Related papers: The Structure and Enumeration of Link Projections
A new deconvolution algorithm based on orthogonal projections onto the epigraph set of a convex cost function is presented. In this algorithm, the dimension of the minimization problem is lifted by one and sets corresponding to the cost…
Every link in R^3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.
This paper presents a new algorithm "A" for constructing Seifert surfaces from n-bridge projections of links. The algorithm produces minimal complexity surfaces for large classes of braids and alternating links. In addition, we consider a…
We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…
Many biological and medical tasks require the delineation of 3D curvilinear structures such as blood vessels and neurites from image volumes. This is typically done using neural networks trained by minimizing voxel-wise loss functions that…
In recent years, there have been intense research efforts to develop efficient methods for probabilistic inference in probabilistic influence diagrams or belief networks. Many people have concluded that the best methods are those based on…
This paper gives an introduction to the theory of orthogonal projection of functions or signals. Several kinds of decomposition are explored: Fourier, Fourier-Legendre, Fourier-Bessel series for 1D signals, and Spherical Harmonic series for…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
A classification of spanning surfaces for alternating links is provided up to genus, orientability, and a new invariant that we call aggregate slope. That is, given an alternating link, we determine all possible combinations of genus,…
Tverberg's theorem says that a set with sufficiently many points in $\mathbb{R}^d$ can always be partitioned into $m$ parts so that the $(m-1)$-simplex is the (nerve) intersection pattern of the convex hulls of the parts. In…
Learning to infer graph representations and performing spatial reasoning in a complex surgical environment can play a vital role in surgical scene understanding in robotic surgery. For this purpose, we develop an approach to generate the…
X-ray tomography has been studied in various fields. Although a great deal of effort has been directed at reconstructing the projection image set from a rigid-type specimen, little attention has been addressed to the reconstruction of…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
We construct a cobordism group for embedded graphs in two different ways, first by using sequences of two basic operations, called "fusion" and "fission", which in terms of cobordisms correspond to the basic cobordisms obtained by attaching…
We discuss, on general grounds, how two subgraphs of a given Feynman graph can overlap with each other. For this, we use the notion of connecting and returning lines that describe how any subgraph is inserted within the original graph.…
Many natural, technological, and social systems incorporate multiway interactions, yet are characterized and measured on the basis of weighted pairwise interactions. In this article, I propose a family of models in which pairwise…
Vertex splitting is a graph modification operation in which a vertex is replaced by multiple vertices such that the union of their neighborhoods equals the neighborhood of the original vertex. We introduce and study vertex splitting as a…
Graphs can represent relational information among entities and graph structures are widely used in many intelligent tasks such as search, recommendation, and question answering. However, most of the graph-structured data in practice suffers…
An LR-structure is a tetravalent vertex-transitive graph together with a special type of a decomposition of its edge-set into cycles. LR-structures were introduced in a paper by P. Poto\v{c}nik and S. Wilson, titled `Linking rings…
A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…