Actually, Ca supply in LLL, LHL, LLH, and cLLL treatments was same during first week.
# HI HII Ca Al Ca Al LLL 927 [+ or -] 35 ND 127 [+ or -] 16 5134 [+ or -] 387 HLL 2915 [+ or -] 275 ND 305 [+ or -] 22 3883 [+ or -] 122 LHL 927 [+ or -] 27 ND 515 [+ or -] 31 3415 [+ or -] 272 LLH 935 [+ or -] 25 ND 132 [+ or -] 12 5101 [+ or -] 402 cLLL 942 [+ or -] 23 ND 1245 [+ or -] 98 ND # HIII Ca Al LLL 159 [+ or -] 22 4325 [+ or -] 503 HLL 387 [+ or -] 51 2552 [+ or -] 202 LHL 649 [+ or -] 105 2347 [+ or -] 131 LLH 193 [+ or -] 21 4061 [+ or -] 263 cLLL 1727 [+ or -] 235 ND # Treatment condition: 3 letters indicate 3 weeks.
At the RS, we use the CLLL algorithm, which is a suboptimum solution of the shortest vector problem with a polynomial-time computational complexity , to reduce the lattice basis of and obtain H = U, where is the right pseudoinverse of [H.sub.MR] (i.e., [H.sup.[dagger].sub.MR] = [H.sup.H.sub.MR] [([H.sub.MR][H.sup.H.sub.MR]).sup.-1]; U = [[[u.sub.i,j]].sub.1[less than or equal to]t[less than or equal to]k,1[less than or equal to]j[less than or equal to]k] is a Kx K unimodular matrix, i.e., a square matrix with Gaussian integer entries, such that det(U) = [+ or -]1).
The average complexity of the CLLL reduction algorithm is correlated to the distribution of the random basis matrix.
The CLLL algorithm is utilized and its reduction parameter is set to 0.75, which is a factor selected to yield a good quality-complexity tradeoff.