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By Sren Baldi Pierre;Brunak

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In general, the above algorithm can be applied to input data for N genes and A attractor states. The total number of attractor state orderings is A!. For each ordering, there can be up to O(N 3 ) predictors per gene. 2N ). Typically, the number of attractor states A recorded through gene expression measurements 3 is small. As such, A! is thus much smaller than 2(N ) , so the runtime complexity is dominated by the All-SAT operation. 5 Experimental Results To evaluate our SAT-based algorithm for inferring gene predictors, the algorithm was tested on gene-expression data from a melanoma study done by Bittner and Weeraratna [3].

All satisfying cubes are recorded, where each satisfying cube corresponds to a predictor set. The first two steps are repeated for all attractor cycle orderings. 3. Predictor Set Selection: Statistical analysis on the All-SAT results determines the most frequent (likely) predictor set for the GRN. This step is explained in Sect. 5. To illustrate the SAT-based algorithm, we apply it to a simple example with three genes (g1 , g2 , g3 ) and gene expression data with three lines (010, 110, 111). The present state of these genes is represented by the variables < x1 , x2 , x3 > and the next state is represented by the variables < y1 , y2 , y3 >.

We first define basic terms in Boolean satisfiability. 12: Boolean satisfiability (SAT). Given a Boolean formula S (on a set of binary variables X) expressed in CNF, the objective of SAT is to identify an assignment of the binary variables in X that satisfies S, if such an assignment exists. If no such assignment exists, S is concluded to be unsatisfiable (UNSAT). e. make it evaluate to true), each clause of S must have at least one literal evaluate to true. Satisfying S is equivalent to satisfying all ci ∈ S.

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Bioinformatics The Machine Learning Approach by Sren Baldi Pierre;Brunak

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