diff --git "a/merges.txt" "b/merges.txt" new file mode 100644--- /dev/null +++ "b/merges.txt" @@ -0,0 +1,49740 @@ +#version: 0.2 +Ġ t +Ġ a +h e +Ġ â +Ġ i +o n +Ġt he +t i +r e +Ġ s +Ġ ( +Ġ o +Ġ c +i n +e r +Ġâ Ī +Ġ f +o r +Ġ w +e n +Ġ p +Ġo f +n d +a t +Ġ 1 +ti on +a l +Ġ d +Ġ b +e s +Ġ Î +Ġ 2 +Ġ n +Ġi n +e d +Ġ m +r o +Ġ = +Ġa nd +i t +Ġi s +Ġt h +a r +Ġ e +Ġ T +a n +Ġ ) +l e +i s +Ġ , +ĠâĪ Ĵ +Ġ . +Ġt o +in g +i c +Ġ 0 +Ġ Ï +e t +Ġth at +o m +Ġf or +Ġâ Ģ +v e +Ġ re +a s +l y +Ġ h +Ġ g +Ġ + +Ġ l +Ġ u +a tion +e c +Ġc on +Ġw e +l l +â Ī +a c +en t +Ġ k +Ġ A +Ġ S +ĠT he +Ġ L +s t +o w +s i +Ġ v +Ġ I +Ġ on +Ġ F +it h +Ġp ro +i m +Ġ q +Ġ C +c e +o t +Ġ P +o u +Ġb e +Ġs u +Ġ [ +Ġ r +ĠâĪ Ī +Ġâ ī +Ġa s +Ġ x +s e +u l +Ġw ith +Ġa n +Ġ R +o l +Ġb y +Ġ j +Ġ W +Ġ 3 +Ġ N +ĠâĢ ² +Ġs t +Ġe x +q u +Ġ B +a m +v er +Ġ H +Ġ | +Ġ M +i g +ĠâĢ ¢ +o re +t s +o d +u m +âĪ Ĵ +r i +Ġa re +u r +Ġd e +Ġ E +u t +Ġ G +a b +e m +Ġ D +Ġc om +c h +a in +) . +re s +p p +it y +) , +Ġa l +Ġ X +c tion +ti c +i l +at e +Ġâī ¤ +ti n +Ġw h +Ġw he +a p +Ġ * +f in +i v +Ġp o +Ġ 4 +Ġth is +c t +e l +t er +Ġc an +Ġ : +Ġcom p +ĠW e +i f +i r +u re +Ġh a +g e +u n +ĠÎ ± +Ĩ Ĵ +Ġ y +ti ve +ro m +o ll +Ġâ Ĭ +Ġ ï +p l +Ġï £ +Ġ K +ic h +ĠI n +Ġo r +tin g +Ġ le +he r +t e +i d +Ġa ll +Ġ  +Ġwh ich +Ġf rom +i z +Ġ V +p er +Ġre s +Ġha ve +u s +Ġi f +Ġs p +Ġ O +Ġ { +o g +oll ow +Ġâ ĨĴ +a d +Ġwhe re +i tion +or m +Ġn ot +Ġf ollow +Ġi t +Ġ z +a y +Ġa t +Ġd is +Ġâ Ħ +Ġs et +Ġp ar +ĠÎ » +ĠâĪ ¥ +m a +Ġs e +Ġs h +si on +b le +Ġu s +d er +en ce +ar i +ĠT h +ore m +ec t +Ġ U +Ġde fin +o f +al ly +p o +en d +un ction +es s +Ġsu ch +o c +an t +ac h +ation s +Ġu n +Ġt r +Ġc h +en er +ec tion +t ain +Ġc l +Ġf unction +ĠL et +Ġe qu +ou nd +Ġo b +Ġa pp +al l +as e +Ġthe n +p le +ĠP ro +Ġc o +u tion +e re +ar y +ab le +m ent +st r +i es +Ġ à +at ed +Ġâī ¥ +d u +ac t +Ġ Q +ĠÏ ĥ +ig h +Ġthe re +Ġ µ +Ġ > +ro u +Ġ 5 +Ġn e +a nd +Ġ Z +Ġ < +Ġsu b +ĠÎ ² +ti m +ĠÎ ³ +ĠF or +Ġon e +it e +ac e +Ġb ound +Ġm od +er m +Ġm a +ĠThe orem +in e +ĠÎ ´ +a ti +ĠâĪ ŀ +t her +Ġg ener +Ġs y +Ġq u +on d +Ġi m +Ġ Y +Ġan y +Ġt w +Ġh as +i ll +si tion +Ġfor m +b er +Ġas s +Ġi nd +Ġg iv +Ġsh ow +al u +Ġres ul +Ġv er +r ic +) ) +ĠÎ µ +ĠÏ ģ +Ġe ach +om e +ĠâĪ Ĥ +Ġtw o +Ġpo in +ou s +ĠÎ ¸ +] . +ĠTh is +f f +s o +em ma +ĠÏ Ħ +in ce +f orm +o s +t h +Ġs im +Ġf in +d s +ĠÏ Ģ +o se +ĠL emma +ul ar +g or +ĠâĦ ĵ +Ġc ase +i al +Ġn um +Ġa d +ri b +Ġd en +ĠÃ Ĺ +Î ± +d ition +Ġa b +] , +Ġex p +Ġw ill +re e +Ġa r +if f +am e +Ġfollow ing +Ġst r +Ġg r +Ġm at +Ġs ol +Ġm e +Ġn on +Ġ 6 +âĪ ¥ +an s +ir st +Ġ J +ot e +ere n +ic al +Ł © +ĠThe n +u d +Ġ) , +Ġon ly +g r +Ġs ome +ap h +Ġal so +at or +Ġc or +âĪ Ī +Ġd iff +Ġf i +e p +ith m +po sition +Ġin t +Ġgiv en +at es +c l +a k +Ġt im +â Ģ +igh t +Ġ ] +Ġ } +ab il +et w +ble m +er s +Ġnum ber +as s +Ġin ter +an ce +Ġex is +ĠÎ ĵ +ĠF ig +ĠÏ ķ +Ġ) . +i re +Ġdis t +p h +Ġ es +res ent +ati s +Ġp re +en ti +Ġv ari +si der +â Ħ +Ġ - +Ġm in +or k +gor ithm +Ġl og +ĠÏ ī +r a +Ġpro blem +ĠÏ µ +Ġfollow s +Ġass um +en sion +x im +Ġob tain +Ġ: = +Ġcomp le +Ġmod el +Ġf irst +ĠâĪ Ĩ +a tive +ĠI f +Ġo p +Ġ / +Ġcon dition +Ġs o +ar d +rou p +Î » +g es +ĠÎ · +Ġre l +ĠÏ Ĩ +Ġo ur +i ent +Ł ¨ +Ġn o +on g +ct or +o p +Ġm et +Ġv alu +v es +Ġin te +Ġtim e +Ġcon str +res p +t y +st em +atis f +u ct +or ph +Ġo ver +abil ity +. , +ĠPro of +Ġs atisf +Ġpro of +ĠA s +al ity +Ġo ther +Ġcon t +ot h +Ġd es +is e +ti es +Ġapp ro +Ġ he +Ġgr aph +Ġwhe n +Ġp er +Ġre p +ĠÎ ¾ +Ġs c +ĠâĦ ¦ +Ġdiff eren +ver y +Ġa c +Ġs m +Ġsy stem +ff ic +ĠÏ Ī +ec tive +Ġle t +Ġi d +Ġsol ution +ð Ŀ +Ġsp ace +Ġi ts +u st +Ġt erm +an g +ĠÎ ½ +y p +Ġres p +Ġal gorithm +Ġd et +Ġl ine +ĠâĬ Ĺ +i e +as t +Ġpoin t +Ġ " +Ġd o +f ore +Ġdefin ed +or t +o ve +Ġu se +ĠI t +is m +Ġor der +g h +s is +Ġe v +Ġtr ans +Ġcon sider +am ple +Ġm ap +u e +Ġf act +im ension +nd er +Ġe very +Ġs ame +resp ond +Ġ ve +Ġre g +or d +Ġo per +c es +le ment +c ed +Ġ en +Ġh ol +i ed +Ġcor respond +ĠFig ure +Ġthe se +Î ¸ +Ï Ģ +Ġus ing +Ġpro per +Ġl im +Ġgener al +v i +am et +Ġd ec +ar k +Ġpro v +Ġes tim +Ġ 7 +om orph +Ġcl ass +Ï Ħ +â Ł© +o st +ĠPro position +s er +ri x +ent s +0 0 +l d +Ġ ro +Ì ¸ +ĠB y +i on +Ġo ut +Ġg roup +Ġfin ite +Ġ ed +ĠâĪ ļ +Ġdist rib + µ +Î ² +Ġâ Ł¨ +Ġex t +ĠÎ £ +e en +Ġcomp ut +etw een +ĠS ince +Ġ 8 +ac k +Ġb etween +n ow +i a +c ess +Ġdis c +Ï ĥ +Ġl oc +ou r +iz ation +Ġu nder +a u +Ġpro b +p tion +l es +Ġb as +Î ³ +Ġp l +Ġme as +Ġsub s +Ġmat rix +Ġve ctor +ĠThe re +' s +Ġe lement +Ġre c +ffic ient +Ġth an +Ġresul t +e fin +ĠâĪ © +Ġresul ts +Ġan al +a re +Ġab ove +Ġpar tic +Ġse e +Ġm ore +ou ld +ti al +Ġse qu +Ġcon st +Ġd at +ig n +Ġexis ts +1 0 +âĪ ŀ +h od +ge b +x t +âĢ ¢ +pl ic +ĠS ection +id e +Ġ ̸ +Ġrep resent +Ġcon tain +ĠÎ ¦ +a ge +ĠC on +iz e +m m +t ed +Ġs ince +Ġpar amet +i qu +ĠÎ Ľ +Ġm an +ul ti +Ġmet hod +i p +ou t +ĠâĬ Ĥ +and om +Ġb ut +Ġop tim +k e +Ġpo ly +ðĿ ij +e ver +Ġc ur +Ġï£ ´ +Ï ģ +Ġ ; +Ġl ar +i an +Ġdistrib ution +n t +iz ed +Ġdefin e +v ari +Ġâ ĸ +Ġm ay +Ġs ection +Î ´ +Ġden ote +iv al +il ar +Ġline ar +Ġr andom +ĠÎ º +Î ¾ +an n +1 1 +es t +Ġt yp +â ĨĴ +Ġfunction s +Ġst ate +Ġde p +si tive +Ġm ulti +tic al +Ġs ec +ow er +â ī +Ġprob ability +Ġpoin ts +ect ed +e qu +Ġoper ator +âĦ ¦ +Ġint o +s ed +Ġsm all +ĠTh us +ro du +Ġ) ) +Ġp r +b it +Ġcon ver +ol og +Ġpro ve +Ġstr uct +p t +Ġus ed +or y +Ġp at +a ir +l ow +Ġmin im +tin u +ĠT o +Ġma x +or s +1 2 +ve l +ĠS u +Ġdefin ition +Ġpartic ular +Ġdes c +Ġdat a +Ġt ak +in t +Ġch o +Ġb oth +a ting +ĠD efin +Ġn orm +Ġc ol +Ġim p +Ġre m +Ġpro cess +) | +er o +Ġn ow +Ġconst ant +u ction +Ġsu pp +Ġk now +Ġanal y +Ï ī +ĠN ote +Ġfi x +Ġcon n +geb ra +Î µ +Ġcomple x +om ial +Ġequ ival +Ġmeas ure +Ġde g +o ver +Ġb ec +Ġ Ä +Ġin c +Ġt ri +Ġthe orem +ic ation +Ġform ul +u res +et ric +Ġim pl +Ġe m +Ġn od +Ġwe ll +Ġp ap +si ble +a il +ĠâĪ ª +i x +u al +p ar +v ing +ep end +Ġd ire +Ġpo s +Ġw ork +Ġassum e +Ġsequ ence +ĠA l +omorph ism +âĢ ² +Ġcorrespond ing +cl ud +à © +Ġdifferen t +Ġ1 0 +Ġequ ation +Ġob ser +Ġvalu e +s ing +ĠâĪ ĩ +Ġhol ds +ac es +Ġimpl ies +Ġc all +Ġpro du +Ġpo sitive +Ġd er +Ġsec ond +Ġâ Ł© +Ġne ed +ow ever +Ġma xim +n e +Ġcom m +Ï ķ +Ġs ing +o b +Ġsu r +Ġpap er +form ation +âĦ ĵ +i le +t en +j ect +Ġu p +Ġa g +Ġdep end +Ġre al +p ut +Ġ 9 +Ġsp ec +Ġ \ +se e +ĠÏ ĩ +Ġcon tinu +i i +Ġi j +ĠâĪ ¼ +Ġappro xim +Ġdo es +Ġex ample +Ġre qu +Î · +Ġw as +ur ther +Ġ er +al s +te x +iqu e +Ġp air +tic es +Ġd imension +v ed +ol d +as es +ĠâĬ Ĩ +Ġapp l +Ġm ost +1 3 +Ġthe ir +au se +ĠM ore +Ġch ar +Ġre du +Ġin equ +n omial +i ve +am pl +Ġbound ed +el d +ic e +epend ent +Ġâĸ ¡ +ĥ Ĺ +Ġpat h +Ġst ud +Ġterm s +o od +Ġcomp on +ective ly +Ġs ign +) ( +Ġâ ĭ +Ġe t +Ġdet erm +Ġstruct ure +ĠThere fore +w ise +g er +Ġp resent +Ġ( âĪĴ +Ġlar ge +Ġpoly nomial +en s +n ce +Ġst ep +Ġin st +etw ork +Ġac c +Ġcl os +Ġid enti +Ġg et +Ġ ðĿij +Ġint rodu +Ġsatisf y +he d +Ġre f +ĠDefin ition +Ġinte gr +Ġh om +oc i +ĠH ence +g y +Ï µ +Ġar g +ĠÎ ¶ +s um +Î ½ +Ġver tices +e x +r y +Ġobtain ed +ab les +Ï Ī +ou gh +i ly +Ġexis t +âĪ Ĩ +2 0 +Ġw r +1 4 +Ġver tex +Ġvalu es +Ġl at +ĠâĢ² âĢ² +Ġsim ilar +Ġden ot +Ġr an +Ġbound ary +l oc +k s +en g +1 5 +Ġn etwork +Ġ1 2 +n ot +Ġd om +Ġal gebra +it s +Ġassum ption +si d +Ġcondition s +Ġloc al +Ġd ia +Ġfin d +Ġ ent +ay s +Ġfix ed +ere d +ac tion +ac ter +gr am +ec h +e ll +Ġass oci +m e +Ġer r +rou gh +vi ous +) - +Ġtyp e +Ġper form +Ġbe en +f t +at ure +e ed +is tic +Ï Ĩ +Ġ end +Ġz ero +a us +ĠN ow +Ġind ependent +Ġresp ectively +Ġdesc rib +v alu +Ġle ast +ation al +Ġsatisf ies +is t +Ġ á +oll ary +Ġf r +er n +Î ĵ +Ġed ge +âī ¤ +Ġresp ect +o v +Ġder iv +enti al +ic ally +Ġchar acter +1 6 +Ġthe y +Ġin f +Ġsy mm +Ġe ig +ti ce +he n +eng th +u nd +u ll +ĠH owever +y n +Ġâ © +c y +Ġinequ ality +Ġoptim al +Ġs ize +Ġâ Ĩ +Ġcont r +. . +Ġset s +ver s +ĠSu pp +y m +Ġg e +n ess +ĠR em +c on +âĪ ĩ +Ġex act +Ġequival ent +Ġ ± +Ġto p +t r +ve x +if orm +âĪ Ĥ +he re +he s +b in +Ġm ust +in c +Ġm ain +is h +Ġsu m +Ġst and +Ġeig en +Ġcontinu ous +i b +Ġthe ory +1 9 +ĠâĪ § +Ġin i +Ġsim ple +Ġa ut +a g +ĠâĪ Ģ +Ġth us +Ġr ight +Ġsubs et +o oth +Ġp h +ĠÎ ¨ +at ur +Ġa f +Ġsu p +ĠAs sum +Ġc ou +} . +Ġcon sis +Ġexp res +ĠC or +1 7 +Ġne w +Ġdeterm in +Ġh y +ic tion +Ġshow n +se qu +Ġc od +u le +g ence +Ġed ges +ĠRem ark +olog y +Ġpos sible +Ġpro po +Ġvari ables +Ġconstr ain +ĠMore over +Ġproper ties +Ġelement s +Ġm on +Ġun ique +Ġâ ĥĹ +Ġbec ause +ĠSupp ose +Ġproper ty +ly ing +Ġl ength +Ġe as +Ġev en +Ġ Å +Ġlim it +Ġth ree +Ġa ction +Ġha nd +Ġin fin +f ul +vari ant +Ġ2 0 +Ġa m +imension al +n ing +Ġinc re +rou nd +i ke +g et +Ġind u +ĠE x +Ġdeg ree +Ġw ould +em ent +Ġgiv es +Ġshow s +Ġdire ct +Ġpro j +Ġpar t +ĠA n +Ġcall ed +Ġparamet er +on al +Ġl in +Ġfi eld +ĠÎ ł +Ġsc he +el ds +Ġâĭ Ĩ +Ġcont ro +ter n +o int +Ġun iform +Ġf e +1 8 +ol ic +Ġassoci ated +Ġc y +Ġs em +} , +c c +e ar +Ġerr or +Ġdisc us +re d +d ing +l ine +r al +Ġbas ed +Ġini tial +Ġsc al +d