Table 1.

Some Mathematical Symbols Used in the CRF Models

Symbols	Annotations
X	The PSIPRED-predicted secondary structure likelihood scores. A matrix with 3×N elements where N is the number of residues in a protein.
Xi	The predicted likelihood of three secondary structure types at position i. It is a vector of three values, indicating the likelihood of helix, beta and loop, respectively.
Xi(x)	The predicted likelihood of secondary structure type x at position i.
M	The position-specific frequency matrix with 20×N entries, each being the occurring frequency of one amino acid at a given position.
Mi	A vector of 20 elements, denoting the occurring frequency of 20 amino acids at position i.
Mi(aa)	The occurring frequency of amino acid aa at position i.
H	, the set of 100 backbone angle states, each representing an FB5 distribution (see Methods for its detailed description).