Dyam Prg h Arl Idury R. Pro MAf ad Vra Vld Calfora Iu of hology Abra: Dyam r drmao adu r bad o h oo alu of fuur al, whh ar wh m ad u aalabl. h ar ury h horal lraur o dyam r drmao, ad ofro h hor wh w daa from arl rg bhaor. Corrod o: R. Pro MAf, ar Hall, Calfora Iu of hology, Paada, CA 95, ro@maf..
Comurzd rrao ym wr dlod h 95 o ra of arl a boog ad far formao. Ially h wr ral ym, bu wr oo mad aalabl o ral ag. Drgulao of arl rg 978 rmd muh mor u of h ym for oom ay, ally rg. h al dlom of dyamally adud rg of rdd o Amra Arl Robr Cradall, a a ro o h r of dou arl Pol r h arly 98. h omly ad oau of arl rg ha grow or m. A a rul, h yld maagm ym mloyd by arl for rg ha bom o of h mo ara ad oml formao ym o h la, ad o wh a ry larg oom omo. Arl rg rr a gra hallg for modr oom aaly bau o da from h law of o r ll of aaly. h ar ury h horal lraur, whh moly foud orao rarh oural, dlo om w hory, a h hol our owldg, ad drb om rul from a w daaba of arl r. Dyam rg, whh alo ow a yld maagm or ru maagm, a of rg rag amd a rag rof. h hu ar mo uful wh wo rodu harar o-. Fr, h rodu r a a o m, l hol room, arl flgh, grad lry, or m-dad ll bfor rodu. Sod, aay fd wll ada ad a b augmd oly a a rlaly hgh margal o. h harar ra h oal for ry larg wg h ooruy o of al, bau h ooruy o of al a oal forgo ubu al. h alu of a u a horag uao h hgh alu of a urd uomr. Forag h alu g urr al ad aalabl aay rr dyam rg. Yld maagm hu ar rordly u aluabl. O ma ugg ha Amra Arl mad a ra $5 mllo r yar bad o yld maagm hu Da 994. h umbr may b flad for ral rao. Fr, lud al of yld maagm ragy o ohr, a ood o Amra ow u of h hu, alhough h alu of Amra ral u u a u lghly l. Sod, orora damagd good odrao h form of Saurday-gh ayor rro, a wll dyam rg. Suh rro fala a r drmao, ad ar raoably wll-udrood ohr o Dr ad MAf 996. Nrhl, hr ll doub ha dyam r drmao oomally mora. h rg ym ud by mo maor arl ar rmarably oau o h oumr, whh o urrg g o ma ha Amra Arl hag half a mllo r r day. h mld fruy of r hag m ally larg g ha Amra arr aroud 5, agr r day. hr urrgly ll rarh oom oural org yld maagm, g rom rg gfa dur ad h oom mora aahd o. h ar orbu o our udradg of yld maagm f way. Fr, rod a ury of yld maagm rarh orao rarh oural. Sod, w lor a g modl of Gallgo ad a Ryz 994 ha ha a umbr of drabl ror, ludg lod form oluo ad har rdo, o addr dyam rg odrao. hrd, mo of h lraur aum dmad a a o bu ully form. W odr h mlao of oa lay of dmad ad dmora om w ual org h mor adard a. W am h a h o of a ff alloao, rahr ha h rof-mamzg alloao, ad how ha may of h oluo arbud o rof-mamzao ar aually ou of h dyam ffy. Fourh, w a a w loo a dyam rg from h r of llg oo. A roblm arl fa ha la arral may ha gfaly hghr alu ha arly arral, uggg h arl ough o ll wo d of : a guarad u ad a ha a b dlayd a h arl ru. Ffh, w olld arl rg daa ad grad ylzd fa abou h drma of rg, falag h aluao of modl.
. Arl Prg Arl rg h Ud Sa oau. I o uommo for o-way far o d roud-r r. h dffr r bw rfudabl ad o-rfudabl of a faor of four or f. Pr hag fruly, wh low far o a arular flgh bg aalabl, h o, ad h aalabl aga. Arag r for roud-r bw Pho ad Lo Agl dffr ddg o whhr hy orga Lo Agl or Pho. h arularly myrou ha h am arl fly h roud-r wh h am of offrg. W olld daa o far for,6 flgh from Amra Arl, Orbz ad raloy. Ially w olld daa o ah flgh gh m daly, bu wh Amra Arl obd o h olum of arh, w od ug Amra ad ald ba h ohr wo o o r day r flgh. A w omld om of h arh, w ald h fruy u. Nrhl, h rr a mor loo a dyam rg ha aalabl from ay ohr our o our owldg. W wll a u our fdg afr rg h hory o u h fdg r. W wll u h followg rmology. W wll u r dro o rfr o a radomzao by frm rg, whh ah uomr ay a dal r, bu ha r drmd by a radom ro. W wll u dyam r drmao o rfr o hargg dffr uomr d maru or margal o bad o h m of urha; wh uh rg ff mamz h d r alu of h ga of rad, w ll all dyam rg rahr ha dyam r drmao. Rro l Saurday-gh ayor, ha ra l aluabl rodu, ol a r drmao.. g Lraur Radr g a gral duo of yld maagm ar rfrrd o Wllam 999, roo ad uo 994, ad Km 989. Km 989 du uao arora for yld maagm oluo, arular u old uh a dmad forag ad orboog, oluo hu, ad maagral mlao of yld maagm ym. roo ad uo 994 du h r of yld maagm durg ad afr drgulao of h 97 ad 98, ug h hg dury a a dald aml, ad Wllam 999 du yld maagm rm of h rao bw h frm, rour, rodu, uomr, ad omor. allur ad a Ryz 4 ha rad a horough boo for h ud of yld maagm. Yld maagm alao h mad-o-ordr MO maufaurg dury lud Harr ad Pdr 995, Srdhara 998, ad aru ad Srdhara 4. oh MO frm ad r rodr uh a arl fa h roblm of ffly ulzg a fd aay udr ura or hgh dmad ordr o mamz ru, ad hu may yld maagm rul ar alabl o h MO maufaurg dury. Howr, MO maufaurg dffr o h y o of f m horzo ad uhagg aay. h horzo f, h faory r o all orao a a f m or a ommo dadl for all ay, ad h aay o fd, ha a ordr ar omld, aay rlhd. hu, h MO roblm mor of a o ou roblm ha a yld maagm roblm. Harr ad Pdr 995 du h alably of radoal yld maagm o MO maufaurg ad maagral mlao ad dlo a rla horal framwor ug r la bad o u-aay ra. Srdhara 998 drb h u of yld maagm maufaurg uao wh hghr dmad ha aay, dug hr mhod of A horough lraur rw oad MGll ad Va Ryz 999, alog wh a oml gloary of rm alabl o yld maagm, arularly h arl dury. h lraur rw largly d from hr ad may b odrd adm.
