%PDF-1.3 %âãÏÓ 1 0 obj << /Width 1 /Filter[/CCITTFaxDecode] /Type/XObject /Subtype/Image /ImageMask true /Length 4 /BitsPerComponent 1 /Decode[1 0] /Height 1 /DecodeParms[<>] >> stream € €endstream endobj 2 0 obj << /Length 3257 >> stream /GS4 gs BT /F0 1 Tf 20.66256 0 0 20.66256 171.24 641.88 Tm 0 g [(Rates)-389(of)-372(con)28(v)29(ergence)-379(for)-371(a)]TJ 0.16842 -1.20217 TD [(self-organizing)-367(sc)28(heme)-383(for)]TJ 1.66678 -1.20798 TD [(binary)-372(searc)29(h)-378(trees)]TJ /F1 1 Tf 14.34624 0 0 14.34624 136.68 559.32 Tm [([short)-316(title:)-410(Con)26(v)26(ergence)-309(rates)-316(for)-309(self-organizing)-299(trees])]TJ /F2 1 Tf 11.95517 0 0 11.95517 168.84 524.28 Tm [(by)-372(R)30(ober)70(t)-382(P.)-371(Dobr)19(o)20(w)-382(and)-382(James)-372(Allen)-381(Fill)]TJ /F3 1 Tf 7.97011 0 0 7.97011 437.64 528.6 Tm (1)Tj /F4 1 Tf 11.95517 0 0 11.95517 228 502.68 Tm [(The)-350(Johns)-341(Hopkins)-340(University)]TJ /F5 1 Tf 10.90909 0 0 10.90909 281.64 460.68 Tm (Abstract)Tj /F6 1 Tf -12.925 -1.573 TD [(The)-297(mo)33(v)33(e-to-ro)-33(ot)-352(heuristic)-308(is)-308(a)-319(self-organizing)-319(rule)-308(whic)33(h)-308(attempts)-319(to)]TJ 0 -1.243 TD [(k)33(eep)-363(a)-374(binary)-352(searc)33(h)-363(tree)-374(in)-363(near-optimal)-374(form.)-528(It)-363(is)-363(a)-363(tree)-363(analogue)]TJ T* [(of)-352(the)-352(mo)33(v)33(e-to-fron)33(t)-385(sc)33(heme)-352(\(also)-363(kno)33(wn)-352(as)-352(the)-352(w)33(eigh)33(ted)-363(random-to-)]TJ 0 -1.232 TD [(top)-352(card)-341(sh)33(u\017e)-341(or)-352(Tsetlin)-352(library\))-352(for)-341(self-organizing)-374(lists.)-495(W)88(e)-363(study)]TJ 0 -1.243 TD [(con)33(v)33(ergence)-319(of)-297(the)-297(mo)33(v)33(e-to-ro)-33(ot)-330(Mark)33(o)33(v)-308(c)33(hain)-297(to)-308(its)-297(stationary)-308(distri-)]TJ T* [(bution)-308(and)-297(sho)33(w)-319(that)-308(mo)33(v)33(e-to-ro)-33(ot)-352(con)33(v)33(erges)-330(t)33(w)33(o)-330(to)-319(four)-308(times)-308(faster)]TJ T* [(than)-374(mo)33(v)33(e-to-fron)33(t)-407(for)-374(man)33(y)-385(examples.)-583(W)88(e)-385(also)-385(discuss)-374(asymptotics)]TJ T* [(for)-363(exp)-33(ected)-363(searc)33(h)-374(cost.)-550(F)88(or)-374(equal)-363(w)33(eigh)33(ts,)]TJ /F7 1 Tf 19.734 0 Td (cn=)Tj /F6 1 Tf 1.694 0 Td (ln)Tj /F7 1 Tf 1.001 0 Td (n)Tj /F6 1 Tf 0.968 0 Td [(steps)-363(are)-363(neces-)]TJ -23.397 -1.243 TD [(sary)-330(and)-330(su\016cien)33(t)-341(to)-341(driv)33(e)-330(maxim)33(um)-330(relativ)33(e)-363(error)-330(to)-341(0.)]TJ ET q 155.52 0 0 -0.48 111.348 171.588 cm /Im1 Do Q BT /F8 1 Tf 6.97385 0 0 6.97385 124.8 163.68 Tm (1)Tj /F9 1 Tf 9.96264 0 0 9.96264 129.24 160.08 Tm [(Researc)24(h)-313(for)-338(b)-24(oth)-337(authors)-315(supp)-25(orted)-325(b)24(y)-338(NSF)-337(gran)24(t)-314(DMS-9311367.)]TJ /F8 1 Tf 6.97385 0 0 6.97385 124.8 151.8 Tm (2)Tj /F10 1 Tf 9.96264 0 0 9.96264 129.24 148.2 Tm [(AMS)-362(1991)-373(subje)50(ct)-362(classi\fc)50(ations.)]TJ /F9 1 Tf 14.94784 0 Td [(Primary)-302(60J10;)-312(secondary)-314(68P10,)-300(68P05.)]TJ /F8 1 Tf 6.97385 0 0 6.97385 124.8 139.8 Tm (3)Tj /F10 1 Tf 9.96264 0 0 9.96264 129.24 136.2 Tm [(Keywor)49(ds)-481(and)-482(phr)49(ases.)]TJ /F9 1 Tf 10.99708 0 Td [(Mark)23(o)25(v)-422(c)24(hains,)-470(con)25(v)24(ergence)-421(to)-458(stationarit)22(y)84(,)-458(self-organizing)]TJ -12.79179 -1.2045 TD [(searc)24(h,)-313(binary)-326(searc)24(h)-313(trees,)-326(mo)24(v)24(e-to-ro)-25(ot)-302(rule,)-325(mo)24(v)24(e-to-fron)23(t)-302(rule.)]TJ /F11 1 Tf 11.95517 0 0 11.95517 302.64 94.32 Tm (1)Tj ET endstream endobj 3 0 obj << /SA false /Type/ExtGState >> endobj 4 0 obj << /Length 7344 >> stream /GS4 gs BT /F12 1 Tf 17.21544 0 0 17.21544 111.36 644.28 Tm 0 g [(1)-1122(In)27(tro)-27(duction)-356(and)-377(Summary)]TJ /F11 1 Tf 11.95517 0 0 11.95517 111.36 618 Tm [(Supp)-30(ose)-402(that)-382(a)-381(collection)-400(of)]TJ /F13 1 Tf 12.54688 0 Td (n)Tj /F11 1 Tf 0.97364 0 Td [(records)-392(is)-392(arranged)-391(in)-392(a)-381(sequen)31(tial)-412(list.)-624(As-)]TJ -13.52051 -1.2045 TD [(so)-30(ciated)-432(with)-431(the)]TJ /F13 1 Tf 7.99989 0 Td (i)Tj /F11 1 Tf 0.33124 0 Td [(th)-422(record)-432(is)-432(a)-421(w)30(eigh)31(t)]TJ /F13 1 Tf 9.636 0 Td (y)Tj /F14 1 Tf 7.97011 0 0 7.97011 331.92 601.8 Tm (i)Tj /F11 1 Tf 11.95517 0 0 11.95517 340.32 603.6 Tm [(measuring)-432(the)-432(frequency)-440(of)-422(its)]TJ -19.15155 -1.21454 TD [(use.)-572(W)80(e)-371(assume)-391(that)]TJ /F13 1 Tf 9.51555 0 Td (y)Tj /F14 1 Tf 7.97011 0 0 7.97011 230.88 587.28 Tm (i)Tj /F13 1 Tf 11.95517 0 0 11.95517 238.44 589.08 Tm (>)Tj /F11 1 Tf 1.11416 0 Td [(0)-361(and)-371(normalize)-381(so)-372(that)]TJ /F15 1 Tf 9.96264 0 0 9.96264 379.92 597.12 Tm (P)Tj /F13 1 Tf 11.95517 0 0 11.95517 392.4 589.08 Tm (y)Tj /F14 1 Tf 7.97011 0 0 7.97011 398.16 587.28 Tm (i)Tj /F11 1 Tf 11.95517 0 0 11.95517 405.72 589.08 Tm [(=)-341(1.)-562(A)30(t)-382(eac)32(h)-372(unit)]TJ -24.62199 -1.2045 TD [(of)-412(time,)-451(indep)-30(enden)31(tly)-452(of)-412(all)-421(other)-422(mo)30(v)30(es,)-462(item)]TJ /F13 1 Tf 21.18916 0 Td (i)Tj /F11 1 Tf 0.75281 0 Td [(is)-432(remo)30(v)30(ed)-431(from)-422(the)-422(list)]TJ -21.94197 -1.21453 TD [(with)-321(probabilit)29(y)]TJ /F13 1 Tf 7.21696 0 Td (y)Tj /F14 1 Tf 7.97011 0 0 7.97011 203.4 558.36 Tm (i)Tj /F11 1 Tf 11.95517 0 0 11.95517 210.6 560.16 Tm [(and)-321(replaced)-330(at)-322(the)-321(fron)29(t)-321(of)-321(the)-322(list.)-442(This)-331(pro)-31(cess,)-331(whic)31(h)]TJ -8.30101 -1.2045 TD [(giv)30(es)-291(a)-271(Mark)30(o)30(v)-291(c)31(hain)-281(on)-281(the)-271(p)-30(erm)30(utation)-282(group)]TJ /F13 1 Tf 20.37612 0 Td (S)Tj /F14 1 Tf 7.97011 0 0 7.97011 362.16 543.96 Tm (n)Tj /F11 1 Tf 11.95517 0 0 11.95517 367.8 545.76 Tm [(,)-281(is)-282(kno)31(wn)-291(as)-281(the)-281(mo)30(v)30(e-to-)]TJ -21.45014 -1.2045 TD [(fron)30(t)-282((MTF))-282(heuristic)-292(for)-271(self-organizing)-281(lists.)-433(Other)-281(names)-291(are)-281(the)-281(w)30(eigh)31(ted)]TJ 0 -1.21454 TD [(random-to-top)-272(card)-281(sh)29(u\017e,)-300(the)-281(Tsetlin)-302(library)80(,)-291(and)-281(the)-281(heaps)-291(pro)-31(cess.)-431(Bac)31(k-)]TJ 0 -1.2045 TD [(ground)-351(references)-381(for)-342(this)-362(mo)-30(del)-361(include)-361(Riv)31(est)-372((1976),)-352(Bitner)-361((1979),)-352(Hen-)]TJ T* [(dric)30(ks)-311((1989),)-292(and)-291(Fill)-291((1993).)-412(Fill)-292((1993))-281(and)-291(Diaconis)-290((1993))-282(study)-312(rates)-291(of)]TJ 0 -1.21454 TD [(con)31(v)30(ergence)-350(for)-322(MTF)-331(under)-342(v)50(arious)-321(assumptions)-353(on)-321(the)-331(w)30(eigh)31(ts.)]TJ 1.46548 -1.2045 TD [(There)-250(has)-251(b)-31(een)-240(recen)31(t)-261(in)30(terest)-252(in)-241(self-organizing)-241(rules)-251(for)-242(other)-241(data)-231(struc-)]TJ -1.46548 -1.21454 TD [(tures.)