Related papers: A note on lattice knots
An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the…
We study the reduced fidelity between local states of lattice systems exhibiting topological order. By exploiting mappings to spin models with classical order, we are able to analytically extract the scaling behavior of the reduced fidelity…
Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics, and science. As topologically stable objects within field theories, they have been speculatively proposed as explanations for diverse persistent…
This work focuses on the identifiability of dynamical networks with partial excitation and measurement: a set of nodes are interconnected by unknown transfer functions according to a known topology, some nodes are subject to external…
This note has an experimental nature and contains no new theorems. We introduce certain moves for classical knot diagrams that for all the very many examples we have tested them on give a monotonic complete simplification. A complete…
We generalize the classical study of Alexander polynomials of smooth or PL locally-flat knots to PL knots that are not necessarily locally-flat. We introduce three families of generalized Alexander polynomials and study their properties.…
We propose a new formulation of lattice theory. It is given by a matrix form and suitable for satisfying Leibniz rule on lattice. The theory may be interpreted as a multi-flavor system. By realizing the difference operator as a commutator,…
This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best known bound for closed surfaces.
Active quantum error correction has been identified as a crucial ingredient of future quantum computers, motivating the recent experimental efforts to encode logical quantum bits using small topological codes. In addition to the…
This paper details a series of experiments in searching for minimal energy configurations for knots and links using the computer program KnotPlot. The most interesting phenomena found in these experiments is the dependence of the…
This note describes a way of obtaining e that differs from the standard one. It could be used as an alternate way of showing how the value of e is obtained. No attempt is made to show the existence of the limit in the definition of e that…
We take an order-theoretic approach to circuit (string diagram) syntax, treating a circuit as a partial order with additional input-output structure. We define morphisms between circuits and prove a factorisation theorem showing that these…
This is a review article on Lorenz knots.
In this short paper, we point out that a single local stability controller can pin the complex network to a specified solution (or its equilibrium) of the coupled complex network. A rigorous mathematical proof is given, too.
The characterisation of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic…
The altenating knots, links and twists projected on the S_2 sphere are identified with the phase Space of a Hamiltonian dynamic system of one degree of freedom. The saddles of the system correspond to the crossing points, the edges, to the…
The purpose of these notes is to introduce some of the problems the enumeration of lattice walks is dedicated to and familiarize with some of the arguments they can be addressed with. We discuss the enumeration of lattice walks, their…
We show that if a classical knot diagram satisfies a certain combinatorial condition then it is minimal with respect to the number of classical crossings. This statement is proved by using the Kauffman bracket and the construction of atoms…
The aim of this paper is to define certain algebraic structures coming from generalized Reidemeister moves of singular knot theory. We give examples, show that the set of colorings by these algebraic structures is an invariant of singular…
The goal of this note is to show that in the case of transversal intersections the "true local terms" appearing in the Lefschetz trace formula equal to the "naive local terms". To prove the result we extend the method of [Va], where the…