4.3.1 Model and algorithm: the replica exchange method
h h h avY H ReP Hu V H D S IUhIIpUkhRGHUDgegIhRIIXBpxIFgW B De qe H H D sv H V Re V aeFP a q V a uBe aeFP HBe ReP H H `WGVrfYrgTIF9`xTIdFGbraGHgIIGarne`BIPqIgGHgIIbGVUDIggregfhBUHpCiDsv HIYwehRphHgWVxDGVIreRIGFQr`WGVrfBGURHDIHrGeIhYUbg`WGVUDUbGHIIYv}fIIFD R D HP D B aB D H D W B De V Hu D R be B hB av a D HB H XB%hHIIGWGR9BuQrfGFkr`G qIGFXDV``r`IrfdFfebXVIhPHSFIBVI9eUuHreIhYXbgeb V bYu D V H i De D RW qe HBe b H q R H D aY sv D q q HgeI`WTfUFsGarne`BIPjIGF`WGaURHDegGegfhRIu`IF2FXD%qI`XWghkDhaHhRGHlXBgW Re RY V e Hv a q V a H D R H ReP H RW H D V i B qe D V
e V a a qWF i H D VuBW B DY Vu Vvev RP H Dk H R D HP dBhGHDsH`I%IFvSBIIIg`WGVSIvVRgDaICsxDVXqIgf`WIIGFlhkhaHIYwehRphHD HGaUR`9BgUDH%EUB`XT6hUqHXqgegIBhuGHrneSVatVShebVShPGHQ SF`W H HIYwehRphHD HT VW a e H V y q ReP V D qY a k q R H DR R D HP HGaUR`9BrW FrIdrheIFXD%IYVIvXVqIlhBV dFreUkgeXbVIUPGHR g`WGVSYg`UTiIFD HT V Dev D HF e V i R VY H b H a q W B D qW H H uW H V D A uW H y y z  H D aY H R HP IGFUDaSFCBhr`q qIGFUD#dgS GpCdySFIBVIhuGgWhRpaV DhaHhRGHlXBcgpUaHGVXDV9gIsgeXbGV9IIGFghaggeUR`TyrhRIGFuIFre`XWVreIhYXbgeS D VW DBeYq asFP H DW H H eqe H D H DW B D q q b HF hhahRIGFggfFHIYrGehRpeUHURI`Se H DW Be D R D HP D HF VF De B D D RW R q ReP e D V D H H H a HF i as qe R q ReP rgWVwde9hBXHGV`rgneShYbGVDgId'W9BUHhtUHGHRuGalUBeUHUqegGWGHURI%tWXqggneIUYbGVDgfgW RY V e Hv a q V a H D qv R HP RP VF a q e a V i HuWB H I`XWTfUFsGage`XBIGPSFUaHIUGHUaGH1CsDhRp`WIXaIUhlIBXViHgDIY%GFXD%UaISIFD WUuGHgf`UWd`WGVreS`fS`UWQrneIUYbVgDgfvW9B hHhtUHGHRg WXsUqgXVuH`eGHg%SIlIFD D ReP b B D RYB b R q ReP e D V D H q RW Re avYF H hkIgWVDhbIS`hWg GFXD%BIPv IGF`WEHgeEIGFXBuIlh %# Ir aB HBB b V i V a H D R a b H D V aYF $ kxhqGHGaXDV XBIGPjIFrdI`XWVUDUbII`UWgURsvIlIF`'IIUBsUPIXsXqgf"e GYUDg@XPf XBIGPe V a H D W a B H B B b W H v Y B H D B W a u H H u" q b e V V a BhHIUBGHURyxwIqgGURIhBIs hkIgWVDhbIS`hWQgEhRpIl`gneFXD%haSIXaErfFD V b H Vu s H H HF h aB HBB b W Hv YB H R q e V i HuWB V De k avY W B DY Vu ue Rv eW b V H H D Va W R q HP H DWB I SIlF r`WGVSIvVRgDaIg9WIIrQUHIhBGHDa}fIFXar SIgCsXDGVrneVShYhbpchRIGFgI h a aqeB a H V iUHgDgsygI`WVIhBIu F VF e V i q Hu qP V Re H i De D b H D aeFP Hk `IFxD%IBXVgeIXsqxDhVXbVIGHrvQrfGFrDgeIFSBhVXtGVgIIeUfSt 3 aG`QCiUDS3pqIF`WCsXDXTGVUDUbII`UWu`gGehRgtTuIFrkXDXV%bgfSehRIGFIGFCBSh t V RW HB H D R V HBB b H H e H D V q V eBsuW H D H D A xshqGHrXtfWIIgghHXbVGDwnegneS`hHigvhRpIl`XWVrIBIu`UWijWiSBIIgsPhaGHR`hWb De V RPPe W D q R qY R e BW Hv YB B De V RW b e D VuBW R k 1Spp`QCiUDIIGFQgj`WGVreXtVgheGHdFre`WchkUR`thWH`ifUhI`WGVreXtVge f H ik RW HB H D W B D q R b H R HT RW aB D q mHG`QCiUDSj``tUR`tThu`gGehRgtTdGHgUHtGVa hHgDsdFge1`WDUaGHURH9BrgUaHGVXDV9gI R RW HB H W H H e Re a a b H R D V W DBeY qgeXbGV9IXqggheHgDICBhhS`WGVreXtVgheGHEGahaXHggeErIiSeQgUsgGehRIUB`hIGHrdegDIS`GW` asFP qe u a A aB D q R q H D DWB Wu H i k b H H Hu D a uBY R ruGHreGHURIBIF9dGFXD%UuGHhRHghRGHlXBQXapUahHtV7UHDgsUR`Grne`WUaHGVXDV9gIsgeXbGV9IgW W a b V H D sv V i D V V a a a H R q R DBeYq asFP V H a H D b a H H W q hH H a D u D D q H D ae a a IBggeUR`TenmxhqGHuIFuUHIBVfhkUR`UTQtir`geUR`TenmxhqHWdIUBHhRGHGDreIFQghaUHtV7hGHDsa H R q R q uBe `gne`WGahaXHIrdhaUHtVa UHDgsqgeG`WvS`WGVreXtVgheGHGH`d9I`UWhbgW9XBhargdeD a a qe a R aB D q R RW DBY be D V H HBW q H H A h uBe k k k I`kgGehRIUB`2CB9IrQ`9S9 gQI 9t GHr'HreIXGVprIFhaUHtGVa Re D qY a H i De D h D a yhuHweRgDIGYR GHghaHgIgneVRhuSgfGFIvp`QCiUDIIGFrDgIQgq`XWVre9hBGHUaGHIUPruS IyGHS` Re qB D Hue a HF h RW HB H D W ReP e W B D D R H h RY V

