(with Robert Davis and Dhagash Mehta)
"Counting equilibria of the Kuramoto model using birationally invariant intersection index
"
SIAM Journal on Applied Algebra and Geometry
[ link ]
[ pdf ]
[ arXiv ]
[
abstract
]
[
bibtex
]
@article{chen_counting_2017,
archivePrefix = {arXiv},
arxivId = {1708.09246},
author = {Chen, Tianran and Davis, Robert and Mehta, Dhagash},
eprint = {1708.09246},
month = {aug},
title = {{Counting equilibria of the Kuramoto model using birationally invariant intersection index}},
url = {http://arxiv.org/abs/1708.09246},
year = {2017}
}
"libtropicon: A Scalable Library for Computing Intersection Points of Generic Tropical Hyper-surfaces
"
Mathematical Software -- ICMS 2018
[ link ]
[
abstract
]
[
bibtex
]
@InProceedings{10.1007/978-3-319-96418-8_13,
author="Chen, Tianran",
editor="Davenport, James H. and Kauers, Manuel and Labahn, George and Urban, Josef",
title="libtropicon: A Scalable Library for Computing Intersection Points of Generic Tropical Hyper-surfaces",
booktitle="Mathematical Software -- ICMS 2018",
year="2018",
publisher="Springer International Publishing",
address="Cham",
pages="105--112",
isbn="978-3-319-96418-8"
}
(with Robert Davis)
"A Product Formula for the Normalized Volume of Free Sums of Lattice Polytopes
"
Advances in Algebra: Research from the Southern Regional Algebra Conference 2017
[ link ]
[ arXiv ]
[
abstract
]
[
bibtex
]
@article{chen_product_2017,
author = {Chen, Tianran and Davis, Robert},
month = {nov},
title = {A Product Formula for the Normalized Volume of Free Sums of Lattice Polytopes},
journal = {Advances in Algebra: Research from the Southern Regional Algebra Conference 2017},
pages = {(To appear)},
year = {2017}
}
(with Christian Knoll, Dhagash Mehta, 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
]
[
bibtex
]
@article{knoll_fixed_2017,
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 = {{Fixed Points of Belief Propagation - An Analysis via Polynomial Homotopy Continuation}},
url = {http://ieeexplore.ieee.org/document/8027142/},
year = {2017}
}
(with Dhagash Mehta)
"On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations"
IEEE Transactions on Power Systems (2018)
[ link ]
[ pdf ]
[
abstract
]
[
bibtex
]
@article{chen_network_2017,
author = {Chen, Tianran and Mehta, Dhagash},
doi = {10.1109/TPWRS.2017.2724030},
archivePrefix = {arXiv},
arxivId = {1512.04987},
eprint = {1512.04987},
issn = {08858950},
journal = {IEEE Transactions on Power Systems},
keywords = {Power systems,load flow,power system analysis computing,power system control},
title = {On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations},
url = {http://ieeexplore.ieee.org/document/7971956/},
number = {2},
pages = {1451--1460},
volume = {33},
year = {2018}
}
(with Tsung-Lin Lee and Tien-Yien Li)
"Mixed cell computation in Hom4PS-3"
Journal of Symbolic Computation (2017), pp. 516-534
[ link ]
[
abstract
]
[
bibtex
]
@article{chen_mixed_2017,
author = {Chen, Tianran and Lee, Tsung-Lin and Li, Tien-Yien},
doi = {10.1016/j.jsc.2016.07.017},
issn = {0747-7171},
journal = {Journal of Symbolic Computation},
month = {mar},
pages = {516--534},
series = {SI: Numerical Algebraic Geometry},
title = {{Mixed cell computation in Hom4PS-3}},
url = {http://www.sciencedirect.com/science/article/pii/S0747717116300542},
volume = {79, Part 3},
year = {2017}
}
(with Dhagash Mehta)
"Parallel degree computation for binomial systems"
