%PDF-1.6
%
1 0 obj
<>
endobj
2 0 obj
<>stream
Lucas Wetzel, David J. Jörg, Alexandros Pollakis, Wolfgang Rave, Gerhard Fettweis, Frank Jülicher
Self-organized synchronization of digital phase-locked loops with delayed coupling in theory and experiment
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]
endobj
15 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref011)>>
endobj
16 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref011)>>
endobj
17 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref012)>>
endobj
18 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref013)>>
endobj
19 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref011)>>
endobj
20 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref014)>>
endobj
21 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref015)>>
endobj
22 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref016)>>
endobj
23 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref017)>>
endobj
24 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref018)>>
endobj
25 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref019)>>
endobj
26 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref024)>>
endobj
27 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref025)>>
endobj
28 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref026)>>
endobj
29 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref027)>>
endobj
30 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref028)>>
endobj
31 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref030)>>
endobj
32 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref027)>>
endobj
33 0 obj
<>/Border[0 0 0]/Dest(Rpone.0171590.ref031)>>
endobj
14 0 obj
[34 0 R 35 0 R 36 0 R 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
34 0 obj
<>stream
q
0.83 0.64 0.02 0 k
522.085 667.3323 m
531.6094 667.3323 l
h
f*
324.1701 641.3102 m
333.6378 641.3102 l
h
f*
338.1165 641.3102 m
347.6409 641.3102 l
h
f*
258.0094 628.3276 m
267.5339 628.3276 l
h
f*
351.0425 615.3449 m
360.5669 615.3449 l
h
f*
364.989 615.3449 m
374.5134 615.3449 l
h
f*
419.2441 602.3055 m
428.7118 602.3055 l
h
f*
433.1906 602.3055 m
442.715 602.3055 l
h
f*
330.3496 550.3181 m
339.7606 550.3181 l
h
f*
344.1827 550.3181 m
353.6504 550.3181 l
h
f*
394.8094 524.2961 m
404.2772 524.2961 l
h
f*
409.3795 524.2961 m
418.8472 524.2961 l
h
f*
501.6189 511.3134 m
511.0866 511.3134 l
h
f*
541.2472 459.326 m
550.715 459.326 l
h
f*
298.3181 433.3039 m
307.7291 433.3039 l
h
f*
530.7024 420.3213 m
540.1701 420.3213 l
h
f*
545.2724 420.3213 m
554.7402 420.3213 l
h
f*
534.7843 407.3386 m
544.252 407.3386 l
h
f*
326.2677 264.3024 m
335.6787 264.3024 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
(signals)Tj
2.9026 0 Td
(send)Tj
2.0806 0 Td
(at)Tj
0.9525 0 Td
(the)Tj
1.4683 0 Td
(speed)Tj
2.4718 0 Td
(of)Tj
1.0148 0 Td
(light)Tj
2.0239 0 Td
(can)Tj
1.6271 0 Td
(travel)Tj
2.4491 0 Td
(30cm.)Tj
2.6419 0 Td
(This)Tj
1.9842 0 Td
(implies)Tj
3.1238 0 Td
(significant)Tj
4.388 0 Td
(transmission)Tj
