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[(tio)3.9(ns)-327.4(to)-320.5(mod)3.9(e)-3.6(rn)-326.2(medicine.)-325.8(T)4(his)-321.7(r)1.9(ev)3.9(iew)-324.4(i)1.1(s)-321.7(not)-323.3(a)-322.3(c)-3.6(o)3.9(m).3(prehensive)-322.3(su)3.9(rvey)-326.2(o)3.9(f)-328.2(metho)3.9(d)-1.8(s,)-325.8(n)3.9(o)-1.8(r)-322.5(o)-1.8(f)-322.5(t)1.1(he)-322.3(speci)4.6(c)]TJ
T*
.0209 Tc
[(techniques)-208.7(and)-213.2(i).3(mplementations)-214.4(in)-207.5(the)-209.3(literature,)]TJ
20.5031 0 TD
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-20.5031 -1.2007 TD
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23.9003 0 TD
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-23.9003 -1.195 TD
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[(gic)-214.4(m).1(ethods)-208.1(may)-206.9(p)-2(rovide)-208.7(powerful)-209.6(n)]TJ
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[(ew)-210.4(approaches)-207.7(to)-212.2(the)-214(s)2.9(ometimes)]TJ
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T*
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-28.1568 -1.2007 TD
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[(be)-5.7(low.)]TJ
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T*
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T*
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T*
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T*
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1.0015 -1.2007 TD
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T*
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T*
[(proba)-7.6(bilistic)-335.9(logi)-8.6(c)-332.6(are)-337.9(where)-337.7(mos)-7(t)-333.6(o)0(f)-333.6(the)-336.9(restrict)-11.7(ions)-337.1(occur.)]TJ
1.0015 -1.2007 TD
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T*
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T*
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0 -1.2007 TD
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T*
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T*
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T*
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1.0015 -1.2007 TD
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T*
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1.0015 -1.2007 TD
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-1.0015 -1.2007 TD
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T*
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T*
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T*
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1.0015 -2.3957 TD
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1.2519 -1.2007 TD
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1.2519 -1.2007 TD
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-1.2519 -1.2007 TD
[(3.)-501.9(The)-305.5(represe)-10.1(ntatio)-9(n)-302.4(o)0(f)-299.4(the)-308.4(logical)-307.4(relations)-10.5(hips)-302.9(in)-305.9(MLN)-303.9(is)-307.1(much)-304.3(mor)-7.8(e)-298.5(com)-7.6(pact)-305.3(than)-309.2(in)-300.2(BN)-306.1(\(for)-304.9(thos)-7(e)]TJ
1.2519 -1.2007 TD
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/F2 1 Tf
-2.2535 67.0005 TD
[(PROB)-9.3(ABILISTI)-9.9(C)-334.7(LOG)-8.4(IC)-336.7(METHOD)-10.5(S)-335.7(I)0(N)-336.7(BIOLOG)-8.7(Y)-18060.8(317)]TJ
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22.8077 0 TD
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[(usin)-7(g)-336.5(a)-332.6(search)-343.2(method)-342.7(that)-334.7(allow)-9.4(s)-337.7(u)0(s)-332.8(t)0(o)-334.3(solv)-7(e)-332.6(vari)-9.6(ous)-333.5(mode)-8.4(l)-333.6(selection)-346.1(problems)-341.7(with)-336.9(dif)-7(ferent)-339.2(biologi)-7.9(cal)]TJ
T*
[(kn)-7.2(owledge)-243.2(constra)-9.1(ints)-237.4(n)-6.5(aturally)-241.9(emb)-7.6(edded)-240.7(in)-237.6(them.)-244.8(In)-236.8(a)-241.6(previous)-247.1(article,)-243.3(we)-240.6(used)-239.3(ML)-9(N)-238(t)0(o)-237.6(select)-244.3(mode)-8.4(ls)-238.8(for)]TJ
T*
[(the)-365.3(inue)-7.6(nce)-364.4(of)-362(the)-365.3(genotype)-370.9(\(specic)-369.4(sets)-362.8(of)-362(mar)-9.6(kers,)-361.2(indicat)-11.5(ing)-363.6(gene)-365.1(variants\))-368.2(on)-365.7(the)-359.7(ph)-7.2(enotype)-364.5(\(e.g.,)]TJ
T*
[(prope)-7.6(rties)-333(of)-327.9(the)-331.2(organ)-7.6(ism)-328.4(as)-334.6(expresse)-10.1(d)-325.1(i)0(n)-328.7(mea)-9.4(sureme)-9.1(nts:)-328.4(size,)-335.3(color,)-329.4(shape)-8.6(,)-330.4(gene)-331(expressi)-11.1(on)-325.9(leve)-9.4(ls\).)-327.3(We)]TJ
T*
[(rst)-361(u)-6.5(sed)-358.1(a)-361.1(single-m)-8.7(arker)-364.2(model)-359(it)-7(eratively)-363.9(that)-363.2(focused)-364.9(on)-360(relations)-10.5(hips)-359.8(betwee)-10.9(n)-359.3(genetic)-363.3(marker)-9.9(s)-354.8(and)-362.6(a)]TJ
0 -1.195 TD
[(give)-7.6(n)-245.5(phenot)-9.1(ype)-248.8(\(Sakhanenko)-253.9(and)-248.8(Galas)-9.6(,)-245.1(2010\).)-250.9(Every)-252.1(marker)-254.6(associated)-256(with)-251.5(a)-247.2(gene)-245.6(sel)-8(ected)-250.9(in)-249(the)-245.8(model)]TJ
0 -1.2007 TD
[(had)-311.4(a)-304.2(speci)-11.3(c)-304.2(inue)-7.6(nce)-307.5(on)-308.8(the)-308.4(phenotype,)-315.2(even)-308.2(when)-310.4(consider)-9.9(ed)-304.9(alon)-7.6(e.)-304.5(The)-311.2(model)-307.8(is)-307.1(asked)-310.2(to)-311.6(predict)-312.3(the)]TJ
T*
[(ph)-7.2(enotype)-330.3(given)-327(the)-325.5(genot)-8.4(ype)-328.4(of)-322.2(a)-326.9(sing)-7(le)-324.7(organism,)-330.7(and)-328.4(the)-325.5(mar)-9.6(kers)-326.7(were)-331.2(iterativel)-11.7(y)-325.1(selected)-332.9(to)-323(improv)-7.1(e)]TJ
T*
[(the)-280(predi)-10.3(ction.)-279(Late)-9.2(r,)-276.3(in)-277.4(this)-282.9(review,)-284.7(we)-280.4(discuss)-280.9(a)-281.4(natural)-283.9(extension)-284.6(of)-276.6(this)-282.9(applica)-10.5(tion)-276(that)-283.5(uses)-280.4(a)-275.7(pair)-9.6(-wise)]TJ
T*
[(gene)-359.4(mode)-8.4(l)-350.7(that)-357.5(expl)-7.6(icitly)-358.8(represe)-10.1(nts)-353.4(relat)-9.2(ionships)-361.1(between)-364.5(a)-355.4(phenotype)-360.3(and)-356.9(pair-wi)-9.1(se)-357.3(interact)-10.3(ing)-352.2(genes)-8.6(.)]TJ
T*
[(Th)-7(e)-395.2(models)-400.8(disc)-8.8(ussed)-400.6(here)-401.2(to)-396.9(illustrate)-403.7(the)-399.5(appro)-7.6(ach,)-398.9(while)-402(comple)-8.7(x)-393.4(i)0(n)-396.9(imple)-9(mentatio)-10.1(n,)-393.8(are)-400.5(still)-397.3(rather)]TJ
T*
[(simpl)-8.4(e)-349.7(genetic)-357.7(mode)-8.4(ls,)-347.3(and)-351.2(the)-354(full)-352(powe)-8.8(r)-349.9(o)0(f)-350.6(MLNs)-357.1(will)-351(come)-357.3(with)-353.9(the)-348.3(natu)-7.6(ral)-350.2(extensi)-9.9(on)-348.7(to)-351.4(much)-355.5(more)]TJ
T*
[(com)-7.6(plex)-326.3(models)-8.1(.)-324.7(This)-325.5(is)-324.2(one)-322.7(of)-327.9(the)-325.5(major)-326.8(points)-330(we)-325.9(would)-329.2(like)-323.3(to)-328.7(emphasize)-11.6(that)-329(much)-327(more)-329(powerful)]TJ
0 -1.195 TD
[(appl)-7.6(ications)-383.3(are)-372(to)-374.2(com)-7.6(e,)-372.8(but)-374.9(proba)-7.6(bilistic)-381.4(logic)-375.3(represe)-10.1(nts)-376.1(a)-372.4()48.5(languag)-8.7(e)45.9()-372.6(for)-376.1(expression)-382.5(and)-374(cal)-8.6(culation)]TJ
0 -1.2007 TD
[(wi)-8.2(th)-334.3(such)-336.1(comple)-8.7(x)-330.8(mode)-8.4(ls.)]TJ
1.0015 -1.2007 TD
[(To)-263.1(illustrate)-267.2(the)-257.2(method)-268.7(in)-254.7(a)-258.6(simpl)-8.4(e)-258.6(form,)-261.3(a)-258.6(single-)-10.1(marker)-260.3(mode)-8.4(l)-259.6(encodes)-262.3(an)-259.4(inue)-7.6(nce)-261.9(of)-259.6(a)-258.6(set)-258.4(of)-259.6(genet)-10.1(ic)]TJ
-1.0015 -1.2007 TD
[(mar)-9.6(kers)-343.7(on)-343(a)-338.3(phenot)-9.1(ype)-345.5(as)-340.2(an)-344.7(aggregat)-10.5(ion)-340.8(of)-344.9(inuences)-351.1(of)-339.2(indivi)-7.2(dual)-343.3(marker)-9.9(s.)-343.8(When)-343.1(condi)-8.4(tioned)-347.6(on)-343(the)]TJ
T*
[(allel)-10(es)-289(of)-293.7(the)-297.1(markers)-296.4(\(pred)-9.6(icting)-293.5(the)-291.4(ph)-7.2(enotype)-296.2(values)-296.6(give)-7.6(n)-291(the)-291.4(genot)-8.4(ype)-288.6(d)-6.5(ata\),)-290.6(mode)-8.4(ling)-293.1(usin)-7(g)-291(a)-287.1(sing)-7(le-)]TJ
T*
[(mar)-9.6(ker)-262.1(mode)-8.4(l)-265.3(can)-267.6(be)-265.1(seen)-269.6(\(as)-269(we)-263.3(speci)-11.3(cally)-269(show)-264.3(in)-266.1(a)-264.3(later)-271(sectio)-9.2(n\))-265.3(as)-266.3(performi)-8.7(ng)-263.3(a)-264.3(logist)-8.4(ic)-267.8(regression)-270.7(of)]TJ
T*
[(the)-291.4(marker)-288.8(alleles)-293.3(on)-280.4(the)-285.7(phenot)-9.1(ype)-282.9(valu)-7.6(es.)-283.7(Note)-290.4(however)-293.6(that)-283.5(the)-285.7(sing)-7(le-marke)-10.3(r)-281.6(mode)-8.4(l)-282.4(does)-284.9(not)-289.6(make)-289(the)]TJ
T*
[(assum)-11.5(ption)-407.7(that)-414.4(the)-410.9(data)-413.4(is)-409.5(iden)-7.6(tically,)-413(inde)-7.6(pendently)-414.3(distribut)-9.7(ed)-407.3(\(iid\))-417.3(as)-408.5(oppose)-7.6(d)-404.8(t)0(o)-414(the)-410.9(case)-413.6(of)-407.5(a)-412.3(true)]TJ
0 -1.195 TD
[(logi)-8.6(stic)-341.6(regr)-8.8(ession.)-347.6(At)-344(the)-342.6(rst)-349.6(iteration)-347.8(of)-344.9(the)-342.6(sear)-9.8(ch)-339.1(method)-348.4(\(see)-351.2(Algorit)-8.1(hm)-340.8(1)-342.2(o)0(f)-344.9(Section)-349.4(4\),)-345.3(when)-344.5(each)]TJ
0 -1.2007 TD
[(mode)-8.4(l)-327.9(i)0(s)-329.8(based)-332.9(on)-331.6(only)-330.2(one)-328.4(marker)-9.9(,)-324.7(the)-331.2(correspo)-9.1(nding)-330.9(logi)-8.6(stic)-330.2(regress)-9.6(ion)-329.4(has)-329.6(two)-333.3(predictors)-334.8(\(assum)-8.6(ing)-329.4(a)]TJ
T*
[(genet)-10.1(ic)-290.6(marker)-294.5(can)-290.4(have)-296.8(two)-293.5(possible)-294.6(alleles\))-11.5(.)-284.9(F)0(o)-6.4(r)-287.3(the)-291.4(followi)-8.1(ng)-286.1(itera)-9.2(tions,)-295.4(as)-289(we)-291.8(add)-288.6(mor)-7.8(e)-287.1(marker)-9.9(s)-286.5(t)0(o)-294.5(the)]TJ
T*
[(predi)-10.3(ctive)-303.1(marker)-9.9(s)-303.6(set,)-304.3(the)-302.7(correspo)-9.1(nding)-302.5(logist)-8.4(ic)-302(regress)-9.6(ion)-301(is)-301.4(expand)-8.2(ed)-304.9(to)-300.2(include)-310.3(more)-306.3(predictors)-312.1(\(four,)]TJ
T*
[(six,)-251.3(and)-248.8(so)-247.4(on\).)-249.3(It)-245.3(is)-250.2(important)-255.7(to)-243.3(note)-252.3(however)-253.8(that)-249.4(the)-251.5(MLN)-252.7(description)-256.7(of)-242.5(the)-251.5(models)-252.8(at)-245.1(d)-6.5(ifferent)-254.4(levels)-248.2(of)]TJ
T*
[(itera)-9.2(tion)-270.3(does)-273.5(not)-266.8(change)-9.9(;)-265.3(wha)-8(t)-265.3(change)-9.9(s)-263.7(i)0(s)-272.9(a)-270(set)-269.8(of)-265.3(possi)-9(ble)-268.6(values)-273.9(of)-271(the)-268.6(MLN)-269.7(vari)-9.6(ables)-273.1(that)-266.4(corr)-8.8(espond)-269.3(to)]TJ
T*
[(the)-262.9(predictors)-260.9(of)-259.6(the)-257.2(logist)-8.4(ic)-256.5(regress)-9.6(ion.)-255.8(The)-260(method)-257.3(is)-261.6(then)-258(a)-252.9(syst)-8.2(ematic)-263.7(application)-263.8(of)-259.6(a)]TJ
/F5 1 Tf
35.9131 0 TD
[(templ)-9.4(ate)]TJ
/F1 1 Tf
3.7216 0 TD
(specied)Tj
-39.6347 -1.2007 TD
[(by)-251.9(MLN)-247(to)-249(different)-255.2(subse)-8(ts)-244.5(of)-248.2(the)-245.8(data)-9.4(.)-245.1(This)-245.8(templ)-9(ate)-247.6(is)-250.2(essential)-11.5(ly)-243.3(a)-247.2(mode)-8.4(l.)-242.9(We)-250.6(can)-250.6(use)-250(this)-248.8(templat)-9.3(e)-247.2(then)]TJ
0 -1.195 TD
[(for)-302.1(adding)-305(biological)-306.8(domain)-302.9(know)-7(ledge)-300.4(into)-298.8(the)-302.7(proba)-7.6(bilistic)-301.7(searchi)-12.5(nforma)-8.1(tion)-298.8(about)-304.3(how)-296.4(the)-302.8(various)]TJ
0 -1.2007 TD
[(part)-9.6(s)-280.8(o)0(f)-288(a)-287.1(biologi)-7.9(cal)-287.5(system)-293.9(interact)-294.9(or)-282.3(inue)-7.6(nce)-290.4(one)-288.6(another.)-292.9(For)-288(example,)-290.5(by)-286.1(usin)-7(g)]TJ
/F5 1 Tf
34.5246 0 TD
[(pair-wis)-9.3(e)]TJ
/F1 1 Tf
4.0744 0 TD
[(models)-8.1(,)-284.9(w)0(e)]TJ
-38.599 -1.2007 TD
[(expand)-343.9(the)-336.9(templat)-9.3(e)-332.6(t)0(o)-334.3(specica)-10.7(lly)-337.9(allow)-339.4(for)-336.3(pair-wi)-9.1(se)-334.6(gene)-336.7(intera)-10(ctions.)]TJ
1.0015 -1.2007 TD
[(A)-386(pair-wi)-9.1(se)-385.8(mode)-8.4(l)-384.8(encodes)-393.2(an)-384.6(aggregat)-10.5(ion)-386.3(of)-384.8(joint)-387.7(inue)-7.6(nces)-389.1(of)-384.8(pairs)-387.1(of)-384.8(marker)-9.9(s)-383.2(toge)-7.6(ther)-385.2(with)-388.1(their)]TJ
-1.0015 -1.2007 TD
[(int)-7.8(eractions)-385.1(on)-377.1(a)-372.4(p)-6.5(henotype.)-382.7(This)-376.7(mode)-8.4(l)-373.4(i)0(s)-381.1(a)0(n)-373.2(M)0(L)-9(N)-374.6(templ)-9(ate)-378.5(that)-380.2(explicitly)-383.5(takes)-381.2(into)-378.5(accou)-9.2(nt)-374.2(possi)-9(ble)]TJ
T*
[(gene)-444.8(interact)-10.3(ions.)-439.9(As)-439.1(with)-445(the)-439.3(single-m)-8.7(arker)-443.8(model,)-444.7(when)-441.2(predictin)-9.3(g)-438.9(phenotype)-445.7(values)-444.6(from)-443(genotype)]TJ
T*
[(valu)-7.6(es,)-352(the)-348.3(pair-w)-11.3(ise)-349.5(model)-353.3(can)-353(also)-350.2(be)-350.4(seen)-354.9(as)-351.6(a)-349.7(logistic)-355.9(regress)-9.6(ion.)-352.6(The)-351(difference)-359.2(betwee)-10.9(n)-347.9(the)-348.3(sing)-7(le-)]TJ
T*
[(mar)-9.6(ker)-307.7(and)-305.7(the)-314.1(pair-wise)-315.2(models)-309.7(becom)-10.9(es)-306.1(appar)-9.4(ent)-308.4(when)-310.4(we)-308.8(look)-307.4(clos)-8.8(ely)-308.4(at)-307.7(their)-309(corr)-8.8(esponding)-314.2(forms)-308.4(of)]TJ
0 -1.195 TD
[(regr)-8.8(ession.)-307.8(A)-306.3(logist)-8.4(ic)-302(regr)-8.8(ession)-307.4(derived)-315.2(from)-306.4(the)-308.4(pair-wise)-309.6(mode)-8.4(l)-305.1(contain)-8.7(s)-303.6(all)-305.5(the)-308.4(terms)-311(of)-305.1(the)-308.4(regression)]TJ
0 -1.2007 TD
[(of)-436(the)-433.6(single-m)-8.7(arker)-438.1(model)-438.7(given)-435.2(the)-433.6(same)-438.1(set)-434.8(of)-430.3(marker)-9.9(s,)-429.1(plus)-433.8(the)-433.6(terms)-441.8(that)-431.5(correspo)-9.1(nd)-434(to)-431.1(possi)-9(ble)]TJ
T*
[(int)-7.8(eractions)-248.5(in)-237.6(each)-247.4(pair)-242.9(of)-236.8(the)-240.2(mar)-9.6(kers.)-241.7(If)-238.8(the)-245.8(markers)-245.2(have)-245.6(no)-240.5(gene)-239.9(intera)-10(ctions,)-241.1(then)-246.6(a)-241.6(correspo)-9.1(nding)-239.9(pair-)]TJ
T*
[(wi)-8.2(se)-289(mode)-8.4(l)-293.7(reduces)-298.4(to)-294.5(a)-292.8(sing)-7(le-marke)-10.3(r)-293(model.)-296.8(On)-295.7(the)-297.1(other)-294.9(hand,)-295.4(if)-296.5(the)-291.4(mar)-9.6(kers)-292.5(do)-297.4(interact,)-300.9(then)-292.1(the)-297.1(pair-)]TJ
T*
[(wi)-8.2(se)-237.8(mode)-8.4(l)-236.8(can)-244.9(encompas)-10.5(s)-235.3(that)-243.7(effect)-244.3(whe)-8(n)-239.8(predictin)-9.3(g)-239.8(the)-240.2(phenot)-9.1(ype,)-237.8(even)-245.6(if)-239.6(the)-240.2(marker)-9.9(s)-241(individual)-9.1(ly)-237.6(have)]TJ
T*
[(litt)-8.4(le)-267.8(inue)-7.6(nce)-279(on)-269(the)-274.3(phenot)-9.1(ype)-271.5(and)-277.2(cannot)-278.4(therefore)-282.7(be)-270.8(detect)-9.8(ed)-270.8(as)-277.7(contributing)-280(in)-271.7(the)-274.3(sing)-7(le)-273.5(gene)-274.1(model.)]TJ
T*
[(Th)-7(is)-244.5(is)-250.2(why)-250.9(the)-251.5(pair-wi)-9.1(se)-249.2(models)-252.8(have)-251.3(been)-251.3(succe)-10.4(ssful)-249.9(at)-250.8(capturing)-256.9(synthet)-8.1(ic)-245.1(g)-6.5(ene)-250.6(interact)-10.3(ions)-246(that)-255.1(confer)-251.1(a)]TJ
T*
[(ph)-7.2(enotype)-341.7(only)-347.2(when)-344.5(both)-341.6(specic)-343.9(allel)-10(es)-340.2(of)-339.3(a)-344(pair)-339.6(of)-339.2(g)-6.5(enes)-343.6(are)-343.6(present.)-345.3(Howeve)-10.3(r,)-338.9(if)-342(two)-339(g)-6.5(enes)-343.6(have)-342.4(an)]TJ
0 -1.195 TD
[(eff)-8(ect)-270.4(on)-269(phenot)-9.1(ype)-271.5(individual)-9.1(ly,)-272.1(but)-266.8(also)-276.2(have)-274.1(a)-264.3(sign)-7(icant)-274.7(intera)-10(ction,)-273.3(the)-268.6(intera)-10(ction)-272.9(may)-269.4(be)-270.8(dete)-9.4(cted)-271.2(by)]TJ