-754(In)-432(particular,)-462(the)-432(binary)-432(searc)31(h)-442(tree)-442(is)-432(a)-431(commonly)-441(used)-432(structure)]TJ 0 -1.2045 TD [(whic)31(h)-321(exploits)-312(the)-311(ordering)-311(of)-301(records)-312(to)-301(ac)30(hiev)31(e)-321(faster)-312(searc)30(h)-321(time.)-432(Records)]TJ T* [(are)-381(stored)-382(at)-372(the)-382(no)-30(des)-391(of)-371(a)-372(tree)-391(in)-382(suc)30(h)-391(a)-371(w)30(a)30(y)-391(that)-372(a)-381(tra)29(v)30(ersal)-391(of)-372(the)-381(tree)]TJ 0 -1.21454 TD [(pro)-30(duces)-341(the)-332(records)-331(in)-332(their)-331(linear)-331(order.)]TJ 1.46548 -1.2045 TD [(Allen)-270(and)-251(Munro)-262((1978))-241(in)30(tro)-31(duced)-270(the)-261(mo)30(v)30(e-to-ro)-30(ot)-241((MTR))-262(heuristic)-272(for)]TJ -1.46548 -1.2045 TD [(binary)-311(searc)30(h)-321(trees.)-443(Dobro)31(w)-311(and)-311(Fill)-302((1993))-301(sho)30(w)-321(that)-302(the)-321(Mark)29(o)31(v)-321(c)30(hain)-311(for)]TJ 0 -1.21454 TD [(MTR)-341(can)-331(b)-30(e)-341(deriv)30(ed)-351(b)31(y)-342(lumping)-341(the)-341(Mark)29(o)31(v)-342(c)31(hain)-341(for)-332(MTF)-341(and)-332(determine)]TJ 0 -1.2045 TD [(n)30(umerous)-342(c)31(haracteristics)-353(of)-321(the)-331(c)31(hain.)]TJ 1.46548 -1.21454 TD [(In)-342(Section)-340(2)-342(w)31(e)-341(review)-350(binary)-342(searc)30(h)-351(trees)-352(and)-331(giv)30(e)-351(some)-341(of)-331(the)-341(relev)50(an)31(t)]TJ -1.46548 -1.2045 TD [(results)-383(from)-362(previous)-381(w)30(ork.)-572(\(See)-371(Dobro)30(w)-361(and)-371(Fill)-362((1993))-362(for)-361(more)-372(details.\))]TJ T* [(In)-332(Section)-340(3)-331(w)30(e)-341(analyze)-340(the)-331(con)30(v)31(ergence)-361(of)-321(the)-341(MTR)-331(c)31(hain)-342(to)-331(its)-332(stationary)]TJ 0 -1.21454 TD [(distribution.)-494(Roughly)81(,)-351(the)-351(results)-353(are)-341(as)-352(follo)31(ws.)-492(F)80(or)-332(most)-352(w)31(eigh)30(t)-352(classes,)-371(if)]TJ /F13 1 Tf 0 -1.2045 TD (k)Tj /F11 1 Tf 0.8833 0 Td [(steps)-352(are)-341(necessary)-362(and)-341(su\016cien)31(t)-362(for)-332(con)31(v)30(ergence)-360(of)-331(MTF)-352(with)-341(resp)-31(ect)-351(to)]TJ -0.8833 -1.21454 TD [(total)-292(v)51(ariation)-292(distance,)-321(then)]TJ /F13 1 Tf 12.64725 0 Td 0.03 Tc (k=)Tj /F11 1 Tf 1.03386 0 Td 0 Tc [(2)-291(steps)-322(are)-291(su\016cien)30(t)-321(for)-292(MTR)-301(and)]TJ /F13 1 Tf 14.86554 0 Td 0.03 Tc (k=)Tj /F11 1 Tf 1.03386 0 Td 0 Tc [(4)-291(steps)]TJ -29.58051 -1.2045 TD [(are)-351(necessary)80(.)-542(These)-371(b)-30(ounds)-361(are)-352(gotten)-351(b)30(y)-371(common)-361(tec)31(hniques:)-512(Su\016ciency)]TJ T* [(is)-472(pro)30(v)30(en)-482(b)30(y)-481(exhibiting)-482(a)-462(natural)-472(coupling)-471(of)-472(the)-472(MTR)-471(c)31(hain.)-874(Necessit)31(y)]TJ 0 -1.21454 TD [(is)-422(sho)30(wn)-431(b)30(y)-432(iden)31(tifying)-432(a)-412(sp)-30(eci\fc)-441(ev)31(en)30(t)-432(from)-422(whic)31(h)-432(v)51(ariation)-412(distance)-432(can)]TJ 0 -1.2045 TD [(b)-30(e)-411(suitably)-423(b)-30(ounded)-421(from)-402(b)-30(elo)31(w.)-692(W)80(e)-421(ha)30(v)30(e)-421(b)-30(een)-411(unable)-421(to)-402(bridge)-421(the)-412(gap)]TJ T* [(b)-30(et)30(w)30(een)]TJ /F13 1 Tf 3.78414 0 Td 0.03 Tc (k=)Tj /F11 1 Tf 1.03386 0 Td 0 Tc [(4)-321(and)]TJ /F13 1 Tf 2.71013 0 Td 0.03 Tc (k=)Tj /F11 1 Tf 1.03386 0 Td 0 Tc (2.)Tj -7.09651 -1.21454 TD [(In)-392(Section)-401(4)-381(w)30(e)-401(study)-402(con)31(v)30(ergence)-410(of)-382(exp)-30(ected)-410(searc)30(h)-402(cost,)-412(the)-391(a)30(v)30(erage)]TJ -1.46548 -1.2045 TD [(cost)-362(of)-351(accessing)-371(a)-351(record.)-522(In)-361(the)-362(case)-361(of)-351(equal)-361(w)31(eigh)30(ts)-372(\()]TJ /F13 1 Tf 24.43127 0 Td (p)Tj /F14 1 Tf 7.97011 0 0 7.97011 409.32 153.96 Tm (i)Tj /F16 1 Tf 11.95517 0 0 11.95517 416.52 155.76 Tm <11>Tj /F11 1 Tf 1.10413 0 Td (1)Tj /F13 1 Tf 0.49184 0 Td (=n)Tj /F11 1 Tf 1.07401 0 Td [(\))-352(w)31(e)-371(sho)30(w)]TJ -28.19534 -1.21454 TD (that)Tj /F13 1 Tf 2.05769 0 Td (cn=)Tj /F11 1 Tf 1.66622 0 Td (ln)Tj /F13 1 Tf 0.98367 0 Td (n)Tj /F11 1 Tf 0.84315 0 Td [(steps)-282(are)-271(necessary)-281(and)-271(su\016cien)31(t)-292(to)-261(driv)30(e)-271(the)-271(maxim)30(um)-281(relativ)30(e)]TJ -5.55074 -1.2045 TD [(error)-322(to)-331(0.)]TJ 15.99977 -3.80421 TD (2)Tj ET endstream endobj 5 0 obj << /Length 6755 >> stream /GS4 gs BT /F12 1 Tf 17.21544 0 0 17.21544 111.36 644.28 Tm 0 g [(2)-1122(Binary)-376(searc)28(h)-363(trees)-362(and)-377(mo)28(v)28(e-to-ro)-28(ot)]TJ /F11 1 Tf 11.95517 0 0 11.95517 111.36 618 Tm (A)Tj /F4 1 Tf 1.07401 0 Td [(binary)-360(tr)50(e)51(e)]TJ /F11 1 Tf 4.93845 0 Td [(is)-352(a)-341(\fnite)-351(tree)-342(with)-351(at)-342(most)-352(t)30(w)31(o)-352(\\c)31(hildren")-351(for)-342(eac)31(h)-351(no)-30(de)-351(and)]TJ -6.01246 -1.2045 TD [(in)-361(whic)30(h)-371(eac)31(h)-371(c)30(hild)-371(is)-362(distinguished)-382(as)-362(either)-372(a)-361(left)-351(or)-362(righ)30(t)-362(c)31(hild.)-542(Consider)]TJ 0 -1.21454 TD [(a)-351(binary)-352(tree)-361(in)-351(whic)30(h)-361(the)-361(no)-30(des)-352(are)-351(lab)-30(eled)-361(with)-351(elemen)31(ts)-382(of)-341(some)-362(linearly)]TJ 0 -1.2045 TD [(ordered)-381(set.)-603(Inorder)-392(tra)29(v)30(ersal)-391(is)-382(a)-382(common)-380(metho)-30(d)-382(for)-382(tra)30(v)30(ersing)-392(the)-381(tree:)]TJ 0 -1.21453 TD [(visit)-503(the)-492(ro)-30(ot)-472(after)-492(visiting)-493(the)-502(left)-482(subtree)-502(and)-492(b)-30(efore)-491(visiting)-503(the)-492(righ)30(t)]TJ 0 -1.2045 TD [(subtree.)-442(If)-312(this)-312(tra)30(v)30(ersal)-322(yields)-321(the)-311(lab)-30(els)-311(in)-302(order,)-321(the)-311(tree)-312(is)-311(called)-310(a)]TJ /F4 1 Tf 29.81137 0 Td (binary)Tj -29.81137 -1.2045 TD [(se)51(ar)51(ch)-291(tr)51(e)50(e.)]TJ /F11 1 Tf 5.15928 0 Td [(F)80(or)-261(example,)-301(the)-271(set)-271(of)-271(all)-261(binary)-281(searc)30(h)-281(trees)-282(on)-260(3)-271(no)-30(des)-271(is)-282(giv)31(en)]TJ -5.15927 -1.21454 TD -0.03 Tc [(by)-30(:)]TJ 14.32351 -8.25082 TD 0 Tc [(Figure)-332(1.)]TJ -12.85804 -2.28855 TD [(Consider)-311(the)-311(ordered,)-312(indexed)-310(set)-312(of)-291([)]TJ /F13 1 Tf 15.94959 0 Td (n)Tj /F11 1 Tf 0.58217 0 Td 0.281 Tc [(]:)281(=)]TJ /F16 1 Tf 1.86698 0 Td 0 Tc (f)Tj /F11 1 Tf 0.50187 0 Td (1)Tj /F13 1 Tf 0.49184 0 Td (;)Tj /F11 1 Tf 0.44165 0 Td (2)Tj /F13 1 Tf 0.49184 0 Td 0.171 Tc [(;:)1(::)31(;n)]TJ /F16 1 Tf 2.76031 0 Td 0 Tc (g)Tj /F11 1 Tf 0.803 0 Td (of)Tj /F13 1 Tf 1.08405 0 Td (n)Tj /F11 1 Tf 0.8833 0 Td [(records.)-442(Let)]TJ /F13 1 Tf -27.32207 -1.21454 TD (B)Tj /F14 1 Tf 7.97011 0 0 7.97011 120.24 374.52 Tm (n)Tj /F11 1 Tf 11.95517 0 0 11.95517 129.24 376.32 Tm [(b)-30(e)-291(the)-291(set)-292(of)-271(all)-290(lab)-30(eled)-291(binary)-291(searc)30(h)-291(trees)-302(on)]TJ /F13 1 Tf 19.69357 0 Td (n)Tj /F11 1 Tf 0.86323 0 Td [(no)-30(des.)