Journal of Symbolic Computation (2017)
[ link ]
[
abstract
]
[
bibtex
]
@article{chen_parallel_2017,
author = {Chen, Tianran and Mehta, Dhagash},
doi = {10.1016/j.jsc.2016.07.018},
issn = {0747-7171},
journal = {Journal of Symbolic Computation},
keywords = {Algebraic Geometry,BKK root-count,Binomial systems,Folder - Unmixing,GPU computing,Supersymmetric gauge theories,homotopy continuation},
month = {mar},
pages = {535--558},
series = {SI: Numerical Algebraic Geometry},
title = {{Parallel degree computation for binomial systems}},
url = {http://www.sciencedirect.com/science/article/pii/S0747717116300554},
volume = {79, Part 3},
year = {2017}
}
(with Dhagash Mehta, 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
[ link ]
[
abstract
]
[
bibtex
]
@article{mehta_response_2015,
author = {Mehta, Dhagash and Chen, Tianran and Morgan, John W. R. and Wales, David J.},
doi = {10.1063/1.4939011},
issn = {0021-9606, 1089-7690},
journal = {The Journal of Chemical Physics},
keywords = {Bifurcations,Difference equations,Flow instabilities,Flow simulations,Folder - LogEval,Folder - Unmixing,Singularity theory},
month = {dec},
number = {24},
pages = {247102},
title = {{Response to “Comment on ‘Exploring the potential energy landscape of the Thomson problem via Newton homotopies”' [J. Chem. Phys. 143, 247101 (2015)]}},
url = {http://scitation.aip.org/content/aip/journal/jcp/143/24/10.1063/1.4939011 http://scitation.aip.org/deliver/fulltext/aip/journal/jcp/143/24/1.4939011.pdf;jsessionid=23ev3700uj07.x-aip-live-03?itemId=/content/aip/journal/jcp/143/24/10.1063/1.4939011{\&}mimeTyp},
volume = {143},
year = {2015}
}
(with 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 ]
[
abstract
]
[
bibtex
]
@article{chen_homotopy_2015,
author = {Chen, Tianran and Li, Tien-Yien},
doi = {10.4310/CIS.2015.v15.n2.a1},
issn = {15267555, 21634548},
journal = {Commun. Inf. Syst.},
number = {2},
pages = {119--307},
title = {Homotopy continuation method for solving systems of nonlinear and polynomial equations},
volume = {15},
year = {2015}
}
(with Dhagash Mehta, 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 ]
[
abstract
]
[
bibtex
]
@article{mehta_exploring_2015,
author = {Mehta, Dhagash and Chen, Tianran and Morgan, John W. R. and Wales, David J.},
doi = {10.1063/1.4921163},
issn = {0021-9606, 1089-7690},
journal = {The Journal of Chemical Physics},
keywords = {Eigenvalues,Folder - Finished - NewtonHomotopyReply,Folder - Finished - Solving survey,Folder - LogEval,Folder - Power flow,Folder - Unmixing,Newton Raphson method,Nonlinear dynamics,Numerical solutions,Potential energy surfaces},
month = {may},
number = {19},
pages = {194113},
title = {{Exploring the potential energy landscape of the Thomson problem via Newton homotopies}},
url = {http://scitation.aip.org/content/aip/journal/jcp/142/19/10.1063/1.4921163},
volume = {142},
year = {2015}
}
(with Tien-Yien Li and Xiaoshen Wang)
"Theoretical aspects of mixed volume computation via mixed subdivision"
Communications in Information and Systems (2014)
[ link ]
[ pdf ]
[
abstract
]
[
bibtex
]
@article{chen_theoretical_2014,
author = {Chen, Tianran and Li, Tien-Yien and Wang, Xiaoshen},
doi = {10.4310/CIS.2014.v14.n4.a1},
issn = {15267555, 21634548},
journal = {Communications in Information and Systems},
number = {4},
pages = {213--242},
title = {Theoretical aspects of mixed volume computation via mixed subdivision},