0 -1.2007 TD
[(the)-325.5(single)-326.1(gene)-325.3(templat)-9.3(e)-321.2(a)0(s)-323.2(a)-321.2(non-additi)-8.3(ve)-322(effect)-329.6(of)-316.5(the)-325.5(two)-322(genes)-327.2(on)-320.2(predict)-10.7(ion)-318(accur)-11.1(acy)-324.5(\(because)-329.4(of)-322.2(the)]TJ
T*
[(induc)-8.4(ed)-356.1(corr)-8.8(elation)-364.3(or)-356.3(depend)-8.1(ence\).)-364.3(The)-362.4(pair-wi)-9.1(se)-357.3(model,)-365.1(on)-354.3(the)-359.7(othe)-7.6(r)-355.6(hand)-363.3(can)-358.7(detect)-362.6(sign)-7(icant)-365.7(inter-)]TJ
T*
[(act)-8.6(ion)-255.4(effect)-11(s)-252.3(even)-262.7(if)-256.6(the)-257.2(single)-257.8(gene)-262.7(effects)-263.3(are)-258.2(in)-260.4(the)-257.2(noise)-259.9(and)-254.5(no)-7.2(t)-253.9(detectabl)-10.9(e.)-259(The)-254.3(pair-w)-11.3(ise)-258.4(model,)-257(whi)-9(le)]TJ
T*
[(mor)-7.8(e)-361.1(com)-7.6(plex)-366.1(than)-371.8(the)-365.3(single)-371.6(gene)-370.8(model,)-365.1(is)-369.7(clearly)-371(just)-368.3(the)-365.3(tip)-366.3(of)-367.7(the)-365.3(iceb)-9.4(erg)-364.6(of)-367.7(the)-365.3(kinds)-366.3(of)-367.7(com)-7.6(plex)]TJ
T*
[(mode)-8.4(ls)-335.5(that)-334.7(likel)-8.2(y)-330.8(under)-7.6(lie)-334(real)-341.4(comple)-8.7(x)-330.8(genet)-10.1(ic)-330.4(tra)-8.8(its.)]TJ
/F2 1 Tf
0 67.0005 TD
[(31)-7.2(8)-28191.7(SAKH)-7.6(ANENKO)-346.8(AND)-338.4(GALAS)]TJ
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[(MLNs)-419.7(are)-417.6(powe)-8.8(rful)-419.5(tools)-414.6(for)-421.7(systems)-421(genet)-10.1(ics)-417.7(since)-421.1(they)-417.3(allow)-419.1(us)-418.1(to)-419.7(incorpor)-8.9(ate)-418.3(explicit)-419.1(biol)-8.6(ogical)]TJ
-1.0015 -1.195 TD
[(know)-7(ledge)-357.3(into)-355.7(genom)-9.1(e-wide)-358.2(stud)-7(ies.)-355.5(For)-356.3(exam)-10.2(ple,)-354.3(whe)-8(n)-353.6(using)-354.9(the)-359.7(pair-wi)-9.1(se)-357.3(model,)-359.4(we)-354.4(can)-358.7(cont)-7.6(rol)-354.2(the)]TJ
0 -1.2007 TD
[(interact)-10.3(ion)-357.9(terms)-362.2(of)-356.3(the)-359.7(correspo)-9.1(nding)-359.4(logistic)-361.6(regress)-9.6(ion)-357.9(through)-357.2(speci)-11.3(c)-355.3(constra)-9.2(ints)-356.9(in)-357.1(the)-359.6(logical)-364.3(rela-)]TJ
T*
[(tionships)-262.2(based)-259(on)-257.6(our)-254.7(biologi)-7.9(cal)-259(knowled)-8.1(ge.)-254.1(We)-256.2(coul)-7.6(d)-256.8(also)-253.5(de)-9(ne)-253.7(specic)-264.2(constra)-9.1(ints)-254.5(conce)-9.2(rning)-258.9(the)-257.2(gene)]TJ
T*
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/F1 1 Tf
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(\()Tj
/F2 1 Tf
.33 0 TD
(V)Tj
/F1 1 Tf
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(,)Tj
/F2 1 Tf
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(E)Tj
/F1 1 Tf
.6715 0 TD
(\))Tj
-42.8669 -1.2007 TD
[(based)-264.7(on)-263.3(the)-268.6(set)]TJ
/F2 1 Tf
6.6807 0 TD
(V)Tj
/F1 1 Tf
.9788 0 TD
[(\(thus,)-266.2(ever)-8.6(y)]TJ
/F5 1 Tf
5.0077 0 TD
(V)Tj
7.4718 0 0 6.641 239.981 366.4062 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 244.6866 368.0503 Tm
[(will)-265.6(be)-259.4(ref)-8(erred)-267.4(to)-260.4(as)-266.3(either)-266(a)]TJ
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11.8876 0 TD
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/F1 1 Tf
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[(or)-265.3(a)]TJ
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/F1 1 Tf
2.464 0 TD
[(\).)-264.9(Given)-268.4(a)-258.6(para)-8.6(meter)-266(set)]TJ
/F12 1 Tf
-33.523 -1.2007 TD
(Y)Tj
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(f)Tj
/F12 1 Tf
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/F1 1 Tf
6.9738 0 0 6.9738 140.0314 354.6141 Tm
(1)Tj
9.9626 0 0 9.9626 144 356.0881 Tm
()Tj
/F10 1 Tf
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()Tj
/F12 1 Tf
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(Y)Tj
/F5 1 Tf
6.9738 0 0 6.9738 176.9385 354.6141 Tm
(N)Tj
/F6 1 Tf
9.9626 0 0 9.9626 182.5511 356.0881 Tm
(g)Tj
/F1 1 Tf
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[(,)-529.6(whe)-8(re)-528.8(each)]TJ
/F12 1 Tf
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(Y)Tj
/F5 1 Tf
7.4718 0 0 6.641 256.9322 354.444 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 264.359 356.0881 Tm
[(is)-529(a)-531.8(condi)-8.4(tional)-532.5(p)-6.5(robability)-540.3(distributio)-8.3(n)-530(o)0(f)]TJ
/F5 1 Tf
18.7105 0 TD
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7.4718 0 0 6.641 456.8881 354.444 Tm
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/F1 1 Tf
9.9626 0 0 9.9626 464.3148 356.0881 Tm
[(given)-531.9(its)-532.5(p)-6.5(arents,)]TJ
/F12 1 Tf
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/F5 1 Tf
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(i)Tj
/F11 1 Tf
9.9626 0 0 9.9626 121.2661 344.1826 Tm
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7.4718 0 0 6.641 148.3653 342.4818 Tm
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(j)Tj
/F5 1 Tf
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/F5 1 Tf
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(V)Tj
7.4718 0 0 6.641 192.5858 342.4818 Tm
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/F1 1 Tf
9.9626 0 0 9.9626 194.6834 344.1826 Tm
[(\)\),)-279(then)]TJ
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/F1 1 Tf
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/F1 1 Tf
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[(can)-284.7(be)-276.5(factor)-9.2(ized)-282.5(as)]TJ
-21.8745 -2.8737 TD
(Pr)Tj
/F9 1 Tf
1.0528 0 TD
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/F2 1 Tf
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(V)Tj
/F9 1 Tf
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(\))Tj
/F6 1 Tf
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()Tj
/F14 1 Tf
1.1267 .9503 TD
(Y)Tj
/F5 1 Tf
6.9738 0 0 6.9738 280.7432 327.0046 Tm
(N)Tj
-.5772 -3.1867 TD
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/F6 1 Tf
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()Tj
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9.9626 0 0 9.9626 291.5149 315.5527 Tm
(Y)Tj
/F5 1 Tf
6.9738 0 0 6.9738 299.7354 314.0786 Tm
(i)Tj
/F6 1 Tf
9.9626 0 0 9.9626 303.8739 315.5527 Tm
()Tj
/F14 1 Tf
1.1324 .9503 TD
(Y)Tj
/F5 1 Tf
6.9738 0 0 6.9738 318.9542 327.0046 Tm
(N)Tj
-.5853 -3.1867 TD
(i)Tj
/F6 1 Tf
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()Tj
/F1 1 Tf
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(1)Tj
9.9626 0 0 9.9626 329.7259 315.5527 Tm
(Pr)Tj
/F9 1 Tf
1.0527 0 TD
(\()Tj
/F5 1 Tf
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(V)Tj
6.9738 0 0 6.9738 349.5684 314.0786 Tm
(i)Tj
/F6 1 Tf
9.9626 0 0 9.9626 352.0629 315.5527 Tm
(j)Tj
/F5 1 Tf
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[(parent)-10.3(s)]TJ
/F9 1 Tf
3.0103 0 TD
(\()Tj
/F5 1 Tf
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(V)Tj
6.9738 0 0 6.9738 394.0723 314.0786 Tm
(i)Tj
/F9 1 Tf
9.9626 0 0 9.9626 396.5101 315.5527 Tm
(\)\))Tj
/F15 1 Tf
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(:)Tj
/F9 1 Tf
12.4054 0 TD
(\()Tj
/F1 1 Tf
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(1)Tj
/F9 1 Tf
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(\))Tj
/F1 1 Tf
-41.8768 -2.8282 TD
[(Note)-358.7(that)-363.2(in)-357.1(many)-361.2(applica)-10.5(tions)-357.7(of)-362(BNs)-359.2(researc)-11.9(hers)-360.8(give)-360.4(causal)-361(mea)-9.4(ning)-358.6(to)-357.1(the)-359.6(edges)-361.4(of)-362(a)-355.4(networ)-9.3(k.)-359.6(In)]TJ
-1.0015 -1.2007 TD
[(general)-9.7(,)-376(however)-9.1(,)-376(the)-376.7(dir)-7(ectionalit)-9.7(y)-376.3(o)0(f)-379.1(edges)-378.5(d)-6.5(oes)-375.2(not)-380.6(imply)-382.7(causality)-10.3(.)-376(Note)-381.4(the)-376.7(sign)-7(icance)-384.3(of)-379.1(the)-376.7(fac-)]TJ
T*
[(torization)-411.2(is)-403.8(relat)-9.2(ed)-401.7(to)-408.3(the)-405.2(chain)-408.5(rule)-407.9(for)-404.6(condi)-8.4(tional)-407.3(probabilit)-11.1(ies.)-406.7(The)-402.2(interp)-8.2(retat)-9.2(ion)-403.4(of)-401.8(this)-408.1(rule)-407.9(is)-403.8(the)]TJ
T*
[(source)-341.4(of)-333.6(these)-341.4(incorrect)-340.4(causa)-10.4(lity)-335.7(argumen)-8.7(ts.)]TJ
1.0015 -1.2007 TD
[(Consider)-388.4(h)-6.5(ere)-383.4(an)-390.3(exampl)-8.7(e)-383.8(from)-386.1(a)-389.5(textbook)-389(\(Luger)-10.1(,)-381.6(2008\).)-387.4(Su)-6.4(ppose)-388.1(there)-387.7(is)-386.7(one)-391(event)-385.7(that)-391.6(can)-387.1(cause)]TJ
-1.0015 -1.2007 TD
[(orang)-7.6(e)-309.8(barrel)-9.2(s)-309.2(t)0(o)-311.6(appea)-9.2(r)-310(o)0(n)-308.8(the)-314.1(road,)]TJ
/F5 1 Tf
15.3759 0 TD
(B)Tj
/F11 1 Tf
.9446 0 TD
(=)Tj
/F5 1 Tf
.8877 0 TD
(true)Tj
/F1 1 Tf
1.6218 0 TD
[(:)-310.8(a)-309.8(road)-314.1(construc)-9.9(tion,)]TJ
/F5 1 Tf
8.974 0 TD
(C)Tj
/F11 1 Tf
1.0015 0 TD
(=)Tj
/F5 1 Tf
.8877 0 TD
(true)Tj
/F1 1 Tf
1.6161 0 TD
[(.)-307.7(T)0(h)-7(ere)-315.1(is)-307.1(als)-8(o)-308.1(one)-317.1(event)-317.4(that)]TJ
-31.3094 -1.195 TD
[(can)-273.3(cause)-277.8(ashi)-8.8(ng)-269(li)-7.1(ghts)-274.5(to)-271.7(appear)-279.4(on)-269(the)-274.3(road,)]TJ
/F5 1 Tf
19.2113 0 TD
(L)Tj
/F11 1 Tf
.8877 0 TD
(=)Tj
/F5 1 Tf
.882 0 TD
(true)Tj
/F1 1 Tf
1.6218 0 TD
[(:)-271(a)0(n)-270.8(accident)-13.1(,)]TJ
/F5 1 Tf
5.6564 0 TD
(A)Tj
/F11 1 Tf
.9446 0 TD
(=)Tj
/F5 1 Tf
.8877 0 TD
(true)Tj
/F1 1 Tf
1.6218 0 TD
[(.)-267.8(Supp)-8(ose)-272.7(then)-275.1(that)-272.1(ther)-9.6(e)-270(are)]TJ
-31.7134 -1.2007 TD
[(two)-282.1(events)-285.2(that)-277.8(can)-284.7(cause)-283.5(bad)-282.9(trafc,)]TJ
/F5 1 Tf
15.2621 0 TD
(T)Tj
/F11 1 Tf
.8877 0 TD
(=)Tj
/F5 1 Tf
.882 0 TD
(true)Tj
/F1 1 Tf
1.6218 0 TD
[(:)-276.7(either)-283.1(an)-282.2(accident)-286.2(or)-282.3(a)-281.4(road)-280(construc)-9.9(tion.)-282.1(This)-280(examp)-10.9(le)-279.2(can)]TJ
-18.6536 -1.2007 TD
[(be)-299.2(mode)-8.4(led)-302.7(by)-297.4(a)-304.2(B)0(N)-300.4(shown)-304.8(in)-300.2(Figure)-306.2(1,)-297.1(whos)-8.2(e)-298.5(para)-8.6(meters)-302.1(are)-303.7(give)-7.6(n)-296.7(i)0(n)-300.2(the)-302.7(tables)-305.1(belo)-7.6(w.)-301(Note)-301.8(that)-306.3(all)-299.8(the)]TJ
T*
[(variables)-345.3(are)-337.9(binary)-335.5(in)-334.3(this)-339.8(case.)]TJ
1.0015 -1.2007 TD
[(The)-282.7(proba)-7.6(bilis)-7.6(tic)-282.7(inde)-7.6(pendencie)-11.1(s)-280.8(encode)-9.9(d)-285.3(b)0(y)-280.4(the)-285.7(BN)-289(in)-283.1(Figur)-7.8(e)-281.4(1)-285.3(allow)-9.4(s)-280.8(u)0(s)-287.2(t)0(o)-283.1(express)-292.1(a)-281.4(joint)-290.9(probability)]TJ
-1.0015 -1.2007 TD
[(distribut)-9.7(ion)-380.6(in)-385.6(a)-383.8(com)-7.6(pact)-385(way)-389.3(with)-388.1(a)-383.8(small)-385.7(n)-6.5(umber)-386.7(of)-384.8(parame)-9.7(ters.)-386.7(Here,)-388.5(the)-388.1(rule)-385.2(is)-386.8(the)-382.4(proba)-7.6(biliti)-7(es)-385.8(of)]TJ
T*
[(nodes)-336.8(not)-335.1(dir)-7(ectly)-337.3(connec)-9.9(ted)-336.9(by)-331.6(edges)-338.6(are)-337.9(inde)-7.6(penden)-8.1(t)-333.6(and)-334.1(can)-335.9(be)-339.1(multiplie)-8.9(d:)]TJ
7.5286 -1.9177 TD
(Pr)Tj
/F9 1 Tf
1.0528 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(C)Tj
/F1 1 Tf
.6999 0 TD
()Tj
/F5 1 Tf
.5008 0 TD
(A)Tj
/F1 1 Tf
.6146 0 TD
()Tj
/F5 1 Tf
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(B)Tj
/F1 1 Tf
.6146 0 TD
()Tj
/F5 1 Tf
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(T)Tj
/F1 1 Tf
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()Tj
/F5 1 Tf
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(L)Tj
/F9 1 Tf
.552 0 TD
(\))Tj
/F6 1 Tf
.4894 0 TD
()Tj
/F1 1 Tf
1.104 0 TD
(Pr)Tj
/F9 1 Tf
1.0528 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(C)Tj
/F9 1 Tf
.6999 0 TD
(\))Tj
/F11 1 Tf
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()Tj
/F1 1 Tf
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(Pr)Tj
/F9 1 Tf
1.0528 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(A)Tj
/F9 1 Tf
.6146 0 TD
(\))Tj
/F11 1 Tf
.4894 0 TD
()Tj
/F1 1 Tf
.8877 0 TD
(Pr)Tj
/F9 1 Tf
1.0527 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(B)Tj
/F6 1 Tf
.6146 0 TD
(j)Tj
/F5 1 Tf
.2732 0 TD
(C)Tj
/F9 1 Tf
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(\))Tj
/F11 1 Tf
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()Tj
/F1 1 Tf
.882 0 TD
(Pr)Tj
/F9 1 Tf
1.0584 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(T)Tj
/F6 1 Tf
.6317 0 TD
(j)Tj
/F5 1 Tf
.2731 0 TD
(C)Tj
/F1 1 Tf
.6942 0 TD
()Tj
/F5 1 Tf
.5008 0 TD
(A)Tj
/F9 1 Tf
.6203 0 TD
(\))Tj
/F11 1 Tf
.4894 0 TD
()Tj
/F1 1 Tf
.8877 0 TD
(Pr)Tj
/F9 1 Tf
1.0527 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(L)Tj
/F6 1 Tf
.552 0 TD
(j)Tj
/F5 1 Tf
.2675 0 TD
(A)Tj
/F9 1 Tf
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(\))Tj
/F15 1 Tf
.3244 0 TD
(:)Tj
/F1 1 Tf
-34.3994 -1.9006 TD
[(MRFs)-328.8(are)-332.2(anot)-7.6(her)-330.4(kind)-330.2(of)-327.9(probabilis)-9.5(tic)-328.3(graph)-7.6(ical)-330.8(model,)-330.9(which)-336.7(is)-329.8(similar)-329.4(to)-328.7(BNs)-336.5(in)-328.7(how)-330.6(dependenci)-11.8(es)]TJ
-1.0015 -1.2007 TD
[(are)-246.8(represe)-10.1(nted)-240.9(\(K)-7.4(indermann)-246.3(and)-248.8(Snell,)-244(1980;)-245.6(Pearl,)-250.7(1988;)-245.6(Koller)-245.4(and)-248.8(Friedman,)-250.8(2009\).)-245.2(As)-245.7(opposed)-247.3(to)-243.3(BNs)]TJ
T*
[(thoug)-6.6(h,)-331.2(MRFs)-334.5(are)-332.2(dened)-337.4(on)]TJ
/F5 1 Tf
12.3656 0 TD
[(undir)-7.8(ected)]TJ
/F1 1 Tf
4.6321 0 TD
[(graphs.)-334.3(Re)-8(moving)-335.2(edge)-336.7(direction)-9.3(ality)-332.6(elimina)-9.3(tes)-332.4(the)-331.2(asym)-9.6(metry)]TJ
-16.9977 -1.2007 TD
[(betwee)-10.9(n)-421.9(a)-418(p)-6.5(arent)-421.8(v)-6.5(ertex)-421.8(and)-425.2(a)-423.7(child)-426.5(vertex,)-428.7(which)-427.7(allow)-9.4(s)-423.1(MRFs)-425.5(to)-425.4(represent)-429.8(cyclic)-430.9(dependenci)-11.8(es)-419.9(that)]TJ
ET
187.313 709.965 270.992 .51019 re
f
187.313 625.89 270.992 .51025 re
f
BT
/F3 1 Tf
8.9663 0 0 8.9663 206.7023 716.1447 Tm
(Table)Tj
/F1 1 Tf
3.0034 0 TD
(3.)Tj
/F3 1 Tf
1.7451 0 TD
[(Possible)-334.8(World)-338.1(\(in)]TJ
/F1 1 Tf
8.9406 0 TD
(FOL)Tj
/F3 1 Tf
1.8842 0 TD
[(\))-330.9(for)-334.7(the)-333.5(Program)]TJ
/F1 1 Tf
8.6561 0 TD
(\(13\))Tj
/F2 1 Tf
-26.3918 -2.036 TD
(Phenotype)Tj
/F1 1 Tf
4.4956 0 TD
(\()Tj
/F5 1 Tf
.3351 0 TD
(s)Tj
/F1 1 Tf
6.7246 0 0 5.9768 234.085 696.4156 Tm
(1)Tj
8.9663 0 0 8.9663 237.4299 697.8896 Tm
(,)Tj
/F5 1 Tf
.588 0 TD
(t)Tj
/F1 1 Tf
6.7246 0 0 5.9768 245.1968 696.4156 Tm
(1)Tj
8.9663 0 0 8.9663 248.5983 697.8896 Tm
[(\))-21044.8(True)]TJ
/F2 1 Tf
-6.8351 -1.2203 TD
(Phenotype)Tj
/F1 1 Tf
4.4956 0 TD
(\()Tj
/F5 1 Tf
.3351 0 TD
(s)Tj
/F1 1 Tf
6.7246 0 0 5.9768 234.085 685.4171 Tm
(1)Tj
8.9663 0 0 8.9663 237.4299 686.9479 Tm
(,)Tj
/F5 1 Tf
.588 0 TD
(t)Tj
/F1 1 Tf
6.7246 0 0 5.9768 245.1968 685.4171 Tm
(2)Tj
8.9663 0 0 8.9663 248.5983 686.9479 Tm
[(\))-20937.3(False)]TJ
/F6 1 Tf
-6.8351 -1.2266 TD
.1663 Tc
[()-27283.3()]TJ
/F2 1 Tf
0 -1.2203 TD
0 Tc
(Phenotype)Tj
/F1 1 Tf
4.4956 0 TD
(\()Tj
/F5 1 Tf
.3351 0 TD
(s)Tj
6.2762 0 0 6.2762 234.085 663.6471 Tm
(N)Tj
/F1 1 Tf
4.483 0 0 4.483 238.2802 662.74 Tm
(4)Tj
8.9663 0 0 8.9663 241.5117 665.0077 Tm
()Tj
/F5 1 Tf
.4995 0 TD
(t)Tj
6.2762 0 0 6.2762 248.485 663.6471 Tm
(N)Tj
/F1 1 Tf
4.483 0 0 4.483 252.6802 662.74 Tm
(3)Tj
8.9663 0 0 8.9663 255.9117 665.0077 Tm
[(\))-20229.1(True)]TJ
/F2 1 Tf
-7.6507 -1.2203 TD
(Allele)Tj
/F1 1 Tf
2.4533 0 TD
(\()Tj
/F5 1 Tf
