START: a system for flexible analysis of hundreds of genomic signal tracks in few lines of SQL-like queries

BMC Genomics

Table 2 The full list of mathematical operations defined for STQL operations that create intervals

STQL operation	Coalesce, discretize	Intersectjoin	Exclusivejoin
	or project on
Values involved	v ₁...v _n	v ₁, v ₂	v ₁
vd_sum	\(\sum _{i=1}^{n} v_{i}\)	v ₁+v ₂	N/A
vd_avg	\(\frac {\sum _{i=1}^{n} v_{i}}{n}\)	(v ₁+v ₂)/2	N/A
vd_diff	N/A	v ₁−v ₂	N/A
vd_product	\(\prod _{i=1}^{n} v_{i}\)	v ₁×v ₂	N/A
vd_quotient	N/A	v ₁÷v ₂	N/A
vd_max	\(\max _{i=1}^{n} v_{i}\)	max(v ₁,v ₂)	N/A
vd_min	\(\min _{i=1}^{n} v_{i}\)	min(v ₁,v ₂)	N/A
vd_left	N/A	v ₁	v ₁
vd_right	N/A	v ₂	N/A

Starting from the third row, the first column shows the names of these mathematical operations that can be used in the <vd > placeholders in statements involving coalesce, discretize, project, intersectjoin and exclusivejoin. These mathematical operations are used in Step 2 of value derivation. The second row defines the values involved in the operations. In the case of intersectjoin, exactly two values are involved, namely v ₁ from the first track and v ₂ from the second track. In the case of exclusivejoin, exactly one value is involved, namely v ₁ from the first track. In the case of coalesce, discretize and project, all values come from the same track and there can be one or more values involved. N/A indicates mathematical operators that cannot be used with the STQL operations

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