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. Author manuscript; available in PMC: 2011 Sep 1.
Published in final edited form as: J Biomed Sci Eng. 2010 Sep 1;3:848–860. doi: 10.4236/jbise.2010.39115
Relations Sign equation
X and Y are independent, if
FX,Y=0
(x,y) (equation 19.1)
Instantaneous causality only without direction, if
FX,Y0,FYX=0,FXY=0
(x–y) (equation 19.2)
X causes Y, with instantaneous causality, if
FX,Y0,FYX=0,FXY0
(x→y) (equation 19.3)
X causes Y, without instantaneous causality, if
FX,Y=0,FYX=0,FXY0
(x=>y) (equation 19.4)
Y causes X, with instantaneous causality, if
FX,Y0,FYX0,FXY=0
(x←y) (equation 19.5)
Y causes X, without instantaneous causality, if
FX,Y=0,FYX0,FXY=0
(x<=y) (equation 19.6)
Feedback with instantaneous causality, if
FX,Y0,FYX0,FXY0
(x↔y) (equation 19.7)
Feedback without instantaneous causality
FX,Y=0,FYX0,FXY0
(x⇔y) (equation 19.8)