Be Aware Of ErbB Problems Plus Methods To Identify It

(21) The distribution function for tijr is the shifted Heaviside function hijr (t) = h(t ? tijr), The conditional interaction contrast cr(t) is defined by (13). For the observable (i.e., estimable from data) interaction contrast C(t)=H11(t)?H12(t)?H21(t)+H22(t), (24) we have then C(t)=��?cr(t)d��r. (25) Note that it follows from our Prolongation Assumption that H11(t)��H12(t),?H21(t)��H22(t),H11(t)��H21(t),?H12(t)��H22(t). (26) We also define two conditional cumulative interaction contrasts (conditioned on R = r): c(0,t)=��0tc(��)d��. (27) c(t,��)=��t��c(��)d��=limu���ޡ�tuc(��)d��. (28) The corresponding observable cumulative interaction contrasts are C(0,t)=��?c(0,t)d��r=��?(��0tc(��)d��)d��r???????????????=��0t(��?c(��)d��r)d��=��0tC(��)d��. (29) C(t,��)=��?c(t,��)d��r=��?(��t��c(��)d��)d��r????????????????=��t��(��?c(��)d��r)d��=��t��C(��)d��. (30) In these formulas we could switch the order of integration by Fubini's theorem, because, for any interval of reals I, ��I��?|c(��)|d(�ӡ���r)�ܡ�I��?2d(�ӡ���r)��2. (31) 2.1. Four GSK J4 molecular weight Lemmas Recall the definition of cr(t) in (13). We follow our Notation Convention and drop the index r in cr(t) and all other expressions for a fixed r. Lemma 2.1. In any SP architecture, for any r, t11��t12��t21��t12��t21��t22. Proof. Follows from the (nonstrict) monotonicity of the SP composition in all arguments. ??????????�� Lemma 2.2. In any SP architecture, for any r, c(t) equals 0 for all values of t except for two cases: (Case+)if?t11��t0, and (Case?)if?t12��t21��t