rag ffy ad ru: aay raog bad o r la, rad oordao bw marg ad maufaurg, ad uborag. aru ad Srdhara 4 furhr lor aay raog by dlog a dyam aay aorom rodur bad o drmag faor of ro wh a hghr d rof marg. Rahr ha a ouou ram of o-m maufaurg ru, Carr ad Looy odr a o-om frm ha agr o ommm of a ormally drbud radom aual dmad. h r wdor roblm mah a ow aay wh a drd aggrga dmad drbuo. hy alo odr h ff of mull r la. F ad Wag 998 udy a mlar aual aay maagm roblm: dlog a omal harg oly of a rwabl rour. h rour oulao modld a a m-dd log uao wh rod off, ad h mamum aual-uaabl yld drmd alog wh h orrodg harg oly. h mo ommo g for yld maagm rarh moad by h arl ad hol dur. h rmadr of h lraur rw fou o h alao, ad h r of h ar dal wh h arl dury luly. omr 996 ad lobaba ad Wlo 997 ga ff of yld maagm ral o h frm ug. omr 996 r argum for ffy of yld maagm rg h arl dury, ad lobaba ad Wlo 997 ga h ma of yld maagm roduo om arl mar. Mo yld maagm rarh, howr, dal wh how o aually mamz ru. O aroah o aum ha uomr arr o ru a flgh, a h r hy wll ay, ad h h frm dd whhr or o o r hm. Va Sly ad Youg udy h uao rm of fllg a aa of fd aay wh ob of ow wgh or or wgh, o fll mul-dmoal aa ad alu, ah y whh arr a a m-dd Poo ro. Wh h goal of mamzg alu, ah ob ad or rd a h m of arral. h a of ual wgh ald o arl a ory orol, ah uomr u o a, ad h mul-dmoal aa ald o h roblm of alloag a a mull org ad dao flgh wor. Sawa 3 addr a mlar uo: Cuomr arr hroughou h ouou m horzo ad a hr r ad dmad z, ad h frm dd whhr o a h ru. A m-maro do ro ud, ad a omal oly ad aalyal ror ar foud wh dmad arr a a m-maro ro. A mor ral way o ra uomr r rfr wh r o h arl dury, howr, o aum ha h uomr wllg o ay uow wh hy ru a. Gallgo ad a Ryz 994 u y orol hory orollg h dmad y wh r hag o udy dyam rg udr mrf omo., dmad r- ad oha dmad modld a a Poo ro. A lod-form oluo foud for oal dmad fuo ad a ur-boud o ru udr gral dmad fuo foud ug a drm hur. Alo, moooy of h omal r oly how, a wll a aymo omaly of a fd-r hur wh mar z. h rul ar h dd o allow omoud Poo dmad, dr r, m-dd dmad, orboog, ruly ad allao, holdg o ad doug, ad arabl al aay. Fg ad Xao a odr h roblm from h r of whg bw a rdrmd f of r a alulad m hrhold ddg o rmag m ad o. Dmad a Poo ro a ah r ll, ad hy fd h omal ouou m whg oly of a arbrary umbr of hr r mar-u or mar-dow. Fg ad Xao b d h o allow rrbl r hag. hy how ha ay ub of r h omal oluo ar of h 3
mamum oa lo oad h full of allowd r. Fg ad Gallgo alo addr h dr r m-hrhold roblm, bu allow dmad o b Maroa,.. far ad dmad ar o oly dd o rmag m bu alo o ror al. Chaw addoally allow dmad Poo o b m ad rod h oo of r-og a a u o. Zhao ad Zhg fd ruural ror of h omal r-whg oly from a oma, bu o arly f, r wh dmad a ohomogou Poo ro ad ga oluo mhod h a of dr r. adll odr rodu-dffrad mar gm, ah of whh allowd o adrd r a a m, ad formula a ffly omud dyam rogrammg oluo allowg gral dmad fuo. I h modl, uomr ru a hol room or flgh wh a arular of arbu ad hy ar g a r uo bad o rmag m ad aalably of all rla ommod. Rahr ha dyamally hagg r o mamz ru, om auhor rao aay wh r la o ur ha hgh-ayg uomr ar rd, ffly mlmg a mar-u oly bad o rmag aay ad, f a alloao bw la dyamally orolld, rmag m. Laday 996, aumg drm o-lar dmad ad a fd o for rag ah r la, dlo a dyam-rogrammg oluo for fdg h omal umbr of r la, h omal umbr of aay u fally, hol room alload o ah r la, ad h omal r a ah la. odly ad Wahrford 995 allow ura dmad, ad udy wh o ural low-r al bad o h robably of olag ad d margal ru. hy do allow r-og of r la, bu do o aum ha all low-far uomr wll arr bfor hgh-far uomr hrby forg all hgh-far uomr o ay hr full aabl r. L aga odr drm dmad, ad ud h u of al rro uh a ada urhag, or mmum r durao for gmg dmad. H dlo ral y ror of h omal rro ol, ad al h rul o arl rg, whr lur ralr rla r lay omard o bu ralr rm h ff u of rro. Daa 999a,b ud a of mar gmao ohr ha mhod of omal alloao. Daa 999a ud h homo of ulbrum r dro, howg ha h omal rg ym udr ura dmad r drd moool, mrfly ad rfly om mar. H how ha h amou of r dro ra wh h ll of omo, ug h o la h obrao ha rou rd by mor arl hb mor r dro. Daa 999b dmora how g mull r ll o flgh a dffr m a hf dmad from h hghr-dmad darur m o h alra flgh, wh uow whh m h a. H addr h om ad moooly a ad u h modl o how ha hgh-far uomr may bf from r dro a wll a low-far uomr. Mog byod gl flgh-lg aaly, ral auhor odr org-dao wor. Fg ad Xao odr a wor of mull org, o hub, ad o dao. Pr for ah flgh lg ar d, ad dmad a ah org a Poo ro. hy u a d far ruur for ory orol ad fd h omal m hrhold for log org-hub flgh. hy h d hr rul o allow mull far o ah org-dao flgh ad m-dd dmad. Kuyumu ad Gara-Daz ad Gara-Daz ad Kuyumu 997 u a grah-hory aroah for alloag a a flgh wor. Gara-Daz ad Kuyumu 997 aum a o-d a alloao ym, ormally drbud radom dmad ha dd bw r ll, ad a fd umbr of far la. hy dlo a algorhm ulzg ug-la for alloag a hroughou h org-dao wor ad ga omuaoal m. Kuyumu ad Gara- Daz u h am aumo ha dmad o ah day of h w may b dffr, ad arl aa ar odrd. hy dlo hr modl for h wor rg ad a alloao roblm, h hrd bg a olyhdral grah hory aroah, ad a oluo rodur ha hy omuaoally. h dooral h of Wllamo 99 omar h u of ral wor-ll a 4
ory orol hur mulao. Sh olud ha odrg wor-wd ff may ra ru by -4%, bu oly wh h load faor ry hgh. d or, Frlg ad Prma d hr rarh by dug h fdg ha drm aromao mhod ourform robabl hur whh hy lam du o a dffr far la ruur modlg ad mulao. I h ud of dyam r drmao, hr a o bw h raal ad h ghful. Comuao-bad aaly rl ould b ud o ol ral-world roblm of omal rg, whl mlr hor luda oal rl for udradg rg grally. A ommo aumo h lraur o a dr r grd, or u wo r, whh mlf h roblm o o of ddg wh o wh o aohr r Fg ad Xao a, b, Fg ad Gallgo, Sawa 3. h aumo of a dr r grd do m ufd, hr o horal groud, hr o oomy of ug fw r, or o raal groud, arl ad hol fa mloy a larg of r. hu, h df of h aumo rl o h mlfao of h mahmaal roblm. h ma adaag of h aumo ha rog of a omal oluo ral, bu ll l gad. A o Chaw 999, whh lo h f grd o dlo a uo for wh r r ad fall. h u of a f fuoal form for dmad ommo. h mo ommo aumo oal dmad, a -b, for oa a, ad b. h form of dmad uful o aum bau a oa, ad hu margal ru r mu a oa. A a rul, a moool would hoo o harg a r whh margal o lu a oa. h faur of oal dmad ma h oluo o h moooly roblm rdu o h roblm of alulag margal o, a mlr hough oral roblm. Gallgo ad a Ryz 994 h b ar of h of oal dmad ar, ad w du ly blow ad dd a om addoal uo of h hory. A ary of mham for brgg uomr o h llr ar odrd h lraur. h mo ommo aumo a oa Poo ro bu obly wh m-aryg arral ra Zhao ad Zhg. A rg ara o h arral ra ro a maro whg modl, whh ol a gal rao roblm: dg from h bhaor of buyr whhr dmad odo ha hagd Fg ad Gallgo. h oo bw h la a-load rg roblm ad dyam rg lord Daa 999b. h ar olud ha r hould b rag o arag, bau of a orrlao bw hgh dmad ad hgh r. A Daa aaly, ral auhor o mull la of uomr, who may arr a d ro. Whl h mo ommo ob fuo o mamz d ru, Carr ad Looy odr h alra aumo of rg o ll ou. Prg o ll ou a bad ragy for ral rao. Fr, a rof mamzg frm would o r o ll ou. Howr, mor alarmgly, h ff oluo ha mamz h ga from rad do r o ll ou. Mo of h lraur fou o h roblm of a gl flgh, rag omo ad alra flgh a fd, bu ral auhor ha mad hadway o h roblm of mull flgh ad rou. Fg ad Xao am a ml Y-had ar hrough a hub. Nwor u ar alo amd d or, Frlg ad Prma. Daa 999a h oly auhor o dlo a full hory of omo bw dyamally rg llr. h hory, olg wo frm rg or wo rod, mhaz ha r dro may rul from uh omo. h rul alo aalabl a, o-rod roblm. 5
