In breast cancer stem cells, GW6471 (a PPARα antagonist) is anti-proliferative and pro-apoptotic, while Wy14643 (a PPARα agonist) induces the clonal expansion of breast cancer mammospheres by promoting the signaling activities of the nuclear receptor κB (NF-κB)/ interleukin-6 (IL-6) axis, SLUG, Notch3, and Jagged 1 [16,17]. This evidence concerns the gene NFKB1 and breast carcinoma.