W b Hu H Hu HF Vu a H DW V i RY V e Hv V ReP b D D V V gUHIhBSIhBphPIIhhUaHISYDQhRIGFgFXD%I`XWTfUFsGaXDrGHgf`UWvWEIBGVDUaGHhRGH9BaXDV k`XWVxDGVIgGeRagnegCXBIGPIGFBvCsXDV9gIaIGF`WeUuHDhbpS}faECsxDGVgeI`IXBGVI`S`IFxDu B aB D a q m V a H D V DBeY V D R HP H V R qY a WB FYW q h `xIi u ` a q ae HB Huk D HF b H a H D W RY VTe Hv H D su a qe H %tiXWq`WgjhuIfIfg hkreSEIXhVUbsPIFgI`XWtIhFpESF'SIGYDGWXagE hhIgWVDgeURH9BXBIGPa aB b D V V H D H Hv B D R b H D bY R D u D a e qe H H qe H D b a q SFUBhHQCiUDp`WGVrneUqGHR`hWIGFUHIIUuGHWqIhBGHspXigEGaUDhbsUwghRIGFhHIXBGVkxDIGYUaGHR huGHUDUbsfg1aEaIhhUa`TShYSFqr1gWgsgfIS`s1UDUbHURse G`WhaHIYrGehRpeUHD HP H Be V VF H R b H D qe R ReuBYWv HP R R D HP gDhaQtiWIggDhaI`XIIGFUuhHIICBSeahR`UHb@IgHIYwehRphHSBGVreGHURIB@GFXD%i H q uBe HF VF H D k Hu A h HT VT uBe R D HP D a b V V haHgeHhRUbIegWVwnehqHGR`UWuIGFgrIYrg%HY`WIgShhI`XWVreUDUbsfIFFxD%Gu`UWhbgBV a Hu B D R b H DW H qeT D q ave HF aB D HP H H D V i R be WagXaphHShBIIUBsUPIGHIGYreURshGHI`XWVrGehRIXuGVIghWhRIISSIIGF3`GWRhHSgdegDaIu qe V b Hu H Hu R D HP D HF hB D H aB b HuBY HuWB H D bB V H D V i a Hu B D R b DYe HF h a b H D V HP H aek D R SFFXD%haGHreGHURhbI'gWVwnehqHGR`UWGWSgvIgHgeEIGFXBhuHDhbpfrghuGHrneUqGHR`hWb xmGVlrpWIhBGH%r`gGehR`T`hkIXBIGPIXBGV`pl`UVIB tIUahHtVgfIhgXWII DBe Hv D u D kH H e BW a V a RWvF H iWF aeFP H D qP HF hxDeXVaSFiUuhHUHS}fulGgpCiDIiHdXsI`SS3 V q V D b H a RW HB e qBWk dFgheGHEI`XWVrGeI`fSghWg@SFqreXHqI'UuGHURH9I`UWIhBEa7 guXDXV1URsISge b R aB D RYB b H D qe VF h DBY b H V W V q HPPY B khhaSIE 9 `W9ISIggXWIrIFCBhw9q iGgpCiDISFyrrUHtVIGFGFXD%i HuWB R k hh V W D qP H D A RW HB H DW a H D V XsXqgeXbeSFXDVg9`XWvgDIYhaGHreGHURIBFrIhBXHGFrf`geUR`TeIFhkhRgthWGHgi@hh9gdegDaIsUR`T q V Re q a a b V D q DeP H H e H D HT RW DB Vu H Ha%gihRIGFghaGHXDGVpIBlIXBVBXH`GWggde9hBgfSIYpsneSwhkUDgeXBrS IIlF II HIYDIGYGRDa V H DW a V q V q Rq D H euB e qP b Vk avY HF h R b XuGq`QpXqga RUVIFXaewfF r SgCsUDXHGVI`WI9geD`peXr`sreURIgheGHIFD RW i qe H D V De D a W RP RP DB RWP V Be DYWve Hu R H u V R H i h h V V D qP H D W B D R D V Hv e H V D H RW SBhGHQI IXBgWSiIGFug`XWVreUDHIGPURH9BhRGHGDUDpgXT`WhRIu`CBA hhlrdeDS`hWb DB aB BBe qW H D V uBe a V a H Hv D a qPY b H D V HF ik IgehtxD`pxIGFaIgrIXBIGPihBUHpCiDsFgShBGHGRDIXBVIS`hWIGFaq GHhRS%S gaxDIIjXBUuGHahaGHSS}fvHgURsgI9hBGHUaGHIvIFBuUaGHIGYreURshGHvIGFcXqu%I `t# W VBY V RP H Re HPeP D RP H D V R D HP D H D q h R hh V V B iW a Rek uBe R D HP D H D H Hv aB `WIeIXB%SGFGHrf`x Ir @ haGHSYrGehRpeUHIGFihBUHpCiDsShkI`XWVD mweIgfS`UWgVUR`tThuggeUR`TUkaXDSGYhaHIrhr$ l `9hBIShBphPIha`hWUbsv RYB b H W H H e q R HF k BW D Hu H Hu H H h h W R De V W Hu H D uBe HuWB W D H Hv DeP df d H D ae 9txIiQgr`WrIB`IhBSIFIrhaIIpCiqhBUHpCiDsGFrfeRCdfYIFg HB Hu H D H H DWBe D HuWB V b Vu q a DeP q H a Hv e IIUIhBIGFUhhRIGFgIgiWIIBgeDhRUHe `GWR'IXBIgeXHIFrIpgGehR`TGHps HhRIGFhHIXBGVhuGHreXbVI`UWGH`agWVwfYxDGVIF SCBUuGHURIuVI`hWgWGVShBIu H D b a D qP b RW V B De a H D e A h H aB b B a H V H D BW a au H Hu uBe bB Vu De VeP W v YB q D D H D SF`DIYIIUBsUPIIg UHIgdegDaIwGaXRgfghRp1H IlpgegW'IGFaV HhRI%i HF % 9txIi h & II r$ ae D q R qY R gUHbGVGDregneIghGHe BW HB Hu V VF i B bB B D R b DYe q De a H D W aY Ve sv `UuIfIadFXbI%j`XWVDIIY`WGVrneUqGHGRghWWSggeVrfPIGFgGHSIXBrjl S H D V a V a H DW B D R bq De aW D D H H D De HT V H i a R e a SFeXBIXBIGPSFge`WGVrneUqGHR`hWgeVrfPcg%9hBGH}fuIGFGHr9GVDUa`9BQdhPGHDgDGafEu

