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BT
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(i)Tj
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[(,)-239.4(w)0(e)-251.9(call)]TJ
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f
BT
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(1)Tj
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[(.)-245.1(For)-248.2(an)-242.3(interv)-8.2(al)]TJ
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[([0,)-168.9(1],)-248.6(we)]TJ
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[(will)-339.6(refer)-337.7(to)]TJ
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(m)Tj
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9.9626 0 0 9.9626 170.759 596.3526 Tm
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(I)Tj
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[(\))-338.5(a)0(s)-334.6(its)]TJ
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[(For)-447.3(applying)-451.6(a)-446.4(sta)-8(tistical)-451.5(test)-449.7(we)-451.1(need)-450.5(to)-448.2(comp)-8.4(ute,)-445.4(for)-450.1(a)-446.4(give)-7.6(n)-444.6(weight)]TJ
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30.507 0 TD
(h)Tj
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[(and)-447.9(a)-452.1(given)-446.5(leng)-7.6(th)]TJ
/F6 1 Tf
8.4334 0 TD
(r)Tj
/F1 1 Tf
.387 0 TD
[(,)-444.3(the)]TJ
-41.2736 -1.2007 TD
[(proba)-7.6(bility,)-374.5(under)-371.8(the)-376.7(null)-372.8(hypothesi)-9.7(s,)-366.5(of)-373.4(nding)-376.4(somew)-8.6(here)-372.8(in)-374.2(the)-371(genom)-9.1(e)-366.8(B)-375.4(an)-373.2(orthologo)-8.7(us)-366.9(clus)-8.8(ter)-373(of)]TJ
T*
[(weight)-340.2(greater)-341.8(than)]TJ
/F6 1 Tf
8.2627 0 TD
(h)Tj
/F1 1 Tf
.8308 0 TD
[(and)-339.8(of)-333.6(leng)-7.6(th)-334.3(smaller)-339.8(than)]TJ
/F6 1 Tf
11.1649 0 TD
(r)Tj
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[(.)-330.4(W)0(e)-341.6(will)-333.9(cal)-8.6(l)-333.6(such)-336.1(a)-332.6(clus)-8.8(ter)]TJ
/F6 1 Tf
11.9729 0 TD
[(of)-334.3(type)]TJ
/F1 1 Tf
3.1298 0 TD
(\()Tj
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(h)Tj
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(:)Tj
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(\).)Tj
-36.9146 -1.195 TD
[(In)-379.1(this)-379.7(article)-9.6(,)-376(w)0(e)-382.8(focus)-384.3(on)-377.1(the)-382.4(computa)-9.5(tion)-378.5(of)-379.1(this)-379.7(proba)-7.6(bility.)-385.9(For)-379.1(technical)-386.5(simpl)-8.4(ications,)-383.7(we)-382.8(rst)]TJ
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[(consider)-340(the)-336.9(case)-339.7(whe)-8(n)-330.8(B)-335.5(is)-335.5(a)-332.6(circul)-10(ar)-335.3(genome,)-342.1(hence)-339.2(the)-336.9(circle)-341.8(of)-333.6(leng)-7.6(th)-334.3(1)-330.8(i)0(n)-334.3(our)-334.3(mode)-8.4(l.)]TJ
/F6 1 Tf
10.959 0 0 10.959 107.6031 507.9117 Tm
[(2.2.)-496.9(The)-332.3(circular)-333.2(case)]TJ
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(Let)Tj
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[(be)-339.1(xed,)-334.5(of)-339.2(the)-336.9(form)]TJ
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(h)Tj
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()Tj
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(P)Tj
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(m)Tj
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ET
274.62 492.264 6.5764 .39685 re
f
BT
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6.9738 0 0 6.9738 275.1873 494.0786 Tm
(n)Tj
4.9813 0 0 4.9813 278.7023 493.0581 Tm
(i)Tj
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(/)Tj
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(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 281.1968 489.94 Tm
[(,)-330.4(with)-336.9(0)]TJ
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6.9738 0 0 6.9738 331.3133 488.466 Tm
(i)Tj
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()Tj
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(i)Tj
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9.9626 0 0 9.9626 356.0881 489.94 Tm
(,)Tj
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(m)Tj
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(r)Tj
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(2)Tj
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[(\(0,)-168.9(1\))-333.6(be)-339.1(also)-338.8(xed.)]TJ
-3.3062 -1.195 TD
[(We)-444(denot)-8.4(e)-446.4(b)0(y)]TJ
/F6 1 Tf
6.4132 0 TD
(U)Tj
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(\(1\))Tj
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()Tj
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(U)Tj
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(\(2\))Tj
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9.9626 0 0 9.9626 229.096 466.0723 Tm
.1682 Tc
[()-114.6()-108.1()]TJ
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3.5281 0 TD
0 Tc
(U)Tj
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6.9738 0 0 6.9738 271.3889 464.5416 Tm
(\()Tj
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(n)Tj
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(\))Tj
9.9626 0 0 9.9626 284.485 466.0723 Tm
[(the)-445(order)-9.6(ed)-447.2(positions)-450(in)-448.2(B)-443.7(o)0(f)-447.4(the)]TJ
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14.545 0 TD
(n)Tj
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[(ort)-7(hologs,)-447.1(i.e.)-450.7(the)-445(order)]TJ
-33.2442 -1.2007 TD
[(statist)-9.2(ics)-332.4(of)]TJ
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-4.7971 -1.2007 TD
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(m)Tj
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()Tj
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(W)Tj
7.4718 0 0 6.641 166.1102 440.5038 Tm
(m)Tj
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9.9626 0 0 9.9626 171.496 442.1479 Tm
(\()Tj
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(h)Tj
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(,)Tj
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(r)Tj
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[(\))-207.6(denot)-8.4(e)-213.1(the)-211.7(r.v.)-209.1(repr)-8.8(esenting)-215.6(the)-211.7(numb)-6.6(er)-210.1(of)-214.1(\(possibly)-215.9(overlapp)-8.7(ing\))-212.6(clus)-8.8(ters)-209.9(of)-214.1(type)-212.5(\()]TJ
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(h)Tj
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(r)Tj
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(\))Tj
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[(in)-283.1(the)-280(genom)-9.1(e)-281.4(B)0(.)-279(L)0(e)-8.8(t)-276.7(also)]TJ
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(k)Tj
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(A)Tj
6.9738 0 0 6.9738 264.1322 409.5495 Tm
(k)Tj
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9.9626 0 0 9.9626 267.8739 411.0802 Tm
(\()Tj
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(r)Tj
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(:)Tj
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(f)Tj
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0 Tc
(l)Tj
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(m)Tj
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(\([)Tj
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(U)Tj
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6.9738 0 0 6.9738 335.2818 409.5495 Tm
(\()Tj
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(k)Tj
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9.9626 0 0 9.9626 343.729 411.0802 Tm
(,)Tj
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(\()Tj
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(k)Tj
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(\))Tj
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9.9626 0 0 9.9626 365.1023 411.0802 Tm
()Tj
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(r)Tj
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(h)Tj
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(g)Tj
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[(denote)-341(the)-336.9(event)-340.2(of)-333.6(having)-339.2(in)-334.3(B)-335.5(a)-332.6(cluste)-9.2(r)-332.8(o)0(f)-333.6(type)-337.7(\()]TJ
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(h)Tj
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(:)Tj
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(r)Tj
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[(\))-338.5(starting)-338(with)-336.9(the)]TJ
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(k)Tj
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[(-th)-337.1(ortholo)-7.1(g.)]TJ
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[(We)-500.9(have)]TJ
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(W)Tj
6.9738 0 0 6.9738 168.6047 378.5385 Tm
(m)Tj
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()Tj
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1.104 .7511 TD
(P)Tj
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6.9738 0 0 6.9738 197.2913 384.7747 Tm
(n)Tj
0 -1.0893 TD
(k)Tj
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()Tj
/F1 1 Tf
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(1)Tj
9.9626 0 0 9.9626 213.9023 380.0125 Tm
(1)Tj
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6.9738 0 0 6.9738 218.8913 378.5385 Tm
(A)Tj
4.9813 0 0 4.9813 223.1999 377.4613 Tm
(k)Tj
/F1 1 Tf
9.9626 0 0 9.9626 226.5448 380.0125 Tm
[(.)-495.5(W)0(e)-500.9(are)-497.2(intere)-10(sted)-498.2(in)-499.4(computin)-11.2(g)]TJ
/F14 1 Tf
14.8523 0 TD
(P)Tj
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(\()Tj
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(W)Tj
6.9738 0 0 6.9738 393.3353 378.5385 Tm
(m)Tj
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9.9626 0 0 9.9626 401.6125 380.0125 Tm
()Tj
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[(1\),)-499(the)-501.9(probabilit)-11.1(y)-495.8(o)0(f)-498.6(nding,)]TJ
-30.5583 -1.2007 TD
[(somew)-8.6(here)-338.7(in)-334.3(the)-336.9(genome)-341.7(B,)-335.9(at)-330.4(lea)-8.6(st)-335.5(one)-334.1(cluste)-9.2(r)-332.8(o)0(f)-333.6(type)-337.7(\()]TJ
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(h)Tj
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(:)Tj
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(r)Tj
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[(We)-335.9(will)-339.6(further)-340.2(simplify)-339.7(the)-336.9(parame)-9.7(trization)-342.1(of)-333.6(the)-336.9(problem)-9.7(.)]TJ
T*
(Let)Tj
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1.6332 0 TD
(/)Tj
/F8 1 Tf
6.9738 0 0 6.9738 140.5417 348.4912 Tm
(0)Tj
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0 -1.0243 TD
(1)Tj
/F15 1 Tf
9.9626 0 0 9.9626 146.1543 344.1259 Tm
(5)Tj
/F8 1 Tf
1.3373 0 TD
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()Tj
/F15 1 Tf
1.4795 0 TD
0 Tc
(5)Tj
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1.1666 0 TD
(/)Tj
/F8 1 Tf
6.9738 0 0 6.9738 192.5291 348.4912 Tm
(0)Tj
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0 -1.0243 TD
(J)Tj
/F1 1 Tf
9.9626 0 0 9.9626 199.3889 344.1259 Tm
[(denot)-8.4(e)-292.8(all)-288.4(the)-297.1(different)-300.7(values)-296.6(amo)-7.6(ng)-291.7(the)-291.4(multigen)-8.3(e)-292.8(famili)-8.8(es)-291.8(sizes)]TJ
/F12 1 Tf
27.3886 0 TD
(/)Tj
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6.9738 0 0 6.9738 478.9416 341.8015 Tm
(1)Tj
9.9626 0 0 9.9626 482.9101 344.1259 Tm
(,)Tj
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[(..)-5.7(.)]TJ
/F1 1 Tf
1.3088 0 TD
0 Tc
(,)Tj
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(/)Tj
/F6 1 Tf
6.9738 0 0 6.9738 512.6172 341.8015 Tm
(m)Tj
/F1 1 Tf
9.9626 0 0 9.9626 518.1164 344.1259 Tm
[(,)-296.3(and)]TJ
-41.2053 -1.2007 TD
(let)Tj
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1.343 0 TD
(g)Tj
6.9738 0 0 6.9738 125.9716 330.6897 Tm
(j)Tj
/F8 1 Tf
9.9626 0 0 9.9626 130.1102 332.1637 Tm
.1689 Tc
[(j)168.9(f)]TJ
/F6 1 Tf
1.7129 0 TD
0 Tc
(i)Tj
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()Tj
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(1,)Tj
/F9 1 Tf
1.0812 0 TD
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(...)Tj
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1.3145 0 TD
0 Tc
(,)Tj
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(m)Tj
/F9 1 Tf
1.0015 0 TD
(:)Tj
/F12 1 Tf
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(/)Tj
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6.9738 0 0 6.9738 211.1244 329.8393 Tm
(i)Tj
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9.9626 0 0 9.9626 215.2062 332.1637 Tm
()Tj
/F12 1 Tf
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(/)Tj
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6.9738 0 0 6.9738 231.2503 336.5291 Tm
(0)Tj
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0 -1.0162 TD
(j)Tj
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9.9626 0 0 9.9626 233.6881 332.1637 Tm
(gj)Tj
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(,)Tj
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(j)Tj
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(1,)Tj
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.1682 Tc
(...)Tj
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1.3145 0 TD
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(,)Tj
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(J)Tj
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[(denote)-335.3(their)-343.2(multiplic)-8.9(ities.)]TJ
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-18.0504 -2.8794 TD
[(Remark)-492(1.)]TJ
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5.7418 0 TD
[(We)-489.7(can)-487.8(represent)-490.9(the)-490.5(measure)]TJ
/F10 1 Tf
13.5663 0 TD
(m)Tj
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7.4718 0 0 6.641 315.4393 301.833 Tm
(m)Tj
9.9626 0 0 9.9626 325.644 303.4771 Tm
(as)Tj
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(l)Tj
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6.9738 0 0 6.9738 344.8062 301.1526 Tm
(m)Tj
/F8 1 Tf
9.9626 0 0 9.9626 351.9495 303.4771 Tm
()Tj
/F13 1 Tf
1.1097 .7512 TD
(P)Tj
/F6 1 Tf
6.9738 0 0 6.9738 373.4361 308.296 Tm
(n)Tj
0 -1.0975 TD
(i)Tj
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()Tj
/F1 1 Tf
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[(range)-359.6(\(almost\))-356.4(independe)-9.3(nce)]TJ
/F1 1 Tf
11.9103 0 TD
[(.)-347.5(Becaus)-10.1(e)-349.7(o)0(f)-350.6(the)-354(strong)-351.9(d)-6.5(ependence)-357.2(betwee)-10.9(n)-347.9(the)-354(neig)-7.6(hboring)-351.5(indicat)-11.5(ors,)-353(the)]TJ
-11.9103 -1.2007 TD
[(event)-10.1(s)]TJ
/F6 1 Tf
2.8908 0 TD
(A)Tj
7.4718 0 0 6.641 109.0771 689.8959 Tm
(k)Tj
/F1 1 Tf