A mora orgh of h lraur h ab of doug. Vrually h r lraur rum o doug. I h hol o, zro doug ma, bau f o boo a hol ada, grally aym mad ul h m o ay h hol, whh ml h am dou faor whhr o boo h room arly or lar. Wh arl, howr, grally aym mad a h m of boog, o a h m of darur. h mar bau h m ral ar log ough for doug o b gfa, g h may b bood moh ada. 3. Dyam Pr Drmao wh Pr Commm h of r hag foud aual arl rg myrou bau a moool wh ommm ably, a adard framwor, do wa o gag a all! o dlo h oluo fr rod by Soy 979, w ar wh a mlfd ro of hr aaly. h aaly wa dramaally dd by oard 4. h llr ll hr a durabl good or a o-m u good l a arla r. m omod of dr rod,, ad buyr ad h llr ha a ommo dou faor. hr ar a ouum of oal buyr who ha alu rrd by a dmad, o ha g h maur of buyr wllg o ay. W aum ha a oumr dmad r ul h oumr urha. h moool hoo a r u,, whh a b a o b o-rag whou lo of graly. A oumr wh a alu wll rfr m o m f > [] h uao rodug dffr,, df a u of ral alu ha ma h buyr dffr bw urhag a ad urhag a. No ha h ora o buyr how ha, f a buyr wh alu hoo o buy bfor m, h all buyr wh alu dg ha alo urhad by h m. [] h of uao a b old for rm of h ral alu:... [3]. h moool ll - - rod, whr dfd o ha. h moool rof ar π [4] 6
7. hu, h omum ll of oa a h o-ho rof mamzg ll, whh rur h rof aoad wh a a moooly. h ably o dyamally drma do o ra h ably of h moool o ra r from h buyr. hr a mora lo o b draw from Soy horm. If dyam r drmao layg a rol, bau of w uomr arrg, rahr ha a am o ra mor rof from a g of uomr by hrag low alu uomr wh dlayd urha. ha, dyam r drmao dr by uomr dyam rahr ha r drmao or a g of uomr. 4. Couou m hory Gallgo ad a Ryz 994 rodud a lod form modl of dr m omal rg. h modl ry uful for raably, ad w rrodu om of hr aaly hr, a wll a d by grag rdo abou h arag ah of r. L λ b h arral robably of uomr r u of m, aumd oa. A oa arral a b aumd whou lo of graly by dg m rm of uomr arral. m wll ar a ad d a. If o old, h rodu rh a, whh mgh our bau a flgh a off or h rodu m-dad l a hol room or m-har odomum, whr wha for al h u of h rodu o da. For hal rao, o doug odrd h o. Howr, om alao, o doug h rgh aumo. For aml, hol grally do o harg ul h uomr arr, ddly of h m h room bood, a uao whh orrod o o doug bad o la boog. h margal o of h rodu, a alu whh mgh lud ormal margal o lag a hol room, a mal rd o a arl bu ould alo lud lo
bu h uomr ha a a arular flgh l lly o a a alra flgh by h am arl. Poal uomr dmad a gl u, ad hr wllg o ay g by a umula drbuo fuo F. h alu of hag m for al a m dod by. Clarly hag ohg o ll oy zro alu. Moror, f o old by, a ory of m alo ha zro alu, yldg:. [5] Codr a mall rm of m,, byod a urr m. Wh robably -λ, o uomr arr, o ha h urr alu bom. Alraly, wh robably λ, a uomr arr ad h frm hr ma a al or do o. For r, h al our wh robably -F. Wh a al our, h alu bom - -, bau h ory drad by o. Summarzg: or F λ F ma λ λ λ λ [6] λ λ ma F λ λ [7] hrfor, ddg by ad dg o zro, λ ma F [8] h ro for omod of wo rm. Fr, hr ar rof from a al, -. Sod, hr h lo oo of llg h u h fuur, a oo ha ha alu. I o obl o ol h dffral uao for a arbrary dmad fuo F. Howr, wh a o ho of F, obl o rod a l oluo. L a F. [9] No ha - -a -m mamzd a * m. a h L h - -a a -m. h a h ml h. hu, ry rm o a mamum, ad o f hr a rm o, h global mamum. Moror, * a rm o. 8
9, * a [] ad. a a a λ [] h mulla oa a λ β rr h arral ra of buyr wllg o ay h a moooly r. a hu, a m, h d umbr of buyr wllg o ay h moooly r β-. h obrao hl la why! β [] wll aar h oluo. h fr rul hararz h alu fuo ad r a lod-form mar. Lmma Gallgo & a Ryz 994: Log a ad. * Log a β λ A m zro, uo hr a al aay. L b h robably ha hr ar u lf for al a m. horm :! β. h d umbr of a old β Lmma ad horm g a oml, lod form dro of rof, r ad al for h dyam moool rag yld maagm. For aml, h robably ha hr o aalabl aay a m.!! β β [3]
h formula ur ha, wh uff m ad a g aay, h flgh ll ou, bau lm. [4] How do a h mar aff h ouom? o modl h, odr rag boh h aay ad h arral ra of uomr, λ, rooroally. L γβ/, o ha! β!! γ! γ γ f γ > [5] f γ Wha rg abou h ro ha h robably of llg all h aay,, org o h am ll a would ar f h r wa u oa a h moooly r. S h a r d h ll alway, bau h oo alu o, h r mu g ry lo o h a moooly r mo of h m ordr for h lmg robabl o od. Pr u rof of h dyamally drmag frm ar a Log a Log γ! a γ Log γ f γ < [6] f γ A a alra o yld maagm ad dyam r drmao, odr a frm ha a r ad la fd. Suh a frm, a o-r moool, wll ar lowr rof ha h yldmaagm frm. I h rof rduo gfa? A moool who oly offr o r wll ha a flow-ra of al of λ-f. If η h umbr of fuur al g aay a m, h η ad η η d. [7] Lmma 3: η! h rof aoad wh a gl r a b umrally mamzd.
Fgur rod a aml of dyam r drmao, arg wh u for al. h aramr lud zro margal o, a 365 day rod wh a arag of o uomr ry ohr day, ad dmad h form F -. h r aoad wh arou umbr of u o b old ar llurad, for aml, 3 how h omal r aoad wh hr u o b old. h arag r, odoal o u rmag for al, dod by ; h rr h arag of od r. No ha u may o b aalabl for al, o ha h d r a b of a fo, alhough h omaro o h o r moool bl ha r may alo o b offrd. h omal oa r dod. Prof ar 5.45% hghr udr dyam r drmao ha hy ar wh a oa r. I h fgur, h moooly r h horzoal a, a, ad hr hm mro ubaally o h a moooly r. 5 4 3 3 5 5 5 3 35 Fgur : Pr, ad d r,, λ½, α,, 365. Fgur llura a ommo faur of mulao: h d r r, h fall. h for old ar a follow. Fr, r mu ually fall bau hr a o oo alu ror o m, ad h oo alu zro a m. hu, ror o, r ar rly largr ha h a moooly r ad org o h a moooly r a. Whl obl ha r fall for h r m ral, hy may ally r bau arly al, by rdug aalabl aay, dr u h r. Fgur llura h robably ha all u ll udr dyam r drmao. h org o lghly or 85.35% by h d of h rod.