-6 -4 -2 0

=0 =a =10a =20a Gaussian
h 6 `WGHgheGHhRSBgeV9hBIgsfH R a b Vq D HBWP B W a aB D q q b HF h RW HB H D W aB D RYB b HTW H H e H ge tiIGF1I`XWVreIhYXbgeI2p`QCiUDIIGFgS`WGVreIgfS`UWqr@UR`t`geUR`TIFD RhGHDrBgeS`UBhHpgfF dFge`WIXYgrgffIhhghesSgWDgeD`gGehR`TeIFD e V DvW Hv ae b H R H qeT qeB HF R HPPe D R a H H e H aB D V Hu H R q R VF i 6 b RP VWB B aYe y e RW h `WRQIgWVwneUTI`Grne@( 6 `WuXHqI%1 7GahaUHWIuHa`S'gneVGaIgfg RhGHUDgegIe`ShuCH}mIIIGFpg`WGVUDISY1ggggeUR`TgegshGHIGF1UaHgIUBIu H ReP H HuWB H D W B bB e ae kH H e q RWP D H D DW H HhRI%k F F 6 ghuIIUIUkaV`WgDIliIGFugjhHIUBIIhBphPn StxI GHSR ` HF i ae HB Hu a RY H D W b Hu H H h Y V
H D R a q W Hv YB H H e H D uBe D He W Hv YB H D f H ik a Wu SF`WulIXBVghRpIl`gGehRgtTSFIgEa9UB`gpghRpIlIGFSpIW'IWD URIGugCBUhhaXbegISFdW9grUTXHhqHhaHGVDURs`WI9geD`pDgeIGFS`pgqGBgheHq H RW A V eBsu H D D DBe R HP RP DB RWP V aW H D DYWve R GWIg2UuGHIr`W`p`GWIFiWDhbpGPhaHFxD%hqIe1I`%gahaIGBDIS`GWdSFvgDhaGHjWD D uBe aY s qWP D H D D H R V i HuW RYW W H aYv R H D D IGgGSggeQyhS`WGlUeiXsI`XWGIuuEh9UHhUdIBhGIXYhqgeGa H FD W Ha Y He H i k uH B VD BH qa Y V THR P a haD B Vb H Wb VRHDa qb qe uBe B DY Vu R Hu B VW e H eF HP RP RW i qe IrkI Uk9)`XWVSSvGVGRDXaI'hHH`hI2`WGaag i`TfhkUaHVgDhRp`GWS2XuGq`QqgeGa V RP VF i a RW HB WuBe H H H a b DB V e HF i aeFP IXBThRHhaHIXHqI%hkl`pCiDI!`IIgrh ha`hRhURHDSYhq19gnegjGHURI%GHrfIje GWl`pCiDICBIGYhklXB`WXaIkqgeGrggWVDhbXHq`UWur2UuGH`p`hWXaXDHhRI%dHgfIP D a RW H mv a D V Vu qe a W B q b e W aWP b V V HF i aeF e `WRhagtTeXDHhRI%2`WGVXDGVSgeGRjGHgIIgheb``XW`p`WUagGhRSII2G`QCiUDIjIFD H W V HF i B aB D aeFP q V qWP D e HW HuBY RW HB H H D VF i R k SFdFbS%E`W S gSYgrghebVxDGVURjagDafeGHURIFUkhR`tUWGH`Ire kH qeT q b e V H H D HT RW kuB a b V D A k k qW H H D H q Re HuWB W D De @ GHgheXaIF2CBhw9in9)dn`QihRSFUDg`WhurIBXVHgehaIIQCirfGFD CsxDVqSgf`WIIGFv9huIfIXa`uhkhaSIpghRpIlhuSuhBgXTy `g`XW`p`WD V v e v R P H D s v H B H u V e k H u W B W H v Y B e H f e H V h s q W P V HuBY H D ae  ~  RW ~ y ~  e aY DYv a SBXsqhRIISdIFEgigd pg`jwvwpmuy d pgSBGVSSIhGHDsa H a H D W B D qY a q H YB e V R HP sv HuW RYW V H H RW egGeIGFg`WGVrneSVghebVhRIlSBG`WghRp9rhqII`BUDhbsUwuGqgpi qreIGFIFqIgg`Wgs`GW0 SeIFQghHSgdegD`sIGFHr9XVgDha`9XB1URIFgDIY qe a H D H D uBe s qWP D H D W bB RWP V H D De HT V H R H Uh`QCiUDIsgneUVfXGVDgiIgreGHFrs'XBge`hWgshRgexsqgfGYUDg%XaIkw9jn a RW HBq b Re uBeq R DWv V BW b HT qe be V k k qW y y ~ u z x H D ae D 9p)`pd xzwpzgd IGFg1WhuHGRhRHGHhkahaIGBUDgf`UWg%bGVDXaGVhRGHUDgGegfdFb R H beP bW b Re XaIgUHtI`WIdFIsEWa9UB`gSF`WhRXHGVghepha`UWhbpQoD`XWVrefGWSIgdXuhqfghee VF h VB R bB a D D He H D R a H H Hv AhB De V RPPe H B H H D W De D D auBW R a a RYW W V eBsu H D RW H D V RW HB H SFrwfFWrII`pGPUaGHGRghWb hGHDs%I`g%haXbegI1IGFGH`IFa`pCiDIEIFD UDgf`UWH`QIGFwy`WVGaIUYGbaSIgWUTHIcI`rW`XWVrehqGH1CBhhUDgIe`UWGH`ha`hWUbsv beP b RW H DkB a Vu aY V RP RYW D B D R A beP b RW H H uBe a R RW HB H D V De D HuWB H Hv D q DeP H H e H D Ir lIXBGVIFa G`QCiUDSIGFUkaErfGF haSIUBhHQCiUDpGFgIUBHGFrfe`geUR`TeIFqBV HgeHhRhbSjGWhuGHrneUqGHEa W H a e H R b B V B e D e F D D Y W B V D B V W P F D R W i W a q e a V D a Hu e D D R V gdGrGUIgwfES`IG9`pg`QiGXg1oA hwCI{I qq I )C`Eqs`UWIFD k k q q k k R H aWe b V Vu a H a D H ggfdFBEhuXHIIYgDEXshqgXTVIhBGH}fz f w~geIgyCyd Cyf G~fwp`WgUqIe  uBe |~ R HuW XbGVURIhB`1 uXa%tSiprjgevI}hx`dnmprg&e gThRGHlXBvIGFiXBuGaURsvIlgIIgGe%5 H H e V h h W Pe HF k q D V H D V Hv YB WuB R uBe uBe D b H b qPY b Re uB H q h RW i D RP H D V aY HB Ir SgGalUBHUVeUWSBVSI`hWQGHg( Ige GHUR`plUBGHUaGHIIFEBUuGHII`W H D D R V a a a q V e B s u a e b a& e W B D e V R P P e H B H e a SFdWgeqVhHgDsgeXbegIbVgDgfdFW2gD1 dprj`XWVrefGWISgquUqfge'ge h Ii ( F 5 F Pe V i q H D aWP R rSB%tWXq`WIFhuH`sgGWIP q q z y V V R p HuW H D W V eBsu H D H Hu D D RP RPP w9qpQgldhbXH%tiGehhhqIeIGFpgEhaXberfSIFsXvGVhRbhaIWGHrneVI`WIIge UaeghWhbpdFg9GWSIgeuhqIgheeeIgGgpCiDI%IFSXqgQhR`teFgIUBGHGRDr`geUR`TrIF9v H Hv be RPPe H B H e uBe RW HB H D qe HTW D a H H e H D s qhqQ'huGHrXtfWIIgpgera9hBggUBhHQCiUDpIGFgIUBGHRgDIBXVII`UWIFhBIGFI3 H i De V RPPe Hv B b D He H Hv a D a qPY b H D H Dk hkXDXVbgfSehRIGFSFFXD%S`Wge GHURI%GHgheESF%hRIXuGVI`UW1QoA V q V eBsuW H D H D V i B q HF i a b H D H aB b Hi

