scholarly journals A Symmetry Motivated Link Table

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 604 ◽  
Author(s):  
Shawn Witte ◽  
Michelle Flanner ◽  
Mariel Vazquez
Keyword(s):  
Monte Carlo ◽  
Dna Topology ◽  
Mirror Image ◽  
Symmetry Groups ◽  
Linking Number ◽  
Link Diagrams ◽  
Local Lattice ◽  
Geometrical Data ◽  
Prime 2 ◽  
Link Table

Proper identification of oriented knots and 2-component links requires a precise link nomenclature. Motivated by questions arising in DNA topology, this study aims to produce a nomenclature unambiguous with respect to link symmetries. For knots, this involves distinguishing a knot type from its mirror image. In the case of 2-component links, there are up to sixteen possible symmetry types for each link type. The study revisits the methods previously used to disambiguate chiral knots and extends them to oriented 2-component links with up to nine crossings. Monte Carlo simulations are used to report on writhe, a geometric indicator of chirality. There are ninety-two prime 2-component links with up to nine crossings. Guided by geometrical data, linking number, and the symmetry groups of 2-component links, canonical link diagrams for all but five link types (9 5 2, 9 34 2, 9 35 2, 9 39 2, and 9 41 2) are proposed. We include complete tables for prime knots with up to ten crossings and prime links with up to nine crossings. We also prove a result on the behavior of the writhe under local lattice moves.

scholarly journals A Symmetry Motivated Link Table

2018 ◽  
Author(s):  
Shawn Witte ◽  
Michelle Flanner ◽  
Mariel Vazquez
Keyword(s):  
Monte Carlo ◽  
Dna Topology ◽  
Mirror Image ◽  
Symmetry Groups ◽  
Link Diagram ◽  
Linking Number ◽  
Local Lattice ◽  
Geometrical Data ◽  
Prime 2 ◽  
Link Table

Proper identification of oriented knots and 2-component links requires a precise link nomenclature. Motivated by questions arising in DNA topology, this study aims to produce a nomenclature unambiguous with respect to link symmetries. For knots, this involves distinguishing a knot type from its mirror image. In the case of 2-component links, there are up to sixteen possible symmetry types for each topology. The study revisits the methods previously used to disambiguate chiral knots and extends them to oriented 2-component links with up to nine crossings. Monte Carlo simulations are used to report on writhe, a geometric indicator of chirality. There are ninety-two prime 2-component links with up to nine crossings. Guided by geometrical data, linking number and the symmetry groups of 2-component links, a canonical link diagram for each link type is proposed. All diagrams but six were unambiguously chosen ( 8 1 2 5 , 9 5 2 , 9 3 2 4 , 9 3 2 5 , 9 3 2 9 , and 9 4 2 1 ). We include complete tables for prime knots with up to ten crossings and prime links with up to nine crossings. We also prove a result on the behavior of the writhe under local lattice moves.

A Study on First Principle Calculation of Alloy Phase Diagram by Monte Carlo Simulation

1992 ◽  
Vol 291 ◽  
Author(s):  
Hideaki Sawada ◽  
Atsushi Nogami ◽  
Wataru Yamada ◽  
Tooru Matsiuniya
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Alloy Phase Diagram ◽  
Lattice Constant ◽  
Local Concentration ◽  
First Principle ◽  
Principle Calculation ◽  
First Principle Calculation ◽  
Local Lattice ◽  
Mc Simulation

ABSTRACTA method of first principle calculation of alloy phase diagram was developed by the combination of first principle energy band calculation, cluster expansion method (CEM) and Monte Carlo (MC) simulation, where the effective multi-body potential energy for the flip test in MC simulation was obtained by the decomposition of the total energy by CEM. This method was applied to Cu-Au binary system. The calculated phase diagram agreed with that of CVM by introducing the dependence of the lattice constant on the concentration of the whole system. Furthermore an attempt of introducing the effect of local lattice relaxation was performed by the consideration of the local concentration. The order-disorder transition temperature became closer to the experimental value by adjustment of the local lattice constant depending on the concentration in the local region consisted of up to the second nearest neighbors of the atom tested for flipping.