9.9626 0 0 9.9626 115.6535 691.5967 Tm
[(will)-328.2(tend)-326.3(to)-323(occur)-333.7(in)-323(clumps)-8.1(.)-324.7(Conseque)-9.9(ntly,)-327.6(it)-325.7(seems)-332(reasonable)-333.7(to)-328.7(approach)-332.1(the)-325.5(distribut)-9.7(ion)-323.7(of)]TJ
/F6 1 Tf
-4.1712 -1.2007 TD
(W)Tj
7.4718 0 0 6.641 82.4315 677.9337 Tm
(m)Tj
/F1 1 Tf
9.9626 0 0 9.9626 91.1055 679.6345 Tm
[(b)-6.5(y)-330.8(a)-332.6(com)-7.6(pound)-339.6(Poisson)-339.7(distributio)-8.3(n)]TJ
/F6 1 Tf
15.1027 0 TD
(CP)Tj
/F1 1 Tf
1.2804 0 TD
(\()Tj
/F10 1 Tf
.3357 0 TD
(l)Tj
/F1 1 Tf
.5008 0 TD
[(\),)-333.2(with)-336.9(a)-338.3()82.6(good)82.5()-338.5(choice)-337.1(of)-339.2(the)-336.9(parameter)]TJ
/F10 1 Tf
17.3789 0 TD
(l)Tj
/F1 1 Tf
.5008 0 TD
(.)Tj
-35.8049 -1.2007 TD
[(We)-421.3(will)-419.3(quant)-8.4(ify)-416.7(the)-416.6(erro)-8.8(r)-412.5(usin)-7(g)-416.2(the)-416.6(Kolm)-7.6(ogorov)-422(distance.)-422.6(We)-421.3(recall)-421.5(that)-420.1(the)-422.3(Kolmo)-8.3(gorov)-415.5(distanc)-9.9(e)]TJ
-1.0015 -1.2007 TD
[(betwee)-10.9(n)-336.5(two)-333.3(mea)-9.4(sures)]TJ
/F10 1 Tf
9.5886 0 TD
(m)Tj
/F1 1 Tf
.8877 0 TD
(and)Tj
/F10 1 Tf
1.7868 0 TD
(n)Tj
/F1 1 Tf
.7682 0 TD
(on)Tj
/F14 1 Tf
1.3373 0 TD
(R)Tj
/F8 1 Tf
6.9738 0 0 6.9738 225.581 654.2361 Tm
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 235.9558 655.7101 Tm
(is)Tj
/F6 1 Tf
-2.2307 -1.9177 TD
(d)Tj
6.9738 0 0 6.9738 218.7212 635.0739 Tm
(K)Tj
/F1 1 Tf
9.9626 0 0 9.9626 224.2771 636.6046 Tm
(\()Tj
/F12 1 Tf
.3357 0 TD
(l)Tj
/F1 1 Tf
.552 0 TD
(,)Tj
/F11 1 Tf
.4211 0 TD
()Tj
/F1 1 Tf
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(\))Tj
/F8 1 Tf
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()Tj
/F1 1 Tf
1.104 0 TD
(sup)Tj
/F6 1 Tf
6.9738 0 0 6.9738 258.6897 628.1006 Tm
(k)Tj
/F8 1 Tf
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(2)Tj
/F14 1 Tf
.6585 0 TD
(N)Tj
/F8 1 Tf
9.9626 0 0 9.9626 274.0535 636.6046 Tm
(j)Tj
/F12 1 Tf
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(l)Tj
/F1 1 Tf
.552 0 TD
(\([)Tj
/F6 1 Tf
.6715 0 TD
(k)Tj
/F1 1 Tf
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(,)Tj
/F8 1 Tf
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(1)Tj
/F1 1 Tf
1.0015 0 TD
(\))Tj
/F8 1 Tf
.5008 0 TD
()Tj
/F11 1 Tf
.9389 0 TD
()Tj
/F1 1 Tf
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(\([)Tj
/F6 1 Tf
.6658 0 TD
(k)Tj
/F1 1 Tf
.4666 0 TD
(,)Tj
/F8 1 Tf
.4211 0 TD
(1)Tj
/F1 1 Tf
1.0015 0 TD
(\)\))Tj
/F8 1 Tf
.6658 0 TD
(j)Tj
/F11 1 Tf
.2731 0 TD
(:)Tj
/F1 1 Tf
-27.9178 -2.6233 TD
[(We)-700.1(will)-703.8(approx)-8.3(imate)-699.3(our)-698.5(proba)-7.6(bility)-704.2(of)-697.8(interest)]TJ
/F14 1 Tf
22.4208 0 TD
(P)Tj
/F1 1 Tf
.7227 0 TD
(\()Tj
/F6 1 Tf
.33 0 TD
(W)Tj
6.9738 0 0 6.9738 326.2676 608.9951 Tm
(m)Tj
/F8 1 Tf
9.9626 0 0 9.9626 334.5448 610.4691 Tm
()Tj
/F1 1 Tf
1.0527 0 TD
[(1\))-697.8(by)-695.8(the)-701.1(correspo)-9.1(nding)-700.8(proba)-7.6(bility)]TJ
/F6 1 Tf
-27.1951 -1.8039 TD
(CP)Tj
/F1 1 Tf
1.2861 0 TD
(\()Tj
/F12 1 Tf
.3357 0 TD
(k)Tj
/F1 1 Tf
.5008 0 TD
(\)\([1,)Tj
/F8 1 Tf
1.9177 0 TD
(1)Tj
/F1 1 Tf
1.0015 0 TD
(\)\))Tj
/F8 1 Tf
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()Tj
/F1 1 Tf
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(1)Tj
/F8 1 Tf
.6658 0 TD
()Tj
/F1 1 Tf
1.1097 0 TD
(exp)Tj
/F8 1 Tf
1.4454 0 TD
.1715 Tc
(f)Tj
/F13 1 Tf
1.912 .7455 TD
0 Tc
(P)Tj
/F8 1 Tf
6.9738 0 0 6.9738 194.9102 601.9652 Tm
(1)Tj
/F6 1 Tf
-.4471 -2.6258 TD
(i)Tj
/F8 1 Tf
.4471 0 TD
()Tj
/F1 1 Tf
.943 0 TD
(1)Tj
/F12 1 Tf
9.9626 0 0 9.9626 206.6456 592.4975 Tm
(k)Tj
/F6 1 Tf
6.9738 0 0 6.9738 211.6346 590.9668 Tm
(i)Tj
/F8 1 Tf
9.9626 0 0 9.9626 214.0724 592.4975 Tm
(g)Tj
/F1 1 Tf
.8365 0 TD
[(for)-336.3(the)-336.9(compound)-341.5(Poisson)-339.7(distributio)-8.3(n,)-336.9(with)-336.9(an)-333.4(error)]TJ
/F8 1 Tf
-3.7387 -2.8567 TD
(j)Tj
/F14 1 Tf
.2731 0 TD
(P)Tj
/F1 1 Tf
.717 0 TD
(\()Tj
/F6 1 Tf
.3357 0 TD
(W)Tj
6.9738 0 0 6.9738 206.7023 562.5637 Tm
(m)Tj
/F8 1 Tf
9.9626 0 0 9.9626 214.9795 564.0377 Tm
()Tj
/F1 1 Tf
1.0528 0 TD
(1\))Tj
/F8 1 Tf
1.0015 0 TD
()Tj
/F6 1 Tf
.9389 0 TD
(CP)Tj
/F1 1 Tf
1.2804 0 TD
(\()Tj
/F12 1 Tf
.3357 0 TD
(k)Tj
/F1 1 Tf
.5008 0 TD
(\)\([1,)Tj
/F8 1 Tf
1.9177 0 TD
(1)Tj
/F1 1 Tf
1.0015 0 TD
(\)\))Tj
/F8 1 Tf
.6715 0 TD
.2763 Tc
(j)Tj
/F6 1 Tf
1.599 0 TD
0 Tc
(d)Tj
6.9738 0 0 6.9738 322.5826 562.5637 Tm
(K)Tj
/F1 1 Tf
9.9626 0 0 9.9626 328.1385 564.0377 Tm
(\()Tj
/F8 1 Tf
.3357 0 TD
(L)Tj
/F1 1 Tf
.6886 0 TD
(\()Tj
/F6 1 Tf
.3357 0 TD
(W)Tj
6.9738 0 0 6.9738 349.9653 562.5637 Tm
(m)Tj
/F1 1 Tf
9.9626 0 0 9.9626 355.5211 564.0377 Tm
(\),)Tj
/F6 1 Tf
.7512 0 TD
(CP)Tj
/F1 1 Tf
1.2804 0 TD
(\()Tj
/F12 1 Tf
.3357 0 TD
(k)Tj
/F1 1 Tf
.5008 0 TD
(\)\))Tj
/F11 1 Tf
.6658 0 TD
(:)Tj
/F1 1 Tf
-30.7802 -2.1966 TD
[(It)-256.6(is)-255.9(therefore)-259.9(sufc)-8(ient)-255.1(to)-254.7(obta)-7.6(in)-254.7(bounds)-256.1(for)-256.6(the)-257.2(Kolm)-7.6(ogorov)-256.9(distanc)-9.9(e)-252.9(betwee)-10.9(n)-251.2(the)-257.2(two)-253.7(distri)-10.3(butions.)-257.1(For)]TJ
-1.0015 -1.2007 TD
[(bo)-7.2(unding)-365.8(the)-371(Kolm)-7.6(ogorov)-370.7(distance,)-377.1(we)-365.7(will)-373.8(use)-369.5(the)-365.3(Stein-Che)-10.5(n)-370.7(method)-371.2(for)-364.7(com)-7.6(pound)-368(Poiss)-8.2(on)-365.7(appro)-7.6(xi-)]TJ
T*
[(mati)-8.2(on.)]TJ
1.0015 -1.2007 TD
[(The)-339.6(Stein-Che)-10.5(n)-336.5(method)-342.7(is)-335.5(a)-332.6(gener)-9.4(al)-336.1(method)-342.7(to)-334.3(obta)-7.6(in)-334.3(bounds)-341.5(on)-331.6(the)-342.6(distance)-342.5(betwee)-10.9(n)-330.8(two)-339(proba)-7.6(bility)]TJ
-1.0015 -1.2007 TD
[(distri)-10.3(butions)-336.4(with)-336.9(respect)-335.3(to)-334.3(a)-332.6(proba)-7.6(bility)-334.3(metric.)-338.2(It)-336.3(was)-333.6(origina)-8.9(lly)-332.2(formul)-9.1(ated)-333.7(for)-336.3(normal)-333.3(appro)-7.6(ximat)-9(ions)]TJ
T*
[(by)-422.6(Stein)-425.8(\(1972\))-8.5(,)-415.8(t)0(o)-425.4(obtain)-421.6(a)-423.7(bound)-424.9(for)-421.6(the)-422.2(Kolm)-7.6(ogorov)-422(distanc)-9.9(e)-418(b)-6.5(etween)-426.3(the)-422.3(distribut)-9.7(ion)-420.5(of)-418.9(a)-423.7(sum)-422.4(of)]TJ
/F6 1 Tf
T*
(m)Tj
/F1 1 Tf
.7227 0 TD
[(-depen)-10.1(dent)-269.4(seque)-8.6(nce)-273.3(of)-265.3(rando)-7.6(m)-271.8(variables)-277(and)-271.5(a)-270(standar)-9.1(d)-268.2(normal)-276.4(distribut)-9.7(ion.)-267.2(Th)-7(e)-270(Poisson)-271.5(appro)-7.6(ximation)]TJ
-.7227 -1.195 TD
[(vers)-8(ion)-335.1(was)-339.2(developed)-345(by)-331.6(Chen)-339.6(\(1975\))-8.5(.)-330.4(See)-340.8(also)-333.2(Stein)-340.4(\(1986\).)]TJ
1.0015 -1.2007 TD
[(The)-311.2(Stein-Che)-10.5(n)-302.4(method)-308.6(for)-307.8(compound)-313(Poisson)-311.3(approximat)-10.8(ion)-301(was)-310.8(introdu)-7.1(ced)-307.5(by)-303.1(Barbour)-311.7(et)-307.7(al.)-302.4(\(1992\))-8.5(.)]TJ
-1.0015 -1.2007 TD
[(In)-339.2(this)-334.1(artic)-9.2(le,)-336.5(we)-331.6(use,)-341.4(more)-334.7(prec)-8.6(isely,)-337.1(the)]TJ
/F6 1 Tf
17.6635 0 TD
[(coupl)-8.4(ing)-335.1(approac)-8.3(h)]TJ
/F1 1 Tf
8.0237 0 TD
[(develo)-10.9(ped)-334.1(by)-337.3(Roos)-333.3(\(1993)-341.5(a,b\).)]TJ
/F6 1 Tf
10.959 0 0 10.959 74.0976 412.6109 Tm
[(2.3.)-502(The)-332.3(Stein-Chen)-330.2(method,)-327(the)-334.3(coupling)-329.5(approach)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 84.0755 394.696 Tm
(Let)Tj
/F6 1 Tf
1.7811 0 TD
(W)Tj
/F8 1 Tf
1.0812 0 TD
()Tj
/F13 1 Tf
1.1097 .7512 TD
(P)Tj
/F12 1 Tf
6.9738 0 0 6.9738 134.1354 391.8613 Tm
(a)Tj
/F8 1 Tf
.4959 0 TD
(2)Tj
/F16 1 Tf
.6585 0 TD
(C)Tj
/F6 1 Tf
9.9626 0 0 9.9626 148.9889 394.696 Tm
(I)Tj
/F12 1 Tf
6.9738 0 0 6.9738 152.3338 393.2219 Tm
(a)Tj
/F1 1 Tf
9.9626 0 0 9.9626 160.6677 394.696 Tm
[(be)-435.8(a)-435(sum)-439.5(of)-436(indi)-8.6(cators.)-441.2(We)-438.3(assume)-440.8(that)-442.8(there)-438.9(exists)-441.1(a)-435(loca)-9.4(l-depend)-8.7(ence)-440.9(structure)]TJ
-8.6895 -1.2007 TD
[(betwee)-10.9(n)-342.2(these)-347.1(indicator)-9.3(s)-343.4(\(of)-342(the)-342.6(type)-349(short-range)-351.9(depend)-8.2(ence,)-344.5(long-ra)-8.1(nge)-345.5(independe)-9.3(nce\),)-344.7(so)-344.2(that)-346.1(we)-343(can,)]TJ
T*
[(for)-336.3(ever)-8.6(y)]TJ
/F12 1 Tf
4.0687 0 TD
(a)Tj
/F8 1 Tf
.7796 0 TD
(2)Tj
/F16 1 Tf
.9389 0 TD
(C)Tj
/F1 1 Tf
.6658 0 TD
[(,)-330.4(d)-6.5(ivide)]TJ
/F15 1 Tf
3.4314 0 TD
(G)Tj
/F1 1 Tf
1.0015 0 TD
[(into)-338.6(four)-331.4(d)-6.5(isjoint)-336.2(subse)-8(ts)-335.5({)]TJ
/F10 1 Tf
10.9543 0 TD
(a)Tj
/F1 1 Tf
.5008 0 TD
(},)Tj
/F16 1 Tf
1.0641 0 TD
(C)Tj
/F6 1 Tf
6.9738 0 0 6.9738 313.9086 374.8535 Tm
(vs)Tj
/F12 1 Tf
0 -.9837 TD
(a)Tj
/F1 1 Tf
9.9626 0 0 9.9626 320.2582 370.7716 Tm
(,)Tj
/F16 1 Tf
.5804 0 TD
(C)Tj
/F6 1 Tf
6.9738 0 0 6.9738 332.7306 374.8535 Tm
(vw)Tj
/F12 1 Tf
0 -.9837 TD
(a)Tj
/F1 1 Tf
9.9626 0 0 9.9626 344.296 370.7716 Tm
(and)Tj
/F16 1 Tf
1.7868 0 TD
(C)Tj
/F6 1 Tf
6.9738 0 0 6.9738 368.7306 374.8535 Tm
(b)Tj
/F12 1 Tf
0 -.9837 TD
(a)Tj
/F1 1 Tf
9.9626 0 0 9.9626 372.7558 370.7716 Tm
(:)Tj
/F16 1 Tf
-23.8662 -2.3217 TD
(C)Tj
/F6 1 Tf
6.9738 0 0 6.9738 141.6189 351.7794 Tm
(vs)Tj
/F12 1 Tf
0 -.9837 TD
(a)Tj
/F9 1 Tf
9.9626 0 0 9.9626 150.6897 347.6409 Tm
(:)Tj
/F8 1 Tf
.717 0 TD
.1689 Tc
(f)Tj
/F12 1 Tf
1.4397 0 TD
0 Tc
(b)Tj
/F8 1 Tf
.8308 0 TD
(2)Tj
/F16 1 Tf
.9389 0 TD
(C)Tj
/F8 1 Tf
.6658 0 TD
(nf)Tj
/F12 1 Tf
1.0015 0 TD
(a)Tj
/F8 1 Tf
.5008 0 TD
(g)Tj
/F9 1 Tf
.7796 0 TD
(:)Tj
/F6 1 Tf
.5463 0 TD
(I)Tj
/F12 1 Tf
6.9738 0 0 6.9738 227.9621 346.1668 Tm
(b)Tj
/F1 1 Tf
9.9626 0 0 9.9626 235.6724 347.6409 Tm
[(very)-336.7(strongl)-8.3(y)-336.3(depend)-8.1(ent)-336.9(on)]TJ
/F6 1 Tf
12.872 0 TD
(I)Tj
/F12 1 Tf
6.9738 0 0 6.9738 367.2566 346.1668 Tm
(a)Tj
/F8 1 Tf
9.9626 0 0 9.9626 371.2251 347.6409 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F16 1 Tf
-24.4125 -1.4966 TD
(C)Tj
/F6 1 Tf
6.9738 0 0 6.9738 139.6346 336.8125 Tm
(vw)Tj
/F12 1 Tf
0 -.9837 TD
(a)Tj
/F9 1 Tf
9.9626 0 0 9.9626 150.6897 332.7306 Tm
(:)Tj
/F8 1 Tf
.717 0 TD
.1689 Tc
(f)Tj
/F12 1 Tf
1.4397 0 TD
0 Tc
(b)Tj
/F8 1 Tf
.8308 0 TD
(2)Tj
/F16 1 Tf
.9389 0 TD
(C)Tj
/F8 1 Tf
.6658 0 TD
(nf)Tj
/F12 1 Tf
1.0015 0 TD
(a)Tj
/F8 1 Tf
.5008 0 TD
(g)Tj
/F9 1 Tf
.7796 0 TD
(:)Tj
/F6 1 Tf
.5463 0 TD
(I)Tj
/F12 1 Tf
6.9738 0 0 6.9738 227.9621 331.1999 Tm
(b)Tj
/F1 1 Tf
9.9626 0 0 9.9626 235.6724 332.7306 Tm
[(very)-336.7(weakly)-9.2()-335.5(depend)-8.2(ent)-336.9(on)]TJ
/F8 1 Tf
12.4851 0 TD
(f)Tj
/F6 1 Tf
.5008 0 TD
(I)Tj
/F12 1 Tf
6.9738 0 0 6.9738 368.3904 331.1999 Tm
(c)Tj
/F1 1 Tf
9.9626 0 0 9.9626 371.9621 332.7306 Tm
(,)Tj
/F12 1 Tf
.4154 0 TD
(c)Tj
/F8 1 Tf
.717 0 TD
.2773 Tc
(2f)Tj
/F12 1 Tf
1.434 0 TD
0 Tc
(a)Tj
/F8 1 Tf
.5008 0 TD
.2284 Tc
(g[)Tj
/F16 1 Tf
1.6047 0 TD
0 Tc
(C)Tj
/F6 1 Tf
6.9738 0 0 6.9738 425.14 336.8125 Tm
(vs)Tj
/F12 1 Tf
0 -.9837 TD
(a)Tj
/F8 1 Tf
9.9626 0 0 9.9626 431.4897 332.7306 Tm
(gg)Tj
/F1 1 Tf
1.0015 0 TD
(,)Tj
/F16 1 Tf
-30.5298 -1.6389 TD
(C)Tj
/F6 1 Tf
6.9738 0 0 6.9738 143.9433 320.5416 Tm
(b)Tj
/F12 1 Tf
0 -.9918 TD
(a)Tj
/F9 1 Tf
9.9626 0 0 9.9626 150.6897 316.4031 Tm
(:)Tj
/F8 1 Tf
.717 0 TD
()Tj
/F16 1 Tf
.9389 0 TD
(C)Tj
/F8 1 Tf
.6715 0 TD
(nff)Tj
/F12 1 Tf
1.5023 0 TD
(a)Tj
/F8 1 Tf
.5008 0 TD
.2227 Tc
(g[)Tj
/F16 1 Tf
1.599 0 TD
0 Tc
(C)Tj
/F6 1 Tf
6.9738 0 0 6.9738 216.4535 320.5416 Tm
(vs)Tj
/F12 1 Tf
0 -.9918 TD
(a)Tj
/F8 1 Tf
9.9626 0 0 9.9626 224.9574 316.4031 Tm
([)Tj
/F16 1 Tf
.882 0 TD
(C)Tj
/F6 1 Tf
6.9738 0 0 6.9738 240.3779 320.5416 Tm
(vw)Tj
/F12 1 Tf
0 -.9918 TD
(a)Tj
/F8 1 Tf
9.9626 0 0 9.9626 248.6551 316.4031 Tm
(g)Tj
/F11 1 Tf
.5008 0 TD
(:)Tj
/F1 1 Tf
-17.0204 -2.1966 TD
[(We)-335.9(let)]TJ
/F6 1 Tf
3.0786 0 TD
(U)Tj
/F12 1 Tf
6.9738 0 0 6.9738 121.8897 292.9889 Tm
(a)Tj
/F9 1 Tf
9.9626 0 0 9.9626 128.6929 294.5196 Tm
(:)Tj
/F8 1 Tf
.7113 0 TD
()Tj
/F13 1 Tf
1.1097 .7455 TD
(P)Tj
/F12 1 Tf
6.9738 0 0 6.9738 157.3228 291.685 Tm
(b)Tj
/F8 1 Tf
.5528 0 TD
(2)Tj
/F16 1 Tf
.6504 0 TD
(C)Tj
/F6 1 Tf
4.9813 0 0 4.9813 170.4189 294.4629 Tm
(vs)Tj
/F12 1 Tf
0 -.956 TD
(a)Tj
/F6 1 Tf
9.9626 0 0 9.9626 177.222 294.5196 Tm
(I)Tj
/F12 1 Tf
6.9738 0 0 6.9738 180.5669 292.9889 Tm
(b)Tj
/F1 1 Tf
9.9626 0 0 9.9626 184.8755 294.5196 Tm
(,)Tj
/F6 1 Tf
.4211 0 TD
(Z)Tj
/F12 1 Tf
6.9738 0 0 6.9738 194.57 292.9889 Tm
(a)Tj
/F9 1 Tf
9.9626 0 0 9.9626 201.3165 294.5196 Tm
(:)Tj
/F8 1 Tf
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()Tj
9.9626 0 0 9.9626 259.8802 339.8172 Tm
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[(2\))-339.2(and)]TJ
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(j)Tj
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6.9738 0 0 6.9738 359.3763 336.9826 Tm
()Tj
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(2)Tj
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9.9626 0 0 9.9626 371.6219 339.8172 Tm
(I)Tj
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[(We)-335.9(will)-339.6(explicitly)-338(const)-9.6(ruct)-333.9(the)-336.9(coupl)-8.4(ing)-335.1(describ)-9.1(ed)-333.4(in)-334.3(Th)-7(eorem)-337.3(1.)]TJ
T*
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9.9626 0 0 9.9626 273.8834 315.8928 Tm
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(U)Tj
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7.4718 0 0 6.641 290.381 314.2487 Tm
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[(..)-5.7(.)]TJ
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[(,)-330.4(with)-336.9(the)-336.9(circul)-10(ar)-335.3(conven)-8.2(tion)-332.9(modu)-6.6(lo)]TJ
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[(Notation)-340.3(1.)]TJ
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[(For)-339(a)-330.8(seque)-8.6(nce)]TJ
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7.4718 0 0 6.641 250.4125 290.3243 Tm
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(\))Tj
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[(we)-338.1(will)-334.7(denot)-8.4(e)-332.6(a)]TJ
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(i)Tj
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[()-165.8()-165()]TJ
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(.)Tj
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[(For)-333.5(ever)-8.6(y)]TJ
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7.4718 0 0 6.641 378.4251 266.4566 Tm
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()Tj
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[(be)-322(xed.)-323.1(The)-322.6(indicator)-9.3(s)-320.6(appea)-9.2(ring)-320.8(in)-317.3(the)-319.8(expre)-9.4(ssion)-321.9(of)]TJ
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(Z)Tj
7.4718 0 0 6.641 428.7684 254.4944 Tm
(k)Tj
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9.9626 0 0 9.9626 435.2881 256.1385 Tm
[(are)-320.8(those)-322.5(from)]TJ
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7.4718 0 0 6.641 500.9384 254.4944 Tm
(k)Tj
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(2)Tj