10 -10 --5

-6 -4 -2

-10 6000

3 States 2 States

8000 10

20 -10 -5

P(x) x

UaIGFgGehRWUuHrehqGHHgGa9hB`TlUBGHURI`hWp`Gge%IFGHreaSFCB`pEIFXBaXqgde2ineq H a b D D R Re D H H D HF b H R q H D a b V D Ah n H D V V D URptip'9jhuUHtVhRHDgerfdFGWarkwS`o xyS8hHShBHSIGvIGYbgfSu H WP sv b Re b qe k k k b qY R D V eBs m RusF H D H ae H a V a q De qv R RY V e Hv D V D V H D uB wGWI9IGFShkGaUDhbpGPr`GWeBgDgeXHrIhkhaXHIUGHhaHpIgWTfhFpp9UBHGDxDehRGHlXBpXRhVIGFIge q H VBY ae H aB b Hv B b uBe H Re R q ReP H DW D Hu H Hu rgeahR`xTIIg'UuGHhRSuGVS`hWrsegeIgpUDggegneIUYbGVDgfrIGFg9UBIIhBphPSIBV HgQrfGFUaGHIGYreH@tiIFQIBIYDGHrIFhkahRHgfdFI`WTGHIrIFXB'hu`gThRHI`SreGHXRgpi Re De D R D W a a R R H D DPe b aY V RP H D V H avW su qe H a q q ae HB Hu Hv D q R H i VF i x   RW aB }hWqXBvrtht6EXBSW gUuIfIppW9XqgeUbGHQdFbI%rkSifdy`rhkI`XWVD me bY RP H D Re q H DW HP RP H D V i R q ReP Vk uBe fYDIfUUHbVIIGFfgW IFxDGVg``WSFfgUaHGVDhRp`WIIGFvFxD%wUkgneIUYbGVDgfvB9Irt6 khhaXHGVURGHuGVuhHXbGVIuIFIXBIGBURhHIghWQxUGwxr1`GWFXD%QaXDSGYhaHI`uGHgf`UWWD a H D RP H D V bB b { y z x H a V i q R RYW ReP b aeSudXBgSdWgDqUqGH`9W9hB`rggyXqq%uIGFWIIgsPhaGHR`hWuIYgrT V H V Ve HF h b a e a RW sv D D He Be W V i H D D auBW R b H qe XBIGPIGFEHgefxhVhbpGP%XaIFCBhUDrGge'dWDEIGFGgpCiDIgehVGWgheGH%tIlrDUasv V a H D a b b H a V D A H Re b a H D RW HB q b a q R B iWB H H D a Vee D Hv B b R aY D a Vu B De R B V VPW R HuW HF SFEDIXBg9gUuHDUaHsreEgevIlFUuGHGaShYGbXaIq`WGVreG`Wq`WSBI`E`WhqSdI
4.4.5 Possible application: opinion formation and the stock market
hB V VPW Be D Vu V qe b y`WIXBI`gGHreXbIIBeXsXqgfGYUDge a9gfXPhVbGVDgIdIFrDgeEaXq`s`WSBI`BrIF`XWVrrgThRGHS`dIGFFxD%lUBHgDaGVS`hWb DBe ReP H D W aW qWP B V VPW V De D B De avW H D V i D aB aEaI'd tugEhRIu`eSFghuSuhVUbIIIEaEa9UB`g%g`XWVUDreRXqgiqxsI`W V VF h W H RW H D Wk H HuBY V D He W B b qe a e qB kUhRgUWGH`gIXuGV%I``huQUigaxDSIr`gGehR`T%IGFSI`GWrhuHIvVRDXaIgneVGaIrEy HT RW hH a HBW BW H H a V V DYv H H e H D uBY Re DY Vu B aYe h hh V xIS XBhuHIurvge1IFGHrhuHIuahRHDeregf1IhhqIeEHwdeD1hHHIFEIFrgWVwneIY V aY ae H a H D Re aY H ReP HF HuW D a R D H D W B D q m a H D RYuk D He H be V W Hv YB H D W n h RY V XGVIGFIXBGVIIyS0uIhkGa9hB`g`XTGVUDgIBghRpIlIGFg)SXItGHIg

