Related papers: 1D Effectively Closed Subshifts and 2D Tilings

We show that the physical subspace in the Z2-slave-spin theory is conserved under the time evolution of the system. Thus, when restricted to the physical subspace, this representation gives a complete and consistent description of the…

Suppose $f\in L^1(\mathbb{R}^d)$, $\Lambda\subset\mathbb{R}^d$ is a finite union of translated lattices such that $f+\Lambda$ tiles with a weight. We prove that there exists a lattice $L\subset{\mathbb{R}}^d$ such that $f+L$ also tiles,…

This paper introduces a simulation preorder among lifted systems, a generalization of finite-dimensional Koopman approximations (also known as approximate immersions) to systems with inputs. It is proved that this simulation relation…

We call "flippable tilings" of a constant curvature surface a tiling by "black" and "white" faces, so that each edge is adjacent to two black and two white faces (one of each on each side), the black face is forward on the right side and…

In this paper we present two different problems within the framework of shift-invariant theory. First, we develop a triangular form for shift-preserving operators acting on finitely generated shift-invariant spaces. In case of the normal…

Using large scale quantum Monte Carlo simulations of lattice bosonic models, we precisely investigate the effect of weak Josephson tunneling between 2D superfluid or superconducting layers. In the clean case, the Kosterlitz-Thouless…

Two-dimensional (2-D) incompressible, inviscid fluids produce fascinating patterns of swirling motion. How and why the patterns emerge are long-standing questions, first addressed in the 19th century by Helmholtz, Kirchhoff, and Kelvin.…

The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…

A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings are sofic, that is, can be enforced by finitely many local…

Following ideas of G. Moore and G. Segal, we explicitly construct a G-equivariant topological field theory from an arbitrary Frobenius algebra equipped with a twisted action of a finite group G.

We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyper-pseudo-Hermitian curvature…

Let F be a finite set of circles in the plane. We point out that the usual convex closure restricted to F yields a convex geometry, that is, a combinatorial structure introduced by P. H Edelman in 1980 under the name "anti-exchange closure…

Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…

In arXiv:0902.4032 [hep-th] an O(D,D)-covariant sigma model describing the embedding of a closed world-sheet into the 2D-dimensional twisted torus was proposed. Such sigma models provide a universal description of string theory with target…

We show that the action of residual supersymmetries in holomorphic-topological twists of $N = 2$ theories in three dimensions naturally extends to the action of certain infinite dimensional Lie superalgebras. We demonstrate this in a range…

Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by…

We discuss the art and science of producing conformally correct euclidean and hyperbolic tilings of compact surfaces. As an example, we present a tiling of the Chmutov surface by hyperbolic (2, 4, 6) triangles.

We construct a pair of transverse genuine laminations on an atoroidal 3-manifold admitting transversely orientable uniform 1-cochain. The laminations are induced by the uniform 1-cochain and they are indeed the "straightening" of the coarse…

We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…

Unified and scalable Transformers have recently achieved remarkable success in modeling diverse phenomena traditionally associated with computer graphics, such as 3D visual effects, rendering processes, and motion in videos. In this work,…