5.3631 0 Td
(delays)Tj
-34.4917 -1.3039 Td
(at)Tj
0.9524 0 Td
(length)Tj
2.7269 0 Td
(scales)Tj
2.4718 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.474 0 Td
(centimetre)Tj
4.5127 0 Td
(range)Tj
2.4662 0 Td
(for)Tj
1.3833 0 Td
(such)Tj
2.0636 0 Td
(frequencies.)Tj
5.0059 0 Td
(In)Tj
1.1112 0 Td
(most)Tj
2.2053 0 Td
(cases,)Tj
2.4492 0 Td
(the)Tj
1.4683 0 Td
(time)Tj
2.0296 0 Td
(reference)Tj
-33.3522 -1.2982 Td
(in)Tj
1.0318 0 Td
(electronic)Tj
4.1555 0 Td
(systems)Tj
3.2995 0 Td
(relies)Tj
2.3131 0 Td
(on)Tj
1.2756 0 Td
(hierarchical)Tj
4.9379 0 Td
(concepts,)Tj
3.9458 0 Td
(i.e.,)Tj
1.5874 0 Td
(a)Tj
0.6519 0 Td
(high)Tj
2.007 0 Td
(quality)Tj
2.9593 0 Td
(master-clock)Tj
5.3745 0 Td
(feeds)Tj
2.2393 0 Td
(for-)Tj
-35.7786 -1.2983 Td
(ward)Tj
2.2336 0 Td
(a)Tj
0.6577 0 Td
(synchronization)Tj
6.6954 0 Td
(signal)Tj
2.5398 0 Td
(into)Tj
1.8425 0 Td
(a)Tj
0.6576 0 Td
(clock-tree,)Tj
4.405 0 Td
(entraining)Tj
4.3937 0 Td
(all)Tj
1.1452 0 Td
(other)Tj
2.3471 0 Td
(slave-clocks)Tj
4.9492 0 Td
([)Tj
0.83 0.64 0.02 0 k
(11)Tj
0 g
(].)Tj
2.075 0 Td
(In)Tj
1.1112 0 Td
(such)Tj
-35.053 -1.2983 Td
(systems,)Tj
3.5206 0 Td
(signal)Tj
2.5455 0 Td
(transmission)Tj
5.3631 0 Td
(delays)Tj
2.6702 0 Td
(have)Tj
2.0579 0 Td
(to)Tj
1.0262 0 Td
(be)Tj
1.1508 0 Td
(compensated,)Tj
5.726 0 Td
(e.g.,)Tj
1.7858 0 Td
(all)Tj
1.1452 0 Td
(connections)Tj
5.0796 0 Td
(in)Tj
1.0318 0 Td
(a)Tj
0.6577 0 Td
(clock-)Tj
-33.7604 -1.3039 Td
(tree)Tj
1.7347 0 Td
(have)Tj
2.058 0 Td
(to)Tj
1.0261 0 Td
(be)Tj
1.1509 0 Td
(of)Tj
1.0148 0 Td
(equal)Tj
2.3584 0 Td
(length)Tj
2.7326 0 Td
([)Tj
0.83 0.64 0.02 0 k
(11)Tj
0 g
(,)Tj
0.83 0.64 0.02 0 k
1.7348 0 Td
(12)Tj
0 g
(].)Tj
1.7347 0 Td
(Such)Tj
2.177 0 Td
(strategies)Tj
3.9232 0 Td
(become)Tj
3.3222 0 Td
(space)Tj
2.381 0 Td
(and)Tj
1.7292 0 Td
(energy)Tj
2.9083 0 Td
(inefficient)Tj
4.2633 0 Td
(for)Tj
-36.2492 -1.2982 Td
(large)Tj
2.1599 0 Td
(systems)Tj
3.2995 0 Td
([)Tj
0.83 0.64 0.02 0 k
(13)Tj
0 g
(].)Tj
2.075 0 Td
(Moreover,)Tj
4.3993 0 Td
(hierarchical)Tj
4.9323 0 Td
(entrainment)Tj
5.2044 0 Td
(is)Tj
0.8447 0 Td
(vulnerable)Tj
4.405 0 Td
(to)Tj
1.0261 0 Td
(fluctuations)Tj
4.9493 0 Td
(and)Tj
1.7291 0 Td
(fail-)Tj
-35.0246 -1.2983 Td
(ures,)Tj
2.1259 0 Td
(e.g.,)Tj
1.7858 0 Td
(due)Tj
1.7008 0 Td
(to)Tj
1.0261 0 Td
(noise)Tj
2.3244 0 Td
(and)Tj
1.7292 0 Td
(cross-talk)Tj
4.0705 0 Td
([)Tj
0.83 0.64 0.02 0 k
(11)Tj
0 g
(,)Tj
0.83 0.64 0.02 0 k
1.7348 0 Td
(14)Tj
0 g
(].)Tj
1.7404 0 Td
(Hence)Tj
2.8063 0 Td
(it)Tj
0.7824 0 Td
(is)Tj
0.8504 0 Td
(a)Tj
0.6519 0 Td
(challenge)Tj
3.9628 0 Td
(to)Tj
1.0205 0 Td
(achieve)Tj
3.1748 0 Td
(precise)Tj
3.0104 0 Td
(and)Tj
-34.4974 -1.3039 Td
(robust)Tj
2.7892 0 Td
(synchronization)Tj
6.7011 0 Td
(of)Tj
1.0148 0 Td
(autonomous)Tj
5.2554 0 Td
(clocking)Tj
3.6 0 Td
(units)Tj
2.2223 0 Td
([)Tj
0.83 0.64 0.02 0 k
(15)Tj
0 g
(,)Tj
0.83 0.64 0.02 0 k
1.7348 0 Td
(16)Tj
0 g
(].)Tj
-0.007 Tc
-22.1214 -1.2983 Td
(Robust)Tj
3.0273 0 Td
(self-organized)Tj
5.8054 0 Td
(synchronization)Tj
6.65 0 Td
(without)Tj
