REMARKS ON THE SPHERE OF INFLUENCE GRAPH

1985 ◽  
Vol 440 (1 Discrete Geom) ◽  
pp. 323-327 ◽  
Author(s):  
David Avis ◽  
Joe Horton
1999 ◽  
Vol 31 (3) ◽  
pp. 596-609 ◽  
Author(s):  
T. K. Chalker ◽  
A. P. Godbole ◽  
P. Hitczenko ◽  
J. Radcliff ◽  
O. G. Ruehr

We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point, Xi, draw an open ball (‘sphere of influence’) with radius equal to the distance to Xi's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.


1999 ◽  
Vol 31 (03) ◽  
pp. 596-609 ◽  
Author(s):  
T. K. Chalker ◽  
A. P. Godbole ◽  
P. Hitczenko ◽  
J. Radcliff ◽  
O. G. Ruehr

We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point, X i , draw an open ball (‘sphere of influence’) with radius equal to the distance to X i 's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.


2016 ◽  
Vol 21 (3) ◽  
pp. 206-217 ◽  
Author(s):  
Verónica Sevillano ◽  
Susan T. Fiske

Abstract. Nonhuman animals are typically excluded from the scope of social psychology. This article presents animals as social objects – targets of human social responses – overviewing the similarities and differences with human targets. The focus here is on perceiving animal species as social groups. Reflecting the two fundamental dimensions of humans’ social cognition – perceived warmth (benign or ill intent) and competence (high or low ability), proposed within the Stereotype Content Model ( Fiske, Cuddy, Glick, & Xu, 2002 ) – animal stereotypes are identified, together with associated prejudices and behavioral tendencies. In line with human intergroup threats, both realistic and symbolic threats associated with animals are reviewed. As a whole, animals appear to be social perception targets within the human sphere of influence and a valid topic for research.


1971 ◽  
Vol 16 (12) ◽  
pp. 780-781
Author(s):  
JEFFREY Z. RUBIN
Keyword(s):  

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