9.9626 0 0 9.9626 530.192 256.1385 Tm
(to)Tj
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(I)Tj
7.4718 0 0 6.641 110.948 242.5322 Tm
(k)Tj
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/F6 1 Tf
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(h)Tj
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/F1 1 Tf
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(2)Tj
9.9626 0 0 9.9626 137.0267 244.1763 Tm
[(.)-609.3(Conseque)-9.9(ntly,)-612.2(if)]TJ
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(L)Tj
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[(,)-609.3(the)-610(spaci)-11.3(ngs)-606.7(appea)-9.2(ring)-611(in)-613.2(the)-610(expressi)-11.1(on)-610.4(of)]TJ
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20.9071 0 TD
(Z)Tj
7.4718 0 0 6.641 456.3211 242.5322 Tm
(k)Tj
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9.9626 0 0 9.9626 465.7322 244.1763 Tm
(are)Tj
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(S)Tj
6.9738 0 0 6.9738 489.0896 242.7023 Tm
(k)Tj
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(h)Tj
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6.9738 0 0 6.9738 507.6849 242.7023 Tm
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(2)Tj
9.9626 0 0 9.9626 518.2298 244.1763 Tm
(,)Tj
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(S)Tj
7.4718 0 0 6.641 112.5921 230.57 Tm
(k)Tj
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9.9626 0 0 9.9626 182.3243 232.2141 Tm
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6.9738 0 0 6.9738 139.5212 218.7779 Tm
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6.9738 0 0 6.9738 181.1338 218.7779 Tm
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6.9738 0 0 6.9738 199.7291 218.7779 Tm
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9.9626 0 0 9.9626 210.274 220.2519 Tm
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6.9738 0 0 6.9738 238.3369 218.7779 Tm
(k)Tj
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4.9813 0 0 4.9813 252.7936 217.7574 Tm
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6.9738 0 0 6.9738 256.9889 218.7779 Tm
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(h)Tj
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4.9813 0 0 4.9813 267.0236 220.7622 Tm
()Tj
6.9738 0 0 6.9738 271.1621 218.7779 Tm
()Tj
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(4)Tj
9.9626 0 0 9.9626 281.707 220.2519 Tm
[(\).)-242.1(Note)-244.8(that)]TJ
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(V)Tj
7.4718 0 0 6.641 335.3952 218.6078 Tm
(k)Tj
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9.9626 0 0 9.9626 341.1212 220.2519 Tm
[(contain)-8.7(s)-241(all)-242.9(the)-245.8(spacings)-248.1(which)-245.6(may)-246.6(appear)-245.2(in)]TJ
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7.4718 0 0 6.641 532.1196 218.6078 Tm
(k)Tj
/F1 1 Tf
9.9626 0 0 9.9626 535.4645 220.2519 Tm
(,)Tj
-42.9466 -1.2007 TD
[(for)-336.3(different)-340.6(valu)-7.6(es)-334.6(of)]TJ
/F11 1 Tf
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-8.7748 -1.195 TD
[(For)-453(ever)-8.6(y)]TJ
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[()-171.5()-165()]TJ
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[(we)-246.2(wi)-8.2(ll)-246.1(construc)-9.9(t)-242.5(o)0(n)-251.9(the)-245.8(same)-250.3(proba)-7.6(bility)-248.9(space)-255.1(the)-251.5(indicator)-9.3(s)]TJ
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(0)Tj
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(n)Tj
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[(\(not)-337.8(depend)-8.2(ing)-335.1(on)]TJ
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[(\))-332.8(verifyi)-10.9(ng)-331.6(the)-336.9(relat)-9.2(ions)-337.1(\(1\))-336.3(and)-334.1(\(2\))-336.3(in)-334.3(Theore)-9.9(m)-334.4(1)0(.)]TJ
-7.2498 -1.2007 TD
[(Note)-353(that)-357.5(the)-354(event)-357.3({)]TJ
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(k)Tj
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(1)Tj
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({)Tj
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()Tj
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()Tj
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[(1})-352.6(is)]TJ
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(V)Tj
7.4718 0 0 6.641 279.6094 158.8535 Tm
(k)Tj
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[(-)-349.9(mea)-9.4(surable)-356.3(and)-356.9(thus,)-354.5(for)-353.4(the)-354(condi)-8.4(tion)-350(\(1\))-353.4(to)-357.1(be)-350.4(ful)-7(lled,)-352.2(it)]TJ
-17.9537 -1.2007 TD
[(sufc)-8(es)-334.6(to)-334.3(construc)-9.9(t)-333.6(the)-336.9(family)-336.1(of)-339.2(indicator)-9.3(s)]TJ
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(0)Tj
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(\()Tj
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[(\(not)-337.8(depend)-8.2(ing)-335.1(on)]TJ
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(j)Tj
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(j)Tj
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(k)Tj
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(2)Tj
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()Tj
6.9738 0 0 6.9738 427.6912 127.4456 Tm
()Tj
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(h)Tj
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()Tj
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(\)\))Tj
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(0)Tj
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(1)Tj
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(,)Tj
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(U)Tj
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(0)Tj
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[(be)-333.4(r.v.)-7(s)-332(inde)-7.6(penden)-8.2(t)-333.6(o)0(n)]TJ
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(0)Tj
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(U)Tj
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(0)Tj
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(n)Tj
/F1 1 Tf
9.9626 0 0 9.9626 408.0188 108.3401 Tm
(\))Tj
/F8 1 Tf
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(L)Tj
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1.6275 0 TD
0 Tc
(\()Tj
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(U)Tj
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6.9738 0 0 6.9738 439.7101 106.8094 Tm
(\(1\))Tj
9.9626 0 0 9.9626 448.3275 108.3401 Tm
(,)Tj
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(U)Tj
/F1 1 Tf
6.9738 0 0 6.9738 478.6014 106.8094 Tm
(\()Tj
/F6 1 Tf
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(n)Tj
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(\))Tj
9.9626 0 0 9.9626 487.2188 108.3401 Tm
(\).)Tj
-37.1024 -1.2007 TD
[(Dene)-812.9(the)-814.9(correspo)-9.1(nding)-814.6(spacings)]TJ
/F6 1 Tf
16.3319 0 TD
(S)Tj
/F8 1 Tf
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(0)Tj
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(j)Tj
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9.9626 0 0 9.9626 289.4172 96.3779 Tm
()Tj
/F6 1 Tf
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(U)Tj
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6.9738 0 0 6.9738 306.4251 100.0063 Tm
(0)Tj
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(j)Tj
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()Tj
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(1)Tj
/F8 1 Tf
9.9626 0 0 9.9626 321.222 96.3779 Tm
()Tj
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(U)Tj
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6.9738 0 0 6.9738 338.2865 100.0063 Tm
(0)Tj
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(j)Tj
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9.9626 0 0 9.9626 340.6676 96.3779 Tm
(,)Tj
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[(\(w)-7.4(ith)-810.2(the)-809.2(circul)-10(ar)-807.7(conven)-8.1(tion)]TJ
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(U)Tj
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(0)Tj
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(n)Tj
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(0)Tj
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(1)Tj
9.9626 0 0 9.9626 152.1637 84.4157 Tm
[(\).)-333.2(We)-335.9(thus)-337.1(have)]TJ
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(0)Tj
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9.9626 0 0 9.9626 239.9243 84.4157 Tm
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(0)Tj
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9.9626 0 0 9.9626 271.9558 84.4157 Tm
(\))Tj
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(S)Tj
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6.9738 0 0 6.9738 301.4928 82.9417 Tm
(1)Tj
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(S)Tj
6.9738 0 0 6.9738 333.5243 82.9417 Tm
(n)Tj
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9.9626 0 0 9.9626 337.4928 84.4157 Tm
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9.9626 0 0 9.9626 169.5685 72.4535 Tm
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6.9738 0 0 6.9738 196.4976 70.9795 Tm
(2)Tj
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4.9813 0 0 4.9813 203.4708 69.9023 Tm
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6.9738 0 0 6.9738 207.6094 70.9795 Tm
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(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 217.644 72.9637 Tm
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6.9738 0 0 6.9738 221.8393 70.9795 Tm
()Tj
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(5)Tj
9.9626 0 0 9.9626 232.3842 72.4535 Tm
[(\))-332.8(with)]TJ
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2.7827 0 TD
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(2)Tj
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(K)Tj
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6.9738 0 0 6.9738 291.4015 70.9795 Tm
(1)Tj
9.9626 0 0 9.9626 295.4267 72.4535 Tm
(,)Tj
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(z)Tj
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[(all)-339.7(the)-336.9(quantitie)-10.1(s)-332(appea)-9.2(ring)-337.8(in)-334.3(the)-336.9(error)-335.9(bound)-339.6(in)-334.3(Theorem)-344.3(1.)]TJ
1.0015 -1.2007 TD
[(The)-271.3(canonica)-10.3(l)-265.3(choice)-274.5(for)-268(the)-268.6(parameter)-12.9(s)-263.7(o)0(f)-265.3(the)-268.6(com)-7.6(pound)-265.6(Po)-6.4(isson)-265(distri)-10.3(bution)-266.2(is)]TJ
/F17 1 Tf
32.7662 0 TD
(k)Tj
/F8 1 Tf
.7227 0 TD
()Tj
/F13 1 Tf
1.104 .7512 TD
(P)Tj
/F1 1 Tf
6.9738 0 0 6.9738 439.1999 523.0487 Tm
(2)Tj
/F6 1 Tf
.4959 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 446.1731 522.0282 Tm
()Tj
6.9738 0 0 6.9738 450.3117 523.0487 Tm
()Tj
/F1 1 Tf
.943 0 TD
(3)Tj
/F6 1 Tf
-2.5364 -1.0893 TD
(i)Tj
/F8 1 Tf
.4471 0 TD
()Tj
/F1 1 Tf
.9349 0 TD
(1)Tj
/F12 1 Tf
9.9626 0 0 9.9626 462.5573 518.2865 Tm
(k)Tj
/F6 1 Tf
6.9738 0 0 6.9738 467.5463 516.8124 Tm
(i)Tj
/F12 1 Tf
9.9626 0 0 9.9626 469.9841 518.2865 Tm
(d)Tj
/F6 1 Tf
6.9738 0 0 6.9738 474.9731 516.8124 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 477.4676 518.2865 Tm
[(,)-165.4(,)-262.1(with)]TJ
/F12 1 Tf
-40.4883 -1.2007 TD
(k)Tj
/F6 1 Tf
6.9738 0 0 6.9738 79.0866 504.8503 Tm
(i)Tj
/F8 1 Tf
9.9626 0 0 9.9626 83.2252 506.3243 Tm
()Tj
ET
94.224 508.649 3.515 .39685 re
f
BT
/F1 1 Tf
6.9738 0 0 6.9738 94.2236 509.9526 Tm
(1)Tj
/F6 1 Tf
.1138 -1.008 TD
(i)Tj
/F13 1 Tf
9.9626 0 0 9.9626 99.3826 513.8077 Tm
(P)Tj
/F6 1 Tf
6.9738 0 0 6.9738 109.8708 511.0865 Tm
(n)Tj
0 -1.0893 TD
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/F8 1 Tf
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()Tj
/F1 1 Tf
.943 0 TD
(1)Tj
/F14 1 Tf
9.9626 0 0 9.9626 126.5385 506.3243 Tm
(E)Tj
/F1 1 Tf
.552 0 TD
(\()Tj
/F6 1 Tf
.3301 0 TD
(I)Tj
6.9738 0 0 6.9738 138.6708 504.8503 Tm
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 142.4693 506.3243 Tm
(1)Tj
/F8 1 Tf
6.9738 0 0 6.9738 147.4582 504.5101 Tm
(f)Tj
/F6 1 Tf
.4959 0 TD
(Z)Tj
4.9813 0 0 4.9813 154.7716 503.4896 Tm
(k)Tj
/F8 1 Tf
6.9738 0 0 6.9738 158.7968 504.5101 Tm
()Tj
/F6 1 Tf
.9349 0 TD
(i)Tj
/F8 1 Tf
.2845 0 TD
(g)Tj
/F1 1 Tf
9.9626 0 0 9.9626 171.2692 506.3243 Tm
(\).)Tj
-8.7521 -1.2007 TD
[(In)-333.6(our)-340(approximat)-10.8(ion)-335.1(we)-337.3(will)-333.9(u)-6.5(s)0(e)-334.6(only)-335.9(half)-339.6(of)-333.6(the)-336.9(parame)-9.7(ters,)-335.5(by)-337.3(truncatin)-9.3(g)-330.8(a)0(t)]TJ
/F11 1 Tf
32.6638 0 TD
()Tj
/F8 1 Tf
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()Tj
/F6 1 Tf
.9389 0 TD
(h)Tj
/F1 1 Tf
7.4718 0 0 6.641 429.5621 492.718 Tm
(*)Tj
/F8 1 Tf
9.9626 0 0 9.9626 434.9479 494.3621 Tm
()Tj
/F1 1 Tf
.9446 0 TD
[(1.)-331.2(Instead)-339.2(o)-6.5(f)]TJ
/F15 1 Tf
5.4857 0 TD
(l)Tj
/F1 1 Tf
-42.6507 -1.2007 TD
[(we)-826.7(will)-829(use)]TJ
/F9 1 Tf
6.5384 .2788 TD
(^)Tj
/F12 1 Tf
0 -.2788 TD
(k)Tj
0 0 TD
(k)Tj
/F8 1 Tf
.6658 0 TD
()Tj
/F13 1 Tf
1.104 .7512 TD
(P)Tj
/F6 1 Tf
6.9738 0 0 6.9738 167.3574 487.2188 Tm
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 170.8724 486.1416 Tm
()Tj
6.9738 0 0 6.9738 175.011 487.2188 Tm
()Tj
/F1 1 Tf
.943 0 TD
(1)Tj
/F6 1 Tf
-2.0405 -1.0975 TD
(i)Tj
/F8 1 Tf
.4471 0 TD
()Tj
/F1 1 Tf
.943 0 TD
(1)Tj
/F9 1 Tf
9.9626 0 0 9.9626 187.1999 485.1778 Tm
(^)Tj
/F12 1 Tf
0 -.2788 TD
(k)Tj
0 0 TD
(k)Tj
/F6 1 Tf
6.9738 0 0 6.9738 192.1889 480.9258 Tm
(i)Tj
/F12 1 Tf
9.9626 0 0 9.9626 194.6834 482.3999 Tm
(d)Tj
/F6 1 Tf
6.9738 0 0 6.9738 199.6724 480.9258 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 202.1102 482.3999 Tm
[(,)-825.5(where)]TJ
/F9 1 Tf
4.3476 .2788 TD
(^)Tj
/F12 1 Tf
0 -.2788 TD
(k)Tj
0 0 TD
(k)Tj
/F6 1 Tf
6.9738 0 0 6.9738 250.4125 480.9258 Tm
(i)Tj
/F8 1 Tf
9.9626 0 0 9.9626 254.5511 482.3999 Tm
()Tj
/F12 1 Tf
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(k)Tj
/F6 1 Tf
6.9738 0 0 6.9738 268.8944 480.9258 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 279.496 482.3999 Tm
(for)Tj
/F6 1 Tf
1.9917 0 TD
(i)Tj
/F8 1 Tf
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()Tj
/F1 1 Tf
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(2,)Tj
/F9 1 Tf
1.0869 0 TD
.1682 Tc
(...)Tj
/F1 1 Tf
1.3145 0 TD
0 Tc
(,)Tj
/F6 1 Tf
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(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 346.2235 480.9258 Tm
()Tj
9.9626 0 0 9.9626 351.8928 482.3999 Tm
()Tj
/F1 1 Tf
.9389 0 TD
[(1)-820.2(and)]TJ
/F9 1 Tf
3.5907 .2788 TD
(^)Tj
/F12 1 Tf
0 -.2788 TD
(k)Tj
0 0 TD
(k)Tj
/F1 1 Tf
6.9738 0 0 6.9738 402.0093 480.9258 Tm
(1)Tj
/F8 1 Tf
9.9626 0 0 9.9626 407.6786 482.3999 Tm