Ns 1500 2000

lW D E IBy4D 4WD d & #! 4q C)& )8)D GPB4jCA 1( ) E 0 E 0 ! $ E E $ $ $ E R $ & E 7 7 & & $ & $ ! 0 & H 0 % & A 0 7q dI7 r4 8I "8 I F% D 8ID & & 4D& x0 0 0 lk e R % 7 R E &$ A H ! & % 7 & & 2 % 0 & 9 ! 0 & E $ $ $ 9 ! % & A 0 E & 9 )84$ $ 81 D4$ 'd 8j& #! 4jC4C j& B0 D x
h hh V tXII7`GWR Uu`TURGHIgErgXH`GWXBgeSFsneIrIFI`XWtTIhFp'IBIuhRIIGFuaXDhRSFrrgWVD H avW aek q R Ve H D a qP De D RY V e Hv V HF H D V V H De hB mY Vu H DW HPe a R b H DW B bYu R R H D R D V R Vq D H B IXvGVGRDaSIFcgpgfF%UDUbGHGRghWIGFcgd`XWVUDSIWIhPHIF`W9hBXHIhuH`IXBgneGV9hBGHaha'ge DWB V bev RP H D HF z y e sv aWP RP V eBsu H Re gIadgfIUuhHHrhHbVIrIFuHhRIkwgg 9dUuGH`p`GWSQUabgfSDgg dWDr`WUqIhuUHtIg`G`oWnmXhqH1SFeGWgDgeGR9`hWBkwfFHgr h UaHVhRGHGV1IGFgW b a R HuW VBe R a H D D a DB b V De D DW aH DH D haXbegIgXVoqm9hBXHIIGvSYIGFSBGVahaHIfUkaXqgdeineURptp9hupvVhRbhaIdHgsIFD V eBsu H D qY R D H D RP H V D q H iWP sv H Hu Re H kUgneIUYbGVDgfBSg'pgfGFE}f vC~pCygtTIES`WGVSIvVRgDaIGFgp gHSgwGgehHvaV R q ReP V kuBe HPe a  z e H eF aB DY Vu DW h qve Re R haI`g tiVIGFIgshqSIGFUBhHQCiUDphaXHVXDVgneXqeXGVSy%SGFpXafQCiuIFD HBW W n H D uBe HuW H D H Hv R V a HF hB iW a V a n W D H UBhHQCiUDp`GWXaGVgIe`UWsSxIeICBhhUaHIge `ggdegGWegWgg` tWD H Hv B ReP b ek hh V A qP a W q D D e R HB R H D aBe a a Deu HF h Hu V HBW iW n H D W R a b Ve ``$`IgGeIFIgIGP%UDHderfSs}fIIBUaI`g tIFcg%haHIGYgWhqxsqgfu rdhaXHGVhRHiGVjIGFDSBg9ruUqIGHrdegDpCijSF2lUuHrGehRIUB`gWIXBI``gGehRgte W a H D H D a Vee HuW D a W D H D sv D H H B V VPW H HT rhaXHGVURGH'VIF'Hgf`hWipSg F SW `WIXBI`i`geUR`TiIFWgfgWVD W a H D H D ReP b H i uBe B V VPW H H e H D D qeB mggs`WIGHgEIBIYDGHIGFyuXVgrXqqGVDu9 Spgq`WGVSeSGYGareSF'IBVhRIXuGVIgp RWP RP Re a R R H Dk qeT a h h W B DP ae H D H aBW h RP W aB D ReT aY qe WBe H DW R gUHbGVSgpI`WGVrneVgrpI`XWge`IgrhRSFg`W hhaXqgdeweSFhHXtGVgfSeUGWhRIu`'BhuH`sVhRpIGYa V D D H D aeFP H D H RW V aWP HP GWXagagneVGaIgS`xshq`xTVDhbpGPhaHuHI`pGPhaH`WSBI`Sgf`XW`eSgS`GW`rIGF`WvG qe V B aYe y h H H R aBW R B V VPWqev q uBe PY R H D R 3 uBe kHuWB HB b H W a q R k Vvev RP a b H Ig 3 gIIiIdFgheg%lIBXV%`W % gCsXDXVqIgI`GWIIXBGVhRGHDIXYhqEIFD R`We UkhaII! rGHgugWSIFiBRIGFhHISWIhPHdWhuHIhqIe HuWB Re D qP H D V n H D bYu R R D aY HuW H D W H ReP HF h D Hu V HBW iW n H D IFgGaURHDegGegfIEI`r` GWe``$ `WRfSIBhaS`g tfIGFQgW haHVhRHdeXVdIGFIgUqIeIgr IGFUBhHQCiUDp`GWXaGVgf`pdSxI@GHS` a H D H D uBe HuW RYW W n H D H Hv B ReP W h RY V

