Related papers: Twisted Edges: A Unified Framework for Designing L…
Topological states of matter are robust quantum phases, characterised by propagating or localised edge states in an insulating bulk. Topological boundary states can be triggered by various mechanisms, for example by strong spin-orbit…
We introduce twisted trilayer graphene (tTLG) with two independent twist angles as an ideal system for the precise tuning of the electronic interlayer coupling to maximize the effect of correlated behaviors. As established by experiment and…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
In this paper, we study surfaces embedded in $4$-manifolds. We give a complete set of moves relating banded unlink diagrams of isotopic surfaces in an arbitrary $4$-manifold. This extends work of Swenton and Kearton-Kurlin in $S^4$. As an…
Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a virtual knot, which corresponds to a link diagram on a…
A network can contain numerous spanning trees. If two spanning trees $T_i,T_j$ do not share any common edges, $T_i$ and $T_j$ are said to be pairwisely edge-disjoint. For spanning trees $T_1, T_2, ..., T_m$, if every two of them are…
Twisting and classical background fields are two foundational techniques in supersymmetric quantum field theory, central to developments ranging from the Higgs mechanism to topological twisting and supersymmetric localisation. While…
Twisted graphene multilayers provide tunable platforms to engineer flat bands and exploit the associated strongly correlated physics. The two-dimensional nature of these systems makes them suitable for encapsulation by materials that break…
This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence…
We introduce a model of fracture which includes the out-of-plane degrees of freedom necessary to describe buckling in a thin-sheet material. The model is a regular square lattice of elastic beams, rigidly connected at the nodes so as to…
In recent years, the study of topologically non-trivial structures in one-dimensional models has been dominated by the Su--Schrieffer--Heeger model due to its simplicity in design and its ability to support edge states with robustness to…
A labelled, undirected graph is a graph whose edges have assigned labels, from a specific set. Given a labelled, undirected graph, the well-known minimum labelling spanning tree problem is aimed at finding the spanning tree of the graph…
In this paper we introduce TWIG (Topologically-Weighted Intelligence Generation), a novel, embedding-free paradigm for simulating the output of KGEs that uses a tiny fraction of the parameters. TWIG learns weights from inputs that consist…
Twisted links are a generalization of classical links and correspond to stably equivalence classes of links in thickened surfaces. In this paper we introduce twisted intersection colorings of a diagram and construct two invariants of a…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
A $d$-dimensional tensegrity framework $(T,p)$ is an edge-labeled geometric graph in ${\mathbb R}^d$, which consists of a graph $T=(V,B\cup C\cup S)$ and a map $p:V\to {\mathbb R}^d$. The labels determine whether an edge $uv$ of $T$…
Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena…
The property of a surface being developable can be expressed in different equivalent ways, by vanishing Gauss curvature, or by the existence of isometric mappings to planar domains. Computational contributions to this topic range from…