15 citations · 43 across the 20 of their papers we have counts for
21 papers
Hidden symmetries of ReLU networks
J. Elisenda Grigsby, Kathryn Lindsey, David Rolnick
The parameter space for any fixed architecture of feedforward ReLU neural networks serves as a proxy during training for the associated class of functions - but how faithful is thi…
On the deck groups of iterates of bicritical rational maps
Sarah Koch, Kathryn Lindsey, Thomas Sharland
Given a rational map on the Riemann sphere, we define to be the group of Möbius transformations satisfying $f \…
Bicritical rational maps with a common iterate
Sarah Koch, Kathryn Lindsey, Thomas Sharland
Let be a degree bicritical rational map with critical point set and critical value set . Using the group of deck transfo…
Functional dimension of feedforward ReLU neural networks
J. Elisenda Grigsby, Kathryn Lindsey, Robert Meyerhoff +1
It is well-known that the parameterized family of functions representable by fully-connected feedforward neural networks with ReLU activation function is precisely the class of pie…
Local and global topological complexity measures OF ReLU neural network functions
J. Elisenda Grigsby, Kathryn Lindsey, Marissa Masden
We apply a generalized piecewise-linear (PL) version of Morse theory due to Grunert-Kuhnel-Rote to define and study new local and global notions of topological complexity for fully…
Existence of maximum likelihood estimates in exponential random graph models
Henry Bayly, Aditya Khanna, Kathryn Lindsey
We present a streamlined proof of the foundational result in the theory of exponential random graph models (ERGMs) that the maximum likelihood estimate exists if and only if the ta…
Master Teapots and Entropy Algorithms for the Mandelbrot Set
Kathryn Lindsey, Giulio Tiozzo, Chenxi Wu
We construct an analogue of W. Thurston's "Master teapot" for each principal vein in the Mandelbrot set, and generalize geometric properties known for the corresponding object for…
On transversality of bent hyperplane arrangements and the topological expressiveness of ReLU neural networks
J. Elisenda Grigsby, Kathryn Lindsey
Let F:R^n -> R be a feedforward ReLU neural network. It is well-known that for any choice of parameters, F is continuous and piecewise (affine) linear. We lay some foundations for…
A characterization of Thurston's Master Teapot
Kathryn Lindsey, Chenxi Wu
We prove an explicit characterization of the points in Thurston's Master Teapot. This description can be implemented algorithmically to test whether a point in $\mathbb{C} \times \…
Degree-d-invariant laminations
William P. Thurston, Hyungryul Baik, Yan Gao +4
Degree--invariant laminations of the disk model the dynamical action of a degree- polynomial; such a lamination defines an equivalence relation on that corresponds to d…
The Shape of Thurston's Master Teapot
Harrison Bray, Diana Davis, Kathryn Lindsey +1
We establish basic geometric and topological properties of Thurston's Master Teapot and the Thurston set for superattracting unimodal self-maps of intervals. In particular, the Mas…
A Game of Life on Penrose tilings
Duane A. Bailey, Kathryn A. Lindsey
We define rules for cellular automata played on quasiperiodic tilings of the plane arising from the multigrid method in such a way that these cellular automata are isomorphic to Co…
Fekete polynomials and shapes of Julia sets
Kathryn A. Lindsey, Malik Younsi
We prove that a nonempty, proper subset of the complex plane can be approximated in a strong sense by polynomial filled Julia sets if and only if is bounded and $\hat{\math…
Shapes of polynomial Julia sets, revisited
Kathryn A. Lindsey
Any finite union of disjoint, mutually exterior Jordan curves in the complex plane can be approximated arbitrarily well in the Hausdorff topology by polynomial Julia sets. Furtherm…
Convex shapes and harmonic caps
Laura DeMarco, Kathryn Lindsey
Any planar shape can be embedded isometrically as part of the boundary surface of a convex subset of such that supports the po…
Horocycle flow orbits and lattice surface characterizations
Jon Chaika, Kathryn Lindsey
The orbit closure of any translation surface under the horocycle flow in almost any direction equals its orbit closure. This result gives rise to new characteriz…
Flat surface models of ergodic systems
Kathryn Lindsey, Rodrigo Treviño
We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possi…
Counting invariant components of hyperelliptic translation surfaces
Kathryn Lindsey
The flow in a fixed direction on a translation surface S determines a decomposition of S into closed invariant sets, each of which is either periodic or minimal. We study this deco…
Shapes of Polynomial Julia Sets
Kathryn A. Lindsey
Any Jordan curve in the complex plane can be approximated arbitrarily well in the Hausdorff topology by Julia sets of polynomials. Finite collections of disjoint Jordan domains can…
On ergodic transformations that are both weakly mixing and uniformly rigid
Jennifer James, Thomas Koberda, Kathryn Lindsey +2
We examine some of the properties of uniformly rigid transformations, and analyze the compatibility of uniform rigidity and (measurable) weak mixing along with some of their asympt…
Measurable Sensitivity
Jennifer James, Thomas Koberda, Kathryn Lindsey +2
We introduce the notion of measurable sensitivity, a measure-theoretic version of the condition of sensitive dependence on initial conditions. It is a consequence of light mixing,…