Development of the CAD/MCNP Automatic Conversion Code GEOMIT

2009 ◽  
Author(s):  
Hesham R. Nasif ◽  
Fukuzo Masuda ◽  
Hiromasa Iida ◽  
Hidetsugu Morota ◽  
Satoshi Sato ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Point Of View ◽  
International Thermonuclear Experimental Reactor ◽  
Cad Model ◽  
First Wall ◽  
Benchmark Model ◽  
Heat Loading ◽  
Geometrical Data ◽  
The Difference ◽  
Representation Scheme

GEOMIT is the CAD/MCNP conversion interface code. The old version of GEOMIT had a limited capability from CAD model handling point of view. It is developed to automatically generate Monte Carlo geometrical data from CAD data due to the difference in the representation scheme. GEOMIT is capable of importing different CAD format as well as exporting different CAD format. GEOMIT has a capability to produce solid cells as well as void cells without using complement operator. While loading the CAD shapes (Solids), each shape is assigning material number and density according to its color. Shape fixing process is been applied to cure the errors in the CAD data. Vertices location correctness is evaluated first, then a removal of free edges and removal of small faces processes. Binary Space Portioning (BSP) tree technique is used to automatically split complicated solids into simpler cells to avoid excessive complicated cells for MCNP to run faster. MCNP surfaces are subjected to an automatic reduction before creating the model. CAD data of International Thermonuclear Experimental Reactor (ITER) benchmark model has been converted successfully to MCNP geometrical input. The first wall heat loading calculations agree very well with other countries results.

scholarly journals Introduction to disoriented knot theory

2018 ◽  
Vol 16 (1) ◽  
pp. 346-357
Author(s):  
İsmet Altıntaş
Keyword(s):  
Knot Theory ◽  
Jones Polynomial ◽  
Polynomial Invariants ◽  
Linking Number ◽  
Link Diagrams ◽  
New Ideas ◽  
Numerical Invariants ◽  
Bracket Polynomial ◽  
Knots And Links

AbstractThis paper is an introduction to disoriented knot theory, which is a generalization of the oriented knot and link diagrams and an exposition of new ideas and constructions, including the basic definitions and concepts such as disoriented knot, disoriented crossing and Reidemesiter moves for disoriented diagrams, numerical invariants such as the linking number and the complete writhe, the polynomial invariants such as the bracket polynomial, the Jones polynomial for the disoriented knots and links.

ON A LOCAL MOVE FOR VIRTUAL KNOTS AND LINKS

2009 ◽  
Vol 18 (11) ◽  
pp. 1577-1596 ◽  
Author(s):  
TOSHIYUKI OIKAWA
Keyword(s):  
Sufficient Conditions ◽  
Virtual Link ◽  
Link Invariant ◽  
Virtual Knot ◽  
Virtual Knots ◽  
Linking Number ◽  
Reidemeister Moves ◽  
Link Diagrams ◽  
Necessary And Sufficient ◽  
Knots And Links

We define a local move called a CF-move on virtual link diagrams, and show that any virtual knot can be deformed into a trivial knot by using generalized Reidemeister moves and CF-moves. Moreover, we define a new virtual link invariant n(L) for a virtual 2-component link L whose virtual linking number is an integer. Then we give necessary and sufficient conditions for two virtual 2-component links to be deformed into each other by using generalized Reidemeister moves and CF-moves in terms of a virtual linking number and n(L).

Linking invariants of even virtual links

2017 ◽  
Vol 26 (12) ◽  
pp. 1750072 ◽  
Author(s):  
Haruko A. Miyazawa ◽  
Kodai Wada ◽  
Akira Yasuhara
Keyword(s):  
Lower Bound ◽  
The Other ◽  
Virtual Link ◽  
Link Diagram ◽  
Linking Number ◽  
Reidemeister Moves ◽  
Link Diagrams ◽  
Classical Link ◽  
Virtual Links ◽  
The Difference

A virtual link diagram is even if the virtual crossings divide each component into an even number of arcs. The set of even virtual link diagrams is closed under classical and virtual Reidemeister moves, and it contains the set of classical link diagrams. For an even virtual link diagram, we define a certain linking invariant which is similar to the linking number. In contrast to the usual linking number, our linking invariant is not preserved under the forbidden moves. In particular, for two fused isotopic even virtual link diagrams, the difference between the linking invariants of them gives a lower bound of the minimal number of forbidden moves needed to deform one into the other. Moreover, we give an example which shows that the lower bound is best possible.

