Related papers: Symmetric Criticality for Tight Knots

We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive. This answers a question of Stoimenow's in the (strong) positive. As a second main result, we give simple and complete characterizations of…

A thick link is a link in $\mathbb{R}^3$ such that each component of the link lies at distance at least $1$ from every other component. Strengthening the notion of thickness, we define a thickly embedded link to be a thick link whose open…

In this paper, we consider the knot complement problem for not null-homologous knots in homology lens spaces. Let $M$ be a homology lens space with $H_1(M; \mathbb{Z}) \cong \mathbb{Z}_p$ and $K$ a not null-homologous knot in $M$. We show…

The knot group is the fundamental group of a knot or link complement. A necessary and sufficient conditions for a group to be realized as the knot group of some link was provided. This result was shown using the closed braid method.…

Model checking is the process of deciding whether a system satisfies a given specification. Often, when the setting comprises multiple processes, the specifications are over sets of input and output signals that correspond to individual…

Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…

The ribbonlength Rib$(K)$ of a knot $K$ is the infimum of the ratio of the length of any flat knotted ribbon with core $K$ to its width. A twisted torus knot $T_{p,q;r,s}$ is obtained from the torus knot $T_{p,q}$ by twisting $r$ adjacent…

We analyse the relationship between the full additivity of the entanglement cost and its full monotonicity under local operations and classical communication. We show that the two properties are equivalent for the entanglement cost. The…

Here we prove critical exponents for Random Connections Models (RCMs) with random marks. The vertices are given by a marked Poisson point process on $\mathbb{R}^d$ and an edge exists between any pair of vertices independently with a…

We solve for the critical coupling in the symmetric phase of two-dimensional $\phi^4$ field theory using Discretized Light-Cone Quantization. We adopt periodic boundary conditions, neglect the zero mode, and obtain a critical coupling…

Theoretical description of anisotropic systems, such as layered superconductors and coupled spin chains, is often a challenge due to the different natures of interactions along different directions. As a model of such a system, we present…

A revised version of the compactness criterion for families of quantum operations in the strong convergence topology (obtained previously) is presented, along with a more detailed proof and the examples showing the necessity of this…

We show that for large coupling delays the synchronizability of delay-coupled networks of identical units relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability…

Besides mathematical interest, knots and knot theory have important applications in physics, chemistry, and biology. Stasiak and colleagues devised a constructive method for a knot "energy" using a Metropolis Monte Carlo algorithm to…

In this paper we prove that if a knot or link has a sufficiently complicated plat projection, then that plat projection is unique. More precisely, if a knot or link has a $2m$-plat projection, where $m$ is at least four, and height at least…

Physical knots and links are one-dimensional submanifolds of R^3 with fixed length and thickness. We show that isotopy classes in this category can differ from those of classical knot and link theory. In particular we exhibit a Gordian…

Links and knots are exotic topological structures that have garnered significant interest across multiple branches of natural sciences. Coherent links and knots, such as those constructed by phase or polarization singularities of coherent…

In this paper, we study Legendrian realizations of cable links of knot types that are uniformly thick but not Legendrian simple, extending prior work of Dalton, the second author, and Traynor. This leads to new phenomena, such as stabilized…

Quantum coherence and entanglement are two key features in quantum mechanics and play important roles in quantum information processing and quantum computation. We provide a general triangle-like inequality satisfied by the $l_1$-norm…

Knot theory is actively studied both by physicists and mathematicians as it provides a connecting centerpiece for many physical and mathematical theories. One of the challenging problems in knot theory is distinguishing mutant knots. Mutant…