Example of Estimating the Boolean Function for a Gene Module
The state-count table for a set of three genes is used to create the 4 × 2 table shown on the right, known as a “Karnaugh map.” The binary coordinates in the rows and columns of Karnaugh maps are arranged according to the “Gray code” (consecutive coordinates differ by one bit only) for easier derivation of the logical function. Each entry of the Karnaugh map corresponds to one of the states and the numbers shown are equal to the counts N0 and N1 for that state. In this example, there are three entries (010, 110, 111) identified as predominantly associated with a particular disease. States 010 and 110 can be jointly described by the function bc′. Similarly, states 110 and 111 can be jointly described by the function ba. The overall Boolean function describing the area highlighted by bold lines in the Karnaugh map is bc′+ba = b(c′+a).