.3351 0 TD
(s)Tj
/F1 1 Tf
6.7246 0 0 5.9768 215.7732 652.5353 Tm
(1)Tj
8.9663 0 0 8.9663 219.1747 654.066 Tm
(,)Tj
/F5 1 Tf
.5817 0 TD
(m)Tj
/F1 1 Tf
6.7246 0 0 5.9768 230.7968 652.5353 Tm
(1)Tj
8.9663 0 0 8.9663 234.1983 654.066 Tm
(,)Tj
/F5 1 Tf
.5817 0 TD
(v)Tj
/F1 1 Tf
6.7246 0 0 5.9768 243.4393 652.5353 Tm
(1)Tj
8.9663 0 0 8.9663 246.7842 654.066 Tm
[(\))-21139.6(False)]TJ
/F6 1 Tf
-6.6327 -1.2266 TD
.1663 Tc
[()-27283.3()]TJ
/F2 1 Tf
0 -1.2203 TD
0 Tc
(Allele)Tj
/F1 1 Tf
2.4533 0 TD
(\()Tj
/F5 1 Tf
.3351 0 TD
(s)Tj
6.2762 0 0 6.2762 215.7732 630.7652 Tm
(N)Tj
/F1 1 Tf
4.483 0 0 4.483 219.9684 629.8581 Tm
(4)Tj
8.9663 0 0 8.9663 223.1999 632.1259 Tm
()Tj
/F5 1 Tf
.4995 0 TD
(m)Tj
6.2762 0 0 6.2762 234.1417 630.7652 Tm
(N)Tj
/F1 1 Tf
4.483 0 0 4.483 238.3369 629.8581 Tm
(1)Tj
8.9663 0 0 8.9663 241.5684 632.1259 Tm
()Tj
/F5 1 Tf
.4995 0 TD
(v)Tj
6.2762 0 0 6.2762 250.0157 630.7652 Tm
(N)Tj
/F1 1 Tf
4.483 0 0 4.483 254.2109 629.8581 Tm
(2)Tj
8.9663 0 0 8.9663 257.4424 632.1259 Tm
[(\))-19950.9(False)]TJ
7.9702 0 0 7.9702 195.2503 614.9479 Tm
[(Here)-281.4(predicates)]TJ
/F2 1 Tf
6.5797 0 TD
[(Phenoty)12.5(pe)]TJ
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/F5 1 Tf
6.8287 0 TD
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7.4718 0 0 6.641 358.9227 327.0046 Tm
(i)Tj
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1.7641 0 TD
(V)Tj
7.4718 0 0 6.641 387.8928 327.0046 Tm
(j)Tj
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9.9626 0 0 9.9626 389.9904 328.7054 Tm
[(.)-319.1(Note)-318.8(als)-8(o)-313.8(that)-317.6(two)-322(directly)]TJ
-31.7077 -1.2007 TD
[(connec)-9.9(ted)-291.4(vertices)-293.3(are)-286.7(not)-289.6(condition)-11.2(ally)-283.5(inde)-7.6(penden)-8.1(t)-282.4(give)-7.6(n)-285.3(all)-288.4(other)-289.2(vertic)-10(es.)-283.7(Th)-7(is)-284.3(can)-290.4(be)-287.8(used)-290.6(to)-283.1(factor)-9.2(ize)]TJ
T*
[(an)-339.1(MRF.)]TJ
1.0015 -1.2007 TD
[(A)-266.5(clique)]TJ
/F5 1 Tf
3.7102 0 TD
(c)Tj
/F1 1 Tf
.7113 0 TD
[(of)-259.6(a)-264.3(graph)]TJ
/F5 1 Tf
4.3533 0 TD
(G)Tj
/F1 1 Tf
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[(is)-261.6(a)-264.3(subgr)-7(aph)-265.8(such)-267.8(that)-266.4(all)-260(v)-6.5(ertices)-269.8(of)]TJ
/F5 1 Tf
15.2165 0 TD
(c)Tj
/F1 1 Tf
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[(are)-269.6(fully)-267.4(connec)-9.9(ted.)-263.3(A)-266.5(Gibbs)-267.8(distributio)-8.3(n)]TJ
-26.683 -1.2007 TD
[(de)-9(ned)-334.1(on)]TJ
/F5 1 Tf
4.6264 0 TD
(G)Tj
/F1 1 Tf
1.0528 0 TD
(is)Tj
8.9854 -2.5152 TD
(Pr)Tj
/F9 1 Tf
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/F6 1 Tf
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()Tj
/F2 1 Tf
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(\))Tj
/F6 1 Tf
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()Tj
ET
273.033 258.066 6.1228 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 273.5999 262.5448 Tm
(1)Tj
/F5 1 Tf
-.0569 -1.3657 TD
(Z)Tj
/F14 1 Tf
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(Y)Tj
/F5 1 Tf
6.9738 0 0 6.9738 280.7999 244.97 Tm
(c)Tj
/F6 1 Tf
.4471 0 TD
(2)Tj
/F5 1 Tf
.6585 0 TD
(Cl)Tj
/F1 1 Tf
9.9626 0 0 9.9626 296.7873 255.7984 Tm
(exp)Tj
/F9 1 Tf
1.6161 0 TD
(\()Tj
/F6 1 Tf
.4894 0 TD
()Tj
/F17 1 Tf
.9389 0 TD
(/)Tj
/F5 1 Tf
6.9738 0 0 6.9738 333.8078 253.4739 Tm
(c)Tj
/F9 1 Tf
9.9626 0 0 9.9626 337.4361 255.7984 Tm
(\()Tj
/F2 1 Tf
.3244 0 TD
(v)Tj
/F5 1 Tf
6.9738 0 0 6.9738 345.6566 254.3244 Tm
(c)Tj
/F9 1 Tf
9.9626 0 0 9.9626 349.2849 255.7984 Tm
(\)\))Tj
/F15 1 Tf
.643 0 TD
(:)Tj
/F9 1 Tf
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/F1 1 Tf
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(2)Tj
/F9 1 Tf
.5008 0 TD
(\))Tj
/F1 1 Tf
-41.8768 -2.8623 TD
[(The)-328.2(so-c)-8(alled)-331.6(partition)-329(funct)-10.3(ion)]TJ
/F5 1 Tf
13.259 0 TD
(Z)Tj
/F6 1 Tf
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()Tj
/F14 1 Tf
1.104 .7512 TD
(P)Tj
/F2 1 Tf
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(v)Tj
/F14 1 Tf
9.9626 0 0 9.9626 251.0928 234.7653 Tm
(Q)Tj
/F5 1 Tf
6.9738 0 0 6.9738 260.4472 224.4472 Tm
(c)Tj
/F6 1 Tf
.4552 0 TD
(2)Tj
/F5 1 Tf
.6504 0 TD
(Cl)Tj
/F1 1 Tf
9.9626 0 0 9.9626 276.9448 227.2818 Tm
(exp)Tj
/F9 1 Tf
1.6218 0 TD
(\()Tj
/F6 1 Tf
.4894 0 TD
()Tj
/F17 1 Tf
.9389 0 TD
(/)Tj
/F5 1 Tf
6.9738 0 0 6.9738 313.9653 224.9574 Tm
(c)Tj
/F9 1 Tf
9.9626 0 0 9.9626 317.5936 227.2818 Tm
(\()Tj
/F2 1 Tf
.3244 0 TD
(v)Tj
/F5 1 Tf
6.9738 0 0 6.9738 325.8141 225.8078 Tm
(c)Tj
/F9 1 Tf
9.9626 0 0 9.9626 329.4424 227.2818 Tm
(\)\))Tj
/F1 1 Tf
.9731 0 TD
[(normaliz)-9.3(es)-328.9(the)-325.5(proba)-7.6(bility)-328.6(to)-328.7(ensure)-330(that)]TJ
/F14 1 Tf
-26.6033 -.4496 TD
(P)Tj
/F2 1 Tf
6.9738 0 0 6.9738 84.5858 212.485 Tm
(v)Tj
/F1 1 Tf
9.9626 0 0 9.9626 90.2551 215.3196 Tm
(Pr)Tj
/F9 1 Tf
1.0528 0 TD
(\()Tj
/F2 1 Tf
.3244 0 TD
(V)Tj
/F6 1 Tf
.8877 0 TD
()Tj
/F2 1 Tf
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(v)Tj
/F9 1 Tf
.5008 0 TD
(\))Tj
/F6 1 Tf
.4894 0 TD
()Tj
/F1 1 Tf
.9389 0 TD
[(1.)-245.8(He)15.5(re)]TJ
/F5 1 Tf
3.1526 0 TD
-.0116 Tc
(Cl)Tj
/F1 1 Tf
1.1723 0 TD
0 Tc
[(is)-227.4(th)18.5(e)-235.9(s)0(e)18.3(t)-236.8(of)-225.4(al)16.7(l)-231.1(c)0(l)16.7(i)0(q)18.5(u)0(e)13.8(s)-235.3(of)]TJ
/F5 1 Tf
10.0381 0 TD
(G)Tj
/F1 1 Tf
.7113 0 TD
(,)Tj
/F2 1 Tf
.4837 0 TD
(v)Tj
/F5 1 Tf
7.4718 0 0 6.641 301.2661 213.6755 Tm
(c)Tj
/F1 1 Tf
9.9626 0 0 9.9626 306.9353 215.3196 Tm
[(is)-227.4(a)-235.9(r)0(e)17.5(s)0(t)17.3(r)0(i)16.5(c)0(t)16.7(i)13.5(on)-229.2(of)-225.4(a)-235.9(c)0(o)19.4(n)0()16.3(g)0(u)15.5(r)14.3(at)16.7(io)18.5(n)-239.8(o)0(f)]TJ
/F2 1 Tf
14.0727 0 TD
(v)Tj
/F1 1 Tf
.7341 0 TD
[(to)-226.2(a)-235.9(c)0(l)16.7(i)13.5(qu)15.5(e)]TJ
/F5 1 Tf
4.3362 0 TD
(c)Tj
/F1 1 Tf
.4382 0 TD
(,)Tj
-42.9523 -1.2007 TD
[(an)-9(d)]TJ
/F17 1 Tf
1.7868 0 TD
(/)Tj
/F5 1 Tf
7.4718 0 0 6.641 98.5889 201.7133 Tm
(c)Tj
/F1 1 Tf
9.9626 0 0 9.9626 105.2787 203.3574 Tm
[(is)-335.5(a)-338.3(real-v)-9.2(alue)-9.4(d)-336.5(pote)-7.6(nti)-7.8(al)-336.1(funct)-10.3(ion)-340.8(assig)-10.7(ned)-339.8(to)-334.3(a)-338.3(clique)]TJ
/F5 1 Tf
22.7167 0 TD
(c)Tj
/F1 1 Tf
.4496 0 TD
[(.)-336.1(Given)-342.3(a)-338.3(Gibb)-9.7(s)-332(dist)-9.8(ribu)-7.8(tion)-338.6(on)]TJ
/F5 1 Tf
13.2021 0 TD
(G)Tj
/F1 1 Tf
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(,)Tj
-34.388 -2.5664 TD
(Pr)Tj
/F9 1 Tf
1.0528 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(V)Tj
/F1 1 Tf
6.9738 0 0 6.9738 152.0504 176.3149 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 157.7196 177.7889 Tm
()Tj
/F5 1 Tf
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(v)Tj
/F1 1 Tf
6.9738 0 0 6.9738 171.5527 176.3149 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 175.5212 177.7889 Tm
(j)Tj
/F2 1 Tf
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(V)Tj
/F6 1 Tf
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.2284 Tc
(nf)Tj
/F5 1 Tf
1.2292 0 TD
0 Tc
(V)Tj
/F1 1 Tf
6.9738 0 0 6.9738 205.9653 176.3149 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 209.9338 177.7889 Tm
.1715 Tc
(g)Tj
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1.6104 0 TD
0 Tc
(v)Tj
/F6 1 Tf
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(nf)Tj
/F5 1 Tf
1.2235 0 TD
0 Tc
(v)Tj
/F1 1 Tf
6.9738 0 0 6.9738 249.8456 176.3149 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 253.8141 177.7889 Tm
(g)Tj
/F9 1 Tf
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(\))Tj
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ET
274.677 180.113 97.568 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 303.4204 184.5921 Tm
(Pr)Tj
/F9 1 Tf
1.0528 0 TD
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(V)Tj
/F6 1 Tf
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(v)Tj
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(\))Tj
/F1 1 Tf
-6.5897 -1.3657 TD
(Pr)Tj
/F9 1 Tf
1.0584 0 TD
(\()Tj
/F2 1 Tf
.3244 0 TD
(V)Tj
/F6 1 Tf
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.2227 Tc
(nf)Tj
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(V)Tj
/F1 1 Tf
6.9738 0 0 6.9738 316.1196 169.4551 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 320.1448 170.9858 Tm
.1658 Tc
(g)Tj
/F2 1 Tf
1.6047 0 TD
0 Tc
(v)Tj
/F6 1 Tf
.7227 0 TD
.2227 Tc
(nf)Tj
/F5 1 Tf
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(v)Tj
/F1 1 Tf
6.9738 0 0 6.9738 359.9999 169.4551 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 364.0251 170.9858 Tm
(g)Tj
/F9 1 Tf
.5008 0 TD
(\))Tj
/F6 1 Tf
-23.7694 -2.9932 TD
()Tj
ET
143.206 143.49 131.131 .39685 re
f
BT
/F14 1 Tf
9.9626 0 0 9.9626 149.7826 162.6519 Tm
(Q)Tj
/F5 1 Tf
6.9738 0 0 6.9738 147.2881 146.2677 Tm
(c)Tj
/F6 1 Tf
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(2)Tj
/F5 1 Tf
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(Cl)Tj
/F1 1 Tf
9.9626 0 0 9.9626 163.2755 155.1684 Tm
(exp)Tj
/F9 1 Tf
1.6218 0 TD
(\()Tj
/F6 1 Tf
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()Tj
/F17 1 Tf
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(/)Tj
/F5 1 Tf
6.9738 0 0 6.9738 200.296 152.844 Tm
(c)Tj
/F9 1 Tf
9.9626 0 0 9.9626 203.9243 155.1684 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(v)Tj
/F1 1 Tf
6.9738 0 0 6.9738 211.6346 153.6377 Tm
(1)Tj
9.9626 0 0 9.9626 215.6031 155.1684 Tm
()Tj
/F5 1 Tf
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(v)Tj
/F1 1 Tf
6.9738 0 0 6.9738 225.0708 153.6377 Tm
(2)Tj
9.9626 0 0 9.9626 229.0393 155.1684 Tm
()Tj
/F10 1 Tf
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.1682 Tc
(...)Tj
/F1 1 Tf
1.3145 0 TD
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()Tj
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(v)Tj
6.9738 0 0 6.9738 258.2361 153.6377 Tm
(N)Tj
/F9 1 Tf
9.9626 0 0 9.9626 263.8488 155.1684 Tm
(\)\))Tj
/F14 1 Tf
-12.1095 -1.3373 TD
(P)Tj
/F5 1 Tf
6.9738 0 0 6.9738 146.8913 125.8582 Tm
(x)Tj
/F14 1 Tf
9.9626 0 0 9.9626 157.833 141.8456 Tm
(Q)Tj
/F5 1 Tf
6.9738 0 0 6.9738 155.3385 125.4614 Tm
(c)Tj
/F6 1 Tf
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(2)Tj
/F5 1 Tf
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(Cl)Tj
/F1 1 Tf
9.9626 0 0 9.9626 171.3826 134.3622 Tm
(exp)Tj
/F9 1 Tf
1.6161 0 TD
(\()Tj
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()Tj
/F17 1 Tf
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(/)Tj
/F5 1 Tf
6.9738 0 0 6.9738 208.3464 132.0378 Tm
(c)Tj
/F9 1 Tf
9.9626 0 0 9.9626 211.9747 134.3622 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(x)Tj
/F1 1 Tf
.4496 0 TD
()Tj
/F5 1 Tf
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(v)Tj
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6.9738 0 0 6.9738 229.1527 132.8315 Tm
(2)Tj
9.9626 0 0 9.9626 233.1212 134.3622 Tm
()Tj
/F10 1 Tf
.6715 0 TD
.1682 Tc
[(..)5.7(.)]TJ
/F1 1 Tf
1.3088 0 TD
0 Tc
()Tj
/F5 1 Tf
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(v)Tj
6.9738 0 0 6.9738 262.318 132.8315 Tm
(N)Tj
/F9 1 Tf
9.9626 0 0 9.9626 267.9306 134.3622 Tm
(\)\))Tj
/F6 1 Tf
.9788 .6829 TD
()Tj
ET
288.68 143.49 155.055 .39685 re
f
BT
/F14 1 Tf
9.9626 0 0 9.9626 307.2188 164.5795 Tm
(Q)Tj
/F6 1 Tf
6.9738 0 0 6.9738 292.7621 147.7417 Tm
(f)Tj
/F5 1 Tf
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(2)Tj
/F5 1 Tf
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(Cl)Tj
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(j)Tj
/F5 1 Tf
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(V)Tj
/F1 1 Tf
4.9813 0 0 4.9813 316.7999 146.6645 Tm
(1)Tj
/F6 1 Tf
6.9738 0 0 6.9738 319.8046 147.7417 Tm
(2)Tj
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(c)Tj
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(g)Tj
/F1 1 Tf
9.9626 0 0 9.9626 332.6739 157.096 Tm
(exp)Tj
/F9 1 Tf
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(\()Tj
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/F17 1 Tf
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6.9738 0 0 6.9738 369.6377 154.7716 Tm
(c)Tj
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9.9626 0 0 9.9626 373.2661 157.096 Tm
(\()Tj
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(v)Tj
/F1 1 Tf
6.9738 0 0 6.9738 380.9763 155.622 Tm
(1)Tj
9.9626 0 0 9.9626 384.9448 157.096 Tm
()Tj
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(v)Tj
/F1 1 Tf
6.9738 0 0 6.9738 394.4125 155.622 Tm
(2)Tj
9.9626 0 0 9.9626 398.4377 157.096 Tm
()Tj
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.1682 Tc
(...)Tj
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(v)Tj
6.9738 0 0 6.9738 427.6345 155.622 Tm
(N)Tj
/F9 1 Tf
9.9626 0 0 9.9626 433.1904 157.096 Tm
(\)\))Tj
/F14 1 Tf
-14.5052 -1.5308 TD
(P)Tj
/F5 1 Tf
6.9738 0 0 6.9738 292.3653 125.8582 Tm
(x)Tj
/F14 1 Tf
9.9626 0 0 9.9626 315.2692 141.8456 Tm
(Q)Tj
/F6 1 Tf
6.9738 0 0 6.9738 300.8125 124.9511 Tm
(f)Tj
/F5 1 Tf
.504 0 TD
(c)Tj
/F6 1 Tf
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(2)Tj
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(j)Tj
/F5 1 Tf
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(V)Tj
/F1 1 Tf
4.9813 0 0 4.9813 324.8503 123.9306 Tm
(1)Tj
/F6 1 Tf
6.9738 0 0 6.9738 327.855 124.9511 Tm
(2)Tj
/F5 1 Tf
.6585 0 TD
(c)Tj
/F6 1 Tf
.4471 0 TD
(g)Tj
/F1 1 Tf
9.9626 0 0 9.9626 340.7243 134.3622 Tm
(exp)Tj
/F9 1 Tf
1.6161 0 TD
(\()Tj
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()Tj
/F17 1 Tf
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6.9738 0 0 6.9738 377.7448 132.0378 Tm
(c)Tj
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9.9626 0 0 9.9626 381.3731 134.3622 Tm
(\()Tj
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(x)Tj
/F1 1 Tf
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()Tj
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(v)Tj
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6.9738 0 0 6.9738 398.4944 132.8315 Tm
(2)Tj
9.9626 0 0 9.9626 402.5196 134.3622 Tm
()Tj
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.1682 Tc
(...)Tj
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1.3145 0 TD
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(v)Tj
6.9738 0 0 6.9738 431.7164 132.8315 Tm
(N)Tj
/F9 1 Tf
9.9626 0 0 9.9626 437.2723 134.3622 Tm
(\)\))Tj
/F15 1 Tf
.8138 .6829 TD
(:)Tj
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-37.2674 -3.5452 TD
[(Not)-9(e)-321.2(that)-329(although)-337.8(for)-324.9(conven)-8.1(ience)-330.6(we)-331.6(write)]TJ
/F17 1 Tf
18.6935 0 TD
(/)Tj
/F5 1 Tf
6.9738 0 0 6.9738 266.9669 103.5212 Tm
(c)Tj
/F9 1 Tf
9.9626 0 0 9.9626 270.5952 105.8456 Tm
(\()Tj
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.3244 0 TD
(V)Tj
/F1 1 Tf
6.9738 0 0 6.9738 279.9495 104.3716 Tm
(1)Tj
9.9626 0 0 9.9626 283.9747 105.8456 Tm
()Tj
/F10 1 Tf
.6658 0 TD
.1682 Tc
(...)Tj
/F1 1 Tf
1.3145 0 TD
0 Tc
()Tj
/F5 1 Tf
.5008 0 TD
(V)Tj
6.9738 0 0 6.9738 314.8157 104.3716 Tm
(N)Tj
/F9 1 Tf
9.9626 0 0 9.9626 320.3716 105.8456 Tm
(\))Tj
/F1 1 Tf
.3244 0 TD
[(,)-324.7(this)-328.4(pote)-7.6(ntial)-326.9(functi)-8.2(on)-325.9(depend)-8.1(s)-326.3(only)-324.5(on)-331.6(the)]TJ
-25.0441 -1.2007 TD
[(vert)-9.6(ices)-289.4(from)-295.1(the)-291.4(clique)]TJ
/F5 1 Tf
9.9357 0 TD
(c)Tj
/F1 1 Tf
.4439 0 TD
[(,)-290.6(hence)-293.7(the)-291.4(rig)-7(ht)-288.8(side)-293.3(of)-288(the)-291.4(derivat)-10.7(ion)-289.6(above)-297.6(depends)-294.6(only)-290.3(on)-291.7(the)-291.4(variabl)-10.7(es)-289(from)]TJ
