%PDF-1.6
%
1 0 obj
<>
endobj
2 0 obj
<>stream
Yu Liu, David J. T. Sumpter
Is the golden ratio a universal constant for self-replication?
www.plosone.org
www.plosone.org
endstream
endobj
3 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 12 0 R/Annots 13 0 R/Contents 14 0 R/TrimBox[0 0 612 792]>>
endobj
13 0 obj
[15 0 R 16 0 R 17 0 R 18 0 R 19 0 R 20 0 R 21 0 R 22 0 R 23 0 R 24 0 R 25 0 R 26 0 R 27 0 R 28 0 R 29 0 R 30 0 R 31 0 R 32 0 R 33 0 R 34 0 R 35 0 R]
endobj
15 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref001)>>
endobj
16 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref002)>>
endobj
17 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref003)>>
endobj
18 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref002)>>
endobj
19 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref004)>>
endobj
20 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref002)>>
endobj
21 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref003)>>
endobj
22 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref002)>>
endobj
23 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref005)>>
endobj
24 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref006)>>
endobj
25 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref006)>>
endobj
26 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref008)>>
endobj
27 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref007)>>
endobj
28 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref009)>>
endobj
29 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref010)>>
endobj
30 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref011)>>
endobj
31 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref012)>>
endobj
32 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e003)>>
endobj
33 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e003)>>
endobj
34 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e003)>>
endobj
35 0 obj
<>/Border[0 0 0]/A 36 0 R>>
endobj
36 0 obj
<>
endobj
14 0 obj
[37 0 R 38 0 R 39 0 R 40 0 R 41 0 R 42 0 R 43 0 R 44 0 R 45 0 R 46 0 R 47 0 R 48 0 R 49 0 R 50 0 R 51 0 R]
endobj
37 0 obj
<>stream
q
0.83 0.64 0.02 0 k
510.9732 680.315 m
515.7354 680.315 l
h
f*
357.5055 654.3496 m
362.2677 654.3496 l
h
f*
388.5732 654.3496 m
393.3354 654.3496 l
h
f*
434.6646 576.3402 m
439.4835 576.3402 l
h
f*
444.8126 576.3402 m
449.6315 576.3402 l
h
f*
551.0551 537.3354 m
555.9307 537.3354 l
h
f*
521.8016 524.2961 m
526.6205 524.2961 l
h
f*
446.7969 485.348 m
451.6724 485.348 l
h
f*
234.9354 459.326 m
239.811 459.326 l
h
f*
203.4142 394.2992 m
208.1764 394.2992 l
h
f*
518.6835 288.3402 m
523.5591 288.3402 l
h
f*
528.8315 288.3402 m
533.7071 288.3402 l
h
f*
509.726 275.3008 m
514.6016 275.3008 l
h
f*
519.137 275.3008 m
524.0126 275.3008 l
h
f*
341.9717 249.3354 m
351.7228 249.3354 l
h
f*
560.0693 249.3354 m
569.7638 249.3354 l
h
f*
200.0126 236.2961 m
209.7071 236.2961 l
h
f*
302.9102 223.3134 m
327.4583 223.3134 l
h
f*
248.5984 158.3433 m
273.0898 158.3433 l
h
f*
396.1701 93.3165 m
420.7748 93.3165 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 200.0125 707.4141 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
[()11()20()11()4()2()-19()7()4()8()]TJ
4.0365 0 Td
[()10()6()22()]TJ
1.8085 0 Td
[()6(\r)4()6()2()20()7(\r)]TJ
3.3505 0 Td
[(!)-13()14()10()]TJ
1.9559 0 Td
[()7()2()-9()4()]TJ
2.0239 0 Td
[()1()-4()6(\n)-4()7()14()7()4(\r)4()]TJ
4.2179 0 Td
[()11()]TJ
0.9808 0 Td
[()10()6()]TJ
1.4173 0 Td
[()20()22()7()4()]TJ
2.0976 0 Td
[()11( )]TJ
0.9525 0 Td
[()14()]TJ
1.8368 0 Td
[()11()]TJ
0.9808 0 Td
[(%)]TJ
/F8 1 Tf
0 Tc
(.)Tj
0.9014 0 Td
(.)Tj
0.4365 0 Td
(.)Tj
/F7 1 Tf
-0.004 Tc
0.4876 0 Td
[(&)14()14()9()89()]TJ
2.7496 0 Td
[()14()11()4(')14()12()14()-3()]TJ
3.4923 0 Td
[()12( )]TJ
-33.7264 -1.3039 Td
[( )6()22()7()12()20()2()166(\()]TJ
3.4072 0 Td
[()-3()16( )13()2(\r)4()11( )]TJ
3.6566 0 Td
[()-3()16()4(\r)]TJ
2.024 0 Td
[(")18()4()4()12()12( )13()]TJ
2.6305 0 Td
[()10()6()]TJ
1.4116 0 Td
[()12()10()-2()22()1()]TJ
2.4945 0 Td
[(&)80(\n)13()4()7()16()8()15()]TJ
3.1124 0 Td
[()1()-4(\n)7()7()7(\r)-4()]TJ
3.0558 0 Td
[(\n)7()11()12( )6(\n)1()4(\r)4()2( )6(\n)7()2()]TJ
4.8925 0 Td
[()16( )6(\r)]TJ
1.7292 0 Td
[()-3()]TJ
1.0091 0 Td
[()10()6()]TJ
1.4173 0 Td
[()16( )6(\n)1()4()2( )22()]TJ
3.4129 0 Td
[()10()10()12()6()7(\r)]TJ
-34.2536 -1.2982 Td
[()10()6()]TJ
1.4173 0 Td
[( )18()12()17()4()2()]TJ
3.2825 0 Td
[()14()]TJ
1.8311 0 Td
[()18()-4()9()]TJ
2.1543 0 Td
[()6()22($)3()]TJ
2.041 0 Td
[()4()7()2( )]TJ
2.0069 0 Td
[()11()20()7()11()20(\r)4()16()12( )6()7(\r)]TJ
4.9436 0 Td
[()12()]TJ
1.1282 0 Td
[()10()6()]TJ
1.4173 0 Td
[()13()20()7()22()11()11()]TJ
3.2031 0 Td
[()11( )]TJ
0.9524 0 Td
[()10()6()]TJ
1.4174 0 Td
[()12( )18()15($)3()2()5()-3()]TJ
/F8 1 Tf
0 Tc
(.)Tj
3.668 0 Td
(.)Tj
0.4308 0 Td
(.)Tj
/F7 1 Tf
-0.004 Tc
[(\()]TJ
/F14 1 Tf
0.8618 0 Td
([)Tj
0.83 0.64 0.02 0 k
(1)Tj
0 g
(])Tj
-29.5595 -1.2983 Td
(The)Tj
1.7858 0 Td
(basis)Tj
2.1486 0 Td
(of)Tj
1.0148 0 Td
(Dan)Tj
1.9389 0 Td
(Brown's)Tj
3.4866 0 Td
(fictional)Tj
3.4979 0 Td
(discussion)Tj
4.371 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(golden)Tj
2.9367 0 Td
(ratio)Tj
/F7 1 Tf
2.0976 0 Td
[()]TJ
/F14 1 Tf
0.771 0 Td
(originated)Tj
4.3257 0 Td
(from)Tj
2.2053 0 Td
(scien-)Tj
-34.2649 -1.2983 Td
(tific)Tj
2.1543 0 Td
(studies)Tj
2.9877 0 Td
(\(as)Tj
1.3549 0 Td
(documented)Tj
5.2441 0 Td
(by)Tj
1.1849 0 Td
(paper)Tj
2.4831 0 Td
([)Tj
0.83 0.64 0.02 0 k
(2)Tj
0 g
(])Tj
1.3776 0 Td
(and)Tj
1.7291 0 Td
([)Tj
0.83 0.64 0.02 0 k
(3)Tj
0 g
(]\).)Tj
1.9389 0 Td
(For)Tj
1.6271 0 Td
(example,)Tj
3.7757 0 Td
(the)Tj
1.4684 0 Td
(Great)Tj
2.4604 0 Td
(Pyramid)Tj
3.6567 0 Td
(of)Tj
1.0148 0 Td
(Khufu)Tj
-34.4577 -1.3039 Td
(was)Tj
1.6951 0 Td
(claimed)Tj
3.3618 0 Td
(to)Tj
1.0262 0 Td
(be)Tj
1.1508 0 Td
(designed)Tj
3.7644 0 Td
(by)Tj
1.1849 0 Td
(ancient)Tj
3.1634 0 Td
(Egyptians)Tj
4.1329 0 Td
(to)Tj
1.0261 0 Td
(manifest)Tj
/F7 1 Tf
3.6624 0 Td
[()]TJ
/F14 1 Tf
(,)Tj
0.9921 0 Td
(i.e.,)Tj
1.5874 0 Td
(the)Tj
1.4683 0 Td
(ratio)Tj
2.0977 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(slant)Tj
2.109 0 Td
(height)Tj
-34.9056 -1.2982 Td
(to)Tj
1.0261 0 Td
(half)Tj
1.7121 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(length)Tj
2.7269 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(base)Tj
1.9446 0 Td
(was)Tj
1.7008 0 Td
(designed)Tj
3.7644 0 Td
(to)Tj
1.0261 0 Td
(be)Tj
/F7 1 Tf
1.1509 0 Td
[()]TJ
/F14 1 Tf
(.)Tj
0.9921 0 Td
(Moreover,)Tj
4.3993 0 Td
(nautilus)Tj
3.4299 0 Td
(shell)Tj
2.0239 0 Td
(was)Tj
1.7008 0 Td
(believed)Tj
3.4923 0 Td
(to)Tj
-36.0621 -1.2983 Td
(be)Tj
1.1508 0 Td
(a)Tj
0.652 0 Td
(logarithmic)Tj
4.8472 0 Td
(spiral)Tj
2.4151 0 Td
(whose)Tj
2.7269 0 Td
(growth)Tj
3.0727 0 Td
(factor)Tj
2.5399 0 Td
(is)Tj
/F7 1 Tf
0.8504 0 Td
[()]TJ
/F14 1 Tf
(.)Tj
0.9921 0 Td
(Other)Tj
2.5908 0 Td
(examples)Tj
3.9061 0 Td
(include)Tj
3.1862 0 Td
(the)Tj
1.4683 0 Td
(design)Tj
2.8119 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4741 0 Td
(Par-)Tj
-35.6993 -1.3039 Td
(thenon,)Tj
3.2995 0 Td
(Leonardo)Tj
4.0762 0 Td
(da)Tj
1.1792 0 Td
(Vinci's)Tj
2.999 0 Td
(paintings,)Tj
4.1499 0 Td
(the)Tj
1.474 0 Td
(ratios)Tj
2.4548 0 Td
(in)Tj
1.0375 0 Td
(a)Tj
0.6519 0 Td
(human)Tj
3.0784 0 Td
(body,)Tj
2.4435 0 Td
(lengths)Tj
3.0897 0 Td
(of)Tj
1.0148 0 Td
(passages)Tj
3.5773 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
-35.5632 -1.2983 Td
(Aeneid.)Tj
0.007 Tc
1.1962 -1.2983 Td
(These)Tj
2.6248 0 Td
(claims)Tj
2.8347 0 Td
(are,)Tj
1.7177 0 Td
(however,)Tj
3.9288 0 Td
(mostly)Tj
2.9707 0 Td
(false)Tj
2.0296 0 Td
(or)Tj
1.1169 0 Td
(misleading)Tj
4.6941 0 Td
([)Tj
0.83 0.64 0.02 0 k
(2)Tj
0 g
()Tj
0.83 0.64 0.02 0 k
(4)Tj
0 g
(].)Tj
2.6589 0 Td
(For)Tj
1.6611 0 Td
(example,)Tj
3.8607 0 Td
(although)Tj
3.8438 0 Td
(today)Tj
-35.138 -1.3039 Td
(the)Tj
1.5023 0 Td
(ratio)Tj
2.1543 0 Td
(of)Tj
1.0318 0 Td
(the)Tj
1.5024 0 Td
(slant)Tj
2.1656 0 Td
(height)Tj
2.795 0 Td
(to)Tj
1.0488 0 Td
(half)Tj
1.7575 0 Td
(of)Tj
1.0374 0 Td
(the)Tj
1.5024 0 Td
(length)Tj
2.7949 0 Td
(of)Tj
1.0375 0 Td
(the)Tj
1.5024 0 Td
(base)Tj
1.9899 0 Td
(of)Tj
1.0374 0 Td
(the)Tj
1.5024 0 Td
(Great)Tj
2.5171 0 Td
(Pyramid)Tj
3.7304 0 Td
(happened)Tj
-32.6095 -1.2982 Td
(to)Tj
1.0488 0 Td
(be)Tj
/F7 1 Tf
1.1678 0 Td
[()]TJ
/F14 1 Tf
0.7824 0 Td
(approximately,)Tj
6.3552 0 Td
(the)Tj
1.5024 0 Td
(height)Tj
2.7949 0 Td
(was)Tj
1.7291 0 Td
(quite)Tj
2.3018 0 Td
(different)Tj
3.753 0 Td
(when)Tj
2.4491 0 Td
(it)Tj
0.8051 0 Td
(was)Tj
1.7348 0 Td
(built)Tj
2.1203 0 Td
(over)Tj
2.0239 0 Td
(four)Tj
1.9559 0 Td
(thousand)Tj
-32.5245 -1.2983 Td
(years)Tj
2.3187 0 Td
(ago,)Tj
1.8935 0 Td
(and)Tj
1.7631 0 Td
(there)Tj
2.3188 0 Td
(is)Tj
0.873 0 Td
(no)Tj
1.2983 0 Td
(evidence)Tj
3.7984 0 Td
(that)Tj
1.8198 0 Td
(ancient)Tj
3.2428 0 Td
(Egyptians)Tj
4.235 0 Td
(even)Tj
2.1146 0 Td
(knew)Tj
2.4151 0 Td
(the)Tj
1.5024 0 Td
(golden)Tj
3.0047 0 Td
(ratio)Tj
2.1543 0 Td
([)Tj
0.83 0.64 0.02 0 k
(2)Tj
0 g
(].)Tj
1.6441 0 Td
(A)Tj
-36.3966 -1.3039 Td
(field)Tj
2.0239 0 Td
(study)Tj
2.4491 0 Td
(by)Tj
1.2019 0 Td
(Falbo)Tj
2.4944 0 Td
(showed)Tj
3.3166 0 Td
(that)Tj
1.8255 0 Td
(nautilus)Tj
3.5149 0 Td
(shell)Tj
2.0806 0 Td
(is)Tj
0.8731 0 Td
(quite)Tj
2.296 0 Td
(far)Tj
1.3493 0 Td
(from)Tj
2.2507 0 Td
(a)Tj
0.6633 0 Td
(golden)Tj
3.0047 0 Td
(spiral)Tj
2.4832 0 Td
([)Tj
0.83 0.64 0.02 0 k
(3)Tj
0 g
(].)Tj
1.644 0 Td
(For)Tj
1.6555 0 Td
(the)Tj
-35.1267 -1.2983 Td
(Parthenon,)Tj
4.7735 0 Td
(there)Tj
2.3187 0 Td
(are)Tj
1.4797 0 Td
(many)Tj
2.5228 0 Td
(different)Tj
3.753 0 Td
(numbers)Tj
3.8551 0 Td
(of)Tj
1.0375 0 Td
(its)Tj
1.1792 0 Td
(dimensions)Tj
4.9606 0 Td
(in)Tj
1.0602 0 Td
(the)Tj
1.5023 0 Td
(literature)Tj
3.9912 0 Td
(\(probably)Tj
-32.4338 -1.2982 Td
(because)Tj
3.3958 0 Td
(measurements)Tj
6.1625 0 Td
(are)Tj
1.4854 0 Td
(made)Tj
2.4661 0 Td
(between)Tj
3.6056 0 Td
(different)Tj
3.7531 0 Td
(points)Tj
2.7893 0 Td
(by)Tj
1.2018 0 Td
(different)Tj
3.7531 0 Td
(people\),)Tj
3.5093 0 Td
(allowing)Tj
3.7076 0 Td
(a)Tj
-35.8296 -1.2983 Td
(golden)Tj
3.0047 0 Td
(ratio)Tj
2.1486 0 Td
(enthusiast)Tj
4.3767 0 Td
(to)Tj
1.0488 0 Td
(choose)Tj
3.0387 0 Td
(whatever)Tj
3.9231 0 Td
(numbers)Tj
3.8551 0 Td
(to)Tj
1.0488 0 Td
(fit)Tj
/F7 1 Tf
1.1055 0 Td
[()]TJ
/F14 1 Tf
0.7824 0 Td
([)Tj
0.83 0.64 0.02 0 k
(2)Tj
0 g
(].)Tj
1.6441 0 Td
(But)Tj
1.6554 0 Td
(sadly,)Tj
2.5342 0 Td
(despite)Tj
3.118 0 Td
(the)Tj
1.5024 0 Td
(dubi-)Tj
-34.7865 -1.3039 Td
(ous)Tj
1.6497 0 Td
(nature)Tj
2.8857 0 Td
(of)Tj
1.0374 0 Td
(the)Tj
1.5024 0 Td
(claims,)Tj
3.0727 0 Td
(the)Tj
1.5024 0 Td
(golden)Tj
3.0047 0 Td
(ratio)Tj
2.1543 0 Td
(even)Tj
2.1146 0 Td
(remains)Tj
3.5206 0 Td
(a)Tj
0.6633 0 Td
(feature)Tj
3.0671 0 Td
(of)Tj
1.0375 0 Td
(some)Tj
2.3754 0 Td
(school)Tj
2.8573 0 Td
(textbooks,)Tj
-32.4451 -1.2983 Td
(such)Tj
2.1032 0 Td
(as)Tj
1.0375 0 Td
([)Tj
0.83 0.64 0.02 0 k
(5)Tj
0 g
(].)Tj
-0.004 Tc
-1.9445 -1.2983 Td
(One)Tj
1.9388 0 Td
(area)Tj
1.8879 0 Td
(of)Tj
1.0148 0 Td
(biology)Tj
3.1691 0 Td
(in)Tj
1.0375 0 Td
(which)Tj
2.6532 0 Td
(the)Tj
1.4683 0 Td
(golden)Tj
2.9367 0 Td
(ratio)Tj
2.0976 0 Td
(has)Tj
1.5421 0 Td
(a)Tj
0.6519 0 Td
(genuine)Tj
3.4243 0 Td
(role)Tj
1.7688 0 Td
(is)Tj
0.8504 0 Td
(in)Tj
1.0374 0 Td
(phyllotaxis,)Tj
4.7679 0 Td
(i.e.,)Tj
1.5874 0 Td
(the)Tj
-35.0303 -1.3039 Td
(arrangement)Tj
5.3574 0 Td
(of)Tj
1.0148 0 Td
(leaves)Tj
2.5625 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(stem)Tj
2.126 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.6519 0 Td
(plant.)Tj
2.4889 0 Td
(The)Tj
1.7801 0 Td
(seeds)Tj
2.3187 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(head)Tj
2.1317 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.6576 0 Td
(ripe)Tj
1.7972 0 Td
(sunflower)Tj
4.1782 0 Td
(fit)Tj
-34.3443 -1.2982 Td
(neatly)Tj
2.6248 0 Td
(together)Tj
3.532 0 Td
(into)Tj
1.8425 0 Td
(two)Tj
1.7121 0 Td
(interlocking)Tj
5.0796 0 Td
(families)Tj
3.3279 0 Td
(of)Tj
1.0148 0 Td
(helical)Tj
2.7893 0 Td
(spirals.)Tj
3.0047 0 Td
(The)Tj
1.7801 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
1.0148 0 Td
(clockwise)Tj
4.0535 0 Td
(and)Tj
-35.1947 -1.2983 Td
(anti-clockwise)Tj
5.947 0 Td
(winding)Tj
3.5319 0 Td
(spirals)Tj
2.778 0 Td
(are)Tj
1.4456 0 Td
(often)Tj
2.2848 0 Td
(both)Tj
2.0636 0 Td
(successive)Tj
4.2462 0 Td
(numbers)Tj
3.7758 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(Fibonacci)Tj
4.1215 0 Td
(sequence)Tj
-32.6832 -1.3039 Td
([)Tj
0.83 0.64 0.02 0 k
(6)Tj
0 g
(].)Tj
1.5987 0 Td
(For)Tj
1.6271 0 Td
(example,)Tj
3.7757 0 Td
(a)Tj
0.6519 0 Td
(sunflower)Tj
4.1783 0 Td
(might)Tj
2.5965 0 Td
(have)Tj
2.0636 0 Td
(34)Tj
1.1679 0 Td
(clockwise)Tj
4.0535 0 Td
(spirals)Tj
2.7779 0 Td
(and)Tj
1.7292 0 Td
(21)Tj
1.1735 0 Td
(anti-clockwise)Tj
5.947 0 Td
(spirals,)Tj
-33.3408 -1.2983 Td
(where)Tj
2.6475 0 Td
(34)Tj
1.1735 0 Td
(and)Tj
1.7292 0 Td
(21)Tj
1.1735 0 Td
(are)Tj
1.4456 0 Td
(two)Tj
1.7122 0 Td
(successive)Tj
4.2462 0 Td
(numbers)Tj
3.7758 0 Td
(in)Tj
1.0374 0 Td
(the)Tj
1.4684 0 Td
(Fibonacci)Tj
4.1272 0 Td
(sequence,)Tj
4.0819 0 Td
(i.e.,)Tj
1.5873 0 Td
(1,)Tj
0.9185 0 Td
(1,)Tj
0.9241 0 Td
(2,)Tj
0.9184 0 Td
(3,)Tj
0.9241 0 Td
(5,)Tj
0.9184 0 Td
(8,)Tj
0.9241 0 Td
(13,)Tj
-35.7333 -1.2983 Td
(21,)Tj
1.3946 0 Td
(34,)Tj
1.3946 0 Td
(55,)Tj
1.4003 0 Td
(89,)Tj
1.3947 0 Td
(144,)Tj
/F8 1 Tf
0 Tc
1.8708 0 Td
(.)Tj
0.4366 0 Td
(.)Tj
0.4308 0 Td
(.)Tj
/F14 1 Tf
-0.004 Tc
(,)Tj
0.72 0 Td
(which)Tj
2.6476 0 Td
(satisfies)Tj
/F7 1 Tf
0 Tc
3.1124 -2.5001 Td
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 354.3874 341.9149 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 359.7165 344.4094 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
1.0488 0 Td
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 376.5543 341.9149 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
/F11 1 Tf
0.3496 0 Td
( )Tj
/F8 1 Tf
0.7653 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 388.97 344.4094 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
0.9921 0 Td
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 405.2976 341.9149 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
/F11 1 Tf
0.3401 0 Td
( )Tj
/F8 1 Tf
0.7748 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 563.4708 344.4094 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F14 1 Tf
(1)Tj
/F11 1 Tf
()Tj
/F14 1 Tf
0.007 Tc
-35.1493 -2.9026 Td
(The)Tj
1.8198 0 Td
(limit)Tj
2.1713 0 Td
(of)Tj
1.0375 0 Td
(the)Tj
1.5023 0 Td
(ratio)Tj
2.1544 0 Td
(between)Tj
3.6056 0 Td
(two)Tj
1.7405 0 Td
(successive)Tj
4.354 0 Td
(Fibonacci)Tj
4.2236 0 Td
(numbers)Tj
3.8607 0 Td
(is)Tj
0.8674 0 Td
(the)Tj
1.5024 0 Td
(golden)Tj
3.0047 0 Td
(ratio,)Tj
-33.0404 -1.2983 Td
(namely,)Tj
3.4469 0 Td
(lim)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 248.1448 300.6992 cm
BT
/F7 1 Tf
1 TL
0.0093 Tc
0 0 Td
[()]TJ
/F11 1 Tf
0 Tc
(!1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 267.7039 302.4 cm
BT
/F7 1 Tf
1 TL
0.007 Tc
0 0 Td
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 274.1102 300.6992 cm
BT
/F7 1 Tf
1 TL
0.0093 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 276.4913 302.4 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(/)Tj
/F7 1 Tf
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 286.2992 300.6992 cm
BT
/F7 1 Tf
1 TL
0.0093 Tc
0 0 Td
[()]TJ
/F18 1 Tf
[()]TJ
/F14 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 298.885 302.4 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(=)Tj
/F7 1 Tf
0.8107 0 Td
[()]TJ
/F14 1 Tf
(.)Tj
1.0148 0 Td
(These)Tj
2.6248 0 Td
