Related papers: Parameterizing Fullerenes with Vertex Combinations
Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer…
These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…
We develop a general approach to finding combinatorial models for cluster algebras. The approach is to construct a labeled graph called a framework. When a framework is constructed with certain properties, the result is a model…
A planar portrait of a manifold is the pair of the image and the critical values of the manifold through a stable map into the plane. It can be considerd a geometric representation of the manifold drawn in the plane. The cusped fan is its…
Modern graph embedding procedures can efficiently process graphs with millions of nodes. In this paper, we propose GEMSEC -- a graph embedding algorithm which learns a clustering of the nodes simultaneously with computing their embedding.…
A quadrangle in the Euclidean plane is called $n$-self-affine if it has a dissection into $n$ affine images of itself. All convex quadrangles are known to be $n$-self-affine for every $n \ge 5$. The only $2$-self-affine convex quadrangles…
We consider the problem of clustering misaligned curves. According to our similarity measure, two curves are considered similar if they have the same shape after being aligned, and the warping function does not differ from the identity…
While convolutional neural networks (CNNs) have recently made great strides in supervised classification of data structured on a grid (e.g. images composed of pixel grids), in several interesting datasets, the relations between features can…
Our main theoretical result is that, if a simple polytope has a pair of complementary vertices (i.e., two vertices with no facets in common), then it has at least two such pairs, which can be chosen to be disjoint. Using this result, we…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
Motivated by applications in community detection and dense subgraph discovery, we consider new clustering objectives in hypergraphs and bipartite graphs. These objectives are parameterized by one or more resolution parameters in order to…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
In this article we present theoretical and computational results on the existence of polyhedral embeddings of graphs. The emphasis is on cubic graphs. We also describe an efficient algorithm to compute all polyhedral embeddings of a given…
A successive vertex ordering of a graph is a linear ordering of its vertices in which every vertex except the first has at least one neighbour appearing earlier. Such orderings arise naturally in incremental growth and…
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…
Finding (bi-)clusters in bipartite graphs is a popular data analysis approach. Analysts typically want to visualize the clusters, which is simple as long as the clusters are disjoint. However, many modern algorithms find overlapping…
Graph clustering aims at discovering a natural grouping of the nodes such that similar nodes are assigned to a common cluster. Many different algorithms have been proposed in the literature: for simple graphs, for graphs with attributes…
Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct…
Graphs drawn in the plane are ubiquitous, arising from data sets through a variety of methods ranging from GIS analysis to image classification to shape analysis. A fundamental problem in this type of data is comparison: given a set of such…