-432(It)-281(is)-292(easy)-301(to)-281(sho)30(w)]TJ -22.05239 -1.2045 TD (that)Tj /F16 1 Tf 2.0878 0 Td (j)Tj /F13 1 Tf 0.28105 0 Td (B)Tj /F14 1 Tf 7.97011 0 0 7.97011 148.56 360.12 Tm (n)Tj /F16 1 Tf 11.95517 0 0 11.95517 154.2 361.92 Tm (j)Tj /F11 1 Tf 0.55206 0 Td (=)Tj /F15 1 Tf 9.96264 0 0 9.96264 173.4 373.44 Tm <10>Tj /F3 1 Tf 7.97011 0 0 7.97011 179.4 367.2 Tm (2)Tj /F14 1 Tf 0.52697 0 Td (n)Tj -0.27101 -1.17439 TD (n)Tj /F15 1 Tf 9.96264 0 0 9.96264 188.76 373.44 Tm <11>Tj /F13 1 Tf 11.95517 0 0 11.95517 198.24 361.92 Tm (=)Tj /F11 1 Tf 0.49184 0 Td (\()Tj /F13 1 Tf 0.38142 0 Td (n)Tj /F11 1 Tf 0.73274 0 Td 0.15 Tc [(+1)150(\))]TJ /F13 1 Tf 1.78667 0 Td 0 Tc (;)Tj /F11 1 Tf 0.57214 0 Td [(whic)31(h)-301(is)-302(the)]TJ /F13 1 Tf 5.37006 0 Td (n)Tj /F11 1 Tf 0.58218 0 Td [(th)-302(Catalan)-290(n)30(um)30(b)-30(er.)-442(In)-291(what)-301(follo)30(ws)]TJ -17.1842 -1.2045 TD [(w)30(e)-340(use)-332(the)-331(term)-332(\\tree")-331(for)-321(binary)-332(searc)30(h)-341(tree.)]TJ 1.46548 -1.81679 TD (The)Tj /F4 1 Tf 2.11791 0 Td [(move-to-r)51(o)50(ot)]TJ /F11 1 Tf 5.7816 0 Td [((MTR))-432(op)-30(eration)-422(is)-442(de\fned)-431(as)-432(a)-421(series)-442(of)-422(simple)-442(ex-)]TJ -9.36499 -1.2045 TD [(c)30(hanges)-441(b)-30(et)30(w)31(een)-441(no)-30(des.)-743(A)]TJ /F4 1 Tf 12.19556 0 Td [(simple)-431(exchange)]TJ /F11 1 Tf 7.36753 0 Td [(for)-422(a)-421(requested)-452(record)]TJ /F13 1 Tf 10.08769 0 Td (j)Tj /F11 1 Tf 0.89334 0 Td [(is)-432(as)]TJ -30.54411 -1.21454 TD [(follo)30(ws:)]TJ 1.46548 -1.2045 TD [((i))-332(Do)-321(nothing)-321(if)]TJ /F13 1 Tf 7.41771 0 Td (j)Tj /F11 1 Tf 0.78292 0 Td [(is)-332(the)-331(ro)-30(ot.)]TJ -8.20064 -1.2045 TD [((ii))-432(If)]TJ /F13 1 Tf 2.82054 0 Td (j)Tj /F11 1 Tf 0.8833 0 Td [(is)-442(the)-432(left)-432(c)31(hild)-432(of)-431(its)-433(paren)30(t)]TJ /F13 1 Tf 13.01864 0 Td (m)Tj /F11 1 Tf 0.85319 0 Td [(,)-462(the)-431(resulting)-443(tree)-432(will)-431(b)-30(e)-431(the)]TJ -19.04113 -1.21454 TD [(same)-452(as)-442(the)-441(original)-442(except)-451(for)-442(the)-442(subtree)-462(whose)-451(ro)-30(ot)-432(w)30(as)]TJ /F13 1 Tf 26.68971 0 Td (m)Tj /F11 1 Tf 0.85319 0 Td [(.)-783(Record)]TJ /F13 1 Tf 4.4968 0 Td (j)Tj /F11 1 Tf -32.0397 -1.2045 TD [(is)-412(\\rotated")-402(up)-411(to)]TJ /F13 1 Tf 8.32109 0 Td (m)Tj /F11 1 Tf 1.26473 0 Td [(so)-412(that)]TJ /F13 1 Tf 3.48301 0 Td (j)Tj /F11 1 Tf 0.87326 0 Td [(b)-30(ecomes)-421(the)-411(ro)-31(ot)-402(of)-401(this)-412(subtree.)-694(The)-420(old)]TJ -13.94209 -1.21454 TD [(left)-372(subtree)-382(of)]TJ /F13 1 Tf 6.38385 0 Td (j)Tj /F11 1 Tf 0.82307 0 Td [(do)-30(esn't)-382(c)31(hange)-371(in)-372(relation)-371(to)]TJ /F13 1 Tf 12.77774 0 Td (j)Tj /F11 1 Tf 0.46173 0 Td [(.)-562(The)-371(old)-371(righ)30(t)-372(subtree)-382(of)]TJ /F13 1 Tf 11.59331 0 Td (j)Tj /F11 1 Tf -32.0397 -1.2045 TD [(b)-30(ecomes)-351(the)-331(left)-341(subtree)-342(of)]TJ /F13 1 Tf 11.87436 0 Td (m)Tj /F11 1 Tf 0.85319 0 Td [(.)-462(The)-340(old)-331(righ)29(t)-341(subtree)-342(of)]TJ /F13 1 Tf 11.3223 0 Td (m)Tj /F11 1 Tf 1.19446 0 Td [(k)30(eeps)-351(its)-342(relation)]TJ -25.24431 -1.2045 TD (to)Tj /F13 1 Tf 1.19446 0 Td (m)Tj /F11 1 Tf 0.85319 0 Td [(.)-442(The)-330(transformation)-333(is)-332(b)-30(est)-332(understo)-31(o)-29(d)-332(b)30(y)-341(examining)-330(Figure)-332(2-L.)]TJ -0.58217 -1.21454 TD [((iii))-402(If)]TJ /F13 1 Tf 3.03132 0 Td (j)Tj /F11 1 Tf 0.85319 0 Td [(is)-402(the)-401(righ)29(t)-402(c)31(hild)-412(of)]TJ /F13 1 Tf 8.87315 0 Td (m)Tj /F11 1 Tf 0.85319 0 Td [(,)-422(p)-30(erform)-392(the)-401(analogous)-401(transformation.)]TJ -15.07632 -1.2045 TD [(\(See)-331(Figure)-331(2-R.\))]TJ 1.46548 -1.2045 TD [(The)-401(MTR)-391(op)-30(eration)-391(p)-31(erforms)-392(a)-381(sequence)-421(of)-381(simple)-402(exc)31(hanges)-411(un)30(til)-392(the)]TJ -1.46548 -1.21454 TD [(requested)-291(record)-281(is)-282(mo)31(v)30(ed)-291(to)-271(the)-271(ro)-31(ot)-271(of)-271(the)-271(tree.)-432(F)80(or)]TJ /F13 1 Tf 22.75501 0 Td (n)Tj /F11 1 Tf 0.58218 0 Td [(-no)-30(de)-271(trees)-281(it)-282(is)-281(easily)]TJ -23.33719 -1.2045 TD [(sho)30(wn)-381(that)-372(the)-372(sequence)-400(of)-361(op)-30(erations)-372(generated)-381(b)30(y)-382(MTR)-371(giv)31(es)-392(an)-371(ergo)-30(dic)]TJ 15.99977 -3.5332 TD (3)Tj ET endstream endobj 6 0 obj << /Length 9109 >> stream /GS4 gs BT /F11 1 Tf 11.95517 0 0 11.95517 111.36 644.28 Tm 0 g [(\(ap)-30(erio)-30(dic,)-442(irreducible,)-461(and)-422(p)-30(ositiv)30(e)-432(recurren)30(t\))-442(Mark)29(o)31(v)-432(c)31(hain)-432(on)-411(the)-432(space)]TJ /F13 1 Tf 0 -1.2045 TD (B)Tj /F14 1 Tf 7.97011 0 0 7.97011 120.24 628.08 Tm (n)Tj /F11 1 Tf 11.95517 0 0 11.95517 125.88 629.88 Tm (.)Tj 13.10897 -7.75899 TD [(Figure)-332(2.)]TJ -12.85804 -2.38892 TD -0.08 Tc [(Fo)-80(r)]TJ /F13 1 Tf 1.77664 0 Td 0 Tc (T)Tj /F16 1 Tf 1.02383 0 Td (2)Tj /F13 1 Tf 0.98367 0 Td (B)Tj /F14 1 Tf 7.97011 0 0 7.97011 183 506.76 Tm (n)Tj /F11 1 Tf 11.95517 0 0 11.95517 192.84 508.56 Tm (and)Tj /F13 1 Tf 1.9272 0 Td (i)Tj /F16 1 Tf 0.65244 0 Td (6)Tj /F11 1 Tf (=)Tj /F13 1 Tf 1.07401 0 Td (j)Tj /F11 1 Tf 0.46173 0 Td [(,)-361(w)30(e)-351(sa)30(y)-361(that)]TJ /F13 1 Tf 5.95224 0 Td (i)Tj /F11 1 Tf 0.68255 0 Td [(is)-352(an)]TJ /F4 1 Tf 2.38892 0 Td [(anc)51(estor)]TJ /F11 1 Tf 3.99492 0 Td (of)Tj /F13 1 Tf 1.13424 0 Td (j)Tj /F11 1 Tf 0.81304 0 Td (in)Tj /F13 1 Tf 1.16435 0 Td (T)Tj /F11 1 Tf 0.71266 0 Td [(,)-351(and)-352(write)]TJ /F13 1 Tf -27.77376 -1.2045 TD 0.392 Tc (i<)Tj /F14 1 Tf 7.97011 0 0 7.97011 129.12 498.48 Tm 0 Tc (T)Tj 0 -0.91843 TD (a)Tj /F13 1 Tf 11.95517 0 0 11.95517 140.28 494.16 Tm (j)Tj /F11 1 Tf 0.46172 0 Td 0.402 Tc [(,i)402(f)]TJ /F13 1 Tf 1.63611 0 Td 0 Tc (j)Tj /F11 1 Tf 0.85319 0 Td [(is)-392(an)-391(elemen)31(t)-412(of)-381(the)-392(subtree)-402(whic)31(h)-412(has)]TJ /F13 1 Tf 17.24442 0 Td (i)Tj /F11 1 Tf 0.7227 0 Td [(as)-392(its)-402(ro)-30(ot.)-613(A)-391(tree)-392(is)]TJ -23.33718 -1.21454 TD [(uniquely)-351(determined)-341(b)30(y)-331(its)-332(ancestry)-352(relations.)]TJ 1.46548 -1.2045 TD [(A)-411(k)30(ey)-421(observ)50(ation)-402(for)-402(analyzing)-410(MTR)-412(is)-412(based)-411(on)-401(Lemma)-412(3.2)-401(in)-412(Allen)]TJ -1.46548 -1.21454 TD [(and)-331(Munro)-332((1978),)-311(whic)30(h)-341(w)31(e)-341(repro)-31(duce,)-340(with)-332(a)-321(sligh)30(t)-331(extension:)]TJ /F17 1 Tf 0 -1.78667 TD [(Lemma)-392(2.1)]TJ /F4 1 Tf 5.91209 0 Td [(Supp)50(ose)-300(r)51(e)50(c)51(or)51(d)]TJ /F13 1 Tf 6.52437 0 Td (i)Tj /F4 1 Tf 0.65244 0 Td [(has)-300(b)50(e)51(en)-311(r)50(e)51(queste)51(d)-311(at)-311(le)51(ast)-311(onc)50(e)-300(in)-312(a)-311(tr)51(e)50(e)-321(mo)51(d-)]TJ -13.0889 -1.2045 TD [(i\fe)50(d)-381(ac)51(c)50(or)51(ding)-371(to)-392(MTR.)