.8.6.4. 5 5 5 3 35 Fgur : h Probably of Zro Caay I dyam r drmao rofabl wh ad λ ar boh ry larg? L θ rr λ/. I h a, h oluo for dmad η m { θ a, } [8] h mamzd a h a moooly r,, a rodd γθ--a <. Ohrw, h omal γ f γ < r af θ -a. I follow ha rof ar ad agr wh a Log γ f γ drmaory rof h lm for larg. ha, r u ga rof of dyam r drmao or a omally ho oa r org o zro, alhough h oal ga wll ll b o. h ha bau mo al a la a a aromaly oa r; dyam r drmao adaagou oly a h robably of aually llg ou hag, for a rlaly mall oro of h ry larg umbr of al. O a raoably rr h rul o ay ha dyam r drmao oly mar o h la wy or o al, o wh a larg umbr of u ar old, dyam r drmao do mar ry muh. Dyam r drmao ha a rlaly mod ff wh hr ar or mor a aalabl. h d of rof rdd, for raoabl aramr alu, udr dyam r drmao ar o ry larg, l ha %, wh omard o a aroraly oa r. A mora a of h oluo ha dyam r drmao do o aar o aou for h d of alu lamd for Amra Arl u of yld maagm. 5. ffy h Gallgo & a Ryz Modl A ff oluo h modl ha h rory ha h alu fuo mamz h ga from rad rahr ha h rof. h alu fuo, h, af
F C λ F ma λ λ λ λ [9] whr C h oumr alu, lu llr rof, odoal o h oumr alu dg. I h modl, F C F d F [] a d a a a. hu h ff oluo h oluo a moooly who o ar rdud by /a, h a moooly rof, would hoo. h aumd ruur of dmad ur ha all h uala oluo draw aly ually o ffy a o moooly. I arular, h ha of h m ah of r ad h oluo ha for larg roblm h ga of dyam r drmao ar mall aly ually o ff oluo a hy do o moooly oluo. I our w, h Gallgo & a Ryz modl o a ry uful rum for amg ffy, bau of h mlary of h moooly r ad ff r. Rdug a moool margal o by h moool maru do o rodu h ff r, bu a hghr r udr h adard rgulary odo l log oay. Howr, worh mhazg ha h ff oluo ad h moooly oluo lad o h am of r ah, o ha f o ar uobrabl, h wo modl ar obraoally ual. 6. ffly Alloag Lmd Caay udr Uray h lod form of Gallgo a Ryz fala omuao bu obur oom odrao bau of h aur of h dmad. I h o, w odr ffly olg h alloao roblm, rahr ha mamzg rof. ffy o uraoabl, arl fa omo ad a rfly om modl would ugg h ff alloao of h aalabl uay. I m lly ha hr h moooly or h fully ff oluo auraly rr h ral world, whh robably fall omwhr bw h wo rm. or ad Ro 994 rha h formo aml of a am o a arl r omo, bu a h ll of arag far. Dlog a hory ha rm ag h dgr of omo a h dald ll of h r ah, ora, r a formdabl hallg. Obrao of ua ar gog o b ral o h am of h dgr of omo, bau r obrao alo ar o uff o dfy h modl. h d of ff alloao roblm wa fr udd h o of lry grao. Co of aay du a a load roblm oau 949, Wllamo 966, o amd bau h margal o of lry grao muh hghr wh h la aay rahd ha blow ha ll, o ha h a load mar a lo o h oom of lry grao. h adard aumo a load roblm ha dmad ah rod ar dd, ad ha h full uly aalabl ah rod. h a-load roblm rally a aay lag roblm, whr h 3
dd aay dd o r. For a wo rod modl, l b h dmad rod. h frm rof ar g by π β ma {, } m, [] whr β h margal o of aay ad m h margal o of roduo. I h arl ad hol o, h adard a load modl oorly ud, bau aay old o rod aalabl h ubu rod. hu, h adard modl of h a load roblm a how larg a la ha fl roud-r bw Dalla ad Chago hould b, g arao oal dmad from day o day or from w o w. Whl h roblm rr a mora logal roblm, ha ll or ohg o do wh dyam rg. I ora, arl alo fa h roblm ha a o a arular flgh a b oud by wo agr, ad h roblm of alloag lmd aay ugg a u d a load modl. Moror, h fa ha fuur dmad ow a h m of orag h fr rod a rual a of h a load roblm fag arl ad hol. ha, arl ad hol ora for al al, o owg h ralzao of orall dmad. W rodu a w modl of radom arral ha ha om ara ror. h radom om h form of radom arabl rod, wh rod dmad bg, h, for r. W alo aum ha obrabl a h bgg of rod, o ha h frm a hr r or uay ha rod; wha ura h fuur dmad, o h urr dmad. 3 W wll fou o h oa lay of dmad a, α -, bau h a adard mral modl ad a raably. W wll rfr o a r aa al, ad a oal al, bu h rrao a h arl o. I h arl o, f h umbr of uomr, would ha o b h robably of al, whh a hould b o grar ha o, whh o wh h oa lay aumo. A b, h modl rr a aromao for h arl o. h o odr oly h ff alloao. h ff alloao rg for ral rao. Fr, omo wh ohr rodr wll grally uh frm rodu offrg oward ffy ad away from moooly, o wh gorou omo, ffy mamzao robably a br modl ha moooly rof mamzao. Sod, h moooly modl ha b br udd ha h om, ff modl. hrd, om of h rg bhaor h moooly modl do o ar from r drmao bu bau of h da of ffy. h our of h bhaor hallgg o whou udyg h ff alloao. ha, wha aard o b r drmao mrly arao margal o. h llr ha a aay K. W wll fou o h wo-rod a hroughou h o, alhough h radly gralz o mor rod. If r aa al ar of h fr rod dmad, h umbr of a aalabl for al h od rod K. h ar alud by oumr a a r afyg K [] 3 Daa 998 modl a al a, wh ag o wo o alu, rrd a a wllg o ay for lur ad bu ralr. 4
5 or K [3] h o of fr rod al r u dramaally h umbr of al. Suo ha oa lay of dmad, α -. W aum > o ha h oumr urlu f. For ay g, α K [4] h r ha lar h mar rod af. h uomr alu of uay α. hu h orall ga from rad ar α α K W [5] α K h ga from rad ar mamzd a. K [6] h r aa od rod al ar K K [7]
6 au α, a rudmary alulao o how ha h d r h fr rod ad od rod od. ualy of h r a ary odo for mamzg h ga from rad; ohrw would ra h ga from rad o alloa mor of h a o h hgh-rd m. Som a ar malload, bau orag wh h arly uomr our ror o owg h ralzao of umbr of lar uomr. Moror, worh mhazg ha h malloao ff mamz h ga from rad ad o a ou of moooly rg. I our rmology, dyam rg bu o dyam r drmao. How larg h ff? h arag rduo h har of rod wo uomr af. [8] horm 4: h od rod har largr o arag ha h fr rod har, ha,. Proof Ad. horm 4 how ha h har of uomr rd h od rod a la a gra a ar rd h fr rod. h a ou of h obly of mall domaor ladg o larg har; wh fw uomr arr, h r low ough o ur h la ll ou. h al a a frao of h arag alu of ar l ha rod. ha,.
7 Igh o h magud of h ff malloao g by h rul. L Var CV b h off of arao of. horm 5: CV Proof Ad. h har of a alload o h fr rod may da from h ff ual har by a muh a CV ; for h a of ad CV, h ould b 5%. h boud horm 5 a, h ha for a bomal radom arabl wh o alu ual o zro, h rgh ualy hold wh ualy, ad a, h lf ualy hold wh ualy. h ga from rad grad ar α α K K K W. h frm ru α α α K K K K K hu, frm ru rooroal o wlfar udr oa lay of dmad, ad h aaly of ru mamzao udr ffy, of our aalyz wlfar mamzao. o rform h aaly, w ur o h log ormal a. h ffy h modl ar bau orag wh arly uomr our ror o h m ha rod wo dmad ralzd. How larg h ffy? o awr ha uo, w odr h a whr log-ormally drbud. I h log ormal drbuo a, h wlfar lo aoad wh h mg mar a b ry larg.