(sequences)Tj
4.3143 0 Td
(are)Tj
1.4854 0 Td
(genuine)Tj
3.4979 0 Td
(biological)Tj
4.2009 0 Td
(phenomenon,)Tj
5.9357 0 Td
(not)Tj
-33.7716 -1.2982 Td
(just)Tj
1.7064 0 Td
(in)Tj
1.0602 0 Td
(sunflowers,)Tj
4.8812 0 Td
(but)Tj
1.5874 0 Td
(in)Tj
1.0544 0 Td
(plants)Tj
2.6929 0 Td
(such)Tj
2.1033 0 Td
(as)Tj
1.0374 0 Td
(pinecones,)Tj
4.5751 0 Td
(aloe,)Tj
2.1147 0 Td
(pineapples,)Tj
4.8188 0 Td
(and)Tj
1.7632 0 Td
(cacti)Tj
2.1203 0 Td
([)Tj
0.83 0.64 0.02 0 k
(6)Tj
0 g
()Tj
0.83 0.64 0.02 0 k
(8)Tj
0 g
(].)Tj
2.6645 0 Td
(It)Tj
-34.1798 -1.3039 Td
(should)Tj
2.982 0 Td
(be)Tj
1.1735 0 Td
(stressed)Tj
3.4356 0 Td
(however)Tj
3.6849 0 Td
(that)Tj
1.8255 0 Td
(non-Fibonacci)Tj
6.2249 0 Td
(phyllotaxy)Tj
4.4787 0 Td
(is)Tj
0.8674 0 Td
(also)Tj
1.8141 0 Td
(abundant)Tj
4.1329 0 Td
([)Tj
0.83 0.64 0.02 0 k
(7)Tj
0 g
(,)Tj
0.83 0.64 0.02 0 k
1.2926 0 Td
(9)Tj
0 g
(].)Tj
1.2983 0 Td
(Several)Tj
-33.2104 -1.2983 Td
(theories)Tj
3.4866 0 Td
(have)Tj
2.1033 0 Td
(been)Tj
2.1656 0 Td
(proposed)Tj
4.0421 0 Td
(to)Tj
1.0431 0 Td
(explain)Tj
3.2032 0 Td
(the)Tj
1.5023 0 Td
(biochemical)Tj
5.1874 0 Td
(and)Tj
1.7631 0 Td
(mechanical)Tj
4.8756 0 Td
(mechanisms)Tj
5.3177 0 Td
(for)Tj
-34.69 -1.2983 Td
(these)Tj
2.3074 0 Td
(patterns)Tj
3.5602 0 Td
(\(reviewed)Tj
4.2349 0 Td
(by)Tj
1.2019 0 Td
(paper)Tj
2.5398 0 Td
([)Tj
0.83 0.64 0.02 0 k
(10)Tj
0 g
(]\),)Tj
2.4831 0 Td
(including)Tj
4.1386 0 Td
(Alan)Tj
2.177 0 Td
(Turing's)Tj
3.6793 0 Td
(morphogenesis)Tj
6.463 0 Td
(theory)Tj
2.8686 0 Td
([)Tj
0.83 0.64 0.02 0 k
(11)Tj
0 g
(,)Tj
0.83 0.64 0.02 0 k
-35.6538 -1.3039 Td
(12)Tj
0 g
(].)Tj
-0.004 Tc
1.1962 -1.2982 Td
(The)Tj
1.7858 0 Td
(Fibonacci)Tj
4.1215 0 Td
(process)Tj
0.83 0.64 0.02 0 k
3.1861 0 Td
(Eq)Tj
1.2982 0 Td
(\(1\))Tj
0 g
1.3777 0 Td
(corresponds)Tj
5.1363 0 Td
(to)Tj
1.0261 0 Td
(self-replicating)Tj
6.1512 0 Td
(processes,)Tj
4.1952 0 Td
(having)Tj
2.914 0 Td
(its)Tj
1.1452 0 Td
(origin)Tj
2.6476 0 Td
(in)Tj
-36.1811 -1.2983 Td
(the)Tj
1.4683 0 Td
(growth)Tj
3.0727 0 Td
(pattern)Tj
3.1125 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4682 0 Td
(Fibonacci)Tj
4.5184 0 Td
(rabbit,)Tj
3.2201 0 Td
(an)Tj
1.2076 0 Td
(idealised)Tj
3.6963 0 Td
(scenario)Tj
3.5547 0 Td
(first)Tj
1.8028 0 Td
(considered)Tj
4.6034 0 Td
(by)Tj
1.1792 0 Td
(the)Tj
1.474 0 Td
(Ital-)Tj
-35.393 -1.3039 Td
(ian)Tj
1.4683 0 Td
(mathematician)Tj
6.2135 0 Td
(Fibonacci)Tj
4.1271 0 Td
(in)Tj
1.0375 0 Td
(his)Tj
1.372 0 Td
(book)Tj
/F7 1 Tf
2.2393 0 Td
[()22()14()4()2()]TJ
2.245 0 Td
[(*)46()4()6(\n)1()]TJ
/F14 1 Tf
2.4718 0 Td
(\(1202\).)Tj
3.0274 0 Td
(The)Tj
1.7802 0 Td
(idea)Tj
1.8765 0 Td
(is)Tj
0.8447 0 Td
(as)Tj
1.0148 0 Td
(follows:)Tj
3.2882 0 Td
(rabbits)Tj
-33.0063 -1.2983 Td
(never)Tj
2.4377 0 Td
(die;)Tj
1.6668 0 Td
(it)Tj
0.7824 0 Td
(takes)Tj
2.2337 0 Td
(one)Tj
1.7007 0 Td
(month)Tj
2.9196 0 Td
(for)Tj
1.389 0 Td
(a)Tj
0.6519 0 Td
(pair)Tj
1.8085 0 Td
(of)Tj
1.0148 0 Td
(infant)Tj
2.6079 0 Td
(rabbits)Tj
2.965 0 Td
(to)Tj
1.0261 0 Td
(become)Tj
3.3222 0 Td
(a)Tj
0.652 0 Td
(pair)Tj
1.8141 0 Td
(of)Tj
1.0148 0 Td
(adults;)Tj
2.8403 0 Td
(an)Tj
1.2019 0 Td
(adult)Tj
-34.0494 -1.2983 Td
(pair)Tj
1.8085 0 Td
(always)Tj
2.8346 0 Td
(gives)Tj
2.1883 0 Td
(birth)Tj
2.194 0 Td
(to)Tj
1.0261 0 Td
(an)Tj
1.2018 0 Td
(infant)Tj
2.6022 0 Td
(pair;)Tj
2.0353 0 Td
(the)Tj
1.474 0 Td
(system)Tj
2.9367 0 Td
(starts)Tj
2.3414 0 Td
(with)Tj
2.0012 0 Td
(one)Tj
1.6951 0 Td
(pair)Tj
1.8085 0 Td
(of)Tj
1.0148 0 Td
(adult)Tj
2.2564 0 Td
(rabbits.)Tj
3.1918 0 Td
(This)Tj
-34.6107 -1.2982 Td
(gives)Tj
2.1883 0 Td
(rise)Tj
1.6441 0 Td
(to)Tj
0.83 0.64 0.02 0 k
1.0261 0 Td
(Eq)Tj
1.2983 0 Td
(\(1\))Tj
0 g
(,)Tj
1.5987 0 Td
(where)Tj
/F7 1 Tf
2.6531 0 Td
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 310.3937 157.7196 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 314.8157 159.4204 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8503 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(adult)Tj
2.2507 0 Td
(pairs)Tj
2.1714 0 Td
(at)Tj
0.9524 0 Td
(month)Tj
/F7 1 Tf
2.9253 0 Td
[()]TJ
/F14 1 Tf
(,)Tj
0.7427 0 Td
(and)Tj
1.7291 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(infant)Tj
-34.9055 -1.3039 Td
(pairs)Tj
2.1713 0 Td
(at)Tj
0.9525 0 Td
(month)Tj
/F7 1 Tf
2.9196 0 Td
[()]TJ
/F14 1 Tf
0.5159 0 Td
(is)Tj
/F7 1 Tf
0.8504 0 Td
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 280.4031 144.737 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F18 1 Tf
[()]TJ
/F14 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 290.4944 146.3811 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
0.4422 0 Td
(So)Tj
1.2018 0 Td
(the)Tj
1.474 0 Td
(ratio)Tj
2.0977 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
1.0148 0 Td
(adult)Tj
2.2507 0 Td
(pairs)Tj
2.1713 0 Td
(over)Tj
1.9785 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(infant)Tj
-33.4825 -1.2982 Td
(pairs)Tj
2.1713 0 Td
(goes)Tj
1.9729 0 Td
(to)Tj
/F7 1 Tf
1.0262 0 Td
[()]TJ
/F14 1 Tf
0.771 0 Td
(as)Tj
/F7 1 Tf
1.0148 0 Td
[()]TJ
/F11 1 Tf
0 Tc
0.5159 0 Td
(!)Tj
1.2246 0 Td
(1)Tj
/F14 1 Tf
-0.004 Tc
(.)Tj
-7.5005 -1.2983 Td
(Recently,)Tj
3.8891 0 Td
(the)Tj
1.4684 0 Td
(golden)Tj
2.9366 0 Td
(ratio)Tj
2.0976 0 Td
(was)Tj
1.7008 0 Td
(suggested)Tj
4.0705 0 Td
(to)Tj
1.0261 0 Td
(appear)Tj
2.9197 0 Td
(in)Tj
1.0375 0 Td
(another)Tj
3.3278 0 Td
(totally)Tj
2.7042 0 Td
(different)Tj
3.6567 0 Td
(field:)Tj
2.1997 0 Td
(the)Tj
-34.2309 -1.3039 Td
(human)Tj
3.0784 0 Td
(genome.)Tj
3.6283 0 Td
(Dress)Tj
/F7 1 Tf
2.4774 0 Td
[()8()]TJ
0.9071 0 Td
[()11()]TJ
/F14 1 Tf
(.)Tj
1.1679 0 Td
(proposed)Tj
3.9514 0 Td
(that)Tj
1.7802 0 Td
(the)Tj
1.4683 0 Td
(growth)Tj
3.0728 0 Td
(pattern)Tj
3.1124 0 Td
(of)Tj
1.0148 0 Td
(repetitive)Tj
3.9684 0 Td
(DNAs)Tj
2.7326 0 Td
(is)Tj
0.8504 0 Td
(analogous)Tj
-33.2104 -1.2983 Td
(to)Tj
1.0262 0 Td
(the)Tj
1.4683 0 Td
(pattern)Tj
3.1124 0 Td
(described)Tj
4.0478 0 Td
(by)Tj
1.1848 0 Td
(the)Tj
1.4684 0 Td
(Fibonacci)Tj
4.1272 0 Td
(process)Tj
0.83 0.64 0.02 0 k
3.1804 0 Td
(Eq)Tj
1.2983 0 Td
(\(1\))Tj
0 g
1.3776 0 Td
(\(repetitive)Tj
4.303 0 Td
(DNAs)Tj
2.7382 0 Td
(are)Tj
1.4514 0 Td
(those)Tj
2.3357 0 Td
(built)Tj
2.0636 0 Td
(from)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 107.1496 23.6976 re
W* n
q
107.0929 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 468.17 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Goden)Tj
3.1748 0 Td
(ratio)Tj
2.126 0 Td
(and)Tj
1.8567 0 Td
(self-replica)Tj
4.7339 0 Td
(tion)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
81.5811 34.9228 m
237.8835 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(ONE)Tj
2.3669 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https://doi.or)Tj
5.4142 0 Td
(g/10.137)Tj
3.8198 0 Td
(1/journal.po)Tj
5.1236 0 Td
(ne.02006)Tj
4.089 0 Td
(01)Tj
0 g
2.0906 0 Td
(July)Tj
1.9701 0 Td
(16,)Tj
1.5874 0 Td
(2018)Tj
35.3483 0 Td
(2)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
38 0 obj
<>stream
endstream
endobj
39 0 obj
<>stream
endstream
endobj
40 0 obj
<>stream
endstream
endobj
41 0 obj
<>stream
endstream
endobj
42 0 obj
<>stream
endstream
endobj
43 0 obj
<>stream
endstream
endobj
44 0 obj
<>stream
endstream
endobj
45 0 obj
<>stream
endstream
endobj
46 0 obj
<>stream
endstream
endobj
47 0 obj
<>stream
endstream
endobj
48 0 obj
<>stream
endstream
endobj
49 0 obj
<>stream
endstream
endobj
50 0 obj
<>stream
endstream
endobj
51 0 obj
<>stream
BT
66.402 0 Td
(18)Tj
ET
Q
endstream
endobj
52 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 12 0 R/Annots 54 0 R/Contents 55 0 R/TrimBox[0 0 612 792]>>
endobj
54 0 obj
[56 0 R 57 0 R 58 0 R 59 0 R 60 0 R 61 0 R 62 0 R 63 0 R 64 0 R 65 0 R 66 0 R 67 0 R 68 0 R]
endobj
56 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref013)>>
endobj
57 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e003)>>
endobj
58 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref014)>>
endobj
59 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref015)>>
endobj
60 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref016)>>
endobj
61 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e004)>>
endobj
62 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref017)>>
endobj
63 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref018)>>
endobj
64 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref013)>>
endobj
65 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref015)>>
endobj
66 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref019)>>
endobj
67 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref019)>>
endobj
68 0 obj
<>/Border[0 0 0]/A 69 0 R>>
endobj
69 0 obj
<>
endobj
55 0 obj
[70 0 R 71 0 R 72 0 R 73 0 R 74 0 R 75 0 R 76 0 R 77 0 R 78 0 R 79 0 R 80 0 R]
endobj
70 0 obj
<>stream
q
0.83 0.64 0.02 0 k
441.5244 693.2976 m
450.9921 693.2976 l
h
f*
351.8362 667.3323 m
376.3843 667.3323 l
h
f*
348.9449 654.3496 m
358.4126 654.3496 l
h
f*
509.4992 641.3102 m
518.9669 641.3102 l
h
f*
560.2961 602.3055 m
569.8205 602.3055 l
h
f*
477.2976 432.9071 m
501.8457 432.9071 l
h
f*
472.7622 406.9417 m
482.2866 406.9417 l
h
f*
486.7654 406.9417 m
496.2331 406.9417 l
h
f*
363.2882 354.8976 m
372.7559 354.8976 l
h
f*
377.9717 354.8976 m
387.4394 354.8976 l
h
f*
381.4866 289.9276 m
391.1811 289.9276 l
h
f*
285.2787 172.9134 m
294.8031 172.9134 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 200.0125 707.4141 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(a)Tj
0.6519 0 Td
(basic)Tj
2.211 0 Td
(short)Tj
2.2847 0 Td
(DNA)Tj
2.3811 0 Td
(sequence)Tj
3.8551 0 Td
(that)Tj
1.7802 0 Td
(is)Tj
0.8447 0 Td
(repeated)Tj
3.6396 0 Td
(many)Tj
2.4775 0 Td
(times,)Tj
2.6192 0 Td
(often)Tj
2.2847 0 Td
(referred)Tj
3.4186 0 Td
(to)Tj
1.0261 0 Td
(as)Tj
1.0148 0 Td
(junk)Tj
2.4435 0 Td
(DNA)Tj
2.7666 0 Td
(and)Tj
-35.6993 -1.3039 Td
(accounted)Tj
4.3313 0 Td
(for)Tj
1.3889 0 Td
(a)Tj
0.652 0 Td
(large)Tj
2.16 0 Td
(fraction)Tj
3.3562 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(whole)Tj
2.6078 0 Td
(human)Tj
3.0784 0 Td
(genome\))Tj
3.7474 0 Td
([)Tj
0.83 0.64 0.02 0 k
(13)Tj
0 g
(].)Tj
2.075 0 Td
(Yamagishi)Tj
4.4277 0 Td
(and)Tj
1.7291 0 Td
(Shimabukuro)Tj
-32.0426 -1.2982 Td
(argued)Tj
2.9706 0 Td
(that)Tj
1.7745 0 Td
(the)Tj
1.4684 0 Td
(distribution)Tj
4.9719 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(values)Tj
2.6646 0 Td
(of)Tj
/F7 1 Tf
1.0204 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 378.9921 679.748 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[(*)]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 386.0787 681.3921 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(+)Tj
/F7 1 Tf
0.7993 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 399.5716 679.748 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 406.4314 681.3921 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(for)Tj
1.3832 0 Td
(the)Tj
1.4741 0 Td
(24)Tj
1.1678 0 Td
(human)Tj
3.0784 0 Td
(chromosomes)Tj
5.8507 0 Td
(can)Tj
1.6271 0 Td
(also)Tj
-35.223 -1.2982 Td
(be)Tj
1.1508 0 Td
(explained)Tj
4.0706 0 Td
(by)Tj
1.1848 0 Td
(the)Tj
1.4684 0 Td
(Fibonacci)Tj
4.1215 0 Td
(process)Tj
0.83 0.64 0.02 0 k
3.1862 0 Td
(Eq)Tj
1.2982 0 Td
(\(1\))Tj
0 g
1.372 0 Td
(where)Tj
/F7 1 Tf
2.6532 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 410.57 666.7086 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[(*)]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 417.6566 668.4094 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8447 0 Td
(the)Tj
1.474 0 Td
(frequency)Tj
4.1839 0 Td
(of)Tj
1.0148 0 Td
(codon)Tj
2.7326 0 Td
(A)Tj
0.907 0 Td
(and)Tj
1.7292 0 Td
(like-)Tj
-34.6504 -1.2982 Td
(wise,)Tj
/F7 1 Tf
2.177 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 227.2818 653.7259 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 234.1417 655.4267 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8503 0 Td
(the)Tj
1.4684 0 Td
(frequency)Tj
4.1896 0 Td
(of)Tj
1.0148 0 Td
(codon)Tj
2.7325 0 Td
(C)Tj
0.8844 0 Td
([)Tj
0.83 0.64 0.02 0 k
(14)Tj
0 g
(].)Tj
2.075 0 Td
(Moreover,)Tj
4.3937 0 Td
(Perez)Tj
2.4151 0 Td
(calculated)Tj
4.2009 0 Td
(that)Tj
1.7801 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(single-)Tj
-31.9234 -1.3039 Td
(stranded)Tj
3.7132 0 Td
(whole)Tj
2.6079 0 Td
(human)Tj
3.0784 0 Td
(DNA,)Tj
2.6022 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 328.8755 640.7433 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 335.7354 642.3874 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(+)Tj
/F7 1 Tf
0.7993 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 349.2283 640.7433 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[(+)]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 354.274 642.3874 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\)/\()Tj
/F7 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 369.8645 640.7433 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[(*)]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 376.9511 642.3874 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(+)Tj
/F7 1 Tf
0.7993 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 390.444 640.7433 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 394.8661 642.3874 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\))Tj
0.5555 0 Td
(is)Tj
0.8504 0 Td
(approximately)Tj
5.9754 0 Td
(\(3)Tj
/F18 1 Tf
1.0375 0 Td
[()]TJ
/F7 1 Tf
0.788 0 Td
[()]TJ
/F14 1 Tf
(\)/2)Tj
1.9162 0 Td
([)Tj
0.83 0.64 0.02 0 k
(15)Tj
0 g
(].)Tj
2.075 0 Td
(These)Tj
-32.6832 -1.2982 Td
(empirical)Tj
3.9912 0 Td
(examples)Tj
3.9061 0 Td
(continue)Tj
3.7644 0 Td
(to)Tj
1.0261 0 Td
(give)Tj
1.8312 0 Td
(credence)Tj
3.787 0 Td
(to)Tj
1.0205 0 Td
(the)Tj
1.4739 0 Td
(idea)Tj
1.8709 0 Td
(that)Tj
/F7 1 Tf
1.7801 0 Td
[()]TJ
/F14 1 Tf
0.7654 0 Td
(is)Tj
0.8504 0 Td
(a)Tj
0.6519 0 Td
(universal)Tj
3.8551 0 Td
(constant,)Tj
3.8664 0 Td
(not)Tj
-34.4406 -1.2983 Td
(only)Tj
1.9729 0 Td
(in)Tj
1.0375 0 Td
(mathematics)Tj
5.3291 0 Td
(but)Tj
1.5534 0 Td
(also)Tj
1.7631 0 Td
(for)Tj
1.389 0 Td
(biology.)Tj
-11.8488 -1.3039 Td
(Another)Tj
3.583 0 Td
(famous)Tj
3.1578 0 Td
(model)Tj
2.7439 0 Td
(that)Tj
1.7801 0 Td
(can)Tj
1.6214 0 Td
(generate)Tj
/F7 1 Tf
3.6114 0 Td
[()]TJ
/F14 1 Tf
0.7653 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4682 0 Td
(L-system)Tj
3.8268 0 Td
(\(a)Tj
0.9978 0 Td
(type)Tj
1.9105 0 Td
(of)Tj
1.0148 0 Td
(formal)Tj
2.8857 0 Td
(grammar\))Tj
4.2746 0 Td
([)Tj
0.83 0.64 0.02 0 k
(16)Tj
0 g
(].)Tj
-35.6879 -1.2983 Td
(The)Tj
1.7802 0 Td
(specific)Tj
3.1918 0 Td
(L-system)Tj
3.8267 0 Td
(that)Tj
1.7801 0 Td
(generates)Tj
/F7 1 Tf
3.9685 0 Td
[()]TJ
/F14 1 Tf
0.7654 0 Td
(has)Tj
1.542 0 Td
(the)Tj
1.474 0 Td
(following)Tj
3.9797 0 Td
(rules:)Tj
2.3755 0 Td
(for)Tj
1.3833 0 Td
(each)Tj
2.0295 0 Td
(generation,)Tj
4.7339 0 Td
(each)Tj
2.0239 0 Td
(Q)Tj
-34.8545 -1.2982 Td
(becomes)Tj
3.685 0 Td
(a)Tj
0.652 0 Td
(Q)Tj
0.9694 0 Td
(and)Tj
1.7292 0 Td
(an)Tj
1.2018 0 Td
(S,)Tj
0.9185 0 Td
(while)Tj
2.3697 0 Td
(each)Tj
2.0296 0 Td
(S)Tj
0.6973 0 Td
(becomes)Tj
3.685 0 Td
(a)Tj
0.652 0 Td
(Q.)Tj
1.1905 0 Td
(The)Tj
1.7858 0 Td
(system)Tj
2.9366 0 Td
(is)Tj
0.8504 0 Td
(initialised)Tj
4.1272 0 Td
(with)Tj
1.9956 0 Td
(a)Tj
0.652 0 Td
(string)Tj
2.5341 0 Td
(com-)Tj
-34.6617 -1.3039 Td
(posed)Tj
2.5569 0 Td
(of)Tj
1.0147 0 Td
(only)Tj
1.973 0 Td
(one)Tj
1.7007 0 Td
(Q.)Tj
1.1906 0 Td
(So)Tj
1.2019 0 Td
(at)Tj
0.9524 0 Td
(the)Tj
1.474 0 Td
(first)Tj
1.8028 0 Td
(generation,)Tj
4.7338 0 Td
(the)Tj
1.4683 0 Td
(string)Tj
2.5341 0 Td
(becomes)Tj
3.6851 0 Td
(QS;)Tj
1.6667 0 Td
