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Mariko I. Ito, Hisashi Ohtsuki, Akira Sasaki
Emergence of opinion leaders in reference networks
www.plosone.org
www.plosone.org
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[()]TJ
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[()]TJ
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228.5875 228.2241 l
228.5875 228.7242 l
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228.0875 215.7242 l
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228.0875 203.2243 l
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228.0875 203.7243 l
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228.0875 189.6806 l
228.0875 203.2243 l
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228.5875 190.1806 l
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228.0875 176.1369 l
228.0875 189.6806 l
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228.5875 176.1369 l
228.5875 176.637 l
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228.5875 163.3635 l
228.0875 163.3635 l
228.0875 176.1369 l
f*
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200.0001 163.8635 l
228.0875 163.8635 l
f*
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228.5875 163.3635 l
228.5875 163.8635 l
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228.5875 163.3635 m
228.5875 150.8635 l
228.0875 150.8635 l
228.0875 163.3635 l
f*
228.0875 150.8635 m
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200.0001 151.3636 l
228.0875 151.3636 l
f*
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228.5875 151.3636 l
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f*
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228.0875 128.8636 l
228.0875 150.8635 l
f*
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f*
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228.5875 128.8636 l
228.5875 129.3636 l
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228.0875 115.3996 l
228.0875 128.8636 l
f*
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200.0001 115.8996 l
228.0875 115.8996 l
f*
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228.5875 115.3996 l
228.5875 115.8996 l
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228.0875 101.6529 l
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f*
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1 J
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10 0 0 10 435.2314 615.0614 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4478 0 Td
(is)Tj
0.8447 0 Td
(updated)Tj
3.4753 0 Td
(as)Tj
1.0148 0 Td
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3.2882 0 Td
(When)Tj
2.6815 0 Td
(agent)Tj
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-35.274 -1.4286 Td
[()]TJ
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0.4876 0 Td
(newly)Tj
2.5738 0 Td
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3.5376 0 Td
(referent)Tj
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3.3676 0 Td
[()]TJ
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0.4762 0 Td
(at)Tj
0.9524 0 Td
(time)Tj
/F10 1 Tf
2.0296 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 337.2094 599.1307 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 339.7039 600.7748 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4422 0 Td