0.0001 -10 -r 5 10

"
0.Dow Jones Model Gaussian
lk r4I dG$ H 4$ H 4y4@& x#! GqD 8q8dDC@& ')4)d ( $ R ! 0 R $ 9 $ & 0 & E 7 & $ & Sc X` b u s ` uc` hu T e ! % 4fgag6fc frGGG14D& 0 )& 9 E G)1@& @'D I)Q'D 41da ( & ( $ & % $ R H $ & $ & ( e & E $ 9 f
W B D qW Hq RWP D HF hB De Re D He R Vu ReP e ae aY a ggWVY`gUTge`phHS`WGVr9UGH``rElUB`ggW gIgGegfdrUuGHIUkGahRGHDIXYhqb B D q HPq V eBsu D qPPe V aB D qY a D RP H D V aY HBW H D `WGVrne`UWGbURscghebgfSGWiUuHVSIgafhkS`WGVrneIvGV9UBGHhaHIvSFiXBhuHIvIgIFWD R V a V eBsu Dev D HF e HuW V D A h DPeF V D RP HuW geqVIhkUabgfSFrI%reIhqIepaIGFCBURHSrfpBihuH9UBGHhaHIyUqIe p H D R B bB B D R b DYe H D bYu R R qe H i DW hh V SFQgW`WGVUDISYe`XWVrehqGHR`hWWgIGFhHIIGWShPGH1GWXagp`WDgsv'g IeICBA hhhaXberfSiGFrfFrheIXHIeXGV9lS`hWUbgW9BhBrgdeD V eBsu Dev D HF qP a e sv DBY be D V H Hv DWBB b H Re b a H D V H H RW H q V mBWB iWF D a V D VW pgSIgeuUDrGgejdWgDIFiBaDhbsUwgs`eUecgeXTGVGRoDgISUaHrGeRDSYqXq9BgsP uB a VF b RP WuB R D R b HB RW a e H q q D HBW I`UWhbHaIhrjvhaHGahaUHWI7gIIgGe'huHwnehqHGR`UW`IreCRgmD`SGFrVxsqgeV9hBIgsP m H a Hu HuW H D sv D H H a H D H D V RW H H D RY V e H l}ftshehbIUqIeIFq9UuHrGehRIUB`vUaHVhRGHGVSFqBgs`eUeIGFk I`WTfUFsv inerhRQtisv`TURGHIg1Q%UDggeESF`WXHqI%y`WGVrneUqGHGRghWr9hBGHURyxwIeXshqgXTGVrdexDVgfl q H WP e H avW H i H Re H D R VF i B D R b D H Vu H D qeY e H avW H DW hh V k D qWT H D R qWF DWB Wu R V a H u`gThRGHS`%ch`WDgpvg IIX`gCsXDXVqVwne`g%SF`WugIgIIhaHGVXDVgneXqeXGVgea H D P h h V RY V e Hv D qe VY H Be H eF Hu V HBW iW n H D uB SFp}k`WD g IIXUkI`WTfUFslUBHgrxTIlhr`Tf2}fIIBehaIggQ"IF2Ige hqIrSF9UuHrGehRIUB`QSGBIGYUDGHsghaXHGVhRHV%IGFpHXqIhg spg`CsXDXVqGVrne`gIFD HuW H D sv D H H a R RW a H D H D VF h h k D qWT H R uBe a R R H D R DWv h h aB bB B D R b DYe H D D q q `WIgEIGBSYUDHIFgWFgpk`gSpcUkI`WGVUDISYi`XWVrehqGHR`hWWgIF1HreIhYXbgeb H ik DPeF V HBWu su qe a aB D R b q RWP D D aB De bY H D QphRGHSgfpqXBvIgISgeHRgurhhI`XWVrehqHGR`UWre`peUHGWIgWVwfYDIftSFgW n H D V V D D H D uBW Hv u D H H Re b a H D uBe RW HB q b IGFXBvXaqgere'IFI`gUspIUBHfUDrGgedWgDSFIg2GgpCiDIpgehVGWa qe VT H D sv D H H a H D q b Re H D H Hv R V a HF gfGYDRdIGF9UuHrGehRIUB`haXHGVURGHdGVgehVfxVgDgIF2hBUHpCiDshaXHVxDGVgeqGVI h H H gXshqgXTGVUDhbpGPUaGHR HI`pGPhaH'`WSBI`ygf`XW`iSgI`GWg1IGF`We3 Ig BrISB UiIidFgegW aBW R B V VPWqev q uBe PY R H D R uBe 3kHuW HB b H a q H D R k Vvev RP a b H D R HuWB SBVIGF`W " gCsXDXVqIgI`GWIIXBGVURHDSYhqIGF`Wg 1 UkhaIIt gGHrDGHjUuhHXsrfg1IFEhHIIGWSeGWjhuHIahRGHUDgegIvIh`WDgpvEsCsxDVXqVre``T Re a t qeBe H D bYu RP D aY H ReP HF DW D qW H D uBe P aB De bY H D R aB bB B D R b DY h RY V SFIr1`GWDe F S`WGVrfYDIfIFE`W1IgWVDIIYq`WGVrneUqGHR`hWWSSg IGHIg

hH a uBe DF R H D BW HuW rIuV'IgfoFm9`XGVIF`%haSIB UuHUDUbII`UWXsq`sQIFc`W9hBHhaHIQHgUaIdFIgegrc`XWVreS19guSBhVSIIBS`SFXD%i HBB b RWWP H DR D RP Re H bB qeT hB D DY sBe bYu V DYW V qXggshRghBgUTsgeeGHghe1XaIFqB UkGahaSBInmXhqHI rSYgrq`Ilv qe a HT H H Hv B b a b V D V k H D a HF h W H qeT F VF e s UuhHXtGVhRGHUDgGegfdFHgUkI`WGVUDUbII`UWvGHgeGFXD%uUaI`IGFygSuGVjIgfoFmDUXHIGF`haSIB b Re b Re aB HBB b RW V i HBW H DkH a uBe q H D BW HuW HF h V RW HB H DW a b H D a b V D A h H Dqev q uB IS aGgpCiDISFgEIXBGVhRGHDIXYhqIFrGHgheXaIFeCB GaUaIBIIrf`WgIge
ahaIGBI`RW`BXWVrDGeI`YfSgBhWHSgvdegDXB9Vk t yuGVgRrSFggDIFIgPfS GHS`Y H D R b q a e k H D W W a eB h R V
lk $ l ! & & & 7 & ( & 5 & & & $ i46R j )8" A & 0 )6D D '"0 l " 40 8qIB4W)& jC4W8 DDUIH ! 0 A 7 H $ 9 & E $ & &
uBY H q h RYu H qP HW Hv YBq D D H D sv HB Hu ae VBeP IS`Wr$IXBGVIIShkhaUH`tsWSeUgURsSgegWIF9huIfIprSUkhaHSgf`hWb h h W B DY Vu a H D t qeBe Df Df R q ReP A hH V De sEg`XWVSSvGVGRDXaIvUHtGVEIGFihuUHXsgfrUSdrQqUqHrfUkgneIUYbGVDgfiCBgIYGaXajhuGHrfv }mIEaIGF`ElgVeegGWhuIFjGWhuXHGVRdgTfhaXHIIGYDghebGVXRIh`W`XsGq9hBhHUbr Hu V D BW DF q H a H a D D H eF Vu a q VP H H a k D H th9hBI`WR9hBIGFGW SgIgGe W`TfggXTTSGYWhRSGu`BfydFbI%i D H B V T H H D D D P e u D H eFkH V R a D H RW Vk VF UHgDgs`hWUbgB1haXHhVhbpGPgvwfFWurneqV1XagWVY`gUTRUVIFrGH`WGHURIgWVxDVD a a H Be V H a W De D D R V a V B D qW H H D k R HF hB mpe`UWqIg1haHUVIhBSIhBphPIuhRGHlXBprG`QCiUDIfXHIeghW'q9qhuHSGYaUkefgdFIGYa HP b uBe b Hu H H D V W RW HB qP b e sv q R V a R ae b khUaHVxDV9hB1b`I`UWhbr9hBI`WUq`TIIGFurfGFXajgs`hWIGFrXaIFiIBIUFseeIXujBr1IFD D H V WB H W D H P H Hu H D De D V R H D V D u V Hv H V Ve H kXqhqIFaSl'CB1ISB%tiGW`xsIuIreaEDhbHIYIF`1GHIGYreURHxDVIGFqSgagDa`I`UWhbH H DYB e A h V R q VP R V v a H D BW R D q H D uBe V WB sBe BW e R qYPWP H Hv aeF kB D qW H W q b RP B V V Re n H 9gI`g1gneSI`p`hWUbs1gfy`WGVSY`gUTr1UaHIXPhVIXBGVIqgeIB%gigYIGFD `GWR B D V a V H D VF ik R H D VF ~ y ~  y  z~ y H DW D `WGVreXRIGPSBhagrdedFbI%`gs`hWIGFaIhdxd ywd~d{wd~fCrgpw~ifwgSFg}fHD mB b H D V HuW A H D R B D qPPe q aWP e H a B b a VuB HF `hWrIGFXBIhqS IGFgWv`WGVreXbVISg%HIXvGVa`spDhag`IGYghegIBISfHhaI h`pCiDIhHGHRmXHgeb9huGHlUBGHUaGHIUPGHEar`W`p`GWIXBXsGqURIIIIGFhBI%CsxDV9gfl RW HB q a e sv D R R V s qWP D V HuBY H D HF i DBeY HegGeIF1BIGFvB2ineURptipIg%GHreb nIGFvB gygeegIXs`pPd`WGVSIvVRgDaIu a H D V H D V q H WP e uBe a H D V W q V WB qW B DY V ue Rv e bYu RP HuW A H D De D aB a aY V RP H D V a H eF H r9GWIUahHIIGWSUqIeq @IGF1rIFI`WGVUDUbGHvS`WUTHIIFBUBhHGH`Tf