()Tj
/F14 1 Tf
.9389 0 TD
(E)Tj
/F1 1 Tf
.552 0 TD
(\()Tj
/F6 1 Tf
.3357 0 TD
(W)Tj
6.9738 0 0 6.9738 434.2109 480.9258 Tm
(m)Tj
/F1 1 Tf
9.9626 0 0 9.9626 439.7101 482.3999 Tm
(\))Tj
/F8 1 Tf
.5008 0 TD
()Tj
/F13 1 Tf
1.104 .7512 TD
(P)Tj
/F6 1 Tf
6.9738 0 0 6.9738 466.1857 487.2188 Tm
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 469.7007 486.1416 Tm
()Tj
6.9738 0 0 6.9738 473.8392 487.2188 Tm
()Tj
/F1 1 Tf
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(1)Tj
/F6 1 Tf
-2.0323 -1.0975 TD
(i)Tj
/F8 1 Tf
.4471 0 TD
()Tj
/F1 1 Tf
.943 0 TD
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 486.0282 482.3999 Tm
(k)Tj
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6.9738 0 0 6.9738 491.0172 480.9258 Tm
(i)Tj
/F8 1 Tf
9.9626 0 0 9.9626 495.1558 482.3999 Tm
()Tj
/F12 1 Tf
-42.2637 -1.195 TD
(k)Tj
/F1 1 Tf
6.9738 0 0 6.9738 79.0866 468.9637 Tm
(1)Tj
/F8 1 Tf
9.9626 0 0 9.9626 84.7559 470.4944 Tm
()Tj
/F13 1 Tf
1.104 .7455 TD
(P)Tj
/F1 1 Tf
6.9738 0 0 6.9738 106.2425 475.2566 Tm
(2)Tj
/F6 1 Tf
.504 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 113.2724 474.1794 Tm
()Tj
6.9738 0 0 6.9738 117.411 475.2566 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(3)Tj
/F6 1 Tf
-2.5364 -1.0975 TD
(i)Tj
/F8 1 Tf
.4471 0 TD
()Tj
/F6 1 Tf
.943 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 119.4519 466.5826 Tm
()Tj
/F6 1 Tf
9.9626 0 0 9.9626 129.5999 470.4944 Tm
(i)Tj
/F12 1 Tf
.2845 0 TD
(k)Tj
/F6 1 Tf
6.9738 0 0 6.9738 137.4236 468.9637 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 139.8614 470.4944 Tm
(.)Tj
-5.5995 -1.2007 TD
[(We)-335.9(wi)-8.2(ll)-331.4(appro)-7.6(ximate)-341.6(the)-336.9(probability)-341.9(of)-333.6(intere)-10(st)]TJ
/F14 1 Tf
19.769 0 TD
(P)Tj
/F1 1 Tf
.7227 0 TD
(\()Tj
/F6 1 Tf
.3357 0 TD
(W)Tj
6.9738 0 0 6.9738 299.8488 457.0014 Tm
(m)Tj
/F8 1 Tf
9.9626 0 0 9.9626 308.1826 458.5322 Tm
()Tj
/F1 1 Tf
1.0471 0 TD
[(1\))-333.6(by)]TJ
/F6 1 Tf
-8.5244 -3.2152 TD
(p)Tj
/F9 1 Tf
.7796 0 TD
(:)Tj
/F8 1 Tf
.3813 0 TD
()Tj
/F1 1 Tf
.9389 0 TD
(1)Tj
/F8 1 Tf
.6715 0 TD
()Tj
/F1 1 Tf
1.104 0 TD
(exp)Tj
/F8 1 Tf
2.4185 0 TD
()Tj
/F13 1 Tf
1.2747 .9446 TD
(X)Tj
/F6 1 Tf
6.9738 0 0 6.9738 307.4456 438.066 Tm
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 310.9039 437.0456 Tm
()Tj
6.9738 0 0 6.9738 315.0424 438.066 Tm
()Tj
/F1 1 Tf
.943 0 TD
(1)Tj
/F6 1 Tf
-1.7153 -3.203 TD
(i)Tj
/F8 1 Tf
.4552 0 TD
()Tj
/F1 1 Tf
.9349 0 TD
(1)Tj
/F9 1 Tf
9.9626 0 0 9.9626 326.7779 429.2219 Tm
(^)Tj
/F12 1 Tf
0 -.2731 TD
(k)Tj
0 0 TD
(k)Tj
/F6 1 Tf
6.9738 0 0 6.9738 331.7668 424.97 Tm
(i)Tj
/F13 1 Tf
9.9626 0 0 9.9626 286.7527 443.5652 Tm
3.961 Tc
(\(\))Tj
/F11 1 Tf
5.571 -1.7129 TD
0 Tc
(:)Tj
/F2 1 Tf
-25.9091 -4.1541 TD
[(Remark)-577.4(3.)]TJ
/F6 1 Tf
5.8271 0 TD
[(As)-577.3(the)-575.9(indicators)]TJ
/F8 1 Tf
8.018 0 TD
(f)Tj
/F6 1 Tf
.5008 0 TD
(I)Tj
/F8 1 Tf
6.9738 0 0 6.9738 230.9102 388.7432 Tm
(00)Tj
/F6 1 Tf
-.0732 -.9186 TD
(jv)Tj
/F1 1 Tf
9.9626 0 0 9.9626 236.0125 385.1148 Tm
(\()Tj
/F6 1 Tf
.3301 0 TD
(k)Tj
/F1 1 Tf
.4723 0 TD
(\),)Tj
/F6 1 Tf
.7512 0 TD
(j)Tj
/F8 1 Tf
.4496 0 TD
()Tj
/F1 1 Tf
.9389 0 TD
(1,)Tj
/F9 1 Tf
1.0812 0 TD
.1682 Tc
(...)Tj
/F1 1 Tf
1.3145 0 TD
0 Tc
(,)Tj
/F6 1 Tf
.4154 0 TD
(n)Tj
/F8 1 Tf
.5008 0 TD
(g)Tj
/F6 1 Tf
1.0755 0 TD
[(do)-570.6(not)-574.1(depend)-582.9(on)-570.6(i,)-573(also)-576.1(the)-575.9(term)]TJ
/F12 1 Tf
16.0303 0 TD
(h)Tj
/F6 1 Tf
6.9738 0 0 6.9738 473.7258 383.5841 Tm
(j)Tj
/F1 1 Tf
.2845 0 TD
(,)Tj
/F6 1 Tf
.4146 0 TD
(k)Tj
/F1 1 Tf
9.9626 0 0 9.9626 482.3432 385.1148 Tm
(\()Tj
/F6 1 Tf
.3357 0 TD
(v)Tj
/F1 1 Tf
.4496 0 TD
(\))Tj
/F8 1 Tf
.5008 0 TD
()Tj
/F14 1 Tf
-42.2637 -1.2007 TD
(E)Tj
/F6 1 Tf
.8763 0 TD
(I)Tj
/F8 1 Tf
6.9738 0 0 6.9738 86.6834 376.781 Tm
(00)Tj
/F6 1 Tf
-.0732 -.9186 TD
(jv)Tj
/F1 1 Tf
9.9626 0 0 9.9626 91.7858 373.1527 Tm
(\()Tj
/F12 1 Tf
.3357 0 TD
(a)Tj
/F1 1 Tf
.5008 0 TD
(\))Tj
/F8 1 Tf
.5008 0 TD
()Tj
/F6 1 Tf
.9389 0 TD
(I)Tj
/F8 1 Tf
6.9738 0 0 6.9738 118.2614 376.781 Tm
(0)Tj
/F6 1 Tf
-.0732 -.9186 TD
(jv)Tj
/F1 1 Tf
9.9626 0 0 9.9626 123.3637 373.1527 Tm
(\()Tj
/F12 1 Tf
.3357 0 TD
(a)Tj
/F1 1 Tf
.5008 0 TD
(\))Tj
/F13 1 Tf
-5.2239 1.1495 TD
()Tj
0 -.5918 TD
()Tj
0 -.5975 TD
()Tj
5.554 1.1893 TD
()Tj
0 -.5918 TD
()Tj
0 -.5975 TD
()Tj
/F6 1 Tf
.6601 .0398 TD
[(appear)-7.6(ing)-335.1(in)-334.3(Theore)-8.6(m)-334.7(1)-330.8(does)-336.1(n)-6.5(o)0(t)-334.3(depend)-338.2(on)-337.3(i)-333.6(and)-332.3(thus)]TJ
.8593 -2.7941 TD
(d)Tj
6.9738 0 0 6.9738 155.1118 343.7857 Tm
(K)Tj
/F1 1 Tf
9.9626 0 0 9.9626 160.6677 345.3164 Tm
(\()Tj
/F8 1 Tf
.3357 0 TD
(L)Tj
/F1 1 Tf
.6886 0 TD
(\()Tj
/F6 1 Tf
.3357 0 TD
(W)Tj
6.9738 0 0 6.9738 182.5511 343.7857 Tm
(m)Tj
/F1 1 Tf
9.9626 0 0 9.9626 188.0503 345.3164 Tm
(\),)Tj
/F6 1 Tf
.7512 0 TD
(CP)Tj
/F1 1 Tf
1.2861 0 TD
(\()Tj
/F9 1 Tf
.3301 .2788 TD
(^)Tj
/F12 1 Tf
0 -.2788 TD
(k)Tj
0 0 TD
(k)Tj
/F1 1 Tf
.5008 0 TD
(\)\))Tj
/F8 1 Tf
.9503 0 TD
()Tj
/F6 1 Tf
1.0471 0 TD
(c)Tj
6.9738 0 0 6.9738 241.0015 343.7857 Tm
(K)Tj
/F1 1 Tf
9.9626 0 0 9.9626 246.5574 345.3164 Tm
(\()Tj
/F9 1 Tf
.3357 .2788 TD
(^)Tj
/F12 1 Tf
0 -.2788 TD
(k)Tj
0 0 TD
(k)Tj
/F1 1 Tf
.5008 0 TD
(\))Tj
/F13 1 Tf
1.1438 .9446 TD
(X)Tj
/F6 1 Tf
6.9738 0 0 6.9738 271.729 356.7117 Tm
(n)Tj
-.7885 -3.1867 TD
(k)Tj
/F8 1 Tf
.6341 0 TD
()Tj
/F1 1 Tf
.943 0 TD
(1)Tj
/F8 1 Tf
9.9626 0 0 9.9626 280.6865 345.3164 Tm
(f)Tj
/F1 1 Tf
.5008 0 TD
(\()Tj
/F14 1 Tf
.3357 0 TD
(E)Tj
/F6 1 Tf
.552 0 TD
(I)Tj
6.9738 0 0 6.9738 297.8645 343.7857 Tm
(k)Tj
/F1 1 Tf
9.9626 0 0 9.9626 301.6062 345.3164 Tm
(\))Tj
6.9738 0 0 6.9738 304.9511 349.3983 Tm
(2)Tj
/F8 1 Tf
9.9626 0 0 9.9626 310.6204 345.3164 Tm
()Tj
/F14 1 Tf
.9389 0 TD
(E)Tj
/F6 1 Tf
.552 0 TD
(I)Tj
6.9738 0 0 6.9738 328.8188 343.7857 Tm
(k)Tj
/F14 1 Tf
9.9626 0 0 9.9626 332.5605 345.3164 Tm
(E)Tj
/F1 1 Tf
.552 0 TD
(\()Tj
/F6 1 Tf
.3357 0 TD
(U)Tj
6.9738 0 0 6.9738 348.5479 343.7857 Tm
(k)Tj
/F8 1 Tf
9.9626 0 0 9.9626 353.9904 345.3164 Tm
()Tj
/F6 1 Tf
.9389 0 TD
(X)Tj
6.9738 0 0 6.9738 369.4676 343.7857 Tm
(k)Tj
/F1 1 Tf
9.9626 0 0 9.9626 373.2661 345.3164 Tm
(\))Tj
/F8 1 Tf
.5008 0 TD
()Tj
/F14 1 Tf
.9389 0 TD
(E)Tj
/F1 1 Tf
.552 0 TD
(\()Tj
/F6 1 Tf
.3357 0 TD
(I)Tj
6.9738 0 0 6.9738 399.7416 343.7857 Tm
(k)Tj
9.9626 0 0 9.9626 403.54 345.3164 Tm
(X)Tj
6.9738 0 0 6.9738 409.6629 343.7857 Tm
(k)Tj
/F1 1 Tf
9.9626 0 0 9.9626 413.4046 345.3164 Tm
(\))Tj
/F13 1 Tf
-15.575 1.7129 TD
(\()Tj
/F8 1 Tf
.165 -5.4003 TD
()Tj
/F13 1 Tf
1.2519 .9503 TD
(X)Tj
/F6 1 Tf
6.9738 0 0 6.9738 270.8787 297.4677 Tm
(j)Tj
/F8 1 Tf
.2845 0 TD
(2)Tj
/F16 1 Tf
.6585 0 TD
(C)Tj
/F6 1 Tf
4.9813 0 0 4.9813 282.1039 300.3023 Tm
(vw)Tj
0 -1.0129 TD
(k)Tj
/F14 1 Tf
9.9626 0 0 9.9626 289.8141 308.5795 Tm
(E)Tj
/F1 1 Tf
.552 0 TD
(\()Tj
/F6 1 Tf
.3357 0 TD
(I)Tj
6.9738 0 0 6.9738 302.0031 307.1054 Tm
(k)Tj
/F12 1 Tf
9.9626 0 0 9.9626 305.7448 308.5795 Tm
(h)Tj
/F6 1 Tf
6.9738 0 0 6.9738 310.7338 307.1054 Tm
(j)Tj
/F1 1 Tf
.2845 0 TD
(,)Tj
/F6 1 Tf
.4146 0 TD
(k)Tj
/F1 1 Tf
9.9626 0 0 9.9626 319.4078 308.5795 Tm
(\()Tj
/F6 1 Tf
.3301 0 TD
(V)Tj
6.9738 0 0 6.9738 328.8755 307.1054 Tm
(k)Tj
/F1 1 Tf
9.9626 0 0 9.9626 332.6172 308.5795 Tm
(\)\))Tj
/F8 1 Tf
.6658 0 TD
.1715 Tc
(g)Tj
/F13 1 Tf
2.1226 .9503 TD
0 Tc
(X)Tj
/F1 1 Tf
6.9738 0 0 6.9738 356.9385 320.2015 Tm
(2)Tj
/F6 1 Tf
.504 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 363.9117 319.1243 Tm
()Tj
6.9738 0 0 6.9738 368.107 320.2015 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(3)Tj
/F6 1 Tf
-2.1787 -3.2192 TD
(i)Tj
/F8 1 Tf
.4471 0 TD
()Tj
/F6 1 Tf
.943 0 TD
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BT
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f
BT
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f
BT
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f
BT
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[(We)-335.9(make)-340.2(the)-336.9(followi)-8.1(ng)-331.6(\(biolog)-7.1(ically)-340.8(realistic\))-342.1(assumpt)-10.1(ion)-335.1(on)-337.3(the)-336.9(data.)]TJ
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[(Assumpt)-9.1(ion)-334.3(1.)]TJ
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[(We)-336.1(assum)-10.1(e)-332.6(that)-338.6(we)-332.4(have)-342.4(n)]TJ
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f
BT
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[(Based)-337.7(on)-337.3(Assum)-8(ption)-333.7(1,)-336.9(we)-337.3(obtain)]TJ
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[(gj)-269.8()-276.3(j)]TJ
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[(This)-336.9(further)-340.2(implies)-338.8(that)]TJ
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ET
245.367 525.883 8.7874 .39685 re
f
BT
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[(Lemma)-338.6(1,)-336.9(we)-337.3(have)]TJ
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189.468 472.479 188.391 .39685 re
f
BT
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6.9738 0 0 6.9738 283.5779 475.4833 Tm
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(h)Tj
6.9738 0 0 6.9738 255.1747 461.877 Tm
(j)Tj
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9.9626 0 0 9.9626 257.6125 463.3511 Tm
(\()Tj
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6.9738 0 0 6.9738 284.3716 461.877 Tm
(k)Tj
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9.9626 0 0 9.9626 288.1133 463.3511 Tm
(\()Tj
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405.127 226.091 4.989 .39685 re
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[(1,)-336.9(using)-337.8(Lemma)-338.6(1,)]TJ
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BT
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[()-336.5(for)-336.3(every)-339.4(other)]TJ
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[(It)-336.3(follows)-342.3(from)-334.9(\(9\))-336.3(that)]TJ
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(I)Tj
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f
BT
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(\()Tj
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BT
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[(can)-341.6(be)-333.4(treated)-342.6(in)-334.3(a)-332.6(simi)-7.6(lar)-333.2(man)-7.6(ner)-336.1(and)-334.1(the)-336.9(upper)-337.6(bou)-8(nd)-331.6(stated)-339.2(in)-334.3(\()]TJ
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[(easi)-10.6(ly)-334.3(follows.)]TJ
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[(Proof)-787(of)]TJ
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[(\(d\).)-786.2(We)-785.5(will)-789.2(condition)-790.8(on)-781.1(the)-786.4(r.v.)]TJ
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(k)Tj
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(L)Tj
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(h)Tj
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(4)Tj
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[(\).)-782.7(Given)-786.2(that)]TJ
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(V)Tj
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(k)Tj
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(5)Tj
9.9626 0 0 9.9626 177.222 407.1684 Tm
[(\),)-333.2(we)-337.3(have)]TJ
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9.9626 0 0 9.9626 303.1936 407.1684 Tm
[(\(hence)-342(determin)-9.3(istic\))-336.5(and)-339.8(thus)]TJ
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(X)Tj
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(n)Tj
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(X)Tj
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(vw)Tj
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(E)Tj
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(I)Tj
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(h)Tj
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(X)Tj
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(vw)Tj
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ET
322.356 382.28 12.586 .39685 re
f
BT
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(1)Tj
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(X)Tj
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()Tj
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(2)Tj
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(K)Tj
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9.9626 0 0 9.9626 352.5731 380.0125 Tm
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[(whe)-8(re)-335.3(for)-336.3(each)]TJ
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[(n,)-331.2(j)]TJ
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(vw)Tj
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[(,)-330.4(w)0(e)-337.3(let)]TJ
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(h)Tj
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(j)Tj
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6.9738 0 0 6.9738 257.2723 327.6283 Tm
(k)Tj
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(2)Tj
9.9626 0 0 9.9626 358.0723 329.159 Tm
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(k)Tj
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(\),)Tj
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(d)Tj
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6.9738 0 0 6.9738 171.8362 306.6519 Tm
(1)Tj
9.9626 0 0 9.9626 175.8047 308.1259 Tm
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(Z)Tj
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(1)Tj
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(f)Tj
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(z)Tj
4.9813 0 0 4.9813 243.0424 305.2346 Tm
(h)Tj
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()Tj
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(h)Tj
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(\()Tj
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(\))Tj
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(1)Tj
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6.9738 0 0 6.9738 277.7952 306.3117 Tm
()Tj
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(r)Tj
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(g)Tj
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9.9626 0 0 9.9626 290.0409 308.1259 Tm
(P)Tj
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(\()Tj
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(S)Tj
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6.9738 0 0 6.9738 305.5747 312.2645 Tm
(00)Tj
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(h)Tj
4.9813 0 0 4.9813 313.9086 304.3275 Tm
(j)Tj
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6.9738 0 0 6.9738 315.8361 305.348 Tm
(\()Tj
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()Tj