-391(If)]TJ /F13 1 Tf 11.74387 0 Td 0.342 Tc [(i<)-9(j)342(;)]TJ /F4 1 Tf 2.85065 0 Td 0 Tc (then)Tj /F13 1 Tf 2.20825 0 Td 0.352 Tc (i<)Tj /F14 1 Tf 7.97011 0 0 7.97011 329.52 413.16 Tm 0 Tc (a)Tj /F13 1 Tf 11.95517 0 0 11.95517 338.64 414.96 Tm (j)Tj /F4 1 Tf 0.85319 0 Td [(if)-382(and)-381(only)-391(if)-382(the)-391(most)-381(r)51(e)50(c)51(ent)]TJ -19.86421 -1.21454 TD [(r)51(e)50(quest)-420(for)]TJ /F13 1 Tf 4.96856 0 Td (i)Tj /F4 1 Tf 0.75281 0 Td [(has)-411(o)51(c)50(curr)51(e)51(d)-421(sinc)50(e)-411(the)-411(most)-421(r)50(e)51(c)50(ent)-421(r)50(e)51(quest)-421(\(if)-411(any\))-421(for)-411(any)-421(of)]TJ /F13 1 Tf -5.72137 -1.2045 TD (i)Tj /F11 1 Tf 0.60225 0 Td 0.261 Tc (+1)Tj /F13 1 Tf 1.51566 0 Td 0.171 Tc [(;:)1(::)10(;)1(j)]TJ /F4 1 Tf 2.65994 0 Td 0 Tc [(.)-622(Similarly,)-422(if)]TJ /F13 1 Tf 6.49426 0 Td 0.392 Tc [(i>)1(j)]TJ /F4 1 Tf 2.33874 0 Td 0 Tc [(,)-422(then)]TJ /F13 1 Tf 2.95103 0 Td 0.392 Tc (i<)Tj /F14 1 Tf 7.97011 0 0 7.97011 327.12 384.24 Tm 0 Tc (a)Tj /F13 1 Tf 11.95517 0 0 11.95517 336.84 386.04 Tm (j)Tj /F4 1 Tf 0.86322 0 Td [(if)-412(and)-401(only)-411(if)-412(the)-401(most)-411(r)50(e)51(c)50(ent)]TJ -19.72368 -1.2045 TD [(r)51(e)50(quest)-310(for)]TJ /F13 1 Tf 4.74774 0 Td (i)Tj /F4 1 Tf 0.6424 0 Td [(has)-310(o)50(c)50(curr)52(e)50(d)-311(sinc)51(e)-301(the)-311(most)-310(r)50(e)51(c)50(ent)-311(r)51(e)50(quest)-310(for)-311(any)-310(of)]TJ /F13 1 Tf 22.36355 0 Td 0.17 Tc [(j)170(;:)-1(::)9(;)-1(i)]TJ /F16 1 Tf 3.07147 0 Td 0 Tc <00>Tj /F11 1 Tf 0.91341 0 Td (1)Tj /F13 1 Tf 0.49184 0 Td (:)Tj /F17 1 Tf -32.23041 -1.79671 TD [(Pro)-30(of)]TJ /F11 1 Tf 3.34249 0 Td [(When)-291(either)-291(simple)-301(exc)31(hange)-300(or)-282(MTR)-291(is)-291(used,)-301(if)]TJ /F13 1 Tf 20.72744 0 Td (i)Tj /F11 1 Tf 0.62233 0 Td [(is)-292(requested)-311(then)]TJ /F13 1 Tf 7.47794 0 Td (i)Tj /F11 1 Tf -32.17019 -1.2045 TD [(is)-261(the)-251(only)-261(record)-261(whic)31(h)]TJ /F4 1 Tf 10.24829 0 Td [(b)50(e)51(c)50(omes)]TJ /F11 1 Tf 3.68376 0 Td [(an)-251(ancestor)-261(of)-251(an)30(y)-261(records.)-421(Also,)]TJ /F13 1 Tf 14.0525 0 Td (i)Tj /F11 1 Tf 0.59221 0 Td (will)Tj /F4 1 Tf 1.77664 0 Td [(c)51(e)50(ase)]TJ /F11 1 Tf -30.3534 -1.21454 TD [(to)-372(b)-30(e)-371(an)-371(ancestor)-382(of)]TJ /F13 1 Tf 9.09398 0 Td 0.411 Tc [(j>)60(i)]TJ /F11 1 Tf 2.63986 0 Td 0 Tc [(if)-372(and)-371(only)-371(if)-372(an)-371(elemen)31(t)]TJ /F13 1 Tf 11.09144 0 Td (k)Tj /F11 1 Tf 0.54202 0 Td [(,)-381(where)]TJ /F13 1 Tf 3.52316 0 Td 0.362 Tc [(i<)11(k)]TJ /F16 1 Tf 2.70009 0 Td 0 Tc <14>Tj /F13 1 Tf 1.13424 0 Td (j)Tj /F11 1 Tf 0.46173 0 Td 0.381 Tc [(,i)381(s)]TJ -31.18651 -1.2045 TD 0 Tc [(requested.)-462(This)-341(giv)30(es)-341(the)-331(\frst)-333(part)-322(of)-331(the)-331(lemma.)-442(The)-340(second)-341(part)-322(is)-332(sho)30(wn)]TJ T* [(similarly)80(.)]TJ ET q 6.24 0 0 -6.24 493.668 298.668 cm /Im1 Do Q BT /F11 1 Tf 11.95517 0 0 11.95517 128.88 256.32 Tm [(Consider)-391(the)-382(op)-30(eration)-371(of)-372(inserting)-392(records)-392(in)30(to)-371(an)-382(initially)-381(empt)30(y)-392(tree.)]TJ -1.46548 -1.2045 TD [(This)-462(de\fnes)-471(a)-452(mapping)]TJ /F13 1 Tf 10.80035 0 Td (t)Tj /F11 1 Tf 0.84315 0 Td (:)Tj /F13 1 Tf 0.76285 0 Td (S)Tj /F14 1 Tf 7.97011 0 0 7.97011 266.88 240.12 Tm (n)Tj /F16 1 Tf 11.95517 0 0 11.95517 278.4 241.92 Tm (!)Tj /F13 1 Tf 1.49559 0 Td (B)Tj /F14 1 Tf 7.97011 0 0 7.97011 305.16 240.12 Tm (n)Tj /F11 1 Tf 11.95517 0 0 11.95517 316.2 241.92 Tm [(where)-461(for)]TJ /F13 1 Tf 4.5771 0 Td <1B>Tj /F16 1 Tf 1.08405 0 Td (2)Tj /F13 1 Tf 1.15431 0 Td (S)Tj /F14 1 Tf 7.97011 0 0 7.97011 404.88 240.12 Tm (n)Tj /F11 1 Tf 11.95517 0 0 11.95517 410.52 241.92 Tm (,)Tj /F13 1 Tf 0.76285 0 Td (t)Tj /F11 1 Tf 0.35131 0 Td (\()Tj /F13 1 Tf 0.38143 0 Td <1B>Tj /F11 1 Tf 0.59221 0 Td [(\))-452(is)-462(the)-452(tree)]TJ -27.11128 -1.2045 TD [(obtained)-291(b)30(y)-301(successiv)30(ely)-331(inserting)-301(records)]TJ /F13 1 Tf 17.92697 0 Td <1B>Tj /F3 1 Tf 7.97011 0 0 7.97011 332.28 225.72 Tm (1)Tj /F13 1 Tf 11.95517 0 0 11.95517 337.08 227.52 Tm 0.171 Tc [(;:)1(::)20(;)1<1B>]TJ /F14 1 Tf 7.97011 0 0 7.97011 369.84 225.72 Tm 0 Tc (n)Tj /F11 1 Tf 11.95517 0 0 11.95517 378.96 227.52 Tm [(in)30(to)-291(an)-291(empt)30(y)-301(tree.)-432(Do-)]TJ -22.38362 -1.21454 TD [(bro)30(w)-321(and)-321(Fill)-322((1993))-301(sho)30(w)-331(that)-312(the)-331(MTR)-321(c)30(hain)-321(can)-320(b)-31(e)-320(obtained)-321(b)30(y)-331(lumping)]TJ 0 -1.2045 TD [(the)-331(MTF)-332(c)31(hain)-332(with)-341(resp)-31(ect)-330(to)-332(the)-331(mapping)]TJ /F13 1 Tf 19.33222 0 Td (t)Tj /F11 1 Tf 0.35131 0 Td [(.)-432(In)-331(particular,)]TJ /F17 1 Tf -18.21806 -1.81679 TD [(Theorem)-512(0)]TJ /F4 1 Tf 6.38385 0 Td -0.05 Tc [(Le)-50(t)]TJ /F13 1 Tf 1.79671 0 Td 0 Tc (Q)Tj /F4 1 Tf 1.21454 0 Td [(denote)-451(the)-441(tr)50(ansition)-452(matrix)-441(for)-451(MTR)-451(and)]TJ /F13 1 Tf 19.15155 0 Td (P)Tj /F4 1 Tf 1.21454 0 Td (the)Tj -31.22666 -1.2045 TD [(tr)50(ansition)-311(matrix)-320(for)-311(MTF.)-311(L)49(et)]TJ /F11 1 Tf 13.55062 0 Td <0528>Tj /F13 1 Tf 1.11416 0 Td (T)Tj /F11 1 Tf 0.71266 0 Td (\))Tj /F4 1 Tf 0.69259 0 Td [(denote)-311(the)-321(set)-320(of)-311(p)50(ermutations)-310(that)-321(ar)50(e)]TJ -16.07004 -1.2045 TD [(mapp)51(e)50(d)-341(to)-351(a)-342(given)-340(tr)50(e)51(e)]TJ /F13 1 Tf 9.9572 0 Td (T)Tj /F4 1 Tf 1.06397 0 Td (by)Tj /F13 1 Tf 1.27476 0 Td (t)Tj /F4 1 Tf 0.35131 0 Td [(.)-452(Then)-340(for)]TJ /F13 1 Tf 4.86819 0 Td [(S;)-171(T)]TJ /F16 1 Tf 2.02758 0 Td (2)Tj /F13 1 Tf 0.94352 0 Td (B)Tj /F14 1 Tf 7.97011 0 0 7.97011 365.16 146.28 Tm (n)Tj /F4 1 Tf 11.95517 0 0 11.95517 375 148.08 Tm (and)Tj /F13 1 Tf 1.90712 0 Td (k)Tj /F16 1 Tf 0.81304 0 Td <15>Tj /F11 1 Tf 1.05394 0 Td (0)Tj /F4 1 Tf 0.49184 0 Td (,)Tj /F13 1 Tf -19.48278 -1.77664 TD (Q)Tj /F14 1 Tf 7.97011 0 0 7.97011 202.32 131.76 Tm (k)Tj /F11 1 Tf 11.95517 0 0 11.95517 207.48 126.84 Tm (\()Tj /F13 1 Tf 0.38142 0 Td [(S;)-171(T)]TJ /F11 1 Tf 1.75656 0 Td 0.271 Tc (\)=)Tj /F15 1 Tf 9.96264 0 0 9.96264 261 136.8 Tm 0 Tc (X)Tj /F14 1 Tf 7.97011 0 0 7.97011 253.32 114.24 Tm <1B>Tj /F18 1 Tf 0.63236 0 Td (2)Tj /F3 1 Tf 0.70764 0 Td <0528>Tj /F14 1 Tf 1.2045 0 Td (T)Tj /F3 1 Tf 0.76787 0 Td (\))Tj /F13 1 Tf 11.95517 0 0 11.95517 285.12 126.84 Tm (P)Tj /F14 1 Tf 7.97011 0 0 7.97011 294.36 131.76 Tm (k)Tj /F11 1 Tf 11.95517 0 0 11.95517 299.4 126.84 Tm (\()Tj /F13 1 Tf 0.38142 0 Td 0.04 Tc [<193B>-131<1B>]TJ /F11 1 Tf 1.62608 0 Td 0 Tc (\))Tj /F4 1 Tf 0.7227 0 Td [(for)-351(al)-50(l)]TJ /F13 1 Tf 2.96106 0 Td <19>Tj /F16 1 Tf 0.87326 0 Td (2)Tj /F11 1 Tf 0.94353 0 Td <0528>Tj /F13 1 Tf 1.11416 0 Td (S)Tj /F11 1 Tf 0.66247 0 Td (\))Tj /F13 1 Tf 0.38142 0 Td (:)Tj /F11 1 Tf 5.85186 0 Td ((1))Tj -15.24696 -3.80421 TD (4)Tj ET endstream endobj 7 0 obj << /Length 13346 >> stream /GS4 gs BT /F12 1 Tf 17.21544 0 0 17.21544 111.36 644.28 Tm 0 g [(3)-1122(Con)29(v)27(ergence)-348(rates)-369(for)-376(MTR)]TJ /F11 1 Tf 11.95517 0 0 11.95517 111.36 618 Tm [(Let)-342(0)]TJ /F13 1 Tf 2.54953 0 Td 0.291 Tc (
