Publications (22)
Clustering Complex Zeros of Triangular Systems of Polynomials
Rémi Imbach, Marc Pouget, Chee Yap
This paper gives the first algorithm for finding a set of natural -clusters of complex zeros of a triangular system of polynomials within a given polybox in , for…
Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves
Michael Burr, Sung Woo Choi, Ben Galehouse +1
Given a real valued function f(X,Y), a box region B_0 in R^2 and a positive epsilon, we want to compute an epsilon-isotopic polygonal approximation to the restriction of the curve…
End Cover for Initial Value Problem: Complete Validated Algorithms with Complexity Analysis
Bingwei Zhang, Chee Yap
We consider the first-order autonomous ordinary differential equation \[ \mathbf{x}' = \mathbf{f}(\mathbf{x}), \] where is locally Lips…
Complexity Analysis of Root Clustering for a Complex Polynomial
Ruben Becker, Michael Sagraloff, Vikram Sharma +2
Let be an arbitrary complex polynomial. We introduce the local root clustering problem, to compute a set of natural -clusters of roots of in some box reg…
A Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration
Ruben Becker, Michael Sagraloff, Vikram Sharma +1
We describe a subdivision algorithm for isolating the complex roots of a polynomial . Given an oracle that provides approximations of each of the coefficients of…
Global Identifiability of Differential Models
Hoon Hong, Alexey Ovchinnikov, Gleb Pogudin +1
Many real-world processes and phenomena are modeled using systems of ordinary differential equations with parameters. Given such a system, we say that a parameter is globally ident…
Emerging Challenges in Computational Topology
Marshall Bern, David Eppstein, Pankaj K. Agarwal +19
Here we present the results of the NSF-funded Workshop on Computational Topology, which met on June 11 and 12 in Miami Beach, Florida. This report identifies important problems inv…
Soft Subdivision Motion Planning for Complex Planar Robots
Bo Zhou, Yi-Jen Chiang, Chee Yap
The design and implementation of theoretically-sound robot motion planning algorithms is challenging. Within the framework of resolution-exact algorithms, it is possible to exploit…
Implementation of a Near-Optimal Complex Root Clustering Algorithm
Rémi Imbach, Victor Y. Pan, Chee Yap
We describe Ccluster, a software for computing natural -clusters of complex roots in a given box of the complex plane. This algorithm from Becker et al.~(2016) is near-optimal…
Proceedings of the 1st Workshop on Robotics Challenges and Vision (RCV2013)
Aitor Aladren, Sasa Bodiroza, Hamidreza Chitsaz +12
Proceedings of the 1st Workshop on Robotics Challenges and Vision (RCV2013)
SIAN: software for structural identifiability analysis of ODE models
Hoon Hong, Alexey Ovchinnikov, Gleb Pogudin +1
Biological processes are often modeled by ordinary differential equations with unknown parameters. The unknown parameters are usually estimated from experimental data. In some case…
Bivariate range functions with superior convergence order
Bingwei Zhang, Thomas Chen, Kai Hormann +1
Range functions are a fundamental tool for certified computations in geometric modeling, computer graphics, and robotics, but traditional range functions have only quadratic conver…
Distortion Bounds of Subdivision Models for SO(3)
Zhaoqi Zhang, Chee Yap
In the subdivision approach to robot path planning, we need to subdivide the configuration space of a robot into nice cells to perform various computations. For a rigid spatial rob…
Taylor Tube Method for Validated IVP
Bingwei Zhang, Chee Yap
We recently introduced a novel architecture for the design of validated IVP algorithms. This architecture forms the basis of our complete validated algorithm for IVP. A key subrout…
A Novel Approach to the Initial Value Problem with a complete validated algorithm
Bingwei Zhang, Chee Yap
We consider the first order autonomous differential equation (ODE) where is locally Lipschitz. For ${\bf x}_0\i…
Robust Parameter Estimation for Rational Ordinary Differential Equations
Oren Bassik, Yosef Berman, Soo Go +6
We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the paramete…
An Algorithmic Approach to Limit Cycles of Nonlinear Differential Systems: the Averaging Method Revisited
Bo Huang, Chee Yap
This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method.…
Theory and Explicit Design of a Path Planner for an SE(3) Robot
Zhaoqi Zhang, Yi-Jen Chiang, Chee Yap
We consider path planning for a rigid spatial robot with 6 degrees of freedom (6 DOFs), moving amidst polyhedral obstacles. A correct, complete and practical path planner for such…
Root-finding with Implicit Deflation
Remi Imbach, Victor Y. Pan, Chee Yap +2
Functional iterations such as Newton's are a popular tool for polynomial root-finding. We consider realistic situation where some (e.g., better-conditioned) roots have already been…
Effective Subdivision Algorithm for Isolating Zeros of Real Systems of Equations, with Complexity Analysis
Juan Xu, Chee Yap
We describe a new algorithm \texttt{Miranda} for isolating the simple zeros of a function within a box .…
Isotopic Arrangement of Simple Curves: an Exact Numerical Approach based on Subdivision
Jyh-Ming Lien, Vikram Sharma, Gert Vegter +1
This paper presents the first purely numerical (i.e., non-algebraic) subdivision algorithm for the isotopic approximation of a simple arrangement of curves. The arrangement is "sim…
Rods and Rings: Soft Subdivision Planner for R^3 x S^2
Ching-Hsiang Hsu, Yi-Jen Chiang, Chee Yap
We consider path planning for a rigid spatial robot moving amidst polyhedral obstacles. Our robot is either a rod or a ring. Being axially-symmetric, their configuration space is R…