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removedGRAPHIC 2 K (2 K - l 2)>1 (2 K - l^2>0
constraint 2 K (1- θ)- l^2>0 should hold if (p θ ,2, e θ ,2
alpha=1 + alpha + alpha gamma delta 1=64 K 2 gamma 2 + l 4 (ξ b + 3 gamma) 2 -8 K gamma l 2 (ξ b + 6 gamma)>0 delta 2=64 K 2 gamma 2 + l 4 (ξ alpha + 3 gamma) 2 -8 K gamma l 2 (ξ alpha + 6 gamma)>0
tau=b<disp formula id="pone.0204482.e205">removedGRAPHIC F 1 tau=(1 - tau - tau gamma + 3 gamma) 3 l 8 4096 + (1 - tau - tau gamma + 3 gamma) (1 - tau - tau gamma) 2 K l 6 2048 -3 gamma (1 - tau - tau gamma) 2 K 2 l 6 512 - K 3 gamma 3 (K - l 2 2) F 2 tau=1 32 l 4 (1 - tau - tau gamma + 3 gamma) 2 - gamma (K -1 4 l 2) (1 - tau - tau gamma + 2 gamma) L 1 tau=(1 - tau - tau gamma + 3 gamma) 2 l 6 4096 - (1 + gamma) 2 tau 2 + 2
gamma -1 -12 gamma 2 -2 gamma + 1 2048 - gamma 2 K 2 (16 K + (1 - tau - tau gamma -2 gamma) l 2) 128 L 2 tau=1 32 l 2 (1 - tau - tau gamma + 3 gamma) -1 8 K (1 - tau - tau gamma + 2
removedGRAPHIC w=w ~ 1 (θ) can be reduced-<disp formula id="pone.0204482.e207">removedGRAPHIC Π θ, 1 m (w ¯ θ, 1, θ ¯ 1)=2 (1
c 2 - F 1 tau + L 1 tau delta 1 (F 2 tau + L 2 tau delta 1) 2 s. t. { { b>1 -2 gamma 1 + gamma -3
removedGRAPHIC 0<b<=1 -2 gamma 1 + gamma ⇒ 0<gamma<1 2
c 2 - F 1 tau + L 1 tau delta 1 (F 2 tau + L 2 tau delta 1) 2 if { { b>1 -2 gamma 1 + gamma -3
c 2 - F 1 tau + L 1 tau delta (F 2 tau + L 2 tau delta) 2 s. t. { { alpha>2 gamma -1 1 + gamma + 3
removedGRAPHIC 2 gamma -1 1 + gamma<2 gamma -1 1 + gamma + 3
alpha gamma (2 K - l 2) s. t. { 0<alpha<=2 gamma -1 1 + gamma } ∩ { 4 K<=3 l 2
removedGRAPHIC { 0<alpha<=2 gamma -1 1 + gamma } ∩ { 4 K<=3 l 2
l 2 } ∩ { alpha<=2 gamma -1 1 + gamma + 3
l 2 } ∩ { alpha>2 gamma -1 1 + gamma + 3
pone.0204482.e292">removedGRAPHIC { e θ, 1 r=6
1 r<U 1 r if 0<b<b ¯ r, 1 U θ, 1 r<U 1 r if b ¯ r, 1<=b<1 -2 gamma 1
r<Π 1 r if 0<b<b ¯ r, 2 Π θ, 1 r<Π 1 r if b ¯ r, 2<=b<1 -2 gamma 1
l 2 } } ∪ { { 4 K<=3 l 2 } ∩ { { gamma<gamma ¯ } ∪ { { gamma<gamma ¯ } ∩ { alpha>alpha ¯ 3 } } } } Π θ, 3 r<Π 3
l 2 } } ∪ { { 4 K<=3 l 2 } ∩ { { gamma<gamma ¯ } ∪ { { gamma<gamma ¯ } ∩ { alpha>alpha ¯ 3 } } } } U θ, 2 r<U 2
pone.0204482.e310">removedGRAPHIC { Π 1 c=3
pone.0204482.e311">removedGRAPHIC { Π θ, 1 c=6
1, θ ¯ 1)=1 + gamma gamma - Π θ, 1 r(w ¯ θ, 1, θ ¯ 1)=1 + gamma gamma - U θ, 1 r(w ¯ θ, 1, θ ¯ 1
removedGRAPHIC 3 gamma 1 + gamma - (1 - b)<0