Tj
/F13 1 Tf
1.07401 0 Td
(p)Tj
/F3 1 Tf
7.97011 0 0 7.97011 187.32 616.2 Tm
(2)Tj
/F16 1 Tf
11.95517 0 0 11.95517 195.6 618 Tm
0.301 Tc
[<1401>130<01>131<01>20<14>]TJ
/F13 1 Tf
3.6135 0 Td
0 Tc
(p)Tj
/F14 1 Tf
7.97011 0 0 7.97011 244.68 616.2 Tm
(n)Tj
/F11 1 Tf
11.95517 0 0 11.95517 254.28 618 Tm
[(b)-30(e)-341(a)-331(\fxed)-351(ordered)-351(list)-342(of)-332(w)31(eigh)30(ts)-352(with)]TJ
/F15 1 Tf
9.96264 0 0 9.96264 452.88 625.92 Tm
(P)Tj
/F13 1 Tf
11.95517 0 0 11.95517 465.36 618 Tm
(p)Tj
/F14 1 Tf
7.97011 0 0 7.97011 471.24 616.2 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 478.2 618 Tm
0.291 Tc
[(=1)291(.)]TJ
-30.68464 -1.2045 TD
0 Tc
(Let)Tj
/F13 1 Tf
1.66623 0 Td
<1B>Tj
/F16 1 Tf
0.87326 0 Td
(2)Tj
/F13 1 Tf
0.94352 0 Td
(S)Tj
/F14 1 Tf
7.97011 0 0 7.97011 160.2 601.8 Tm
(n)Tj
/F11 1 Tf
11.95517 0 0 11.95517 168.6 603.6 Tm
[(and)-241(supp)-30(ose)-261(that)]TJ
/F17 1 Tf
7.44782 0 Td
(y)Tj
/F11 1 Tf
0.89334 0 Td
(=)Tj
/F17 1 Tf
1.03386 0 Td
(p)Tj
/F16 1 Tf
0.66247 0 Td
<0E>Tj
/F13 1 Tf
0.54202 0 Td
<1B>Tj
/F11 1 Tf
0.83311 0 Td
[(is)-251(suc)30(h)-251(that)]TJ
/F13 1 Tf
5.0589 0 Td
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 371.28 601.8 Tm
(i)Tj
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11.95517 0 0 11.95517 325.32 494.64 Tm
0.281 Tc
(\)=)Tj
/F15 1 Tf
9.96264 0 0 9.96264 348.72 504.6 Tm
0 Tc
(X)Tj
/F14 1 Tf
7.97011 0 0 7.97011 345.6 482.4 Tm
(i)Tj
/F3 1 Tf
0.85821 0 Td
0.03 Tc
[(od)30(d)]TJ
/F13 1 Tf
11.95517 0 0 11.95517 368.28 494.64 Tm
0 Tc
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 374.04 492.84 Tm
(i)Tj
/F13 1 Tf
11.95517 0 0 11.95517 377.4 494.64 Tm
0.05 Tc
(=Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 390.72 492.84 Tm
0 Tc
(i)Tj
/F13 1 Tf
11.95517 0 0 11.95517 394.08 494.64 Tm
(;)Tj
/F11 1 Tf
7.59839 0 Td
((9))Tj
-31.24673 -2.88076 TD
(and)Tj
/F13 1 Tf
9.40514 -1.21454 TD
(E)Tj
/F14 1 Tf
7.97011 0 0 7.97011 233.16 450.72 Tm
(k)Tj
-0.09034 -0.99371 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 239.04 445.68 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
0.281 Tc
(\)=)Tj
/F15 1 Tf
9.96264 0 0 9.96264 277.68 455.76 Tm
0 Tc
(X)Tj
/F14 1 Tf
7.97011 0 0 7.97011 274.56 433.56 Tm
(i)Tj
/F3 1 Tf
0.84315 0 Td
0.03 Tc
[(od)30(d)]TJ
/F13 1 Tf
11.95517 0 0 11.95517 298.92 453.84 Tm
0 Tc
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 304.68 452.04 Tm
(i)Tj
ET
q
10.2 0 0 -0.48 298.428 449.028 cm
/Im1 Do
Q
BT
/F13 1 Tf
11.95517 0 0 11.95517 298.44 437.52 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 305.28 435.72 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 309.72 445.68 Tm
(\(1)Tj
/F16 1 Tf
1.09409 0 Td
<00>Tj
/F11 1 Tf
1.00375 0 Td
(\(1)Tj
/F16 1 Tf
1.09409 0 Td
<00>Tj
/F13 1 Tf
0.99371 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 366.6 443.88 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 369.96 445.68 Tm
(\))Tj
/F14 1 Tf
7.97011 0 0 7.97011 374.52 450.72 Tm
(k)Tj
/F11 1 Tf
11.95517 0 0 11.95517 379.68 445.68 Tm
(\))Tj
/F13 1 Tf
0.38142 0 Td
(:)Tj
/F11 1 Tf
7.92963 0 Td
((10))Tj
-29.28942 -2.46922 TD
-0.08 Tc
[(Fo)-80(r)]TJ
/F16 1 Tf
1.75656 0 Td
0 Tc
(j)Tj
/F13 1 Tf
0.28105 0 Td
(i)Tj
/F16 1 Tf
0.55206 0 Td
<00>Tj
/F13 1 Tf
1.00375 0 Td
(j)Tj
/F16 1 Tf
0.46173 0 Td
0.271 Tc
<6A15>Tj
/F11 1 Tf
1.606 0 Td
0 Tc
(2)Tj
/F13 1 Tf
0.49184 0 Td
0.492 Tc
(;Q)Tj
/F18 1 Tf
7.97011 0 0 7.97011 220.8 420.48 Tm
0 Tc
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 229.8 416.16 Tm
(\()Tj
/F13 1 Tf
0.38143 0 Td
(A)Tj
/F14 1 Tf
7.97011 0 0 7.97011 243.12 414.36 Tm
(i)Tj
/F16 1 Tf
11.95517 0 0 11.95517 249.24 416.16 Tm
(\\)Tj
/F13 1 Tf
0.8833 0 Td
(A)Tj
/F14 1 Tf
7.97011 0 0 7.97011 268.56 414.36 Tm
(j)Tj
/F11 1 Tf
11.95517 0 0 11.95517 273 416.16 Tm
0.271 Tc
(\)=)Tj
/F13 1 Tf
1.69634 0 Td
0 Tc
(Q)Tj
/F18 1 Tf
7.97011 0 0 7.97011 302.52 420.48 Tm
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 311.52 416.16 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(A)Tj
/F14 1 Tf
7.97011 0 0 7.97011 324.84 414.36 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 328.2 416.16 Tm
(\))Tj
/F13 1 Tf
0.38142 0 Td
(Q)Tj
/F18 1 Tf
7.97011 0 0 7.97011 342 420.48 Tm
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 351 416.16 Tm
(\()Tj
/F13 1 Tf
0.38143 0 Td
(A)Tj
/F14 1 Tf
7.97011 0 0 7.97011 364.32 414.36 Tm
(j)Tj
/F11 1 Tf
11.95517 0 0 11.95517 368.76 416.16 Tm
[(\).)-432(Hence)]TJ
-17.5054 -2.46922 TD
-0.081 Tc
[(Va)-81(r)]TJ
/F18 1 Tf
7.97011 0 0 7.97011 177.72 391.56 Tm
0 Tc
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 186.72 386.64 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
0.281 Tc
(\)=)Tj
/F15 1 Tf
9.96264 0 0 9.96264 225.24 396.6 Tm
0 Tc
(X)Tj
/F14 1 Tf
7.97011 0 0 7.97011 222.12 374.4 Tm
(i)Tj
/F3 1 Tf
0.85821 0 Td
0.03 Tc
[(od)30(d)]TJ
/F13 1 Tf
11.95517 0 0 11.95517 244.8 386.64 Tm
0 Tc
(Q)Tj
/F18 1 Tf
7.97011 0 0 7.97011 254.04 391.56 Tm
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 263.04 386.64 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(A)Tj
/F14 1 Tf
7.97011 0 0 7.97011 276.36 384.84 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 279.72 386.64 Tm
(\)\(1)Tj
/F16 1 Tf
1.47551 0 Td
<00>Tj
/F13 1 Tf
1.00375 0 Td
(Q)Tj
/F18 1 Tf
7.97011 0 0 7.97011 318.6 391.56 Tm
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 327.6 386.64 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(A)Tj
/F14 1 Tf
7.97011 0 0 7.97011 340.92 384.84 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 344.28 386.64 Tm
[(\)\))-272(=)]TJ
/F15 1 Tf
9.96264 0 0 9.96264 372.24 396.6 Tm
(X)Tj
/F14 1 Tf
7.97011 0 0 7.97011 369.12 374.4 Tm
(i)Tj
/F3 1 Tf
0.85821 0 Td
0.03 Tc
[(od)30(d)]TJ
/F13 1 Tf
11.95517 0 0 11.95517 393 394.68 Tm
0 Tc
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 398.76 392.88 Tm
(i)Tj
/F13 1 Tf
11.95517 0 0 11.95517 402.12 394.68 Tm
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 407.88 392.88 Tm
(i)Tj
/F3 1 Tf
0.36135 0 Td
(+1)Tj
ET
q
29.04 0 0 -0.48 392.988 389.868 cm
/Im1 Do
Q
BT
/F13 1 Tf
11.95517 0 0 11.95517 400.44 378.36 Tm
(Y)Tj
/F3 1 Tf
7.97011 0 0 7.97011 409.8 382.56 Tm
(2)Tj
/F14 1 Tf
-0.31618 -0.87326 TD
(i)Tj
/F16 1 Tf
11.95517 0 0 11.95517 426.48 386.64 Tm
<14>Tj
/F13 1 Tf
1.15431 0.67251 TD
(n)Tj
ET
q
7.08 0 0 -0.48 440.268 389.868 cm
/Im1 Do
Q
BT
/F11 1 Tf
11.95517 0 0 11.95517 440.88 378.36 Tm
