Further analysis on graph rigidity

2016 ◽  
Author(s):  
Minh Hoang Trinh ◽  
Myoung-Chul Park ◽  
Zhiyong Sun ◽  
Brian. D. O. Anderson ◽  
Viet Hoang Pham ◽  
...  
Keyword(s):  
Graph Rigidity

scholarly journals Graph Rigidity Application for Localization in WSN

2012 ◽  
Vol 49 (9) ◽  
pp. 15-21 ◽  
Author(s):  
Shamantha Rai.B ◽  
Shirshu Varma
Keyword(s):  
Graph Rigidity

The loss of tension in an infinite membrane with holes distributed according to a Poisson law

2002 ◽  
Vol 34 (02) ◽  
pp. 292-312 ◽  
Author(s):  
M. V. Menshikov ◽  
K. A. Rybnikov ◽  
S. E. Volkov
Keyword(s):  
Probabilistic Model ◽  
Mathematical Theory ◽  
Natural Sciences ◽  
Rigidity Theory ◽  
Graph Rigidity ◽  
Poisson Law ◽  
Rigidity Percolation

What is the effect of punching holes at random in an infinite tensed membrane? When will the membrane still support tension? This problem was introduced by Connelly in connection with applications of rigidity theory to natural sciences. The answer clearly depends on the shapes and the distribution of the holes. We briefly outline a mathematical theory of tension based on graph rigidity theory and introduce a probabilistic model for this problem. We show that if the centers of the holes are distributed in ℝ2 according to a Poisson law with density λ > 0, and the shapes are i.i.d. and independent of the locations of their centers, the tension is lost on all of ℝ2 for any λ. After introducing a certain step-by-step dynamic for the loss of tension, we establish the existence of a nonrandom N = N(λ) such that N steps are almost surely enough for the loss of tension. Also, we prove that N(λ) > 2 almost surely for sufficiently small λ. The processes described in the paper are related to bootstrap and rigidity percolation.

scholarly journals Spectral conditions for graph rigidity in the Euclidean plane

2021 ◽  
Vol 344 (10) ◽  
pp. 112527
Author(s):  
Sebastian M. Cioabă ◽  
Sean Dewar ◽  
Xiaofeng Gu
Keyword(s):  
Euclidean Plane ◽  
Graph Rigidity

scholarly journals Atlasing of Assembly Landscapes using Distance Geometry and Graph Rigidity

2020 ◽  
Vol 60 (10) ◽  
pp. 4924-4957
Author(s):  
Rahul Prabhu ◽  
Meera Sitharam ◽  
Aysegul Ozkan ◽  
Ruijin Wu
Keyword(s):  
Distance Geometry ◽  
Graph Rigidity
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