-10.3796 -1.195 TD
[(the)-314.1(cliques)-322.9(containing)]TJ
/F5 1 Tf
9.2585 0 TD
(V)Tj
7.4718 0 0 6.641 172.5165 80.2771 Tm
(1)Tj
/F1 1 Tf
9.9626 0 0 9.9626 176.2582 81.9779 Tm
[(.)-307.7(Thus,)-317.4(the)-314.1(variable)]TJ
/F5 1 Tf
8.2228 0 TD
(V)Tj
7.4718 0 0 6.641 264.3023 80.2771 Tm
(1)Tj
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/F5 1 Tf
.8877 0 TD
(v)Tj
/F6 1 Tf
.4496 0 TD
(j)Tj
/F2 1 Tf
.2675 0 TD
(U)Tj
/F11 1 Tf
1.0584 0 TD
(=)Tj
/F2 1 Tf
.882 0 TD
(u)Tj
/F1 1 Tf
.5577 0 TD
[(\))-293(from)-300.8(a)-298.5(correspo)-9.1(nding)-302.5(CPT)-301.9(of)-293.7(the)-302.7(BN.)-295.1(Con)-7(seque)-8.6(ntly,)-299.2(the)-297.1(proba)-7.6(bility)-300.2(of)-293.7(an)-299.2(event)]TJ
/F5 1 Tf
33.5401 0 TD
(e)Tj
/F1 1 Tf
.7398 0 TD
[(can)-301.8(be)]TJ
-40.5565 -1.2007 TD
[(com)-7.6(puted)-338.4(by)-331.6(weight)-10.1(ed)-333.4(mode)-8.4(l)-333.6(counting)-343.5(of)-333.6(the)-336.9(CNF)-334.5(in)-334.3(conj)-7.6(unction)-337(wi)-8.2(th)]TJ
/F5 1 Tf
29.6762 0 TD
(e)Tj
/F1 1 Tf
.4439 0 TD
(.)Tj
-29.1185 -1.2007 TD
[(For)-276.6(exampl)-8.7(e,)-276.1(one)-277.2(of)-276.6(the)-274.3(32)-274.7(\(2)]TJ
/F6 1 Tf
7.4718 0 0 6.641 204.0944 492.7747 Tm
(j)Tj
/F2 1 Tf
.2732 0 TD
(V)Tj
/F6 1 Tf
.7132 0 TD
(j)Tj
/F11 1 Tf
9.9626 0 0 9.9626 216.8503 488.3526 Tm
(=)Tj
/F1 1 Tf
.8877 0 TD
(2)Tj
7.4718 0 0 6.641 230.6834 492.7747 Tm
(5)Tj
9.9626 0 0 9.9626 234.4251 488.3526 Tm
[(\))-270.2(p)0(o)-7.2(ssible)-276(CNF)-277.6(mode)-8.4(ls)-272.9(corr)-8.8(espond)-275(to)-277.4(the)-274.3(fol)-7(lowing)-275.8(instant)-10.9(iation)-276.4(of)]TJ
-16.0929 -1.2007 TD
[(the)-336.9(rando)-7.6(m)-334.3(variabl)-10.7(es)-334.6(of)-333.6(the)-336.9(BN:)]TJ
/F5 1 Tf
13.902 -1.9234 TD
(C)Tj
/F8 1 Tf
.6999 0 TD
(\))Tj
/F5 1 Tf
1.195 0 TD
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 235.9558 455.7542 Tm
(2)Tj
9.9626 0 0 9.9626 239.981 457.2282 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(A)Tj
/F8 1 Tf
.6146 0 TD
(\))Tj
/F5 1 Tf
1.195 0 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 267.9873 455.7542 Tm
(1)Tj
9.9626 0 0 9.9626 272.0125 457.2282 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(B)Tj
/F8 1 Tf
.6146 0 TD
(\))Tj
/F5 1 Tf
1.195 0 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 300.0188 455.7542 Tm
(1)Tj
9.9626 0 0 9.9626 304.044 457.2282 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(T)Tj
/F8 1 Tf
.6317 0 TD
(\))Tj
/F5 1 Tf
1.2007 0 TD
(t)Tj
/F1 1 Tf
6.9738 0 0 6.9738 330.066 455.7542 Tm
(1)Tj
9.9626 0 0 9.9626 334.0912 457.2282 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(L)Tj
/F8 1 Tf
.552 0 TD
(\))Tj
/F5 1 Tf
1.195 0 TD
(l)Tj
/F1 1 Tf
6.9738 0 0 6.9738 359.3196 455.7542 Tm
(2)Tj
/F15 1 Tf
9.9626 0 0 9.9626 363.2881 457.2282 Tm
(:)Tj
/F1 1 Tf
-29.0275 -1.895 TD
[(In)-339.2(this)-334.1(mode)-8.4(l,)-334(the)-336.9(followin)-8.9(g)-330.8(propos)-7.7(itional)-336.8(lett)-7.4(ers)-337.3(are)-337.9(true:)]TJ
/F17 1 Tf
11.8193 -1.9234 TD
(k)Tj
/F5 1 Tf
6.9738 0 0 6.9738 196.8377 417.7133 Tm
(c)Tj
/F1 1 Tf
4.9813 0 0 4.9813 200.0125 416.6361 Tm
(2)Tj
9.9626 0 0 9.9626 203.4708 419.1873 Tm
()Tj
/F17 1 Tf
.5008 0 TD
(k)Tj
/F5 1 Tf
6.9738 0 0 6.9738 213.4488 417.7133 Tm
(a)Tj
/F1 1 Tf
4.9813 0 0 4.9813 216.9637 416.6361 Tm
(1)Tj
9.9626 0 0 9.9626 220.422 419.1873 Tm
()Tj
/F17 1 Tf
.5008 0 TD
(k)Tj
/F5 1 Tf
6.9738 0 0 6.9738 230.3999 417.7133 Tm
(b)Tj
/F1 1 Tf
4.9813 0 0 4.9813 233.9149 416.6361 Tm
(1)Tj
9.9626 0 0 9.9626 237.4299 419.1873 Tm
()Tj
/F17 1 Tf
.5008 0 TD
(k)Tj
/F5 1 Tf
6.9738 0 0 6.9738 247.4078 417.7133 Tm
(t)Tj
/F1 1 Tf
4.9813 0 0 4.9813 249.3354 416.6361 Tm
(1)Tj
9.9626 0 0 9.9626 252.8503 419.1873 Tm
()Tj
/F17 1 Tf
.5008 0 TD
(k)Tj
/F5 1 Tf
6.9738 0 0 6.9738 262.8283 417.7133 Tm
(l)Tj
/F1 1 Tf
4.9813 0 0 4.9813 264.8125 416.6361 Tm
(2)Tj
9.9626 0 0 9.9626 268.2708 419.1873 Tm
()Tj
/F17 1 Tf
.5008 0 TD
(h)Tj
/F5 1 Tf
6.9738 0 0 6.9738 278.2487 417.7133 Tm
(c)Tj
/F1 1 Tf
4.9813 0 0 4.9813 281.3668 416.6361 Tm
(2)Tj
9.9626 0 0 9.9626 284.8818 419.1873 Tm
()Tj
/F17 1 Tf
.5008 0 TD
(h)Tj
/F5 1 Tf
6.9738 0 0 6.9738 294.8597 417.7133 Tm
(a)Tj
/F1 1 Tf
4.9813 0 0 4.9813 298.3747 416.6361 Tm
(1)Tj
9.9626 0 0 9.9626 301.833 419.1873 Tm
()Tj
/F17 1 Tf
.5008 0 TD
(h)Tj
/F5 1 Tf
6.9738 0 0 6.9738 311.8109 417.4298 Tm
(b)Tj
/F1 1 Tf
4.9813 0 0 4.9813 315.3259 416.3526 Tm
(1)Tj
/F6 1 Tf
6.9738 0 0 6.9738 318.3306 417.4298 Tm
(j)Tj
/F5 1 Tf
.2683 0 TD
(c)Tj
/F1 1 Tf
4.9813 0 0 4.9813 323.3196 416.3526 Tm
(2)Tj
9.9626 0 0 9.9626 326.8346 419.1873 Tm
()Tj
/F17 1 Tf
.5008 0 TD
(h)Tj
/F5 1 Tf
6.9738 0 0 6.9738 336.8125 417.4298 Tm
(t)Tj
/F1 1 Tf
4.9813 0 0 4.9813 338.7401 416.3526 Tm
(1)Tj
/F6 1 Tf
6.9738 0 0 6.9738 341.7448 417.4298 Tm
(j)Tj
/F5 1 Tf
.2764 0 TD
(c)Tj
/F1 1 Tf
4.9813 0 0 4.9813 346.7905 416.3526 Tm
(2)Tj
6.9738 0 0 6.9738 349.7952 417.4298 Tm
()Tj
/F5 1 Tf
.4959 0 TD
(a)Tj
/F1 1 Tf
4.9813 0 0 4.9813 356.7684 416.3526 Tm
(1)Tj
9.9626 0 0 9.9626 360.2267 419.1873 Tm
()Tj
/F17 1 Tf
.5008 0 TD
(h)Tj
/F5 1 Tf
6.9738 0 0 6.9738 370.2046 417.4298 Tm
(l)Tj
/F1 1 Tf
4.9813 0 0 4.9813 372.1889 416.3526 Tm
(2)Tj
/F6 1 Tf
6.9738 0 0 6.9738 375.1936 417.4298 Tm
(j)Tj
/F5 1 Tf
.2683 0 TD
(a)Tj
/F1 1 Tf
4.9813 0 0 4.9813 380.5794 416.3526 Tm
(1)Tj
/F15 1 Tf
9.9626 0 0 9.9626 384.0377 419.1873 Tm
(:)Tj
/F1 1 Tf
-31.1102 -1.9974 TD
[(Con)-7(seque)-8.6(ntly,)-686.1(the)-689.7(weight)-693(of)-692.1(this)-686.9(model)-694.7(is)-682.7(a)-691.1(produc)-8.3(t)-686.4(o)0(f)-686.4(weights)-694.9(of)-686.4(these)-694.2(propos)-7.7(itional)-689.7(letters,)]TJ
0 -1.2007 TD
(0.6)Tj
/F11 1 Tf
1.5877 0 TD
()Tj
/F1 1 Tf
.8877 0 TD
(0.5)Tj
/F11 1 Tf
1.5877 0 TD
()Tj
/F1 1 Tf
.8877 0 TD
(0.2)Tj
/F11 1 Tf
1.5877 0 TD
()Tj
/F1 1 Tf
.882 0 TD
[(0.)-6.8(8)]TJ
/F11 1 Tf
1.5877 0 TD
()Tj
/F1 1 Tf
.8877 0 TD
(0.01)Tj
/F12 1 Tf
2.0884 0 TD
(&)Tj
/F1 1 Tf
1.3373 0 TD
(0.0005.)Tj
-12.32 -1.2007 TD
[(Thus,)-243.4(it)-240.4(is)-233.1(p)-6.5(ossible)-242.7(to)-237.6(represe)-10.1(nt)-237.6(and)-237.4(eluc)-9.4(idate)-240.5(the)-240.1(logical)-244.8(struct)-9.4(ure)-239.4(of)-236.8(BNs)-239.7(usin)-7(g)-234.1(the)-240.2(CNF)-243.5(formul)-9.1(ation.)-239.1(We)]TJ
-1.0015 -1.195 TD
[(can)-341.6(use)-335.3(this)-334.1(in)-340(turn)-332.2(to)-334.3(mak)-7.6(e)-332.6(the)-336.9(connec)-9.9(tion)-332.9(d)-6.5(irectly)-337.8(to)-334.3(MLN)-8(s.)]TJ
/F5 1 Tf
10.959 0 0 10.959 74.0976 339.5338 Tm
[(3.2.)-502(Representing)-331.1(Bayesian)-330.1(networks)-331(with)-330.9(Markov)-333.4(logic)-329.3(networks)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 84.0755 321.5621 Tm
[(The)-333.9(relat)-9.2(ionship)-336.4(between)-336.1(thes)-8.8(e)-326.9(t)0(w)-8.2(o)-330.8(kinds)-332.1(of)-333.6(networks)-336.4(can)-335.9(best)-333.2(be)-333.4(elucida)-10.5(ted)-331.2(by)-331.6(expl)-7.6(icitly)-336.1(formulating)]TJ
-1.0015 -1.195 TD
[(on)-7.2(e)-383.8(i)0(n)-391.2(terms)-396.3(of)-384.8(the)-393.8(other.)-392(Let)-393.6(us)-389.7(then)-388.9(encode)-396.9(a)-389.5(B)0(N)-391.4(using)-389(ML)-9(Ns)-387.9(by)-388.5(a)-389.5(construc)-9.9(tion)-389.8(simi)-7.6(lar)-390.1(to)-385.6(the)-393.8(CNF)]TJ
ET
113.953 259.88 350.702 .51022 re
f
113.953 69.732 350.702 .51025 re
f
113.953 241.568 350.702 .45351 re
f
BT
/F3 1 Tf
8.9663 0 0 8.9663 128.8629 277.0015 Tm
(Table)Tj
/F1 1 Tf
2.9971 0 TD
(4.)Tj
/F3 1 Tf
1.7514 0 TD
[(Set)-332.2(of)-335.1(Propositional)-333.1(Clauses)-337.2(Representing)-333.5(Each)-331.4(Element)-336(of)-335.1(Every)]TJ
-2.0992 -1.2203 TD
[(Conditional)-336.5(Probability)-332.1(Table)]TJ
/F1 1 Tf
14.5996 0 TD
(\(CPT\))Tj
/F3 1 Tf
2.8327 0 TD
[(of)-335.1(the)]TJ
/F1 1 Tf
3.2816 0 TD
(BN)Tj
/F3 1 Tf
1.7198 0 TD
[(Given)-332.1(in)-331.6(Figure)]TJ
/F1 1 Tf
7.5622 0 TD
(1)Tj
/F5 1 Tf
-34.3081 -2.0423 TD
[(BN)-338.7(component)-9081.1(CNF)-336.6(clauses)]TJ
/F1 1 Tf
0 -2.0486 TD
(Variable)Tj
/F5 1 Tf
3.7937 0 TD
(C)Tj
/F17 1 Tf
9.0544 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 228.0188 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 236.4661 227.1117 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 241.6818 229.3795 Tm
(_)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 254.0409 228.0188 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 256.8755 227.1117 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 377.5747 229.3795 Tm
(:)Tj
/F17 1 Tf
.6576 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 387.9495 228.0188 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 390.7274 227.1117 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 395.9999 229.3795 Tm
.2229 Tc
(_:)Tj
/F17 1 Tf
1.5301 0 TD
0 Tc
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 414.1983 228.0188 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 417.033 227.1117 Tm
(2)Tj
8.9663 0 0 8.9663 113.9527 218.4377 Tm
(Variable)Tj
/F5 1 Tf
3.7937 0 TD
(A)Tj
/F17 1 Tf
9.0544 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 217.0771 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 236.8062 216.17 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 242.022 218.4377 Tm
(_)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 254.381 217.0771 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 257.4991 216.17 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 377.5747 218.4377 Tm
(:)Tj
/F17 1 Tf
.6576 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 387.9495 217.0771 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 391.0676 216.17 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 396.2834 218.4377 Tm
.2229 Tc
(_:)Tj
/F17 1 Tf
1.5365 0 TD
0 Tc
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 414.5385 217.0771 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 417.7133 216.17 Tm
(2)Tj
8.9663 0 0 8.9663 113.9527 207.496 Tm
(Variable)Tj
/F5 1 Tf
3.7937 0 TD
(B)Tj
/F17 1 Tf
9.0544 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 206.1354 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 236.8062 205.1716 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 242.022 207.496 Tm
(_)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 254.381 206.1354 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 257.4991 205.1716 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 377.5747 207.496 Tm
(:)Tj
/F17 1 Tf
.6576 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 387.9495 206.1354 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 391.0676 205.1716 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 396.2834 207.496 Tm
.2229 Tc
(_:)Tj
/F17 1 Tf
1.5365 0 TD
0 Tc
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 414.5385 206.1354 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 417.7133 205.1716 Tm
(2)Tj
8.9663 0 0 8.9663 113.9527 196.4976 Tm
(Variable)Tj
/F5 1 Tf
3.7937 0 TD
(T)Tj
/F17 1 Tf
9.0544 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 195.1937 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 235.4456 194.2298 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 240.6613 196.4976 Tm
(_)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 253.0204 195.1937 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 254.7779 194.2298 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 377.5747 196.4976 Tm
(:)Tj
/F17 1 Tf
.6576 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 387.9495 195.1937 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 389.707 194.2298 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 394.9227 196.4976 Tm
.2229 Tc
(_:)Tj
/F17 1 Tf
1.5365 0 TD
0 Tc
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 413.1779 195.1937 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 414.9353 194.2298 Tm
(2)Tj
8.9663 0 0 8.9663 113.9527 185.5559 Tm
(Variable)Tj
/F5 1 Tf
3.7937 0 TD
(L)Tj
/F17 1 Tf
9.0544 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 184.1952 Tm
(l)Tj
/F1 1 Tf
4.483 0 0 4.483 235.4456 183.2881 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 240.6613 185.5559 Tm
(_)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 253.0204 184.1952 Tm
(l)Tj
/F1 1 Tf
4.483 0 0 4.483 254.7779 183.2881 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 377.5747 185.5559 Tm
(:)Tj
/F17 1 Tf
.6576 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 387.9495 184.1952 Tm
(l)Tj
/F1 1 Tf
4.483 0 0 4.483 389.707 183.2881 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 394.9227 185.5559 Tm
.2229 Tc
(_:)Tj
/F17 1 Tf
1.5365 0 TD
0 Tc
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 413.1779 184.1952 Tm
(l)Tj
/F1 1 Tf
4.483 0 0 4.483 414.9353 183.2881 Tm
(2)Tj
8.9663 0 0 8.9663 113.9527 174.6141 Tm
[(CPT)-336.8(for)]TJ
/F5 1 Tf
3.6673 0 TD
(C)Tj
/F17 1 Tf
9.1809 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 173.2535 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 236.4661 172.2897 Tm
(1)Tj
/F8 1 Tf
8.9663 0 0 8.9663 239.6976 174.6141 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 254.8913 173.2535 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 257.7259 172.2897 Tm
(1)Tj
/F17 1 Tf
8.9663 0 0 8.9663 377.5747 174.6141 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 382.0534 173.2535 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 384.8881 172.2897 Tm
(2)Tj
/F8 1 Tf
8.9663 0 0 8.9663 388.1196 174.6141 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 403.3133 173.2535 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 406.1479 172.2897 Tm
(2)Tj
8.9663 0 0 8.9663 113.9527 163.6157 Tm
[(CPT)-336.8(for)]TJ
/F5 1 Tf
3.6673 0 TD
(A)Tj
/F17 1 Tf
9.1809 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 162.3118 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 236.8062 161.348 Tm
(1)Tj
/F8 1 Tf
8.9663 0 0 8.9663 240.0377 163.6157 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 255.2314 162.3118 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 258.3495 161.348 Tm
(1)Tj
/F17 1 Tf
8.9663 0 0 8.9663 377.5747 163.6157 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 382.0534 162.3118 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 385.1716 161.348 Tm
(2)Tj
/F8 1 Tf
8.9663 0 0 8.9663 388.4597 163.6157 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 403.6534 162.3118 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 406.7715 161.348 Tm
(2)Tj
8.9663 0 0 8.9663 113.9527 152.674 Tm
[(CPT)-336.8(for)]TJ
/F5 1 Tf
3.6673 0 TD
(B)Tj
/F17 1 Tf
9.1809 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 151.3133 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 236.8062 150.4062 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 242.022 152.674 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 254.381 151.3133 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 257.2157 150.4062 Tm
(1)Tj
/F8 1 Tf
8.9663 0 0 8.9663 260.4472 152.674 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 275.6409 151.0866 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 278.759 150.1228 Tm
(1)Tj
/F6 1 Tf
6.2762 0 0 6.2762 281.5369 151.0866 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 286.0157 150.1228 Tm
(1)Tj
/F17 1 Tf