(4)Tj
/F13 1 Tf
0.63236 0.69259 TD
(:)Tj
/F11 1 Tf
2.55956 0 Td
((11))Tj
-30.7549 -3.01125 TD
[(T)81(o)-321(compute)]TJ
/F13 1 Tf
5.40018 0 Td
(Q)Tj
/F14 1 Tf
7.97011 0 0 7.97011 185.16 354.96 Tm
(k)Tj
0 -0.91843 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 191.76 350.64 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(A)Tj
/F14 1 Tf
7.97011 0 0 7.97011 205.08 348.84 Tm
(i)Tj
/F16 1 Tf
11.95517 0 0 11.95517 210.96 350.64 Tm
(\\)Tj
/F13 1 Tf
0.87326 0 Td
(A)Tj
/F14 1 Tf
7.97011 0 0 7.97011 230.16 348.84 Tm
(j)Tj
/F11 1 Tf
11.95517 0 0 11.95517 234.6 350.64 Tm
[(\),)-322(w)31(e)-331(condition)-321(on)-321(the)-321(times)-332(records)]TJ
/F13 1 Tf
15.70869 0 Td
(i)Tj
/F11 1 Tf
0.65244 0 Td
(and)Tj
/F13 1 Tf
1.89709 0 Td
(j)Tj
/F11 1 Tf
0.78292 0 Td
[(are)-321(last)]TJ
-29.34965 -1.21454 TD
(requested:)Tj
/F13 1 Tf
1.06397 -2.90084 TD
(Q)Tj
/F14 1 Tf
7.97011 0 0 7.97011 133.32 306.36 Tm
(k)Tj
0 -0.99371 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 139.92 301.44 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(A)Tj
/F14 1 Tf
7.97011 0 0 7.97011 153.24 299.64 Tm
(i)Tj
/F16 1 Tf
11.95517 0 0 11.95517 159.36 301.44 Tm
(\\)Tj
/F13 1 Tf
0.8833 0 Td
(A)Tj
/F14 1 Tf
7.97011 0 0 7.97011 178.68 299.64 Tm
(j)Tj
/F11 1 Tf
11.95517 0 0 11.95517 183.12 301.44 Tm
0.844 Tc
(\)=)Tj
/F13 1 Tf
2.82054 0 Td
0 Tc
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 222.6 299.64 Tm
(i)Tj
/F13 1 Tf
11.95517 0 0 11.95517 225.96 301.44 Tm
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 231.72 299.64 Tm
(j)Tj
0.79798 1.85192 TD
(k)Tj
/F18 1 Tf
0.58719 0 Td
<00>Tj
/F3 1 Tf
0.82809 0 Td
(2)Tj
/F15 1 Tf
9.96264 0 0 9.96264 238.56 311.4 Tm
(X)Tj
/F14 1 Tf
7.97011 0 0 7.97011 239.04 289.2 Tm
(l)Tj
/F3 1 Tf
0.33124 0 Td
(=0)Tj
/F11 1 Tf
11.95517 0 0 11.95517 253.44 301.44 Tm
(\(1)Tj
/F16 1 Tf
1.09409 0 Td
<00>Tj
/F13 1 Tf
1.00375 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 285.36 299.64 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 288.72 301.44 Tm
(\))Tj
/F14 1 Tf
7.97011 0 0 7.97011 293.28 306.36 Tm
(l)Tj
0.63236 1.00877 TD
(k)Tj
/F18 1 Tf
0.58719 0 Td
<00>Tj
/F3 1 Tf
0.82809 0 Td
(2)Tj
/F18 1 Tf
0.52697 0 Td
<00>Tj
/F14 1 Tf
0.82809 0 Td
(l)Tj
/F15 1 Tf
9.96264 0 0 9.96264 303.48 311.4 Tm
(X)Tj
/F14 1 Tf
7.97011 0 0 7.97011 301.56 289.56 Tm
(m)Tj
/F3 1 Tf
0.93349 0 Td
(=0)Tj
/F11 1 Tf
11.95517 0 0 11.95517 323.04 301.44 Tm
(\(1)Tj
/F16 1 Tf
1.08405 0 Td
<00>Tj
/F13 1 Tf
1.00375 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 354.84 299.64 Tm
(i)Tj
/F16 1 Tf
11.95517 0 0 11.95517 360.84 301.44 Tm
<00>Tj
/F13 1 Tf
1.00375 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 379.68 299.64 Tm
(j)Tj
/F11 1 Tf
11.95517 0 0 11.95517 384 301.44 Tm
(\))Tj
/F14 1 Tf
7.97011 0 0 7.97011 388.56 306.36 Tm
(m)Tj
/F11 1 Tf
11.95517 0 0 11.95517 216.84 264.72 Tm
(+)Tj
/F13 1 Tf
0.76285 0 Td
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 231.72 262.92 Tm
(j)Tj
/F13 1 Tf
11.95517 0 0 11.95517 236.04 264.72 Tm
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 241.8 262.92 Tm
(i)Tj
0.67753 1.85192 TD
(k)Tj
/F18 1 Tf
0.58719 0 Td
<00>Tj
/F3 1 Tf
0.82809 0 Td
(2)Tj
/F15 1 Tf
9.96264 0 0 9.96264 247.68 274.68 Tm
(X)Tj
/F14 1 Tf
7.97011 0 0 7.97011 248.16 252.6 Tm
(l)Tj
/F3 1 Tf
0.33124 0 Td
(=0)Tj
/F11 1 Tf
11.95517 0 0 11.95517 262.56 264.72 Tm
(\(1)Tj
/F16 1 Tf
1.09409 0 Td
<00>Tj
/F13 1 Tf
1.00375 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 294.48 262.92 Tm
(j)Tj
/F11 1 Tf
11.95517 0 0 11.95517 298.8 264.72 Tm
(\))Tj
/F14 1 Tf
7.97011 0 0 7.97011 303.36 269.64 Tm
(l)Tj
0.63236 1.00877 TD
(k)Tj
/F18 1 Tf
0.58719 0 Td
<00>Tj
/F3 1 Tf
0.82809 0 Td
(2)Tj
/F18 1 Tf
0.52697 0 Td
<00>Tj
/F14 1 Tf
0.82809 0 Td
(l)Tj
/F15 1 Tf
9.96264 0 0 9.96264 313.56 274.68 Tm
(X)Tj
/F14 1 Tf
7.97011 0 0 7.97011 311.64 252.96 Tm
(m)Tj
/F3 1 Tf
0.93349 0 Td
(=0)Tj
/F11 1 Tf
11.95517 0 0 11.95517 333.12 264.72 Tm
(\(1)Tj
/F16 1 Tf
1.09409 0 Td
<00>Tj
/F13 1 Tf
0.99371 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 364.92 262.92 Tm
(j)Tj
/F16 1 Tf
11.95517 0 0 11.95517 372 264.72 Tm
<00>Tj
/F13 1 Tf
0.99371 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 390.72 262.92 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 394.08 264.72 Tm
(\))Tj
/F14 1 Tf
7.97011 0 0 7.97011 398.64 269.64 Tm
(m)Tj
/F11 1 Tf
11.95517 0 0 11.95517 197.76 229.68 Tm
(=)Tj
/F13 1 Tf
1.78667 0.67251 TD
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 224.88 235.92 Tm
(i)Tj
/F13 1 Tf
11.95517 0 0 11.95517 228.24 237.72 Tm
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 234 235.92 Tm
(j)Tj
ET
q
21.36 0 0 -0.48 218.028 232.908 cm
/Im1 Do
Q
BT
/F13 1 Tf
11.95517 0 0 11.95517 218.04 221.52 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 224.88 219.72 Tm
(i)Tj
/F13 1 Tf
11.95517 0 0 11.95517 228.24 221.52 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 235.08 219.72 Tm
(j)Tj
/F15 1 Tf
9.96264 0 0 9.96264 242.64 247.2 Tm
(")Tj
/F13 1 Tf
11.95517 0 0 11.95517 261.96 237.72 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 268.8 235.92 Tm
(j)Tj
ET
q
35.88 0 0 -0.48 249.588 232.908 cm
/Im1 Do
Q
BT
/F13 1 Tf
11.95517 0 0 11.95517 249.6 221.52 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 256.44 219.72 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 262.44 221.52 Tm
(+)Tj
/F13 1 Tf
0.98368 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 281.04 219.72 Tm
(j)Tj
/F16 1 Tf
11.95517 0 0 11.95517 289.2 229.68 Tm
<00>Tj
/F11 1 Tf
1.00375 0 Td
(\(1)Tj
/F16 1 Tf
1.09409 0 Td
<00>Tj
/F13 1 Tf
0.99371 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 333 227.88 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 336.36 229.68 Tm
(\))Tj
/F14 1 Tf
7.97011 0 0 7.97011 340.92 234.6 Tm
(k)Tj
/F11 1 Tf
11.95517 0 0 11.95517 348.72 229.68 Tm
(+)Tj
/F13 1 Tf
2.14802 0.67251 TD
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 381.24 235.92 Tm
(i)Tj
ET
q
35.88 0 0 -0.48 361.668 232.908 cm
/Im1 Do
Q
BT
/F13 1 Tf
11.95517 0 0 11.95517 361.68 221.52 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 368.52 219.72 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 374.52 221.52 Tm
(+)Tj
/F13 1 Tf
0.98367 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 393.12 219.72 Tm
(j)Tj
/F11 1 Tf
11.95517 0 0 11.95517 398.64 229.68 Tm
(\(1)Tj
/F16 1 Tf
1.09409 0 Td
<00>Tj
/F13 1 Tf
0.99371 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 430.44 227.88 Tm
(i)Tj
/F16 1 Tf
11.95517 0 0 11.95517 436.44 229.68 Tm
<00>Tj
/F13 1 Tf
1.00375 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 455.28 227.88 Tm
(j)Tj
/F11 1 Tf
11.95517 0 0 11.95517 459.6 229.68 Tm
(\))Tj
/F14 1 Tf
7.97011 0 0 7.97011 464.16 234.6 Tm
(k)Tj
/F15 1 Tf
9.96264 0 0 9.96264 469.32 247.2 Tm
