Tianran Chen

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All published works

Action	Title	Year	Authors
+ PDF Chat	Volume of convex polytopes equals mixed volume of simplices	2023	Tianran Chen
+ PDF Chat	Facets and facet subgraphs of symmetric edge polytopes	2022	Tianran Chen Robert Davis Evgeniia Korchevskaia
+ PDF Chat	Directed acyclic decomposition of Kuramoto equations	2019	Tianran Chen
+ PDF Chat	Unmixing the Mixed Volume Computation	2019	Tianran Chen
+ PDF Chat	On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations	2017	Tianran Chen Dhagash Mehta
+ PDF Chat	Response to “Comment on ‘Exploring the potential energy landscape of the Thomson problem via Newton homotopies”’ [J. Chem. Phys. 143, 247101 (2015)]	2015	Dhagash Mehta Tianran Chen John W. R. Morgan David J. Wales
+ PDF Chat	Exploring the potential energy landscape of the Thomson problem via Newton homotopies	2015	Dhagash Mehta Tianran Chen John W. R. Morgan David J. Wales
+ PDF Chat	Homotopy continuation method for solving systems of nonlinear and polynomial equations	2015	Tianran Chen Tien-Yien Li
+ PDF Chat	Communication: Newton homotopies for sampling stationary points of potential energy landscapes	2014	Dhagash Mehta Tianran Chen Jonathan D. Hauenstein David J. Wales
+ PDF Chat	Spherical projective path tracking for homotopy continuation methods	2012	Tianran Chen Tien-Yien Li