8.9663 0 0 8.9663 377.5747 152.674 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 382.0534 151.3133 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 385.1716 150.4062 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 390.444 152.674 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 402.803 151.3133 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 405.581 150.4062 Tm
(2)Tj
/F8 1 Tf
8.9663 0 0 8.9663 408.8125 152.674 Tm
(5)Tj
/F17 1 Tf
1.2014 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 424.0629 151.0866 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 427.181 150.1228 Tm
(1)Tj
/F6 1 Tf
6.2762 0 0 6.2762 429.9022 151.0866 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 434.4377 150.1228 Tm
(2)Tj
/F17 1 Tf
8.9663 0 0 8.9663 229.1527 141.7323 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 140.3716 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 236.8062 139.4078 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 242.022 141.7323 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 254.381 140.3716 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 257.2157 139.4078 Tm
(1)Tj
/F8 1 Tf
8.9663 0 0 8.9663 260.4472 141.7323 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 275.6409 140.0882 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 278.759 139.1811 Tm
(2)Tj
/F6 1 Tf
6.2762 0 0 6.2762 281.5369 140.0882 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 286.0157 139.1811 Tm
(1)Tj
/F17 1 Tf
8.9663 0 0 8.9663 377.5747 141.7323 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 382.0534 140.3716 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 385.1716 139.4078 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 390.444 141.7323 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 402.803 140.3716 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 405.581 139.4078 Tm
(2)Tj
/F8 1 Tf
8.9663 0 0 8.9663 408.8125 141.7323 Tm
(5)Tj
/F17 1 Tf
1.2014 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 424.0629 140.0882 Tm
(b)Tj
/F1 1 Tf
4.483 0 0 4.483 427.181 139.1811 Tm
(2)Tj
/F6 1 Tf
6.2762 0 0 6.2762 429.9022 140.0882 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 434.4377 139.1811 Tm
(2)Tj
8.9663 0 0 8.9663 113.9527 130.7338 Tm
[(CPT)-336.8(for)]TJ
/F5 1 Tf
3.6673 0 TD
(T)Tj
/F17 1 Tf
9.1809 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 129.4299 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 235.4456 128.4661 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 240.6613 130.7338 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 253.0204 129.4299 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 255.7983 128.4661 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 261.0708 130.7338 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 273.4298 129.4299 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 276.5479 128.4661 Tm
(1)Tj
/F8 1 Tf
8.9663 0 0 8.9663 279.7794 130.7338 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 294.9731 129.1464 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 296.7306 128.1826 Tm
(1)Tj
/F6 1 Tf
6.2762 0 0 6.2762 299.5086 129.1464 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 303.9873 128.1826 Tm
(1)Tj
6.2762 0 0 6.2762 306.7653 129.1464 Tm
()Tj
/F5 1 Tf
.4968 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 313.0015 128.1826 Tm
(1)Tj
/F17 1 Tf
8.9663 0 0 8.9663 377.5747 130.7338 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 382.0534 129.4299 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 383.8109 128.4661 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 389.0267 130.7338 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 401.3857 129.4299 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 404.2203 128.4661 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 409.4361 130.7338 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 421.7952 129.4299 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 424.97 128.4661 Tm
(2)Tj
/F8 1 Tf
8.9663 0 0 8.9663 428.2015 130.7338 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 443.3951 129.1464 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 445.1526 128.1826 Tm
(1)Tj
/F6 1 Tf
6.2762 0 0 6.2762 447.8739 129.1464 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 452.4093 128.1826 Tm
(1)Tj
6.2762 0 0 6.2762 455.1306 129.1464 Tm
()Tj
/F5 1 Tf
.5058 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 461.4235 128.1826 Tm
(2)Tj
/F17 1 Tf
8.9663 0 0 8.9663 229.1527 119.7921 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 118.4315 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 235.4456 117.5244 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 240.6613 119.7921 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 253.0204 118.4315 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 255.7983 117.5244 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 261.0708 119.7921 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 273.4298 118.4315 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 276.5479 117.5244 Tm
(1)Tj
/F8 1 Tf
8.9663 0 0 8.9663 279.7794 119.7921 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 294.9731 118.2047 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 296.7306 117.2409 Tm
(1)Tj
/F6 1 Tf
6.2762 0 0 6.2762 299.5086 118.2047 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 303.9873 117.2409 Tm
(2)Tj
6.2762 0 0 6.2762 306.7653 118.2047 Tm
()Tj
/F5 1 Tf
.4968 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 313.0015 117.2409 Tm
(1)Tj
/F17 1 Tf
8.9663 0 0 8.9663 377.5747 119.7921 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 382.0534 118.4315 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 383.8109 117.5244 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 389.0267 119.7921 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 401.3857 118.4315 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 404.2203 117.5244 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 409.4361 119.7921 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 421.7952 118.4315 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 424.97 117.5244 Tm
(2)Tj
/F8 1 Tf
8.9663 0 0 8.9663 428.2015 119.7921 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 443.3951 118.2047 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 445.1526 117.2409 Tm
(1)Tj
/F6 1 Tf
6.2762 0 0 6.2762 447.8739 118.2047 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 452.4093 117.2409 Tm
(2)Tj
6.2762 0 0 6.2762 455.1306 118.2047 Tm
()Tj
/F5 1 Tf
.5058 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 461.4235 117.2409 Tm
(2)Tj
/F17 1 Tf
8.9663 0 0 8.9663 229.1527 108.8504 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 107.4897 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 235.4456 106.5826 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 240.6613 108.8504 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 253.0204 107.4897 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 255.7983 106.5826 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 261.0708 108.8504 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 273.4298 107.4897 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 276.5479 106.5826 Tm
(1)Tj
/F8 1 Tf
8.9663 0 0 8.9663 279.7794 108.8504 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 294.9731 107.2063 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 296.7306 106.2992 Tm
(2)Tj
/F6 1 Tf
6.2762 0 0 6.2762 299.5086 107.2063 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 303.9873 106.2992 Tm
(1)Tj
6.2762 0 0 6.2762 306.7653 107.2063 Tm
()Tj
/F5 1 Tf
.4968 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 313.0015 106.2992 Tm
(1)Tj
/F17 1 Tf
8.9663 0 0 8.9663 377.5747 108.8504 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 382.0534 107.4897 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 383.8109 106.5826 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 389.0267 108.8504 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 401.3857 107.4897 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 404.2203 106.5826 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 409.4361 108.8504 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 421.7952 107.4897 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 424.97 106.5826 Tm
(2)Tj
/F8 1 Tf
8.9663 0 0 8.9663 428.2015 108.8504 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 443.3951 107.2063 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 445.1526 106.2992 Tm
(2)Tj
/F6 1 Tf
6.2762 0 0 6.2762 447.8739 107.2063 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 452.4093 106.2992 Tm
(1)Tj
6.2762 0 0 6.2762 455.1306 107.2063 Tm
()Tj
/F5 1 Tf
.5058 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 461.4235 106.2992 Tm
(2)Tj
/F17 1 Tf
8.9663 0 0 8.9663 229.1527 97.9086 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 96.548 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 235.4456 95.5842 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 240.6613 97.9086 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 253.0204 96.548 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 255.7983 95.5842 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 261.0708 97.9086 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 273.4298 96.548 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 276.5479 95.5842 Tm
(1)Tj
/F8 1 Tf
8.9663 0 0 8.9663 279.7794 97.9086 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 294.9731 96.2646 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 296.7306 95.3575 Tm
(2)Tj
/F6 1 Tf
6.2762 0 0 6.2762 299.5086 96.2646 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 303.9873 95.3575 Tm
(2)Tj
6.2762 0 0 6.2762 306.7653 96.2646 Tm
()Tj
/F5 1 Tf
.4968 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 313.0015 95.3575 Tm
(1)Tj
/F17 1 Tf
8.9663 0 0 8.9663 377.5747 97.9086 Tm
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 382.0534 96.548 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 383.8109 95.5842 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 389.0267 97.9086 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 401.3857 96.548 Tm
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 404.2203 95.5842 Tm
(2)Tj
/F6 1 Tf
8.9663 0 0 8.9663 409.4361 97.9086 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 421.7952 96.548 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 424.97 95.5842 Tm
(2)Tj
/F8 1 Tf
8.9663 0 0 8.9663 428.2015 97.9086 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 443.3951 96.2646 Tm
(t)Tj
/F1 1 Tf
4.483 0 0 4.483 445.1526 95.3575 Tm
(2)Tj
/F6 1 Tf
6.2762 0 0 6.2762 447.8739 96.2646 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(c)Tj
/F1 1 Tf
4.483 0 0 4.483 452.4093 95.3575 Tm
(2)Tj
6.2762 0 0 6.2762 455.1306 96.2646 Tm
()Tj
/F5 1 Tf
.5058 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 461.4235 95.3575 Tm
(2)Tj
8.9663 0 0 8.9663 113.9527 86.9102 Tm
[(CPT)-336.8(for)]TJ
/F5 1 Tf
3.6673 0 TD
(L)Tj
/F17 1 Tf
9.1809 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 233.6314 85.5496 Tm
(l)Tj
/F1 1 Tf
4.483 0 0 4.483 235.4456 84.6425 Tm
(1)Tj
/F6 1 Tf
8.9663 0 0 8.9663 240.6613 86.9102 Tm
(^)Tj
/F17 1 Tf
.8789 0 TD
(k)Tj
/F5 1 Tf
6.2762 0 0 6.2762 253.0204 85.5496 Tm
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 256.1385 84.6425 Tm
(1)Tj
/F8 1 Tf
8.9663 0 0 8.9663 259.37 86.9102 Tm
(5)Tj
/F17 1 Tf
1.195 0 TD
(h)Tj
/F5 1 Tf
6.2762 0 0 6.2762 274.5637 85.3228 Tm
(l)Tj
/F1 1 Tf
4.483 0 0 4.483 276.3779 84.359 Tm
(1)Tj
/F6 1 Tf
6.2762 0 0 6.2762 279.0992 85.3228 Tm
(j)Tj
/F5 1 Tf
.271 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 283.918 84.359 Tm
(1)Tj
/F17 1 Tf
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/F6 1 Tf
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(^)Tj
/F10 1 Tf
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(...)Tj
/F6 1 Tf
1.3714 0 TD
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(^)Tj
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(IV)Tj
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(i)Tj
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(K)Tj
/F9 1 Tf
9.9626 0 0 9.9626 382.1101 501.9022 Tm
(\()Tj
/F5 1 Tf
.3187 0 TD
(v)Tj
6.9738 0 0 6.9738 389.7637 500.4282 Tm
(i)Tj
4.9813 0 0 4.9813 391.7479 499.351 Tm
(K)Tj
/F9 1 Tf
9.9626 0 0 9.9626 396.3967 501.9022 Tm
12.7435 Tc
(\)\()Tj
/F1 1 Tf
13.3899 0 TD
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(8)Tj
/F9 1 Tf
.5008 0 TD
(\))Tj
/F10 1 Tf
-28.8226 -1.5023 TD
.1682 Tc
(...)Tj
/F1 1 Tf
-14.0557 -1.9974 TD
0 Tc
[(where)-935.2(the)-934.4(weight)]TJ
/F5 1 Tf
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6.9738 0 0 6.9738 205.9653 465.5621 Tm
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()Tj
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/F1 1 Tf
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(Pr)Tj
/F9 1 Tf
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(V)Tj
6.9738 0 0 6.9738 255.3448 465.5621 Tm
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()Tj
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(v)Tj
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(1)Tj
9.9626 0 0 9.9626 310.9605 467.0361 Tm
()Tj
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(...)Tj
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1.3088 0 TD
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()Tj
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(V)Tj
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(i)Tj
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9.9626 0 0 9.9626 350.0786 467.0361 Tm
()Tj
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(i)Tj
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(K)Tj
/F9 1 Tf
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(\)\))Tj
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[(.)-933.6(Note)-933.4(that)-932.2(the)-934.4(set)-935.6(\(8\))-933.8(contain)-8.7(s)]TJ
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(i)Tj
/F11 1 Tf
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()Tj
/F5 1 Tf
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(N)Tj
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()Tj
/F10 1 Tf
.8877 0 TD
.1682 Tc
(...)Tj
/F11 1 Tf
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()Tj
/F5 1 Tf
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(N)Tj
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(i)Tj
4.9813 0 0 4.9813 178.696 452.5227 Tm
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/F12 1 Tf
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[(.)-267.8(Here)]TJ
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(N)Tj
7.4718 0 0 6.641 535.8613 453.4298 Tm
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9.9626 0 0 9.9626 140.2015 443.1117 Tm
[(are)-360.7(the)-365.3(number)-364.7(of)-362(values)-364.9(variables)]TJ
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14.7158 0 TD
(V)Tj
7.4718 0 0 6.641 292.9322 441.4676 Tm
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[(can)-364.4(take.)-362.6(If)-358.3(Pr)]TJ
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(K)Tj