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9.9626 0 0 9.9626 337.7763 308.1259 Tm
()Tj
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(r)Tj
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(S)Tj
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6.9738 0 0 6.9738 361.5306 312.2645 Tm
(0)Tj
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(j)Tj
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(h)Tj
4.9813 0 0 4.9813 369.9211 304.3275 Tm
(j)Tj
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6.9738 0 0 6.9738 371.792 305.348 Tm
(\()Tj
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()Tj
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(1)Tj
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(4)Tj
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(r)Tj
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(\))Tj
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-18.6935 -2.1112 TD
(dF)Tj
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(\()Tj
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(z)Tj
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6.9738 0 0 6.9738 240.9448 285.6188 Tm
(1)Tj
9.9626 0 0 9.9626 244.9133 287.0929 Tm
(,)Tj
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(,)Tj
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(z)Tj
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6.9738 0 0 6.9738 271.8424 285.6188 Tm
(2)Tj
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(h)Tj
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4.9813 0 0 4.9813 278.8157 284.5984 Tm
()Tj
6.9738 0 0 6.9738 283.011 285.6188 Tm
()Tj
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(h)Tj
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4.9813 0 0 4.9813 293.0456 287.6598 Tm
()Tj
6.9738 0 0 6.9738 297.1842 285.6188 Tm
()Tj
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(5)Tj
9.9626 0 0 9.9626 307.729 287.0929 Tm
(\),)Tj
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(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 171.8362 264.5858 Tm
(2)Tj
9.9626 0 0 9.9626 175.8047 266.1165 Tm
(\()Tj
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(k)Tj
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(,)Tj
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(Z)Tj
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(1)Tj
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6.9738 0 0 6.9738 236.8629 264.3023 Tm
(f)Tj
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(z)Tj
4.9813 0 0 4.9813 243.0424 263.2251 Tm
(h)Tj
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()Tj
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(1,)Tj
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(h)Tj
.5008 -.33 TD
(k)Tj
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(\()Tj
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()Tj
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(\))Tj
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()Tj
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(1)Tj
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6.9738 0 0 6.9738 277.7952 264.3023 Tm
()Tj
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(r)Tj
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(g)Tj
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9.9626 0 0 9.9626 290.0409 266.1165 Tm
(P)Tj
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(\()Tj
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(S)Tj
/F8 1 Tf
6.9738 0 0 6.9738 305.5747 270.1984 Tm
(00)Tj
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0 -.9837 TD
(j)Tj
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(,)Tj
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(h)Tj
4.9813 0 0 4.9813 313.9086 262.2614 Tm
(j)Tj
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6.9738 0 0 6.9738 315.8361 263.3385 Tm
(\()Tj
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()Tj
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()Tj
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(1)Tj
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9.9626 0 0 9.9626 336.6991 266.1165 Tm
(4)Tj
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(r)Tj
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(,)Tj
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(S)Tj
/F8 1 Tf
6.9738 0 0 6.9738 361.5873 270.1984 Tm
(0)Tj
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0 -.9837 TD
(j)Tj
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(,)Tj
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.4146 0 TD
(h)Tj
4.9813 0 0 4.9813 369.9778 262.2614 Tm
(j)Tj
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6.9738 0 0 6.9738 371.9054 263.3385 Tm
(\()Tj
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()Tj
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(\))Tj
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()Tj
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(1)Tj
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9.9626 0 0 9.9626 393.8456 266.1165 Tm
()Tj
/F6 1 Tf
1.0527 0 TD
(r)Tj
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(\))Tj
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-18.6935 -2.1112 TD
(dF)Tj
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1.1609 0 TD
(\()Tj
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(z)Tj
/F1 1 Tf
6.9738 0 0 6.9738 240.9448 243.6094 Tm
(1)Tj
9.9626 0 0 9.9626 244.9133 245.0834 Tm
(,)Tj
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.1682 Tc
(...)Tj
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1.3145 0 TD
0 Tc
(,)Tj
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.4154 0 TD
(z)Tj
/F1 1 Tf
6.9738 0 0 6.9738 271.8424 243.6094 Tm
(2)Tj
/F6 1 Tf
.504 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 278.8157 242.5322 Tm
()Tj
6.9738 0 0 6.9738 283.011 243.6094 Tm
()Tj
/F6 1 Tf
.9349 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 293.0456 245.5937 Tm
()Tj
6.9738 0 0 6.9738 297.1842 243.6094 Tm
()Tj
/F1 1 Tf
.943 0 TD
(5)Tj
9.9626 0 0 9.9626 307.729 245.0834 Tm
(\),)Tj
-23.4508 -1.9974 TD
[(wi)-8.2(th)]TJ
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2.1226 0 TD
(F)Tj
/F1 1 Tf
.9446 0 TD
[(bein)-7.6(g)-330.8(the)-336.9(distribut)-9.7(ion)-335.1(of)-333.6(\()]TJ
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10.6015 0 TD
(S)Tj
6.9738 0 0 6.9738 215.2629 223.6535 Tm
(k)Tj
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.6341 0 TD
()Tj
/F6 1 Tf
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(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 229.7196 222.633 Tm
()Tj
6.9738 0 0 6.9738 233.9149 223.6535 Tm
()Tj
/F1 1 Tf
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(2)Tj
9.9626 0 0 9.9626 244.4598 225.1842 Tm
(,)Tj
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(...)Tj
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1.3145 0 TD
0 Tc
(,)Tj
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(S)Tj
6.9738 0 0 6.9738 272.4661 223.6535 Tm
(k)Tj
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()Tj
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.9349 0 TD
(2)Tj
9.9626 0 0 9.9626 229.1527 673.5116 Tm
(\()Tj
/F6 1 Tf
.3357 0 TD
(h)Tj
6.9738 0 0 6.9738 237.4865 672.0376 Tm
(k)Tj
/F8 1 Tf
9.9626 0 0 9.9626 242.8724 673.5116 Tm
()Tj
/F1 1 Tf
.9389 0 TD
(2\))Tj
/F9 1 Tf
.8365 0 TD
(!)Tj
/F13 1 Tf
.717 2.0429 TD
(Z)Tj
/F1 1 Tf
6.9738 0 0 6.9738 277.9653 691.1998 Tm
(1)Tj
/F6 1 Tf
-.6829 -2.8372 TD
(ar)Tj
/F8 1 Tf
1.0893 0 TD
()Tj
/F6 1 Tf
.9349 0 TD
(u)Tj
ET
292.989 682.639 79.087 .39685 re
f
BT
9.9626 0 0 9.9626 297.0141 687.1179 Tm
(n)Tj
/F1 1 Tf
.5008 0 TD
(\()Tj
/F6 1 Tf
.3357 0 TD
(nv)Tj
/F1 1 Tf
.9503 0 TD
(\))Tj
6.9738 0 0 6.9738 318.1039 691.0864 Tm
(2)Tj
/F6 1 Tf
.504 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 325.1338 690.0093 Tm
()Tj
6.9738 0 0 6.9738 329.2723 691.0864 Tm
()Tj
/F6 1 Tf
.9349 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 339.307 693.5809 Tm
()Tj
6.9738 0 0 6.9738 343.4456 691.0864 Tm
()Tj
/F6 1 Tf
.943 0 TD
(h)Tj
4.9813 0 0 4.9813 353.4802 690.0093 Tm
(k)Tj
/F8 1 Tf
6.9738 0 0 6.9738 357.5054 691.0864 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(5)Tj
9.9626 0 0 9.9626 292.9889 673.5116 Tm
(\(2)Tj
/F6 1 Tf
.8308 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 306.255 672.0376 Tm
()Tj
9.9626 0 0 9.9626 311.9243 673.5116 Tm
()Tj
/F6 1 Tf
.9389 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 326.2676 676.403 Tm
()Tj
9.9626 0 0 9.9626 331.9369 673.5116 Tm
()Tj
/F6 1 Tf
.9389 0 TD
(h)Tj
6.9738 0 0 6.9738 346.2802 672.0376 Tm
(k)Tj
/F8 1 Tf
9.9626 0 0 9.9626 351.7227 673.5116 Tm
()Tj
/F1 1 Tf
.9389 0 TD
(5\))Tj
/F9 1 Tf
.8308 0 TD
(!)Tj
/F1 1 Tf
.4382 .6829 TD
(\(1)Tj
/F8 1 Tf
1.0015 0 TD
()Tj
/F6 1 Tf
.9389 0 TD
(u)Tj
/F8 1 Tf
.6715 0 TD
()Tj
/F6 1 Tf
.9389 0 TD
(v)Tj
/F1 1 Tf
.4496 0 TD
(\))Tj
/F6 1 Tf
6.9738 0 0 6.9738 416.8629 684.4534 Tm
(n)Tj
/F8 1 Tf
.6666 0 TD
()Tj
/F1 1 Tf
.943 0 TD
(\(2)Tj
/F6 1 Tf
.8373 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 437.3857 683.4329 Tm
()Tj
6.9738 0 0 6.9738 441.5243 684.4534 Tm
()Tj
/F6 1 Tf
.943 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 451.6156 687.0045 Tm
()Tj
6.9738 0 0 6.9738 455.7542 684.4534 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(4\))Tj
/F18 1 Tf
9.9626 0 0 9.9626 209.9905 652.9888 Tm
()Tj
/F1 1 Tf
.7227 0 TD
(\(1)Tj
/F8 1 Tf
1.0015 0 TD
.1689 Tc
(O)Tj
ET
251.66 655.313 4.989 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 251.6598 659.792 Tm
0 Tc
(1)Tj
/F6 1 Tf
0 -1.3657 TD
(n)Tj
/F13 1 Tf
-.7284 2.0941 TD
.5002 Tc
()Tj
/F1 1 Tf
1.9632 -1.4113 TD
0 Tc
(\))Tj
/F6 1 Tf
.3357 0 TD
(dvdu)Tj
/F8 1 Tf
-6.6409 -2.868 TD
()Tj
/F13 1 Tf
1.0528 1.36 TD
(Z)Tj
/F6 1 Tf
6.9738 0 0 6.9738 221.896 635.3006 Tm
(nr)Tj
/F1 1 Tf
-.6829 -2.8372 TD
(0)Tj
ET
230.457 626.74 34.072 .39685 re
f
BT
/F6 1 Tf
9.9626 0 0 9.9626 236.2393 631.2188 Tm
(x)Tj
6.9738 0 0 6.9738 240.718 634.847 Tm
(h)Tj
4.9813 0 0 4.9813 244.233 633.7699 Tm
(k)Tj
/F8 1 Tf
6.9738 0 0 6.9738 248.2015 634.847 Tm
()Tj
/F1 1 Tf
.943 0 TD
(2)Tj
9.9626 0 0 9.9626 230.4566 617.6124 Tm
(\()Tj
/F6 1 Tf
.3301 0 TD
(h)Tj
6.9738 0 0 6.9738 238.7338 616.0817 Tm
(k)Tj
/F8 1 Tf
9.9626 0 0 9.9626 244.1763 617.6124 Tm
()Tj
/F1 1 Tf
.9389 0 TD
(2\))Tj
/F9 1 Tf
.8365 0 TD
(!)Tj
/F6 1 Tf
.4382 .6829 TD
(e)Tj
/F8 1 Tf
6.9738 0 0 6.9738 271.8424 628.5542 Tm
()Tj
/F6 1 Tf
.943 0 TD
(x)Tj
/F11 1 Tf
.4471 0 TD
(=)Tj
/F1 1 Tf
.4959 0 TD
(2)Tj
/F13 1 Tf
9.9626 0 0 9.9626 290.6645 637.9652 Tm
(Z)Tj
/F6 1 Tf
6.9738 0 0 6.9738 300.9259 635.3006 Tm
(n)Tj
-.6829 -2.8372 TD
(anr)Tj
/F8 1 Tf
1.5852 0 TD
()Tj
/F6 1 Tf
.943 0 TD
(x)Tj
ET
319.068 626.74 79.087 .39685 re
f
BT
9.9626 0 0 9.9626 331.4267 631.2188 Tm
(y)Tj
/F1 1 Tf
6.9738 0 0 6.9738 335.9054 634.847 Tm
(2)Tj
/F6 1 Tf
.504 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 342.8786 633.7699 Tm
()Tj
6.9738 0 0 6.9738 347.0172 634.847 Tm
()Tj
/F6 1 Tf
.943 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 357.1086 637.3416 Tm
()Tj
6.9738 0 0 6.9738 361.2471 634.847 Tm
()Tj
/F6 1 Tf
.9349 0 TD
(h)Tj
4.9813 0 0 4.9813 371.2818 633.7699 Tm
(k)Tj
/F8 1 Tf
6.9738 0 0 6.9738 375.2503 634.847 Tm
()Tj
/F1 1 Tf
.943 0 TD
(5)Tj
9.9626 0 0 9.9626 319.0676 617.6124 Tm
(\(2)Tj
/F6 1 Tf
.8365 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 332.3904 616.0817 Tm
()Tj
9.9626 0 0 9.9626 338.0598 617.6124 Tm
()Tj
/F6 1 Tf
.9389 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 352.403 620.4471 Tm
()Tj
9.9626 0 0 9.9626 358.0156 617.6124 Tm
()Tj
/F6 1 Tf
.9389 0 TD
(h)Tj
6.9738 0 0 6.9738 372.3589 616.0817 Tm
(k)Tj
/F8 1 Tf
9.9626 0 0 9.9626 377.8015 617.6124 Tm
()Tj
/F1 1 Tf
.9389 0 TD
(5\))Tj
/F9 1 Tf
.8365 0 TD
(!)Tj
/F6 1 Tf
.4382 .6829 TD
(e)Tj
/F8 1 Tf
6.9738 0 0 6.9738 405.4676 628.5542 Tm
()Tj
/F6 1 Tf
.943 0 TD
(y)Tj
/F11 1 Tf
.4471 0 TD
(=)Tj
/F1 1 Tf
.4959 0 TD
(2)Tj
/F18 1 Tf
9.9626 0 0 9.9626 209.9905 597.0896 Tm
()Tj
/F1 1 Tf
1.4511 0 TD
(1)Tj
/F8 1 Tf
.6658 0 TD
.1689 Tc
(O)Tj
ET
255.628 599.414 4.989 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 255.6283 603.8928 Tm
0 Tc
(1)Tj
/F6 1 Tf
0 -1.3657 TD
(n)Tj
/F13 1 Tf
-.7284 2.0941 TD
.5002 Tc
()Tj
-3.1298 0 TD
4.364 Tc
()Tj
/F6 1 Tf
5.8214 -1.4113 TD
0 Tc
(dydx)Tj
/F1 1 Tf
2.2307 0 TD
[(\()-338.5(b)0(y)-331.6(a)-338.3(change)-340(of)-384.8(variabl)-10.7(e)]TJ
/F8 1 Tf
10.6015 0 TD
()Tj
/F1 1 Tf
.9389 0 TD
[(Lemma)-344.3(3\))]TJ
/F8 1 Tf
-21.203 -2.9534 TD
()Tj
/F1 1 Tf
1.0528 0 TD
(2)Tj
6.9738 0 0 6.9738 216.6236 571.7479 Tm
(2)Tj
/F6 1 Tf
.4959 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 223.5968 570.7274 Tm
()Tj
6.9738 0 0 6.9738 227.7354 571.7479 Tm
()Tj
/F6 1 Tf
.943 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 237.77 574.2991 Tm
()Tj
6.9738 0 0 6.9738 241.9653 571.7479 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(5)Tj
/F13 1 Tf
9.9626 0 0 9.9626 254.1543 581.1589 Tm
(Z)Tj
/F6 1 Tf
6.9738 0 0 6.9738 264.4156 578.4943 Tm
(nr)Tj
/F11 1 Tf
.9186 0 TD
(=)Tj
/F1 1 Tf
.4959 0 TD
(2)Tj
-2.0974 -2.8372 TD
(0)Tj
ET
279.95 569.934 34.129 .39685 re
f
BT
/F6 1 Tf
9.9626 0 0 9.9626 286.0724 574.4125 Tm
(z)Tj
6.9738 0 0 6.9738 289.9275 578.0408 Tm
(h)Tj
4.9813 0 0 4.9813 293.4424 576.9636 Tm
(k)Tj
/F8 1 Tf
6.9738 0 0 6.9738 297.4109 578.0408 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(2)Tj
9.9626 0 0 9.9626 279.9495 560.8062 Tm
(\()Tj
/F6 1 Tf
.3357 0 TD
(h)Tj
6.9738 0 0 6.9738 288.2834 559.3322 Tm
(k)Tj
/F8 1 Tf
9.9626 0 0 9.9626 293.6692 560.8062 Tm
()Tj
/F1 1 Tf
.9389 0 TD
.0065 Tc
(2\))Tj
/F9 1 Tf
.8365 0 TD
0 Tc
(!)Tj
/F6 1 Tf
.4382 .6886 TD
(e)Tj
/F8 1 Tf
6.9738 0 0 6.9738 321.392 571.7479 Tm
()Tj
/F6 1 Tf
.9349 0 TD
(z)Tj
/F13 1 Tf
9.9626 0 0 9.9626 332.7873 581.1589 Tm
(Z)Tj
/F8 1 Tf
6.9738 0 0 6.9738 343.0487 578.4943 Tm
(1)Tj
/F6 1 Tf
-.6829 -2.8372 TD
(anr)Tj
/F11 1 Tf
1.4145 0 TD
(=)Tj
/F1 1 Tf
.504 0 TD
(2)Tj
/F8 1 Tf
.6666 0 TD
()Tj
/F6 1 Tf
.943 0 TD
(z)Tj
ET
367.71 569.934 79.087 .39685 re
f
BT
9.9626 0 0 9.9626 380.8062 574.4125 Tm
(t)Tj
/F1 1 Tf
6.9738 0 0 6.9738 383.8109 578.0408 Tm
(2)Tj
/F6 1 Tf
.504 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 390.7841 576.9636 Tm
()Tj
6.9738 0 0 6.9738 394.9794 578.0408 Tm
()Tj
/F6 1 Tf
.9349 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 405.0141 580.592 Tm
()Tj
6.9738 0 0 6.9738 409.1526 578.0408 Tm
()Tj
/F6 1 Tf
.943 0 TD
(h)Tj
4.9813 0 0 4.9813 419.1873 576.9636 Tm
(k)Tj
/F8 1 Tf
6.9738 0 0 6.9738 423.2125 578.0408 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(5)Tj
9.9626 0 0 9.9626 367.7101 560.8062 Tm
(\(2)Tj
/F6 1 Tf
.8365 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 381.033 559.3322 Tm
()Tj
9.9626 0 0 9.9626 386.7023 560.8062 Tm
()Tj