(his/her)Tj
3.033 0 Td
(initial)Tj
2.5455 0 Td
(level)Tj
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(of)Tj
1.0148 0 Td
(estimated)Tj
4.0762 0 Td
(performance,)Tj
/F10 1 Tf
0 Tc
5.5729 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 531.2692 605.707 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()12()]TJ
-0.0377 -1.096 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 532.8566 597.6 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 535.5212 600.7748 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4478 0 Td
(is)Tj
0.8447 0 Td
(set)Tj
1.304 0 Td
(to)Tj
/F10 1 Tf
-36.1471 -1.5023 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 204.3212 584.107 cm
BT
/F5 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 210.1039 585.7511 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(for)Tj
1.3832 0 Td
(any)Tj
1.6611 0 Td
(pair)Tj
1.8085 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F5 1 Tf
0.4876 0 Td
(and)Tj
/F10 1 Tf
1.7291 0 Td
[()]TJ
/F5 1 Tf
(.)Tj
0.703 0 Td
(Let)Tj
/F10 1 Tf
0 Tc
1.4797 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 316.6299 590.6834 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
-0.085 -1.096 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 320.8818 585.7511 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(be)Tj
1.1508 0 Td
(a)Tj
0.652 0 Td
(variable)Tj
3.3618 0 Td
(whose)Tj
2.7213 0 Td
(value)Tj
2.3074 0 Td
(of)Tj
1.0148 0 Td
(0)Tj
0.6916 0 Td
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4.32 0 Td
(the)Tj
1.4683 0 Td
(failure)Tj
2.778 0 Td
(of)Tj
1.0148 0 Td
(agent)Tj
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2.3924 0 Td
[()]TJ
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0.4762 0 Td
(to)Tj
-36.4362 -1.2982 Td
(give)Tj
1.8312 0 Td
(a)Tj
0.6519 0 Td
(correct)Tj
3.0388 0 Td
(answer,)Tj
3.2654 0 Td
(and)Tj
1.7348 0 Td
(a)Tj
0.652 0 Td
(value)Tj
2.3073 0 Td
(of)Tj
1.0148 0 Td
(1)Tj
0.6916 0 Td
(represents)Tj
4.32 0 Td
(the)Tj
1.474 0 Td
(agent's)Tj
2.965 0 Td
(success)Tj
3.1011 0 Td
(at)Tj
0.9525 0 Td
(the)Tj
1.4683 0 Td
(iteration)Tj
3.634 0 Td
(time)Tj
/F10 1 Tf
2.0296 0 Td
[()]TJ
/F5 1 Tf
(.)Tj
0.7426 0 Td
(We)Tj
-35.8749 -1.4343 Td
(assume)Tj
3.1464 0 Td
(that)Tj
1.7802 0 Td
(the)Tj
1.4683 0 Td
(evaluated)Tj
3.9855 0 Td
(performance)Tj
5.3517 0 Td
(of)Tj
1.0148 0 Td
(agent)Tj
/F10 1 Tf
2.3867 0 Td
[()]TJ
/F5 1 Tf
0.4763 0 Td
(by)Tj
1.1848 0 Td
(agent)Tj
/F10 1 Tf
2.3868 0 Td
[()]TJ
/F5 1 Tf
0.4875 0 Td
(at)Tj
0.9525 0 Td
(iteration)Tj
3.634 0 Td
(time)Tj
/F10 1 Tf
2.0296 0 Td
[()]TJ
/F5 1 Tf
(,)Tj
/F10 1 Tf
0 Tc
0.7426 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 514.885 563.3574 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()12()]TJ
-0.0283 -1.096 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 518.5133 558.4251 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4478 0 Td
(is)Tj
0.8504 0 Td
(updated)Tj
-33.148 -1.2982 Td
(recursively)Tj
4.541 0 Td
(by)Tj
/F10 1 Tf
0 Tc
9.0425 -1.9842 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 340.4409 530.5889 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()12()]TJ