8 7. h Log Normal Ca If h drbuo of log-ormal, o ha h log ormally drbud wh ma ad ara σ, may of h ro ha lod form, graly falag omuao. I arular, ½ σ ad σ σ [9] h off of arao for. ½ σ σ σ Var CV [3] hu, σ CV, ad [3] σ CV. [3] h d ga from rad ar σ α α K K W [33] How muh do ual orag o rm of ru or wlfar? W ra a h d alu of a logormal wh h am ara bu dffr ma ha. h rooro of h ga from rad rrd hrough orag or wo rod dod % W. I ha h alu
% W [34] W how by aml ha % W a b a low a 64%, ha, h ably o ora ada rdu wlfar by a hrd rla o mulaou orag. 4 h aml ha a muh largr fuur oulao of dmad ha fr rod dmad. Howr, h ara of dmad larg oo, ad h au h lo aoad wh uray o b ry larg. I arular, a glgbl frao of { } h aml, a dffr whh aou for mo of h ffy lo. for mor raoabl aramr, lo a b 5% or mor. A aml, wh u o % lo, llurad Fgur 3. I h aml, h a o h alu.6, ad 88, whl h d alu of a o h alu 9, 98 ad 68337. 4 6 8.95 σ 3.9 σ 5 σ 4.85.8 W Fgur 3: ffy lo rla o mulaou orag. Paramr: -5,. 4 Sfally, o of aramr 3.474, σ.65, 45.53, ad.8 8. h of aramr g h followg d alu for. { }. 49, ad 8.4. 9
h ma oluo ha h mora ff dyam rg ar o from a am o ra mor moy from h oumr, bu from oml mar, ad arular from mobly of mulaou orag wh all oal buyr. Dyam rg ud rmarly o mga h o of h mg mar. Moror, wlfar o of h mg mar ar oally u larg. h oluo ugg ha oo, whh ra mar for ada orag, ar a mora a of boh mamzg ru ad of ffly alloag rour. 8. Oo ad Irrubl Sal h wlfar lo dfd h rou o ar bau of oml mar. I arular, o obl o ora wh h rod ag a h m ha h rod mar lar. h la of orag lad o ffy bau omm oo may a ar old h fr rod, wh h dmad h od rod uuually hgh, whl omm oo fw ar old, bau dmad wa udly low. A oluo o h roblm grally o ll og a, ha, o ll a oo. I h a, h ma alu of h oo o rm h llr o ll h a o a hghr alu buyr h od rod. h d of oo ll ud hol ad arl, bu u ommo l raor whr go by h am of rrubl ramo rgh, a ood o frm guarad rgh. Prl.om old a d of rrubl r, whr hy old h wll ada bu dd fy h m of h flgh ul a day or o ada. o ga om gh o h al of rrubl r, odr fr llg wo ual of r, >, whr h robably of r, ad h ar old a r >. A oumr wh y alu good a. A y oumr rfr y f, [35] or. [36] I addo, a oumr rfr good o ohg a all f. If, h o oumr r buy good, o w mo h odo, whou lo of graly, ha. L F h umula drbuo of alu. h dmad for good F ad h dmad for good F F. L b h margal o of r y. h llr rof ar
, π F F F Ma. [37] I hlful o rodu h oao F Ma R, whh h rof mamzao aoad wh o good. L arg * F Ma b h oluo o h o good mamzao roblm. Margal ru drag f * a rag fuo, o ha a ra o rdu h uay ad ra h r hargd by h moool. h a adard aumo. horm 6: Suo margal ru drag. A rof-mamzg moool ll h low ualy good f ad oly f, whh a π R R, * * ad *. Ohrw, π R ad *. h roof h ad. h rrubl good roblm bra u o wo ara mamzao roblm, o for h low ualy good, ad o for h dffr of h low ualy good ad h hgh ualy good. h y of rul d from h uual rul whr a moool llg o wo y of oumr offr wo ual; hr h moool llg wo good o a ouum of oumr. h r rul rm of Mua ad Ro 978 aaly, howr. Codr a llr ha dd ll good, ad h bg llg good. Do ha llr r r, or fall? h r fall f < * * * [38] hu, f * oa, h r fall wh h od good rodud, ad h r r wh * o. I h a of uform drbuo of alu, or oal drbuo, or oa lay, * lar o, ad hu roduo of h od good do hag h r. Mor grally, may ra or dra.
I h arl o, h o of a al grally a hadow o how muh ru forgo bau h a a? Couly, h odo auomaally afd. h o of a robably of r al a lo flbly rla o h r ll. ha lo flbly ma o rhdulg h r ruma whh would b drabl o do o. hu h o hould b a arag of or h flgh wh h rrubl r offrd a hduld, lu h o ruma whr wa rofabl o rru. S h lar hould d h formr g omal rruo, h o of r for a hould d h o a, whh ma alway omal o offr h rrubl r. A a raal mar, h rgh rrubl r robably a ha l h arl hoo h m h agr fl, bu h flgh a day. h d o oorda ar ral wh hol ad ohr dao a rr h ably of h mo agr o b flbl or mull day. Nrhl, flbly wh r o h m of ral oally rodu gfa ga h d alu of ar ral, boh h ably of h r ym o dfy ad alloa a o h hgh alu agr, ad h ably o ulz mor aay. h ga from radg oo ar largr wh h frm o a r ha good for a arabl amou of m. h homo wa udd by Daa 999a. Radom dmad wll grally ra a malloao, whh w modld by alloag fr rod a whou y owg od rod dmad. Howr, udr a od r, a wll b malload bau h od r wll grally o b h orr r o lar h mar, hr rag a urlu or a horag. Codr h modl dlod h rou o, wh a radom dmad h form ad oa lay α -. L K b h aay ad uo ha wh aay bd, h uomr ar a radom lo of ho wllg o urha. h ga from rad udr a oa r ar W M d [39] α { K, } M{ K, α} h uao ar bau, wh K<, h aay ora bd, ad h ga from rad ar h arag of h alu of a or h of oumr wllg o buy ho a. O rg faur of h uao ha ffy rur a o robably of my a. If hr a zro robably of my a, h h r lowr ha h mar larg r. Low r ra radom agm wh dmad larg, whh al a lo of ffy; h lo balad aga h ra a old wh dmad low. Idd, h fr ordr odo for mamzg W a b rd a: W K Pr{ K } [4] hu, h robably ha aay bd, K, o a h r mamzg h ga from rad.