/F6 1 Tf
.9389 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 401.0456 563.6975 Tm
()Tj
9.9626 0 0 9.9626 406.6581 560.8062 Tm
()Tj
/F6 1 Tf
.9389 0 TD
(h)Tj
6.9738 0 0 6.9738 421.0015 559.3322 Tm
(k)Tj
/F8 1 Tf
9.9626 0 0 9.9626 426.444 560.8062 Tm
()Tj
/F1 1 Tf
.9389 0 TD
(5\))Tj
/F9 1 Tf
.8365 0 TD
(!)Tj
/F6 1 Tf
.4382 .6886 TD
(e)Tj
/F8 1 Tf
6.9738 0 0 6.9738 454.1101 571.7479 Tm
()Tj
/F6 1 Tf
.943 0 TD
(t)Tj
/F18 1 Tf
9.9626 0 0 9.9626 209.9905 538.6959 Tm
()Tj
/F1 1 Tf
1.4511 0 TD
(1)Tj
/F8 1 Tf
.6658 0 TD
.1689 Tc
(O)Tj
ET
255.628 541.02 4.989 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 255.6283 545.4991 Tm
0 Tc
(1)Tj
/F6 1 Tf
0 -1.3657 TD
(n)Tj
/F13 1 Tf
-.7284 2.0941 TD
.5002 Tc
()Tj
-3.1298 0 TD
4.364 Tc
()Tj
/F6 1 Tf
5.8214 -1.4113 TD
0 Tc
(dydx)Tj
/F8 1 Tf
-7.4319 -2.9022 TD
()Tj
ET
211.635 512.107 38.778 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 211.6346 516.5857 Tm
(4\()Tj
/F6 1 Tf
.8308 0 TD
(nr)Tj
/F1 1 Tf
.9162 0 TD
(\))Tj
/F6 1 Tf
6.9738 0 0 6.9738 232.3842 520.4975 Tm
(h)Tj
4.9813 0 0 4.9813 235.8991 519.4771 Tm
(k)Tj
/F8 1 Tf
6.9738 0 0 6.9738 239.8676 520.4975 Tm
()Tj
/F1 1 Tf
.943 0 TD
(1)Tj
9.9626 0 0 9.9626 213.959 502.9794 Tm
(\()Tj
/F6 1 Tf
.3357 0 TD
(h)Tj
6.9738 0 0 6.9738 222.2928 501.4487 Tm
(k)Tj
/F8 1 Tf
9.9626 0 0 9.9626 227.6787 502.9794 Tm
()Tj
/F1 1 Tf
.9389 0 TD
(1\))Tj
/F9 1 Tf
.8365 0 TD
(!)Tj
ET
252.057 512.107 79.143 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 256.3086 516.5857 Tm
(\()Tj
/F6 1 Tf
.3301 0 TD
(anr)Tj
/F1 1 Tf
1.4226 0 TD
(\))Tj
6.9738 0 0 6.9738 277.0582 520.4975 Tm
(2)Tj
/F6 1 Tf
.504 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 284.0314 519.4771 Tm
()Tj
6.9738 0 0 6.9738 288.2267 520.4975 Tm
()Tj
/F6 1 Tf
.9349 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 298.2613 523.0487 Tm
()Tj
6.9738 0 0 6.9738 302.3999 520.4975 Tm
()Tj
/F6 1 Tf
.943 0 TD
(h)Tj
4.9813 0 0 4.9813 312.4346 519.4771 Tm
(k)Tj
/F8 1 Tf
6.9738 0 0 6.9738 316.4597 520.4975 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(5)Tj
9.9626 0 0 9.9626 252.0566 502.9794 Tm
(\(2)Tj
/F6 1 Tf
.8365 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 265.3795 501.4487 Tm
()Tj
9.9626 0 0 9.9626 271.0487 502.9794 Tm
()Tj
/F6 1 Tf
.9389 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 285.3921 505.8707 Tm
()Tj
9.9626 0 0 9.9626 291.0613 502.9794 Tm
()Tj
/F6 1 Tf
.9389 0 TD
(h)Tj
6.9738 0 0 6.9738 305.4046 501.4487 Tm
(k)Tj
/F8 1 Tf
9.9626 0 0 9.9626 310.7904 502.9794 Tm
()Tj
/F1 1 Tf
.9389 0 TD
(5\))Tj
/F9 1 Tf
.8365 0 TD
(!)Tj
/F6 1 Tf
.4382 .6829 TD
(e)Tj
/F8 1 Tf
6.9738 0 0 6.9738 338.4566 513.9211 Tm
()Tj
/F6 1 Tf
.943 0 TD
(anr)Tj
/F11 1 Tf
1.4145 0 TD
(=)Tj
/F1 1 Tf
.504 0 TD
(2)Tj
9.9626 0 0 9.9626 369.6944 509.7825 Tm
(1)Tj
/F8 1 Tf
.6658 0 TD
.1689 Tc
(O)Tj
ET
400.875 512.107 4.989 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 400.8755 516.5857 Tm
0 Tc
(1)Tj
/F6 1 Tf
0 -1.3657 TD
(n)Tj
/F13 1 Tf
-.7284 2.0941 TD
.5002 Tc
()Tj
-3.1355 0 TD
4.364 Tc
()Tj
/F1 1 Tf
5.8271 -1.4113 TD
0 Tc
[(\()-332.8(b)0(y)-337.3(Lemma)-338.6(2\))]TJ
/F8 1 Tf
-22.011 -2.9022 TD
()Tj
ET
211.635 483.194 53.008 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 211.6346 487.6723 Tm
(4\()Tj
/F6 1 Tf
.8308 0 TD
(nr)Tj
/F1 1 Tf
.9162 0 TD
(\))Tj
/F6 1 Tf
6.9738 0 0 6.9738 232.3842 491.6408 Tm
(h)Tj
4.9813 0 0 4.9813 235.8991 490.5637 Tm
(k)Tj
/F8 1 Tf
6.9738 0 0 6.9738 239.8676 491.6408 Tm
()Tj
/F6 1 Tf
.943 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 249.9023 490.5637 Tm
()Tj
6.9738 0 0 6.9738 254.0976 491.6408 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(2)Tj
9.9626 0 0 9.9626 220.9322 474.066 Tm
(\()Tj
/F6 1 Tf
.3357 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 229.2661 472.5353 Tm
()Tj
9.9626 0 0 9.9626 234.9354 474.066 Tm
()Tj
/F1 1 Tf
.9389 0 TD
(1\))Tj
/F9 1 Tf
.8308 0 TD
(!)Tj
ET
266.287 483.194 4.989 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 266.2865 487.6723 Tm
(1)Tj
/F6 1 Tf
0 -1.3657 TD
(n)Tj
ET
278.135 483.194 33.959 .39685 re
f
BT
9.9626 0 0 9.9626 292.6487 487.6723 Tm
(n)Tj
/F1 1 Tf
-1.4568 -1.4397 TD
(\()Tj
/F6 1 Tf
.3357 0 TD
(nr)Tj
/F1 1 Tf
.9162 0 TD
(\))Tj
/F6 1 Tf
6.9738 0 0 6.9738 293.896 477.2408 Tm
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 297.4109 476.2203 Tm
()Tj
6.9738 0 0 6.9738 301.5495 477.2408 Tm
()Tj
/F1 1 Tf
.943 0 TD
(1)Tj
ET
313.795 483.194 79.087 .39685 re
f
BT
9.9626 0 0 9.9626 317.9904 487.6723 Tm
(\()Tj
/F6 1 Tf
.3301 0 TD
(anr)Tj
/F1 1 Tf
1.4226 0 TD
(\))Tj
6.9738 0 0 6.9738 338.7401 491.6408 Tm
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f
BT
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BT
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f
BT
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[(3\))-168.5(log)]TJ
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[( )125.8( )]TJ
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[(,)-330.4(enta)-9.4(iling)-336.5(that)]TJ
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[(,)-330.4(and)-339.8(if)-330.6(mor)-7.8(eover)]TJ
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[(1)-330.8(and)]TJ
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[(4\))-333.6(for)-336.3(appl)-7.6(ying)-335.9(Lemma)-338.6(2)-336.5(and)-334.1(Lemma)-344.3(3.)-331.2(Th)-7(e)-332.6(last)-335.9(ineq)-7.6(uality)-339(is)-335.5(hence)-339.2(valid)-335.5(for)]TJ
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[(3\))-168.5(log)]TJ
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[( )125.8( )]TJ
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(n)Tj
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(p)Tj
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ET
413.405 356.372 4.989 .39685 re
f
BT
9.9626 0 0 9.9626 413.4046 360.907 Tm
(1)Tj
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[(In)-333.6(a)-332.6(simi)-7.6(lar)-333.2(man)-7.6(ner)-336.1(we)-337.3(can)-335.9(bound)]TJ
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(1)Tj
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(,)Tj
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(j)Tj
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[(\),)-338.9(then)-337.7(decompos)-8.7(e)-332.6(and)-339.8(bound)]TJ
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(2)Tj
9.9626 0 0 9.9626 427.5779 330.8597 Tm
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[(We)-842.4(nally)-841.9(obtain)-842.7(that,)-841.6(if)-842.8(we)-843.8(take)]TJ
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ET
1 i
q 1 0 0 1 315.213 321.562 cm 0 0 m
54.822 0 l
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f*
Q
BT
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()Tj
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[(3\))-166.9(log)]TJ
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[(then)-7.6(,)-836.9(uniform)-9.9(ly)-840.8(in)]TJ
ET
471.005 321.165 3.515 .39685 re
f
BT
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(1)Tj
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[(1)-837.3(and)]TJ
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(n)Tj
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(4)Tj
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9.9626 0 0 9.9626 169.8519 306.9353 Tm
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(4\))Tj
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(_)Tj
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ET
219.515 309.203 43.483 .39685 re
f
BT
6.9738 0 0 6.9738 219.5149 311.1873 Tm
(4\(2)Tj
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(h)Tj
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6.9738 0 0 6.9738 250.6393 311.1873 Tm
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(4\))Tj
-4.8207 -1.0975 TD
(3)Tj
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(3)Tj
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9.9626 0 0 9.9626 212.9385 317.9905 Tm
4.3688 Tc
(no)Tj
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5.6849 -1.1097 TD
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[(,)-336.1(w)0(e)-337.3(have)-336.7(the)-336.9(upper)-337.6(bound)-339.6(stated)-339.2(in)-334.3(\()]TJ
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[(Proof)-468.3(of)-464.4(\(e\))]TJ
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[(.)-461.3(F)0(o)-6.4(r)-463.7(every)]TJ
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[(we)-468.2(let)]TJ
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6.9738 0 0 6.9738 312.3779 281.5369 Tm
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9.9626 0 0 9.9626 322.7527 283.0109 Tm
[(denote)-471.8(the)-467.8(class)-467.8(of)-470.1(all)-464.8(the)-467.8(subse)-8(ts)-466.4(of)-464.4(siz)-8(e)]TJ
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[(1o)467.4(f)]TJ
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(vs)Tj
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(f)Tj
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(h)Tj
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(1,)Tj
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[(..)5.7(.)]TJ
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(2)Tj
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(g)Tj
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[(.)-336.1(W)0(e)-335.9(obtain)]TJ
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(i)Tj
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(i)Tj
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(X)Tj
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6.9738 0 0 6.9738 218.7212 250.7527 Tm
(n)Tj
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(1)Tj
/F13 1 Tf
9.9626 0 0 9.9626 230.9102 248.7684 Tm
(X)Tj
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6.9738 0 0 6.9738 229.3795 228.359 Tm
(C)Tj
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(2C)Tj
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(ik)Tj
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(E)Tj
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(I)Tj
6.9738 0 0 6.9738 266.0598 237.8267 Tm
(k)Tj
/F13 1 Tf
9.9626 0 0 9.9626 271.5023 248.7684 Tm
(Y)Tj
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6.9738 0 0 6.9738 272.0125 228.5291 Tm
(t)Tj
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(C)Tj
9.9626 0 0 9.9626 285.7889 239.3007 Tm
(I)Tj
6.9738 0 0 6.9738 289.1338 237.8267 Tm
(t)Tj
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9.9626 0 0 9.9626 298.0912 248.7684 Tm
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[(We)-290.4(have)-296.8(used)-290.6(the)-291.4(followi)-8.1(ng)-286.1(two)-293.5(elementa)-10.9(ry)-288(lemmas)-292.3(that)-294.9(we)-291.8(state)-292.9(without)-290.7(proof)-7.8(.)-284.9(For)-293.7(a)-287.1(proof)-292.3(of)-288(Lemma)]TJ
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[(Lemm)-9.3(a)-245.5(4)0(.)]TJ
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[(un)-7.2(iformly)-339.2(in)]TJ
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[(we)-332.4(have)-342.4(the)-336.9(following)-341.3(inequalit)-8.3(y:)]TJ
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()Tj
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(:)Tj
/F2 1 Tf
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[(Lemm)-9.3(a)-330.8(5)0(.)]TJ
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(1\))Tj
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[(we)-338.1(have)]TJ
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(1\))Tj
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9.9626 0 0 9.9626 363.0613 487.8424 Tm
()Tj
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(e)Tj
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7.4718 0 0 6.641 376.8944 492.2644 Tm
()Tj
/F6 1 Tf
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(nx/)Tj
/F1 1 Tf
1.2292 0 TD
(2)Tj
9.9626 0 0 9.9626 395.5463 487.8424 Tm
(.)Tj
-31.2639 -2.4014 TD
[(In)-316.5(the)-319.8(followi)-8.1(ng)-314.5(lemma,)-319.2(we)-320.2(show)-321.2(that)-317.7(the)-319.8(chosen)-316.6(para)-8.6(meters)-319.2(for)-319.2(the)-319.8(approximat)-10.8(ing)-318(compound)-318.7(Po)-6.4(isson)]TJ
-1.0015 -1.195 TD
[(distri)-10.3(bution)-334.5(verify)-343.1(the)-336.9(relation)-338.6(\(3\),)-336.7(and)-339.8(hence)-339.2(we)-337.3(can)-335.9(use)-335.3(the)-336.9(bound)-339.6(\(4\))-336.3(of)-333.6(Barbour)-340.1(et)-336.1(al.)-336.5(\(2000\))-8.5(.)]TJ
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1.0015 -2.5038 TD
[(Lemm)-9.3(a)-302.4(6)0(.)]TJ
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5.3434 0 TD
(If)Tj
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(1)Tj
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[(and)-303.9(n)]TJ
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7.4718 0 0 6.641 213.2787 425.4235 Tm
(min)Tj
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(G)Tj
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(,)Tj
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[(then)-309.2(for)-302.2(every)-308.1(i)]TJ
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(2f)Tj
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1.4397 0 TD
0 Tc
(1,)Tj
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9.9626 0 0 9.9626 365.1589 427.0676 Tm
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[(we)-303.9(have)]TJ
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3.6192 .2788 TD
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(k)Tj
0 0 TD
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[(.I)302(f)]TJ
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0 Tc
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7.4718 0 0 6.641 79.0866 413.4613 Tm
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[(mi)8.1(n)]TJ
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0 Tc
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[(n)-336.5(and)-332.3(nr)]TJ
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[(,)-330.4(whe)-8.8(re)]TJ
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3.3688 0 TD
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[(is)-335.5(a)-336.5(xed)-336.7(constant)]TJ
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(1,)Tj
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1.0812 0 TD
[(then)-337.7(i)]TJ
/F9 1 Tf
2.2933 .2788 TD
(^)Tj
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(k)Tj
0 0 TD
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6.9738 0 0 6.9738 326.7212 413.6314 Tm
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9.9626 0 0 9.9626 331.9936 415.1054 Tm
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(1\))Tj
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0 -.2788 TD