-0.0283 -1.1055 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 346.9039 525.6 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
1.0488 0 Td
()Tj
/F16 1 Tf
(1)Tj
/F15 1 Tf
1.1055 0 Td
( )Tj
/F19 1 Tf
0.9921 0 Td
(a)Tj
/F15 1 Tf
()Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 391.8614 530.5889 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()12()]TJ
-0.0377 -1.1811 Td
[()]TJ
/F15 1 Tf
0.34 0 Td
( )Tj
/F16 1 Tf
0.7748 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 404.0503 525.6 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F19 1 Tf
0.9921 0 Td
(a)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 422.8157 530.5889 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
-0.085 -1.1055 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 424.9133 525.6 cm
BT
/F20 1 Tf
1 TL
0 0 Td
(:)Tj
/F15 1 Tf
13.8556 0.068 Td
()Tj
/F5 1 Tf
(1)Tj
/F15 1 Tf
()Tj
/F5 1 Tf
-0.004 Tc
-36.3455 -2.2166 Td
(Here,)Tj
/F18 1 Tf
2.4321 0 Td
()Tj
/F5 1 Tf
0.7654 0 Td
(describes)Tj
3.8891 0 Td
(the)Tj
1.4683 0 Td
(extent)Tj
2.6759 0 Td
(to)Tj
1.0261 0 Td
(which)Tj
2.6476 0 Td
(people)Tj
2.8573 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(society)Tj
2.9536 0 Td
(attach)Tj
2.6362 0 Td
(importance)Tj
4.8302 0 Td
(to)Tj
1.0261 0 Td
(the)Tj
1.4684 0 Td
(current)Tj
-33.1821 -1.2983 Td
(result)Tj
2.4491 0 Td
(as)Tj
1.0148 0 Td
(compared)Tj
4.2406 0 Td
(to)Tj
1.0262 0 Td
(the)Tj
1.4683 0 Td
(referent's)Tj
3.9458 0 Td
(past.)Tj
2.0579 0 Td
(We)Tj
1.6044 0 Td
(also)Tj
1.7689 0 Td
(assume)Tj
3.1463 0 Td
(that)Tj
1.7801 0 Td
(all)Tj
1.1452 0 Td
(agents)Tj
2.7496 0 Td
(adopt)Tj
2.5058 0 Td
(the)Tj
1.4684 0 Td
(same)Tj
2.262 0 Td
(rewir-)Tj
-34.6334 -1.2982 Td
(ing)Tj
1.5024 0 Td
(threshold)Tj
4.0081 0 Td
(to)Tj
1.0262 0 Td
(kick-off)Tj
3.3335 0 Td
(referents,)Tj
/F10 1 Tf
3.9571 0 Td
[()]TJ
/F5 1 Tf
(.)Tj
0.9128 0 Td
(The)Tj
1.7801 0 Td
(threshold)Tj
4.0082 0 Td
(represents)Tj
4.3199 0 Td
(severity)Tj
3.2768 0 Td
(of)Tj
1.0148 0 Td
(assessment)Tj
4.6091 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
-34.7865 -1.3039 Td
(society.)Tj
3.1805 0 Td
(For)Tj
1.627 0 Td
(example,)Tj
3.7701 0 Td
(if)Tj
0.7767 0 Td
(the)Tj
1.4683 0 Td
(threshold)Tj
4.0139 0 Td
(is)Tj
0.8447 0 Td
(low,)Tj
1.8822 0 Td
(people)Tj
2.8573 0 Td
(in)Tj
1.0374 0 Td
(the)Tj
1.4683 0 Td
(society)Tj
2.9537 0 Td
(are)Tj
1.4513 0 Td
(generous)Tj
3.8437 0 Td
(when)Tj
2.4038 0 Td
(they)Tj
1.9276 0 Td
(eval-)Tj
-35.5065 -1.2983 Td
(uate)Tj
1.9049 0 Td
(their)Tj
2.1033 0 Td
(referents.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 413.9149 cm
BT
/F11 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(2.2)Tj
1.4598 0 Td
(Simulation)Tj
4.8378 0 Td
(conditions)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 396.907 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(We)Tj
1.61 0 Td
(conducted)Tj
4.4277 0 Td
(agent-based)Tj
4.989 0 Td
(simulations)Tj
4.8585 0 Td
(using)Tj
2.3924 0 Td
(parameters)Tj
/F10 1 Tf
4.6715 0 Td
[()]TJ
/F5 1 Tf
0.9127 0 Td
(=)Tj
0.7994 0 Td
(100,)Tj
/F10 1 Tf
1.8765 0 Td
[()]TJ
/F5 1 Tf
1.0885 0 Td
(=)Tj
0.7994 0 Td
(5,)Tj
0.9241 0 Td
(and)Tj
/F18 1 Tf
1.7291 0 Td
()Tj
/F5 1 Tf
0.771 0 Td
(=)Tj
0.7994 0 Td
(0.1.)Tj
1.6214 0 Td
(We)Tj
-34.2706 -1.3039 Td
(assume)Tj
3.1464 0 Td
(that)Tj