(at)Tj
0.9525 0 Td
(the)Tj
1.4683 0 Td
(second)Tj
3.0104 0 Td
(genera-)Tj
-33.3862 -1.2983 Td
(tion,)Tj
2.0636 0 Td
(the)Tj
1.4684 0 Td
(string)Tj
2.5341 0 Td
(becomes)Tj
3.685 0 Td
(QSQ;)Tj
2.4151 0 Td
(then)Tj
2.0183 0 Td
(QSQQS,)Tj
3.634 0 Td
(QSQQSQSQ,)Tj
/F8 1 Tf
0 Tc
5.6068 0 Td
(.)Tj
0.4365 0 Td
(.)Tj
0.4309 0 Td
(.)Tj
/F14 1 Tf
-0.004 Tc
0.4932 0 Td
(The)Tj
1.7802 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(Q)Tj
0.9695 0 Td
(at)Tj
0.9524 0 Td
(each)Tj
-32.9213 -1.2983 Td
(generation)Tj
4.5071 0 Td
(forms)Tj
2.5681 0 Td
(the)Tj
1.4684 0 Td
(Fibonacci)Tj
4.1215 0 Td
(sequence)Tj
3.8608 0 Td
(\(as)Tj
1.355 0 Td
(well)Tj
1.8197 0 Td
(as)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
1.0148 0 Td
(S)Tj
0.6973 0 Td
(but)Tj
1.5534 0 Td
(with)Tj
1.9955 0 Td
(one)Tj
1.7008 0 Td
(generation)Tj
-32.5641 -1.3039 Td
(lag\).)Tj
1.9276 0 Td
(So)Tj
1.2018 0 Td
(the)Tj
1.4741 0 Td
(ratio)Tj
2.0976 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
1.0148 0 Td
(Q)Tj
0.9637 0 Td
(over)Tj
1.9786 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4184 0 Td
(of)Tj
1.0148 0 Td
(S)Tj
0.6973 0 Td
(goes)Tj
1.9729 0 Td
(to)Tj
/F7 1 Tf
1.0262 0 Td
[()]TJ
/F14 1 Tf
(.)Tj
0.9978 0 Td
(This)Tj
1.9842 0 Td
(specific)Tj
3.1918 0 Td
(L-system)Tj
3.8267 0 Td
(can)Tj
-36.1584 -1.2983 Td
(actually)Tj
3.2825 0 Td
(be)Tj
1.1509 0 Td
(written)Tj
3.1124 0 Td
(as)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(following)Tj
3.9798 0 Td
(reaction)Tj
3.8835 0 Td
(system,)Tj
/F18 1 Tf
0 Tc
-1.6781 -2.8686 Td
[()]TJ
/F11 1 Tf
1.0148 0 Td
(!)Tj
/F18 1 Tf
1.2812 0 Td
[()]TJ
/F11 1 Tf
0.9638 0 Td
()Tj
/F18 1 Tf
0.992 0 Td
[()]TJ
-4.2518 -1.7008 Td
[()]TJ
/F11 1 Tf
0.7483 0 Td
(!)Tj
/F18 1 Tf
1.2756 0 Td
[()]TJ
/F9 1 Tf
-2.9934 2.5625 Td
(\()Tj
/F11 1 Tf
21.1009 -1.7121 Td
()Tj
/F14 1 Tf
(2)Tj
/F11 1 Tf
()Tj
/F14 1 Tf
-0.004 Tc
-35.1493 -4.1215 Td
(This)Tj
1.9899 0 Td
(process)Tj
3.1862 0 Td
(is)Tj
0.8447 0 Td
(equivalent)Tj
4.354 0 Td
(to)Tj
1.0204 0 Td
(the)Tj
1.474 0 Td
(Fibonacci)Tj
4.1216 0 Td
(rabbit)Tj
2.6077 0 Td
(model.)Tj
2.9707 0 Td
(Note)Tj
2.1827 0 Td
(that)Tj
0.83 0.64 0.02 0 k
1.7801 0 Td
(Eq)Tj
1.2926 0 Td
(\(2\))Tj
0 g
1.3777 0 Td
(also)Tj
1.7688 0 Td
(involves)Tj
3.4809 0 Td
(self-)Tj
-35.6482 -1.2983 Td
(replication,)Tj
4.7452 0 Td
(because)Tj
3.3222 0 Td
(the)Tj
1.4683 0 Td
(two)Tj
1.7121 0 Td
(reactions)Tj
3.8551 0 Td
(add)Tj
1.7065 0 Td
(up)Tj
1.2642 0 Td
(to)Tj
1.0261 0 Td
(Q)Tj
/F11 1 Tf
0 Tc
0.9694 0 Td
(!)Tj
/F14 1 Tf
-0.004 Tc
1.2189 0 Td
(Q)Tj
0.9694 0 Td
(+)Tj
0.7994 0 Td
(Q)Tj
0.9638 0 Td
(\(by)Tj
1.525 0 Td
(cancelling)Tj
4.2463 0 Td
(S)Tj
0.6916 0 Td
(on)Tj
1.2756 0 Td
(both)Tj
2.0636 0 Td
(sides\))Tj
-33.8227 -1.2983 Td
(and)Tj
1.7291 0 Td
(Q)Tj
0.9638 0 Td
(is)Tj
0.8504 0 Td
(thus)Tj
1.9332 0 Td
(self-replicating.)Tj
6.3779 0 Td
(Similarly,)Tj
4.0309 0 Td
(the)Tj
1.4683 0 Td
(genealogical)Tj
5.1022 0 Td
(tree)Tj
1.7348 0 Td
(model)Tj
2.744 0 Td
([)Tj
0.83 0.64 0.02 0 k
(17)Tj
0 g
(,)Tj
0.83 0.64 0.02 0 k
1.7404 0 Td
(18)Tj
0 g
(])Tj
1.508 0 Td
(which)Tj
2.6532 0 Td
(can)Tj
1.6271 0 Td
(also)Tj
-34.4633 -1.3039 Td
(generate)Tj
/F7 1 Tf
3.6057 0 Td
[()]TJ
/F14 1 Tf
0.771 0 Td
(has)Tj
1.542 0 Td
(the)Tj
1.4684 0 Td
(same)Tj
2.2563 0 Td
(argument.)Tj
-8.4472 -1.2982 Td
(These)Tj
2.5682 0 Td
(models)Tj
3.1068 0 Td
(do,)Tj
1.4796 0 Td
(from)Tj
2.2054 0 Td
(a)Tj
0.6519 0 Td
(mathematical)Tj
5.6466 0 Td
(viewpoint,)Tj
4.4163 0 Td
(give)Tj
1.8311 0 Td
(rise)Tj
1.6384 0 Td
(to)Tj
1.0262 0 Td
(the)Tj
1.4683 0 Td
(golden)Tj
2.9424 0 Td
(ratio,)Tj
2.3187 0 Td
(but)Tj
1.5534 0 Td
(our)Tj
-34.0495 -1.2983 Td
(question)Tj
3.651 0 Td
(is)Tj
0.8391 0 Td
(whether)Tj
3.4639 0 Td
(the)Tj
1.4627 0 Td
(golden)Tj
2.9253 0 Td
(ratio)Tj
2.0919 0 Td
(has)Tj
1.5307 0 Td
(a)Tj
0.6463 0 Td
(special)Tj
2.8799 0 Td
(role)Tj
1.7632 0 Td
(in)Tj
1.0261 0 Td
(natural)Tj
3.0671 0 Td
(self-replicating)Tj
6.1454 0 Td
(systems)Tj
3.2882 0 Td
(in)Tj
1.0261 0 Td
(gen-)Tj
-35.8069 -1.3039 Td
(eral,)Tj
1.9162 0 Td
(as)Tj
1.0148 0 Td
(implied)Tj
3.2882 0 Td
(by)Tj
1.1792 0 Td
(the)Tj
1.4683 0 Td
(authors)Tj
3.2428 0 Td
(in)Tj
1.0319 0 Td
(papers)Tj
2.8459 0 Td
([)Tj
0.83 0.64 0.02 0 k
(13)Tj
0 g
()Tj
0.83 0.64 0.02 0 k
(15)Tj
0 g
(].)Tj
3.5432 0 Td
(Should)Tj
3.0274 0 Td
(we)Tj
1.3266 0 Td
(expect,)Tj
2.9934 0 Td
(in)Tj
1.0374 0 Td
(a)Tj
0.652 0 Td
(wide)Tj
2.1203 0 Td
(range)Tj
2.4605 0 Td
(of)Tj
1.0091 0 Td
(different)Tj
-34.1572 -1.2983 Td
(self-replicating)Tj
6.1512 0 Td
(systems,)Tj
3.5206 0 Td
(to)Tj
1.0261 0 Td
(find)Tj
1.8539 0 Td
(that)Tj
1.7801 0 Td
(the)Tj
1.4683 0 Td
(ratio)Tj
2.0977 0 Td
(of)Tj
1.0148 0 Td
(different)Tj
3.6565 0 Td
(components)Tj
5.1704 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(system)Tj
2.9423 0 Td
(is)Tj
0.8448 0 Td
(the)Tj
-34.0325 -1.2982 Td
(golden)Tj
2.9367 0 Td
(ratio?)Tj
2.4718 0 Td
(And)Tj
1.9786 0 Td
(if)Tj
0.7766 0 Td
(not,)Tj
1.7972 0 Td
(are)Tj
1.4513 0 Td
(there)Tj
2.2621 0 Td
(other)Tj
2.347 0 Td
(important)Tj
4.2802 0 Td
(mathematical)Tj
5.6466 0 Td
(constants)Tj
4.0025 0 Td
(that)Tj
1.7745 0 Td
(we)Tj
1.3322 0 Td
(should)Tj
-33.0573 -1.2983 Td
(expect)Tj
2.7723 0 Td
(to)Tj
1.0205 0 Td
(see)Tj
1.4286 0 Td
(in)Tj
1.0375 0 Td
(connection)Tj
4.7168 0 Td
(to)Tj
1.0261 0 Td
(self-replicating)Tj
6.1512 0 Td
(systems?)Tj
0.005 Tc
-16.9568 -1.3039 Td
(To)Tj
1.3607 0 Td
(answer)Tj
3.0954 0 Td
(these)Tj
2.296 0 Td
(questions)Tj
4.1046 0 Td
(we)Tj
1.3436 0 Td
(employ)Tj
3.2428 0 Td
(a)Tj
0.6633 0 Td
(framework)Tj
4.694 0 Td
(of)Tj
1.0375 0 Td
(chemically)Tj
4.5751 0 Td
(realistic)Tj
3.3902 0 Td
(self-replicating)Tj
-30.9994 -1.2983 Td
(reaction)Tj
3.566 0 Td
(systems,)Tj
3.5943 0 Td
(introduced)Tj
4.7338 0 Td
(by)Tj
1.1962 0 Td
(us)Tj
1.1282 0 Td
(in)Tj
1.0545 0 Td
(paper)Tj
2.5285 0 Td
([)Tj
0.83 0.64 0.02 0 k
(19)Tj
0 g
(].)Tj
2.1202 0 Td
(This)Tj
2.0239 0 Td
(theory)Tj
2.8573 0 Td
(has)Tj
1.5704 0 Td
(practical)Tj
3.7134 0 Td
(significance)Tj
5.0456 0 Td
(to)Tj
-35.1323 -1.2983 Td
(real)Tj
1.7291 0 Td
(chemistry)Tj
4.2463 0 Td
(and)Tj
1.7575 0 Td
(biology,)Tj
3.4752 0 Td
(and)Tj
1.7575 0 Td
(instantiations)Tj
5.7826 0 Td
(of)Tj
1.0318 0 Td
(this)Tj
1.7121 0 Td
(framework)Tj
4.6941 0 Td
(can)Tj
1.6554 0 Td
(capture)Tj
3.2769 0 Td
(a)Tj
0.6633 0 Td
(wide)Tj
2.16 0 Td
(range)Tj
-33.9418 -1.3039 Td
(of)Tj
1.0318 0 Td
(different)Tj
3.7361 0 Td
(natural)Tj
3.1464 0 Td
(chemical)Tj
3.8551 0 Td
(systems)Tj
3.3619 0 Td
(such)Tj
2.0976 0 Td
(as)Tj
1.0318 0 Td
(the)Tj
1.4966 0 Td
(citric)Tj
2.3244 0 Td
(acid)Tj
1.9048 0 Td
(cycle)Tj
2.2394 0 Td
(and)Tj
1.7575 0 Td
(the)Tj
/F7 1 Tf
1.4966 0 Td
[( )9()11()-9()6()7()-3()]TJ
/F14 1 Tf
3.3392 0 Td
(reaction.)Tj
-32.8192 -1.2982 Td
(In)Tj
1.1282 0 Td
(this)Tj
1.7064 0 Td
(theory,)Tj
3.0898 0 Td
(a)Tj
0.6633 0 Td
(self-replicating)Tj
6.2985 0 Td
(system)Tj
2.9877 0 Td
(consists)Tj
3.4243 0 Td
(of)Tj
1.0317 0 Td
(a)Tj
0.6633 0 Td
(few)Tj
1.6384 0 Td
(chemical)Tj
3.8607 0 Td
(reactions,)Tj
4.167 0 Td
(and)Tj
1.7574 0 Td
(self-replica-)Tj
-32.4167 -1.2983 Td
(tion)Tj
1.8765 0 Td
(is)Tj
0.8674 0 Td
(a)Tj
0.6633 0 Td
(system-level)Tj
5.1874 0 Td
(property:)Tj
3.9855 0 Td
(each)Tj
2.0693 0 Td
(reaction)Tj
3.5603 0 Td
(in)Tj
1.0544 0 Td
(the)Tj
1.4966 0 Td
(system)Tj
2.9934 0 Td
(is)Tj
0.8674 0 Td
(not)Tj
1.5987 0 Td
(able)Tj
1.8652 0 Td
(to)Tj
1.0432 0 Td
(self-replicate)Tj
5.4198 0 Td
(but)Tj
-34.5484 -1.3039 Td
(the)Tj
1.4967 0 Td
(system)Tj
2.9934 0 Td
(self-replicates)Tj
5.7883 0 Td
(as)Tj
1.0318 0 Td
(a)Tj
0.6633 0 Td
(whole.)Tj
2.8856 0 Td
(If)Tj
0.8674 0 Td
(the)Tj
1.4967 0 Td
(golden)Tj
2.9933 0 Td
(ratio)Tj
/F7 1 Tf
2.143 0 Td
[()]TJ
/F14 1 Tf
0.7767 0 Td
(does)Tj
2.0749 0 Td
(have)Tj
2.0976 0 Td
(a)Tj
0.6577 0 Td
(special)Tj
2.9593 0 Td
(role)Tj
1.8028 0 Td
(in)Tj
1.0545 0 Td
(natural)Tj
-33.783 -1.2983 Td
(self-replicating)Tj
6.2929 0 Td
(systems)Tj
3.3619 0 Td
(in)Tj
1.0544 0 Td
(general,)Tj
3.4299 0 Td
(we)Tj
1.3437 0 Td
(would)Tj
2.7609 0 Td
(expect)Tj
2.8232 0 Td
(to)Tj
1.0431 0 Td
(see)Tj
/F7 1 Tf
1.457 0 Td
[()]TJ
/F14 1 Tf
0.7767 0 Td
(appears)Tj
3.3392 0 Td
(quite)Tj
2.2904 0 Td
(a)Tj
0.6633 0 Td
(lot)Tj
1.2982 0 Td
(in)Tj
1.0545 0 Td
(these)Tj
-32.9893 -1.2983 Td
(systems.)Tj
-0.001 Tc
1.1962 -1.3039 Td
(This)Tj
2.0013 0 Td
(paper)Tj
2.5001 0 Td
(is)Tj
0.8504 0 Td
(organised)Tj
4.1556 0 Td
(as)Tj
1.0204 0 Td
(follows.)Tj
3.3052 0 Td
(Section)Tj
/F7 1 Tf
3.1861 0 Td
[(,)28()22()11()2()-9()4()11()-4()]TJ
3.9741 0 Td
[()16( )6(\r)]TJ
1.7404 0 Td
[()6()8()10()6()4(\r)-4()]TJ
/F14 1 Tf
3.5093 0 Td
(reintroduces)Tj
5.3064 0 Td
(the)Tj
-32.7455 -1.2982 Td
(framework)Tj
4.6431 0 Td
(in)Tj
1.0375 0 Td
(paper)Tj
2.5002 0 Td
([)Tj
0.83 0.64 0.02 0 k
(19)Tj
0 g
(])Tj
1.8651 0 Td
(for)Tj
1.3947 0 Td
(chemically)Tj
4.5127 0 Td
(realistic)Tj
3.3392 0 Td
(self-replicating)Tj
6.2021 0 Td
(reaction)Tj
3.5149 0 Td
(systems.)Tj
3.549 0 Td
(The)Tj
1.7914 0 Td
(first)Tj
-34.3499 -1.2983 Td
(part)Tj
1.8539 0 Td
(of)Tj
1.0204 0 Td
(Section)Tj
/F7 1 Tf
3.1805 0 Td
[(-)2()8()10()4()14()]TJ
/F14 1 Tf
2.948 0 Td
(elaborates)Tj
4.2519 0 Td
(on)Tj
1.287 0 Td
(the)Tj
1.474 0 Td
(scheme)Tj
3.2201 0 Td
(for)Tj
1.3945 0 Td
(population)Tj
4.6205 0 Td
(dynamics)Tj
4.0818 0 Td
(that)Tj
1.7859 0 Td
(we)Tj
1.3379 0 Td
(apply)Tj
2.4038 0 Td
(on)Tj
-34.8602 -1.2983 Td
(self-replicating)Tj
6.1965 0 Td
(systems,)Tj
3.549 0 Td
(and)Tj
1.7404 0 Td
(describe)Tj
3.549 0 Td
(two)Tj
1.7178 0 Td
(self-replicating)Tj
6.202 0 Td
(systems)Tj
3.3165 0 Td
(that)Tj
1.7915 0 Td
(are)Tj
1.457 0 Td
(characterised)Tj
5.5446 0 Td
(by)Tj
/F7 1 Tf
-35.0643 -1.3039 Td
[()]TJ
/F14 1 Tf
(.)Tj
0.9978 0 Td
(In)Tj
1.1169 0 Td
(the)Tj
1.4796 0 Td
(second)Tj
3.0274 0 Td
(part)Tj
1.8539 0 Td
(of)Tj
1.0204 0 Td
(Section)Tj
/F7 1 Tf
3.1861 0 Td
[(-)2()8()10()4()14()]TJ
/F14 1 Tf
(,)Tj
3.1692 0 Td
(we)Tj
1.3379 0 Td
(show)Tj
2.3073 0 Td
(that)Tj
1.7915 0 Td
(all)Tj
1.1565 0 Td
(of)Tj
1.0205 0 Td
(the)Tj
1.4796 0 Td
(analysable)Tj
4.337 0 Td
(self-replicating)Tj
-29.2816 -1.2982 Td
(systems)Tj
3.3165 0 Td
(up)Tj
1.2756 0 Td
(to)Tj
1.0318 0 Td
(a)Tj
0.652 0 Td
(certain)Tj
3.0104 0 Td
(size)Tj
1.6951 0 Td
(are)Tj
1.457 0 Td
(characterised)Tj
5.5445 0 Td
(by)Tj
1.1905 0 Td
(a)Tj
0.6576 0 Td
(limited)Tj
3.0897 0 Td
(number)Tj
3.4356 0 Td
(of)Tj
1.0205 0 Td
(distinct)Tj
3.2371 0 Td
(characteristic)Tj
-30.6139 -1.2983 Td
(equations)Tj
4.1216 0 Td
(and)Tj
1.7348 0 Td
(numbers.)Tj
4.0308 0 Td
(In)Tj
1.1168 0 Td
(the)Tj
1.4741 0 Td
(third)Tj
2.228 0 Td
(part)Tj
1.8538 0 Td
(of)Tj
1.0205 0 Td
(Section)Tj
/F7 1 Tf
3.186 0 Td
[(-)2()8()10()4()14()]TJ
/F14 1 Tf
(,)Tj
3.1748 0 Td
(we)Tj
1.3323 0 Td
(introduce)Tj
4.1385 0 Td
(the)Tj
1.4797 0 Td
(population)Tj
-30.8917 -1.3039 Td
(dynamics)Tj
4.0762 0 Td
(for)Tj
1.4003 0 Td
(chemical)Tj
3.8098 0 Td
(reaction)Tj
3.5149 0 Td
(systems)Tj
3.3222 0 Td
(under)Tj
2.6305 0 Td
(the)Tj
1.4796 0 Td
(law)Tj
1.5931 0 Td
(of)Tj
1.0204 0 Td
(mass)Tj
2.2054 0 Td
(action,)Tj
2.948 0 Td
(and)Tj
1.7404 0 Td
(find)Tj
1.8595 0 Td
(that)Tj
1.7915 0 Td
(the)Tj
-33.3918 -1.2983 Td
(characteristic)Tj
5.5842 0 Td
(number)Tj
3.4356 0 Td
(of)Tj
1.0205 0 Td
(a)Tj
0.6576 0 Td
(self-replicating)Tj
6.2022 0 Td
(system)Tj
2.9536 0 Td
(is)Tj
0.856 0 Td
(a)Tj
0.6576 0 Td
(transient)Tj
3.7928 0 Td
(behaviour)Tj
4.2689 0 Td
(corresponding)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 107.1496 23.6976 re
W* n
q
107.0929 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 468.17 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Goden)Tj
3.1748 0 Td
(ratio)Tj
2.126 0 Td
(and)Tj
1.8567 0 Td
(self-replica)Tj
4.7339 0 Td
(tion)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
81.5811 34.9228 m
237.8835 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(ONE)Tj
2.3669 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https://doi.or)Tj
5.4142 0 Td
(g/10.137)Tj
3.8198 0 Td
(1/journal.po)Tj
5.1236 0 Td
(ne.02006)Tj
4.089 0 Td
(01)Tj
0 g
2.0906 0 Td
(July)Tj
1.9701 0 Td
(16,)Tj
1.5874 0 Td
(2018)Tj
35.3483 0 Td
(3)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
71 0 obj
<>stream
endstream
endobj
72 0 obj
<>stream
endstream
endobj
73 0 obj
<>stream
endstream
endobj
74 0 obj
<>stream
endstream
endobj
75 0 obj
<>stream
endstream
endobj
76 0 obj
<>stream
endstream
endobj
77 0 obj
<>stream
endstream
endobj
78 0 obj
<>stream
endstream
endobj
79 0 obj
<>stream
endstream
endobj
80 0 obj
<>stream
BT
66.402 0 Td
(18)Tj
ET
Q
endstream
endobj
81 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 12 0 R/Annots 84 0 R/Contents 85 0 R/TrimBox[0 0 612 792]>>
endobj
84 0 obj
[86 0 R 87 0 R 88 0 R]
endobj
86 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref019)>>
endobj
87 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref019)>>
endobj
88 0 obj
<>/Border[0 0 0]/A 89 0 R>>
endobj
89 0 obj
<>
endobj
85 0 obj
[90 0 R 91 0 R 92 0 R 93 0 R 94 0 R]
endobj
90 0 obj
<>stream
q
0.83 0.64 0.02 0 k
278.9291 612.9638 m
288.4535 612.9638 l
h
f*
251.3197 235.8992 m
260.8441 235.8992 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 200.0125 707.4141 cm
BT
/F14 1 Tf
1 TL
-0.001 Tc
0 0 Td
(to)Tj
1.0318 0 Td
(the)Tj
1.474 0 Td
(scenario)Tj
3.5829 0 Td
(that)Tj
1.7915 0 Td
(the)Tj
1.4797 0 Td
(resource)Tj
3.651 0 Td
(inside)Tj
2.6305 0 Td
(the)Tj
1.4797 0 Td
(system)Tj
2.9594 0 Td
(is)Tj
0.8503 0 Td
(infinite,)Tj
3.3846 0 Td
(which)Tj
2.6645 0 Td
(is)Tj
0.8504 0 Td
(not)Tj
1.5874 0 Td
(always)Tj
2.8517 0 Td
(the)Tj
1.474 0 Td
(case)Tj
1.8765 0 Td
(in)Tj
-35.6199 -1.3039 Td
(practice.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 649.0204 cm
BT
/F2 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Materials)Tj
4.5071 0 Td
(and)Tj
1.989 0 Td
(methods)Tj
/F19 1 Tf
-6.4961 -1.4976 Td
(Chemically)Tj
4.9087 0 Td
(realistic)Tj
3.5244 0 Td
(self-replicating)Tj
6.4914 0 Td
(reaction)Tj
3.652 0 Td
(systems)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 614.0409 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(In)Tj
1.1055 0 Td
(an)Tj
1.2018 0 Td
(earlier)Tj
2.761 0 Td
(paper)Tj
2.4831 0 Td
([)Tj
0.83 0.64 0.02 0 k
(19)Tj
0 g
(],)Tj
2.0749 0 Td
(we)Tj
1.3267 0 Td
(described)Tj
4.0535 0 Td
(a)Tj
0.6519 0 Td
(general)Tj
3.1351 0 Td
(framework)Tj
4.6148 0 Td
(to)Tj
1.0261 0 Td
(construct)Tj
3.9799 0 Td
(chemically)Tj
4.4843 0 Td
(realistic)Tj
-32.8986 -1.2982 Td
(reaction)Tj
3.4922 0 Td
(systems.)Tj
3.5263 0 Td
(In)Tj
1.1055 0 Td
(this)Tj
1.6724 0 Td
(framework,)Tj
4.8416 0 Td
(a)Tj
0.6576 0 Td
(molecule)Tj
3.8381 0 Td
(is)Tj
0.8447 0 Td
(defined)Tj
3.2258 0 Td
(by)Tj
1.1849 0 Td
(its)Tj
1.1452 0 Td
(integer)Tj
3.016 0 Td
(mass,)Tj
/F7 1 Tf
3.2032 0 Td
[()]TJ
/F14 1 Tf
(,)Tj
0.7143 0 Td
(and)Tj
1.7291 0 Td
(thus)Tj
-34.1969 -1.3946 Td
(denoted)Tj
ET
Q
q
1 j
1 J
0 w
234.7654 595.1622 m
237.9969 595.1622 l
237.9969 594.7654 l
234.7654 594.7654 l
f*
10 0 0 10 234.7653 587.1118 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
-0.004 Tc
0.3231 0 Td
(;)Tj
0.4422 0 Td
(all)Tj
1.1452 0 Td
(reactions)Tj
3.8551 0 Td
(that)Tj
1.7801 0 Td
(conserve)Tj
3.7304 0 Td
(massthe)Tj
4.371 0 Td
(total)Tj
2.0012 0 Td
(mass)Tj
2.1997 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(reactant)Tj
3.4526 0 Td
(side)Tj
1.7972 0 Td
(adds)Tj
2.0692 0 Td
(up)Tj
1.2643 0 Td
(to)Tj
-34.6504 -1.3039 Td
(those)Tj
2.3357 0 Td
(on)Tj
1.2755 0 Td
(the)Tj
1.4683 0 Td
(product)Tj
3.3959 0 Td
(sideare)Tj
3.9515 0 Td
(possible;)Tj
3.634 0 Td
(only)Tj
1.9786 0 Td
(two)Tj
1.7064 0 Td
(types)Tj
2.2734 0 Td
(of)Tj
1.0148 0 Td
(reaction)Tj
3.4979 0 Td
(are)Tj
1.4457 0 Td
(allowed,)Tj
3.5149 0 Td
(synthesis)Tj
3.8211 0 Td
(of)Tj
-35.3137 -1.423 Td
(two)Tj
1.7064 0 Td
