On a higher analog of the linking number of two curves

1998 ◽  
pp. 113-127 ◽  
Author(s):  
P. M. Akhmetiev
Keyword(s):  
Linking Number

scholarly journals FIELD THEORY OF N ENTANGLED POLYMERS

2000 ◽  
Vol 14 (32) ◽  
pp. 3881-3895 ◽  
Author(s):  
FRANCO FERRARI ◽  
HAGEN KLEINERT ◽  
IGNAZIO LAZZIZZERA
Keyword(s):  
Field Theory ◽  
Canonical Ensemble ◽  
Feynman Diagrams ◽  
Linking Number ◽  
Entangled Polymers

We formulate a field theory capable of describing a canonical ensemble of N polymers subjected to linking number constraints in terms of Feynman diagrams.

Effects of histone acetylation on chromatin topology in vivo

1992 ◽  
Vol 12 (11) ◽  
pp. 5004-5014
Author(s):  
L C Lutter ◽  
L Judis ◽  
R F Paretti
Keyword(s):  
Transcriptional Activation ◽  
Simian Virus 40 ◽  
Simian Virus ◽  
Nucleosome Assembly ◽  
Linking Number ◽  
Histone Hyperacetylation ◽  
Proposed Model ◽  
Butyrate Treatment

Recently a model for eukaryotic transcriptional activation has been proposed in which histone hyperacetylation causes release of nucleosomal supercoils, and this unconstrained tension in turn stimulates transcription (V. G. Norton, B. S. Imai, P. Yau, and E. M. Bradbury, Cell 57:449-457, 1989; V. G. Norton, K. W. Marvin, P. Yau, and E. M. Bradbury, J. Biol. Chem. 265:19848-19852, 1990). These studies analyzed the effect of histone hyperacetylation on the change in topological linking number which occurs during nucleosome assembly in vitro. We have tested this model by determining the effect of histone hyperacetylation on the linking number change which occurs during assembly in vivo. We find that butyrate treatment of cells infected with simian virus 40 results in hyperacetylation of the histones of the extracted viral minichromosome as expected. However, the change in constrained supercoils of the minichromosome DNA is minimal, a result which is inconsistent with the proposed model. These results indicate that the proposed mechanism of transcriptional activation is unlikely to take place in the cell.

scholarly journals Measuring topology from dynamics by obtaining the Chern number from a linking number

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Matthias Tarnowski ◽  
F. Nur Ünal ◽  
Nick Fläschner ◽  
Benno S. Rem ◽  
André Eckardt ◽  
...  
Keyword(s):  
Chern Number ◽  
Linking Number

scholarly journals INTRINSICALLY LINKED GRAPHS WITH KNOTTED COMPONENTS

2012 ◽  
Vol 21 (07) ◽  
pp. 1250065 ◽  
Author(s):  
THOMAS FLEMING
Keyword(s):  
Complete Graph ◽  
Cartesian Product ◽  
Complete Graphs ◽  
Linking Number ◽  
A Minor

We construct a graph G such that any embedding of G into R3 contains a nonsplit link of two components, where at least one of the components is a nontrivial knot. Further, for any m < n we produce a graph H so that every embedding of H contains a nonsplit n component link, where at least m of the components are nontrivial knots. We then turn our attention to complete graphs and show that for any given n, every embedding of a large enough complete graph contains a 2-component link whose linking number is a nonzero multiple of n. Finally, we show that if a graph is a Cartesian product of the form G × K2, it is intrinsically linked if and only if G contains one of K5, K3,3 or K4,2 as a minor.

DNA supercoiling and transcription: topological coupling of promoters

1996 ◽  
Vol 29 (3) ◽  
pp. 203-225 ◽  
Author(s):  
David M. J. Lilley ◽  
Dongrong Chen ◽  
Richard P. Bowater
Keyword(s):  
Fundamental Property ◽  
Dna Supercoiling ◽  
The Other ◽  
Linear Dna ◽  
Dna Molecule ◽  
Linking Number ◽  
Closed Circle ◽  
A Chain

DNA supercoiling is a consequence of the double-stranded nature of DNA. When a linear DNA molecule is ligated into a covalently closed circle, the two strands become intertwined like the links of a chain, and will remain so unless one of the strands is broken. The number of times one strand is linked with the other is described by a fundamental property of DNA supercoiling, the linking number (Lk).

scholarly journals A LINKING NUMBER DEFINITION OF THE AFFINE INDEX POLYNOMIAL AND APPLICATIONS

2013 ◽  
Vol 22 (12) ◽  
pp. 1341004 ◽  
Author(s):  
LENA C. FOLWACZNY ◽  
LOUIS H. KAUFFMAN
Keyword(s):  
Virtual Knots ◽  
Linking Number ◽  
Linking Numbers ◽  
Vassiliev Invariant ◽  
Definition Of

This paper gives an alternate definition of the Affine Index Polynomial (called the Wriggle Polynomial) using virtual linking numbers and explores applications of this polynomial. In particular, it proves the Cosmetic Crossing Change Conjecture for odd virtual knots and pure virtual knots. It also demonstrates that the polynomial can detect mutations by positive rotation and proves it cannot detect mutations by positive reflection. Finally it exhibits a pair of mutant knots that can be distinguished by a type 2 vassiliev invariant coming from the polynomial.

scholarly journals Number and twistedness of strands in weavings on regular convex polyhedra

2014 ◽  
Vol 470 (2162) ◽  
pp. 20130608 ◽  
Author(s):  
F. Kovács
Keyword(s):  
Graph Theory ◽  
Structural Engineering ◽  
Closed Surface ◽  
Convex Polyhedra ◽  
Recursive Method ◽  
Simple Method ◽  
Linking Number ◽  
Regular Convex ◽  
Weaving Pattern ◽  
Symmetry Operations

This paper deals with two- and threefold weavings on Platonic polyhedral surfaces. Depending on the skewness of the weaving pattern with respect to the edges of the polyhedra, different numbers of closed strands are necessary in a complete weaving. The problem is present in basketry but can be addressed from the aspect of pure geometry (geodesics), graph theory (central circuits of 4-valent graphs) and even structural engineering (fastenings on a closed surface). Numbers of these strands are found to have a periodicity and symmetry, and, in some cases, this number can be predicted directly from the skewness of weaving. In this paper (i) a simple recursive method using symmetry operations is given to find the number of strands of cubic, octahedral and icosahedral weavings for cases where generic symmetry arguments fail; (ii) another simple method is presented to decide whether or not a single closed strand can run along the underlying Platonic without a turn (i.e. the linking number of the two edges of a strand is zero, and so the loop can be stretched to a circle without being twisted); and (iii) the linking number of individual strands in an alternate ‘check’ weaving pattern is determined.

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