & Awards

• 2016 AMS-Simons Travel Grant
• 2014 A paper selected for Journal of Chemical Physics Editors’ Choice for 2014
• 2010 Dr. Paul & Wilma Dressel endowed scholarship award (Michigan State University)
• 2005 Student leadership recognition award for outstanding leadership (Western Connecticut State University)
• 2005 Sigma Xi research award in Physics, Astronomy & Meteorology (Western Connecticut State University)
• 2004 Wohlever award in Computer Science (Western Connecticut State University)

### Research Interests

• Numerical analysis
• High performance computing
• Scientific computing
• Numerical algebraic geometry
• Application of numerical methods in physics, chemistry, and engineering

### Publications

• Christian Knoll, Dhagash Mehta, Tianran Chen, and Franz Pernkopf
“Fixed points of belief propagation – An analysis via polynomial homotopy continuation”.
IEEE Transactions on Pattern Analysis and Machine Intelligence
[ link ] [ arXiv ] [ ] [ ]
Abstract: Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the model. To understand this dependence it is interesting to find all fixed points.
        
@article{Knoll2017,
author = {Knoll, Christian and Mehta, Dhagash and Chen, Tianran and Pernkopf, Franz},
doi = {10.1109/TPAMI.2017.2749575},
issn = {0162-8828},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
pages = {1--1},
title = ,
url = {http://ieeexplore.ieee.org/document/8027142/},
year = {2017}
}


• Tianran Chen and Dhagash Mehta.
“On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations”.
IEEE Transactions on Power Systems
[ pdf ] [ link ] [ ] [ ]

Abstract: Active research activity in power systems areas has focused on developing computational methods to solve load flow equations where a key question is the maximum number of solutions. Though several upper bounds exist, recent studies have hinted that much sharper upper bounds that depend the topology of underlying power networks may exist. This paper provides a significant refinement of these observations. We also develop a geometric construction called adjacency polytope which accurately captures the topology of a power network and is immensely useful in the computation of the solution bound. Finally we highlight the significant implications of the development of such solution bounds in numerically solving load flow equations.development of such solution bounds in numerically solving load flow equations.
        
@article{chen_network_2017,
author = {Chen, Tianran and Mehta, Dhagash},
doi = {10.1109/TPWRS.2017.2724030},
issn = {0885-8950},
journal = {IEEE Transactions on Power Systems},
pages = {1--1},
title = ,
url = {http://ieeexplore.ieee.org/document/7971956/},
year = {2017}
}


• Tianran Chen, Tsung-Lin Lee, and Tien-Yien Li.
“Mixed cell computation in Hom4PS-3”.
Journal of Symbolic Computation (2017), pp. 516-534

• Tianran Chen and Dhagash Mehta.
“Parallel degree computation for binomial systems”.
Journal of Symbolic Computation (2017), pp. 535-558

• Dhagash Mehta, Tianran Chen, John Morgan, and David Wales.
Response to “Comment on ‘Exploring the potential energy landscape of the Thomson problem via Newton homotopies’”.
The Journal of Chemical Physics 143, 247102 (2015)
[ link ] [ bibtex ].

• Tianran Chen and Tien-Yien Li.
“Homotopy continuation method for solving systems of nonlinear and polynomial equations”.
Communications in Information and Systems 15(2):119–307 (2015).
[ link ] [ bibtex ].

• Dhagash Mehta, Tianran Chen, David Wales, and John Morgan.
“Exploring the potential energy landscape of the Thomson problem via Newton homotopies”.
The Journal of Chemical Physics 142 194113 (2015)
[ link ] [ bibtex ].

• Tianran Chen, Tien-Yien Li, and Xiaoshen Wang.
“Theoretical aspects of mixed volume computation via mixed subdivision”.
Communications in Information and Systems (2014)
[ pdf ] [ link ] [ bibtex ].

• Dhagash Mehta, Tianran Chen, Jonathan Hauenstein, and David Wales.
“Newton homotopies for sampling stationary points of potential energy landscapes”.
The Journal of Chemical Physics 141 (12), 121104 (2014)
(Selected for a Journal of Chemical Physics Editors’ Choice for 2014)
[ arXiv ] [ link ] [ bibtex ].

• Tianran Chen and Tien-Yien Li.
“Solutions to systems of binomial equations”.
Annales Mathematicae Silesianae 28:7–34 (2014).
[ bibtex ].

• Tianran Chen, Tsung-Lin Lee, and Tien-Yien Li.
“Hom4PS-3: A Parallel Numerical Solver for Systems of Polynomial Equations Based on Polyhedral Homotopy Continuation Methods” (Extended abstract).
Mathematical Software – ICMS 2014 – 4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings 8592:183–190
[ link ] [ bibtex ].

• Tianran Chen, Tsung-Lin Lee, and Tien-Yien Li.
“Mixed volume computation in parallel”.
Taiwanese Journal of Mathematics 18(1):93–114 (2014).
[ link ] [ bibtex ].

• Tianran Chen and Tien-Yien Li.
“Spherical projective path tracking for homotopy continuation methods”.
Communications in Information and Systems 12(3):195-220 (2012)
[ link ] [ bibtex ].

### Teaching Experience

2016 to 2017 Multivariable Calculus, Modern Algebra II, Mathematical modeling and simulation
2016 to 2017 Pre-calculus, Calculus I,II
2012 to 2016 Calculus sequence, Linear Algebra, Transition to Advanced Mathematics, Abstract algebra.
2006 to 2012 Teaching Assistant for Calculus sequence

### Professional Services

• 2017 Organizer for the Special Session on Algorithms and Implementation in Numerical Algebraic Geometry at 2017 SIAM Conference on Applied Algebraic Geometry, Atlanta USA
• 2015 Co-organizer for the Special Session on Homotopy Continuation Methods and Their Applications to Science and Engineering at the American Mathematical Society 2015 Central Spring Sectional Meeting, East Lansing USA
• Reviewer for ACM Transactions on Mathematical Software
• Reviewer for International Symposium on Symbolic and Algebraic Computation
• Reviewer for LMS Journal of Computation and Mathematics