International Scholarly Research Notices

Research Article

Nonlinear Dependence in the Discovery of Differentially Expressed Genes

Table 1

Notation used for elementary scalar quantities. 𝑣 , 𝑣 1 , and 𝑣 2 are RVs and ℰ denotes the expectation.
Mean, average 𝜇 𝑥 o r 𝜇 ( 𝑥 ) = ℰ { 𝑥 } Standard deviation 𝜎 𝑣 d e f = ℰ { ( 𝑣 − 𝜇 𝑣 ) 2 √ } = 𝜑 ( 𝑣 , 𝑣 )
Covariance 𝜑 ( 𝑣 1 , 𝑣 2 ) d e f = ℰ { ( 𝑣 1 − 𝜇 𝑣 1 ) ( 𝑣 2 − 𝜇 𝑣 2 ) } Variance 𝜎 2 𝑣 d e f = ℰ { ( 𝑣 − 𝜇 𝑣 ) 2 } = 𝜑 ( 𝑣 , 𝑣 )
Correlation ℰ { 𝑣 1 , 𝑣 2 } d e f = 𝜑 ( 𝑣 1 , 𝑣 2 ) + 𝜇 𝑣 1 𝜇 𝑣 2 (no special symbol reserved) Correlation coefficient 𝜌 ( 𝑣 1 , 𝑣 2 ) d e f = 𝜑 ( 𝑣 1 , 𝑣 2 ) 𝜎 𝑣 1 𝜎 𝑣 2 ( n o r m a l i z e d c o v a r i a n c e )