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Additional file 1: Supplementary Methods. Bisulfite treatment, array hybridization, and scanning for DNA Methylation Profiling. Fig. S1. A flow diagram of the study population. Fig. S2. Q-Q plot showing the distribution of the observed versus expected association p-values. Fig. S3. Manhattan plot showing the treatment-specific association of DNA methylation. Fig. S4. The distributions of whole-array and significant treatment-associated CpG sites. Fig. S5. The distribution of beta-values for CpG mediators by groups of CHCs. Table S1. Pairwise correlations among eleven different treatments. Table S2. CpG hits associated with the specific treatment exposure (P

A characterization theorem is proved for a family of non-negative integer valued random variables. The result is based on an inequality of the type proved by Chernoff (1981). Applications of the result for various standard distributions are also discussed.