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0 0 TD
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-31.6167 -2.3957 TD
(Proof.)Tj
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3.6533 0 TD
[(We)-261.9(h)-6.5(ave)]TJ
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3.8184 0 TD
(i)Tj
/F12 1 Tf
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(k)Tj
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6.9738 0 0 6.9738 166.2803 389.707 Tm
(i)Tj
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(P)Tj
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(n)Tj
0 -1.0893 TD
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(E)Tj
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(I)Tj
6.9738 0 0 6.9738 220.7054 389.707 Tm
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(1)Tj
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(f)Tj
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(Z)Tj
4.9813 0 0 4.9813 236.8062 388.403 Tm
(k)Tj
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6.9738 0 0 6.9738 240.8314 389.4235 Tm
()Tj
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(i)Tj
/F8 1 Tf
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(g)Tj
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9.9626 0 0 9.9626 253.3039 391.2377 Tm
[(\).)-264.9(One)-264.1(can)-261.9(easily)-270.9(show)-264.3(that)-260.7(the)-262.9(lea)-8.6(ding)-261.9(terms)-265.4(in)-260.4(the)-262.9(expre)-9.4(ssion)]TJ
-17.9878 -1.2007 TD
(of)Tj
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1.0812 0 TD
(i)Tj
/F10 1 Tf
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(l)Tj
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7.4718 0 0 6.641 92.6929 377.5747 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 97.2283 379.2755 Tm
[(are)-252.5(thos)-7(e)-247.2(which)-251.3(are)-252.5(expectati)-10.9(ons)-248.2(of)-248.2(produc)-8.3(ts)-244.5(o)-6.5(f)]TJ
/F6 1 Tf
19.1658 0 TD
(i)Tj
/F1 1 Tf
.5235 0 TD
[(conse)-8.6(cutive)-252.7(indicat)-11.5(ors.)-244.8(Fo)-6.4(r)-247.4(a)-247.2(term)-252.1(with)]TJ
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15.9165 0 TD
(i)Tj
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.5235 0 TD
[(conse)-8.6(cutive)]TJ
-38.451 -1.2007 TD
[(indi)-8.6(cators,)-338.8(of)-333.6(the)-336.9(form)]TJ
/F14 1 Tf
12.081 -2.5152 TD
(E)Tj
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(\()Tj
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(I)Tj
6.9738 0 0 6.9738 206.6456 340.7243 Tm
(j)Tj
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1.3145 0 TD
0 Tc
(I)Tj
6.9738 0 0 6.9738 227.1684 340.7243 Tm
(j)Tj
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(i)Tj
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()Tj
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(1)Tj
9.9626 0 0 9.9626 250.5259 342.255 Tm
(\))Tj
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()Tj
ET
266.513 344.523 12.586 .39685 re
f
BT
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9.9626 0 0 9.9626 270.3117 349.0015 Tm
(1)Tj
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(j)Tj
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(K)Tj
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(j)Tj
/F13 1 Tf
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/F8 1 Tf
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.1682 Tc
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()Tj
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(\),)Tj
-30.3705 -2.8851 TD
[(we)-343(have)-342.4(that)-340.4(for)-336.3(each)]TJ
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[(the)-342.6(extreme)-343.3(cluste)-9.2(rs)-334.7(inters)-9.4(ect)-338.7(\(bec)-8.6(ause)-337.9(of)-339.2(the)-336.9(fact)-341.4(that)]TJ
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[(\))-332.8(and)-339.8(hence)]TJ
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[(im)-7.8(plying)-334.5(that)]TJ
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(:)Tj
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[(Using)-341.8(\(6\))-336.3(we)-337.3(obtain)]TJ
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(I)Tj
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(i)Tj
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(,)Tj
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(8)Tj
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(j)Tj
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(.)Tj
-21.4989 -1.2007 TD
[(The)-339.6(results)-341.4(in)-334.3(the)-336.9(statemen)-10.3(t)-333.6(easily)-339.2(follow.)]TJ
/F7 1 Tf
41.1996 0 TD
(&)Tj
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-41.1996 -2.3957 TD
[(For)-339.2(the)-336.9(detailed)-338.4(proof)-7.8(s)-332(o)0(f)-333.6(Propos)-7(ition)-336.5(1)-336.5(and)-334.1(Lemm)-11.7(a)-332.6(2)0(,)-336.9(see)-337.1(Grusea)-339.6(\(2008\))-8.5(.)]TJ
0 -1.2007 TD
[(From)-360.6(Proposition)-360.5(1)-353.6(and)-356.9(Lemma)-361.4(4,)-354(togethe)-8.7(r)-349.9(with)-359.6(Theore)-9.9(m)-351.4(1)-353.6(and)-356.9(relation)-361.4(\(4\),)-353.7(we)-360.1(obtain)-359(the)-354(followi)-8.1(ng)]TJ
-1.0015 -1.2007 TD
[(up)-7.2(per)-336.1(bound)-333.9(on)-337.3(the)-336.9(error)-335.9(of)-339.2(approximat)-10.8(ing)]TJ
/F14 1 Tf
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(W)Tj
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(m)Tj
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()Tj
/F1 1 Tf
1.0471 0 TD
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[(1\))-326.3(b)6.5(y)]TJ
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0 Tc
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(h)Tj
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(i)Tj
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(1)Tj
/F9 1 Tf
9.9626 0 0 9.9626 412.1574 176.5417 Tm
(^)Tj
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(k)Tj
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(i)Tj
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(g)Tj
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[(The)-8(orem)-726.4(7.)]TJ
/F6 1 Tf
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[(Suppo)-9.5(se)-721.5(that)-731.3(n)]TJ
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(0)Tj
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1.2235 0 TD
[(and)-725(n)]TJ
/F1 1 Tf
7.4718 0 0 6.641 309.4865 148.2519 Tm
(min)Tj
/F19 1 Tf
9.9626 0 0 9.9626 322.866 149.896 Tm
(G)Tj
/F6 1 Tf
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[(n.)-723.8(Then,)-727.1(uniform)-10.3(ly)-723.1(in)]TJ
ET
438.179 152.164 3.515 .39685 re
f
BT
/F1 1 Tf
6.9738 0 0 6.9738 438.1794 153.5244 Tm
(1)Tj
/F6 1 Tf
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(n)Tj
/F8 1 Tf
9.9626 0 0 9.9626 444.4156 149.896 Tm
()Tj
/F6 1 Tf
1.0527 0 TD
(nr)Tj
/F15 1 Tf
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(5)Tj
/F1 1 Tf
1.1722 0 TD
(1)Tj
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(and)Tj
-41.7003 -1.2007 TD
(n)Tj
/F15 1 Tf
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(4)Tj
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(2\(2)Tj
/F6 1 Tf
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(h)Tj
/F8 1 Tf
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()Tj
9.9626 0 0 9.9626 116.3905 137.9338 Tm
()Tj
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(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 130.7338 141.5621 Tm
()Tj
9.9626 0 0 9.9626 136.3464 137.9338 Tm
()Tj
/F1 1 Tf
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(4\))Tj
/F8 1 Tf
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(_)Tj
/F1 1 Tf
.882 0 TD
(exp)Tj
ET
186.009 140.258 43.54 .39685 re
f
BT
6.9738 0 0 6.9738 186.0094 142.1858 Tm
(4\(2)Tj
/F6 1 Tf
1.3332 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 198.822 141.1653 Tm
()Tj
6.9738 0 0 6.9738 202.9606 142.1858 Tm
()Tj
/F6 1 Tf
.943 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 213.0519 144.7369 Tm
()Tj
6.9738 0 0 6.9738 217.1905 142.1858 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(4\))Tj
-5.1541 -1.0975 TD
(3\()Tj
/F6 1 Tf
.8373 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 197.0645 133.5118 Tm
()Tj
6.9738 0 0 6.9738 201.2598 134.5323 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(1\))Tj
/F8 1 Tf
.9999 0 TD
()Tj
/F6 1 Tf
.943 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 224.7873 136.5732 Tm
()Tj
/F13 1 Tf
9.9626 0 0 9.9626 179.4897 148.9889 Tm
4.3688 Tc
(no)Tj
/F1 1 Tf
5.6849 -1.1097 TD
0 Tc
(,)Tj
/F6 1 Tf
.5804 0 TD
[(we)-338.1(have:)]TJ
/F14 1 Tf
-6.7547 -2.7201 TD
(P)Tj
/F1 1 Tf
.7227 0 TD
(\()Tj
/F6 1 Tf
.3301 0 TD
(W)Tj
6.9738 0 0 6.9738 193.4362 109.3606 Tm
(m)Tj
/F8 1 Tf
9.9626 0 0 9.9626 201.7133 110.8346 Tm
()Tj
/F1 1 Tf
1.0528 0 TD
(1\))Tj
/F8 1 Tf
1.0015 0 TD
()Tj
/F6 1 Tf
.9389 0 TD
(p)Tj
/F8 1 Tf
-5.9865 -.0057 TD
6.2172 Tc
(jj)Tj
7.0335 .0057 TD
0 Tc
()Tj
/F6 1 Tf
1.0528 0 TD
(C)Tj
ET
261.071 113.159 47.112 .39688 re
f
BT
9.9626 0 0 9.9626 261.0708 117.6377 Tm
(n)Tj
/F1 1 Tf
.5008 0 TD
(\()Tj
/F6 1 Tf
.33 0 TD
(nr)Tj
/F1 1 Tf
.9219 0 TD
(\))Tj
6.9738 0 0 6.9738 281.8204 121.5496 Tm
(2\()Tj
/F6 1 Tf
.8373 0 TD
(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 291.1747 120.5291 Tm
()Tj
6.9738 0 0 6.9738 295.3133 121.5496 Tm
()Tj
/F1 1 Tf
.9349 0 TD
(1\))Tj
9.9626 0 0 9.9626 262.0912 103.4645 Tm
([\()Tj
/F6 1 Tf
.6715 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 273.77 101.9338 Tm
()Tj
9.9626 0 0 9.9626 279.4393 103.4645 Tm
()Tj
/F1 1 Tf
.9389 0 TD
(1\))Tj
/F9 1 Tf
.8308 0 TD
(!)Tj
/F1 1 Tf
.2731 0 TD
(])Tj
6.9738 0 0 6.9738 303.1369 107.3197 Tm
(2)Tj
9.9626 0 0 9.9626 317.1401 110.8346 Tm
(1)Tj
/F8 1 Tf
.6658 0 TD
.1689 Tc
(O)Tj
ET
348.321 113.159 4.989 .39688 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 348.3212 117.6377 Tm
0 Tc
(1)Tj
/F6 1 Tf
0 -1.3657 TD
(n)Tj
/F13 1 Tf
-.7341 2.0941 TD
.5058 Tc
()Tj
/F8 1 Tf
2.1283 -1.4113 TD
.1689 Tc
(O)Tj
/F1 1 Tf
1.7356 0 TD
0 Tc
(\()Tj
/F6 1 Tf
.3301 0 TD
(nr)Tj
/F1 1 Tf
.9219 0 TD
(\))Tj
/F13 1 Tf
-8.2456 1.4113 TD
7.8467 Tc
()Tj
/F1 1 Tf
9.3097 -1.4113 TD
0 Tc
(,)Tj
/F6 1 Tf
-32.971 -2.5892 TD
[(whe)-8.8(re)-334.6(C)]TJ
/F8 1 Tf
3.6533 0 TD
()Tj
/F1 1 Tf
.9389 0 TD
(4)Tj
/F6 1 Tf
.5008 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 129.8267 88.611 Tm
()Tj
9.9626 0 0 9.9626 135.496 85.0393 Tm
()Tj
/F6 1 Tf
.9389 0 TD
(h)Tj
/F8 1 Tf
6.9738 0 0 6.9738 149.8393 83.5086 Tm
()Tj
9.9626 0 0 9.9626 155.4519 85.0393 Tm
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(\()Tj
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[(In)-333.6(this)-334.1(case)-339.7(it)-337.1(sufces)-342.5(to)-334.3(sum)-337.1(over)-336.9(all)-334(dif)-7(ferent)-339.2(\()]TJ
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(h)Tj
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-25.3742 -1.2007 TD
[(For)-333.5(calculat)-10.1(ing)]TJ
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(1,)Tj
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(1)Tj
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[(\))-332.8(and)]TJ
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(S)Tj
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(1,)Tj
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(1)Tj
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(\()Tj
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(1)Tj
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9.9626 0 0 9.9626 321.7322 375.307 Tm
()Tj
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(r)Tj
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(,)Tj
/F6 1 Tf
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(S)Tj
/F1 1 Tf
6.9738 0 0 6.9738 345.4865 373.833 Tm
(2,)Tj
/F6 1 Tf
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/F1 1 Tf
4.9813 0 0 4.9813 355.3511 372.7558 Tm
(2)Tj
6.9738 0 0 6.9738 358.3558 373.833 Tm
(\()Tj
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(1)Tj
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9.9626 0 0 9.9626 380.3527 375.307 Tm
()Tj
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(r)Tj
/F1 1 Tf
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[(\))-332.8(w)0(e)-331.6(use)-335.3(classi)-10.4(c)-326.9(resu)-8(lts)-333.4(on)-331.6(uniform)]TJ
-28.8397 -1.2007 TD
[(spacings)-339.2(\(G)-7.4(laz)-333(et)-336.1(al.,)-336.9(1983\).)]TJ
/F6 1 Tf
10.959 0 0 10.959 107.6031 344.4661 Tm
[(3.3.)-496.9(The)-332.3(linear)-332.3(case)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 117.5811 326.4944 Tm
[(Next)-256.2(we)-257.6(briey)-255(consi)-9.6(der)-256.4(the)-251.5(case)-260(of)-253.9(a)-252.9(linear)-260.3(genom)-9.1(e.)-253.3(As)-257(in)-249(the)-257.2(circul)-10(ar)-250(case)-9.6(,)-250.8(w)0(e)-257.6(see)-257.4(the)-257.2(genome)-256.4(B)-255.9(a)0(s)-254.9(the)]TJ
-1.0015 -1.2007 TD
[(interv)-8.2(al)-273.5([0,)-277(1])-276.6(and)-277.2(the)-280(positions)-279.3(of)-276.6(the)]TJ
/F6 1 Tf
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(n)Tj
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[(ortholo)-7.2(gs)-275.9(as)-277.6(i.i.d.)-276.4(r.v.)-7(s)-275.1(uniforml)-7.7(y)-273.9(distribut)-9.7(ed)-276.5(on)-274.7([0,)-277(1].)-277(The)-277(event)-10.2(s)]TJ
/F6 1 Tf
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(A)Tj
7.4718 0 0 6.641 113.726 300.9259 Tm
(k)Tj
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9.9626 0 0 9.9626 119.6787 302.57 Tm
[(are)-263.9(dened)-269.1(as)-266.3(before,)-268.6(but)-261.1(in)-266.1(this)-260.1(case)-271.4(we)-263.3(have)-268.4(a)-258.6(sma)-8.8(ller)-262.7(numb)-6.6(er)-261.4(of)-265.3(possibl)-7.6(e)-258.6(event)-10.1(s,)-258.4(p)-6.5(recisely)]TJ
/F6 1 Tf
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()Tj
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(h)Tj
7.4718 0 0 6.641 515.7353 300.9259 Tm
(*)Tj
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-42.4458 -1.195 TD
[(We)-267.6(als)-8(o)-268.2(have)-268.4(a)-270(boundar)-9.1(y)-268.2(effect)-272.7(which)-274.1(consists)-273.1(in)-266.1(the)-274.3(fact)-273.1(that)-266.4(for)]TJ
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9.9626 0 0 9.9626 416.4093 290.6645 Tm
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6.9738 0 0 6.9738 474.803 289.1338 Tm
()Tj
9.9626 0 0 9.9626 480.4723 290.6645 Tm
()Tj
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[(1)-268.2(the)-268.6(event)-10.2(s)]TJ
/F6 1 Tf
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(A)Tj
7.4718 0 0 6.641 113.726 277.0015 Tm
(k)Tj
/F1 1 Tf
9.9626 0 0 9.9626 120.4157 278.7023 Tm
[(have)-336.7(a)-332.6(sma)-8.8(ller)-336.7(probabil)-9.7(ity.)]TJ
-.2845 -1.2007 TD