url = {http://www.intlpress.com/site/pub/pages/journals/items/cis/content/vols/0014/0004/a001/},
volume = {14},
year = {2014}
}
(with Dhagash Mehta, Jonathan Hauenstein, and David Wales)
"Newton homotopies for sampling stationary points of potential energy landscapes"
The Journal of Chemical Physics 141 (12), 121104 (2014)
[ link ]
[ arXiv ]
[
abstract
]
[
bibtex
]
@article{mehta_newton_2014,
author = {Mehta, Dhagash and Chen, Tianran and Hauenstein, Jonathan D and Wales, David J},
doi = {10.1063/1.4896657},
issn = {0021-9606, 1089-7690},
journal = {The Journal of Chemical Physics},
keywords = {Atomic and molecular clusters,Biomolecular structure,Nonlinear differential equations,Numerical modeling,Numerical solutions,real homotopy},
month = {sep},
number = {12},
pages = {121104},
shorttitle = {Communication},
title = {Newton homotopies for sampling stationary points of potential energy landscapes},
url = {http://scitation.aip.org/content/aip/journal/jcp/141/12/10.1063/1.4896657},
volume = {141},
year = {2014}
}
(with Tien-Yien Li)
"Solutions to systems of binomial equations"
Annales Mathematicae Silesianae 28:7–34 (2014)
[ link ]
[
abstract
]
[
bibtex
]
@article{chen_solutions_2014,
author = {Chen, Tianran and Li, Tien-Yien},
journal = {Annales Mathematicae Silesianae},
pages = {7--34},
title = {{Solutions to systems of binomial equations}},
volume = {28},
year = {2014}
}
(with 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 ]
[
abstract
]
[
bibtex
]
@incollection{chen_hom4ps-3,
author = {Chen, Tianran and Lee, Tsung-Lin and Li, Tien-Yien},
booktitle = {Mathematical Software – ICMS 2014},
editor = {Hong, Hoon and Yap, Chee},
isbn = {978-3-662-44198-5 978-3-662-44199-2},
keywords = {Algorithm Analysis and Problem Complexity,Discrete Mathematics in Computer Science,Math Applications in Computer Science,Numeric Computing,Software Engineering/Programming and Operating Sy,Theory of Computation,binomial system,homotopy continuation,polyhedral homotopy,polynomial systems},
month = {jan},
number = {8592},
pages = {183--190},
publisher = {Springer Berlin Heidelberg},
series = {Lecture Notes in Computer Science},
shorttitle = {Hom4PS-3},
title = {{Hom4PS-3: A Parallel Numerical Solver for Systems of Polynomial Equations Based on Polyhedral Homotopy Continuation Methods}},
url = {http://link.springer.com/chapter/10.1007/978-3-662-44199-2{\_}30},
year = {2014}
}
(with Tsung-Lin Lee and Tien-Yien Li)
"Mixed volume computation in parallel"
Taiwanese Journal of Mathematics 18(1):93–114 (2014)
[ link ]
[
abstract
]
[
bibtex
]
@article{chen_mixed_2014,
author = {Chen, Tianran and Lee, Tsung-Lin and Li, Tien-Yien},
journal = {Taiwanese Journal of Mathematics},
keywords = {bkk,mixed cells,mixed volume},
number = {1},
pages = {93--114},
title = {Mixed volume computation in parallel},
volume = {18},
year = {2014}
}
(with Tien-Yien Li)
"Spherical projective path tracking for homotopy continuation methods"
Communications in Information and Systems 12(3):195-220 (2012)
[ link ]
[
abstract
]
[
bibtex
]
@article{chen_spherical_2012,
author = {Chen, Tianran and Li, Tien-Yien},
journal = {Communication in Information and Systems},
number = {3},
pages = {195--220},
title = {Spherical projective path tracking for homotopy continuation methods},
volume = {12},
year = {2012}
}
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 |