imensional +i ble +it her +Ġsm ooth +c k +ar t +t al +Ġwh ile +u b +Ġclos ed +Ġhe nce +i ties +Ġstand ard +Ġrequ ire +Ġre str +Ġequ al +Ġhy per +ĠCor ollary +Ġst ates +Ġw ay +Ġin formation +Ġprodu ct +e fficient +Ġle ft +Ġformul a +ĠÎ ĺ +Ġr ate +yn am +Ġall ow +Ġth rough +Ġarg um +ant um +on e +Ġï£ ¬ +Ġappro ach +le ar +Ġf am +Ġnorm al +Ġ1 1 +Ġext end +Ġreg ular +Ġn atur +Ġman y +ul ation +Ġmet ric +Ġconstr uction +m od +Ġconstr uct +v en +ic s +Ġcon vex +id es +Ġï£ · +Ġl ower +Ġconn ected +ur n +Ġad dition +Ġrem ain +Ġs er +Ġcontain s +igh b +ate gor +Ġe ff +Ġco efficient +Ġsur f +in al +an ti +o tic +u sion +Ġcomple te +ro p +an ts +ampl es +ment s +ec ts +g n +an e +Ġid e +Ġset ting +Ġcomp act +Ġd x +pp er +Ġequ ations +Ġc ases +ti tion +an ge +Ġme an +v al +Ã Ĺ +c om +t he +ĠF in +Ġknow n +m ma +ie w +Ġsolution s +Ġsu fficient +Ġun it +v ial +Ġm o +Ġwh ose +Ġanaly sis +ord in +ric es +Ġle mma +v ol +Ġqu antum +Ġcor re +Ġy i +Ġestim ate +Ġi ter +w ard +Ġstud y +Ġpre vious +ti v +ro s +Ġar bit +Ġes t +a im +ann el +Ġ) ( +Ġcon f +Ġl o +plic it +ĠCon sider +ym pt +Ġnot e +Ġsing le +Ġarbit r +al c +Ġ| | +ver se +b ed +Ġi ma +clud e +g ative +Ġw or +ro w +ĠâĬ ķ +Ġdec om +Ġconver gence +Ġâī ¡ +omorph ic +Ġe ither +Ġnod e +Ġdom ain +Ġne ighb +ympt otic +if old +Ġs en +Ġp res +Ġc ent +f or +Ġparamet ers +ĠA pp +Ġpre c +Ġf l +ĠH ere +Ġwe ight +i er +h a +et ry +Ġmodel s +s p +Ġran k +Ġop en +ĠO n +Ġle ad +Ġs l +Ġstr ong +Ġd ynam +Ġgraph s +Ġg ive +Ġcom bin +c le +Ġwr ite +Ġu pper +â Ł¨ +ing s +ĠF rom +Ġrepresent ation +] ) +Ġwe ak +n er +T he +Ġcon c +Ġp ower +Ġsystem s +Ġle vel +iv en +ech n +Ġâ Į +Ġt ree +le ction +Ġdist ance +Ġch annel +as ing +if ic +Ġor ig +Ġd iv +Ġnod es +Ġs ay +Ġsupp ort +Ġex pl +Î £ +si ve +Ġhe re +Ġ ener +ĠR e +Ġsp ect +t o +ec ess +Ġfact or +Ġbe low +Ġdisc re +Ġad d +Ġco ordin +Ġsy m +ĠF urther +Ġl ast +Ġinter s +Ġgener ated +ab el +Ġvari able +u ally +Ġqu anti +ord ing +Ġc alc +) / +er tain +Ġas ymptotic +Ġg l +] ). +s ity +ĠC om +Ġg o +Ġmethod s +Ġâ© ½ +ate ly +Î º +Ġh ow +i od +t on +ch ie +Ġbas is +Ġb loc +Ġro ot +ĠG iven +Ġme ans +Ġnatur al +Ġmat rices +Ġmap s +ĠFin ally +Ġpropo sed +Ġidenti f 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