(molecules)Tj
4.2009 0 Td
(to)Tj
1.0261 0 Td
(create)Tj
2.5908 0 Td
(a)Tj
0.6577 0 Td
(molecule)Tj
3.8324 0 Td
(of)Tj
1.0148 0 Td
(greater)Tj
3.0104 0 Td
(mass)Tj
2.194 0 Td
(\(e.g.,)Tj
ET
Q
q
1 j
1 J
0 w
423.6094 568.063 m
429.1087 568.063 l
429.1087 567.6661 l
423.6094 567.6661 l
f*
10 0 0 10 423.6094 559.8425 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F11 1 Tf
0.771 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
441.2976 568.1764 m
446.7969 568.1764 l
446.7969 567.7795 l
441.2976 567.7795 l
f*
10 0 0 10 441.2976 559.8425 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(4)Tj
/F11 1 Tf
0.8277 0 Td
(!)Tj
ET
Q
q
1 j
1 J
0 w
462.3307 568.063 m
467.8299 568.063 l
467.8299 567.6661 l
462.3307 567.6661 l
f*
10 0 0 10 462.3307 559.8425 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(6)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(\))Tj
0.5612 0 Td
(and)Tj
1.7291 0 Td
(decomposition)Tj
6.1965 0 Td
(into)Tj
-35.2683 -1.4173 Td
(two)Tj
1.7008 0 Td
(molecules)Tj
4.1952 0 Td
(to)Tj
1.0205 0 Td
(create)Tj
2.5908 0 Td
(two)Tj
1.7008 0 Td
(molecules)Tj
4.1953 0 Td
(of)Tj
1.0091 0 Td
(lower)Tj
2.4491 0 Td
(mass)Tj
2.1884 0 Td
(\(e.g.,)Tj
ET
Q
q
1 j
1 J
0 w
431.7165 553.9465 m
437.2157 553.9465 l
437.2157 553.5496 l
431.7165 553.5496 l
f*
10 0 0 10 431.7165 545.6692 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(6)Tj
/F11 1 Tf
0.8277 0 Td
(!)Tj
ET
Q
q
1 j
1 J
0 w
452.8063 553.9465 m
458.3055 553.9465 l
458.3055 553.5496 l
452.8063 553.5496 l
f*
10 0 0 10 452.8062 545.6692 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F11 1 Tf
0.771 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
470.4378 553.9465 m
475.937 553.9465 l
475.937 553.5496 l
470.4378 553.5496 l
f*
10 0 0 10 470.4377 545.6692 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(\);)Tj
0.7823 0 Td
(every)Tj
2.3414 0 Td
(reaction)Tj
3.4923 0 Td
(is)Tj
0.839 0 Td
(chem-)Tj
-35.0472 -1.2982 Td
(ically)Tj
2.2904 0 Td
(spontaneous.)Tj
5.4765 0 Td
(The)Tj
1.7858 0 Td
(last)Tj
1.559 0 Td
(requirement)Tj
5.1987 0 Td
(constrains)Tj
4.3427 0 Td
(the)Tj
1.4683 0 Td
(details)Tj
2.778 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4682 0 Td
(thermodynamic)Tj
6.6444 0 Td
(free)Tj
-34.0268 -1.2983 Td
(energy)Tj
2.9083 0 Td
(of)Tj
1.0148 0 Td
(each)Tj
2.0239 0 Td
(molecule)Tj
3.8381 0 Td
(and)Tj
1.7292 0 Td
(reaction,)Tj
3.719 0 Td
(which)Tj
2.6532 0 Td
(we)Tj
1.3266 0 Td
(do)Tj
1.2529 0 Td
(not)Tj
1.5761 0 Td
(need)Tj
2.1429 0 Td
(to)Tj
1.0262 0 Td
(consider)Tj
3.6509 0 Td
(in)Tj
1.0318 0 Td
(this)Tj
1.6781 0 Td
(paper,)Tj
2.7042 0 Td
(but)Tj
1.5534 0 Td
(it)Tj
-35.8296 -1.3039 Td
(does)Tj
2.0353 0 Td
(have)Tj
2.0579 0 Td
(two)Tj
1.7064 0 Td
(consequences)Tj
5.6977 0 Td
(related)Tj
2.9423 0 Td
(to)Tj
1.0261 0 Td
(this)Tj
1.6725 0 Td
(paper.)Tj
2.7042 0 Td
(The)Tj
1.7801 0 Td
(first)Tj
1.8085 0 Td
(one)Tj
1.6951 0 Td
(is)Tj
0.8448 0 Td
(that)Tj
1.78 0 Td
(a)Tj
0.652 0 Td
(reaction)Tj
3.4922 0 Td
(and)Tj
1.7235 0 Td
(its)Tj
1.1452 0 Td
(reverse)Tj
-34.7638 -1.423 Td
(reaction,)Tj
3.719 0 Td
(e.g.,)Tj
ET
Q
q
1 j
1 J
0 w
255.0614 500.6551 m
260.5606 500.6551 l
260.5606 500.2583 l
255.0614 500.2583 l
f*
10 0 0 10 255.0614 492.4346 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F11 1 Tf
0.771 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
272.6929 500.7685 m
278.1921 500.7685 l
278.1921 500.3717 l
272.6929 500.3717 l
f*
10 0 0 10 272.6929 492.4346 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(4)Tj
/F11 1 Tf
0.8277 0 Td
(!)Tj
ET
Q
q
1 j
1 J
0 w
293.7827 500.6551 m
299.2819 500.6551 l
299.2819 500.2583 l
293.7827 500.2583 l
f*
10 0 0 10 293.7826 492.4346 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(6)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(and)Tj
ET
Q
q
1 j
1 J
0 w
318.7843 500.6551 m
324.2835 500.6551 l
324.2835 500.2583 l
318.7843 500.2583 l
f*
10 0 0 10 318.7842 492.4346 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(6)Tj
/F11 1 Tf
0.8277 0 Td
(!)Tj
ET
Q
q
1 j
1 J
0 w
339.8173 500.6551 m
345.3165 500.6551 l
345.3165 500.2583 l
339.8173 500.2583 l
f*
10 0 0 10 339.8173 492.4346 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F11 1 Tf
0.7766 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
357.5055 500.7685 m
363.0047 500.7685 l
363.0047 500.3717 l
357.5055 500.3717 l
f*
10 0 0 10 357.5055 492.4346 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(4)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(,)Tj
0.4478 0 Td
(cannot)Tj
2.9764 0 Td
(both)Tj
2.0636 0 Td
(appear)Tj
2.914 0 Td
(in)Tj
1.0375 0 Td
(one)Tj
1.6951 0 Td
(system.)Tj
3.1634 0 Td
(The)Tj
1.7858 0 Td
(second)Tj
3.0104 0 Td
(con-)Tj
-35.393 -1.3039 Td
(sequence)Tj
3.8551 0 Td
(will)Tj
1.6667 0 Td
(be)Tj
1.1509 0 Td
(introduced)Tj
4.6431 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.474 0 Td
(next)Tj
1.9501 0 Td
(paragraph.)Tj
-14.5755 -1.2982 Td
(By)Tj
1.2585 0 Td
(choosing)Tj
3.8268 0 Td
(some)Tj
2.3301 0 Td
(reactions)Tj
3.8551 0 Td
(that)Tj
1.7744 0 Td
(satisfy)Tj
2.6872 0 Td
(the)Tj
1.4683 0 Td
(requirements)Tj
5.5615 0 Td
(above,)Tj
2.7723 0 Td
(we)Tj
1.3266 0 Td
(can)Tj
1.6271 0 Td
(construct)Tj
3.9798 0 Td
(a)Tj
0.652 0 Td
(chemi-)Tj
-34.3159 -1.2983 Td
(cally)Tj
2.0239 0 Td
(realistic)Tj
3.3108 0 Td
(reaction)Tj
3.4923 0 Td
(system,)Tj
3.1634 0 Td
(namely,)Tj
3.3732 0 Td
(an)Tj
1.2018 0 Td
(instantiation)Tj
5.3008 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(general)Tj
3.1294 0 Td
(framework.)Tj
4.8416 0 Td
(The)Tj
1.7858 0 Td
(follow-)Tj
-34.1061 -1.3039 Td
(ing)Tj
1.5023 0 Td
(system)Tj
2.9367 0 Td
(is)Tj
0.8447 0 Td
(one)Tj
1.7008 0 Td
(of)Tj
1.0148 0 Td
(such)Tj
2.0579 0 Td
(instantiations,)Tj
ET
Q
q
1 j
1 J
0 w
369.2976 428.9953 m
374.7969 428.9953 l
374.7969 428.5984 l
369.2976 428.5984 l
f*
10 0 0 10 369.2976 420.7748 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F11 1 Tf
1.5477 0 Td
(!)Tj
ET
Q
q
1 j
1 J
0 w
397.5874 428.9953 m
403.0866 428.9953 l
403.0866 428.5984 l
397.5874 428.5984 l
f*
10 0 0 10 397.5874 420.7748 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F11 1 Tf
0.771 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
415.2189 428.9953 m
420.7181 428.9953 l
420.7181 428.5984 l
415.2189 428.5984 l
f*
10 0 0 10 415.2188 420.7748 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
369.2976 402.0661 m
374.7969 402.0661 l
374.7969 401.6693 l
369.2976 401.6693 l
f*
10 0 0 10 369.2976 393.7889 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
/F11 1 Tf
1.5477 0 Td
(!)Tj
ET
Q
q
1 j
1 J
0 w
397.5874 402.0661 m
403.0866 402.0661 l
403.0866 401.6693 l
397.5874 401.6693 l
f*
10 0 0 10 397.5874 393.7889 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F11 1 Tf
0.771 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
415.2189 402.0661 m
420.7181 402.0661 l
420.7181 401.6693 l
415.2189 401.6693 l
f*
10 0 0 10 415.2188 393.7889 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
351.6094 375.137 m
357.1087 375.137 l
357.1087 374.7402 l
351.6094 374.7402 l
f*
10 0 0 10 351.6094 366.8598 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F11 1 Tf
0.771 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
369.2976 375.2504 m
374.7969 375.2504 l
374.7969 374.8535 l
369.2976 374.8535 l
f*
10 0 0 10 369.2976 366.8598 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(4)Tj
/F11 1 Tf
1.5477 0 Td
(!)Tj
ET
Q
q
1 j
1 J
0 w
397.5874 375.137 m
403.0866 375.137 l
403.0866 374.7402 l
397.5874 374.7402 l
f*
10 0 0 10 397.5874 366.8598 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
369.2976 348.1512 m
374.7969 348.1512 l
374.7969 347.7543 l
369.2976 347.7543 l
f*
10 0 0 10 369.2976 339.9307 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
/F11 1 Tf
1.5477 0 Td
(!)Tj
ET
Q
q
1 j
1 J
0 w
397.5874 348.1512 m
403.0866 348.1512 l
403.0866 347.7543 l
397.5874 347.7543 l
f*
10 0 0 10 397.5874 339.9307 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F11 1 Tf
0.771 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
415.2189 348.1512 m
420.7181 348.1512 l
420.7181 347.7543 l
415.2189 347.7543 l
f*
10 0 0 10 415.2188 339.9307 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
/F9 1 Tf
-7.5797 8.7589 Td
(8)Tj
0 -0.8957 Td
(>)Tj
0 -0.2891 Td
(>)Tj
0 -0.2892 Td
(>)Tj
0 -0.2948 Td
(>)Tj
0 -0.2891 Td
(>)Tj
0 -0.2948 Td
(>)Tj
0 -0.2891 Td
(>)Tj
0 -0.2892 Td
(>)Tj
0 -0.2948 Td
(>)Tj
0 -0.2891 Td
(<)Tj
0 -1.7915 Td
(>)Tj
0 -0.2891 Td
(>)Tj
0 -0.2948 Td
(>)Tj
0 -0.2891 Td
(>)Tj
0 -0.2892 Td
(>)Tj
0 -0.2948 Td
(>)Tj
0 -0.2891 Td
(>)Tj
0 -0.2891 Td
(>)Tj
0 -0.2948 Td
(>)Tj
0 -0.2892 Td
(:)Tj
/F11 1 Tf
22.4048 3.2655 Td
()Tj
/F14 1 Tf
(3)Tj
/F11 1 Tf
()Tj
/F14 1 Tf
-0.004 Tc
-35.1493 -6.3494 Td
(We)Tj
1.61 0 Td
(define)Tj
2.6986 0 Td
(the)Tj
/F7 1 Tf
1.4683 0 Td
[()20()8()-3()11()12()20(\n)7()]TJ
3.4243 0 Td
[()6()10()4()7(\n)1()4()4()]TJ
/F14 1 Tf
3.617 0 Td
(to)Tj
1.0261 0 Td
(be)Tj
1.1508 0 Td
(the)Tj
1.4684 0 Td
(molecule)Tj
3.8381 0 Td
(that)Tj
1.78 0 Td
(only)Tj
1.9729 0 Td
(appears)Tj
3.2768 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.474 0 Td
(reactant)Tj
3.4469 0 Td
(side)Tj
-34.724 -1.4287 Td
(\()Tj
ET
Q
q
1 j
1 J
0 w
203.4142 311.5276 m
208.9134 311.5276 l
208.9134 311.1307 l
203.4142 311.1307 l
f*
10 0 0 10 203.4141 303.137 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(4)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(in)Tj
1.0318 0 Td
(this)Tj
1.6781 0 Td
(case\).)Tj
2.4264 0 Td
(For)Tj
1.6271 0 Td
(any)Tj
1.6554 0 Td
(chemically)Tj
4.4844 0 Td
(realistic)Tj
3.3108 0 Td
(self-replicating)Tj
6.1512 0 Td
(system,)Tj
3.1634 0 Td
(there)Tj
2.2677 0 Td
(is)Tj
0.8447 0 Td
(at)Tj
0.9525 0 Td
(least)Tj
1.9842 0 Td
(one)Tj
1.7008 0 Td
(type)Tj
1.9162 0 Td
(of)Tj
-36.3058 -1.2982 Td
(resource)Tj
3.6282 0 Td
(molecule.)Tj
4.0592 0 Td
(This)Tj
1.9899 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4683 0 Td
(second)Tj
3.0104 0 Td
(consequence)Tj
5.3348 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(chemical)Tj
4.1726 0 Td
(spontaneity)Tj
5.2724 0 Td
(requirement)Tj
-32.275 -1.2983 Td
(above.)Tj
2.7722 0 Td
(We)Tj
1.6044 0 Td
(define)Tj
2.6985 0 Td
(an)Tj
/F7 1 Tf
1.2076 0 Td
[()12( )22()11()2()-9()6()7(\r)12()4()22()11()]TJ
5.176 0 Td
[()6()10()4()7(\n)1()4()4()]TJ
/F14 1 Tf
3.617 0 Td
(to)Tj
1.0261 0 Td
(be)Tj
1.1509 0 Td
(any)Tj
1.6554 0 Td
(molecule)Tj
3.8381 0 Td
(that)Tj
1.7801 0 Td
(appears)Tj
3.2769 0 Td
(on)Tj
1.2756 0 Td
(both)Tj
2.0579 0 Td
(the)Tj
1.4683 0 Td
(reac-)Tj
-34.605 -1.4173 Td
(tant)Tj
1.797 0 Td
(side)Tj
1.8029 0 Td
(and)Tj
1.7291 0 Td
(the)Tj
1.4683 0 Td
(product)Tj
3.3902 0 Td
(side)Tj
1.8029 0 Td
(\()Tj
ET
Q
q
1 j
1 J
0 w
323.3197 271.2756 m
328.8189 271.2756 l
328.8189 270.8787 l
323.3197 270.8787 l
f*
10 0 0 10 323.3196 262.9984 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(,)Tj
ET
Q
q
1 j
1 J
0 w
333.2409 271.2756 m
338.7402 271.2756 l
338.7402 270.8787 l
333.2409 270.8787 l
f*
10 0 0 10 333.2409 262.9984 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(,)Tj
ET
Q
q
1 j
1 J
0 w
343.2189 271.2756 m
348.7181 271.2756 l
348.7181 270.8787 l
343.2189 270.8787 l
f*
10 0 0 10 343.2188 262.9984 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(and)Tj
ET
Q
q
1 j
1 J
0 w
368.2205 271.2756 m
373.7197 271.2756 l
373.7197 270.8787 l
368.2205 270.8787 l
f*
10 0 0 10 368.2204 262.9984 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(in)Tj
1.0374 0 Td
(this)Tj
1.6725 0 Td
(case\),)Tj
2.4264 0 Td
(and)Tj
1.7291 0 Td
(the)Tj
/F7 1 Tf
1.474 0 Td
[(!)3()9()11()]TJ
2.3868 0 Td
[()6()10()4()7(\n)1()4()4()]TJ
/F14 1 Tf
3.617 0 Td
(to)Tj
1.0261 0 Td
(be)Tj
1.1509 0 Td
(the)Tj
1.4683 0 Td
(mol-)Tj
-35.5801 -1.2982 Td
(ecule)Tj
2.262 0 Td
(that)Tj
1.7801 0 Td
(only)Tj
1.9786 0 Td
(appears)Tj
3.2768 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4684 0 Td
(product)Tj
3.3902 0 Td
(side)Tj
1.8027 0 Td
(\(there)Tj
2.6022 0 Td
(is)Tj
0.8504 0 Td
(no)Tj
1.2756 0 Td
(in)Tj
1.0374 0 Td
(this)Tj
1.6725 0 Td
(case\).)Tj
-23.4763 -1.3039 Td
(In)Tj
1.1112 0 Td
(paper)Tj
2.4831 0 Td
([)Tj
0.83 0.64 0.02 0 k
(19)Tj
0 g
(],)Tj
2.0749 0 Td
(we)Tj
1.3323 0 Td
(show)Tj
2.2961 0 Td
(that)Tj
1.7801 0 Td
(a)Tj
0.652 0 Td
(chemically)Tj
4.4899 0 Td
(realistic)Tj
3.3109 0 Td
(reaction)Tj
3.4922 0 Td
(system)Tj
2.9367 0 Td
(is)Tj
0.8504 0 Td
(self-replicating)Tj
6.1511 0 Td
(if)Tj
0.7711 0 Td
(the)Tj
-34.9282 -1.2983 Td
(following)Tj
3.9798 0 Td
(three)Tj
2.262 0 Td
(criteria)Tj
3.0784 0 Td
(are)Tj
1.4457 0 Td
(satisfied:)Tj
-10.0743 -1.8992 Td
(1.)Tj
1.3096 0 Td
(For)Tj
1.6214 0 Td
(every)Tj
2.3528 0 Td
(reaction,)Tj
3.7133 0 Td
(at)Tj
0.9525 0 Td
(least)Tj
1.9842 0 Td
(one)Tj
1.7008 0 Td
(type)Tj
1.9105 0 Td
(of)Tj
1.0147 0 Td
(its)Tj
1.1509 0 Td
(reactants)Tj
3.8097 0 Td
(comes)Tj
2.7553 0 Td
(from)Tj
2.2053 0 Td
(the)Tj
1.4683 0 Td
(products)Tj
3.7531 0 Td
(of)Tj
1.0205 0 Td
(other)Tj
-31.4133 -1.2983 Td
(reactions;)Tj
-1.3096 -1.8992 Td
(2.)Tj
1.3096 0 Td
(There)Tj
2.5739 0 Td
(is)Tj
0.8503 0 Td
(at)Tj
0.9525 0 Td
(least)Tj
1.9786 0 Td
(one)Tj
1.7007 0 Td
(intermediate)Tj
5.3235 0 Td
(molecule)Tj
3.8379 0 Td
(that)Tj
1.7802 0 Td
(appears)Tj
3.2768 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(reactant)Tj
3.4526 0 Td
(side)Tj
1.7972 0 Td
(fewer)Tj
2.4094 0 Td
(times)Tj
-32.6775 -1.3039 Td
(than)Tj
2.0239 0 Td
(that)Tj
1.7802 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(product)Tj
3.3959 0 Td
(side;)Tj
-11.2535 -1.8992 Td
(3.)Tj
1.3096 0 Td
(There)Tj
2.5739 0 Td
(are)Tj
1.4513 0 Td
(no)Tj
1.2756 0 Td
(intermediate)Tj
5.3234 0 Td
(molecules)Tj
4.1952 0 Td
(that)Tj
1.7801 0 Td
(appear)Tj
2.914 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.474 0 Td
(reactant)Tj
3.4469 0 Td
(side)Tj
1.8028 0 Td
(more)Tj
2.3414 0 Td
(often)Tj
2.2847 0 Td
(than)Tj
2.0296 0 Td
(on)Tj
-34.1685 -1.2982 Td
(the)Tj
1.4684 0 Td
(product)Tj
3.3902 0 Td
(side.)Tj
-5.6636 -1.8992 Td
(In)Tj
1.1112 0 Td
(this)Tj
1.6724 0 Td
(paper)Tj
2.4831 0 Td
(we)Tj
1.3323 0 Td
(introduce)Tj
4.1102 0 Td
(an)Tj
1.2019 0 Td
(alternative,)Tj
4.6487 0 Td
(narrower)Tj
3.9288 0 Td
(criterion)Tj
3.6963 0 Td
(under)Tj
2.6192 0 Td
(which)Tj
2.6532 0 Td
(certain)Tj
2.9877 0 Td
(chemi-)Tj
-33.6412 -1.304 Td
(cally)Tj
2.0239 0 Td
(realistic)Tj
3.3108 0 Td
(self-replicating)Tj
6.1512 0 Td
(systems)Tj
3.2995 0 Td
(are)Tj
1.4513 0 Td
(analysable.)Tj
4.5297 0 Td
(We)Tj
1.61 0 Td
(say)Tj
1.4684 0 Td
(that)Tj
1.7801 0 Td
(a)Tj
0.6576 0 Td
(self-replicating)Tj
6.1512 0 Td
(system)Tj
2.9367 0 Td
(is)Tj
-35.3704 -1.2982 Td
(analysable)Tj
4.3086 0 Td
(if)Tj
0.7767 0 Td
(it)Tj
0.7823 0 Td
(satisfies)Tj
3.2825 0 Td
(criterion)Tj
3.6964 0 Td
(1,)Tj
0.9184 0 Td
(2,)Tj
0.9241 0 Td
(and)Tj
1.7291 0 Td
(the)Tj
1.4683 0 Td
(following)Tj
3.9798 0 Td
(criterion)Tj
3.6963 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 460.4031 86.6267 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 464.4283 82.9984 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(:)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 107.1496 23.6976 re
W* n
q
107.0929 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 468.17 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Goden)Tj
3.1748 0 Td
(ratio)Tj
2.126 0 Td
(and)Tj
1.8567 0 Td
(self-replica)Tj
4.7339 0 Td
(tion)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
81.5811 34.9228 m
237.8835 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(ONE)Tj
2.3669 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https://doi.or)Tj
5.4142 0 Td
(g/10.137)Tj
3.8198 0 Td
(1/journal.po)Tj
5.1236 0 Td
(ne.02006)Tj
4.089 0 Td
(01)Tj
0 g
2.0906 0 Td