3.3108 0 Td
(hierarchical)Tj
4.8983 0 Td
(structures)Tj
4.1555 0 Td
(has)Tj
1.5364 0 Td
(been)Tj
2.109 0 Td
(found)Tj
2.6022 0 Td
(in)Tj
-35.2911 -1.2983 Td
(large)Tj
2.1429 0 Td
(collections)Tj
4.4391 0 Td
(of)Tj
1.0091 0 Td
(oscillators)Tj
4.2122 0 Td
(in)Tj
1.0262 0 Td
(nature.)Tj
3.0274 0 Td
(In)Tj
1.1055 0 Td
(biological)Tj
4.0591 0 Td
(systems,)Tj
3.498 0 Td
(such)Tj
2.0523 0 Td
(as)Tj
1.0034 0 Td
(neuronal)Tj
3.8041 0 Td
(networks,)Tj
4.1102 0 Td
(cou-)Tj
-35.4895 -1.3039 Td
(pled)Tj
1.9218 0 Td
(genetic)Tj
3.0501 0 Td
(oscillators,)Tj
4.4277 0 Td
(cardiac)Tj
3.0841 0 Td
(pacemaker)Tj
4.5354 0 Td
(cells,)Tj
2.1259 0 Td
(and)Tj
1.7235 0 Td
(in)Tj
1.0261 0 Td
(flashing)Tj
3.3335 0 Td
(fireflies,)Tj
3.3506 0 Td
(synchronization)Tj
6.6557 0 Td
(is)Tj
-35.2344 -1.2982 Td
(attained)Tj
3.4242 0 Td
(in)Tj
1.0318 0 Td
(a)Tj
0.6519 0 Td
(self-organized)Tj
5.8054 0 Td
(way)Tj
1.7801 0 Td
([)Tj
0.83 0.64 0.02 0 k
(17)Tj
0 g
(,)Tj
0.83 0.64 0.02 0 k
1.7235 0 Td
(18)Tj
0 g
(].)Tj
1.7291 0 Td
(Through)Tj
3.736 0 Td
(mutual)Tj
3.0558 0 Td
(coupling)Tj
3.6963 0 Td
(of)Tj
1.0091 0 Td
(individual)Tj
4.2577 0 Td
(oscillatory)Tj
-31.9009 -1.2983 Td
(units,)Tj
2.4264 0 Td
(these)Tj
2.2393 0 Td
(systems)Tj
3.2825 0 Td
(are)Tj
1.44 0 Td
(able)Tj
1.8142 0 Td
(to)Tj
1.0205 0 Td
(synchronize)Tj
5.0343 0 Td
(robustly)Tj
3.4695 0 Td
(in)Tj
1.0262 0 Td
(highly)Tj
2.6929 0 Td
(noisy)Tj
2.3414 0 Td
(environments)Tj
5.7599 0 Td
(and)Tj
1.7178 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
-35.2967 -1.3039 Td
(presence)Tj
3.685 0 Td
(of)Tj
1.0091 0 Td
(considerable)Tj
5.227 0 Td
(communication)Tj
6.5707 0 Td
(delays)Tj
2.6476 0 Td
([)Tj
0.83 0.64 0.02 0 k
(19)Tj
0 g
()Tj
0.83 0.64 0.02 0 k
(24)Tj
0 g
(].)Tj
3.5206 0 Td
(For)Tj
1.6214 0 Td
(instance,)Tj
3.719 0 Td
(in)Tj
1.0318 0 Td
(neuronal)Tj
3.8041 0 Td
(systems,)Tj
-32.8363 -1.2983 Td
(axonal)Tj
2.8346 0 Td
(conduction)Tj
4.7678 0 Td
(delays)Tj
2.6532 0 Td
(are)Tj
1.44 0 Td
(typically)Tj
3.532 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.457 0 Td
(range)Tj
2.4491 0 Td
(of)Tj
1.0091 0 Td
(1-100)Tj
2.4605 0 Td
(of)Tj
1.0091 0 Td
(milliseconds)Tj
5.1817 0 Td
([)Tj
0.83 0.64 0.02 0 k
(25)Tj
0 g
(],)Tj
2.0579 0 Td
(and)Tj
1.7235 0 Td
(therefore)Tj
-33.6073 -1.2982 Td
(a)Tj
0.6519 0 Td
(considerable)Tj
5.2214 0 Td
(fraction)Tj
3.3335 0 Td
(of)Tj
1.0091 0 Td
(the)Tj
1.4627 0 Td
(typical)Tj
2.8403 0 Td
(neural)Tj
2.7496 0 Td
(oscillation)Tj
4.2973 0 Td
(frequencies)Tj
4.7508 0 Td
(between)Tj
3.5036 0 Td
(1)Tj
0.6917 0 Td
(and)Tj
1.7234 0 Td
(100)Tj
1.6385 0 Td
(Hz.)Tj
1.6157 0 Td
(This)Tj
-35.4895 -1.2983 Td
(is)Tj
0.839 0 Td
(achieved)Tj
3.6793 0 Td
(in)Tj
1.0319 0 Td
(the)Tj
1.4569 0 Td
(absence)Tj
3.3222 0 Td
(of)Tj
1.0092 0 Td
(an)Tj
1.1962 0 Td
(entraining)Tj
4.3596 0 Td
(master)Tj
2.914 0 Td
(clock.)Tj
2.5228 0 Td
(It)Tj
0.8504 0 Td
(has)Tj
1.5364 0 Td
(been)Tj
2.109 0 Td
(shown)Tj
2.8346 0 Td
(that)Tj
1.7631 0 Td
(such)Tj
2.0466 0 Td
(a)Tj
0.652 0 Td
(decen-)Tj
-34.1232 -1.3039 Td
(tralized)Tj
3.1747 0 Td