Common Coauthors

Coauthor	Papers Together
Dhagash Mehta	4
David J. Wales	3
John W. R. Morgan	2
Tien-Yien Li	2
Robert Davis	1
Jonathan D. Hauenstein	1
Evgeniia Korchevskaia	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	The number of roots of a system of equations	1979	D. N. Bernshtein	6
+ PDF Chat	A polyhedral method for solving sparse polynomial systems	1995	Birkett Huber Bernd Sturmfels	5
+	Newton polyhedra and the genus of complete intersections	1978	Askold Khovanskiĭ	4
+	DEMiCs: A Software Package for Computing the Mixed Volume Via Dynamic Enumeration of all Mixed Cells	2008	Tomohiko Mizutani Akiko Takeda	3
+ PDF Chat	Exact Volume Computation for Polytopes: A Practical Study	2000	Benno Büeler Andreas Enge Komei Fukuda	3
+	The Cheater’s Homotopy: An Efficient Procedure for Solving Systems of Polynomial Equations	1989	T. Y. Li Timothy Sauer James A. Yorke	3
+ PDF Chat	A Polyhedral Method for Solving Sparse Polynomial Systems	1995	Birkett Huber Bernd Sturmfels	3
+	Newton polytopes and the Bezout theorem	1977	A. G. Kushnirenko	3
+	Analysis of Newton’s Method at Irregular Singularities	1983	Andreas Griewank M. R. Osborne	3
+	Numerical Continuation Methods	1990	Eugene L. Allgower Kurt Georg	3
+	PHoM ? a Polyhedral Homotopy Continuation Method for Polynomial Systems	2004	Takayuki Gunji Sunyoung Kim Masakazu Kojima Akiko Takeda Katsuki Fujisawa Tomohiko Mizutani	3
+	Geometric critical point analysis of lossless power system models	1982	John Baillieul C.I. Byrnes	3
+ PDF Chat	Unmixing the Mixed Volume Computation	2019	Tianran Chen	3
+ PDF Chat	Algorithm 795	1999	Jan Verschelde	3
+ PDF Chat	Bernstein’s theorem in affine space	1997	Birkett Huber Bernd Sturmfels	3
+ PDF Chat	Counting Equilibria of the Kuramoto Model Using Birationally Invariant Intersection Index	2018	Tianran Chen Robert Davis Dhagash Mehta	3
+	The Numerical Solution of Systems of Polynomials Arising in Engineering and Science	2005	Andrew J. Sommese Charles W. Wampler	3
+ PDF Chat	Algebraic geometrization of the Kuramoto model: Equilibria and stability analysis	2015	Dhagash Mehta Noah S. Daleo Florian Dörfler Jonathan D. Hauenstein	3
+	An optimal condition for determining the exact number of roots of a polynomial system	1991	John Canny J. Maurice Rojas	3
+	Power Flow as an Algebraic System	2014	Jakub Mareček Timothy M. McCoy Martin Mevissen	2
+	Continuation and path following	1993	Eugene L. Allgower Kurt Georg	2
+	Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core	2011	Wenrui Hao Jonathan D. Hauenstein Bei Hu Yuan Liu Andrew J. Sommese Yong-Tao Zhang	2
+ PDF Chat	Toric intersection theory for affine root counting	1999	J. Maurice Rojas	2
+ PDF Chat	Communication: Newton homotopies for sampling stationary points of potential energy landscapes	2014	Dhagash Mehta Tianran Chen Jonathan D. Hauenstein David J. Wales	2
+ PDF Chat	Exploring the potential energy landscape of the Thomson problem via Newton homotopies	2015	Dhagash Mehta Tianran Chen John W. R. Morgan David J. Wales	2
+ PDF Chat	Phase Transitions Detached from Stationary Points of the Energy Landscape	2011	Michael Kästner Dhagash Mehta	2
+ PDF Chat	Saddle points and dynamics of Lennard-Jones clusters, solids, and supercooled liquids	2002	Jonathan P. K. Doye David J. Wales	2
+ PDF Chat	Saddles in the Energy Landscape Probed by Supercooled Liquids	2000	L. Angelani Roberto Di Leonardo G. Ruocco Antonio Scala Francesco Sciortino	2
+ PDF Chat	Energy landscape of the finite-size spherical three-spin glass model	2013	Dhagash Mehta Daniel A. Stariolo Michael Kästner	2
+	Numerical Solution of a Class of Deficient Polynomial Systems	1987	Tien-Yien Li Timothy Sauer James A. Yorke	2
+ PDF Chat	Energy-landscape analysis of the two-dimensional nearest-neighbor<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>φ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math>model	2012	Dhagash Mehta Jonathan D. Hauenstein Michael Kästner	2
+	Adaptive kinetic Monte Carlo for first-principles accelerated dynamics	2008	Lijun Xu Graeme Henkelman	2
+ PDF Chat	Phase transitions and configuration space topology	2008	Michael Kästner	2
+ PDF Chat	Dynamic Enumeration of All Mixed Cells	2007	Tomohiko Mizutani Akiko Takeda Masakazu Kojima	2
+ PDF Chat	On the limited memory BFGS method for large scale optimization	1989	Cheng‐Di Dong Jorge Nocedal	2
+ PDF Chat	Comment on “Quasisaddles as relevant points of the potential energy surface in the dynamics of supercooled liquids” [J. Chem. Phys. <b>116</b>, 10297 (2002)]	2003	Jonathan P. K. Doye David J. Wales	2
+ PDF Chat	Updating quasi-Newton matrices with limited storage	1980	Jorge Nocedal	2
+ PDF Chat	Exploring the potential energy landscape over a large parameter-space	2013	Yang‐Hui He Dhagash Mehta Matthew Niemerg Markus Rummel Alexandru Valeanu	2
+	Determining the solutions of the load flow of power systems: Theoretical results and computer implementation	1990	S.X. Guo F.M.A. Salam	2
+	A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots	1991	Göran Björck Ralf Fröberg	2
+	An index-resolved fixed-point homotopy and potential energy landscapes	2015	Tianran Chen Dhagash Mehta	2
+ PDF Chat	Stationary points and dynamics in high-dimensional systems	2003	David J. Wales Jonathan P. K. Doye	2
+ PDF Chat	Finding all the stationary points of a potential-energy landscape via numerical polynomial-homotopy-continuation method	2011	Dhagash Mehta	2
+	Computation of stationary points via a homotopy method	1998	Stefan Ackermann Wolfgang Kliesch	2
+ PDF Chat	MIXED VOLUME COMPUTATION VIA LINEAR PROGRAMMING	2000	Tangan Gao T. Y. Li	2
+ PDF Chat	Minimizing Higgs potentials via numerical polynomial homotopy continuation	2012	M. Maniatis Dhagash Mehta	2
+	The random product homotopy and deficient polynomial systems	1987	Taiyong Li Timothy Sauer James A. Yorke	2
+	SOLUTIONS TO SYSTEMS OF BINOMIAL EQUATIONS	2014	Tianran Chen Tien-Yien Li	2
+	Relations Between Several Path Following Algorithms and Local and Global Newton Methods	1980	C. B. Garcia F. J. Gould	2
+	The critical point analysis of electric power systems	1984	John Baillieul	2