1.7801 0 Td
(the)Tj
1.4684 0 Td
(ability)Tj
2.6929 0 Td
(of)Tj
1.0148 0 Td
(agents,)Tj
/F10 1 Tf
2.9763 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 335.5653 382.2236 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 337.5496 383.8677 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
('s,)Tj
1.0204 0 Td
(are)Tj
1.4513 0 Td
(uniformly)Tj
4.2463 0 Td
(distributed)Tj
4.5978 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(range)Tj
2.4661 0 Td
(of)Tj
1.0148 0 Td
(0.5)Tj
1.3947 0 Td
(to)Tj
1.0261 0 Td
(0.75)Tj
1.8708 0 Td
(by)Tj
-35.3477 -1.2982 Td
(setting)Tj
/F10 1 Tf
2.88 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 233.5748 369.2409 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 237.77 370.885 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(=)Tj
0.7993 0 Td
(0.5)Tj
1.3947 0 Td
(+)Tj
0.805 0 Td
(0.25)Tj
/F10 1 Tf
[()]TJ
/F5 1 Tf
(/)Tj
/F10 1 Tf
[()]TJ
/F5 1 Tf
3.1634 0 Td
(for)Tj
/F10 1 Tf
1.3833 0 Td
[()]TJ
/F5 1 Tf
0.4876 0 Td
(=)Tj
0.7994 0 Td
(0,)Tj
0.924 0 Td
(1,)Tj
/F16 1 Tf
0 Tc
0.9185 0 Td
(.)Tj
0.4308 0 Td
(.)Tj
0.4366 0 Td
(.)Tj
/F5 1 Tf
-0.004 Tc
(,)Tj
/F10 1 Tf
0.7143 0 Td
[()]TJ
/F13 1 Tf
0.9184 0 Td
[()]TJ
/F5 1 Tf
0.788 0 Td
(1.)Tj
0.9184 0 Td
(Note)Tj
2.1884 0 Td
(that)Tj
1.7745 0 Td
(the)Tj
1.474 0 Td
(ability)Tj
2.6929 0 Td
(of)Tj
1.0148 0 Td
(each)Tj
2.0295 0 Td
(agent)Tj
2.3868 0 Td
(does)Tj
2.0409 0 Td
(not)Tj
-34.2592 -1.2982 Td
(change)Tj
3.0387 0 Td
(throughout)Tj
4.7791 0 Td
(a)Tj
0.6577 0 Td
(simulation)Tj
4.4957 0 Td
(run.)Tj
1.8935 0 Td
(The)Tj
1.7802 0 Td
(initial)Tj
2.5511 0 Td
(evaluated)Tj
3.9855 0 Td
(performance)Tj
/F10 1 Tf
5.3518 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 489.6566 356.2015 cm
BT
/F5 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 495.4393 357.9023 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8447 0 Td
(set)Tj
1.3039 0 Td
(to)Tj
1.0261 0 Td
(0.625,)Tj
-32.7171 -1.2982 Td
(which)Tj
2.6475 0 Td
(is)Tj
0.8504 0 Td
(nearly)Tj
2.6986 0 Td
(equivalent)Tj
4.3483 0 Td
(to)Tj
1.0261 0 Td
(the)Tj
1.4683 0 Td
(mean)Tj
2.4492 0 Td
(ability)Tj
2.6929 0 Td
(in)Tj
1.0374 0 Td
(the)Tj
1.4684 0 Td
(population.)Tj
4.8132 0 Td
(We)Tj
1.61 0 Td
(limit)Tj
2.1203 0 Td
(the)Tj
1.4683 0 Td
(range)Tj
2.4604 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
-34.1741 -1.3039 Td
(rewiring)Tj
3.6169 0 Td
(threshold)Tj
/F10 1 Tf
4.0082 0 Td
[()]TJ
/F5 1 Tf
0.686 0 Td
(in)Tj
1.0375 0 Td
(0.5)Tj
/F15 1 Tf
0 Tc
1.3946 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F20 1 Tf
0 Tc
0.686 0 Td
(<)Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 338.5133 330.2362 cm
BT
/F5 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 344.2393 331.8803 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(=)Tj
0.7993 0 Td
(0.625.)Tj
2.5739 0 Td
(The)Tj
1.7801 0 Td
(lower)Tj
2.4548 0 Td
(limit)Tj
2.1203 0 Td
(for)Tj
/F10 1 Tf
1.3833 0 Td
[()]TJ
/F5 1 Tf
(,)Tj
0.9127 0 Td
(0.5,)Tj
1.6214 0 Td
(is)Tj
0.8448 0 Td
(only)Tj
1.9785 0 Td
(the)Tj
1.4684 0 Td
(accuracy)Tj
3.7133 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
-37.0881 -1.2982 Td
(coin-toss.)Tj
4.0705 0 Td
(The)Tj
1.7801 0 Td
(upper)Tj
2.5795 0 Td
(limit)Tj
/F10 1 Tf
2.1147 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 309.8267 317.2535 cm