(synchronization)Tj
6.6557 0 Td
(strategy)Tj
3.2995 0 Td
(enables)Tj
3.1408 0 Td
(robust)Tj
2.7779 0 Td
(self-organization)Tj
6.8995 0 Td
(of)Tj
1.0092 0 Td
(synchronous)Tj
5.3234 0 Td
(states)Tj
2.3754 0 Td
(also)Tj
1.7575 0 Td
(in)Tj
-36.4136 -1.2983 Td
(analog)Tj
2.8346 0 Td
(electronic)Tj
4.1215 0 Td
(networks,)Tj
4.1102 0 Td
(thereby)Tj
3.2032 0 Td
(providing)Tj
4.1215 0 Td
(a)Tj
0.652 0 Td
(position-independent)Tj
8.8383 0 Td
(time)Tj
2.0126 0 Td
(reference)Tj
3.8948 0 Td
([)Tj
0.83 0.64 0.02 0 k
(26)Tj
0 g
(].)Tj
-33.7887 -1.2983 Td
(Recently,)Tj
3.8494 0 Td
(we)Tj
1.3152 0 Td
(have)Tj
2.041 0 Td
(developed)Tj
4.2349 0 Td
(a)Tj
0.6406 0 Td
(phase)Tj
2.4605 0 Td
(oscillator)Tj
3.8437 0 Td
(description)Tj
4.6942 0 Td
(which)Tj
2.6249 0 Td
(captures)Tj
3.5489 0 Td
(the)Tj
1.4513 0 Td
(dynamics)Tj
4.0252 0 Td
(of)Tj
0.9978 0 Td
(digi-)Tj
-35.7276 -1.3039 Td
(tal)Tj
1.1792 0 Td
(electronic)Tj
4.1102 0 Td
(oscillators)Tj
4.2009 0 Td
([)Tj
0.83 0.64 0.02 0 k
(27)Tj
0 g
(].)Tj
2.0523 0 Td
(We)Tj
1.593 0 Td
(also)Tj
1.7461 0 Td
(showed)Tj
3.2259 0 Td
(that)Tj
1.7574 0 Td
(electronic)Tj
4.1102 0 Td
(networks)Tj
3.8778 0 Td
(provide)Tj
3.2598 0 Td
(excellent)Tj
3.6794 0 Td
(experi-)Tj
-34.7922 -1.2982 Td
(mental)Tj
2.9706 0 Td
(conditions)Tj
4.4447 0 Td
(to)Tj
1.0205 0 Td
(study)Tj
2.3754 0 Td
(the)Tj
1.457 0 Td
(nonlinear)Tj
4.0932 0 Td
(dynamics)Tj
4.0309 0 Td
(of)Tj
1.0091 0 Td
(mutually)Tj
3.7474 0 Td
(coupled)Tj
3.3732 0 Td
(oscillators)Tj
4.2122 0 Td
([)Tj
0.83 0.64 0.02 0 k
(28)Tj
0 g
()Tj
0.83 0.64 0.02 0 k
(30)Tj
0 g
(])Tj
3.2939 0 Td
(in)Tj
1.0318 0 Td
(a)Tj
-37.0599 -1.2983 Td
(controlled)Tj
4.2859 0 Td
(environment)Tj
5.4028 0 Td
(with)Tj
1.9842 0 Td
(adjustable)Tj
4.2066 0 Td
(system)Tj
2.9197 0 Td
(parameters)Tj
4.6431 0 Td
(and)Tj
1.7178 0 Td
(transmission)Tj
5.3291 0 Td
(delays)Tj
2.6532 0 Td
([)Tj
0.83 0.64 0.02 0 k
(27)Tj
0 g
(].)Tj
-0.0099 Tc
-31.9462 -1.3039 Td
(Here,)Tj
2.4037 0 Td
(we)Tj
1.3153 0 Td
(study)Tj
2.3584 0 Td
(synchronization)Tj
6.6104 0 Td
(dynamics)Tj
4.0081 0 Td
(in)Tj
1.0262 0 Td
(networks)Tj
3.8607 0 Td
(of)Tj
1.0035 0 Td
(delay-coupled)Tj
5.7543 0 Td
(digital)Tj
2.6872 0 Td
(phase-locked)Tj
-32.224 -1.2983 Td
(loops)Tj
2.33 0 Td
(\(DPLLs\).)Tj
3.8098 0 Td
(We)Tj
1.5987 0 Td
(show)Tj
2.2734 0 Td
(theoretically)Tj
5.0626 0 Td
(that)Tj
1.7575 0 Td
(such)Tj
2.0352 0 Td
(networks)Tj
3.8665 0 Td
(operating)Tj
3.9968 0 Td
(on)Tj
1.2642 0 Td
(digital)Tj
2.6816 0 Td
(signals)Tj
2.863 0 Td
(can)Tj
1.61 0 Td
(be)Tj
-35.1493 -1.2983 Td
(formulated)Tj
4.6034 0 Td
(in)Tj
1.0261 0 Td
(terms)Tj
2.4605 0 Td
(of)Tj
1.0034 0 Td
(a)Tj
0.6463 0 Td
(phase)Tj
2.4548 0 Td
(oscillator)Tj
3.8268 0 Td
(description)Tj
4.6658 0 Td
(and)Tj
1.7121 0 Td
(study)Tj
2.3584 0 Td
(the)Tj
1.4513 0 Td
(existence,)Tj
4.0252 0 Td
(stability)Tj
3.2995 0 Td
(and)Tj
1.7121 0 Td
(the)Tj
-35.2457 -1.2982 Td
(frequencies)Tj
4.7168 0 Td
(of)Tj
1.0034 0 Td
(different)Tj
3.6057 0 Td
(frequency)Tj
4.1329 0 Td
(synchronized)Tj
5.5218 0 Td
(states,)Tj
2.5795 0 Td
(e.g.,)Tj
