The cut-off phenomenon for random reflections II: Complex and quaternionic cases

1996 ◽  
Vol 104 (2) ◽  
pp. 181-209
Author(s):  
U. Porod
Keyword(s):  
Random Reflections

Distributed temperature sensing with unmodified coaxial cable based on random reflections in TDR signal

2018 ◽  
Vol 30 (1) ◽  
pp. 015105
Author(s):  
Baokai Cheng ◽  
Liwei Hua ◽  
Wenge Zhu ◽  
Qi Zhang ◽  
Jincheng Lei ◽  
...  
Keyword(s):  
Temperature Sensing ◽  
Coaxial Cable ◽  
Distributed Temperature Sensing ◽  
Random Reflections

scholarly journals An ergodic algorithm for generating knots with a prescribed injectivity radius

2019 ◽  
Vol 28 (06) ◽  
pp. 1950045
Author(s):  
Kyle Leland Chapman
Keyword(s):  
Markov Chain ◽  
Lattice Model ◽  
Probability Distributions ◽  
Positive Probability ◽  
Bending Angle ◽  
Markov Chain Theory ◽  
Countable Space ◽  
Chain Theory ◽  
Random Reflections ◽  
Planar Polygon

The first provably ergodic algorithm for sampling the space of thick equilateral knots off-lattice, as a function of thickness, will be described. This algorithm is based on previous algorithms of applying random reflections. It is an off-lattice generalization of the pivot algorithm. This move to an off-lattice model provides a huge improvement in power and efficacy in that samples can have arbitrary values for parameters such as the thickness constraint, bending angle, and torsion, while the lattice forces these parameters into a small number of specific values. This benefit requires working in a manifold rather than a finite or countable space, which forces the use of more novel methods in Markov–Chain theory. To prove the validity of the algorithm, we describe a method for turning any knot into the regular planar polygon using only thickness non-decreasing moves. This approach ensures that the algorithm has a positive probability of connecting any two knots with the required thickness constraint which is used to show that the algorithm is ergodic. This ergodic sampling allows for a statistically valid method for estimating probability distributions of arbitrary functions on the space of thick knots.

Sign in / Sign up

Export Citation Format

Share Document