Jonathan Hauenstein

Publications

• Algebraic geometrization of the Kuramoto model: Equilibria and stability analysis
• Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization
• Real solutions to systems of polynomial equations and parameter continuation
• A bootstrapping approach for computing multiple solutions of differential equations
• On the Equations Defining Some Hilbert Schemes
• Binomiality Testing and Computing Sparse Polynomials via Witness Sets
• Locating and Counting Equilibria of the Kuramoto Model with Rank-One Coupling
• On deflation and multiplicity structure
• Real monodromy action
• Estimating the Complete Solution Set of the Approximate Path Synthesis Problem for Four-Bar Linkages Using Random Monodromy Loops
• Finding Straight Line Generators Through the Approximate Synthesis of Symmetric Four-Bar Coupler Curves
• Computing saddle graphs via homotopy continuation for the approximate synthesis of mechanisms
• Algorithm 976
• Sampling Real Algebraic Varieties for Topological Data Analysis
• Trifocal Relative Pose From Lines at Points
• Finding straight line generators through the approximate synthesis of symmetric four-bar coupler curves
• Smooth points on semi-algebraic sets
• On some configurations of oppositely charged trapped vortices in the plane
• Designing Rotary Linkages for Polar Motions
• A General Method for Constructing Planar Cognate Mechanisms
• The Complete Solution of Alt-Burmester Synthesis Problems for Four-Bar Linkages
• On Computing the Nonlinearity Interval in Parametric Semidefinite Optimization
• Experiments on the Zeros of Harmonic Polynomials Using Certified Counting
• Global structure of curves from generalized unitarity cut of three-loop diagrams
• Certification and the potential energy landscape
• Communication: Newton homotopies for sampling stationary points of potential energy landscapes
• Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety
• Gauge-fixing on the lattice via orbifolding
• A Note on Global Newton Iteration Over Archimedean and Non-Archimedean Fields
• Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation
• Equations for Lower Bounds on Border Rank
• Isosingular Sets and Deflation
• A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws
• Cell decomposition of almost smooth real algebraic surfaces
• Communication: Certifying the potential energy landscape
• Homotopy techniques for tensor decomposition and perfect identifiability
• A numerical toolkit for multiprojective varieties
• The Loss Surface Of Deep Linear Networks Viewed Through The Algebraic Geometry Lens
• Unification and extension of intersection algorithms in numerical algebraic geometry
• Computing Geometric Feature Sizes for Algebraic Manifolds
• Tensor decomposition and homotopy continuation
• Adaptive strategies for solving parameterized systems using homotopy continuation
• Identifiability and numerical algebraic geometry
• Numerical algebraic geometry and semidefinite programming
• Certified Evaluations of Hölder Continuous Functions at Roots of Polynomials
• A numerical continuation approach using monodromy to solve the forward kinematics of cable-driven parallel robots with sagging cables
• Computing complete solution sets for approximate four-bar path synthesis
• Multi-graded Macaulay dual spaces
• On parametric semidefinite programming with unknown boundaries
• A Real-Time Algorithm for Computing the Tension Force in a Suspended Elastic Sagging Cable
• Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core
• A three-dimensional steady-state tumor system
• A NUMERICAL LOCAL DIMENSION TEST FOR POINTS ON THE SOLUTION SET OF A SYSTEM OF POLYNOMIAL EQUATIONS
• Numerical Computation of the dimensions of the cohomology of twists of Ideal Sheaves
• One-dimensional slow invariant manifolds for spatially homogenous reactive systems
• Adaptive multiprecision path tracking
• Numerically Solving Polynomial Systems with Bertini
• Numerically Computing Real Points on Algebraic Sets
• Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems
• Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core
• Numerical elimination and moduli space of vacua
• Membership tests for images of algebraic sets by linear projections
• Algebraic boundaries of Hilbert's SOS cones
• Energy-landscape analysis of the two-dimensional nearest-neighbor phi(4) model
• Numerical algebraic geometry: a new perspective on gauge and string theories
• Numerically intersecting algebraic varieties via witness sets
• Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry
• Classification and complete solution of the kinetostatics of a compliant Stewart-Gough platform
• Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials
• Stepsize control for path tracking
• Software for numerical algebraic geometry: A paradigm and progress towards its implementation
• A Parallel Endgame
• Efficient path tracking methods
• Mechanism mobility and a local dimension test
• REGENERATION HOMOTOPIES FOR SOLVING SYSTEMS OF POLYNOMIALS
• Regenerative cascade homotopies for solving polynomial systems
• A counter example to an ideal membership test
• Witness sets of projections
• A Numerical Method for Solving Elliptic Equations on Real Closed Algebraic Curves and Surfaces
• Machine learning the real discriminant locus
• A Preliminary Investigation of the Relationship between Sleep and Nap Behavior of NCAA Division 1 Football Student-Athletes
• Reliability of Markerless Motion Capture Systems for Assessing Movement Screenings
• Multi-objective optimization with homotopy-based strategies for enhanced multimodal automatic target recognition models
• Efficient hyperparameter optimization for ATR using homotopy parametrization
• Branch points of homotopies: Distribution and probability of failure
• Novel Use of Generalizability Theory to Optimize Countermovement Jump Data Collection