1.7575 0 Td
(checkerboard,)Tj
5.8053 0 Td
(m-twist)Tj
3.2598 0 Td
(and)Tj
1.7122 0 Td
(in-phase)Tj
-34.0949 -1.3039 Td
(synchronized)Tj
5.5218 0 Td
(states.)Tj
2.5795 0 Td
(In)Tj
1.0999 0 Td
(contrast)Tj
3.4128 0 Td
(to)Tj
1.0148 0 Td
(implicit)Tj
3.2769 0 Td
(expressions)Tj
4.7621 0 Td
(for)Tj
1.3663 0 Td
(the)Tj
1.4514 0 Td
(frequencies)Tj
4.7225 0 Td
(of)Tj
1.0034 0 Td
(the)Tj
1.4513 0 Td
(synchronized)Tj
-31.6627 -1.2983 Td
(states)Tj
2.3584 0 Td
(in)Tj
1.0261 0 Td
(analog)Tj
2.8176 0 Td
(systems,)Tj
3.4753 0 Td
(we)Tj
1.3209 0 Td
(here)Tj
1.9389 0 Td
(provide)Tj
3.2485 0 Td
(closed)Tj
2.6759 0 Td
(analytical)Tj
3.9458 0 Td
(expressions)Tj
4.7621 0 Td
(for)Tj
1.3663 0 Td
(the)Tj
1.4514 0 Td
(frequencies)Tj
4.7225 0 Td
(of)Tj
-35.1097 -1.2983 Td
(synchronized)Tj
5.5218 0 Td
(states)Tj
2.3584 0 Td
(in)Tj
1.0262 0 Td
(digital)Tj
2.6815 0 Td
(systems.)Tj
3.4809 0 Td
(These)Tj
2.5342 0 Td
(can)Tj
1.6101 0 Td
(be)Tj
1.1395 0 Td
(obtained)Tj
3.685 0 Td
(explicitly)Tj
3.77 0 Td
(due)Tj
1.6838 0 Td
(to)Tj
1.0091 0 Td
(the)Tj
1.457 0 Td
(piecewise)Tj
3.9572 0 Td
(lin-)Tj
-35.9147 -1.3039 Td
(ear)Tj
1.4286 0 Td
(coupling)Tj
3.6793 0 Td
(function.)Tj
3.7985 0 Td
(Furthermore,)Tj
5.5445 0 Td
(we)Tj
1.3152 0 Td
(discuss)Tj
3.0048 0 Td
(the)Tj
1.457 0 Td
(role)Tj
1.7404 0 Td
(of)Tj
1.0035 0 Td
(the)Tj
1.4513 0 Td
(characteristic)Tj
5.4652 0 Td
(integration)Tj
4.5807 0 Td
(time)Tj
-34.469 -1.2982 Td
(related)Tj
2.9026 0 Td
(to)Tj
1.0148 0 Td
(signal)Tj
2.5058 0 Td
(filtering)Tj
3.3392 0 Td
(within)Tj
2.7779 0 Td
(the)Tj
1.4514 0 Td
(DPLLs.)Tj
3.1464 0 Td
(This)Tj
1.9616 0 Td
(integration)Tj
4.5864 0 Td
(time)Tj
2.0012 0 Td
(leads)Tj
2.1827 0 Td
(to)Tj
1.0148 0 Td
(memory)Tj
3.583 0 Td
(effects)Tj
2.6815 0 Td
(that)Tj
-35.1493 -1.2983 Td
(generate)Tj
3.5602 0 Td
(inertia-like)Tj
4.5411 0 Td
(behavior.)Tj
3.8835 0 Td
(This)Tj
1.9672 0 Td
(can)Tj
1.6044 0 Td
(lead)Tj
1.8312 0 Td
(to)Tj
1.0148 0 Td
(transient)Tj
3.7133 0 Td
(waves)Tj
2.5512 0 Td
(that)Tj
1.7518 0 Td
(travel)Tj
2.4151 0 Td
(through)Tj
3.4015 0 Td
(the)Tj
1.4514 0 Td
(network,)Tj
-33.6867 -1.3039 Td
(initiated)Tj
3.4979 0 Td
(by)Tj
1.1678 0 Td
(local)Tj
2.0466 0 Td
(perturbations)Tj
5.5786 0 Td
([)Tj
0.83 0.64 0.02 0 k
(31)Tj
0 g
(].)Tj
2.0466 0 Td
(Our)Tj
1.8482 0 Td
(theoretical)Tj
4.3766 0 Td
(results)Tj
2.7666 0 Td
(are)Tj
1.4287 0 Td
(supported)Tj
4.2179 0 Td
(by)Tj
1.1736 0 Td
(experiments)Tj
5.0739 0 Td
(per-)Tj
-35.223 -1.2983 Td
(formed)Tj
3.118 0 Td
(on)Tj
1.2643 0 Td
(real)Tj
1.6724 0 Td
(networks)Tj
3.8664 0 Td
(of)Tj
0.9978 0 Td
(off-the-shelf)Tj
5.0287 0 Td
(DPLL)Tj
2.5625 0 Td
(integrated)Tj
4.2236 0 Td
(circuitry.)Tj
3.787 0 Td
(These)Tj
2.5399 0 Td
(experiments)Tj
5.0739 0 Td
(include)Tj
-34.1345 -1.2983 Td
(networks)Tj
3.8607 0 Td
(of)Tj
1.0035 0 Td
(up)Tj
1.2529 0 Td
(to)Tj
1.0148 0 Td
(9)Tj
0.6916 0 Td
(DPLLs)Tj
2.9197 0 Td
(with)Tj
1.9729 0 Td
(different)Tj
3.6056 0 Td
(coupling)Tj
3.6737 0 Td
(topologies,)Tj
4.4787 0 Td
(such)Tj
2.041 0 Td
(as)Tj
1.0034 0 Td
(nearest-neighbour)Tj
7.4721 0 Td