(July)Tj
1.9701 0 Td
(16,)Tj
1.5874 0 Td
(2018)Tj
35.3483 0 Td
(4)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
91 0 obj
<>stream
endstream
endobj
92 0 obj
<>stream
endstream
endobj
93 0 obj
<>stream
endstream
endobj
94 0 obj
<>stream
BT
66.402 0 Td
(18)Tj
ET
Q
endstream
endobj
95 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 12 0 R/Annots 97 0 R/Contents 98 0 R/TrimBox[0 0 612 792]>>
endobj
97 0 obj
[99 0 R 100 0 R 101 0 R 102 0 R 103 0 R]
endobj
99 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e010)>>
endobj
100 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e010)>>
endobj
101 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e010)>>
endobj
102 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.t001)>>
endobj
103 0 obj
<>/Border[0 0 0]/A 104 0 R>>
endobj
104 0 obj
<>
endobj
98 0 obj
[105 0 R 106 0 R 107 0 R 108 0 R 109 0 R]
endobj
105 0 obj
<>stream
q
0.83 0.64 0.02 0 k
281.0268 674.3055 m
305.5748 674.3055 l
h
f*
323.4331 563.3008 m
348.0378 563.3008 l
h
f*
445.0394 441.2409 m
469.5307 441.2409 l
h
f*
211.9748 150.3496 m
241.2283 150.3496 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 202.9606 707.4141 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 207.7228 711.0425 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 211.6913 707.4141 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
0.8333 0 Td
(On)Tj
1.5137 0 Td
(the)Tj
1.4684 0 Td
(reactant)Tj
3.4525 0 Td
(side)Tj
1.7972 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(whole)Tj
2.6136 0 Td
(system,)Tj
3.1634 0 Td
(each)Tj
2.0239 0 Td
(intermediate)Tj
5.3235 0 Td
(molecule)Tj
3.838 0 Td
(species)Tj
2.9991 0 Td
(appears)Tj
3.2768 0 Td
(at)Tj
-33.9532 -1.3039 Td
(most)Tj
2.2054 0 Td
(once.)Tj
-3.0104 -1.8992 Td
(Note)Tj
2.1883 0 Td
(that)Tj
1.7802 0 Td
(system)Tj
0.83 0.64 0.02 0 k
2.9366 0 Td
(Eq)Tj
1.2926 0 Td
(\(3\))Tj
0 g
1.3777 0 Td
(satisfies)Tj
3.2825 0 Td
(all)Tj
1.1452 0 Td
(of)Tj
1.0148 0 Td
(criterion)Tj
3.6963 0 Td
(1,)Tj
0.9241 0 Td
(2)Tj
0.6916 0 Td
(and)Tj
1.7348 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 437.3858 679.011 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 441.3543 675.3826 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4478 0 Td
(and)Tj
1.7291 0 Td
(thus)Tj
1.9333 0 Td
(is)Tj
0.8503 0 Td
(an)Tj
1.2019 0 Td
(analysable)Tj
4.3087 0 Td
(self-)Tj
-34.6051 -1.2982 Td
(replicating)Tj
4.4787 0 Td
(chemical)Tj
3.7871 0 Td
(reaction)Tj
3.4923 0 Td
(system.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 612.3968 cm
BT
/F2 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Results)Tj
/F19 1 Tf
0 -1.4976 Td
(Systems)Tj
3.5575 0 Td
(characterised)Tj
5.778 0 Td
(by)Tj
1.2094 0 Td
(the)Tj
1.5449 0 Td
(golden)Tj
3.0378 0 Td
(ratio)Tj
/F20 1 Tf
2.2347 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 577.4173 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(We)Tj
1.61 0 Td
(now)Tj
1.9559 0 Td
(introduce)Tj
4.1159 0 Td
(a)Tj
0.652 0 Td
(scheme)Tj
3.2031 0 Td
(for)Tj
1.3833 0 Td
(population)Tj
4.5921 0 Td
(dynamics)Tj
4.0535 0 Td
(for)Tj
1.389 0 Td
(analysable)Tj
4.3086 0 Td
(self-replicating)Tj
6.1511 0 Td
(chemical)Tj
-33.4145 -1.3039 Td
(reaction)Tj
3.4922 0 Td
(systems,)Tj
3.5263 0 Td
(using)Tj
2.3867 0 Td
(system)Tj
0.83 0.64 0.02 0 k
2.9367 0 Td
(Eq)Tj
1.2983 0 Td
(\(3\))Tj
0 g
1.3776 0 Td
(as)Tj
1.0148 0 Td
(an)Tj
1.2019 0 Td
(example.)Tj
3.7757 0 Td
(Let)Tj
/F7 1 Tf
1.4797 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 431.8299 562.7338 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 433.8141 564.3779 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\))Tj
1.2018 0 Td
(be)Tj
1.1509 0 Td
(the)Tj
1.4683 0 Td
(population)Tj
4.5921 0 Td
(of)Tj
1.0148 0 Td
(molecule)Tj
-32.8079 -1.3946 Td
(species)Tj
ET
Q
q
1 j
1 J
0 w
229.9465 558.4819 m
233.178 558.4819 l
233.178 558.085 l
229.9465 558.085 l
f*
10 0 0 10 229.9464 550.4314 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
-0.004 Tc
0.5442 0 Td
(at)Tj
/F7 1 Tf
0.9524 0 Td
[()2()2( )6()2()20()22()7()4()11( )]TJ
4.3484 0 Td
[()]TJ
/F14 1 Tf
(.)Tj
0.7426 0 Td
(We)Tj
1.6101 0 Td
(initialise)Tj
3.6 0 Td
(the)Tj
1.4683 0 Td
(system)Tj
2.9424 0 Td
(with)Tj
/F7 1 Tf
1.9955 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 418.9039 548.7874 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 422.4755 550.4314 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(0\))Tj
1.3776 0 Td
(=)Tj
/F7 1 Tf
0.7993 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 451.2188 548.7874 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 454.7338 550.4314 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(0\))Tj
1.3776 0 Td
(=)Tj
/F7 1 Tf
0.7993 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 483.4771 548.7874 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 486.9921 550.4314 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(0\))Tj
1.3776 0 Td
(=)Tj
/F7 1 Tf
0.7993 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 515.7354 548.7874 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 519.2503 550.4314 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(0\))Tj
1.3776 0 Td
(=)Tj
0.7993 0 Td
(1,)Tj
0.9241 0 Td
(i.e.,)Tj
-35.0245 -1.2982 Td
(one)Tj
1.6951 0 Td
(of)Tj
1.0148 0 Td
(each)Tj
2.0296 0 Td
(intermediate)Tj
5.3234 0 Td
(molecules.)Tj
4.422 0 Td
(In)Tj
1.1112 0 Td
(addition,)Tj
3.8211 0 Td
(we)Tj
1.3322 0 Td
(assume)Tj
3.1465 0 Td
(that)Tj
1.7745 0 Td
(there)Tj
2.2677 0 Td
(is)Tj
0.8447 0 Td
(an)Tj
1.2019 0 Td
(infinite)Tj
3.1293 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
-36.5326 -1.4287 Td
(resource)Tj
3.6283 0 Td
(molecules)Tj
ET
Q
q
1 j
1 J
0 w
278.2488 531.5528 m
283.748 531.5528 l
283.748 531.1559 l
278.2488 531.1559 l
f*
10 0 0 10 278.2488 523.1622 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(4)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(inside)Tj
2.6192 0 Td
(the)Tj
1.4683 0 Td
(system,)Tj
3.1634 0 Td
(namely)Tj
/F7 1 Tf
3.1465 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 396.8503 521.5181 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(4)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 400.422 523.1622 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\))Tj
1.1962 0 Td
(=)Tj
/F11 1 Tf
0 Tc
0.805 0 Td
(1)Tj
/F14 1 Tf
-0.004 Tc
1.2189 0 Td
(for)Tj
1.3833 0 Td
(all)Tj
/F7 1 Tf
1.1508 0 Td
[()]TJ
/F14 1 Tf
(.)Tj
-24.5988 -1.2982 Td
(We)Tj
1.6101 0 Td
(update)Tj
2.948 0 Td
(molecule)Tj
3.8381 0 Td
(populations)Tj
4.9549 0 Td
(at)Tj
/F7 1 Tf
0.9525 0 Td
[()2()2( )6()2()20()22()7()4()11( )]TJ
4.3483 0 Td
[()]TJ
/F14 1 Tf
0.5158 0 Td
(+)Tj
0.805 0 Td
(1)Tj
0.6917 0 Td
(from)Tj
/F7 1 Tf
2.2053 0 Td
[()]TJ
/F14 1 Tf
0.5216 0 Td
(as)Tj
1.0148 0 Td
(follows:)Tj
3.2825 0 Td
(for)Tj
1.389 0 Td
(each)Tj
2.0239 0 Td
(molecule)Tj
-32.2977 -1.3946 Td
(species)Tj
ET
Q
q
1 j
1 J
0 w
229.9465 504.2835 m
233.178 504.2835 l
233.178 503.8866 l
229.9465 503.8866 l
f*
10 0 0 10 229.9464 496.233 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
-0.004 Tc
0.3231 0 Td
(,)Tj
0.4479 0 Td
(find)Tj
1.8481 0 Td
(the)Tj
1.4684 0 Td
(unique)Tj
3.0217 0 Td
(reaction)Tj
3.4923 0 Td
(that)Tj
1.7801 0 Td
(has)Tj
ET
Q
q
1 j
1 J
0 w
369.1843 504.2835 m
372.4157 504.2835 l
372.4157 503.8866 l
369.1843 503.8866 l
f*
10 0 0 10 369.1842 496.233 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
-0.004 Tc
0.5442 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(reactant)Tj
3.4526 0 Td
(side;)Tj
2.0239 0 Td
(and)Tj
1.7291 0 Td
(all)Tj
1.1452 0 Td
(of)Tj
1.0148 0 Td
(molecules)Tj
ET
Q
q
1 j
1 J
0 w
537.7323 504.2835 m
540.9071 504.2835 l
540.9071 503.8866 l
537.7323 503.8866 l
f*
10 0 0 10 537.7322 496.233 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
-0.004 Tc
0.5385 0 Td
(at)Tj
0.9525 0 Td
(gen-)Tj
-35.2627 -1.3946 Td
(eration)Tj
/F7 1 Tf
3.0671 0 Td
[()]TJ
/F14 1 Tf
(namely)Tj
/F7 1 Tf
4.371 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 281.3102 480.6425 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 283.3511 482.2866 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\))Tj
1.1962 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
305.4614 490.337 m
308.6929 490.337 l
308.6929 489.9402 l
305.4614 489.9402 l
f*
10 0 0 10 305.4614 482.2866 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
-0.004 Tc
0.3231 0 Td
(are)Tj
2.3697 0 Td
(transformed)Tj
5.1704 0 Td
(into)Tj
1.8425 0 Td
(the)Tj
1.4684 0 Td
(products)Tj
3.753 0 Td
(of)Tj
1.0148 0 Td
(this)Tj
1.6781 0 Td
(corresponding)Tj
6.0548 0 Td
(reac-)Tj
-34.2196 -1.2982 Td
(tion.)Tj
2.0636 0 Td
(The)Tj
1.7859 0 Td
(criterion)Tj
3.6963 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 280.233 472.9322 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 285.9023 469.3039 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(above)Tj
2.5454 0 Td
(guarantees)Tj
4.5071 0 Td
(that)Tj
1.7802 0 Td
(there)Tj
2.2677 0 Td
(is)Tj
0.8447 0 Td
(only)Tj
1.9785 0 Td
(one)Tj
1.6951 0 Td
(unique)Tj
3.0218 0 Td
(reaction)Tj
3.4979 0 Td
(that)Tj
1.7745 0 Td
(has)Tj
-32.5018 -1.3946 Td
(molecule)Tj
ET
Q
q
1 j
1 J
0 w
238.3937 463.4079 m
241.5685 463.4079 l
241.5685 463.011 l
238.3937 463.011 l
f*
10 0 0 10 238.3937 455.3574 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
-0.004 Tc
0.5385 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(reactant)Tj
3.4526 0 Td
(side.)Tj
-9.3768 -1.3039 Td
(Consider)Tj
3.889 0 Td
(how)Tj
1.9389 0 Td
(we)Tj
1.3322 0 Td
(apply)Tj
2.3868 0 Td
(this)Tj
1.6724 0 Td
(updating)Tj
3.8098 0 Td
(procedure)Tj
4.3143 0 Td
(to)Tj
1.0204 0 Td
(system)Tj
0.83 0.64 0.02 0 k
2.9424 0 Td
(Eq)Tj
1.2926 0 Td
(\(3\))Tj
0 g
(:)Tj
-25.795 -2.0126 Td
()Tj
0.7823 0 Td
(Firstly,)Tj
2.9707 0 Td
(update)Tj
/F7 1 Tf
2.9479 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 273.9968 420.4913 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 275.9811 422.1921 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(0\))Tj
1.3719 0 Td
(to)Tj
1.0261 0 Td
(obtain)Tj
/F7 1 Tf
2.7836 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 334.7149 420.4913 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 336.7559 422.1921 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(1\).)Tj
1.5987 0 Td
(For)Tj
1.6271 0 Td
(molecule)Tj
ET
Q
q
1 j
1 J
0 w
407.3953 430.4126 m
412.8945 430.4126 l
412.8945 430.0157 l
407.3953 430.0157 l
f*
10 0 0 10 407.3952 422.1921 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(,)Tj
0.4422 0 Td
(due)Tj
1.7007 0 Td
(to)Tj
1.0262 0 Td
(the)Tj
1.4683 0 Td
(fact)Tj
1.6611 0 Td
(that)Tj
1.7802 0 Td
(the)Tj
1.4683 0 Td
(third)Tj
2.2167 0 Td
(reaction)Tj
3.4922 0 Td
(is)Tj
-35.7615 -1.4173 Td
(the)Tj
1.4683 0 Td
(only)Tj
1.9786 0 Td
(reaction)Tj
3.4922 0 Td
(that)Tj
1.7745 0 Td
(has)Tj
1.5421 0 Td
(molecule)Tj
ET
Q
q
1 j
1 J
0 w
348.7748 416.2961 m
354.274 416.2961 l
354.274 415.8992 l
348.7748 415.8992 l
f*
10 0 0 10 348.7748 408.0188 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(reactant)Tj
3.4526 0 Td
(side)Tj
1.8028 0 Td
(and)Tj
/F7 1 Tf
1.7291 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 460.6866 406.3748 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 464.2582 408.0188 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(0\))Tj
1.3776 0 Td
(=)Tj
0.7993 0 Td
(1,)Tj
0.9185 0 Td
(we)Tj
1.3266 0 Td
(let)Tj
1.1905 0 Td
(this)Tj
1.6724 0 Td
(one)Tj
1.7008 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
564.2646 416.2961 m
569.7638 416.2961 l
569.7638 415.8992 l
564.2646 415.8992 l
f*
10 0 0 10 564.2645 408.0188 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F14 1 Tf
-0.004 Tc
-35.6426 -1.4173 Td
(transform)Tj
4.218 0 Td
(into)Tj
1.8425 0 Td
(one)Tj
1.6951 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
295.5402 402.1228 m
301.0394 402.1228 l
301.0394 401.726 l
295.5402 401.726 l
f*
10 0 0 10 295.5401 393.8456 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(through)Tj
3.4469 0 Td
(the)Tj
1.4683 0 Td
(third)Tj
2.211 0 Td
(reaction.)Tj
3.7191 0 Td
(For)Tj
1.627 0 Td
(molecule)Tj
ET
Q
q
1 j
1 J
0 w
466.3559 402.1228 m
471.8551 402.1228 l
471.8551 401.726 l
466.3559 401.726 l
f*
10 0 0 10 466.3559 393.8456 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(,)Tj
0.4478 0 Td
(due)Tj
1.6951 0 Td
(to)Tj
1.0262 0 Td
(the)Tj
1.4683 0 Td
(fact)Tj
1.6668 0 Td
(that)Tj
1.7745 0 Td
(the)Tj
-34.4804 -1.4116 Td
(first)Tj
1.8029 0 Td
(reaction)Tj
3.4922 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4684 0 Td
(only)Tj
1.9785 0 Td
(reaction)Tj
3.4923 0 Td
(that)Tj
1.7801 0 Td
(has)Tj
1.5421 0 Td
(molecule)Tj
ET
Q
q
1 j
1 J
0 w
410.2866 387.9496 m
415.7858 387.9496 l
415.7858 387.5528 l
410.2866 387.5528 l
f*
10 0 0 10 410.2866 379.7291 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F14 1 Tf
-0.004 Tc
0.7653 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.474 0 Td
(reactant)Tj
3.4526 0 Td
(side)Tj
1.7971 0 Td
(and)Tj
/F7 1 Tf
1.7291 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 522.1984 378.0283 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 525.7133 379.7291 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(0\))Tj
1.3776 0 Td
(=)Tj
0.7993 0 Td
(1,)Tj
0.9241 0 Td
(we)Tj
-34.8885 -1.4173 Td
(let)Tj
1.1849 0 Td
(this)Tj
1.6781 0 Td
(one)Tj
1.6951 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
263.5654 373.8331 m
269.0646 373.8331 l
269.0646 373.3795 l
263.5654 373.3795 l
f*
10 0 0 10 263.5653 365.5559 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(transform)Tj
4.2179 0 Td
(into)Tj
1.8425 0 Td
(two)Tj
1.7121 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
359.1496 373.8331 m
364.6488 373.8331 l
364.6488 373.3795 l
359.1496 373.3795 l
f*
10 0 0 10 359.1496 365.5559 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F14 1 Tf
-0.004 Tc
0.7653 0 Td
(through)Tj
3.4469 0 Td
(the)Tj
1.4683 0 Td
(first)Tj
1.8085 0 Td
(reaction.)Tj
3.7191 0 Td
(For)Tj
1.627 0 Td
(molecule)Tj
ET
Q
q
1 j
1 J
0 w
525.8268 373.8331 m
531.326 373.8331 l
531.326 373.3795 l
525.8268 373.3795 l
f*
10 0 0 10 525.8267 365.5559 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(,)Tj
0.4478 0 Td
(because)Tj
-32.7965 -1.4173 Td
(the)Tj
1.4683 0 Td
(second)Tj
3.0104 0 Td
(reaction)Tj
3.4923 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4683 0 Td
(unique)Tj
3.0217 0 Td
(reaction)Tj
3.4923 0 Td
(and)Tj
/F7 1 Tf
1.7291 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 400.1385 349.7385 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 403.7102 351.3826 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(0\))Tj
1.3719 0 Td
(=)Tj
0.7994 0 Td
(1,)Tj
0.9241 0 Td
(we)Tj
1.3266 0 Td
(let)Tj
1.1905 0 Td
(this)Tj
1.6724 0 Td
(one)Tj
1.7008 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
503.7165 359.6598 m
509.2157 359.6598 l
509.2157 359.263 l
503.7165 359.263 l
f*
10 0 0 10 503.7165 351.3826 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
/F14 1 Tf
-0.004 Tc
0.7653 0 Td
(transform)Tj
4.2236 0 Td
(into)Tj
-34.5767 -1.4173 Td
(one)Tj
1.6951 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
234.9354 345.4866 m
240.4346 345.4866 l
240.4346 345.0898 l
234.9354 345.0898 l
f*
10 0 0 10 234.9354 337.2094 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(and)Tj
1.7291 0 Td
(one)Tj
1.7008 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
287.0929 345.4866 m
292.5921 345.4866 l
292.5921 345.0898 l
287.0929 345.0898 l
f*
10 0 0 10 287.0929 337.2094 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(.)Tj
0.4478 0 Td
(For)Tj
1.6271 0 Td
(molecule)Tj
ET
Q
q
1 j
1 J
0 w
351.6661 345.4866 m