BT
/F5 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 315.5527 318.8976 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8503 0 Td
(set)Tj
1.304 0 Td
(for)Tj
1.3833 0 Td
(the)Tj
1.4683 0 Td
(following)Tj
3.9798 0 Td
(reasonif)Tj
4.3483 0 Td
(we)Tj
1.3266 0 Td
(set)Tj
1.304 0 Td
(the)Tj
1.4683 0 Td
(threshold)Tj
4.0082 0 Td
(greater)Tj
-32.995 -1.2982 Td
(than)Tj
2.0296 0 Td
(this)Tj
1.6724 0 Td
(upper)Tj
2.5795 0 Td
(limit,)Tj
2.3414 0 Td
(the)Tj
1.4684 0 Td
(initial)Tj
2.551 0 Td
(performance)Tj
5.3462 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.6519 0 Td
(new)Tj
1.8765 0 Td
(referent)Tj
3.3676 0 Td
(is)Tj
0.8504 0 Td
(always)Tj
2.8346 0 Td
(evaluated)Tj
3.9911 0 Td
(lower)Tj
2.4492 0 Td
(than)Tj
-35.0246 -1.3039 Td
(the)Tj
1.4683 0 Td
(threshold.)Tj
-0.2721 -1.2983 Td
(At)Tj
1.2076 0 Td
(the)Tj
1.4683 0 Td
(initial)Tj
2.5455 0 Td
(state,)Tj
2.262 0 Td
(the)Tj
1.4684 0 Td
(network)Tj
3.5488 0 Td
(is)Tj
0.8504 0 Td
(a)Tj
0.652 0 Td
(directed)Tj
3.4866 0 Td
(random)Tj
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3.7644 0 Td
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1.0148 0 Td
(the)Tj
1.4683 0 Td
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2.4491 0 Td
(performance)Tj
5.3461 0 Td
(of)Tj
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2.3868 0 Td
[()]TJ
/F5 1 Tf
(,)Tj
/F17 1 Tf
0.7143 0 Td
(P)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 407.1118 413.1212 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 409.096 414.7653 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
0.4422 0 Td
(Therefore,)Tj
4.3936 0 Td
(the)Tj
1.4684 0 Td
(definition)Tj
4.1669 0 Td
(of)Tj
/F17 1 Tf
1.0148 0 Td
(P)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 532.1196 413.1212 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 536.3149 414.7653 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
/F17 1 Tf
0 Tc
-33.63 -1.6667 Td
(P)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 208.233 395.6031 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 213.1653 398.0976 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
223.6535 408.8693 m
288.2835 408.8693 l
288.2835 408.4724 l
223.6535 408.4724 l
f*
10 0 0 10 223.6535 405.5811 cm
BT
/F14 1 Tf
1 TL
0 0 Td
(P)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 234.1417 403.2566 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 237.7133 401.7826 cm
BT
/F13 1 Tf
1 TL
0 0 Td
[()1()4()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 234.1417 395.3196 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F15 1 Tf
0.3401 0 Td
()Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 244.4031 393.7889 cm
BT
/F13 1 Tf
1 TL
0 0 Td
[()1()4()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 252.2267 395.3196 cm
BT
/F15 1 Tf
1 TL
0 0 Td
( )Tj
/F10 1 Tf
0.7653 0 Td
[()]TJ
/F15 1 Tf
0.6709 0 Td
()Tj
/F16 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 270.6519 398.0976 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 274.507 400.9889 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
-0.085 -0.9449 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 276.6047 398.0976 cm
BT
/F20 1 Tf
1 TL
0 0 Td
(=)Tj
/F10 1 Tf