9. Aual Arl Prg Par I ordr o a h of dyam r drmao, w olld daa o four y ar: Lo Agl LAX, UR, SNA o La Vga LAS ay Ara SFO, SJC, OAK o Porlad PDX Dalla DFW o Olahoma Cy OKC Dalla DFW o ula, OK UL W olld daa o r offr from Orbz, raloy ad for ar of h rod, from AA.om. Uforualy, Souhw Arl o faurd o ay of h our. Of h aror ar, four LAX ad UR o LAS, SJC ad OAK o PDX ar alo rd by Souhw. O would Souhw o r a modrag flu, g rlaly low ara r, alhough Souhw ha rodud a far ruur whh may rul mor dro, rahr ha l. 5 I ay a, wh h daa aalabl, h ff of Souhw r wll ha o rma a o for furhr rarh. Purhag a Amra Arl o AA.om grally $5 har, bu howd o ohr dffr. h fgur blow oly how far uod by Orbz, whh had h mo offrg. W olld daa o flgh, all h yar 4, darg o 8/6, 8/8 8/9, 9/9, 9/, 9/, 9/3, 9/5, 9/6, /7, /9, /, / /3 ad /4. S arl rr or 99% of h daa, wh h followg rooro of h flgh. Arag r ad h fruy of arl ar rd abl. abl : Arag Pr h Daa Arl AA Alaa Dla Ud AmW USAr NW Prooro of Flgh 5.5%.7% 6.% 4.6% 8.9% 6.% 6.% Arag Pr $8.5 $6.59 $79.3 $44.6 $66.7 $39. $9.48 hr ar f maor rooo ha a b d wh h daa.. Pr fall a aoff aroah. Pr ar rg ally 3. Como rdu ara of r 4. Pr hag wh ah a old 5. Pr of ubu ar orrlad a. Subu m/day b. Subu aror h fr rooo ha r ar fallg a aoff aroah. h a rmarably robu rdo of hor ha ha dal uomr y arrg or m. h robu follow from h followg obrao. h o of llg a a omod of hr omo. Fr, hr h o of r. Sod, hr h o of o llg ha a o a ubu flgh. h od omo lud ay yhologal ff o oumr ao oumr may rao ha urr low r ar daor of lly low fuur r, whh d o ma dmad mor la, o h arl drm. hrd, hr h forgo oo of llg h a lar o h am flgh. h fr wo o ar roughly oa or m, ad raly aromaly oa a h flgh 5 h la, wh aml far UR o LAS ar Rfudabl Aym $94, Rrd $86, Ada Purha $7, Fu Far $49, Promooal $39, ad Ir O-way $39. 3
aroah. h hrd o, howr, go o zro a h flgh aroah. hu, mo hor wll ugg ha r fall h la mom bfor a flgh, o arly o zro bu o om omal r rflg h mar owr of h arl ad h ff of low-r al o al of fuur flgh. u h r hould ll fall. A mor alzd rdo ha h arag r r ally. h a faur of h Gallgo-a Ryz modl alrady dud, ad ohr. I mor u modl whh oumr a arh ha h mor ommo modl whr oumr who do urha daar; f r ar fallg o arag, oumr wll d o wa o urha. La fallg r ar o obouly loabl bau of h gfa llhood of h la fllg u. hu, oumr mu wgh h d ga from dlay aga h o of falg o aur a a a all; h lar o glgbl wh a uffly log m-horzo. o a h rooo, w ra h followg rgro o rd h r. W ha dummy arabl for day wh o, wo, hr ad four w rmag, arl-f dumm Amra omd, hour of aoff orgh omd, ad y-ar dfr LAX o LAS omd. W omd urba, Log ah ad SNA aror bad o fw flgh or h rod. W oly amd o-way oomy far, ad ha 3837 obrao. h 38 arabl aou for 73.5% of h arao. Pr r $5 h w bfor aoff, whh o o of a r of $8. h rou w. h ulma forgh bfor aoff aou for $6 r ra. hr a lgh,.9 r day ra ror o ha. hu, h ma m-ah rdo of h adard hory aar o b mrally fal. h ff ar u gfa, ha o h z of h daaba. W ha o amd o orol for orrlao obrao, o ha h -a, whh ra obrao a dd, lly ora h gfa. h mora oluo ha hagg dmad a al faur of h daa, ad modl ha aum ha h ha of dmad oa or m ar mrally ald. A fw ohr rmar follow from h rgro. Alhough Amra Arl a low rd arl h daa, hgh-rd adug for fd ff, hough o a a US Ar. Pr ar hgh md-day ad arly g. LAX a rlaly aror, whl Sa Frao hghrd. h ugg ha omo ad h mar do o rod a good aou of rg, Sa Frao ha a larg umbr of flgh. Souhw r a LAX, OAK ad SJC mgh hl la h arag rg. No, howr, ha aror dumm ar alo aoug for h lgh of flgh, o omaro hould oly b mad amog d aror ar for a g y-ar. 4
abl : Pr Rgro ma S Sa PValu Coa 54..996 54.6. X - 64 Day.9.67.9.4 WK 5..67 8.4 6.4 X - 44 WK 8..69 46.3.7 X - 464 WK3.6.65 6.3. WK4 5.8.6364 9.. Alaa - 4.6.56-9. 4.3 X - Dla - 4..6-39.4 6.4 X - 337 Ud - 6.3.5894 -.6.4 X - 6 Amw 6.5.675 9.6. USAr 86.8.58 49.6 3. X - 458 NW - 6.9.77-3.9 8.6 X - 6 AM6-5.5.889-8.9. X - 79 AM7-6.3.838-7.5 5.5 X - 4 AM8-3.7.8348-4.4. AM9 -.4.886 -.6.73 AM 9.9.95.8. AM 3.7.8 4.5 6. X - 6 Noo 5.9.854 6.9 4.7 X - PM - 3.6.8696-4.. PM -.3.9844 -.3.93 PM3.6.7849 3.3.9 PM4 -..983 -.3.44 PM5 7.4.873 9.. PM6-3.4.844-4.. PM7 3.5.86 4.3. PM8-5.8.98-6.4. X - PM9 -.. -..496 ULDFW 4.9.787 53. 4.7 X - 6 OKCDFW 4.9.84 49.8. X - 535 DFWUL 4.5.868 5.4 7.4 X - 57 DFWOAK 3.8.838 37.9 4.5 X - 33 SFOPDX 49.6.544 9.8 3.9 X - 433 SJCPDX 44.6.846 54. 3. X - 63 OAKPDX 49.4.7 69.4 8.7 X - 3 PDXSFO 5..564 88.9 6.4 X - 484 PDXSJC 43.7.853 53..3 X - 65 PDXOAK 46.5.735 63..8 X - 858 LASLAX - 6.9.4877-4..9 X - 45 I aohr ar Carboau, MAf, Malo & Malo 4, how ha h hrd rooo o uord a larg daa of arl r. Idd, mor omo wa waly orrlad wh mor dro, o l. h fdg o wh or ad Ro 994 fdg. 5
Som hor o a wo r ruur, ohr rm r o ary ououly. I h daa, om arl larly la oward a wo r ruur. For aml, Amra Arl r o OAK o PDX how d of wo ma r, wh a hrd u ror o aoff. h llurad Fgur 4. 6 Mo of Norhw far how u wo r. Arag of Pr 8 6 4 8 Flgh AA_685_9/3 AA_69_9/3 AA_6966_9/3 AA_748_9/3 6 4 85 8 75 7 65 6 55 5 7 6 6 Day l Fgur 4: Amra OAK o PDX, Smbr 3. Howr, ohr flgh how d of almo ouou adum, ad dd omm Amra aar almo o radomz offr. Fgur 5 how a aml of wo Amra Arl flgh, AA 38 o S 3 ad S 5, wh rmarabl arao. So h d faor of h rooo ouou adum of r md. Why do arl u wo r? A adard oom laao ha hr a alu r ommm o a oumr lag. h h rao g for raura, mo, ad h l o maa a oa r, or wo r, h fa of rdably fluuag dmad. Howr, r do m arly rdabl ough for rdably o b h rao for ug oly wo r. A mor laubl hory ha arl u wo r bau h hory br dlod for wo r ym. h laubl for a o arl l Norhw, bu mlaubl for Amra Arl, whh ha raordary r adum o ohr rou. 6 h fgur dfy flgh Arl_Flgh Numbr_Darur Da. All daa h fgur om from Orbz wb. 6