357.1654 345.4866 l
357.1654 345.0898 l
351.6661 345.0898 l
f*
10 0 0 10 351.6661 337.2094 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(,)Tj
0.4478 0 Td
(because)Tj
3.3222 0 Td
(the)Tj
1.4684 0 Td
(fourth)Tj
2.7382 0 Td
(reaction)Tj
3.4923 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4683 0 Td
(unique)Tj
3.0217 0 Td
(reaction)Tj
3.4923 0 Td
(and)Tj
/F7 1 Tf
-35.2344 -1.4116 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 214.7527 321.3921 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 218.3244 323.0929 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(0\))Tj
1.3776 0 Td
(=)Tj
0.7993 0 Td
(1,)Tj
0.9185 0 Td
(we)Tj
1.3266 0 Td
(let)Tj
1.1905 0 Td
(this)Tj
1.6724 0 Td
(one)Tj
1.7008 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
318.3307 331.3134 m
323.8299 331.3134 l
323.8299 330.9165 l
318.3307 330.9165 l
f*
10 0 0 10 318.3307 323.0929 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(transform)Tj
4.2179 0 Td
(into)Tj
1.8425 0 Td
(one)Tj
1.6951 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
413.7449 331.3134 m
419.2441 331.3134 l
419.2441 330.9165 l
413.7449 330.9165 l
f*
10 0 0 10 413.7448 323.0929 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(and)Tj
1.7291 0 Td
(one)Tj
1.7008 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
465.9024 331.3134 m
471.4016 331.3134 l
471.4016 330.9165 l
465.9024 330.9165 l
f*
10 0 0 10 465.9023 323.0929 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
/F14 1 Tf
-0.004 Tc
0.5499 0 Td
(.)Tj
0.4478 0 Td
(Therefore,)Tj
4.3937 0 Td
(at)Tj
0.9524 0 Td
(generation)Tj
/F7 1 Tf
-32.1502 -1.3039 Td
[()]TJ
/F14 1 Tf
0.5159 0 Td
(=)Tj
0.7994 0 Td
(1,)Tj
0.9241 0 Td
(we)Tj
1.3266 0 Td
(have)Tj
/F7 1 Tf
2.0579 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 271.0488 308.4094 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 274.5637 310.0535 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(1\))Tj
1.3776 0 Td
(=)Tj
0.7993 0 Td
(3,)Tj
/F7 1 Tf
0.9241 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 312.4913 308.4094 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 316.0629 310.0535 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(1\))Tj
1.3776 0 Td
(=)Tj
0.7993 0 Td
(2,)Tj
/F7 1 Tf
0.9185 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 353.9905 308.4094 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 357.5055 310.0535 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(1\))Tj
1.3776 0 Td
(=)Tj
0.7993 0 Td
(1)Tj
0.6974 0 Td
(and)Tj
/F7 1 Tf
1.7291 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 410.5133 308.4094 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 414.0283 310.0535 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(1\))Tj
1.3776 0 Td
(=)Tj
0.7993 0 Td
(1.)Tj
-23.5783 -2.0125 Td
()Tj
0.007 Tc
0.7824 0 Td
(Then,)Tj
2.6078 0 Td
(update)Tj
/F7 1 Tf
3.0161 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 271.1055 288.2267 cm
BT
/F7 1 Tf
1 TL
0.0093 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 273.2598 289.9275 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(\(1\))Tj
1.4059 0 Td
(to)Tj
1.0488 0 Td
(obtain)Tj
/F7 1 Tf
2.846 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 333.3543 288.2267 cm
BT
/F7 1 Tf
1 TL
0.0093 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 335.4519 289.9275 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(\(2\).)Tj
/F7 1 Tf
1.644 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 358.9228 288.2267 cm
BT
/F14 1 Tf
1 TL
0.0093 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 362.6078 289.9275 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(\(1\))Tj
1.4059 0 Td
(=)Tj
0.8164 0 Td
(3)Tj
0.703 0 Td
(of)Tj
1.0375 0 Td
(molecule)Tj
ET
Q
q
1 j
1 J
0 w
441.4677 298.148 m
446.9669 298.148 l
446.9669 297.7512 l
441.4677 297.7512 l
f*
10 0 0 10 441.4677 289.9275 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F14 1 Tf
0.007 Tc
0.771 0 Td
(are)Tj
1.4853 0 Td
(transformed)Tj
5.2894 0 Td
(into)Tj
1.8822 0 Td
(three)Tj
2.3244 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
207.8362 284.0315 m
213.3354 284.0315 l
213.3354 283.6346 l
207.8362 283.6346 l
f*
10 0 0 10 207.8362 275.7543 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
/F14 1 Tf
0.007 Tc
0.771 0 Td
(through)Tj
3.5206 0 Td
(the)Tj
1.5023 0 Td
(third)Tj
2.2677 0 Td
(reaction;)Tj
/F7 1 Tf
3.8154 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 333.6944 274.1102 cm
BT
/F14 1 Tf
1 TL
0.0093 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 337.3228 275.7543 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(\(1\))Tj
1.4116 0 Td
(=)Tj
0.8107 0 Td
(2)Tj
0.703 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
376.9512 284.0315 m
382.4504 284.0315 l
382.4504 283.6346 l
376.9512 283.6346 l
f*
10 0 0 10 376.9511 275.7543 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F14 1 Tf
0.007 Tc
0.771 0 Td
(are)Tj
1.4853 0 Td
(transformed)Tj
5.2894 0 Td
(into)Tj
1.8822 0 Td
(four)Tj
1.9616 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
501.222 284.0315 m
506.7213 284.0315 l
506.7213 283.6346 l
501.222 283.6346 l
f*
10 0 0 10 501.222 275.7543 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F14 1 Tf
0.007 Tc
0.771 0 Td
(through)Tj
3.5206 0 Td
(the)Tj
-33.6299 -1.4173 Td
(first)Tj
1.8595 0 Td
(reaction;)Tj
/F7 1 Tf
3.8154 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 271.6724 259.937 cm
BT
/F14 1 Tf
1 TL
0.0093 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 275.3007 261.5811 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(\(1\))Tj
1.4116 0 Td
(=)Tj
0.8107 0 Td
(1)Tj
0.7087 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
314.9291 269.8583 m
320.485 269.8583 l
320.485 269.4614 l
314.9291 269.4614 l
f*
10 0 0 10 314.9291 261.5811 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
/F14 1 Tf
0.007 Tc
0.771 0 Td
(is)Tj
0.873 0 Td
(transformed)Tj
5.2894 0 Td
(into)Tj
1.8879 0 Td
(one)Tj
ET
Q
q
1 j
1 J
0 w
420.4346 269.8583 m
425.9339 269.8583 l
425.9339 269.4614 l
420.4346 269.4614 l
f*
10 0 0 10 420.4346 261.5811 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F14 1 Tf
0.007 Tc
0.771 0 Td
(and)Tj
1.7631 0 Td
(one)Tj
ET
Q
q
1 j
1 J
0 w
463.1244 269.8583 m
468.6236 269.8583 l
468.6236 269.4614 l
463.1244 269.4614 l
f*
10 0 0 10 463.1244 261.5811 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F14 1 Tf
0.007 Tc
0.7653 0 Td
(through)Tj
3.5263 0 Td
(the)Tj
1.5023 0 Td
(second)Tj
-31.3225 -1.4116 Td
(reaction;)Tj
3.8154 0 Td
(and)Tj
/F7 1 Tf
1.7631 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 270.7086 245.7637 cm
BT
/F14 1 Tf
1 TL
0.0093 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 274.337 247.4645 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(\(1\))Tj
1.4116 0 Td
(=)Tj
0.8107 0 Td
(1)Tj
0.703 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
313.9654 255.685 m
319.4646 255.685 l
319.4646 255.2882 l
313.9654 255.2882 l
f*
10 0 0 10 313.9653 247.4645 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
/F14 1 Tf
0.007 Tc
0.771 0 Td
(is)Tj
0.873 0 Td
(transformed)Tj
5.2894 0 Td
(into)Tj
1.8822 0 Td
(one)Tj
ET
Q
q
1 j
1 J
0 w
419.4709 255.685 m
424.9701 255.685 l
424.9701 255.2882 l
419.4709 255.2882 l
f*
10 0 0 10 419.4708 247.4645 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F14 1 Tf
0.007 Tc
0.771 0 Td
(and)Tj
1.7631 0 Td
(one)Tj
ET
Q
q
1 j
1 J
0 w
462.1039 255.685 m
467.6031 255.685 l
467.6031 255.2882 l
462.1039 255.2882 l
f*
10 0 0 10 462.1039 247.4645 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
/F14 1 Tf
0.007 Tc
0.771 0 Td
(through)Tj
3.5206 0 Td
(the)Tj
1.5023 0 Td
(fourth)Tj
-31.2205 -1.3039 Td
(reaction.)Tj
3.8154 0 Td
(Therefore,)Tj
4.5014 0 Td
(at)Tj
0.9751 0 Td
(generation)Tj
/F7 1 Tf
4.6148 0 Td
[()]TJ
/F14 1 Tf
0.5329 0 Td
(=)Tj
0.8107 0 Td
(2,)Tj
0.9411 0 Td
(we)Tj
1.3493 0 Td
(have)Tj
/F7 1 Tf
2.1033 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 411.3637 232.7811 cm
BT
/F14 1 Tf
1 TL
0.0093 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 415.0488 234.4251 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(\(2\))Tj
1.4059 0 Td
(=)Tj
0.8107 0 Td
(5,)Tj
/F7 1 Tf
0.9411 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 453.7133 232.7811 cm
BT
/F14 1 Tf
1 TL
0.0093 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 457.3984 234.4251 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(\(2\))Tj
1.4059 0 Td
(=)Tj
0.8107 0 Td
(2,)Tj
/F7 1 Tf
0.9411 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 496.0629 232.7811 cm
BT
/F14 1 Tf
1 TL
0.0093 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 499.748 234.4251 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(\(2\))Tj
1.4059 0 Td
(=)Tj
0.8107 0 Td
(1)Tj
0.7087 0 Td
(and)Tj
/F7 1 Tf
-32.1162 -1.2982 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 214.8661 219.7984 cm
BT
/F14 1 Tf
1 TL
0.0093 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 218.5511 221.4425 cm
BT
/F14 1 Tf
1 TL
0.007 Tc
0 0 Td
(\(2\))Tj
1.4059 0 Td
(=)Tj
0.8107 0 Td
(3.)Tj
-0.004 Tc
-4.0704 -1.8992 Td
()Tj
0.7824 0 Td
(Similarly,)Tj
4.025 0 Td
(at)Tj
0.9525 0 Td
(generation)Tj
/F7 1 Tf
4.507 0 Td
[()]TJ
/F14 1 Tf
0.5159 0 Td
(=)Tj
0.8051 0 Td
(3,)Tj
0.9184 0 Td
(we)Tj
1.3266 0 Td
(have)Tj
/F7 1 Tf
2.0636 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 365.896 200.7496 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 369.4677 202.4503 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(3\))Tj
1.3719 0 Td
(=)Tj
0.805 0 Td
(5,)Tj
/F7 1 Tf
0.9185 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 407.3952 200.7496 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 410.9102 202.4503 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(3\))Tj
1.3776 0 Td
(=)Tj
0.7993 0 Td
(4,)Tj
/F7 1 Tf
0.9185 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 448.8377 200.7496 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 452.4094 202.4503 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(3\))Tj
1.3719 0 Td
(=)Tj
0.805 0 Td
(3)Tj
0.6917 0 Td
(and)Tj
/F7 1 Tf
1.7291 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 505.3606 200.7496 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 508.9322 202.4503 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\(3\))Tj
1.3719 0 Td
(=)Tj
0.7994 0 Td
(5.)Tj
-33.063 -1.8992 Td
()Tj
0.7823 0 Td
(Continue)Tj
4.0025 0 Td
(this)Tj
1.6725 0 Td
(updating)Tj
3.8097 0 Td
(procedure.)Tj
4.5354 0 Td
(Finally)Tj
2.948 0 Td
(we)Tj
1.3266 0 Td
(obtain)Tj
2.778 0 Td
(a)Tj
0.6576 0 Td
(sequence)Tj
3.8551 0 Td
(of)Tj
/F7 1 Tf
1.0148 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 480.8125 181.7574 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 484.3842 183.4582 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\),)Tj
/F7 1 Tf
1.4229 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 505.5307 181.7574 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 509.1023 183.4582 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\),)Tj
/F7 1 Tf
1.4229 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 530.3055 181.7574 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 533.8204 183.4582 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\))Tj
1.2018 0 Td
(and)Tj
/F7 1 Tf
-33.8 -1.3039 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 214.7527 168.7748 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 218.3244 170.4188 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\).)Tj
0.83 0.64 0.02 0 k
-0.6349 -1.8992 Td
(Table)Tj
2.4433 0 Td
(1)Tj
0 g
0.6974 0 Td
(shows)Tj
2.6588 0 Td
(the)Tj
1.4684 0 Td
(result)Tj
2.4491 0 Td
(over)Tj
1.9786 0 Td
(six)Tj
1.3096 0 Td
(generations.)Tj
5.0966 0 Td
(Note)Tj
2.1827 0 Td
(that)Tj
1.7801 0 Td
(this)Tj
1.6725 0 Td
(scheme)Tj
3.2031 0 Td
(can)Tj
1.6214 0 Td
(be)Tj
1.1509 0 Td
(applied)Tj
3.1521 0 Td
(to)Tj
1.0261 0 Td
(any)Tj
-35.0869 -1.2982 Td
(analysable)Tj
4.3085 0 Td
(self-replicating)Tj
6.1512 0 Td
(system,)Tj
3.1634 0 Td
(through)Tj
3.4469 0 Td
(the)Tj
1.4683 0 Td
(following)Tj
3.9799 0 Td
(steps)Tj
2.177 0 Td
(in)Tj
1.0374 0 Td
(general:)Tj
3.3562 0 Td
(\(1\))Tj
1.3777 0 Td
(assume)Tj
3.1464 0 Td
(an)Tj
1.2019 0 Td
(infi-)Tj
-34.8148 -1.2983 Td
(nite)Tj
1.7574 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(resource)Tj
3.6283 0 Td
(molecules)Tj
4.1953 0 Td
(inside)Tj
2.6192 0 Td
(the)Tj
1.4683 0 Td
(system;)Tj
3.1635 0 Td
(\(2\))Tj
1.3719 0 Td
(initialise)Tj
3.6 0 Td
(the)Tj
1.474 0 Td
(system)Tj
2.9367 0 Td
(with)Tj
1.9956 0 Td
(one)Tj
1.7007 0 Td
(of)Tj
-34.3442 -1.3039 Td
(each)Tj
2.0295 0 Td
(intermediate)Tj
5.3177 0 Td
(molecule;)Tj
4.0649 0 Td
(and)Tj
1.7291 0 Td
(\(3\))Tj
1.3776 0 Td
(update)Tj
2.9481 0 Td
(molecule)Tj
3.838 0 Td
(populations)Tj
4.9493 0 Td
(by)Tj
1.1849 0 Td
(generations)Tj
4.8642 0 Td
(to)Tj
1.0261 0 Td
(obtain)Tj
-33.3294 -1.2983 Td
(sequences)Tj
4.2178 0 Td
(of)Tj
1.0148 0 Td
(molecule)Tj
3.8381 0 Td
(populations.)Tj
5.176 0 Td
(This)Tj
1.9843 0 Td
(scheme)Tj
3.2031 0 Td
(defines)Tj
3.0557 0 Td
(a)Tj
0.6577 0 Td
(particular)Tj
4.1102 0 Td
(population)Tj
4.5864 0 Td
(dynamics)Tj
4.0592 0 Td
(for)Tj
-35.9033 -1.2982 Td
(self-replicating)Tj
6.151 0 Td
(systems.)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 107.1496 23.6976 re
W* n
q
107.0929 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 468.17 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Goden)Tj
3.1748 0 Td
(ratio)Tj
2.126 0 Td
(and)Tj
1.8567 0 Td
(self-replica)Tj
4.7339 0 Td
(tion)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
81.5811 34.9228 m
237.8835 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(ONE)Tj
2.3669 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https://doi.or)Tj
5.4142 0 Td
(g/10.137)Tj
3.8198 0 Td
(1/journal.po)Tj
5.1236 0 Td
(ne.02006)Tj
4.089 0 Td
(01)Tj
0 g
2.0906 0 Td
(July)Tj
1.9701 0 Td
(16,)Tj
1.5874 0 Td
(2018)Tj
35.3483 0 Td
(5)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
106 0 obj
<>stream
endstream
endobj
107 0 obj
<>stream
endstream
endobj
108 0 obj
<>stream
endstream
endobj
109 0 obj
<>stream
BT
66.402 0 Td
(18)Tj
ET
Q
endstream
endobj
110 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 12 0 R/Annots 116 0 R/Contents 117 0 R/TrimBox[0 0 612 792]>>
endobj
116 0 obj
[118 0 R 119 0 R 120 0 R 121 0 R 122 0 R 123 0 R 124 0 R 125 0 R 126 0 R 127 0 R 128 0 R]
endobj
118 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e049)>>
endobj
119 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e050)>>
endobj
120 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e051)>>
endobj
121 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.g001)>>
endobj
122 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e052)>>
endobj
123 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e049)>>
endobj
124 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.ref020)>>
endobj
125 0 obj
<>/Border[0 0 0]/Dest(Lpone.0200601.t001)>>
endobj
126 0 obj
<>/Border[0 0 0]/Dest(Rpone.0200601.e010)>>
endobj
127 0 obj
<>/Border[0 0 0]/A 129 0 R>>
endobj
129 0 obj
<>
endobj
128 0 obj
<>/Border[0 0 0]/A 130 0 R>>
endobj
130 0 obj
<>
endobj
117 0 obj
[131 0 R 132 0 R 133 0 R 134 0 R 135 0 R 136 0 R 137 0 R 138 0 R 139 0 R 140 0 R 141 0 R 142 0 R 143 0 R 144 0 R 145 0 R]
endobj
131 0 obj
<>stream
q
0.83 0.64 0.02 0 k
251.9433 396.9071 m
276.4913 396.9071 l
h
f*
228.5858 307.7291 m
240.1512 307.7291 l
h
f*
259.6535 307.7291 m
271.2189 307.7291 l
h
f*
480.4724 281.7071 m
500.0315 281.7071 l
h
f*
315.6094 210.4441 m
340.1575 210.4441 l
h
f*
382.7906 210.4441 m