[()]TJ
/F5 1 Tf
-0.004 Tc
1.2188 0 Td
(,)Tj
0.4422 0 Td
(where)Tj
2.6533 0 Td
(the)Tj
1.4683 0 Td
(overline)Tj
3.4582 0 Td
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4.32 0 Td
(the)Tj
1.474 0 Td
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3.2258 0 Td
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1.9729 0 Td
(500)Tj
1.6498 0 Td
(independent)Tj
5.2724 0 Td
(runs.)Tj
-34.8148 -1.4853 Td
(We)Tj
1.6101 0 Td
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1.7631 0 Td
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4.2066 0 Td
(the)Tj
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(group)Tj
2.6079 0 Td
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(and)Tj
1.7291 0 Td
(its)Tj
1.1509 0 Td
(standard)Tj
3.719 0 Td
(deviation.)Tj
4.1726 0 Td
(For)Tj
1.6271 0 Td
(each)Tj
2.0296 0 Td
(single)Tj
-33.8794 -1.4513 Td
(run,)Tj
1.8935 0 Td
(we)Tj
1.3266 0 Td
(regarded)Tj
/F14 1 Tf
0 Tc
3.7644 0.7483 Td
(P)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 280.3464 373.8897 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
0 -1.3323 Td
[()]TJ
/F15 1 Tf
()Tj
/F16 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 291.7984 368.7307 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 295.6535 372.359 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
-0.085 -1.0677 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 297.7511 368.7307 cm
BT
/F20 1 Tf
1 TL
0 0 Td
(=)Tj
/F10 1 Tf
[()]TJ
/F5 1 Tf
-0.004 Tc
1.491 0 Td
(as)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(group)Tj
2.6079 0 Td
(performance)Tj
5.3517 0 Td
(at)Tj
0.9525 0 Td
(time)Tj
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2.0239 0 Td
[()]TJ
/F5 1 Tf
0.5216 0 Td
(and)Tj
1.7291 0 Td
(calculated)Tj
4.2066 0 Td
(the)Tj
1.4683 0 Td
(mean)Tj
2.4435 0 Td
(and)Tj
-35.0529 -1.7291 Td
(the)Tj
1.4683 0 Td
(standard)Tj
3.7247 0 Td
(deviation)Tj
3.9458 0 Td
(\(SD\))Tj
2.1145 0 Td
(of)Tj
/F14 1 Tf
0 Tc
1.6668 0.9468 Td
(X)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 343.6157 358.5826 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
0 -1.9843 Td
[()]TJ
/F15 1 Tf
()Tj
/F16 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 353.3669 351.4393 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 357.222 355.0677 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
-0.085 -1.0677 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 359.3196 351.4393 cm
BT
/F20 1 Tf
1 TL
0 0 Td
(=)Tj
/F10 1 Tf
[()]TJ
/F14 1 Tf
-3.6623 1.1111 Td
(n)Tj
4.9322 0 Td
(o)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 378.5952 344.7496 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 382.1669 343.2755 cm
BT
/F13 1 Tf
1 TL
0 0 Td
[()1()4()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 389.9905 344.7496 cm
BT
/F15 1 Tf
1 TL
0 0 Td
( )Tj
/F10 1 Tf
0.7748 0 Td
[()]TJ
/F15 1 Tf
0.6614 0 Td
()Tj
/F16 1 Tf
(1)Tj
/F15 1 Tf
()Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
2.3906 0 Td
()Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 421.1149 343.2755 cm
BT
/F13 1 Tf
1 TL
0 0 Td
[()1()4()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 429.4488 351.4393 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4422 0 Td
(that)Tj
1.7801 0 Td
(is,)Tj