Arag of Pr 35 3 5 5 Flgh AA_38_9/3 AA_38_9/5 5 85 8 75 7 65 6 55 4 3 5 5 5 Day l Fgur 5: Amra 38 r lod aga day ror o 9/5 h fal rdo of h hor ha h r of ubu hould b orrlad. h, aga, a robu rdo ad rur oly oumr ubuo a a hyoh. o a h, w lood a h orrlao bw r of flgh from h bay ara o Porlad, ad Porlad o h bay ara. ad o ral m, m ha SFO ad SJC hould b h lo ubu, followd by SFO ad OAK, followd by SJC ad OAK. I fa, howr, h orrlao ar almo aly h rr. abl 3: Corrlao Coff Flgh Par ρ Flgh Par ρ SFOPDX, SJCPDX.67 PDXSFO, PDXSJC.596 SFOPDX, OAKPDX.9 PDXSFO, PDXOAK.568 3 SJCPDX, OAKPDX.867 PDXSJC, PDXOAK.954 abl 3 how h orrlao off of arag r, wh h orrlao bw ma r offr o ah rou a a fuo of h umbr of day ror o darur. h rdo ha h fr row of h abl hould ha h hgh orrlao, followd by h od, followd by h hrd. Howr, aromaly h oo ar. h r of Souhw a Sa Jo ad Oalad, bu o a Sa Frao, may b h laaory faor, ally lgh of h fa ha h r ll a SFO muh hghr ha a h ohr wo aror. I mor hallgg o a whhr hr rog orrlao bw ubu flgh o h am rou. h followg ur how om orrlao or m of h ubu flgh bw Porlad 7
ad Oalad a 6PM, 7PM ad 8PM ± ½ hour. h flgh ha a arag orrlao off of abou.8 orall. Arag of Pr 8 6 4 8 Hour 8 9 6 4 5 5 95 9 85 8 75 7 65 6 55 5 45 4 35 3 5 5 5 Day l Fgur 6: PDX o OAK, rur, a arou m O h ohr had, Fgur 7 r a mlar amao of oomy flgh from LAX o LAS. No uh orrlao radly aar ad h flgh ar waly orrlad. Afroo flgh, rd Fgur 8, ar mlar. 8
Arag of Pr 8 6 4 8 Hour 7 8 9 6 4 5 5 95 9 85 8 75 7 65 6 55 5 45 4 35 3 5 5 5 Day l Fgur 7: LAX o LAS oomy la, 6AM o 9AM Orall, h maor rdo ludg h mo robu rdo of h hor aar o b olad h daa. Couly, w hor, ad robably a w aroah o h aaly, ar dd.. Rarh Pro ad Myr hr ar may rarh ro ha flow from h aaly of h ar. Fr, muh of h g wor foudd o a moooly dro. h aaly of h ar ugg ha rag h modl a a om modl may ra h raably of h modl whou arfg hr mral rla or omly of bhaor. Sod, h al of oo r h obly of hag h ffy of ada orag, a obly ha ha b ll lord. Couou m hu from h fa lraur may lay a mora rol dlog a hory of oo for rhabl good. h m a fruful aroah, bau oo hml ar rhabl, ad ouou m oha alulu hu ha layd a mora rol mlfyg mlar roblm. h g hory fard oorly wh ofrod wh h daa. I arular, h falur of r o fall a aoff aroah daag o hor, lag adg oly ho hor whh la arrg oal agr ha a rlaly hgh wllg-o-ay. Whl h a raoabl hyoh, ohl d furhr dlom, ad hallgg o h of aural aumo o mo ordr o h roblm, o dmad a b almo ayhg. 9
h daa r a ary of myr. h ga o arhg ar oaoally ormou. Whl r r a aoff aroah, oaoally hy bou aroud odrably. h fdg mrrord zo al, whh mrally amd h ga o arhg for flgh. hy fd a arag ag of 7% by ug a arh algorhm, rla o u boog h flgh h fr m hd. Arag of Pr 8 6 4 8 Hour 5 7 8 6 4 5 5 95 9 85 8 75 7 65 6 55 5 45 4 35 3 5 5 5 Day l Fgur 8: Afroo LAX o LAS Flgh by m of darur Wha rha mor myrou, ad llumag, a d ha ourrd md-july o Alaa, a flgh from OAK o PDX. For aromaly a w, h r of AL darg 9/3 arly doubld, whl h r of h 9/5 ad 9/6 darur wr aromaly uhagd. h 9/6 darur had b mor. I fa, h r of h 9/6 darur h fll brfly. h llurad Fgur 9. 3
Arag of Pr 8 6 4 8 Flgh AL 9/3 AL 9/5 AL 9/6 6 4 87 8 77 7 67 6 57 4 8 7 6 Day Fgur 9: Pr of AL, darg 9/3, 9/5 ad 9/6 G darur m, Amra Arl 685 a maor ubu for AL. Durg h m, AA 685 flgh rd oly a ry mod ra r, whh llurad Fgur. h r of AA685 had b ubaally hghr ha h r of AL, bu wh AL w u, h r of AL wa muh hghr. h r of h AA 685 w u lghly, h am ba dow o h rouly ralg ll. Wha ma h o myrou ha AA 685 ad AL rr h am arla AA 685 a od-har flgh orad by Alaa arl. ha, h ral myry why h wo dal fgh ar bg mard a uh dffr r, wh h fa ha h flgh ar od-hard larly dad o h wb. o ma mar mor myrou, h bl r of AL od wh a lgh ra h r of AA 685 for flgh darg o ohr day, bu o h r of AL o ohr day. h llurad Fgur. 3
Arag of Pr 8 6 4 Flgh AA_685_9/3 AL 9/3 8 6 4 86 8 76 7 66 6 56 5 7 6 6 Day Fgur : Pr of AL, AA 685 Arag of Pr 8 6 4 Flgh AA_685_9/5 AL 9/5 8 6 4 88 83 78 73 68 63 58 4 8 6 5 Day Fgur : AL, AA 685 darg 9/5 3
I m lly ha Amra rad o h r of ral. h fa ha h dal flgh wa bg offrd for o muh mor wh bood a a od-har o Amra rahr ha o Alaa, Alaa r ra wa rfld h r of alra day, h r of Amra dal flgh oly ro lghly ad alo ro o alra day, ugg ha oumr brg a ubaal brad loyaly o h flgh, arl u a far rogram ha ra o rg by ohr aro a of ubu flgh, ad 3 h ro oorly udrood by rarhr. h a of ollg daa for o-ommral u ugg ha rr-grg h rg mham of arl a fabl ad oally ry rg rarh ro.. Coluo h ar ha odrd o may dffr hor ad daa ha worh mhazg a fw hghlgh. Dyam r drmao rmarly dr by uomr dyam rahr ha r drmao or a g of uomr. Wh a larg umbr of u o ll, h r u ga rof of dyam r drmao or a oa r mall, alhough h oal ga wll ll b o. Mo al a la a a aromaly oa r; dyam r drmao adaagou oly a h robably of aually llg ou hag, for a rlaly mall oro of a larg umbr of al. O way o ummarz h oluo ha dyam r drmao oly mar gfaly o h la wy or o al. Moooly ad ff dyam rg may b obraoally ual, ad ar h mora modl of Gallgo ad a Ryz 994. Drly olg for ff oluo r a alra aroah wh oal mral mr ad rla raably. h mo mora ff dyam r drmao ar o from a am o ra mor moy from h oumr, bu from addrg oml mar, ad arular from h alu ad o of ada orag. Oo, whh ra mar for ada orag, ar a mora a of boh mamzg ru ad of ffly alloag rour. h rrubl good roblm bra u o wo ara mamzao roblm, o for h low ualy good, ad o for h dffr of h low ualy good ad h hgh ualy good. I h arl o, a rrubl good o ha rod h arl grar flbly wh r o h m of flgh. h o of dlrg a a rrg grar arl flbly auomaally lowr, ad hu ar of boh rof mamzao ad ff roo of r. ffy rur a o robably of my a. Prg o ll ou ff. Syma hag dmad ar a al faur of h daa, ad modl ha aum ha arly ad la arral ar dal ar mrally ald. 33