407.3386 210.4441 l
h
f*
438.0094 118.9984 m
447.5339 118.9984 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 211.9748 548.2771 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(Note)Tj
2.1883 0 Td
(that)Tj
/F7 1 Tf
1.7801 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 258.5763 546.5763 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 260.5606 548.2771 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
0.8617 0 Td
(+)Tj
0.7993 0 Td
(1\))Tj
1.0318 0 Td
(only)Tj
1.9786 0 Td
(depends)Tj
3.549 0 Td
(on)Tj
/F7 1 Tf
1.2756 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 362.4944 546.5763 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 364.4787 548.2771 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\),)Tj
1.4229 0 Td
(so)Tj
1.0885 0 Td
(we)Tj
1.3266 0 Td
(can)Tj
1.6271 0 Td
(derive)Tj
2.6872 0 Td
(a)Tj
0.652 0 Td
(recurrence)Tj
4.5297 0 Td
(relation)Tj
3.3166 0 Td
(\(written)Tj
3.4525 0 Td
(as)Tj
-36.5496 -1.3039 Td
(a)Tj
0.652 0 Td
(matrix)Tj
2.8743 0 Td
(form\):)Tj
/F7 1 Tf
0 Tc
6.3779 -2.0579 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 306.0283 512.1637 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 309.5433 514.6582 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9467 0 Td
()Tj
/F8 1 Tf
0.9978 0 Td
(1)Tj
/F11 1 Tf
()Tj
/F7 1 Tf
-2.9933 -2.1996 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 306.0283 490.1669 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 309.5433 492.6614 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9467 0 Td
()Tj
/F8 1 Tf
0.9978 0 Td
(1)Tj
/F11 1 Tf
()Tj
/F7 1 Tf
-2.9933 -2.194 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 306.0283 468.2267 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 309.5433 470.7212 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9467 0 Td
()Tj
/F8 1 Tf
0.9978 0 Td
(1)Tj
/F11 1 Tf
()Tj
/F7 1 Tf
-2.9933 -2.1996 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 306.0283 446.2299 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 309.5433 448.7244 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9467 0 Td
()Tj
/F8 1 Tf
0.9978 0 Td
(1)Tj
/F11 1 Tf
()Tj
/F9 1 Tf
-4.0364 7.3473 Td
(0)Tj
0 -1.7461 Td
(B)Tj
0 -0.5953 Td
(B)Tj
0 -0.5896 Td
(B)Tj
0 -0.5953 Td
(B)Tj
0 -0.5952 Td
(B)Tj
0 -0.5896 Td
(B)Tj
0 -0.5953 Td
(B)Tj
0 -0.5896 Td
(@)Tj
5.0852 5.896 Td
(1)Tj
0 -1.7461 Td
(C)Tj
0 -0.5953 Td
(C)Tj
0 -0.5896 Td
(C)Tj
0 -0.5953 Td
(C)Tj
0 -0.5952 Td
(C)Tj
0 -0.5896 Td
(C)Tj
0 -0.5953 Td
(C)Tj
0 -0.5896 Td
(A)Tj
/F11 1 Tf
1.1565 1.8368 Td
()Tj
/F8 1 Tf
2.092 3.2995 Td
(0)Tj
1.4967 0 Td
(2)Tj
1.5023 0 Td
(1)Tj
1.5024 0 Td
(0)Tj
-4.5014 -2.1996 Td
(0)Tj
1.4967 0 Td
(0)Tj
1.5023 0 Td
(1)Tj
1.5024 0 Td
(1)Tj
-4.5014 -2.194 Td
(0)Tj
1.4967 0 Td
(0)Tj
1.5023 0 Td
(0)Tj
1.5024 0 Td
(1)Tj
-4.5014 -2.1996 Td
(1)Tj
1.4967 0 Td
(0)Tj
1.5023 0 Td
(0)Tj
1.5024 0 Td
(0)Tj
/F9 1 Tf
-5.5445 7.3529 Td
(0)Tj
0 -1.7461 Td
(B)Tj
0 -0.5953 Td
(B)Tj
0 -0.5896 Td
(B)Tj
0 -0.5953 Td
(B)Tj
0 -0.5952 Td
(B)Tj
0 -0.5896 Td
(B)Tj
0 -0.5953 Td
(B)Tj
0 -0.5896 Td
(@)Tj
6.2135 5.896 Td
(1)Tj
0 -1.7461 Td
(C)Tj
0 -0.5953 Td
(C)Tj
0 -0.5896 Td
(C)Tj
0 -0.5953 Td
(C)Tj
0 -0.5952 Td
(C)Tj
0 -0.5896 Td
(C)Tj
0 -0.5953 Td
(C)Tj
0 -0.5896 Td
(A)Tj
/F7 1 Tf
1.9162 5.142 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 449.8015 512.1637 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 453.3165 514.6582 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.7256 0 Td
()Tj
/F7 1 Tf
-1.7744 -2.1996 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 449.8015 490.1669 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 453.3165 492.6614 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.7256 0 Td
()Tj
/F7 1 Tf
-1.7744 -2.194 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 449.8015 468.2267 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 453.3165 470.7212 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.7256 0 Td
()Tj
/F7 1 Tf
-1.7744 -2.1996 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 449.8015 446.2299 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 453.3165 448.7244 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.7256 0 Td
()Tj
/F9 1 Tf
-2.8175 7.3473 Td
(0)Tj
0 -1.7461 Td
(B)Tj
0 -0.5953 Td
(B)Tj
0 -0.5896 Td
(B)Tj
0 -0.5953 Td
(B)Tj
0 -0.5952 Td
(B)Tj
0 -0.5896 Td
(B)Tj
0 -0.5953 Td
(B)Tj
0 -0.5896 Td
(@)Tj
3.3731 5.896 Td
(1)Tj
0 -1.7461 Td
(C)Tj
0 -0.5953 Td
(C)Tj
0 -0.5896 Td
(C)Tj
0 -0.5953 Td
(C)Tj
0 -0.5952 Td
(C)Tj
0 -0.5896 Td
(C)Tj
0 -0.5953 Td
(C)Tj
0 -0.5896 Td
(A)Tj
/F11 1 Tf
9.7341 1.8368 Td
()Tj
/F14 1 Tf
(4)Tj
/F11 1 Tf
()Tj
/F14 1 Tf
-0.004 Tc
-35.1493 -5.7598 Td
(We)Tj
1.6101 0 Td
(call)Tj
1.5704 0 Td
(this)Tj
/F7 1 Tf
1.6724 0 Td
[()]TJ
/F18 1 Tf
1.0035 0 Td
[()]TJ
/F7 1 Tf
0.788 0 Td
[()]TJ
/F14 1 Tf
0.9978 0 Td
(matrix)Tj
2.8743 0 Td
(as)Tj
1.0148 0 Td
(the)Tj
/F7 1 Tf
1.4683 0 Td
[()20()7(\n)1()12()-9()20()2( )6(\n)7()]TJ
4.2803 0 Td
[()6()22()7()-9()]TJ
/F14 1 Tf
(,)Tj
3.1011 0 Td
(denoted)Tj
3.4753 0 Td
(as)Tj
/F19 1 Tf
1.0147 0 Td
(A)Tj
/F14 1 Tf
(,)Tj
1.1508 0 Td
(where)Tj
/F7 1 Tf
2.6476 0 Td
[()]TJ
/F14 1 Tf
0.9977 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
-36.6006 -1.2983 Td
(intermediate)Tj
5.3234 0 Td
(molecules.)Tj
4.4221 0 Td
(Denote)Tj
3.1577 0 Td
(the)Tj
1.4684 0 Td
(vector)Tj
2.6985 0 Td
(of)Tj
1.0148 0 Td
(molecule)Tj
3.8381 0 Td
(populations)Tj
4.9492 0 Td
(\()Tj
/F7 1 Tf
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 479.1118 409.3228 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 482.6267 411.0236 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\),)Tj
/F7 1 Tf
1.4286 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 503.8299 409.3228 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 507.4015 411.0236 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\),)Tj
/F7 1 Tf
1.4229 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 528.6047 409.3228 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 532.1196 411.0236 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\),)Tj
/F7 1 Tf
1.4229 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 553.3228 409.3228 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 556.8944 411.0236 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\)\))Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 570.0472 415.4456 cm
BT
/F21 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[(y)]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 397.9842 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(as)Tj
/F19 1 Tf
1.0147 0 Td
(N)Tj
/F14 1 Tf
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\),)Tj
2.16 0 Td
(then)Tj
0.83 0.64 0.02 0 k
2.0183 0 Td
(Eq)Tj
1.2926 0 Td
(\(4\))Tj
0 g
1.3776 0 Td
(becomes)Tj
/F22 1 Tf
0 Tc
6.5877 -2.0239 Td
[()]TJ
/F11 1 Tf
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
1.6894 0 Td
()Tj
/F8 1 Tf
0.9921 0 Td
(1)Tj
/F11 1 Tf
()Tj
1.1622 0 Td
()Tj
/F22 1 Tf
1.0489 0 Td
[()]TJ
/F11 1 Tf
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
2.1656 0 Td
()Tj
14.8364 0 Td
()Tj
/F14 1 Tf
(5)Tj
/F11 1 Tf
()Tj
/F14 1 Tf
-0.004 Tc
-35.1493 -2.4207 Td
(Therefore,)Tj
4.3936 0 Td
(we)Tj
1.3266 0 Td
(can)Tj
1.6271 0 Td
(also)Tj
1.7688 0 Td
(use)Tj
/F19 1 Tf
1.5307 0 Td
(A)Tj
/F14 1 Tf
0.9241 0 Td
(to)Tj
1.0261 0 Td
(calculate)Tj
3.6794 0 Td
(the)Tj
1.4683 0 Td
(population)Tj
4.5921 0 Td
(sequences:)Tj
/F22 1 Tf
0 Tc
-8.6002 -2.0523 Td
[()]TJ
/F11 1 Tf
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
1.4683 0 Td
()Tj
0.6633 0 Td
()Tj
/F22 1 Tf
1.0488 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 388.1196 337.2661 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 394.0157 333.0141 cm
BT
/F22 1 Tf
1 TL
0 0 Td
[()]TJ
/F11 1 Tf
()Tj
/F8 1 Tf
(0)Tj
/F11 1 Tf
()Tj
16.9454 0.017 Td
()Tj
/F14 1 Tf
(6)Tj
/F11 1 Tf
()Tj
/F14 1 Tf
-0.004 Tc
-35.1493 -2.4377 Td
(Eqs)Tj
0.83 0.64 0.02 0 k
1.6611 0 Td
(\(5\))Tj
0 g
1.3719 0 Td
(and)Tj
0.83 0.64 0.02 0 k
1.7348 0 Td
(\(6\))Tj
0 g
1.372 0 Td
(also)Tj
1.7688 0 Td
(represent)Tj
3.9571 0 Td
(this)Tj
1.6781 0 Td
(particular)Tj
4.1102 0 Td
(population)Tj
4.592 0 Td
(dynamics)Tj
4.0535 0 Td
(in)Tj
1.0375 0 Td
(general.)Tj
-27.337 -1.2983 Td
(Through)Tj
3.7587 0 Td
(either)Tj
2.5341 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4684 0 Td
(steps)Tj
2.1826 0 Td
(above,)Tj
2.7723 0 Td
(we)Tj
1.3266 0 Td
(obtain)Tj
2.7779 0 Td
(the)Tj
1.474 0 Td
(sequences)Tj
/F7 1 Tf
4.2179 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 454.1669 294.1228 cm
BT
/F7 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 456.2078 295.8236 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\).)Tj
1.4229 0 Td
(We)Tj
1.6101 0 Td
(further)Tj
3.0274 0 Td
(find)Tj
1.8482 0 Td
(that)Tj
1.7801 0 Td
(the)Tj
-35.308 -1.3039 Td
(normalised)Tj
4.7225 0 Td
(population)Tj
4.5921 0 Td
(of)Tj
1.0148 0 Td
(each)Tj
2.0296 0 Td
(molecule)Tj
3.838 0 Td
(species)Tj
2.9934 0 Td
(saturates,)Tj
3.9572 0 Td
(as)Tj
1.0148 0 Td
(shown)Tj
2.8458 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0375 0 Td
(Fig)Tj
1.4797 0 Td
(1)Tj
0 g
(,)Tj
0.9241 0 Td
(and)Tj
1.7291 0 Td
(that)Tj
/F18 1 Tf
0 Tc
-19.8196 -2.7042 Td
[()1()1()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 323.2062 249.7889 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[()]TJ
/F11 1 Tf
0.3401 0 Td
(!1)Tj
ET
Q
q
1 j
1 J
0 w
340.5543 258.463 m
362.211 258.463 l
362.211 258.0661 l
340.5543 258.0661 l
f*
10 0 0 10 340.5543 262.5448 cm
BT
/F7 1 Tf
1 TL
0 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 347.5275 260.0503 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 351.0425 262.5448 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.7256 0 Td
()Tj
/F7 1 Tf
-1.7744 -1.3662 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 347.5275 246.3874 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 351.0425 248.8818 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.7256 0 Td
()Tj
0.669 0.6859 Td
()Tj
/F8 1 Tf
1.0488 0 Td
(1)Tj
/F12 1 Tf
(:)Tj
/F8 1 Tf
(618)Tj
2.2564 0 Td
(03)Tj
1.1678 0 Td
(.)Tj
0.4309 0 Td
(.)Tj
0.4365 0 Td
(.)Tj
/F11 1 Tf
0.5499 0 Td
()Tj
/F12 1 Tf
1.0489 0 Td
()Tj
/F11 1 Tf
12.9089 0 Td
()Tj
/F14 1 Tf
(7)Tj
/F11 1 Tf
()Tj
/F14 1 Tf
-0.004 Tc
-36.3455 -3.1236 Td
(i.e.,)Tj
1.5873 0 Td
(the)Tj
1.4684 0 Td
(ratio)Tj
2.0976 0 Td
(of)Tj
1.0148 0 Td
(populations)Tj
4.9493 0 Td
(of)Tj
1.0148 0 Td
(molecule)Tj
ET
Q
q
1 j
1 J
0 w
359.7165 232.7811 m
365.2157 232.7811 l
365.2157 232.3843 l
359.7165 232.3843 l
f*
10 0 0 10 359.7165 224.5039 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(over)Tj
1.9785 0 Td
(that)Tj
1.7745 0 Td
(of)Tj
ET
Q
q
1 j
1 J
0 w
415.1055 232.7811 m
420.6047 232.7811 l
420.6047 232.3843 l
415.1055 232.3843 l
f*
10 0 0 10 415.1055 224.5039 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
/F14 1 Tf
-0.004 Tc
0.771 0 Td
(goes)Tj
1.9785 0 Td
(to)Tj
1.0262 0 Td
(the)Tj
1.4683 0 Td
(golden)Tj
2.9367 0 Td
(ratio)Tj
2.0976 0 Td
(as)Tj
/F7 1 Tf
1.0148 0 Td
[()]TJ
/F11 1 Tf
0 Tc
0.5216 0 Td
(!)Tj
1.2189 0 Td
(1)Tj
/F14 1 Tf
-0.004 Tc
(.)Tj
-33.3465 -1.2982 Td
(We)Tj
1.6101 0 Td
(now)Tj
1.9615 0 Td
(rigorously)Tj
4.2973 0 Td
(prove)Tj
0.83 0.64 0.02 0 k
2.4945 0 Td
(Eq)Tj
1.2983 0 Td
(\(7\))Tj
0 g
(.)Tj
1.5987 0 Td
(Based)Tj
2.5455 0 Td
(on)Tj
0.83 0.64 0.02 0 k
1.2756 0 Td
(Eq)Tj
1.2982 0 Td
(\(4\))Tj
0 g
(,)Tj
1.5988 0 Td
(we)Tj
1.3265 0 Td
(have)Tj
/F7 1 Tf
2.0636 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 452.5795 209.8204 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 456.1511 211.5212 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
0.856 0 Td
(+)Tj
0.805 0 Td
(1\))Tj
1.0318 0 Td
(=)Tj
/F7 1 Tf
0.7994 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 498.0472 209.8204 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 501.6188 211.5212 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\),)Tj
1.4229 0 Td
(so)Tj
/F7 1 Tf
1.0885 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 533.6503 209.8204 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 537.222 211.5212 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
0.856 0 Td
(+)Tj
0.7994 0 Td
(1\))Tj
1.0374 0 Td
(=)Tj
/F7 1 Tf
-36.4135 -1.3039 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 206.9291 196.8377 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 210.5007 198.4818 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\))Tj
1.1962 0 Td
(=)Tj
/F7 1 Tf
0.805 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 237.4299 196.8377 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 241.0015 198.4818 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F18 1 Tf
0.856 0 Td
[()]TJ
/F14 1 Tf
0.788 0 Td
(1\),)Tj
1.2643 0 Td
(and)Tj
1.7291 0 Td
(then)Tj
2.0183 0 Td
(we)Tj
1.3266 0 Td
(have)Tj
/F7 1 Tf
2.0636 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 348.3779 196.8377 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 351.9496 198.4818 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
0.856 0 Td
(+)Tj
0.7994 0 Td
(1\))Tj
1.0374 0 Td
(=)Tj
/F7 1 Tf
0.7994 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 393.8456 196.8377 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 397.3606 198.4818 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\))Tj
1.2018 0 Td
(+)Tj
/F7 1 Tf
0.7994 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 424.2897 196.8377 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 427.8614 198.4818 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\))Tj
1.2018 0 Td
(=)Tj
/F7 1 Tf
0.7994 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 454.7905 196.8377 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 458.3622 198.4818 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F18 1 Tf
0.856 0 Td
[()]TJ
/F14 1 Tf
0.7937 0 Td
(2\))Tj
1.0318 0 Td
(+)Tj
/F7 1 Tf
0.7994 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 500.1448 196.8377 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 503.7165 198.4818 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F18 1 Tf
0.856 0 Td
[()]TJ
/F14 1 Tf
0.788 0 Td
(1\).)Tj
1.2643 0 Td
(Finally,)Tj
/F7 1 Tf
0 Tc
-28.7941 -2.0239 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 251.8299 175.748 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 255.3448 178.2425 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9524 0 Td
()Tj
/F8 1 Tf
0.9921 0 Td
(1)Tj
/F11 1 Tf
()Tj
1.8879 0 Td
()Tj
/F8 1 Tf
1.0488 0 Td
(2)Tj
/F7 1 Tf
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 316.1196 175.748 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 319.6346 178.2425 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.7313 0 Td
()Tj
0.6009 0 Td
()Tj
/F7 1 Tf
0.9978 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 349.9086 175.748 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 353.4236 178.2425 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.7256 0 Td
()Tj
0.6633 0 Td
()Tj
/F8 1 Tf
1.0488 0 Td
(2)Tj
/F11 1 Tf
()Tj
/F7 1 Tf
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 393.6188 175.748 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 397.1338 178.2425 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9524 0 Td
( )Tj
/F8 1 Tf
0.9921 0 Td
(3)Tj
/F11 1 Tf
()Tj
1.1055 0 Td
()Tj
/F7 1 Tf
0.9921 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 444.5291 175.748 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 448.044 178.2425 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9524 0 Td
( )Tj
/F8 1 Tf
0.9921 0 Td
(2)Tj
/F11 1 Tf
()Tj
1.491 0 Td
()Tj
/F7 1 Tf