m H RW a H D R a DBW e D R Hs eW q a H D e V ikBW H W HF hgD`IGFIF`WQSF9` iHEGWGaghe`@iH1guXHgeb%eXV1'GFXD%`IUBe`ShBIIP aIchhS`WGVrneXqqhVb`bIWVhRpCPr`XWUuIIhupUeUuGH`peXGVURsIYeGFXD%2inehRQp%XWq`W VF aB D aW Vu H m q Hu Hv H aWP HP a V i q H iWP e a i q XDUkIWGVURs'IXhVUbsPIBVIIhkUDgeCBy}fIIXBdhHXbGVI'IGFg`XWVSXY``T'IFXBhuHre`T V au HP b H a RYu b A h Hu V RP H D W B D qW H H D V q H mH2UBhHpgfvUDrGge'IFBvS`WTfhFpUuhHtSg9GgCWnmXUqGH%gEI`XWVrhebISBURIFgDIf R Hv aeF H Re H D V RY V e Hv VBe R a W aB D Vu V H RY hhGaUDrGgegehVIgIfIFg%UDreUuhHtXVCsDchqgSrgjhuHhRIXuGVI`UWsuS`IGFa H Re q bBeB H D W b q a HTWB e ae H aB b Hv qYW RY V e Hv V D k H RB b H R A q a H D uBe H Re aY ReT a Ve I`XWTfUFsvaIGFyhuGfSghWURIFgDIYoqUhhaHreGbeeXVIgaUDrGgeIgWGVrg1DIXBg9ge DIIgGWGHgEXaGVXsgIgSFg1GaXDIYhaHIhhUabgfS1UDggedGWDqBHgGWE9gdegD`sP aYv R Re a qeBe H D W q R HF V eBsu H Re b a V q R DB RW m Be q B b k q b VBe R a W q VP D b RP H Re V H Re V r2tseIP gheQgCsXDXVgeXbVXDVhRhuhHXtIg9`CWnmxhqHgrgeXbICs%UkGaUahHGWIi`GgIdFGbaSCumgGgfdFb e De D D Vu V kH aYeF H DWB FYW qe a VuB q VP H HF H D Re vwfFGHreXbIIBggXTVgDIgf}f1rIq`I`IGFXDghkgIBISfghebVRIheGHhaSUhhaGVgfBV m q uBe B D RYuk a V B DY Vu q H WP e q H R H bB qe e H D HT gnejIggWVweIIsgUHtGViB`WGVSIXvGVRgDaItiehRQtiseare`TGHUaIdFIgegrTIGFuhRgW aVxsgfgghebVgDaGVrdegDa hhXahqIeiHXqI@IgGe@B@IIgWjI`IGFWgeqVdI`XWTfF a qeBe q D HuW VP uB a V uBY HBW H D D R V a RY V e mpgXVCq}mIdFIgegrtTigi9huUHtVhRHDgerfdF%a%haXbegI1UHbGVS1IGFXBS`WGVrfYDIfIFD Hv H H bB qe e Be sv b Re b V V eBsu RP H D V aB De bY H W B D qW H q RWP D H D k q H e i D RP RPPe Be e De D B iW rgWVY`gUTgGe`peUHqIFrIIBVhRGHXDfUDXHhq`TpHreGVIgGWIIrgURHDrirfGF3%tIGFa H eF q R HF x x x uBe z y  yx R b H V gTfeGaXDIYhaHiI2hSw~SgGtywSIggG}Gwxfg9wG~}|{ ztd`WhHIUBIuUTH q VP H W R R H D D D V Hu Hv aeF R q ReP V k DPeF ghebVRIhrdFbgeHhaHIFWUuHrhebIUuI@hBUHsdrfhkrneIUYbVgDgfB%URHSgIp hhUabgfS%UDrGge'dWDXBSBIuhRIIgd`WGVreXtIg9`CWnmxhqGHa V eBsu H Re b a V V HF uBe B D VBe R W e H W HFP H D aB D qY a q H YB uBe a qeBe Deu VT k De HT rfhB`IUBIIIGFphkS`WGVrneIvGVrghebGVUReS@SgdXaGVXsgIgderInehuGHr9XVDUa`9BV H ik uBe DPeF H b qev q VF i H D V D W ReP R H D pcSSgGaURHSgIpGaUR`tThWXsXqgf`XW`dFXbI%UkaVhaIGFXaIFQg1Dgf1DafIFCBA UhhaXHhVhbpGPgUaH``XW`hWUbIgrhaHGage`iXBIGPSkUDrGge'dWDa H aW V q H uBe a q V a H Re b H D ae b a a a a b H a H a W RY V e Hv qP bk HB Hu H i qe R IFgdFIYvhGHDsfXUVhbpGP`GWpg1S`WTfhFpq}fHI`hWhuSfUIXqhqQixsqgeG`W uBe R q ReP su a H D BW a b aeF HF D RP H D k R D IgUkgneIUYbGVDgfrW SIGYDSF`@UuGHIUYWegfdXaGVhaSlUBGHUaGHISFprGHIGYreURHXDXVq BV GWXagSI`W's2gheXsUqHrIIYgD`WSIrfGFhkUaHGVXDI`XIgiGHUaIFug`TWhRIu`2CBA qe uBY Hv B b DeB R BY De D VY Vv e H D VW e D H RW hV DH H XBIF`hWUbsv sFP a VFP uBe asFP H Hv ReuBYWv H D a b V D V H q a D D qP 9I`W`WXqIIeIgUabGV9I'UBhHQCiUDpegsgfIS`sIFrGHgheQXaIFBg`xT`GW1WhuGHreXbVI`hWb DIYGHg@dFXbI%eUHI`WIgD`WrXqgGWhuGHrneUqGHxsIIXBVIv SgSBIgheHqajpv geb a Re VF i a qv RP W R a qe D D R qu q uBe Vu V H B kISBIghee%gheb`gW`CsUD@g9WIGaXD@XBI CsXDfXHIeghWb GhRGHjIGF%hkUDge@CBhuSfUIu VB H q V qW H ue Rv V V k V qP D H D b A h HB H qUqpgIvHgdFGbgheGHhaHIGFgrIFUBI%XsXqgneUVhbpGPhayghHShBHUVGbGFXD%dIWdFI H i DWB Re R R H D W a Ve H D HF i q H Hk b a V i Wu D bY DWB H eF De D a DeP D q q ae a aY D H D H V D kB a b B gIgTfwfFIFrIWGWXage UuHrfF gneVIlF9hBdlUB`gThRHaIGFp`XWGVghehbW { XhxhgGbUDfhB`IUBIIsgeXbVXDVhRphkUaGHGaUahHGWIP h H e H W HFPq b b R bVgDgfdFWgDpgs`UWIF%`gIdFpUkhaXbIgfdFUberebGVDXaVreD`WRjhuQtGWR`s%IIGFUDiGFXD%huHV ae b ak R H D aWe b VBe H q D a H i RWv auW H V i mu a q De a a iWB Re V WB H RW s q Vv ae b ak Hu RP qeB V IYgDxsqghebVwUHDgsSHgSUkhaXbe`S`hWUbQ`vg`XW`WIQg'dFIYSUuIIXYhqhbHI1Xsqrf`WGVXDIu mwGeRydFGbgheGHhaHyrreGHrlUBGHURyxwhhGare`gDgf%IFXBvCsxDII`hWQhaXbGV9I%IFIgege Dk R RW a Re D H V n R Hs aeP H D V VBY b asFP H D BW CsxDGVgeII`pH`eIrGHgeUuIBg`gf CsXDfXHI`hWb gXuhqfgsgfXBVIXPhVGbXaIGuURH9B%I R qYPWP RW uBe RW H Ve aeF V qP W H Re q V D V HF & ( 5 q #

