RLAC: Random Line Approximation Clustering

Author(s):  
Petros Barbas ◽  
Aristidis G. Vrahatis ◽  
Sotiris K. Tasoulis
Keyword(s):  
1975 ◽  
Vol 12 (S1) ◽  
pp. 303-309
Author(s):  
Herbert Solomon

The trajectory of a car traveling at a constant speed on an idealized infinite highway can be viewed as a straight line in the time-space plane. Entry times are governed by a Poisson process with intensity parameter A leading to all trajectories as random lines in a plane. The Poisson distribution of number of encounters of cars on the highway is developed through random line models and non-homogeneous Poisson fields, and its parameter, which depends on the specific random measure employed, is obtained explicitly.


Nature ◽  
1982 ◽  
Vol 300 (5890) ◽  
pp. 347-349 ◽  
Author(s):  
H. K. Nishihara ◽  
T. Poggio
Keyword(s):  

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Lucas Böttcher

Abstract We study graphs that are formed by independently positioned needles (i.e. line segments) in the unit square. To mathematically characterize the graph structure, we derive the probability that two line segments intersect and determine related quantities such as the distribution of intersections, given a certain number of line segments $N$. We interpret intersections between line segments as nodes and connections between them as edges in a spatial network that we refer to as random-line graph (RLG). Using methods from the study of random-geometric graphs, we show that the probability of RLGs to be connected undergoes a sharp transition if the number of lines exceeds a threshold $N^*$.


1982 ◽  
Vol 72 (1) ◽  
pp. 162-170 ◽  
Author(s):  
J. C. Lockwood ◽  
J. V. Thorn ◽  
N. O. Booth
Keyword(s):  

2012 ◽  
Vol 93 (1-2) ◽  
pp. 91-100
Author(s):  
MICHEL MENDÈS FRANCE ◽  
TADASHI TOKIEDA
Keyword(s):  

AbstractWe introduce the entropy of a family of planar curves in terms of the number of intersections of the family with a random line, calculate it for key examples, and discuss the entropy of a pattern of rings produced by an impulse on the surface of still water.


1969 ◽  
Vol 45 (1) ◽  
pp. 239-241
Author(s):  
S. Gardner ◽  
O. Lindemann

Author(s):  
Petroc Sumner

Abstract. Under certain conditions, masked primes have produced counter-intuitive negative compatibility effects (NCE), such that RT is increased, not decreased, when the target is similar to the prime. This NCE has been interpreted as an index of automatic motor inhibition, triggered to suppress the partial motor activation caused by the prime. An alternative explanation is that perceptual interactions between prime and mask produce positive priming in the opposite direction to the prime, explaining the NCE without postulating inhibition. Here the potential role of this “mask-induced priming” was investigated in two experiments, using masks composed of random lines. Experiment 1 compared masks that included features of the primes and targets with masks that did not. The former should create more mask-induced priming, but the NCE did not differ between masks. Experiment 2 employed masks that contained features of either one target or the other, but not both. These asymmetric masks produced significant mask-induced priming, but it was insufficient in size to account for the prime-related NCE. Thus mask composition can contribute to NCEs, but when random line masks are employed, the major source of the NCE seems to be motor-inhibition.


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