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(\))Tj
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(0,)Tj
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/F6 1 Tf
13.7256 -1.9177 TD
(:)Tj
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(i)Tj
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(\))Tj
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(\))Tj
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(\))Tj
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9.4065 -2.9193 TD
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/F5 1 Tf
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(V)Tj
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6.9738 0 0 6.9738 221.159 362.4944 Tm
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(N)Tj
/F9 1 Tf
9.9626 0 0 9.9626 302.1732 363.9684 Tm
(\))Tj
/F6 1 Tf
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()Tj
ET
318.047 366.236 6.1228 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 318.6141 370.7716 Tm
(1)Tj
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/F1 1 Tf
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(exp)Tj
/F14 1 Tf
1.6218 1.7129 TD
( )Tj
.9503 -.7625 TD
(X)Tj
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(f)Tj
/F5 1 Tf
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(F)Tj
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6.9738 0 0 6.9738 361.644 352.6298 Tm
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.1682 Tc
[(..)5.7(.)]TJ
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6.9738 0 0 6.9738 422.6455 362.4944 Tm
(N)Tj
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9.9626 0 0 9.9626 428.2581 363.9684 Tm
(\))Tj
/F14 1 Tf
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(!)Tj
/F1 1 Tf
.7796 -1.7129 TD
()Tj
/F9 1 Tf
8.2627 0 TD
(\()Tj
/F1 1 Tf
.3187 0 TD
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(10)Tj
/F9 1 Tf
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[(where)-360.4(the)-359.7(sum)-359.8(is)-352.6(take)-9.4(n)-353.6(over)-359.6(all)-356.7(formul)-9.1(as)-357.3(of)-356.3(the)-359.6(MLN.)-361.2(For)-356.3(each)-361.2(formula)]TJ
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7.4718 0 0 6.641 432.2833 331.8802 Tm
(i)Tj
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9.9626 0 0 9.9626 437.9526 333.5243 Tm
[(is)-358.3(its)-356.1(weight)-362.9(and)]TJ
/F5 1 Tf
7.2213 0 TD
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7.4718 0 0 6.641 512.6739 331.8802 Tm
(i)Tj
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9.9626 0 0 9.9626 518.3431 333.5243 Tm
[(is)-358.3(its)]TJ
-41.228 -1.2007 TD
[(charact)-11.5(eristic)-339(functi)-8.2(on:)]TJ
/F5 1 Tf
8.8374 -3.0501 TD
(f)Tj
6.9738 0 0 6.9738 198.4251 289.7007 Tm
(i)Tj
/F9 1 Tf
9.9626 0 0 9.9626 200.9196 291.1747 Tm
(\()Tj
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(v)Tj
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6.9738 0 0 6.9738 208.5732 289.7007 Tm
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(\))Tj
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(1)Tj
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6.9738 0 0 6.9738 307.3322 301.2661 Tm
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(\))Tj
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(\))Tj
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6.9738 0 0 6.9738 396.3401 301.2661 Tm
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9.9626 0 0 9.9626 401.9526 302.7401 Tm
(\))Tj
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(True)Tj
/F1 1 Tf
1.8893 0 TD
()Tj
-16.4343 -2.4014 TD
[(0)-2165.9(othe)-7.6(rwise)]TJ
/F15 1 Tf
6.9026 0 TD
(:)Tj
/F14 1 Tf
-7.8757 2.9591 TD
(\()Tj
/F1 1 Tf
-15.4555 -4.7402 TD
[(Becaus)-10.1(e)-258.6(o)0(f)-253.9(the)-262.9(way)-258.4(we)-257.6(const)-9.6(ructed)-263.3(this)-260.1(MLN)-258.4(to)-260.4(encode)-260.3(a)-258.6(BN,)-260.9(equatio)-8.7(n)-256.8(\(10\))-257.4(is)-261.6(a)-258.6(product)-262.2(of)-253.9(ele)-8.6(ments)-257.8(of)-259.6(the)]TJ
0 -1.2007 TD
[(BN)-425.6(condi)-8.4(tional)-424.4(proba)-7.6(bility)-425.3(tables)-430.3(corr)-8.8(esponding)-428(to)-425.4(the)-427.9(BN)-425.6(instanti)-8.7(ation)]TJ
/F5 1 Tf
30.6038 0 TD
(v)Tj
/F1 1 Tf
6.9738 0 0 6.9738 416.9763 247.5779 Tm
(1)Tj
9.9626 0 0 9.9626 420.9448 249.1086 Tm
()Tj
/F10 1 Tf
.6715 0 TD
.1682 Tc
[(..)5.7(.)]TJ
/F1 1 Tf
1.3088 0 TD
0 Tc
()Tj
/F5 1 Tf
.5008 0 TD
(v)Tj
6.9738 0 0 6.9738 450.1416 247.5779 Tm
(N)Tj
/F1 1 Tf
9.9626 0 0 9.9626 455.7542 249.1086 Tm
[(.)-421.5(Note)-426.9(also)-429.9(that)-425.8(the)]TJ
-34.9457 -1.2007 TD
[(partiti)-8.8(on)-308.8(functi)-8.2(on)]TJ
/F5 1 Tf
7.3806 0 TD
(Z)Tj
/F1 1 Tf
.8593 0 TD
[(d)-6.5(ened)-313.9(as)]TJ
/F5 1 Tf
4.4102 0 TD
(Z)Tj
/F6 1 Tf
.7796 0 TD
()Tj
/F14 1 Tf
1.104 .7512 TD
(P)Tj
/F5 1 Tf
6.9738 0 0 6.9738 262.8849 234.3117 Tm
(v)Tj
/F1 1 Tf
4.9813 0 0 4.9813 266.0031 233.2346 Tm
(1)Tj
6.9738 0 0 6.9738 269.0078 234.3117 Tm
()Tj
/F10 1 Tf
.504 0 TD
(...)Tj
/F1 1 Tf
.8129 0 TD
()Tj
/F5 1 Tf
.504 0 TD
(v)Tj
4.9813 0 0 4.9813 284.8251 233.2346 Tm
(N)Tj
/F1 1 Tf
9.9626 0 0 9.9626 291.118 237.1464 Tm
(exp)Tj
/F9 1 Tf
1.6161 0 TD
(\()Tj
/F14 1 Tf
.4894 .7512 TD
(P)Tj
/F6 1 Tf
6.9738 0 0 6.9738 322.5826 234.3117 Tm
(f)Tj
/F5 1 Tf
.4959 0 TD
(F)Tj
4.9813 0 0 4.9813 330.3495 233.2346 Tm
(i)Tj
/F6 1 Tf
6.9738 0 0 6.9738 332.2771 234.3117 Tm
(g)Tj
/F5 1 Tf
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T*
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T*
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T*
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T*
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6.9738 0 0 6.9738 320.1448 568.3463 Tm
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/F9 1 Tf
9.9626 0 0 9.9626 323.8865 569.8203 Tm
(\))Tj
/F6 1 Tf
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.882 0 TD
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/F9 1 Tf
4.5069 0 TD
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/F5 1 Tf
.3244 0 TD
[(Stra)-7(in)]TJ
/F1 1 Tf
2.4526 0 TD
()Tj
/F5 1 Tf
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6.9738 0 0 6.9738 418.507 568.3463 Tm
(l)Tj
/F9 1 Tf
9.9626 0 0 9.9626 420.9448 569.8203 Tm
9.7787 Tc
(\)\()Tj
/F1 1 Tf
10.4194 0 TD
.0065 Tc
(18)Tj
/F9 1 Tf
1.0072 0 TD
0 Tc
(\))Tj
/F10 1 Tf
-29.864 -1.4966 TD
.1682 Tc
(...)Tj
/F1 1 Tf
-13.0143 -2.4014 TD
0 Tc
[(if)-251(conditioned)-259.2(on)]TJ
/F2 1 Tf
7.1132 0 TD
[(Alle)-8.6(le)]TJ
/F1 1 Tf
2.464 0 TD
(\()Tj
/F5 1 Tf
.3357 0 TD
(Strain)Tj
/F1 1 Tf
2.4526 0 TD
(,)Tj
/F5 1 Tf
.4951 0 TD
(m)Tj
7.4718 0 0 6.641 242.929 529.3416 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 245.0267 530.9857 Tm
(,)Tj
/F5 1 Tf
.5008 0 TD
(v)Tj
7.4718 0 0 6.641 254.4944 529.3416 Tm
(j)Tj
/F1 1 Tf
9.9626 0 0 9.9626 256.592 530.9857 Tm
[(\))-247.4(for)-256.6(all)]TJ
/F5 1 Tf
3.2607 0 TD
(i)Tj
/F1 1 Tf
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[(.)-250.8(The)-254.3(equivalency)-260.1(betwee)-10.9(n)-251.2(models)-252.8(\(15,)-255(16\))-249(and)-254.5(\(17,)-255(18\))]TJ
-20.7307 -1.2007 TD
[(will)-339.6(be)-333.4(discusse)-10.3(d)-330.8(later)-339.2(in)-334.3(this)-339.8(sectio)-9.2(n.)]TJ
1.0015 -1.2007 TD
[(Let)-336.7(us)-332.8(introdu)-7.1(ce)-335.2(char)-8.6(acteristic)-342(functi)-8.2(ons)]TJ
/F5 1 Tf
16.8042 0 TD
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7.4718 0 0 6.641 289.9842 505.4172 Tm
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(p)Tj
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(k)Tj
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(:)Tj
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-14.9605 -2.9136 TD
(a)Tj
6.9738 0 0 6.9738 179.6031 476.5605 Tm
(ij)Tj
/F6 1 Tf
9.9626 0 0 9.9626 185.6692 478.0345 Tm
()Tj
/F1 1 Tf
1.8551 .5804 TD
[(1)-1170.1(allele)-342.6(of)-384.8(marker)]TJ
/F5 1 Tf
8.9285 0 TD
(m)Tj
6.9738 0 0 6.9738 300.3023 482.3432 Tm
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(j)Tj
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9.9626 0 0 9.9626 322.9794 483.8172 Tm
()Tj
-11.9274 -1.2007 TD
[(0)-1170.1(otherw)-9.3(ise)]TJ
/F14 1 Tf
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()Tj
/F5 1 Tf
15.3474 -1.4113 TD
(p)Tj
6.9738 0 0 6.9738 352.9133 476.5605 Tm
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/F6 1 Tf
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[(1)-1164.4(ph)-7.2(enotype)-336(is)]TJ
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6.9738 0 0 6.9738 454.5637 482.3432 Tm
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-8.1773 -1.2007 TD
[(0)-1164.4(othe)-7.6(rwise)]TJ
/F14 1 Tf
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()Tj
/F1 1 Tf
-26.1026 -4.8313 TD
[(Note)-313.1(that)]TJ
/F5 1 Tf
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7.4718 0 0 6.641 153.2976 442.318 Tm
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9.9626 0 0 9.9626 160.8377 443.9621 Tm
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[(1)-308.1(and)]TJ
/F5 1 Tf
2.5721 0 TD
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7.4718 0 0 6.641 200.296 442.318 Tm
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/F11 1 Tf
9.9626 0 0 9.9626 206.9291 443.9621 Tm
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[(1)-313.7(for)-313.5(a)-309.8(strai)-8.6(n)]TJ
/F5 1 Tf
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[(iff)-316.3(the)-314.1(correspo)-9.1(nding)-313.9(predica)-9.7(tes)]TJ
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[(\))-310(and)]TJ
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7.4718 0 0 6.641 122.4566 430.3558 Tm
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[(\))-247.4(are)-241.1(tru)-7(e.)-241.9(The)-242.9(ML)-9(N)-238(repr)-8.8(esented)-248(by)-246.2(the)-240.2(formul)-9.1(as)-243.5(\(17,)-243.6(18\))-243.3(encode)-9.9(s)-241(the)-245.8(joint)-245.4(proba)-7.6(bility)-243.2(distri)-10.3(bution)-243.4(\(see)]TJ
-1.8267 -1.2007 TD
[(equatio)-8.7(n)-330.8(\(4\)\):)]TJ
9.6682 -2.9193 TD
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/F9 1 Tf
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(p)Tj
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()Tj
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(a)Tj
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(1)Tj
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(\))Tj
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()Tj
ET
305.291 393.222 6.1228 .45352 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 305.8582 397.7574 Tm
(1)Tj
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/F14 1 Tf
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( )Tj
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(w)Tj
6.9738 0 0 6.9738 341.4613 389.4802 Tm
(k)Tj
9.9626 0 0 9.9626 345.2031 390.9542 Tm
(p)Tj
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(k)Tj
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()Tj
/F14 1 Tf
1.104 .9503 TD
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 369.9778 402.5763 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 374.6267 401.4991 Tm
(1)Tj
/F5 1 Tf
6.9738 0 0 6.9738 367.2566 380.1826 Tm
(i)Tj
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()Tj
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(1)Tj
/F14 1 Tf
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(X)Tj
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(N)Tj
/F1 1 Tf
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(2)Tj
/F5 1 Tf
6.9738 0 0 6.9738 383.1873 380.1826 Tm
(j)Tj
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/F1 1 Tf
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(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 398.6078 390.9542 Tm
(w)Tj
6.9738 0 0 6.9738 405.2975 389.4802 Tm
(ijk)Tj
9.9626 0 0 9.9626 412.951 390.9542 Tm
(a)Tj
6.9738 0 0 6.9738 417.9401 389.4802 Tm
(ij)Tj
9.9626 0 0 9.9626 422.3621 390.9542 Tm
(p)Tj
6.9738 0 0 6.9738 427.3511 389.4802 Tm
(k)Tj
/F14 1 Tf
9.9626 0 0 9.9626 431.1495 408.0188 Tm
(!)Tj
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(:)Tj
/F9 1 Tf
8.2968 0 TD
(\()Tj
/F1 1 Tf
.3187 0 TD
.0065 Tc
(19)Tj
/F9 1 Tf
1.0072 0 TD
0 Tc
(\))Tj
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-42.8783 -3.3688 TD
[(This)-285.7(equatio)-8.7(n)-279.6(yields)-291.9(a)-281.4(logist)-8.4(ic)-279.2(regr)-8.8(ession)-284.7(formul)-9.1(a)-281.4(whe)-8(re)-284.1(every)-288.2(characteri)-14.6(stic)-284.7(function)]TJ
/F5 1 Tf
34.8774 0 TD
(a)Tj
7.4718 0 0 6.641 460.0629 355.7479 Tm
(ij)Tj
/F1 1 Tf
9.9626 0 0 9.9626 467.0928 357.392 Tm
[(of)-282.3(each)-287.2(allele)-291.4(is)-284.3(a)]TJ
-36.0838 -1.2007 TD
[(binary)-341.2(predictor)-338.6(variabl)-10.7(e)-332.6(o)0(f)-339.2(a)-332.6(phenotype)-343.2(functi)-8.2(on)]TJ
/F5 1 Tf
20.5941 0 TD
(p)Tj
7.4718 0 0 6.641 317.7637 343.7857 Tm
(k)Tj
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9.9626 0 0 9.9626 324.4535 345.4298 Tm
[(\(an)-336.1(outcome)-339.6(variabl)-10.7(e)-332.6(o)0(f)-333.6(the)-336.9(logist)-8.4(ic)-336.1(regress)-9.6(ion\):)]TJ
-11.4608 -3.1184 TD
(log)Tj
/F14 1 Tf
1.2861 1.7129 TD
( )Tj
ET
232.554 316.63 102.387 .39685 re
f
BT
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6.9738 0 0 6.9738 251.2629 319.6346 Tm
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6.9738 0 0 6.9738 315.9495 306.0283 Tm
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(\))Tj
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(!)Tj
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/F6 1 Tf
9.9626 0 0 9.9626 365.8393 314.3621 Tm
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/F14 1 Tf
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(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 380.1826 325.9275 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 384.8314 324.907 Tm
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9.9626 0 0 9.9626 408.8125 314.3621 Tm
(w)Tj
6.9738 0 0 6.9738 415.4456 312.8314 Tm
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9.9626 0 0 9.9626 423.1558 314.3621 Tm
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6.9738 0 0 6.9738 428.1448 312.8314 Tm
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9.9626 0 0 9.9626 432.5668 314.3621 Tm
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8.9342 0 TD
(\()Tj
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(20)Tj
/F9 1 Tf
1.0072 0 TD
0 Tc
(\))Tj
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-42.8783 -3.3688 TD
[(Let)-285.5(us)-287.2(now)-285.1(com)-7.6(e)-287.1(back)-285.5(to)-288.8(the)-285.7(equival)-8.7(ency)-285.5(of)-288(models)-292.7(\(15,)-283.5(16\))-288.8(and)-288.6(\(17,)-283.5(18\).)-289.2(For)-288(simplicit)-10.1(y)-279.6(w)0(e)-291.8(will)-288.4(compare)]TJ
0 -1.2007 TD
[(the)-336.9(followi)-8.1(ng)-331.6(two)-339(models)-8.1(:)]TJ
/F5 1 Tf
18.0959 -2.0201 TD
(w)Tj
/F1 1 Tf
6.9738 0 0 6.9738 294.5196 247.181 Tm
(1)Tj
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9.9626 0 0 9.9626 301.3228 248.7117 Tm
(:)Tj
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/F9 1 Tf
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(\()Tj
