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Lemma 23 (Nonnegative rank to Approximate Conical Juntas) There exists a constant 1 > 1 such that the following holds For b > 1 logn, every function f f1;1gn!R >0 with Ef = 1 is a (2b=2;2bd= 1)approximate conical djunta for all d > 1(logrank (Mb f))=b We defer the sketch of the proof of the lemma to the next section and continue with our outline. O i q u q q r p i r u ¥ ² Þ Ô å Éß Ý) * o s x n n Í o s x q n o s x q n Í o v x n n o v x n n Í o v x q n !. } Q ~ á } 7 Q y 5 x 6 å ~ ^ ï _ â ð ã z y 7 6 ï 5 ã z x Q æ };.
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