[(S)11.4(i)0(m)14.9(i)13.5(la)16.7(rl)16.5(y)-228.4(t)0(o)-220.5(t)0(h)18.5(e)-230.2(ci)16.7(rc)17.5(ul)18.5(ar)-221.5(ca)17.7(se)18.3(,)-228(w)0(e)-223.5(a)0(p)13.8(p)0(r)19.3(o)0(x)21.2(i)0(m)14.9(a)0(t)16.7(e)-230.2(th)18.5(e)-230.2(d)0(i)18.5(s)0(t)17.3(r)0(i)22.2(b)0(u)15.5(t)0(i)15.7(o)0(n)-217.8(o)0(f)-219.7(t)0(h)18.5(e)-230.2(nu)15.5(m)12.8(b)0(e)13.8(r)-230.4(of)-219.7(cl)16.7(us)20(te)16.7(rs)-220.9(of)-219.7(ty)18.5(pe)-219.6(\()]TJ
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[(\)i)245.8(nt)245.8(h)232.3(e)]TJ
-40.4257 -1.2007 TD
0 Tc
[(ge)19.4(no)15.5(me)-268.6(B)11.6(,)]TJ
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(n)Tj
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4.9813 0 0 4.9813 209.9338 258.5196 Tm
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4.9813 0 0 4.9813 235.6157 252.2267 Tm
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9.9626 0 0 9.9626 238.9039 254.7779 Tm
[(,)-290.6(b)0(y)-286.1(a)-287.1(compound)-290.3(Po)-6.4(isson)-287.8(distribut)-9.7(ion)-289.6(of)-282.3(para)-8.6(meter)]TJ
/F9 1 Tf
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(k)Tj
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(P)Tj
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6.9738 0 0 6.9738 481.0959 259.5401 Tm
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(i)Tj
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9.9626 0 0 9.9626 500.7684 254.7779 Tm
(d)Tj
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(i)Tj
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9.9626 0 0 9.9626 508.1951 254.7779 Tm
[(,)-284.9(whe)-8(re)]TJ
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-32.4987 -2.629 TD
(^)Tj
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(i)Tj
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()Tj
ET
205.115 228.076 4.989 .39687 re
f
BT
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9.9626 0 0 9.9626 205.1149 232.611 Tm
(1)Tj
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(i)Tj
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1.2861 1.6389 TD
(X)Tj
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6.9738 0 0 6.9738 211.8047 237.4299 Tm
(n)Tj
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(h)Tj
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4.9813 0 0 4.9813 226.4881 236.3527 Tm
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6.9738 0 0 6.9738 230.6267 237.4299 Tm
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-2.6095 -3.2192 TD
(k)Tj
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(1)Tj
/F14 1 Tf
9.9626 0 0 9.9626 242.3621 225.8078 Tm
(E)Tj
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(I)Tj
6.9738 0 0 6.9738 254.4944 224.3338 Tm
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9.9626 0 0 9.9626 258.2928 225.8078 Tm
(1)Tj
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6.9738 0 0 6.9738 263.2818 223.9937 Tm
(f)Tj
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(Z)Tj
4.9813 0 0 4.9813 270.5952 222.9732 Tm
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6.9738 0 0 6.9738 274.6204 223.9937 Tm
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9.9626 0 0 9.9626 350.4188 225.8078 Tm
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6.9738 0 0 6.9738 377.2912 224.3338 Tm
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6.9738 0 0 6.9738 409.4361 224.3338 Tm
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9.9626 0 0 9.9626 414.9353 225.8078 Tm
(\))Tj
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6.9738 0 0 6.9738 430.9794 237.4299 Tm
(h)Tj
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4.9813 0 0 4.9813 434.4377 236.3527 Tm
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6.9738 0 0 6.9738 438.633 237.4299 Tm
()Tj
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/F1 1 Tf
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/F6 1 Tf
9.9626 0 0 9.9626 450.3117 225.8078 Tm
(i)Tj
/F9 1 Tf
.2219 .2788 TD
(^)Tj
/F16 1 Tf
.0569 -.2788 TD
(k)Tj
0 0 TD
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/F6 1 Tf
6.9738 0 0 6.9738 458.1353 224.3338 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 107.6031 197.5181 Tm
(and)Tj
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1.7811 0 TD
(Z)Tj
6.9738 0 0 6.9738 130.9039 196.044 Tm
(k)Tj
/F8 1 Tf
9.9626 0 0 9.9626 136.2897 197.5181 Tm
()Tj
/F13 1 Tf
1.1097 .7511 TD
(P)Tj
/F6 1 Tf
6.9738 0 0 6.9738 157.7763 202.2803 Tm
(k)Tj
/F8 1 Tf
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(h)Tj
/F8 1 Tf
4.9813 0 0 4.9813 172.2897 201.2598 Tm
()Tj
6.9738 0 0 6.9738 176.4283 202.2803 Tm
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(j)Tj
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4.9813 0 0 4.9813 181.9275 193.6629 Tm
()Tj
6.9738 0 0 6.9738 186.1228 194.6834 Tm
()Tj
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.9349 0 TD
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 198.3117 197.5181 Tm
(1)Tj
/F6 1 Tf
6.9738 0 0 6.9738 203.3007 196.044 Tm
(A)Tj
4.9813 0 0 4.9813 207.6094 194.9669 Tm
(j)Tj
/F1 1 Tf
9.9626 0 0 9.9626 209.9905 197.5181 Tm
[(.)-330.4(Not)-9(ice)-333(that)-340.4(Theorem)-344.3(2)-330.8(i)0(s)-335.5(valid)-335.5(in)-340(this)-334.1(case,)-340(too.)]TJ
-9.2756 -1.2007 TD
[(For)-373.4(the)-376.7(computa)-9.5(tion)-372.8(of)-379.1(the)-371(para)-8.6(meters)-381.8(we)-377.1(ignore)-375.3(the)-376.7(boundar)-9.1(y)-370.7(eff)-8(ects)-374.8(and)-379.7(use)-375.2(a)-372.4(Mar)-8(kovian)-379(approxi-)]TJ
-1.0015 -1.2007 TD
[(mation)-356.8(as)-345.9(in)-351.4(the)-354(circular)-356.7(case.)-351.4(Note)-353(that,)-357.9(based)-350(on)-354.3(Assumption)-358.7(1)-347.9(\(see)-351.2(also)-355.9(the)-348.3(relat)-9.2(ions)-348.4(\(6\))-353.4(and)-351.2(\(9\)\),)-350.8(the)]TJ
0 -1.195 TD
[(error)-335.9(introdu)-7.1(ced)-341.6(in)-334.3(the)-336.9(computatio)-11.6(n)-330.8(o)0(f)-333.6(the)-336.9(para)-8.6(meters)-342(by)-331.6(ignorin)-7.1(g)-336.5(the)-336.9(boundary)-339.9(effects)-343(is)-335.5(negligibl)-8.3(e.)]TJ
/F2 1 Tf
10.959 0 0 10.959 206.2487 130.7905 Tm
[(4.)-501.9(NUMERICAL)-331.5(RESULTS)-330(AND)-334.3(DISCUSSIO)6.7(N)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 117.5811 106.8661 Tm
[(We)-244.9(denote)-244.2(b)-6.5(y)]TJ
/F12 1 Tf
5.8044 0 TD
(/)Tj
/F8 1 Tf
6.9738 0 0 6.9738 182.0409 111.2314 Tm
(0)Tj
/F9 1 Tf
9.9626 0 0 9.9626 187.1999 106.8661 Tm
(:)Tj
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()Tj
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(\()Tj
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(/)Tj
/F8 1 Tf
6.9738 0 0 6.9738 213.6755 111.2314 Tm
(0)Tj
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0 -1.0243 TD
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9.9626 0 0 9.9626 217.7007 106.8661 Tm
(,)Tj
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(...)Tj
/F1 1 Tf
1.3145 0 TD
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[(mu)17.7(lt)21.4(ig)12.8(en)19.4(e)-395.2(f)0(a)17.5(m)0(i)15(l)13.5(ie)16.7(s)-394.6(i)0(n)-385.6(t)0(h)12.8(e)-395.2(O)12.4(r)0(y)13.6(z)0(i)16.7(a)0(s)18.3(-)0(L)19.4(a)0(t)16.7(i)0(p)18.5(e)0(s)-385.8(g)0(e)13.8(n)0(o)21.2(m)0(e)15.9(;)]TJ
/F3 1 Tf
21.1575 0 TD
(g)Tj
/F8 1 Tf
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()Tj
/F1 1 Tf
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[(\(3)19.3(0,)-382.4(8\))13.6(,)-393(t)0(h)18.5(e)-395.2(ve)19.4(ct)16.7(or)-390.5(co)19.5(nt)18.5(ai)16.7(ni)18.5(ng)-382.8(th)18.5(e)-400.9(m)12.8(ul)18.5(ti)15.7(pl)18.5(ic)16.7(it)21.4(ie)16.7(s)-394.6(o)0(f)]TJ
-22.7565 -1.2007 TD
[(th)18.5(e)-201.7(d)0(i)18.5(f)0(f)17.3(e)0(r)17.5(e)0(n)13.8(t)-202.7(si)17.3(ze)17.7(s)-201.1(i)0(n)]TJ
/F10 1 Tf
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(f)Tj
/F8 1 Tf
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(0)Tj
/F1 1 Tf
9.9626 0 0 9.9626 197.1212 332.9007 Tm
(;)Tj
/F6 1 Tf
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(n)Tj
/F8 1 Tf
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()Tj
/F1 1 Tf
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-11.0681 -1.195 TD
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(N)Tj
/F8 1 Tf
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()Tj
/F1 1 Tf
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[(19)15.5(68)15.5(6,)-200.3(th)18.5(e)-213.1(s)0(i)17.3(z)0(e)-210(o)0(f)-202.7(t)0(h)18.5(e)-213.1(ge)13.8(no)21.2(me)-206(of)-208.4(O)12.4(r)0(y)13.6(z)0(i)16.7(a)0(s)18.3(-)0(L)19.4(a)0(t)16.7(i)0(p)18.5(e)0(s)-203.7(\()0(t)16.5(h)0(e)-208.2(t)13.5(ot)18.5(al)-205.2(nu)15.5(mb)17.7(er)-204.5(of)-208.4(ge)19.4(ne)19.4(s\))18.1(.)]TJ
-11.9729 -1.2007 TD
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-1.0015 -1.2007 TD
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1.0015 -1.2007 TD
[(For)-253.9(each)-253.1(of)-253.9(these)-256(regions)-257.7(we)-251.9(dete)-9.4(rmine)-252.9(its)-253.7(weight)]TJ
/F6 1 Tf
20.2242 0 TD
(h)Tj
/F1 1 Tf
.7512 0 TD
[(and)-248.8(its)-253.7(norm)-8.6(alized)-254.5(leng)-7.6(th)]TJ
/F6 1 Tf
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(r)Tj
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[(,)-250.8(and)-254.5(then)-252.3(we)-257.6(calculat)-10.2(e)-252.9(its)]TJ
-32.806 -1.2007 TD
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1.0015 -1.2007 TD
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ET
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f
BT
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(1)Tj
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(2)Tj
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[(;)-259.6(hence,)]TJ
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(h)Tj
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(r)Tj
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()Tj
ET
124.441 239.584 17.461 .39685 re
f
BT
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(9)Tj
-.9999 -1.008 TD
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[(1,)-166.2(2)]TJ
/F18 1 Tf
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ET
146.041 215.66 3.515 .39685 re
f
BT
/F1 1 Tf
6.9738 0 0 6.9738 146.0409 217.0204 Tm
(1)Tj
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(2)Tj
9.9626 0 0 9.9626 149.5558 213.3921 Tm
[(;)-248.2(hence,)]TJ
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(h)Tj
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[(3.)-251.5(For)-248.2(this)-254.5(region)]TJ
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(r)Tj
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ET
287.206 215.66 17.461 .39685 re
f
BT
/F1 1 Tf
6.9738 0 0 6.9738 292.4786 217.0204 Tm
(22)Tj
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-20.0307 -1.2007 TD
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/F10 1 Tf
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(a)Tj
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()Tj
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(0.05.)Tj
-4.4671 -1.2007 TD
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/F18 1 Tf
40.6817 0 TD
()Tj
ET
531.666 191.735 3.515 .39685 re
f
BT
/F1 1 Tf
6.9738 0 0 6.9738 531.666 193.096 Tm
(1)Tj
0 -1.008 TD
(2)Tj
9.9626 0 0 9.9626 535.181 189.4676 Tm
(;)Tj
-42.9181 -1.2007 TD
[(hence)-9.2(,)]TJ
/F6 1 Tf
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(h)Tj
/F8 1 Tf
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[(2.)-240.1(The)-242.9(leng)-7.6(th)-237.6(of)-242.5(this)-243.1(region)-244.4(is)]TJ
/F6 1 Tf
12.0298 0 TD
(r)Tj
/F8 1 Tf
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()Tj
ET
288.51 179.773 17.461 .39685 re
f
BT
/F1 1 Tf
6.9738 0 0 6.9738 295.5401 181.1338 Tm
(3)Tj
-1.008 -1.008 TD
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9.9626 0 0 9.9626 308.3527 177.5054 Tm
[(and)-243.1(the)-245.8(p-value)-247(is)-238.8(0.0010)-9.9(4.)-240.1(The)-242.9(region)-244.4(is)-238.8(very)-245.8(signica)-9.9(nt.)]TJ
-19.1487 -1.2007 TD
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/F18 1 Tf
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()Tj
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(1,)Tj
ET
531.666 167.868 3.515 .39685 re
f
BT
6.9738 0 0 6.9738 531.666 169.1716 Tm
(1)Tj
0 -1.008 TD
(2)Tj
9.9626 0 0 9.9626 535.181 165.5433 Tm
(;)Tj
-42.9181 -1.2007 TD
[(hence)-9.2(,)]TJ
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[(3.5.)-417.7(Fo)-6.4(r)-412.5(this)-419.5(regi)-9.6(on)]TJ
/F6 1 Tf
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255.855 155.905 17.518 .39685 re
f
BT
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6.9738 0 0 6.9738 262.8849 157.2094 Tm
(7)Tj
-1.008 -1.008 TD
(19686)Tj
9.9626 0 0 9.9626 277.5117 153.5811 Tm
[(and)-419.5(its)-418.7(p-value)-423.4(is)-415.2(1.63)]TJ
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(10)Tj
/F8 1 Tf
7.4718 0 0 6.641 390.9542 158.0031 Tm
()Tj
/F1 1 Tf
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(5)Tj
9.9626 0 0 9.9626 400.4786 153.5811 Tm
[(.)-415.8(T)0(h)-7(erefore,)-421(this)-419.5(regi)-9.6(on)-416.9(is)-415.2(highly)]TJ
-29.3974 -1.2007 TD
[(signica)-9.9(nt.)]TJ
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/F18 1 Tf
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[(1,)-171.9(3)]TJ
/F18 1 Tf
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()Tj
ET
532.006 131.981 3.4583 .39685 re
f
BT
/F1 1 Tf
6.9738 0 0 6.9738 532.0062 133.285 Tm
(1)Tj
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9.9626 0 0 9.9626 535.4645 129.7133 Tm
(,)Tj
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[(and)-328.4(thus)]TJ
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ET
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BT
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[(and)-328.4(its)-327.7(p-value)-332.3(is)-329.8(1.27)]TJ
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(4)Tj
9.9626 0 0 9.9626 449.1211 117.7511 Tm
[(.)-324.7(T)0(h)-7(i)0(s)-324.2(region)-329.8(is)-329.8(hence)]TJ
-34.2799 -1.2007 TD
[(very)-336.9(signica)-9.9(nt.)]TJ
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307.446 84.132 17.461 .39685 re
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BT
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6.9738 0 0 6.9738 314.4188 85.4929 Tm
(3)Tj
-.9999 -1.0081 TD
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9.9626 0 0 9.9626 328.3086 81.8646 Tm
[(and)-345.5(its)-344.7(p)-6.5(-value)-348.6(is)-346.9(2.82)]TJ
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/F8 1 Tf
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/F1 1 Tf
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9.9626 0 0 9.9626 448.3842 81.8646 Tm
[(.)-347.5(This)-348.3(region)-346.8(is)-346.9(hence)]TJ
-34.2059 -1.2007 TD
[(very)-336.9(signica)-9.9(nt.)]TJ
/F2 1 Tf
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