scholarly journals SIMULATION OF TWO AND THREE DIMENSIONAL RING POLYMERS USING CLOSED GAUSSIAN RANDOM WALKS

1994 ◽  
Vol 43 (10) ◽  
pp. 1580
Author(s):  
PENG JING-CUI
Keyword(s):  
Random Walks ◽  
Three Dimensional ◽  
Ring Polymers

Scaling in three‐dimensional linear and ring polymers

1986 ◽  
Vol 84 (1) ◽  
pp. 444-446 ◽  
Author(s):  
Marvin Bishop ◽  
J. P. J. Michels
Keyword(s):  
Three Dimensional ◽  
Ring Polymers

Return probabilities for certain three-dimensional random walks

1979 ◽  
Vol 16 (01) ◽  
pp. 45-53 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Random Walks ◽  
Three Dimensional ◽  
Cubic Lattice ◽  
Starting Point

For some three-dimensional random walks on the cubic lattice, the probability of the walk returning to its starting point is given numerically.

Return probabilities for certain three-dimensional random walks

1979 ◽  
Vol 16 (1) ◽  
pp. 45-53 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Random Walks ◽  
Three Dimensional ◽  
Cubic Lattice ◽  
Starting Point

For some three-dimensional random walks on the cubic lattice, the probability of the walk returning to its starting point is given numerically.

scholarly journals Resolving critical degrees of entanglement in Olympic ring systems

2016 ◽  
Vol 25 (14) ◽  
pp. 1650081 ◽  
Author(s):  
Spencer Igram ◽  
Kenneth C. Millett ◽  
Eleni Panagiotou
Keyword(s):  
Large Scale ◽  
Periodic Boundary ◽  
Three Dimensional ◽  
Small Ring ◽  
Kinetoplast Dna ◽  
Circular Dna ◽  
Linking Number ◽  
Ring Polymers ◽  
Condition Systems ◽  
Insight Into

Olympic systems are collections of small ring polymers whose aggregate properties are largely characterized by the extent (or absence) of topological linking in contrast with the topological entanglement arising from physical movement constraints associated with excluded volume contacts or arising from chemical bonds. First, discussed by de Gennes, they have been of interest ever since due to their particular properties and their occurrence in natural organisms, for example, as intermediates in the replication of circular DNA in the mitochondria of malignant cells or in the kinetoplast DNA networks of trypanosomes. Here, we study systems that have an intrinsic one, two, or three-dimensional character and consist of large collections of ring polymers modeled using periodic boundary conditions. We identify and discuss the evolution of the dimensional character of the large scale topological linking as a function of density. We identify the critical densities at which infinite linked subsystems, the onset of percolation, arise in the periodic boundary condition systems. These provide insight into the nature of entanglement occurring in such course grained models. This entanglement is measured using Gauss linking number, a measure well adapted to such models. We show that, with increasing density, the topological entanglement of these systems increases in complexity, dimension, and probability.

scholarly journals GenomeDISCO: A concordance score for chromosome conformation capture experiments using random walks on contact map graphs

2017 ◽  
Author(s):  
Oana Ursu ◽  
Nathan Boley ◽  
Maryna Taranova ◽  
Y.X. Rachel Wang ◽  
Galip Gurkan Yardimci ◽  
...  
Keyword(s):  
Random Walks ◽  
Critical Role ◽  
Three Dimensional ◽  
Cell Types ◽  
Chromosome Conformation Capture ◽  
Supplementary Information ◽  
Contact Map ◽  
Chromosome Conformation ◽  
Contact Maps ◽  
Map Graphs

AbstractMotivationThe three-dimensional organization of chromatin plays a critical role in gene regulation and disease. High-throughput chromosome conformation capture experiments such as Hi-C are used to obtain genome-wide maps of 3D chromatin contacts. However, robust estimation of data quality and systematic comparison of these contact maps is challenging due to the multi-scale, hierarchical structure of chromatin contacts and the resulting properties of experimental noise in the data. Measuring concordance of contact maps is important for assessing reproducibility of replicate experiments and for modeling variation between different cellular contexts.ResultsWe introduce a concordance measure called GenomeDISCO (DIfferences between Smoothed COntact maps) for assessing the similarity of a pair of contact maps obtained from chromosome conformation capture experiments. The key idea is to smooth contact maps using random walks on the contact map graph, before estimating concordance. We use simulated datasets to benchmark GenomeDISCO’s sensitivity to different types of noise that affect chromatin contact maps. When applied to a large collection of Hi-C datasets, GenomeDISCO accurately distinguishes biological replicates from samples obtained from different cell types. GenomeDISCO also generalizes to other chromosome conformation capture assays, such as HiChIP.AvailabilitySoftware implementing GenomeDISCO is available at https://github.com/kundajelab/[email protected] informationSupplementary data are available at Bioinformatics online.

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