(#)Tj
/F11 1 Tf
11.95517 0 0 11.95517 216.84 195.84 Tm
(+)Tj
/F13 1 Tf
0.95356 0.67251 TD
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 234 202.08 Tm
(j)Tj
/F13 1 Tf
11.95517 0 0 11.95517 238.32 203.88 Tm
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 244.08 202.08 Tm
(i)Tj
ET
q
21.36 0 0 -0.48 227.148 199.068 cm
/Im1 Do
Q
BT
/F13 1 Tf
11.95517 0 0 11.95517 227.16 187.56 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 234 185.76 Tm
(j)Tj
/F13 1 Tf
11.95517 0 0 11.95517 238.32 187.56 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 245.16 185.76 Tm
(i)Tj
/F15 1 Tf
9.96264 0 0 9.96264 251.76 213.36 Tm
(")Tj
/F13 1 Tf
11.95517 0 0 11.95517 271.56 203.88 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 278.4 202.08 Tm
(i)Tj
ET
q
35.88 0 0 -0.48 258.708 199.068 cm
/Im1 Do
Q
BT
/F13 1 Tf
11.95517 0 0 11.95517 258.72 187.56 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 265.56 185.76 Tm
(j)Tj
/F11 1 Tf
11.95517 0 0 11.95517 272.52 187.56 Tm
(+)Tj
/F13 1 Tf
0.98367 0 Td
(Y)Tj
/F14 1 Tf
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<<
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(i)Tj
ET
q
14.16 0 0 -0.48 302.628 521.748 cm
/Im1 Do
Q
BT
/F13 1 Tf
11.95517 0 0 11.95517 302.64 510.36 Tm
(Y)Tj
/F3 1 Tf
7.97011 0 0 7.97011 312.12 514.44 Tm
(2)Tj
/F14 1 Tf
-0.33124 -0.85821 TD
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 318 518.52 Tm
(\(1)Tj
/F16 1 Tf
1.09409 0 Td
<00>Tj
/F13 1 Tf
1.00375 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 349.92 516.72 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 353.16 518.52 Tm
(\))Tj
/F14 1 Tf
7.97011 0 0 7.97011 357.72 523.44 Tm
(k)Tj
/F15 1 Tf
9.96264 0 0 9.96264 362.88 536.04 Tm
(!)Tj
/F13 1 Tf
11.95517 0 0 11.95517 372.72 518.52 Tm
(:)Tj
/F11 1 Tf
-21.86167 -2.4893 TD
-0.03 Tc
[(W)51(e)-361(h)-30(ave)]TJ
5.37006 -2.1681 TD
-0.081 Tc
[(Va)-81(r)]TJ
/F14 1 Tf
7.97011 0 0 7.97011 193.8 467.88 Tm
0 Tc
(k)Tj
0 -1.00877 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 200.4 462.84 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
/F16 1 Tf
0.61229 0 Td
<00>Tj
/F11 1 Tf
0.99371 0 Td
-0.081 Tc
[(Va)-81(r)]TJ
/F18 1 Tf
7.97011 0 0 7.97011 252.96 467.88 Tm
0 Tc
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 261.96 462.84 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
/F16 1 Tf
1.21454 0 Td
<14>Tj
/F15 1 Tf
9.96264 0 0 9.96264 313.44 472.8 Tm
(X)Tj
/F14 1 Tf
7.97011 0 0 7.97011 310.92 450.6 Tm
[(i)-482(odd)]TJ
/F13 1 Tf
11.95517 0 0 11.95517 335.28 470.88 Tm
(y)Tj
/F3 1 Tf
7.97011 0 0 7.97011 341.52 475.2 Tm
(2)Tj
/F14 1 Tf
-0.06023 -0.90337 TD
(i)Tj
ET
q
14.16 0 0 -0.48 333.588 466.068 cm
/Im1 Do
Q
BT
/F13 1 Tf
11.95517 0 0 11.95517 333.6 454.68 Tm
(Y)Tj
/F3 1 Tf
7.97011 0 0 7.97011 343.08 458.76 Tm
(2)Tj
/F14 1 Tf
-0.33124 -0.85821 TD
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 348.96 462.84 Tm
(\(1)Tj
/F16 1 Tf
1.09409 0 Td
<00>Tj
/F13 1 Tf
1.00375 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 380.88 461.04 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 384.12 462.84 Tm
(\))Tj
/F14 1 Tf
7.97011 0 0 7.97011 388.68 467.76 Tm
(k)Tj
/F16 1 Tf
11.95517 0 0 11.95517 291.6 432.48 Tm
<14>Tj
/F15 1 Tf
9.96264 0 0 9.96264 314.04 442.44 Tm
(X)Tj
/F14 1 Tf
7.97011 0 0 7.97011 310.92 420.24 Tm
(i)Tj
/F3 1 Tf
0.84315 0 Td
0.03 Tc
[(od)30(d)]TJ
/F13 1 Tf
11.95517 0 0 11.95517 335.28 440.52 Tm
0 Tc
(y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 341.04 438.72 Tm
(i)Tj
ET
q
10.2 0 0 -0.48 334.668 435.708 cm
/Im1 Do
Q
BT
/F13 1 Tf
11.95517 0 0 11.95517 334.68 424.2 Tm
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 341.52 422.4 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 346.08 432.48 Tm
(\(1)Tj
/F16 1 Tf
1.09409 0 Td
<00>Tj
/F13 1 Tf
1.00375 0 Td
(Y)Tj
/F14 1 Tf
7.97011 0 0 7.97011 378 430.68 Tm
(i)Tj
/F11 1 Tf
11.95517 0 0 11.95517 381.24 432.48 Tm
(\))Tj
/F14 1 Tf
7.97011 0 0 7.97011 385.8 437.4 Tm
(k)Tj
/F11 1 Tf
11.95517 0 0 11.95517 291.72 404.76 Tm
(=)Tj
/F13 1 Tf
1.606 0 Td
(E)Tj
/F18 1 Tf
7.97011 0 0 7.97011 320.28 409.68 Tm
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 329.16 404.76 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
/F16 1 Tf
0.61229 0 Td
<00>Tj
/F13 1 Tf
0.99371 0 Td
(E)Tj
/F14 1 Tf
7.97011 0 0 7.97011 372.84 409.68 Tm
(k)Tj
-0.09034 -0.97866 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 378.84 404.76 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
0.281 Tc
[(\)=)281(:)10<01>]TJ
/F14 1 Tf
7.97011 0 0 7.97011 427.2 402.96 Tm
0 Tc
(k)Tj
/F13 1 Tf
11.95517 0 0 11.95517 432.36 404.76 Tm
(:)Tj
/F11 1 Tf
3.90459 0 Td
((12))Tj
-29.28942 -1.81679 TD
[(No)31(w)-392(let)]TJ
/F13 1 Tf
3.76406 0 Td
(B)Tj
/F11 1 Tf
1.18442 0 Td
(:=)Tj
/F16 1 Tf
1.40525 0 Td
(f)Tj
/F13 1 Tf
0.50187 0 Td
(N)Tj
/F16 1 Tf
1.27476 0 Td
<14>Tj
/F13 1 Tf
1.15431 0 Td
(E)Tj
/F18 1 Tf
7.97011 0 0 7.97011 249.24 387.36 Tm
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 258.24 383.04 Tm
(\()Tj
/F13 1 Tf
0.38143 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
/F16 1 Tf
0.65244 0 Td
<00>Tj
/F11 1 Tf
1.03386 0 Td
<01>Tj
/F14 1 Tf
7.97011 0 0 7.97011 303.24 381.24 Tm
(k)Tj
/F13 1 Tf
11.95517 0 0 11.95517 308.4 383.04 Tm
(=)Tj
/F11 1 Tf
0.49184 0 Td
(2)Tj
/F16 1 Tf
0.49184 0 Td
(g)Tj
/F11 1 Tf
0.50187 0 Td
[(.)-612(Once)-401(w)31(e)-391(determine)-412(appropriate)]TJ
-17.96712 -1.21454 TD
[(v)50(alues)-291(of)]TJ
/F13 1 Tf
3.9347 0 Td
(k)Tj
/F11 1 Tf
0.82307 0 Td
[(w)30(e)-290(will)-281(sho)30(w)-291(that)-282(the)-281(probabilit)30(y)-291(of)]TJ
/F13 1 Tf
15.30719 0 Td
(B)Tj
/F11 1 Tf
1.07401 0 Td
[(is)-292(small)-281(in)-281(stationarit)28(y)-291(and)]TJ
-21.13897 -1.2045 TD
[(large)-321(un)30(til)]TJ
/F13 1 Tf
4.70759 0 Td
(k)Tj
/F11 1 Tf
0.86323 0 Td
[(steps)-342(of)-321(MTR.)]TJ
-4.10534 -1.2045 TD
[(F)80(rom)-322(Cheb)31(yc)31(hev's)-372(inequalit)31(y)80(,)]TJ
/F13 1 Tf
10.26836 -2.31866 TD
(Q)Tj
/F18 1 Tf
7.97011 0 0 7.97011 260.88 316.92 Tm
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 269.88 312 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(B)Tj
/F11 1 Tf
0.79296 0 Td
(\))Tj
/F16 1 Tf
0.66248 0 Td
<14>Tj
/F11 1 Tf
1.15431 0.67251 TD
[(4V)81(ar)]TJ
/F18 1 Tf
7.97011 0 0 7.97011 329.64 325.08 Tm
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 338.64 320.04 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
ET
q
52.8 0 0 -0.48 305.628 315.228 cm
/Im1 Do
Q
BT
/F11 1 Tf
11.95517 0 0 11.95517 324.6 303.84 Tm
<01>Tj
/F3 1 Tf
7.97011 0 0 7.97011 334.32 307.92 Tm
(2)Tj
/F14 1 Tf
0 -0.90337 TD
(k)Tj
/F11 1 Tf
11.95517 0 0 11.95517 479.04 312 Tm
((13))Tj
-30.7549 -2.3287 TD
(and)Tj
/F13 1 Tf
4.93845 -1.64615 TD
(Q)Tj
/F14 1 Tf
7.97011 0 0 7.97011 179.64 269.4 Tm
(k)Tj