1.0715 0 Td
(for)Tj
1.389 0 Td
(the)Tj
1.4683 0 Td
(last)Tj
/F10 1 Tf
1.559 0 Td
[()]TJ
/F5 1 Tf
0.8107 0 Td
(=)Tj
0.7994 0 Td
(100)Tj
1.6498 0 Td
(time)Tj
-33.9134 -1.8708 Td
(steps.)Tj
2.4037 0 Td
(Then)Tj
2.3301 0 Td
(we)Tj
1.3323 0 Td
(took)Tj
2.0239 0 Td
(their)Tj
2.109 0 Td
(average)Tj
3.2258 0 Td
(over)Tj
1.9785 0 Td
(500)Tj
1.6441 0 Td
(independent)Tj
5.2781 0 Td
(runs)Tj
2.0295 0 Td
(to)Tj
1.0261 0 Td
(evaluate)Tj
3.4583 0 Td
(the)Tj
1.4683 0 Td
(group)Tj
2.6135 0 Td
(perfor-)Tj
-32.9212 -1.3039 Td
(mance)Tj
2.8686 0 Td
(and)Tj
1.7291 0 Td
(its)Tj
1.1452 0 Td
(fluctuation.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 271.1622 cm
BT
/F2 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(3)Tj
0.7653 0 Td
(Results)Tj
/F11 1 Tf
-0.7653 -1.4976 Td
(3.1)Tj
1.4598 0 Td
(The)Tj
1.8425 0 Td
(heterogeneity)Tj
5.9009 0 Td
(in)Tj
1.0677 0 Td
(the)Tj
1.5402 0 Td
(in-degree)Tj
4.1433 0 Td
(distribution)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 236.1826 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(The)Tj
1.7688 0 Td
(in-degree)Tj
4.0138 0 Td
(distribution)Tj
/F10 1 Tf
0 Tc
4.9606 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 312.9448 233.6881 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 316.5165 232.1574 cm
BT
/F13 1 Tf
1 TL
0 0 Td
[()1()4()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 324.8503 236.1826 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
()Tj
/F5 1 Tf
-0.004 Tc
1.4513 0 Td
(in)Tj
1.0204 0 Td
(the)Tj
1.4627 0 Td
(evolved)Tj
3.2485 0 Td
(network)Tj
3.5376 0 Td
(significantly)Tj
5.0797 0 Td
(differed)Tj
3.3278 0 Td
(from)Tj
2.194 0 Td
(the)Tj
1.4627 0 Td
(initial)Tj
-35.2684 -1.4569 Td
(Poisson)Tj
3.3279 0 Td
(distribution)Tj
4.9719 0 Td
(for)Tj
1.3833 0 Td
(the)Tj
1.4684 0 Td
(random)Tj
3.4298 0 Td
(network)Tj
3.5489 0 Td
(\()Tj
0.83 0.64 0.02 0 k
(Fig)Tj
1.8199 0 Td
(2)Tj
0 g
(\).)Tj
1.2642 0 Td
(As)Tj
1.2642 0 Td
(the)Tj
1.4684 0 Td
(in-degrees)Tj
4.3823 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(evolved)Tj
3.2542 0 Td
(network)Tj
-34.0892 -1.2983 Td
(were)Tj
2.1204 0 Td
(distributed)Tj
4.5977 0 Td
(approximately)Tj
5.9753 0 Td
(exponentially,)Tj
5.828 0 Td
(there)Tj
2.262 0 Td
(were)Tj
2.1203 0 Td
(a)Tj
0.6577 0 Td
(few)Tj
1.6157 0 Td
(nodes)Tj
2.5852 0 Td
(that)Tj
1.7801 0 Td
(had)Tj
1.7065 0 Td
(much)Tj
2.5228 0 Td
(larger)Tj
2.5285 0 Td
(in-)Tj
-36.3002 -1.3039 Td
(degrees)Tj
3.2145 0 Td
(than)Tj
2.0296 0 Td
(the)Tj
1.4683 0 Td
(mean.)Tj
2.6703 0 Td
(In)Tj
1.1111 0 Td
(other)Tj
2.347 0 Td
(words,)Tj
2.897 0 Td
(high)Tj
2.0069 0 Td
(heterogeneity)Tj
5.6523 0 Td
(in)Tj
1.0374 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(followers)Tj
3.8551 0 Td
(evolved)Tj
-34.1912 -1.2983 Td
(through)Tj
3.4356 0 Td
(the)Tj
1.4627 0 Td
(adaptive)Tj
3.5659 0 Td
(rewiring)Tj
3.6114 0 Td
(process.)Tj
3.4014 0 Td
(The)Tj
1.7745 0 Td
(agents)Tj
2.7439 0 Td
(attracting)Tj
4.0535 0 Td
(many)Tj
2.4662 0 Td
(followers)Tj
3.8494 0 Td
(can)Tj
1.6157 0 Td
(be)Tj
1.1452 0 Td
(interpreted)Tj
-33.1254 -1.2983 Td
(as)Tj
1.0148 0 Td
(opinion)Tj
3.7758 0 Td
(leaders)Tj
3.3959 0 Td
(in)Tj
1.0374 0 Td
(our)Tj
1.6271 0 Td
(model.)Tj
-9.6547 -1.6554 Td
(The)Tj
1.7858 0 Td
(mean)Tj
2.4434 0 Td
(in-degree)Tj
ET
Q