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/F9 1 Tf
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(\))Tj
/F5 1 Tf
-3.6704 -1.5023 TD
(w)Tj
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6.9738 0 0 6.9738 294.5196 232.2708 Tm
(2)Tj
/F10 1 Tf
9.9626 0 0 9.9626 301.3228 233.7448 Tm
(:)Tj
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(A)Tj
/F9 1 Tf
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(\()Tj
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(x)Tj
/F9 1 Tf
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(\))Tj
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/F9 1 Tf
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(\()Tj
/F5 1 Tf
.3244 0 TD
(x)Tj
/F9 1 Tf
.4496 0 TD
16.5448 Tc
(\)\()Tj
/F1 1 Tf
17.1855 0 TD
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(21)Tj
/F9 1 Tf
1.0072 0 TD
0 Tc
(\))Tj
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-24.7823 -2.9989 TD
(w)Tj
/F6 1 Tf
6.9738 0 0 6.9738 294.5196 208.0062 Tm
(0)Tj
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0 -.9918 TD
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9.9626 0 0 9.9626 301.3228 203.8676 Tm
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(w)Tj
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6.9738 0 0 6.9738 294.5196 193.0393 Tm
(0)Tj
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0 -.9837 TD
(2)Tj
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9.9626 0 0 9.9626 301.3228 188.9007 Tm
(:)Tj
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/F9 1 Tf
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(x)Tj
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1.195 0 TD
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/F9 1 Tf
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(\()Tj
/F5 1 Tf
.3244 0 TD
(x)Tj
/F9 1 Tf
.4439 0 TD
16.4537 Tc
(\)\()Tj
/F1 1 Tf
17.0944 0 TD
.0065 Tc
(22)Tj
/F9 1 Tf
1.0072 0 TD
0 Tc
(\))Tj
/F1 1 Tf
-42.8783 -2.3957 TD
[(As)-336.7(in)-334.3(our)-334.3(earli)-9.2(er)-335.3(discussion,)-343.2(we)-337.3(introdu)-7.1(ce)-335.2(two)-339(characterist)-14.4(ic)-336.1(functions)]TJ
/F5 1 Tf
11.2844 -2.7941 TD
(a)Tj
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()Tj
/F1 1 Tf
1.8608 .5747 TD
(1)Tj
/F2 1 Tf
1.9974 0 TD
(A)Tj
/F1 1 Tf
1.0527 0 TD
[(is)-335.5(tru)-7(e)]TJ
-3.0501 -1.2007 TD
[(0)-1164.4(othe)-7.6(rwise)]TJ
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1.8608 .7284 TD
[(1)-1164.4(allel)-10(e)-332.6(o)0(f)]TJ
/F5 1 Tf
5.7475 0 TD
(m)Tj
/F1 1 Tf
6.9738 0 0 6.9738 391.3511 662.5132 Tm
(2)Tj
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/F5 1 Tf
1.0015 0 TD
(B)Tj
/F15 1 Tf
.6146 0 TD
(:)Tj
/F1 1 Tf
-8.8147 -1.4966 TD
[(0)-1164.4(o)-6.5(therwise)]TJ
/F14 1 Tf
-.9219 2.1795 TD
()Tj
/F1 1 Tf
-23.4564 -5.6052 TD
[(Figur)-7.8(e)-292.8(5)-296.7(show)-8.2(s)-292.2(a)-298.5(graphica)-10.5(l)-293.7(represe)-10.1(ntation)-299.9(of)-293.7(a)-298.5(mode)-8.4(l)-293.7(generat)-9.7(ed)-293.5(for)-302.2(two)-293.5(mark)-10.3(ers)-297.5(at)-296.3(the)-297.1(secon)-8.6(d)-291(itera)-9.2(tion.)]TJ
-1.0015 -1.2007 TD
[(Not)-9(ice)-270.4(that)-277.8(this)-271.5(mode)-8.4(l)-271(i)0(s)-272.9(simi)-7.6(lar)-270.6(to)-271.7(the)-274.3(mode)-8.4(l)-271(gener)-9.4(ated)-271.2(at)-273.5(the)-274.3(rst)-275.7(itera)-9.2(tion)-276(\(Fig.)-274.8(4\).)-271.3(The)-277(only)-273.3(difference)-285.2(is)]TJ
0 -1.195 TD
[(in)-340(the)-331.2(nu)-7.2(mber)-334.7(of)-333.6(predi)-10.3(ctor)-333.9(variabl)-10.7(es.)]TJ
/F2 1 Tf
10.959 0 0 10.959 230.57 550.7148 Tm
[(6.)-496.7(PAIR-WISE)-329.9(MODEL)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 84.0755 526.7904 Tm
[(Like)-377.3(a)-378.1(single-m)-8.7(arker)-381.2(model)-376.1(\(13\))-7(,)-370.3(a)-378.1(pair-wise)-383.5(model)-376.1(is)-375.4(expre)-9.4(ssed)-377.1(by)-371.4(the)-376.7(fol)-7(lowing)-378.2(program)-378.8(includi)-9.7(ng)]TJ
-1.0015 -1.2007 TD
[(mor)-7.8(e)-332.6(than)-337.7(one)-339.8(marker)-340(and)-334.1(variant)-10.7(:)]TJ
/F2 1 Tf
9.4235 -2.2193 TD
[(Phe)-8.8(notype)]TJ
/F9 1 Tf
4.5126 0 TD
(\()Tj
/F5 1 Tf
.3187 0 TD
[(S)-6.5(train)]TJ
/F1 1 Tf
2.4526 0 TD
()Tj
/F6 1 Tf
.6715 0 TD
()Tj
/F5 1 Tf
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(T)Tj
/F9 1 Tf
.6317 0 TD
(\))Tj
/F2 1 Tf
-9.526 -1.4966 TD
[(Alle)-8.6(le)]TJ
/F9 1 Tf
2.464 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(Strain)Tj
/F1 1 Tf
2.4526 0 TD
()Tj
/F6 1 Tf
.6658 0 TD
()Tj
/F5 1 Tf
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(M)Tj
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6.9738 0 0 6.9738 244.5165 476.277 Tm
(1)Tj
9.9626 0 0 9.9626 248.485 477.8078 Tm
()Tj
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/F5 1 Tf
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(1)Tj
/F9 1 Tf
9.9626 0 0 9.9626 274.6204 477.8078 Tm
(\))Tj
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/F9 1 Tf
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/F5 1 Tf
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[(S)-6.5(train)]TJ
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(M)Tj
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6.9738 0 0 6.9738 365.329 476.277 Tm
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()Tj
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(\))Tj
/F8 1 Tf
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/F9 1 Tf
8.9683 0 TD
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/F1 1 Tf
.3244 0 TD
(29)Tj
/F9 1 Tf
1.0015 0 TD
(\))Tj
/F8 1 Tf
-31.4517 -1.5023 TD
(0)Tj
/F2 1 Tf
1.195 0 TD
[(Phe)-8.8(notype)]TJ
/F9 1 Tf
4.5126 0 TD
(\()Tj
/F5 1 Tf
.3187 0 TD
[(Stra)-7(in)]TJ
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()Tj
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()Tj
/F5 1 Tf
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(T)Tj
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(\))Tj
/F15 1 Tf
.3244 0 TD
(:)Tj
/F1 1 Tf
-21.4704 -2.9989 TD
[(Assum)-8(ing)]TJ
/F5 1 Tf
4.4443 0 TD
(M)Tj
/F1 1 Tf
7.4718 0 0 6.641 136.6299 431.3196 Tm
(1)Tj
/F11 1 Tf
9.9626 0 0 9.9626 143.7165 432.9637 Tm
(=)Tj
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.8877 0 TD
(m)Tj
/F1 1 Tf
7.4718 0 0 6.641 159.7606 431.3196 Tm
(1)Tj
9.9626 0 0 9.9626 163.5023 432.9637 Tm
(,)Tj
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.6316 0 TD
(V)Tj
/F1 1 Tf
7.4718 0 0 6.641 175.9181 431.3196 Tm
(1)Tj
/F11 1 Tf
9.9626 0 0 9.9626 182.948 432.9637 Tm
(=)Tj
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(v)Tj
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7.4718 0 0 6.641 196.2708 431.3196 Tm
(1)Tj
9.9626 0 0 9.9626 200.0125 432.9637 Tm
(,)Tj
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.6317 0 TD
(M)Tj
/F1 1 Tf
7.4718 0 0 6.641 214.6393 431.3196 Tm
(2)Tj
/F11 1 Tf
9.9626 0 0 9.9626 221.7259 432.9637 Tm
(=)Tj
/F5 1 Tf
.8877 0 TD
(m)Tj
/F1 1 Tf
7.4718 0 0 6.641 237.7133 431.3196 Tm
(2)Tj
9.9626 0 0 9.9626 241.455 432.9637 Tm
(,)Tj
/F5 1 Tf
.6317 0 TD
(V)Tj
/F1 1 Tf
7.4718 0 0 6.641 253.8708 431.3196 Tm
(2)Tj
/F11 1 Tf
9.9626 0 0 9.9626 260.9574 432.9637 Tm
(=)Tj
/F5 1 Tf
.8877 0 TD
(v)Tj
/F1 1 Tf
7.4718 0 0 6.641 274.2802 431.3196 Tm
(2)Tj
9.9626 0 0 9.9626 278.0219 432.9637 Tm
[(,)-381.7(and)]TJ
/F5 1 Tf
2.464 0 TD
(T)Tj
/F11 1 Tf
.8877 0 TD
(=)Tj
/F5 1 Tf
.8877 0 TD
(t)Tj
/F1 1 Tf
7.4718 0 0 6.641 323.0361 431.3196 Tm
(1)Tj
9.9626 0 0 9.9626 326.7779 432.9637 Tm
[(,)-381.7(this)-385.3(progr)-7.8(am)-382.4(encode)-9.9(s)-383.2(a)-383.8(statemen)-10.3(t:)]TJ
/F5 1 Tf
15.2222 0 TD
[(for)-387.5(all)]TJ
-40.585 -1.2007 TD
[(str)-7.4(ains,)-314.7(the)-314.1(allel)-8.2(e)-315.5(values)-319.4(v)]TJ
/F1 1 Tf
7.4718 0 0 6.641 180.8503 419.3574 Tm
(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 187.7102 421.0015 Tm
[(and)-315.3(v)]TJ
/F1 1 Tf
7.4718 0 0 6.641 210.274 419.3574 Tm
(2)Tj
/F5 1 Tf
9.9626 0 0 9.9626 217.1338 421.0015 Tm
[(of)-311.6(mar)-7.4(kers)-316.3(m)]TJ
/F1 1 Tf
7.4718 0 0 6.641 270.9921 419.3574 Tm
(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 277.8519 421.0015 Tm
[(and)-315.3(m)]TJ
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7.4718 0 0 6.641 303.0802 419.3574 Tm
(2)Tj
/F5 1 Tf
9.9626 0 0 9.9626 309.9401 421.0015 Tm
[(togethe)-8.7(r)-314.9(\(as)-312.8(a)-313.7(pair\))-317(imply)-316.7(a)-313.8(phenot)-9.1(ype)-313.2(valu)-7.6(e)-315.5(t)]TJ
/F1 1 Tf
7.4718 0 0 6.641 498.2739 419.3574 Tm
(1)Tj
9.9626 0 0 9.9626 502.0156 421.0015 Tm
(.)Tj
-41.9507 -1.2007 TD
[(As)-251.3(in)-254.7(the)-251.5(case)-254.3(of)-253.9(a)-252.9(single-m)-8.7(arker)-256(model,)-257(the)-251.5(pair-wi)-9.1(se)-249.2(MLN)-258.4(\(29\))-251.7(encode)-9.9(s)-246.7(a)-252.9(joint)-256.8(probability)-256.5(distribut)-9.7(ion:)]TJ
6.0832 -3.1469 TD
(Pr)Tj
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1.0527 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(p)Tj
6.9738 0 0 6.9738 163.3889 376.1574 Tm
(m)Tj
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9.9626 0 0 9.9626 168.8881 377.6881 Tm
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(11)Tj
9.9626 0 0 9.9626 186.3495 377.6881 Tm
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(...)Tj
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1.3145 0 TD
0 Tc
()Tj
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(a)Tj
6.9738 0 0 6.9738 216.0566 376.1574 Tm
(N)Tj
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6.9738 0 0 6.9738 223.7102 376.1574 Tm
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9.9626 0 0 9.9626 231.874 377.6881 Tm
(\))Tj
/F6 1 Tf
.4894 0 TD
()Tj
ET
247.748 379.956 6.1228 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 248.3149 384.4345 Tm
(1)Tj
/F5 1 Tf
-.0569 -1.3657 TD
(Z)Tj
.7853 .6886 TD
(exp)Tj
/F14 1 Tf
1.3942 1.7129 TD
( )Tj
/F5 1 Tf
.7853 -1.7129 TD
(w)Tj
6.9738 0 0 6.9738 283.918 376.1574 Tm
(m)Tj
9.9626 0 0 9.9626 289.4739 377.6881 Tm
(p)Tj
6.9738 0 0 6.9738 294.4629 376.1574 Tm
(m)Tj
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9.9626 0 0 9.9626 301.6062 377.6881 Tm
()Tj
/F14 1 Tf
1.1097 .9446 TD
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 316.0062 389.2534 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 320.655 388.233 Tm
(1)Tj
/F5 1 Tf
6.9738 0 0 6.9738 313.2282 366.8597 Tm
(i)Tj
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.4471 0 TD
()Tj
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/F14 1 Tf
9.9626 0 0 9.9626 328.7054 387.0991 Tm
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 332.0503 389.2534 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 336.6991 388.233 Tm
(2)Tj
/F5 1 Tf
6.9738 0 0 6.9738 328.6487 366.803 Tm
(k)Tj
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()Tj
/F1 1 Tf
.9349 0 TD
(1)Tj
/F14 1 Tf
9.9626 0 0 9.9626 344.7495 387.0991 Tm
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 348.0944 389.2534 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 352.7432 388.233 Tm
(1)Tj
/F5 1 Tf
6.9738 0 0 6.9738 345.3164 366.8597 Tm
(j)Tj
/F6 1 Tf
.4471 0 TD
()Tj
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(1)Tj
/F14 1 Tf
9.9626 0 0 9.9626 360.7369 387.0991 Tm
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 364.0818 389.2534 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 368.7306 388.233 Tm
(2)Tj
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6.9738 0 0 6.9738 361.3038 366.803 Tm
(l)Tj
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()Tj
/F1 1 Tf
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(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 376.7243 377.6881 Tm
(w)Tj
6.9738 0 0 6.9738 383.3574 381.77 Tm
(kl)Tj
0 -.9837 TD
(ijm)Tj
9.9626 0 0 9.9626 392.8251 377.6881 Tm
(a)Tj
6.9738 0 0 6.9738 397.8141 376.1574 Tm
(ik)Tj
9.9626 0 0 9.9626 403.54 377.6881 Tm
(a)Tj
6.9738 0 0 6.9738 408.529 376.1574 Tm
(jl)Tj
9.9626 0 0 9.9626 412.951 377.6881 Tm
(p)Tj
6.9738 0 0 6.9738 417.9401 376.1574 Tm
(m)Tj
/F14 1 Tf
9.9626 0 0 9.9626 423.4959 394.7527 Tm
(!)Tj
/F15 1 Tf
.7796 -1.7129 TD
(:)Tj
/F9 1 Tf
5.7019 0 TD
(\()Tj
/F1 1 Tf
.3244 0 TD
(30)Tj
/F9 1 Tf
1.0015 0 TD
(\))Tj
/F1 1 Tf
-41.8768 -2.9705 TD
[(Since)-436.2(a)-429.3(genetic)-437.3(marker)-431(cannot)-437.7(have)-433.4(two)-430.1(differ)-9.4(ent)-427.9(allele)-433.6(valu)-7.6(es)-431.3(at)-427.2(the)-433.6(same)-432.4(time,)-435.4(which)-433.4(means)-433.2(that)]TJ
/F5 1 Tf
-1.0015 -1.2007 TD
(a)Tj
7.4718 0 0 6.641 79.0866 334.4314 Tm
(im)Tj
9.9626 0 0 9.9626 86.57 336.1322 Tm
(a)Tj
7.4718 0 0 6.641 91.559 334.4314 Tm
(in)Tj
/F11 1 Tf
9.9626 0 0 9.9626 100.7433 336.1322 Tm
(=)Tj
/F1 1 Tf
.8877 0 TD
.3365 Tc
[(0i)336.5(f)]TJ
/F5 1 Tf
1.7811 0 TD
0 Tc
(m)Tj
/F18 1 Tf
.8877 0 TD
(s)Tj
/F5 1 Tf
1.1723 0 TD
(n)Tj
/F1 1 Tf
.5008 0 TD
[(,)-330.4(expre)-9.4(ssion)-339(\(30\))-337.1(can)-335.9(be)-333.4(rewri)-10.6(tten)-334.7(as:)]TJ
5.5312 -2.0714 TD
(Pr)Tj
/F9 1 Tf
1.0528 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(p)Tj
6.9738 0 0 6.9738 226.6582 313.9653 Tm
(m)Tj
/F1 1 Tf
9.9626 0 0 9.9626 232.1574 315.496 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 242.1354 313.9653 Tm
(11)Tj
9.9626 0 0 9.9626 249.6188 315.496 Tm
()Tj
/F10 1 Tf
.6658 0 TD
.1682 Tc
(...)Tj
/F1 1 Tf
1.3145 0 TD
0 Tc
()Tj
/F5 1 Tf
.5008 0 TD
(a)Tj
6.9738 0 0 6.9738 279.3259 313.9653 Tm
(N)Tj
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4.9813 0 0 4.9813 283.9747 312.9448 Tm
(1)Tj
/F5 1 Tf
6.9738 0 0 6.9738 286.9794 313.9653 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 291.6283 312.9448 Tm
(2)Tj
9.9626 0 0 9.9626 295.1432 315.496 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 305.1212 319.5779 Tm
(11)Tj
0 -.9837 TD
(11)Tj
9.9626 0 0 9.9626 312.6046 315.496 Tm
()Tj
/F10 1 Tf
.6658 0 TD
.1682 Tc
(...)Tj
/F1 1 Tf
1.3145 0 TD
0 Tc
()Tj
/F5 1 Tf
.5008 0 TD
(b)Tj
6.9738 0 0 6.9738 342.3117 319.9747 Tm
(N)Tj
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4.9813 0 0 4.9813 346.9605 318.8976 Tm
(1)Tj
/F5 1 Tf
6.9738 0 0 6.9738 349.9653 319.9747 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 354.6141 318.8976 Tm
(1)Tj
/F5 1 Tf
6.9738 0 0 6.9738 342.3117 312.8314 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 346.9605 311.7542 Tm
(2)Tj
/F5 1 Tf
6.9738 0 0 6.9738 349.9653 312.8314 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 354.6141 311.7542 Tm
(2)Tj
/F9 1 Tf
9.9626 0 0 9.9626 358.129 315.496 Tm
(\))Tj
/F6 1 Tf
.4894 0 TD
()Tj
-15.5637 -2.5209 TD
()Tj
ET
218.948 292.649 6.1228 .39685 re
f
BT
/F1 1 Tf
9.9626 0 0 9.9626 219.5149 297.1274 Tm
(1)Tj
/F5 1 Tf
-.0569 -1.3657 TD
(Z)Tj
.7796 .6886 TD
(exp)Tj
/F14 1 Tf
1.3999 1.7129 TD
( )Tj
/F5 1 Tf
.7796 -1.7129 TD
(w)Tj
6.9738 0 0 6.9738 255.118 288.8503 Tm
(m)Tj
9.9626 0 0 9.9626 260.6172 290.381 Tm
(p)Tj
6.9738 0 0 6.9738 265.6062 288.8503 Tm
(m)Tj
/F6 1 Tf
9.9626 0 0 9.9626 272.8062 290.381 Tm
()Tj
/F14 1 Tf
1.104 .9446 TD
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 287.1495 301.9464 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 291.7983 300.9259 Tm
(1)Tj
/F5 1 Tf
6.9738 0 0 6.9738 284.3716 279.5527 Tm
(i)Tj
/F6 1 Tf
.4552 0 TD
()Tj
/F1 1 Tf
.9349 0 TD
(1)Tj
/F14 1 Tf
9.9626 0 0 9.9626 299.7921 299.7921 Tm
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 303.1369 301.9464 Tm
(N)Tj
/F1 1 Tf
