Related papers: Reconsideration of Tangle and Ultrafilter using Se…
In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that…
String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…
Edge bundling is an important concept heavily used for graph visualization purposes. To enable the comparison with other established near-planarity models in graph drawing, we formulate a new edge-bundling model which is inspired by the…
We show that, given a $ k $-tangle $ \tau $ in a graph $ G $, there always exists a weight function $ w\colon V(G)\to\mathbb{N} $ such that a separation $ (A,B) $ of $ G $ of order $ {<}k $ lies in $ \tau $ if and only if $ w(A)<w(B) $,…
We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the graph or matroid. This comes as a corollary of a similar decomposition theorem…
In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator. We use the convolution to define tangent bundle filters and tangent bundle neural networks…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
Rank-width is a width parameter of graphs describing whether it is possible to decompose a graph into a tree-like structure by `simple' cuts. This survey aims to summarize known algorithmic and structural results on rank-width of graphs.
A planar Tangle is a smooth simple closed curve piecewise defined by quadrants of circles with constant curvature. We can enumerate Tangles by counting their dual graphs, which consist of a certain family of polysticks. The number of…
Graph partitioning has long been seen as a viable approach to address Graph DBMS scalability. A partitioning, however, may introduce extra query processing latency unless it is sensitive to a specific query workload, and optimised to…
Following recent work by van der Hoeven and Lecerf (ISSAC 2017), we discuss the complexity of linear mappings, called untangling and tangling by those authors, that arise in the context of computations with univariate polynomials. We give a…
Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural…
In this note we gather the theoretical outlines of three basic algorithms for tangles in abstract separation systems: a naive tree search for finding tangles; an algorithm which outputs a certificate for the non-existence of tangles if…
Clustering is a common technique for statistical data analysis, Clustering is the process of grouping the data into classes or clusters so that objects within a cluster have high similarity in comparison to one another, but are very…
Tangles, as introduced by Robertson and Seymour, were designed as an indirect way of capturing clusters in graphs and matroids. They have since been shown to capture clusters in much broader discrete structures too. But not all tangles are…
Given a graph or a matroid, a tree of tangles is a tree decomposition that displays the structure of the connectivity: every edge of the decomposition tree induces a separation, that is, a way to divide the graph or matroid into two parts;…
We continue algebraization of the set of ultrafilters on a metric spaces initiated in [6]. In particular, we define and study metric counterparts of prime, strongly prime and right cancellable ultrafilters from the Stone-$\check{C}$ech…
Using the recently developed mathematical theory of tangles, we re-assess the mathematical foundations for applications of the five factor model in personality tests by a new, mathematically rigorous, quantitative method. Our findings…
This note addresses the construction of a notion of parallel transport along superpaths arising from the concept of a superconnection on a vector bundle over a manifold $M$. A superpath in $M$ is, loosely speaking, a path in $M$ together…
This paper studies questions about duality between crossings and non-crossings in graph drawings via the notions of thickness and antithickness. The "thickness" of a graph $G$ is the minimum integer $k$ such that in some drawing of $G$, the…