0.9921 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 499.3511 175.748 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 502.8094 178.2425 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9524 0 Td
( )Tj
/F8 1 Tf
0.9921 0 Td
(2)Tj
/F11 1 Tf
()Tj
-22.8583 -1.6951 Td
()Tj
/F8 1 Tf
1.0488 0 Td
(3)Tj
/F7 1 Tf
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 316.1196 158.7968 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 319.6346 161.2913 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9524 0 Td
( )Tj
/F8 1 Tf
0.9921 0 Td
(2)Tj
/F11 1 Tf
()Tj
1.1055 0 Td
()Tj
/F8 1 Tf
0.9921 0 Td
(2)Tj
/F7 1 Tf
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 372.0755 158.7968 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 375.5905 161.2913 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9467 0 Td
( )Tj
/F8 1 Tf
0.9978 0 Td
(3)Tj
/F11 1 Tf
()Tj
-15.0178 -1.7007 Td
(,)Tj
/F7 1 Tf
1.2813 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 264.6425 141.7889 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 268.1574 144.2834 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.7256 0 Td
()Tj
1.8255 0 Td
()Tj
/F8 1 Tf
1.0488 0 Td
(3)Tj
/F7 1 Tf
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 316.1196 141.7889 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 319.6346 144.2834 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9524 0 Td
( )Tj
/F8 1 Tf
0.9921 0 Td
(3)Tj
/F11 1 Tf
()Tj
1.1055 0 Td
()Tj
/F8 1 Tf
0.9921 0 Td
(2)Tj
/F7 1 Tf
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 372.0755 141.7889 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 375.5905 144.2834 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F7 1 Tf
[()]TJ
/F11 1 Tf
0.9467 0 Td
( )Tj
/F8 1 Tf
0.9978 0 Td
(4)Tj
/F11 1 Tf
()Tj
/F14 1 Tf
-0.004 Tc
-18.3059 -2.4207 Td
(Based)Tj
2.5511 0 Td
(on)Tj
1.2756 0 Td
(standard)Tj
3.7191 0 Td
(skills)Tj
2.1996 0 Td
(for)Tj
1.3833 0 Td
(solving)Tj
3.0728 0 Td
(recursive)Tj
3.8436 0 Td
(sequences)Tj
4.2179 0 Td
([)Tj
0.83 0.64 0.02 0 k
(20)Tj
0 g
(],)Tj
2.075 0 Td
(the)Tj
1.474 0 Td
(characteristic)Tj
5.5389 0 Td
(equation)Tj
3.736 0 Td
(of)Tj
-36.2831 -1.304 Td
(the)Tj
1.4683 0 Td
(sequence)Tj
/F7 1 Tf
3.8608 0 Td
[(.)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 260.2204 105.3921 cm
BT
/F14 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 263.7921 107.0362 cm
BT
/F14 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\()Tj
/F7 1 Tf
[()]TJ
/F14 1 Tf
(\))Tj
1.1962 0 Td
(is)Tj
/F23 1 Tf
0 Tc
1.4229 -2.1543 Td
(l)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 295.4834 90.2551 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(4)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 301.2094 85.4929 cm
BT
/F11 1 Tf
1 TL
0 0 Td
( )Tj
/F8 1 Tf
0.9921 0 Td
(3)Tj
/F23 1 Tf
(l)Tj
/F11 1 Tf
1.2756 0 Td
( )Tj
/F8 1 Tf
0.9921 0 Td
(2)Tj
/F11 1 Tf
0.7823 0 Td
()Tj
1.0488 0 Td
()Tj
/F23 1 Tf
(l)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 361.474 90.2551 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 367.2 85.4929 cm
BT
/F11 1 Tf
1 TL
0 0 Td
( )Tj
/F23 1 Tf
0.9977 0 Td
(l)Tj
/F11 1 Tf
0.7711 0 Td
( )Tj
/F8 1 Tf
0.9977 0 Td
(1)Tj
/F11 1 Tf
()Tj
/F23 1 Tf
(l)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 413.0645 90.2551 cm
BT
/F8 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 418.7905 85.4929 cm
BT
/F11 1 Tf
1 TL
0 0 Td
()Tj
/F23 1 Tf
0.9977 0 Td
(l)Tj
/F11 1 Tf
0.7711 0 Td
()Tj
/F8 1 Tf
0.9977 0 Td
(2)Tj
/F11 1 Tf
()Tj
1.1566 0 Td
()Tj
/F8 1 Tf
1.0488 0 Td
(0)Tj
/F11 1 Tf
9.496 0.068 Td
()Tj
/F14 1 Tf
(8)Tj
/F11 1 Tf
()Tj
ET
Q
q
0.45 0.36 0.35 0.01 k
1 j
1 J
0 w
199.9998 706.7713 m
575.9997 706.7713 l
575.9997 706.2712 l
199.9998 706.2712 l
f*
293.3728 706.2712 m
293.3728 693.7713 l
292.8728 693.7713 l
292.8728 706.2712 l
f*
292.8728 693.7713 m
199.9998 693.7713 l
199.9998 694.2713 l
292.8728 694.2713 l
f*
364.1545 706.2712 m
364.1545 693.7713 l
363.6544 693.7713 l
363.6544 706.2712 l
f*
363.6544 693.7713 m
293.3728 693.7713 l
293.3728 694.2713 l
363.6544 694.2713 l
f*
434.9361 706.2712 m
434.9361 693.7713 l
434.4361 693.7713 l
434.4361 706.2712 l
f*
434.4361 693.7713 m
364.1545 693.7713 l
364.1545 694.2713 l
434.4361 694.2713 l
f*
505.7178 706.2712 m
505.7178 693.7713 l
505.2178 693.7713 l
505.2178 706.2712 l
f*
505.2178 693.7713 m
434.9361 693.7713 l
434.9361 694.2713 l
505.2178 694.2713 l
f*
575.9994 693.7713 m
505.7178 693.7713 l
505.7178 694.2713 l
575.9994 694.2713 l
f*
293.3728 693.7713 m
293.3728 681.2714 l
292.8728 681.2714 l
292.8728 693.7713 l
f*
292.8728 681.2714 m
199.9998 681.2714 l
199.9998 681.7714 l
292.8728 681.7714 l
f*
364.1545 693.7713 m
364.1545 681.2714 l
363.6544 681.2714 l
363.6544 693.7713 l
f*
363.6544 681.2714 m
293.3728 681.2714 l
293.3728 681.7714 l
363.6544 681.7714 l
f*
434.9361 693.7713 m
434.9361 681.2714 l
434.4361 681.2714 l
434.4361 693.7713 l
f*
434.4361 681.2714 m
364.1545 681.2714 l
364.1545 681.7714 l
434.4361 681.7714 l
f*
505.7178 693.7713 m
505.7178 681.2714 l
505.2178 681.2714 l
505.2178 693.7713 l
f*
505.2178 681.2714 m
434.9361 681.2714 l
434.9361 681.7714 l
505.2178 681.7714 l
f*
575.9994 681.2714 m
505.7178 681.2714 l
505.7178 681.7714 l
575.9994 681.7714 l
f*
293.3728 681.2714 m
293.3728 668.7714 l
292.8728 668.7714 l
292.8728 681.2714 l
f*
292.8728 668.7714 m
199.9998 668.7714 l
199.9998 669.2715 l
292.8728 669.2715 l
f*
364.1545 681.2714 m
364.1545 668.7714 l
363.6544 668.7714 l
363.6544 681.2714 l
f*
363.6544 668.7714 m
293.3728 668.7714 l
293.3728 669.2715 l
363.6544 669.2715 l
f*
434.9361 681.2714 m
434.9361 668.7714 l
434.4361 668.7714 l
434.4361 681.2714 l
f*
434.4361 668.7714 m
364.1545 668.7714 l
364.1545 669.2715 l
434.4361 669.2715 l
f*
505.7178 681.2714 m
505.7178 668.7714 l
505.2178 668.7714 l
505.2178 681.2714 l
f*
505.2178 668.7714 m
434.9361 668.7714 l
434.9361 669.2715 l
505.2178 669.2715 l
f*
575.9994 668.7714 m
505.7178 668.7714 l
505.7178 669.2715 l
575.9994 669.2715 l
f*
293.3728 668.7714 m
293.3728 656.2715 l
292.8728 656.2715 l
292.8728 668.7714 l
f*
292.8728 656.2715 m
199.9998 656.2715 l
199.9998 656.7715 l
292.8728 656.7715 l
f*
364.1545 668.7714 m
364.1545 656.2715 l
363.6544 656.2715 l
363.6544 668.7714 l
f*
363.6544 656.2715 m
293.3728 656.2715 l
293.3728 656.7715 l
363.6544 656.7715 l
f*
434.9361 668.7714 m
434.9361 656.2715 l
434.4361 656.2715 l
434.4361 668.7714 l
f*
434.4361 656.2715 m
364.1545 656.2715 l
364.1545 656.7715 l
434.4361 656.7715 l
f*
505.7178 668.7714 m
505.7178 656.2715 l
505.2178 656.2715 l
505.2178 668.7714 l
f*
505.2178 656.2715 m
434.9361 656.2715 l
434.9361 656.7715 l
505.2178 656.7715 l
f*
575.9994 656.2715 m
505.7178 656.2715 l
505.7178 656.7715 l
575.9994 656.7715 l
f*
293.3728 656.2715 m
293.3728 643.7716 l
292.8728 643.7716 l
292.8728 656.2715 l
f*
292.8728 643.7716 m
199.9998 643.7716 l
199.9998 644.2716 l
292.8728 644.2716 l
f*
364.1545 656.2715 m
364.1545 643.7716 l
363.6544 643.7716 l
363.6544 656.2715 l
f*
363.6544 643.7716 m
293.3728 643.7716 l
293.3728 644.2716 l
363.6544 644.2716 l
f*
434.9361 656.2715 m
434.9361 643.7716 l
434.4361 643.7716 l
434.4361 656.2715 l
f*
434.4361 643.7716 m
364.1545 643.7716 l
364.1545 644.2716 l
434.4361 644.2716 l
f*
505.7178 656.2715 m
505.7178 643.7716 l
505.2178 643.7716 l
505.2178 656.2715 l
f*
505.2178 643.7716 m
434.9361 643.7716 l
434.9361 644.2716 l
505.2178 644.2716 l
f*
575.9994 643.7716 m
505.7178 643.7716 l
505.7178 644.2716 l
575.9994 644.2716 l
f*
293.3728 643.7716 m
293.3728 631.2716 l
292.8728 631.2716 l
292.8728 643.7716 l
f*
292.8728 631.2716 m
199.9998 631.2716 l
199.9998 631.7717 l
292.8728 631.7717 l
f*
364.1545 643.7716 m
364.1545 631.2716 l
363.6544 631.2716 l
363.6544 643.7716 l
f*
363.6544 631.2716 m
293.3728 631.2716 l
293.3728 631.7717 l
363.6544 631.7717 l
f*
434.9361 643.7716 m
434.9361 631.2716 l
434.4361 631.2716 l
434.4361 643.7716 l
f*
434.4361 631.2716 m
364.1545 631.2716 l
364.1545 631.7717 l
434.4361 631.7717 l
f*
505.7178 643.7716 m
505.7178 631.2716 l
505.2178 631.2716 l
505.2178 643.7716 l
f*
505.2178 631.2716 m
434.9361 631.2716 l
434.9361 631.7717 l
505.2178 631.7717 l
f*
575.9994 631.2716 m
505.7178 631.2716 l
505.7178 631.7717 l
575.9994 631.7717 l
f*
293.3728 631.2716 m
293.3728 618.7717 l
292.8728 618.7717 l
292.8728 631.2716 l
f*
292.8728 618.7717 m
199.9998 618.7717 l
199.9998 619.2717 l
292.8728 619.2717 l
f*
364.1545 631.2716 m
364.1545 618.7717 l
363.6544 618.7717 l
363.6544 631.2716 l
f*
363.6544 618.7717 m
293.3728 618.7717 l
293.3728 619.2717 l
363.6544 619.2717 l
f*
434.9361 631.2716 m
434.9361 618.7717 l
434.4361 618.7717 l
434.4361 631.2716 l
f*
434.4361 618.7717 m
364.1545 618.7717 l
364.1545 619.2717 l
434.4361 619.2717 l
f*
505.7178 631.2716 m
505.7178 618.7717 l
505.2178 618.7717 l
505.2178 631.2716 l
f*
505.2178 618.7717 m
434.9361 618.7717 l
434.9361 619.2717 l
505.2178 619.2717 l
f*
575.9994 618.7717 m
505.7178 618.7717 l
505.7178 619.2717 l
575.9994 619.2717 l
f*
293.3728 618.7717 m
293.3728 606.2717 l
292.8728 606.2717 l
292.8728 618.7717 l
f*
292.8728 606.2717 m
199.9998 606.2717 l
199.9998 606.7718 l
292.8728 606.7718 l
f*
364.1545 618.7717 m
364.1545 606.2717 l
363.6544 606.2717 l
363.6544 618.7717 l
f*
363.6544 606.2717 m
293.3728 606.2717 l
293.3728 606.7718 l
363.6544 606.7718 l
f*
434.9361 618.7717 m
434.9361 606.2717 l
434.4361 606.2717 l
434.4361 618.7717 l
f*
434.4361 606.2717 m
364.1545 606.2717 l
364.1545 606.7718 l
434.4361 606.7718 l
f*
505.7178 618.7717 m
505.7178 606.2717 l
505.2178 606.2717 l
505.2178 618.7717 l
f*
505.2178 606.2717 m
434.9361 606.2717 l
434.9361 606.7718 l
505.2178 606.7718 l
f*
575.9994 606.2717 m
505.7178 606.2717 l
505.7178 606.7718 l
575.9994 606.7718 l
f*
293.3728 606.2717 m
293.3728 587.742 l
292.8728 587.742 l
292.8728 606.2717 l
f*
292.8728 587.742 m
199.9998 587.742 l
199.9998 588.242 l
292.8728 588.242 l
f*
364.1545 606.2717 m
364.1545 587.742 l
363.6544 587.742 l
363.6544 606.2717 l
f*
363.6544 587.742 m
293.3728 587.742 l
293.3728 588.242 l
363.6544 588.242 l
f*
434.9361 606.2717 m
434.9361 587.742 l
434.4361 587.742 l
434.4361 606.2717 l
f*
434.4361 587.742 m
364.1545 587.742 l
364.1545 588.242 l
434.4361 588.242 l
f*
505.7178 606.2717 m
505.7178 587.742 l
505.2178 587.742 l
505.2178 606.2717 l
f*
505.2178 587.742 m
434.9361 587.742 l
434.9361 588.242 l
505.2178 588.242 l
f*
575.9994 587.742 m
505.7178 587.742 l
505.7178 588.242 l
575.9994 588.242 l
f*
0.83 0.64 0.02 0 k
478.6016 710.5323 m
498.7276 710.5323 l
h
f*
200.0126 574.6394 m
350.7591 574.6394 l
h
f*
0 g
7.9999 0 0 7.9999 200.0125 711.6094 cm
BT
/F19 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Table)Tj
2.5512 0 Td
(1.)Tj
0.9567 0 Td
(Molecule)Tj
3.9897 0 Td
(populations)Tj
/F20 1 Tf
5.1804 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.3325 306.9921 710.2488 cm
BT
/F20 1 Tf
1 TL
-0.0067 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.9999 0 0 7.9999 308.6929 711.6094 cm
BT
/F19 1 Tf
1 TL
-0.005 Tc
0 0 Td
(\()Tj
/F20 1 Tf
[()]TJ
/F19 1 Tf
(\))Tj
1.2189 0 Td
(for)Tj
1.4669 0 Td
(the)Tj
1.5307 0 Td
(self-repli)Tj
3.6851 0 Td
(cating)Tj
2.7709 0 Td
(chemic)Tj
2.9339 0 Td
(al)Tj
0.9637 0 Td
(reaction)Tj
3.6213 0 Td
(system)Tj
0.83 0.64 0.02 0 k
3.0473 0 Td
(Eq)Tj
1.3252 0 Td
(\(3\))Tj
0 g
1.4103 0 Td
(at)Tj
1.0133 0 Td
(generation)Tj
/F20 1 Tf
4.6773 0 Td
[()]TJ
/F19 1 Tf
(.)Tj
0 Tc
-37.3042 -1.8567 Td
(Generatio)Tj
4.1812 0 Td
(n)Tj
/F20 1 Tf
0.7937 0 Td
[()]TJ
7.1999 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.3325 350.5322 695.4519 cm
BT
/F19 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
7.9999 0 0 7.9999 353.537 696.7559 cm
BT
/F19 1 Tf
1 TL
0 0 Td
(\()Tj
/F20 1 Tf
[()]TJ
/F19 1 Tf
(\))Tj
/F20 1 Tf
7.774 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.3325 421.285 695.4519 cm
BT
/F19 1 Tf
1 TL
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
7.9999 0 0 7.9999 424.2897 696.7559 cm
BT
/F19 1 Tf
1 TL
0 0 Td
(\()Tj
/F20 1 Tf
[()]TJ
/F19 1 Tf
(\))Tj
/F20 1 Tf
7.7811 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.3325 492.0944 695.4519 cm
BT
/F19 1 Tf
1 TL
0 0 Td
(3)Tj
ET
Q
q
1 j
1 J
0 w
7.9999 0 0 7.9999 495.0992 696.7559 cm
BT
/F19 1 Tf
1 TL
0 0 Td
(\()Tj
/F20 1 Tf
[()]TJ
/F19 1 Tf
(\))Tj
/F20 1 Tf
7.774 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.3325 562.8472 695.4519 cm
BT
/F19 1 Tf
1 TL
0 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
7.9999 0 0 7.9999 565.8519 696.7559 cm
BT
/F19 1 Tf
1 TL
0 0 Td
(\()Tj
/F20 1 Tf
[()]TJ
/F19 1 Tf
(\))Tj
/F14 1 Tf
-34.9727 -1.559 Td
(0)Tj
8.8442 0 Td
(1)Tj
8.8512 0 Td
(1)Tj
8.8442 0 Td
(1)Tj
8.8512 0 Td
(1)Tj
-35.3908 -1.5662 Td
(1)Tj
8.8442 0 Td
(3)Tj
8.8512 0 Td
(2)Tj
8.8442 0 Td
(1)Tj
8.8512 0 Td
(1)Tj
-35.3908 -1.559 Td
(2)Tj
8.8442 0 Td
(5)Tj
8.8512 0 Td
(2)Tj
8.8442 0 Td
(1)Tj
8.8512 0 Td
(3)Tj
-35.3908 -1.5662 Td
(3)Tj
8.8442 0 Td
(5)Tj
8.8512 0 Td
(4)Tj
8.8442 0 Td
(3)Tj
8.8512 0 Td
(5)Tj
-35.3908 -1.5591 Td
(4)Tj
8.3694 0 Td
(11)Tj
9.326 0 Td
(8)Tj
8.8442 0 Td
(5)Tj
8.8512 0 Td
(5)Tj
-35.3908 -1.5661 Td
(5)Tj
8.3694 0 Td
(21)Tj
8.8442 0 Td
(10)Tj
9.326 0 Td
(5)Tj
8.3694 0 Td
(11)Tj
-34.909 -1.5591 Td
(6)Tj
8.3694 0 Td
(25)Tj
8.8442 0 Td
(16)Tj
8.8512 0 Td
(11)Tj
8.8442 0 Td
(21)Tj
/F8 1 Tf
-34.7035 -1.9205 Td
(.)Tj
0 -0.3968 Td
(.)Tj
0 0.8008 Td
(.)Tj
35.3908 -0.404 Td
(.)Tj
0 -0.3968 Td
(.)Tj
0 0.8008 Td
(.)Tj
0.83 0.64 0.02 0 k
/F16 1 Tf
-0.025 Tc
-46.3538 -2.6788 Td
(https://d)Tj
3.0827 0 Td
(oi.org/10.1371/j)Tj
5.9173 0 Td
(ournal.pon)Tj
3.9827 0 Td
(e.0200601.t00)Tj
5.3859 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 107.1496 23.6976 re
W* n
q
107.0929 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 468.17 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Goden)Tj
3.1748 0 Td
(ratio)Tj
2.126 0 Td
(and)Tj
1.8567 0 Td
(self-replica)Tj
4.7339 0 Td
(tion)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
81.5811 34.9228 m
237.8835 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(ONE)Tj
2.3669 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https://doi.or)Tj
5.4142 0 Td
(g/10.137)Tj
3.8198 0 Td
(1/journal.po)Tj
5.1236 0 Td
(ne.02006)Tj
4.089 0 Td
(01)Tj
0 g
2.0906 0 Td
(July)Tj
1.9701 0 Td
(16,)Tj
1.5874 0 Td
(2018)Tj
35.3483 0 Td
(6)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
132 0 obj
<>stream
endstream
endobj
133 0 obj
<>stream
endstream
endobj
134 0 obj
<>stream
endstream
endobj
135 0 obj
<>stream
endstream
endobj
136 0 obj
<>stream
endstream
endobj
137 0 obj
<>stream
endstream
endobj
138 0 obj
<>stream
endstream
endobj
139 0 obj
<>stream
endstream
endobj
140 0 obj
<>stream
endstream
endobj
141 0 obj
<>stream
endstream
endobj
142 0 obj
<>stream
endstream
endobj
143 0 obj
<>stream
endstream
endobj
144 0 obj
<>stream
endstream
endobj
145 0 obj
<>stream
BT
66.402 0 Td
(18)Tj
ET
Q
endstream
endobj
146 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 12 0 R/Annots 151 0 R/Contents 152 0 R/TrimBox[0 0 612 792]>>
endobj
148 0 obj
<>
endobj
153 0 obj
<>stream
/CIDInit/ProcSet findresource begin
12 dict begin begincmap
/CMapName/Adobe-Identity-UCS def
/CIDSystemInfo<>def
/CMapType 2 def
1 begincodespacerange
<0000>
endcodespacerange
4 beginbfchar
<010B><03B1>
<010C><03B2>
<010E><03B4>
<0111><03B7>
endbfchar
endcmap
CMapName currentdict /CMap defineresource pop end end
endstream
endobj
154 0 obj
<>/FontDescriptor 155 0 R/DW 250/W[267[558 495] 270[474] 273[510]]>>
endobj
155 0 obj
<>
endobj
156 0 obj
<>stream
cvt 0Y "fpgm2Msf bglyf lheadOd 6hhea $hmtx
loca d H
maxpx prep
y_<