(cou-)Tj
-34.9906 -1.3039 Td
(pled)Tj
1.9105 0 Td
(networks)Tj
3.8608 0 Td
(with)Tj
1.9729 0 Td
(open)Tj
2.194 0 Td
(or)Tj
1.0885 0 Td
(periodic)Tj
3.4752 0 Td
(boundary)Tj
4.0535 0 Td
(conditions.)Tj
4.6375 0 Td
(In)Tj
1.0941 0 Td
(Section)Tj
3.1238 0 Td
(1,)Tj
0.9071 0 Td
(we)Tj
1.3152 0 Td
(develop)Tj
3.2825 0 Td
(a)Tj
0.6463 0 Td
(phase)Tj
-33.5619 -1.2982 Td
(model)Tj
2.7155 0 Td
(of)Tj
/F11 1 Tf
1.0035 0 Td
[()]TJ
/F7 1 Tf
0.9071 0 Td
(mutually)Tj
3.7247 0 Td
(delay-coupled)Tj
5.7543 0 Td
(DPLLs.)Tj
3.1407 0 Td
(In)Tj
1.0999 0 Td
(Section)Tj
3.1237 0 Td
(2)Tj
0.686 0 Td
(and)Tj
1.7121 0 Td
(Section)Tj
3.1238 0 Td
(3,)Tj
0.9071 0 Td
(the)Tj
1.457 0 Td
(existence)Tj
3.7984 0 Td
(and)Tj
1.7121 0 Td
(stabil-)Tj
-34.8659 -1.2983 Td
(ity)Tj
1.2188 0 Td
(of)Tj
1.0035 0 Td
(different)Tj
3.6056 0 Td
(types)Tj
2.2451 0 Td
(of)Tj
1.0034 0 Td
(frequency-synchronized)Tj
9.7795 0 Td
(solutions)Tj
3.7927 0 Td
(for)Tj
1.3663 0 Td
(networks)Tj
3.8664 0 Td
(of)Tj
1.0035 0 Td
(mutually)Tj
3.7247 0 Td
(coupled)Tj
-32.6095 -1.2983 Td
(DPLLs)Tj
2.9196 0 Td
(are)Tj
1.4343 0 Td
(investigated.)Tj
5.1364 0 Td
(In)Tj
1.0998 0 Td
(Section)Tj
3.1181 0 Td
(4,)Tj
0.9128 0 Td
(we)Tj
1.3152 0 Td
(use)Tj
1.5137 0 Td
(our)Tj
1.6101 0 Td
(theory)Tj
2.7666 0 Td
(to)Tj
1.0091 0 Td
(illustrate)Tj
3.6397 0 Td
(the)Tj
1.4513 0 Td
(behavior)Tj
3.6623 0 Td
(of)Tj
1.0035 0 Td
(DPLL)Tj
2.5682 0 Td
(sys-)Tj
-35.1607 -1.3039 Td
(tems)Tj
2.0976 0 Td
(for)Tj
1.3663 0 Td
(specific)Tj
3.1464 0 Td
(examples.)Tj
4.0819 0 Td
(In)Tj
1.0998 0 Td
(Section)Tj
3.1181 0 Td
(5,)Tj
0.9127 0 Td
(we)Tj
1.3153 0 Td
(present)Tj
3.1181 0 Td
(experimental)Tj
5.3915 0 Td
(data)Tj
1.8878 0 Td
(for)Tj
1.372 0 Td
(systems)Tj
3.2541 0 Td
(of)Tj
1.0035 0 Td
(mutually)Tj
-33.1651 -1.2983 Td
(coupled)Tj
3.3505 0 Td
(DPLLs)Tj
2.9253 0 Td
(with)Tj
1.9729 0 Td
(different)Tj
3.6 0 Td
(network)Tj
3.5093 0 Td
(topologies)Tj
4.2632 0 Td
(and)Tj
1.7122 0 Td
(show)Tj
2.2733 0 Td
(that)Tj
1.7575 0 Td
(the)Tj
1.4513 0 Td
(measurements)Tj
5.9584 0 Td
(can)Tj
1.6101 0 Td
(be)Tj
-34.384 -1.2982 Td
(understood)Tj
4.7621 0 Td
(quantitatively)Tj
5.5956 0 Td
(using)Tj
2.3584 0 Td
(our)Tj
1.6101 0 Td
(theory.)Tj
2.9877 0 Td
(Finally,)Tj
3.118 0 Td
(conclusions)Tj
4.8813 0 Td
(are)Tj
1.4286 0 Td
(drawn)Tj
2.7553 0 Td
(in)Tj
1.0261 0 Td
(Section)Tj
3.1238 0 Td
(6.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 112.9889 cm
BT
/F2 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(1)Tj
0.7653 0 Td
(Phase)Tj
3.1418 0 Td
(model)Tj
3.1464 0 Td
(for)Tj
1.5449 0 Td
(networks)Tj
4.5733 0 Td
(of)Tj
1.1622 0 Td
(DPLLs)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 95.9811 cm
BT
/F7 1 Tf
1 TL
-0.004 Tc
0 0 Td
(The)Tj
1.7801 0 Td
(networks)Tj
3.9118 0 Td
(we)Tj
1.3266 0 Td
(propose)Tj
3.4242 0 Td
(consist)Tj
2.9877 0 Td
(of)Tj
1.0148 0 Td
(digital)Tj
2.7269 0 Td
(phase-locked)Tj
5.4538 0 Td
(loops)Tj
2.3585 0 Td
(\(DPLL\).)Tj
3.4979 0 Td
(These)Tj
2.5682 0 Td
(autonomous)Tj
-31.0505 -1.2982 Td
(electronic)Tj
4.1498 0 Td
(oscillators)Tj
