11 citations · 22 across the 12 of their papers we have counts for
17 papers
Generic Rigidity and the Grassmannian
Alexander Heaton
We characterize the generic rigidity of bar-joint frameworks in all dimensions. The conditions are constructed explicitly from the graph alone, independently of any placement, and…
Stable Graded Multiplicities for Harmonics on a Cyclic Quiver
Andrew Frohmader, Alexander Heaton
We consider Vinberg -groups associated to a cyclic quiver on nodes. Let be the product of the general linear groups associated to each node. Then acts naturally on $…
Computing Euclidean distance and maximum likelihood retraction maps for constrained optimization
Alexander Heaton, Matthias Himmelmann
Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the c…
Facet volumes of polytopes
Pavle V. M. Blagojević, Paul Breiding, Alexander Heaton
In this paper, motivated by the work of Edelman and Strang, we show that for fixed integers and the configuration space of all facet volume vectors of all …
Nonlinear Algebra and Applications
Paul Breiding, Türkü Özlüm Çelik, Timothy Duff +5
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, a…
Hilbert series of typical representations for Lie superalgebras
Alexander Heaton, Songpon Sriwongsa
Let g be a basic classical Lie superalgebra over C. In the case of a typical weight whose every nonnegative integer multiple is also typical, we compute a closed form for the Hilbe…
Catastrophe in Elastic Tensegrity Frameworks
Alexander Heaton, Sascha Timme
We discuss elastic tensegrity frameworks made from rigid bars and elastic cables, depending on many parameters. For any fixed parameter values, the stable equilibrium position of t…
Minimality of tensors of fixed multilinear rank
Alexander Heaton, Khazhgali Kozhasov, Lorenzo Venturello
We discover a geometric property of the space of tensors of fixed multilinear (Tucker) rank. Namely, it is shown that real tensors of fixed multilinear rank form a minimal submanif…
Logarithmic Voronoi cells
Yulia Alexandr, Alexander Heaton
We study Voronoi cells in the statistical setting by considering preimages of the maximum likelihood estimator that tessellate an open probability simplex. In general, logarithmic…
Dual matroid polytopes and internal activity of independence complexes
Alexander Heaton, Jose Alejandro Samper
Shelling orders are a ubiquitous tool used to understand invariants of cell complexes. Significant effort has been made to develop techniques to decide when a given complex is shel…
Symmetry Adapted Gram Spectrahedra
Alexander Heaton, Serkan Hoşten, Isabelle Shankar
This paper explores the geometric structure of the spectrahedral cone, called the symmetry adapted PSD cone, and the symmetry adapted Gram spectrahedron of a symmetric polynomial.…
Exact Solutions in Log-Concave Maximum Likelihood Estimation
Alexandros Grosdos, Alexander Heaton, Kaie Kubjas +3
We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential…
Epsilon local rigidity and numerical algebraic geometry
Andrew Frohmader, Alexander Heaton
A well-known combinatorial algorithm can decide generic rigidity in the plane by determining if the graph is of Pollaczek-Geiringer-Laman type. Methods from matroid theory have bee…
An SOS counterexample to an inequality of symmetric functions
Alexander Heaton, Isabelle Shankar
It is known that differences of symmetric functions corresponding to various bases are nonnegative on the nonnegative orthant exactly when the partitions defining them are comparab…
Nonlinear algebra with tensegrity structures
Alexander Heaton
In this paper, we discuss tensegrity from the perspective of nonlinear algebra in a manner accessible to undergraduates. We compute explicit examples and include the SAGE and Julia…
Branching from the General Linear Group to the Symmetric Group and the Principal Embedding
Alexander Heaton, Songpon Sriwongsa, Jeb F. Willenbring
Let S be a principally embedded sl_2 subalgebra in sl_n for n > 2. A special case of results of the third author and Gregg Zuckerman implies that there exists a positive integer b(…
Graded multiplicity in harmonic polynomials from the Vinberg setting
Alexander Heaton
We consider Vinberg -groups associated to a cyclic quiver on nodes. Let be the product of general linear groups associated to the nodes, acting naturally on $V = \oplus…