Related papers: On Sparse Representations of 3-Manifolds
We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a slight variation of this algorithm also works for open books…
We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…
Sparse manifold learning algorithms combine techniques in manifold learning and sparse optimization to learn features that could be utilized for downstream tasks. The standard setting of compressive sensing can not be immediately applied to…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
We show that if a closed, oriented 3-manifold M is promised to be homeomorphic to a lens space L(n,k) with n and k unknown, then we can compute both n and k in polynomial time in the size of the triangulation of M. The tricky part is the…
An arbitrary rigid transformation in $\mathbf{SE}(3)$ can be separated into two parts, namely, a translation and a rigid rotation. This technical report reviews, under a unifying viewpoint, three common alternatives to representing the…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Two important classes of three-dimensional elements in computational meshes are hexahedra and tetrahedra. While several efficient methods exist that convert a hexahedral element to a tetrahedral elements, the existing algorithm for…
Understanding 3D object shapes necessitates shape representation by object parts abstracted from results of instance and semantic segmentation. Promising shape representations enable computers to interpret a shape with meaningful parts and…
A simplified trisection is a trisection map on a 4-manifold such that, in its critical value set, there is no double point and cusps only appear in triples on innermost fold circles. We give a necessary and sufficient condition for a…
We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing…
Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…
The triangulation complexity of a closed orientable 3-manifold is the minimal number of tetrahedra in any triangulation of the manifold. The main theorem of the paper gives upper and lower bounds on the triangulation complexity of any…
Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none…
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…
In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in…
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…