q
1 j
1 J
0 w
294.5197 161.7449 m
299.6787 161.7449 l
299.6787 161.348 l
294.5197 161.348 l
f*
10 0 0 10 294.5196 153.0708 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F15 1 Tf
0.5159 0 Td
()Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 308.3527 150.5763 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 310.4503 153.0708 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
0.6576 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
327.5717 163.7291 m
357.9591 163.7291 l
357.9591 163.3323 l
327.5717 163.3323 l
f*
10 0 0 10 327.5716 160.5543 cm
BT
/F14 1 Tf
1 TL
0 0 Td
(P)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 338.0598 158.2299 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
0 -1.3228 Td
[()]TJ
/F15 1 Tf
()Tj
/F16 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 349.3984 153.0708 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 354.3307 150.5763 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()12()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 360.6803 153.0708 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(of)Tj
1.0147 0 Td
(agent)Tj
/F10 1 Tf
2.3868 0 Td
[()]TJ
/F5 1 Tf
0.4876 0 Td
(with)Tj
1.9955 0 Td
(ability)Tj
/F10 1 Tf
2.6986 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 451.2755 151.37 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 453.2598 153.0708 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4422 0 Td
(that)Tj
1.7801 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4683 0 Td
(mean)Tj
2.4435 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
-35.7275 -1.4796 Td
(followers)Tj
3.8551 0 Td
(of)Tj
1.0148 0 Td
(agent)Tj
/F10 1 Tf
2.3867 0 Td
[()]TJ
/F5 1 Tf
(,)Tj
0.7144 0 Td
(increased)Tj
3.9968 0 Td
(exponentially)Tj
5.6012 0 Td
(with)Tj
/F10 1 Tf
2.0013 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 400.422 136.6299 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 404.6173 138.274 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(for)Tj
1.3889 0 Td
(each)Tj
2.0296 0 Td
(rewiring)Tj
3.617 0 Td
(threshold)Tj
/F10 1 Tf
4.0082 0 Td
[()]TJ
/F5 1 Tf
0.6859 0 Td
(\()Tj
0.83 0.64 0.02 0 k
(Fig)Tj
1.8199 0 Td
(3)Tj
0 g
(\).)Tj
-32.8136 -1.4569 Td
(We)Tj
1.6101 0 Td
(were)Tj
2.126 0 Td
(able)Tj
1.8311 0 Td
(to)Tj
1.0205 0 Td
(obtain)Tj
2.7836 0 Td
(an)Tj
1.2019 0 Td
(approximation)Tj
6.1738 0 Td
(equation)Tj
3.7359 0 Td
(which)Tj
ET
Q
q
1 j
1 J
0 w
443.2819 132.378 m
448.4976 132.378 l
448.4976 131.9811 l
443.2819 131.9811 l
f*
10 0 0 10 443.2818 123.7039 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F15 1 Tf
0.5215 0 Td
()Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 457.1149 121.2094 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 459.2692 123.7039 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F5 1 Tf
-0.004 Tc
0.6066 0 Td
(satisfies)Tj
3.2768 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(equilibrium)Tj
-32.3147 -1.3095 Td
(state.)Tj
2.2621 0 Td
(Its)Tj
1.2189 0 Td
(derivation,)Tj
4.541 0 Td
(which)Tj
2.6533 0 Td
(we)Tj
1.3266 0 Td
(will)Tj
1.6611 0 Td
(describe)Tj
3.5262 0 Td
(in)Tj
1.0375 0 Td
(detail)Tj
2.4151 0 Td
(in)Tj
1.0375 0 Td
(Sections)Tj
3.5206 0 Td
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