4.2463 0 Td
(allow)Tj
2.3358 0 Td
(inputs)Tj
2.7382 0 Td
(that)Tj
1.7801 0 Td
(can)Tj
1.6271 0 Td
(entrain)Tj
3.1124 0 Td
(their)Tj
2.1033 0 Td
(output)Tj
2.897 0 Td
(signal)Tj
2.5455 0 Td
(by)Tj
1.1792 0 Td
(comparing)Tj
4.5751 0 Td
(the)Tj
1.4684 0 Td
(input)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 384.7181 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Self-organ)Tj
4.5283 0 Td
(ized)Tj
2.0197 0 Td
(synchroniz)Tj
4.6914 0 Td
(ation)Tj
2.3457 0 Td
(of)Tj
1.0417 0 Td
(delay-cou)Tj
4.252 0 Td
(pled)Tj
2.0693 0 Td
(DPLLs)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*
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
0.4748 0 Td
(DOI:10.137)Tj
5.0387 0 Td
(1/journal.po)Tj
5.1236 0 Td
(ne.0171)Tj
3.5434 0 Td
(590)Tj
2.6362 0 Td
(February)Tj
4.1599 0 Td
(16,)Tj
1.5874 0 Td
(2017)Tj
37.3538 0 Td
(2)Tj
0.7654 0 Td
(/)Tj
0.496 0 Td
(21)Tj
/F9 1 Tf
-0.025 Tc
-66.402 84.0904 Td
(in)Tj
0.8858 0 Td
(study)Tj
2.2677 0 Td
(design,)Tj
2.8985 0 Td
(data)Tj
1.7929 0 Td
(collection)Tj
3.7347 0 Td
(and)Tj
1.5945 0 Td
(analysis)Tj
2.9622 0 Td
(,)Tj
-16.1363 -1.3748 Td
(decision)Tj
3.2882 0 Td
(to)Tj
0.9496 0 Td
(publish,)Tj
3.1465 0 Td
(or)Tj
0.9992 0 Td
(preparation)Tj
4.4433 0 Td
(of)Tj
0.9496 0 Td
(the)Tj
-13.7764 -1.3749 Td
(manuscript.)Tj
4.6417 0 Td
(The)Tj
1.5874 0 Td
(Vodafo)Tj
2.9764 0 Td
(ne)Tj
1.1197 0 Td
(Chair)Tj
2.1402 0 Td
(Mobile)Tj
-12.4654 -1.3748 Td
(Communica)Tj
4.4858 0 Td
(tions)Tj
2.041 0 Td
(Systems)Tj
3.7984 0 Td
(is)Tj
0.8363 0 Td
(a)Tj
0.6378 0 Td
(chair)Tj
2.0409 0 Td
(at)Tj
0.8929 0 Td
(Technische)Tj
-14.7331 -1.3748 Td
(Universita)Tj
0 Tc
3.3378 0 Td
()Tj
-0.025 Tc
0.3543 0 Td
(t)Tj
0.4819 0 Td
(Dresden.)Tj
3.5504 0 Td
(While)Tj
2.3032 0 Td
(the)Tj
1.3677 0 Td
(company)Tj
3.6638 0 Td
(Vodafon)Tj
3.0898 0 Td
(e)Tj
-18.1489 -1.3748 Td
(financially)Tj
3.8834 0 Td
(supports)Tj
3.515 0 Td
(the)Tj
1.3678 0 Td
(chair,)Tj
2.2677 0 Td
(Vodafon)Tj
3.0898 0 Td
(e)Tj
0.6449 0 Td
(did)Tj
1.3606 0 Td
(not)Tj
-16.1292 -1.3748 Td
(have)Tj
1.9559 0 Td
(any)Tj
1.5378 0 Td
(additional)Tj
3.7913 0 Td
(role)Tj
1.6158 0 Td
(in)Tj
0.8858 0 Td
(the)Tj
1.3678 0 Td
(study)Tj
2.2677 0 Td
(design,)Tj
2.8985 0 Td
(data)Tj
-16.3206 -1.3748 Td
(collection)Tj
3.7417 0 Td
(and)Tj
1.5874 0 Td
(analysis)Tj
2.9623 0 Td
(,)Tj
0.4464 0 Td
(decision)Tj
3.2882 0 Td
(to)Tj
0.9496 0 Td
(publish,)Tj
3.1465 0 Td
(or)Tj
-16.1221 -1.3748 Td
(preparation)Tj
4.4433 0 Td
(of)Tj
0.9496 0 Td
(the)Tj
1.3677 0 Td
(manuscript.)Tj
4.6347 0 Td
(The)Tj
1.5945 0 Td
(funder)Tj
2.6221 0 Td
(provided)Tj
-15.6119 -1.3748 Td
(support)Tj
3.0968 0 Td
(in)Tj
0.8859 0 Td
(the)Tj
1.3748 0 Td
(form)Tj
2.0055 0 Td
(of)Tj
0.9496 0 Td
(contributio)Tj
3.9898 0 Td
(ns)Tj
1.1197 0 Td
(to)Tj
0.9496 0 Td
(salaries)Tj
3.0189 0 Td
(for)Tj
-17.3906 -1.3749 Td
(the)Tj
1.3677 0 Td
(author)Tj
2.6291 0 Td
(GF,)Tj
1.4528 0 Td
(but)Tj
1.4173 0 Td
(did)Tj
1.3607 0 Td
(not)Tj
1.4244 0 Td
(have)Tj
1.9559 0 Td
(any)Tj
1.5378 0 Td
(additional)Tj
3.7914 0 Td
(role)Tj
-16.9371 -1.3748 Td
(in)Tj
0.8858 0 Td
(the)Tj
