Related papers: An Extended Topological Model For High-Contrast Op…
Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…
For a compact, orientable, irreducible 3-manifold with toroidal boundary that is not the product of a torus and an interval or a cable space, each boundary torus has a finite set of slopes such that, if avoided, the Thurston norm of a Dehn…
For $n$-vertex $m$-edge graphs with integer polynomially-bounded costs and capacities, we provide a randomized parallel algorithm for the minimum cost flow problem with $\tilde O(m+n^ {1.5})$ work and $\tilde O(\sqrt{n})$ depth. On…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
An overset grid method was used to investigate the interaction between a particle-laden flow and a circular cylinder. The overset grid method was implemented in the Pencil Code , a high-order finite-difference code for compressible flow…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
We prove a conjecture of Hutchings and Lee relating the Seiberg-Witten invariants of a closed 3-manifold X with b_1 > 0 to an invariant that `counts' gradient flow lines--including closed orbits--of a circle-valued Morse function on the…
Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications. The limitation of existing solutions…
First the title could be also understood as ``3-manifolds related by non-zero degree maps" or "Degrees of maps between 3-manifolds" for some aspects in this survey talk. The topology of surfaces was completely understood at the end of 19th…
Using deep learning, this paper addresses the problem of joint object boundary detection and boundary motion estimation in videos, which we named boundary flow estimation. Boundary flow is an important mid-level visual cue as boundaries…
Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as…
Estimating continuous optical flow is a fundamental yet challenging problem in dynamic visual perception. Event-based cameras, with microsecond latency and high dynamic range, capture brightness changes asynchronously, offering a unique…
We develop a new approach for studying flux anomalies in quadruply-imaged fold lens systems. We show that in the absence of substructure, microlensing, or differential absorption, the expected flux ratios of a fold pair can be tightly…
Turbulence modeling has the potential to revolutionize high-speed vehicle design by serving as a co-equal partner to costly and challenging ground and flight testing. However, the fundamental assumptions that make turbulence modeling such…
Sampling viable 3D structures (e.g., molecules and point clouds) with SE(3)-invariance using diffusion-based models proved promising in a variety of real-world applications, wherein SE(3)-invariant properties can be naturally characterized…
A new filtration of the spaces of tri-/univalent graphs B_m^u that occur in the theory of finite-type invariants of knots and 3-manifolds is introduced. Combining the results of the two preceding articles, the quotients of this filtration…
The main purpose of this article is to classify contact structures on some 3-manifolds, namely lens spaces, most torus bundles over a circle, the solid torus, and the thickened torus T^2 x [0,1]. This classification completes earlier work…
While most scene flow methods use either variational optimization or a strong rigid motion assumption, we show for the first time that scene flow can also be estimated by dense interpolation of sparse matches. To this end, we find sparse…
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations.…
We propose a new multi-frame method for efficiently computing scene flow (dense depth and optical flow) and camera ego-motion for a dynamic scene observed from a moving stereo camera rig. Our technique also segments out moving objects from…