Identification of effects of YOYO-1 intercalation on the topological states of circular DNA

2018 ◽  
Vol 32 (20) ◽  
pp. 1850231
Author(s):  
Xiuyan Li ◽  
Yangtao Fan ◽  
Qingqing Gao ◽  
Hu Chen ◽  
Yanhui Liu
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Persistence Length ◽  
Contour Length ◽  
Circular Dna ◽  
Linking Number ◽  
Number Distribution ◽  
Topological States

YOYO-1 intercalation leads to the reduction of twist rigidity, unwinding of DNA, elongation of DNA contour length and YOYO-1 concentration-dependent persistence length, until now few works identified their roles in determining the topological states of circular DNA. Based on the convolution of the writhe distribution of circular DNA obtained by using Monte Carlo simulation and the twist distribution, effects of YOYO-1 intercalation on the linking number distribution of circular DNA are predicted and identified. YOYO-1 intercalation leads to larger fluctuation, but not to the obvious enlargement of the writhe distribution, so that the variance of the linking number distribution mainly depends on the variance of the twist distribution. The unwinding angle contributes to the drifting of the linking number distribution away from the original equilibrium value of zero and has no effects on the variance of the linking number distribution, converse to the roles of the reduced twist rigidity in the linking number distribution. Furthermore, the method used in the work can be generalized to detect the effects of other intercalators on the topological states of circular DNA.

DNA topoisomerase I controls the kinetics of promoter activation and DNA topology in Saccharomyces cerevisiae

1993 ◽  
Vol 13 (11) ◽  
pp. 6702-6710
Author(s):  
E Di Mauro ◽  
G Camilloni ◽  
L Verdone ◽  
M Caserta
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Topoisomerase I ◽  
Glucose Repression ◽  
Dna Topology ◽  
Dna Topoisomerase I ◽  
Wild Type ◽  
Mrna Accumulation ◽  
Dna Topoisomerase ◽  
Linking Number

Inactivation of the nonessential TOP1 gene, which codes for Saccharomyces cerevisiae DNA topoisomerase I, affects the rate of transcription starting at the ADH2 promoter. For both the chromosomal gene and the plasmid-borne promoter, mRNA accumulation is kinetically favored in the mutant relative to a wild-type isogenic strain. The addition of ethanol causes in wild-type yeast strains a substantial increase in linking number both on the ADH2-containing plasmid and on the resident 2 microns DNA. Evidence has been obtained that such an in vivo increase in linking number depends on (i) the activity of DNA topoisomerase I and of no other enzyme and (ii) ethanol addition, not on the release from glucose repression. A direct cause-effect relationship between the change in supercoiling and alteration of transcription cannot be defined. However, the hypothesis that a metabolism-induced modification of DNA topology in a eukaryotic cell plays a role in regulating gene expression is discussed.

The Writhe of Knots in the Cubic Lattice

1997 ◽  
Vol 06 (01) ◽  
pp. 31-44 ◽  
Author(s):  
E. J. Janse Van Rensburg ◽  
E. Orlandini ◽  
D. W. Sumners ◽  
M. C. Tesi ◽  
S. G. Whittington
Keyword(s):  
Monte Carlo ◽  
Linear Function ◽  
Expected Value ◽  
Monte Carlo Algorithm ◽  
Connected Sum ◽  
Cubic Lattice ◽  
Linking Number ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
The Mean

The writhe of a knot in the simple cubic lattice [Formula: see text] can be computed as the average linking number of the knot with its pushoffs into four non-antipodal octants. We use a Monte Carlo algorithm to generate a sample of lattice knots of a specified knot type, and estimate the distribution of the writhe as a function of the length of the lattice knots. If the expected value of the writhe is not zero, then the knot is chiral. We prove that the writhe is additive under concatenation of lattice knots and observe that the mean writhe appears to be additive under the connected sum operation. In addition we observe that the mean writhe is a linear function of the crossing number in certain knot families.

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