Related papers: An Extended Topological Model For High-Contrast Op…
We complete the theoretical framework required for the construction of a Morse homology theory for certain types of forced mean curvature flows. The main result of this paper describes the asymptotic behaviour of these flows as the forcing…
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…
Previous work of the authors with Bus Jaco determined a lower bound on the complexity of cusped hyperbolic 3-manifolds and showed that it is attained by the monodromy ideal triangulations of once-punctured torus bundles. This paper exhibits…
We consider fixed boundary flow with canonical interpretability as principal components extended on non-linear Riemannian manifolds. We aim to find a flow with fixed starting and ending points for noisy multivariate data sets lying on an…
In the present paper the exhaustive topological classification of nonsingular Morse-Smale flows of $n$-manifolds with two limit cycles is presented. Hyperbolicity of periodic orbits implies that among them one is attracting and another is…
Estimating per-pixel motion between video frames, known as optical flow, is a long-standing problem in video understanding and analysis. Most contemporary optical flow techniques largely focus on addressing the cross-image matching with…
This paper is concerned with the optimal upper bound on mean quantities (torque, dissipation and the Nusselt number) obtained in the framework of the background method for the Taylor--Couette flow with a stationary outer cylinder. Along the…
This paper investigates which smooth manifolds arise as quotients (orbit spaces) of flows of vector fields. Such quotient maps were already known to be surjective on fundamental groups, but this paper shows that every epimorphism of…
In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter space involves both longitudinal momentum and boundary…
This application paper presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence…
This paper presents a novel method for detecting scene changes from a pair of images with a difference of camera viewpoints using a dense optical flow based change detection network. In the case that camera poses of input images are fixed…
Motivated by the moduli theory of taut contact circles on spherical 3-manifolds, we relate taut contact circles to transversely holomorphic flows. We give an elementary survey of such 1-dimensional foliations from a topological viewpoint.…
We report high-resolution measurements of three-dimensional (3D) turbulence in a rapidly rotating fluid. By decomposing the velocity field into a vertically averaged component and a three-dimensional residual, we show that each dominates…
This is an expository note intended to illustrate current research in topological study of partially hyperbolic diffeomorphisms in dimension 3 with a beautiful result due to Margulis and Plante-Thurston on topological obstructions for a…
In this paper, we study discrepancy questions for spanning subgraphs of $k$-uniform hypergraphs. Our main result is that, for any integers $k \ge 3$ and $r \ge 2$, any $r$-colouring of the edges of a $k$-uniform $n$-vertex hypergraph $G$…
We propose MFT -- Multi-Flow dense Tracker -- a novel method for dense, pixel-level, long-term tracking. The approach exploits optical flows estimated not only between consecutive frames, but also for pairs of frames at logarithmically…
State-of-the-art neural network models for optical flow estimation require a dense correlation volume at high resolutions for representing per-pixel displacement. Although the dense correlation volume is informative for accurate estimation,…
Given a $3$-manifold $M$ with multiple incompressible torus boundary components, we develop a general definition of order-detection of tuples of slopes on the boundary components of $M$. In parallel, we arrive at a general definition of…
This paper presents, for the special case of once-punctured torus bundles, a natural method to study the character varieties of hyperbolic 3-manifolds that are bundles over the circle. The main strategy is to restrict characters to the…
In this paper, we study the positive cross curvature flow on locally homogeneous 3-manifolds. We describe the long time behavior of these flows. We combine this with earlier results concerning the asymptotic behavior of the negative cross…