1.3677 0 Td
(study)Tj
2.2677 0 Td
(design,)Tj
2.8985 0 Td
(data)Tj
1.7929 0 Td
(collection)Tj
3.7418 0 Td
(and)Tj
1.5874 0 Td
(analysis,)Tj
-14.5418 -1.3748 Td
(decision)Tj
3.2882 0 Td
(to)Tj
0.9496 0 Td
(publish,)Tj
3.1465 0 Td
(or)Tj
0.9992 0 Td
(preparation)Tj
4.4433 0 Td
(of)Tj
0.9496 0 Td
(the)Tj
-13.7764 -1.3748 Td
(manuscript.)Tj
4.6417 0 Td
(The)Tj
1.5874 0 Td
(Respons)Tj
3.267 0 Td
(e)Tj
0.6449 0 Td
(to)Tj
0.9496 0 Td
(Reviewer)Tj
3.4087 0 Td
(s)Tj
0.6449 0 Td
(specific)Tj
-15.1442 -1.3748 Td
(roles)Tj
2.0338 0 Td
(of)Tj
0.9496 0 Td
(these)Tj
2.2182 0 Td
(authors)Tj
3.0401 0 Td
(are)Tj
1.3749 0 Td
(articulate)Tj
3.359 0 Td
(d)Tj
0.6945 0 Td
(in)Tj
0.8859 0 Td
(the)Tj
1.3748 0 Td
(`author)Tj
-15.9308 -1.3748 Td
(contributio)Tj
3.9897 0 Td
(ns')Tj
1.3111 0 Td
(section.)Tj
/F8 1 Tf
-5.3008 -2.126 Td
(Competing)Tj
4.3795 0 Td
(interests)Tj
3.3307 0 Td
(:)Tj
/F9 1 Tf
0.4819 0 Td
(The)Tj
1.5875 0 Td
(scientists)Tj
3.6921 0 Td
(at)Tj
0.9 0 Td
(the)Tj
-14.3717 -1.3748 Td
(Vodafone)Tj
3.7346 0 Td
(Chair)Tj
2.1402 0 Td
(are)Tj
1.3748 0 Td
(employe)Tj
3.1536 0 Td
(es)Tj
1.063 0 Td
(of)Tj
0.9496 0 Td
(the)Tj
1.3748 0 Td
(State)Tj
2.0977 0 Td
(of)Tj
-15.8883 -1.3749 Td
(Saxony.)Tj
3.1819 0 Td
(This)Tj
1.7787 0 Td
(does)Tj
2.0126 0 Td
(not)Tj
1.4174 0 Td
(alter)Tj
1.8212 0 Td
(our)Tj
1.4741 0 Td
(adherence)Tj
4.0535 0 Td
(to)Tj
0.9497 0 Td
(PLOS)Tj
-16.6891 -1.3748 Td
(ONE)Tj
1.8708 0 Td
(policies)Tj
3.0048 0 Td
(on)Tj
1.1693 0 Td
(sharing)Tj
2.9835 0 Td
(data)Tj
1.7929 0 Td
(and)Tj
ET
endstream
endobj
35 0 obj
<>stream
endstream
endobj
36 0 obj
<>stream
endstream
endobj
37 0 obj
<>stream
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
12.4087 57.2177 Td
(materials.)Tj
ET
Q
endstream
endobj
52 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 12 0 R/Annots 63 0 R/Contents 64 0 R/TrimBox[0 0 612 792]>>
endobj
62 0 obj
<>stream
JFIF C
$, !$4.763.22:ASF:=N>22HbINVX]^]8EfmeZlS[]Y C**Y;2;YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY "
} !1AQa"q2#BR$3br
%&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz
w !1AQaq"2B #3Rbr
$4%&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz ? (
(
(
(
(
(
(
(
(
(
(
(
(
(
I.ˆ!lT_u?E C LJ" N<; A o:u%VI"8 ZYk?c } @eQ +3ٯ4" (r^^}:̒[ ;@6/G"./"PUGN¥ҵ?YIO,D!H?Q^wcB? F ǎ ]S *()jl./X b jm#U5ؚma "_W!F \PE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE QE VQ X^5 GS _PxGF/W0I,3;rux w?.`7aope(ιy ŷF[m3U
yvl{:<=e{z{(cB? F ǎ ]S !{#Z_ R zQ@_/" Z_5 Һ _,E _+ rk {Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@axEOQ[I9}kk< dzGF/Wxs허,.n,
CbEPX p?_uuB֭|C6t"C܊?O _ҿ'e ijl,qj#*I>5x V7!ewo1 =x4|R b/_sqė3G~K0Q;iw <^q 7 U z ޕ A;/Gޕ A;/^A 7 Ux P+PAR2KPXXk$jz*z ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( Ohd9IJHF>Mмaif+ C&d@>%4H/&
K,_2{ւ0 XSQٖ#R3WWUdleݎK4JIq@:Ot_R;l. _j*Z} !E?U 浯&WqܴH{-bI3jZ5I],w'0"en6rDP i.GM@F2Gr=+Zܸ{h&`0 ~4ɏZ! yW 5 ⫳ ީ eii ~W* cxĖ^X
N~RH_Yz' k W]qiouML:w? OipőȲ.Q].VrA=5QB @2(a^h +Uu:^C{nE0ܡ\sMӿU8cE*PM_SGeaHֹYz' k Wc,QhHUu_;|-? G-EyLH 9Bjv63hq&s(SDdu0UA ?_*|??4K2L bjN @OSچEc#@F`X5 ?_*3:wZߕ