0 -0.97866 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 186.36 264.48 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(B)Tj
/F11 1 Tf
0.79296 0 Td
0.271 Tc
(\)=)Tj
/F13 1 Tf
1.69634 0 Td
0 Tc
(Q)Tj
/F14 1 Tf
7.97011 0 0 7.97011 229.92 269.4 Tm
(k)Tj
0 -0.97866 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 236.52 264.48 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F16 1 Tf
1.11416 0 Td
<00>Tj
/F13 1 Tf
0.99371 0 Td
(E)Tj
/F14 1 Tf
7.97011 0 0 7.97011 275.64 269.4 Tm
(k)Tj
-0.09034 -0.97866 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 281.64 264.48 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
/F16 1 Tf
0.66247 0 Td
<14>Tj
/F11 1 Tf
1.05394 0 Td
<01>Tj
/F14 1 Tf
7.97011 0 0 7.97011 327 262.68 Tm
(k)Tj
/F13 1 Tf
11.95517 0 0 11.95517 332.16 264.48 Tm
(=)Tj
/F11 1 Tf
0.49184 0 Td
(2\))Tj
/F16 1 Tf
1.14427 0 Td
<15>Tj
/F11 1 Tf
1.05394 0 Td
(1)Tj
/F16 1 Tf
0.71266 0 Td
<00>Tj
/F11 1 Tf
1.10413 0.68255 TD
[(4V)81(ar)]TJ
/F14 1 Tf
7.97011 0 0 7.97011 410.04 277.56 Tm
(k)Tj
0 -0.99371 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 416.64 272.64 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
ET
q
50.4 0 0 -0.48 386.028 267.708 cm
/Im1 Do
Q
BT
/F11 1 Tf
11.95517 0 0 11.95517 403.8 256.32 Tm
<01>Tj
/F3 1 Tf
7.97011 0 0 7.97011 413.52 260.4 Tm
(2)Tj
/F14 1 Tf
0 -0.88832 TD
(k)Tj
/F13 1 Tf
11.95517 0 0 11.95517 437.52 264.48 Tm
(:)Tj
/F11 1 Tf
3.47297 0 Td
((14))Tj
-30.7549 -2.14802 TD
[(F)80(rom)-322((12),)]TJ
1.05394 -2.0075 TD
-0.081 Tc
[(Va)-81(r)]TJ
/F14 1 Tf
7.97011 0 0 7.97011 142.2 219.84 Tm
0 Tc
(k)Tj
0 -0.99371 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 148.8 214.8 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
ET
q
44.64 0 0 -0.48 123.948 209.988 cm
/Im1 Do
Q
BT
/F11 1 Tf
11.95517 0 0 11.95517 138.84 198.6 Tm
<01>Tj
/F3 1 Tf
7.97011 0 0 7.97011 148.56 202.68 Tm
(2)Tj
/F14 1 Tf
0 -0.88832 TD
(k)Tj
/F16 1 Tf
11.95517 0 0 11.95517 173.04 206.76 Tm
<14>Tj
/F11 1 Tf
1.15431 0.67251 TD
-0.081 Tc
[(Va)-81(r)]TJ
/F18 1 Tf
7.97011 0 0 7.97011 205.08 219.84 Tm
0 Tc
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 214.08 214.8 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
0.221 Tc
<292B01>Tj
/F14 1 Tf
7.97011 0 0 7.97011 257.88 213 Tm
0 Tc
(k)Tj
ET
q
76.2 0 0 -0.48 186.828 209.988 cm
/Im1 Do
Q
BT
/F11 1 Tf
11.95517 0 0 11.95517 217.56 198.6 Tm
<01>Tj
/F3 1 Tf
7.97011 0 0 7.97011 227.28 202.68 Tm
(2)Tj
/F14 1 Tf
0 -0.88832 TD
(k)Tj
/F11 1 Tf
11.95517 0 0 11.95517 267.6 206.76 Tm
(=)Tj
1.13424 0.67251 TD
-0.081 Tc
[(Va)-81(r)]TJ
/F18 1 Tf
7.97011 0 0 7.97011 299.4 219.84 Tm
0 Tc
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 308.4 214.8 Tm
(\()Tj
/F13 1 Tf
0.38143 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
ET
q
46.92 0 0 -0.48 281.148 209.988 cm
/Im1 Do
Q
BT
/F11 1 Tf
11.95517 0 0 11.95517 297.24 198.6 Tm
<01>Tj
/F3 1 Tf
7.97011 0 0 7.97011 306.96 202.68 Tm
(2)Tj
/F14 1 Tf
0 -0.88832 TD
(k)Tj
/F11 1 Tf
11.95517 0 0 11.95517 331.92 206.76 Tm
(+)Tj
3.22204 0.67251 TD
(1)Tj
ET
q
56.88 0 0 -0.48 344.868 209.988 cm
/Im1 Do
Q
BT
/F15 1 Tf
9.96264 0 0 9.96264 344.88 207.6 Tm
(q)Tj
ET
q
46.92 0 0 -0.48 354.828 208.068 cm
/Im1 Do
Q
BT
/F11 1 Tf
11.95517 0 0 11.95517 354.84 195.6 Tm
-0.081 Tc
[(Va)-81(r)]TJ
/F18 1 Tf
7.97011 0 0 7.97011 373.08 200.52 Tm
0 Tc
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 382.08 195.6 Tm
(\()Tj
/F13 1 Tf
0.38143 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
/F15 1 Tf
9.96264 0 0 9.96264 405 224.28 Tm
( )Tj
/F11 1 Tf
11.95517 0 0 11.95517 414 214.8 Tm
-0.081 Tc
[(Va)-81(r)]TJ
/F18 1 Tf
7.97011 0 0 7.97011 432.24 219.84 Tm
0 Tc
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 441.24 214.8 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
ET
q
46.92 0 0 -0.48 413.988 209.988 cm
/Im1 Do
Q
BT
/F11 1 Tf
11.95517 0 0 11.95517 430.08 198.6 Tm
<01>Tj
/F3 1 Tf
7.97011 0 0 7.97011 439.8 202.68 Tm
(2)Tj
/F14 1 Tf
0 -0.88832 TD
(k)Tj
/F15 1 Tf
9.96264 0 0 9.96264 462.12 224.28 Tm
(!)Tj
/F3 1 Tf
7.97011 0 0 7.97011 470.04 221.52 Tm
(1)Tj
/F14 1 Tf
0.52697 0 Td
(=)Tj
/F3 1 Tf
0.52697 0 Td
(2)Tj
/F13 1 Tf
11.95517 0 0 11.95517 485.16 206.76 Tm
(:)Tj
/F11 1 Tf
-31.26681 -2.78039 TD
(Hence)Tj
/F13 1 Tf
4.37635 -1.81679 TD
(d)Tj
/F11 1 Tf
0.51191 0 Td
(\()Tj
/F13 1 Tf
0.38142 0 Td
(k)Tj
/F11 1 Tf
0.54203 0 Td
(\))Tj
/F16 1 Tf
1.21454 0 Td
<15>Tj
/F13 1 Tf
1.606 0 Td
(d)Tj
/F11 1 Tf
0.51191 0 Td
(\()Tj
/F13 1 Tf
0.38142 0 Td
(k)Tj
/F11 1 Tf
0.54203 0 Td
(;)Tj
/F17 1 Tf
0.44165 0 Td
(y)Tj
/F11 1 Tf
0.61229 0 Td
(\))Tj
/F16 1 Tf
0.65244 0 Td
<15>Tj
/F13 1 Tf
1.05394 0 Td
(Q)Tj
/F14 1 Tf
7.97011 0 0 7.97011 273.96 156.72 Tm
(k)Tj
0 -0.99371 TD
(T)Tj
/F11 1 Tf
11.95517 0 0 11.95517 280.56 151.8 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(B)Tj
/F11 1 Tf
0.79296 0 Td
(\))Tj
/F16 1 Tf
0.61229 0 Td
<00>Tj
/F13 1 Tf
0.99371 0 Td
(Q)Tj
/F18 1 Tf
7.97011 0 0 7.97011 323.04 156.72 Tm
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 332.04 151.8 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(B)Tj
/F11 1 Tf
0.79296 0 Td
(\))Tj
/F16 1 Tf
-12.6071 -2.31866 TD
<15>Tj
/F11 1 Tf
1.606 0 Td
(1)Tj
/F16 1 Tf
0.71266 0 Td
<00>Tj
/F11 1 Tf
3.23207 0.67251 TD
(4)Tj
ET
q
56.88 0 0 -0.48 236.268 127.308 cm
/Im1 Do
Q
BT
/F15 1 Tf
9.96264 0 0 9.96264 236.28 124.8 Tm
(q)Tj
ET
q
46.92 0 0 -0.48 246.228 125.268 cm
/Im1 Do
Q
BT
/F11 1 Tf
11.95517 0 0 11.95517 246.24 112.8 Tm
-0.081 Tc
[(Va)-81(r)]TJ
/F18 1 Tf
7.97011 0 0 7.97011 264.36 117.84 Tm
0 Tc
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 273.36 112.8 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
/F15 1 Tf
9.96264 0 0 9.96264 296.28 141.6 Tm
( )Tj
/F11 1 Tf
11.95517 0 0 11.95517 305.4 132.12 Tm
-0.081 Tc
[(Va)-81(r)]TJ
/F18 1 Tf
7.97011 0 0 7.97011 323.64 137.16 Tm
0 Tc
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 332.52 132.12 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
ET
q
46.92 0 0 -0.48 305.388 127.308 cm
/Im1 Do
Q
BT
/F11 1 Tf
11.95517 0 0 11.95517 321.36 115.8 Tm
<01>Tj
/F3 1 Tf
7.97011 0 0 7.97011 331.08 120 Tm
(2)Tj
/F14 1 Tf
0 -0.90337 TD
(k)Tj
/F15 1 Tf
9.96264 0 0 9.96264 353.52 141.6 Tm
(!)Tj
/F3 1 Tf
7.97011 0 0 7.97011 361.32 138.84 Tm
(1)Tj
/F14 1 Tf
0.52697 0 Td
(=)Tj
/F3 1 Tf
0.52697 0 Td
(2)Tj
/F16 1 Tf
11.95517 0 0 11.95517 377.16 124.08 Tm
<00>Tj
/F11 1 Tf
1.10412 0.67251 TD
[(8V)81(ar)]TJ
/F18 1 Tf
7.97011 0 0 7.97011 414.48 137.16 Tm
(1)Tj
/F11 1 Tf
11.95517 0 0 11.95517 423.36 132.12 Tm
(\()Tj
/F13 1 Tf
0.38142 0 Td
(N)Tj
/F11 1 Tf
0.8833 0 Td
(\))Tj
ET
q
52.8 0 0 -0.48 390.348 127.308 cm
/Im1 Do
Q
BT
/F11 1 Tf
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19 0 obj
<<
/Length 10943
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