4.9813 0 0 4.9813 307.7857 300.9259 Tm
(2)Tj
/F5 1 Tf
6.9738 0 0 6.9738 300.359 279.5527 Tm
(j)Tj
/F6 1 Tf
.4471 0 TD
()Tj
/F1 1 Tf
.943 0 TD
(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 315.7794 290.381 Tm
(w)Tj
6.9738 0 0 6.9738 322.4125 288.8503 Tm
(ijm)Tj
9.9626 0 0 9.9626 331.8802 290.381 Tm
(a)Tj
6.9738 0 0 6.9738 336.8692 288.8503 Tm
(ij)Tj
9.9626 0 0 9.9626 341.2913 290.381 Tm
(p)Tj
6.9738 0 0 6.9738 346.2802 288.8503 Tm
(m)Tj
/F6 1 Tf
9.9626 0 0 9.9626 353.4802 290.381 Tm
()Tj
/F9 1 Tf
13.5094 0 TD
(\()Tj
/F1 1 Tf
.3244 0 TD
(31)Tj
/F9 1 Tf
1.0015 0 TD
(\))Tj
/F6 1 Tf
-29.4429 -3.4712 TD
()Tj
/F14 1 Tf
1.8324 .9446 TD
(X)Tj
/F9 1 Tf
4.9813 0 0 4.9813 218.948 246.1039 Tm
(\()Tj
/F5 1 Tf
.3187 0 TD
(i)Tj
/F1 1 Tf
.2845 0 TD
()Tj
/F5 1 Tf
.5008 0 TD
(j)Tj
/F9 1 Tf
.2845 0 TD
(\))Tj
/F6 1 Tf
.3187 0 TD
(2)Tj
/F5 1 Tf
.6601 0 TD
(N)Tj
/F1 1 Tf
.6715 -.3301 TD
(1)Tj
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T*
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-21.8233 -1.2007 TD
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T*
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T*
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T*
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T*
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T*
[(by)-269(their)-274.9(seque)-8.6(nces,)-270(transl)-9.4(ation)-272.9(factors)-272.9(and)-271.5(the)-268.6(levels)-276.6(of)-265.3(modu)-6.6(lators)-271.1(like)-272.1(miR)-7.6(NAs\))-270.1(we)-274.7(need)-268.4(to)-271.8(represe)-10.2(nt)-266.1(this)]TJ
T*
[(kn)-7.2(owledge)-334.3(as)-328.9(constra)-9.1(ints)-328.4(on)-325.9(the)-331.2(models)-332.5(whe)-8(n)-325.1(using)-332.1(the)-325.5(d)-6.5(ata)-327.3(toge)-7.6(ther.)-328.6(This)-331.2(conce)-9.2(pt)-323(is)-329.8(a)-326.9(cent)-9.4(ral)-327.5(aspect)-332.6(of)]TJ
T*
[(tru)-7(e)-264.3(data)-265.5(integr)-8.2(ation)-267.2(and,)-266.2(as)-266.3(the)-268.6(know)-7(ledge)-266.2(of)-265.3(biology)-266.9(and)-271.5(medicine)-270.9(grows,)-273.1(is)-261.6(a)-264.3(major)-269.9(pote)-7.6(ntial)-264.3(appl)-7.6(ication)]TJ
0 -1.195 TD
[(for)-336.3(the)-336.9(methods)-344.7(we)-337.3(describ)-9.1(e)-332.6(here.)]TJ
/F2 1 Tf
10.959 0 0 10.959 245.4802 165.5999 Tm
[(8.)-496.7(CONCLUSION)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 84.0755 141.6755 Tm
[(Probab)-7.6(ilistic)-306.7(logic)-307(methods)-8.9(,)-296.3(partic)-10(ularly)-304.1(thos)-7(e)-298.5(that)-306.3(use)-301.2(graph)-7.6(ical)-302.4(mode)-8.4(l)-299.4(represe)-10.2(ntations)-307.6(as)-300.4(a)-304.2(central)-308.4(part)]TJ
-1.0015 -1.2007 TD
[(of)-390.5(the)-388.1(struct)-9.4(ure,)-387.7(are)-389.1(powe)-8.8(rful)-385.3(tools)-391.8(in)-385.6(the)-393.8(analysis)-393.2(of)-384.8(data)-9.4(.)-387.3(They)-385.9(are)-394.8(particula)-11.1(rly)-388.3(potent)-387.5(in)-391.3(dealing)-390(with)]TJ
T*
[(biol)-8.6(ogical)-332.3(data,)-334.1(as)-328.9(the)-331.2(eld)-331.2(is)-329.8(current)-9.9(ly)-328.7(in)-328.7(a)-326.9(state)-332.8(whe)-8(re)-329.7(the)-331.2(detailed)-338.4(data)-328.1(gener)-9.4(ation)-329.8(volum)-10.1(e)-326.9(i)0(s)-329.8(enormous)]TJ
0 -1.195 TD
[(and)-317.1(the)-314.1(know)-7(ledge)-317.4(of)-316.5(the)-314.1(under)-7.6(lying)-316.6(complex)-316.8(system)-9.3(s)-314.9(i)0(s)-312.8(substantia)-10.5(l,)-311.2(but)-318(very)-314.1(partia)-10(l)-310.8(and)-317.1(often)-317.6(uncertain,)]TJ
0 -1.2007 TD
[(wi)-8.2(th)-249(non-ne)-8.3(gligib)-7.2(le)-250.8(quant)-8.4(itative)-259(error)-256.2(leve)-9.4(ls.)-250.6(Takin)-8.2(g)-251.2(all)-260(of)-253.9(this)-254.5(into)-253.3(accou)-9.2(nth)-6.6(uge)-254.5(diverse)-259.5(data)-259.8(sets,)-255.1(partial)]TJ
T*
[(kn)-7.2(owledge)-322.9(of)-322.2(various)-326(type)-7.6(sis)-321.9(all)-322.6(but)-323.7(imposs)-7.6(ible)-323.3(without)-324.8(the)-319.8(syst)-8.2(ematic)-326.3(structure)-9.7(s)-320.6(provided)-325.6(by)-320.2(methods)]TJ
T*
[(and)-396.7(mode)-8.4(ls)-392.4(that)-397.3(combine)-402.2(the)-393.8(rigors)-399.4(of)-396.2(representi)-12.3(ng)-394.2(and)-391(tracki)-10(ng)-394.2(multipl)-8.5(e)-389.5(logical)-404.2(relations)-10.5(hips)-394(with)-399.5(the)]TJ
ET
74.098 699.023 430.413 .51025 re
f
74.098 577.644 430.413 .51025 re
f
74.098 680.712 430.413 .51019 re
f
BT
/F3 1 Tf
8.9663 0 0 8.9663 130.2803 716.1447 Tm
(Table)Tj
/F1 1 Tf
2.9971 0 TD
(7.)Tj
/F3 1 Tf
1.7514 0 TD
[(Summary)-336.7(of)-335.1(Single-Marker)]TJ
/F1 1 Tf
12.924 0 TD
(MLN)Tj
/F3 1 Tf
2.2193 0 TD
[(s)-335.8(Based)-335.7(on)-332.5(One)-330.4(and)-336.9(Two)-335.6(Markers)]TJ
-14.1886 -1.2203 TD
[(as)-333.9(Well)-335.1(as)-333.9(a)-333.2(Pair-Wise)]TJ
/F1 1 Tf
10.8754 0 TD
(MLN)Tj
/F3 1 Tf
2.5481 0 TD
[(Based)-335.7(on)-332.5(Two)-335.6(Markers)]TJ
/F5 1 Tf
-14.4605 -2.036 TD
[(First-order)-334.7(logic)-16441.3(Logistic)-332.8(regression)]TJ
/F1 1 Tf
-10.9323 -2.0549 TD
(1)Tj
/F2 1 Tf
7.303 0 TD
(Allele)Tj
/F1 1 Tf
2.4533 0 TD
(\()Tj
/F5 1 Tf
.3351 0 TD
(S)Tj
/F1 1 Tf
.4995 0 TD
(,)Tj
/F11 1 Tf
.7524 0 TD
(+)Tj
/F5 1 Tf
.7145 0 TD
(M)Tj
/F1 1 Tf
.8346 0 TD
(,)Tj
/F11 1 Tf
.7524 0 TD
(+)Tj
/F5 1 Tf
.7145 0 TD
(V)Tj
/F1 1 Tf
.6133 0 TD
(\))Tj
/F8 1 Tf
.3351 0 TD
(0)Tj
/F1 1 Tf
12.8924 0 TD
(log)Tj
/F14 1 Tf
1.2836 1.1128 TD
()Tj
ET
345.26 670.62 47.509 .34015 re
f
BT
/F1 1 Tf
6.2762 0 0 6.2762 345.2597 672.8313 Tm
(Pr)Tj
/F9 1 Tf
1.0478 0 TD
(\()Tj
/F5 1 Tf
.3252 0 TD
(p)Tj
4.483 0 0 4.483 356.9952 671.8676 Tm
(k)Tj
/F6 1 Tf
6.2762 0 0 6.2762 360.6802 672.8313 Tm
()Tj
/F1 1 Tf
.9304 0 TD
(1)Tj
/F6 1 Tf
.5058 0 TD
(j)Tj
/F5 1 Tf
.271 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 374.5133 671.8676 Tm
(11)Tj
6.2762 0 0 6.2762 379.5023 672.8313 Tm
()Tj
/F5 1 Tf
.4968 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 385.7952 671.8676 Tm
(12)Tj
/F9 1 Tf
6.2762 0 0 6.2762 390.7274 672.8313 Tm
(\))Tj
/F1 1 Tf
-7.2445 -1.1743 TD
(Pr)Tj
/F9 1 Tf
1.0478 0 TD
(\()Tj
/F5 1 Tf
.3252 0 TD
(p)Tj
4.483 0 0 4.483 356.9952 664.5542 Tm
(k)Tj
/F6 1 Tf
6.2762 0 0 6.2762 360.6802 665.4612 Tm
()Tj
/F1 1 Tf
.9304 0 TD
(0)Tj
/F6 1 Tf
.5058 0 TD
(j)Tj
/F5 1 Tf
.271 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 374.5133 664.5542 Tm
(11)Tj
6.2762 0 0 6.2762 379.5023 665.4612 Tm
()Tj
/F5 1 Tf
.4968 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 385.7952 664.5542 Tm
(12)Tj
/F9 1 Tf
6.2762 0 0 6.2762 390.7274 665.4612 Tm
(\))Tj
/F14 1 Tf
8.9663 0 0 8.9663 392.7684 678.5006 Tm
()Tj
/F6 1 Tf
.7588 -1.1128 TD
()Tj
/F5 1 Tf
.9421 0 TD
(w)Tj
6.7246 0 0 5.9768 413.9715 667.0486 Tm
(k)Tj
/F11 1 Tf
8.9663 0 0 8.9663 419.981 668.5227 Tm
(+)Tj
/F5 1 Tf
.8852 0 TD
(w)Tj
/F1 1 Tf
6.7246 0 0 5.9768 433.8708 667.0486 Tm
(11)Tj
/F5 1 Tf
1.0032 0 TD
(k)Tj
8.9663 0 0 8.9663 443.6219 668.5227 Tm
(a)Tj
/F1 1 Tf
6.7246 0 0 5.9768 448.1573 667.0486 Tm
(11)Tj
/F11 1 Tf
8.9663 0 0 8.9663 457.8518 668.5227 Tm
(+)Tj
/F5 1 Tf
.8852 0 TD
(w)Tj
/F1 1 Tf
6.7246 0 0 5.9768 471.7416 667.0486 Tm
(12)Tj
/F5 1 Tf
1.0033 0 TD
(k)Tj
8.9663 0 0 8.9663 481.5495 668.5227 Tm
(a)Tj
/F1 1 Tf
6.7246 0 0 5.9768 486.0282 667.0486 Tm
(12)Tj
/F2 1 Tf
8.9663 0 0 8.9663 139.5779 657.5809 Tm
(Phenotype)Tj
/F1 1 Tf
4.4956 0 TD
(\()Tj
/F5 1 Tf
.3351 0 TD
(S)Tj
/F1 1 Tf
.4995 0 TD
(,)Tj
/F11 1 Tf
.7461 0 TD
(+)Tj
/F5 1 Tf
.7208 0 TD
(T)Tj
/F1 1 Tf
.5501 0 TD
(\),)Tj
/F5 1 Tf
.9168 0 TD
(M)Tj
/F11 1 Tf
1.1697 0 TD
(=)Tj
/F5 1 Tf
.8852 0 TD
(m)Tj
/F1 1 Tf
6.7246 0 0 5.9768 238.507 656.1069 Tm
(1)Tj
8.9663 0 0 8.9663 74.0976 643.6345 Tm
(2)Tj
/F2 1 Tf
7.303 0 TD
(Allele)Tj
/F1 1 Tf
2.4533 0 TD
(\()Tj
/F5 1 Tf
.3351 0 TD
(S)Tj
/F1 1 Tf
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(,)Tj
/F11 1 Tf
.7524 0 TD
(+)Tj
/F5 1 Tf
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(M)Tj
/F1 1 Tf
.8346 0 TD
(,)Tj
/F11 1 Tf
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/F5 1 Tf
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(V)Tj
/F1 1 Tf
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(\))Tj
/F8 1 Tf
.3351 0 TD
(0)Tj
/F1 1 Tf
12.8924 0 TD
(log)Tj
/F14 1 Tf
1.2836 1.1065 TD
()Tj
ET
345.26 645.675 70.016 .39685 re
f
BT
/F1 1 Tf
6.2762 0 0 6.2762 345.2597 647.9431 Tm
(Pr)Tj
/F9 1 Tf
1.0478 0 TD
(\()Tj
/F5 1 Tf
.3252 0 TD
(p)Tj
4.483 0 0 4.483 356.9952 646.9794 Tm
(k)Tj
/F6 1 Tf
6.2762 0 0 6.2762 360.6802 647.9431 Tm
()Tj
/F1 1 Tf
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(1)Tj
/F6 1 Tf
.5058 0 TD
(j)Tj
/F5 1 Tf
.271 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 374.5133 646.9794 Tm
(11)Tj
6.2762 0 0 6.2762 379.5023 647.9431 Tm
()Tj
/F5 1 Tf
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(a)Tj
/F1 1 Tf
4.483 0 0 4.483 385.7952 646.9794 Tm
(12)Tj
6.2762 0 0 6.2762 390.7274 647.9431 Tm
()Tj
/F5 1 Tf
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(a)Tj
/F1 1 Tf
4.483 0 0 4.483 397.0204 646.9794 Tm
(21)Tj
6.2762 0 0 6.2762 402.0093 647.9431 Tm
()Tj
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(a)Tj
/F1 1 Tf
4.483 0 0 4.483 408.3022 646.9794 Tm
(22)Tj
/F9 1 Tf
6.2762 0 0 6.2762 413.2345 647.9431 Tm
(\))Tj
/F1 1 Tf
-10.8306 -1.1743 TD
(Pr)Tj
/F9 1 Tf
1.0478 0 TD
(\()Tj
/F5 1 Tf
.3252 0 TD
(p)Tj
4.483 0 0 4.483 356.9952 639.6093 Tm
(k)Tj
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6.2762 0 0 6.2762 360.6802 640.5731 Tm
()Tj
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/F5 1 Tf
.271 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 374.5133 639.6093 Tm
(11)Tj
6.2762 0 0 6.2762 379.5023 640.5731 Tm
()Tj
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(a)Tj
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4.483 0 0 4.483 385.7952 639.6093 Tm
(12)Tj
6.2762 0 0 6.2762 390.7274 640.5731 Tm
()Tj
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(a)Tj
/F1 1 Tf
4.483 0 0 4.483 397.0204 639.6093 Tm
(21)Tj
6.2762 0 0 6.2762 402.0093 640.5731 Tm
()Tj
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(a)Tj
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4.483 0 0 4.483 408.3022 639.6093 Tm
(22)Tj
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6.2762 0 0 6.2762 413.2345 640.5731 Tm
(\))Tj
/F14 1 Tf
8.9663 0 0 8.9663 415.2755 653.5557 Tm
()Tj
/F6 1 Tf
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()Tj
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-31.5071 -1.2203 TD
(Phenotype)Tj
/F1 1 Tf
4.4956 0 TD
(\()Tj
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(S)Tj
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(M)Tj
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1.1508 0 TD
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(2f)Tj
/F5 1 Tf
1.4353 0 TD
0 Tc
(m)Tj
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6.2762 0 0 6.2762 243.3259 631.3322 Tm
(1)Tj
8.9663 0 0 8.9663 246.9543 632.6927 Tm
()Tj
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6.2762 0 0 6.2762 257.896 631.3322 Tm
(2)Tj
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8.9663 0 0 8.9663 261.5243 632.6927 Tm
(g)Tj
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7.2966 0 TD
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6.7246 0 0 5.9768 332.9007 631.162 Tm
(k)Tj
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8.9663 0 0 8.9663 338.9102 632.6927 Tm
(+)Tj
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6.7246 0 0 5.9768 352.8566 631.162 Tm
(11)Tj
/F5 1 Tf
1.0032 0 TD
(k)Tj
8.9663 0 0 8.9663 362.6078 632.6927 Tm
(a)Tj
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6.7246 0 0 5.9768 367.0865 631.162 Tm
(11)Tj
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8.9663 0 0 8.9663 376.781 632.6927 Tm
(+)Tj
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(w)Tj
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6.7246 0 0 5.9768 390.7274 631.162 Tm
(12)Tj
/F5 1 Tf
1.0032 0 TD
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8.9663 0 0 8.9663 400.4786 632.6927 Tm
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8.9663 0 0 8.9663 414.7086 632.6927 Tm
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(w)Tj
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6.7246 0 0 5.9768 428.5983 631.162 Tm
(21)Tj
/F5 1 Tf
1.0032 0 TD
(k)Tj
8.9663 0 0 8.9663 438.3495 632.6927 Tm
(a)Tj
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6.7246 0 0 5.9768 442.8282 631.162 Tm
(21)Tj
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8.9663 0 0 8.9663 452.5794 632.6927 Tm
(+)Tj
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(w)Tj
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6.7246 0 0 5.9768 466.4692 631.162 Tm
(22)Tj
/F5 1 Tf
1.0032 0 TD
(k)Tj
8.9663 0 0 8.9663 476.2203 632.6927 Tm
(a)Tj
/F1 1 Tf
6.7246 0 0 5.9768 480.6991 631.162 Tm
(22)Tj
8.9663 0 0 8.9663 74.0976 618.7463 Tm
(3)Tj
/F2 1 Tf
7.303 0 TD
(Allele)Tj
/F1 1 Tf
2.4533 0 TD
(\()Tj
/F5 1 Tf
.3351 0 TD
(S)Tj
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(,)Tj
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6.7246 0 0 5.9768 189.6944 617.2156 Tm
(1)Tj
8.9663 0 0 8.9663 193.0393 618.7463 Tm
(,)Tj
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.7524 0 TD
(+)Tj
/F5 1 Tf
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(V)Tj
/F1 1 Tf
6.7246 0 0 5.9768 211.748 617.2156 Tm
(1)Tj
8.9663 0 0 8.9663 215.0928 618.7463 Tm
(\))Tj
/F6 1 Tf
.3351 0 TD
(^)Tj
/F1 1 Tf
12.14 0 TD
(log)Tj
/F14 1 Tf
1.2836 1.1065 TD
()Tj
ET
345.26 620.787 71.15 .34015 re
f
BT
/F1 1 Tf
6.2762 0 0 6.2762 345.2597 622.9983 Tm
(Pr)Tj
/F9 1 Tf
1.0478 0 TD
(\()Tj
/F5 1 Tf
.3252 0 TD
(p)Tj
4.483 0 0 4.483 356.9952 622.0912 Tm
(m)Tj
/F6 1 Tf
6.2762 0 0 6.2762 361.7574 622.9983 Tm
()Tj
/F1 1 Tf
.9394 0 TD
(1)Tj
/F6 1 Tf
.4968 0 TD
(j)Tj
/F5 1 Tf
.271 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 375.6472 622.0912 Tm
(11)Tj
6.2762 0 0 6.2762 380.6361 622.9983 Tm
()Tj
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.4968 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 386.8723 622.0912 Tm
(12)Tj
6.2762 0 0 6.2762 391.8613 622.9983 Tm
()Tj
/F5 1 Tf
.5058 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 398.1542 622.0912 Tm
(21)Tj
6.2762 0 0 6.2762 403.1432 622.9983 Tm
()Tj
/F5 1 Tf
.4968 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 409.3794 622.0912 Tm
(22)Tj
/F9 1 Tf
6.2762 0 0 6.2762 414.3684 622.9983 Tm
(\))Tj
/F1 1 Tf
-11.0112 -1.1653 TD
(Pr)Tj
/F9 1 Tf
1.0478 0 TD
(\()Tj
/F5 1 Tf
.3252 0 TD
(p)Tj
4.483 0 0 4.483 356.9952 614.7211 Tm
(m)Tj
/F6 1 Tf
6.2762 0 0 6.2762 361.7574 615.6849 Tm
()Tj
/F1 1 Tf
.9394 0 TD
(0)Tj
/F6 1 Tf
.4968 0 TD
(j)Tj
/F5 1 Tf
.271 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 375.6472 614.7211 Tm
(11)Tj
6.2762 0 0 6.2762 380.6361 615.6849 Tm
()Tj
/F5 1 Tf
.4968 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 386.8723 614.7211 Tm
(12)Tj
6.2762 0 0 6.2762 391.8613 615.6849 Tm
()Tj
/F5 1 Tf
.5058 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 398.1542 614.7211 Tm
(21)Tj
6.2762 0 0 6.2762 403.1432 615.6849 Tm
()Tj
/F5 1 Tf
.4968 0 TD
(a)Tj
/F1 1 Tf
4.483 0 0 4.483 409.3794 614.7211 Tm
(22)Tj
/F9 1 Tf
6.2762 0 0 6.2762 414.3684 615.6849 Tm
(\))Tj
/F14 1 Tf
8.9663 0 0 8.9663 416.4093 628.6675 Tm
()Tj
/F6 1 Tf
.7588 -1.1065 TD
()Tj
/F2 1 Tf
-31.6335 -1.2266 TD
(Allele)Tj
/F1 1 Tf
2.4533 0 TD
(\()Tj
/F5 1 Tf
.3351 0 TD
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