Rfr adll, Ralh D., A omal, dyam oly for hol yld maagm, uroa Joural of Oraoal Rarh, ol., o. 3,. 476-53. aru, M., ad Srdhara, V. 4, Dg ad aluao of a dyam aay aorom rodur, uroa Joural of Oraoal Rarh, ol. 55, o.,. -33. lobaba, Pr P., ad Wlo, Joh L. 997, Ima of yld maagm om arl mar, Joural of Ar raor Maagm, ol. 3, o.,. 3-9. oard, Smo Dyam Moooly, Saford Ury, uublhd maur. odly, S.., ad Wahrford, L.R. 995, Prhabl-a ru maagm: gr ad mullr yld maagm wh dro, Iraoal Joural of Maagm S, ol. 3, o.,. 73-85. oau, Marl 949, La arfao d dmad o: alao d la hor d la au ou margal, Ru Gral d l lr, ol. 58 Augu,. 3-34. glh ralao aalabl J u 33, Arl 96. or, Sr, ad Ro, Nay 994, Como ad r dro h U.S. arl dury, Joural of Polal oomy, ol. 3 Augu,. 653-683. omr, hodor C. 996, ffy odrao arl rg ad yld maagm, raorao Rarh Par A, ol. 3, o. 4 July,. 37-37. roo, M., ad uo, K.J. 994, Yld maagm: a homo of h 98 ad 99?, Iraoal Joural of raor oom, ol., o. Ju,. 77-96. Carboau, Sha, MAf, R. Pro, Malo, Hugo ad Malo, Su 4, Pr drmao ad mar owr, uublhd. Carr, So, ad Looy, Wllam, h r wdor roblm: hoog a omal dmad orfolo for aaad rour, Maagm S, ol. 46, o. 7 July,. 9-97. Chaw, Rhard., Omal dyam rg of rhabl rodu wh oha dmad ad a f of r, uroa Joural of Oraoal Rarh, ol. 5, o.,. 49-74. Daa, Jr., Jam D. 999a, ulbrum r dro udr dmad uray: h rol of oly aay ad mar ruur, RAND Joural of oom, ol. 3, o. 4 Wr,. 63-66. Daa, Jr., Jam D. 999b, Ug yld maagm o hf dmad wh h a m uow, RAND Joural of oom, ol. 3, o. 3 Auum,. 456-474. Da, Paul 994, Arl rofably yld o maagm, SIAM Nw, ol. 7, o. 5 May/Ju. d or, Sa V., Frlg, Rhard, ad Prma, Nada, Mahmaal rogrammg for wor ru maagm rd, uroa Joural of Oraoal Rarh, ol. 37, o.,. 7-9. 34
d. Harr, Frdr H., ad Pdr, Joaha P. 995, A ru maagm aroah o dmad maagm ad ordr boog ambl-o-ordr maufaurg, Joural of Orao Maagm, ol. 3, o. 4,. 99-39. Dr, Raymod ad MAf, R. Pro 996, Damagd good, Joural of oom ad Maagm Sragy, ol. 5, o. Summr,. 49-74. zo, Or, Koblo, Crag A., uhda, Raaoom, ad Ya, Aladr 3, o buy or o o buy: mg arl far daa o mmz urha r, Prodg of h 9h ACM SIGKDD Iraoal Cofr o Kowldg Dory ad Daa Mg, Wahgo DC. Fa, Mg, ad Wag, K 998, Omal harg oly for gl oulao wh rod off, Mahmaal o, ol. 5, o.,. 65-77. Fg, Youy, ad Gallgo, Gullrmo, Prhabl a ru maagm wh maroa m dd dmad, Maagm S, ol. 46, o. 7 July,. 94-956. Fg, Youy, ad Xao, ahu a, Omal ol of yld maagm wh mull rdrmd r, Orao Rarh, ol. 48, o. Marh-Arl,. 33-343. Fg, Youy, ad Xao, ahu b. A ouou-m yld maagm modl wh mull r ad rrbl r hag, Maagm S, ol. 46, o. 5 May,. 644-657. Fg, Youy, ad Xao, ahu. A dyam arl a ory orol modl ad omal oly, Orao Rarh, ol. 49, o. 6 Nombr-Dmbr,. 938-949. Gallgo, Gullrmo, ad a Ryz, Garr 994, Omal dyam rg of or wh oha dmad or f horzo, Maagm S, ol. 4, o. 8 Augu,. 999-. Gara-Daz, Albro, ad Kuyumu, Ahm 997, A ug-la rodur for mamzg ru yld maagm, Comur ad Idural grg, ol. 33, o. -,. 5-54. Km, Shryl. 989, Yld maagm: a ool for aay-orad r frm, Joural of Orao Maagm, ol. 8, o. 4 Oobr,. 348-363. Kuyumu, A., ad Gara-Daz, A., A olyhdral grah hory aroah o ru maagm h arl dury, Comur & Idural grg, ol. 38, o. 3,. 375-396. Laday, S.P. 996, Omal mar gmao of hol room-h o-lar a, Iraoal Joural of Maagm S, ol. 4, o.,. 9-36. La, K-Kug, ad Ng, Wa-Lug 3, A oha aroah o hol ru omzao, Comur & Orao Rarh, Arl Pr. L, Mhal Z.F., Prg o-orabl rhabl good by ug a urha rro wh a alao o arl far rg, uroa Joural of Oraoal Rarh, ol. 34, o. 3,. 63-647. MAf, R. Pro, Coar mahg, oomra, ol. 7, o. 5,. 5-34. 35
MGll, Jffry I., ad Va Ryz, Garr J. 999, Ru maagm: rarh orw ad ro, raorao S, ol. 33, o. May,. 33-56. Mua, Mhal ad Ro, Shrw 978, Moooly ad rodu ualy, Joural of oom hory, ol. 8,. 3-37. Or, Shmul, Smh, Sh, ad Wlo, Robr 985, Caay rg, oomra, ol. 53 May,. 545-566. Sawa, K. 3, Omal ol ouou m ory orol modl wh lmd uly, Comur & Mahma wh Alao, ol. 46, o. 7,. 39-45. Srdhara, Sr V. 998, Maagg aay ghly orad ym, Iraoal Joural of Produo oom, ol. 56-57,. 6-6. Soy, Nay L. 979, Irmoral r drmao, h Quarrly Joural of oom, ol. 93, o. 3 Augu,. 355-37. allur, Kalya. ad a Ryz, Garr J. 4, h hory ad Pra of Ru Maagm, Kluwr Aadm Publhr, Dordrh, Nhrlad. Va Sly, Rhard, ad Youg, Y, F horzo oha aa wh alao o yld maagm, Orao Rarh, ol. 48, o. Jauary-Fbruary,. 55-7. Wllam, Lor 999, Ru maagm: mrooom ad bu modlg, u oom Arl,. 39-45. Wllamo, Olr 966, Pa load rg ad omal aay udr dbly ora, Amra oom Rw, ol. 56 Smbr,. 8-87. Wlo, Robr 989, ff ad om raog, oomra, ol. 57 Jauary. Zhao, W, ad Zhg, Yu-Shg, Omal dyam rg for rhabl a wh ohomogou dmad, Maagm S, ol. 46, o. 3 Marh,. 375-388. 36
37 Ad Proof of horm : h oluo of h robably ha hr ar aly uold a gord by h robably of llg a a wh hr ar uold, ad h robably of llg a a wh hr ar uold, o ha F F λ λ λ λ G a aay a m,,, ad. h ud a h ba of a duo o ablh h horm. Suo h horm ru a. h [4]! β h lar dffral uao, wh h boudary odo -, g d! β [4]!! d β β β [43]
h d umbr of uold m, -, af β! [44] β β! β β! β β. Q..D. Lmma A:!! f f > <! Proof of Lmma A: No d L ψ. If <, ψ for [,/], o! d. Now uo >. For, ψ drag. Loally, aroud, ψ. hu, d d d. [45] 38
39 h roof for a b hadld by obrg ha!! o-rag. Q..D. Lmma A: <! f Log f Log Proof of Lmma A: d Log d Log Log!!! d Log! For >, ad larg, h rm - d h gral drag ad hu aromaly ual o fr ordr aylor ao y y. hrfor, for >, d y Log d Log!! [46] Log d y Log!! Log Log!!. Log Log π h la aromao o Srlg Formula, π!
4 For <, h roof mlar, alyg Srlg formula ad obag d Log d Log π! [47] ½ ½ d Log d Log π π Log Γ Γ ½ Q..D. Jufao for om aro h : If h r oa a a, h robably of a al g ha a uomr ha arrd a. hu, l b h robably of mag a la al h rod [, ]., ad for >. d a a λ λ [48] a a λ λ β β h ol for! β β [49] hu, h robably ha h flgh ll ou < > ½!! γ γ γ γ β γ β f f f [5]
4 Proof of Lmma 3: Fr o ha f aay zro, h al ar zro, rfyg h ba of a duo. Now uo Lmma 3 ru for -. d η η d! d!!!! Q..D. Proof of horm 4: L b a oga radom arabl, ad,. ad ar ouga o. L f ad g. h from h Holdr Iualy, { } { } { } fg g f or { }.
4 or Q..D. Proof of horm 5: L b a oga radom arabl, ad,. ad ar ouga o. L f ad g. h from h Holdr Iualy, { } { } { } fg g f or { } } { or { } } { { } } { } { CV Q..D. Proof of horm 6:, π F F F Ma
43, F F Ma, F F Ma R R W aum h adard odo ha margal ru drag, whh a hr ar al of good f ad oly f f ad oly f f ad oly f f ad oly f.