Concept

Crossing number (knot theory)

Related publications (14)

Mechanics of Physical Knots: From Filaments in Contact to Surgical Suturing

In this thesis, we study the mechanics of tight physical knots. Knots are omnipresent in surgery, climbing, and sailing, with disastrous consequences when the filament or the rope fails to perform its function. Even if the importance of mechanical analysis ...

EPFL2023

The shapes of physical trefoil knots

Pedro Miguel Nunes Pereira de Almeida Reis, John Maddocks, Paul Johanns, Changyeob Baek, Paul Grandgeorge

We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed and open configurations. Ideal knots are purely geometric abstractions for the tightest configuration tied in a perfectly fle ...

2021

Note on k-planar crossing numbers

János Pach

The crossing number CR(G) of a graph G = (V, E) is the smallest number of edge crossings over all drawings of G in the plane. For any k >= 1, the k-planar crossing number of G, CRk(G), is defined as the minimum of CR(G(0)) + CR(G(1)) + ... + CR(G(k-i)) ove ...

Elsevier Science Bv2018

We use stochastic simulation techniques to sample the conformational space of linear semiflexible polymers in a crowded medium and study how the knotting properties depend on the crowder size and concentration. The abundance of physical knots in the chains ...

Royal Society of Chemistry2016

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

Pedro Miguel Nunes Pereira de Almeida Reis

We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to q ...

American Physical Society2015

Generation of supercoils in nicked and gapped DNA drives DNA unknotting and postreplicative decatenation

Julien Dorier, Yannis Burnier, Fabrizio Benedetti, Andrzej Stasiak

Due to the helical structure of DNA the process of DNA replication is topologically complex. Freshly replicated DNA molecules are catenated with each other and are frequently knotted. For proper functioning of DNA it is necessary to remove all of these ent ...

Oxford University Press2015

Sedimentation of macroscopic rigid knots and its relation to gel electrophoretic mobility of DNA knots

Giovanni Dietler, Cédric Weber, Andrzej Stasiak, Mathias Carlen

We address the general question of the extent to which the hydrodynamic behaviour of microscopic freely fluctuating objects can be reproduced by macrosopic rigid objects. In particular, we compare the sedimentation speeds of knotted DNA molecules undergoin ...

Nature Publishing Group2013

Study of Topoisomerase-DNA Interaction Using Atomic Force Microscopy

Livan Bladimir Alonso Sarduy

The aim of this thesis was to explore the topoisomerase-DNA interactions using atomic force microscopy (AFM) in a liquid environment. Firstly, we present a programmable microcontroller-driven injection system for the exchange of an imaging medium while usi ...

EPFL2012

Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases

Giovanni Dietler, Andrzej Stasiak, Guillaume Witz

Using numerical simulations, we compare properties of knotted DNA molecules that are either torsionally relaxed or supercoiled. We observe that DNA supercoiling tightens knotted portions of DNA molecules and accentuates the difference in curvature between ...

2011

DNA Topology

Guillaume Witz

This thesis explores different aspects of DNA topology through experimental and numerical techniques. Topology is a vast mathematical field, that deals with the spatial properties of objects undergoing continuous deformations, but here it is restricted to ...

EPFL2010

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