hhUahHbGVGDregneS`hHXBjUu`TURGHIgrIaIgWTfhFp%aI D q R qY R V H avW DWB V RY V e Hv VF hXUqGHGaXDv`QCiUDISFElUuHrGehRIUB`vgWVweRgDIGYR `SIgepIFE9huhHSIIBhaHIYrGehRpeUHD V RW HB H D sv D H H B D a WuB R H D sv bYu V R D HP tiWre gWVxDGVIreRGage` XBIGPtseIGPXaIrhqIeIBVCaXbVDI`ge`GWRhRHxV9gI q D B aB D a q V a e a q Vu HuW A HBe DBe HF h R b a V D sv b HY V q Hu Re HuW DWv iW rGHIGYUDIYRgDaIGF'lhuUHIhBSfBxsIhPUHIGHr%ahqSFgptIF B W a H eFaB D qY aq H YB H DW q R HF hB De R B V VPWW HuW %tiIGFQ`TfS`WGVrneIvGVlghebVhRIlQIGFSgaxDIGYUaGHQI`XWVreG`W`XWIBS`Ig9UqIe B qWW e V uB a H D VF i VBe H q D a V Vu a H V i HuW geXH`Q a2I`hWUbGH'IGFHXqI%hkUabIgIdFhbpghebVgDaGVrdegDBhuXHIIGYDxshqIXu%kUqIe A HBe DBe H D V H DW R HF HuW D H Vu W D V s qWP SBGVCaXbVUDS`ge`GWRhRHXGV9gIGFahSFfgDGaIIchhaUqIe9UBGHhRsXwSpCiEBg`XW`p`WD R q ReP V D W aB D qP V H D Vu a H i a VuB H D sv De DW gneShYbGVDgI1XaIFrI`XWVrhebVSeXIGFhuXHIIYgDQhkgIBISfeHhaIGF9UuHrrxTVgi hhGa9hBhHUqrSBGVURHgDIYUqgIF D H H W a b F V e V i B qe z D H H b H W V HBB b H D V B DY Vu FxD%qS`WgGdyy}{|ygGtCx9hBhXHhqdFregCsxDXTVDhbIS`hWiIFB`XWVSIXvGVGRDaSineq URptip9hBHhaHI'`WGVUDgGehRGHlXBgl`pCiDI%Dge%rIF'II`W'UBhHprrfXDhkrneIUYbVgDgfP H WP e D RP B b D VW a RW HB aW De D uBY Hv aeF V R q Re CB`WGVreURIuVI`UWQURIIIeUHgDgsSFpgHIYwf%fXUVhbpGPrIFsgp9UBIIhBphPSIBXaQwfFD A hB D H aB b HuBY a a a H DW R DeB b H a H DW D Hu H Hu V V De B D VBe RW q R b a q D RP e DF q D DFY Rv VF i a VuBq VP `WGVreXtIg9`gGeIYDIGYGRDrneV9UBGHhRHGHIe9`XV'W9`S`GWIqdFXbI%u`IXBIIfghebVRIhH W a e D HYu q Ve R qYPWP V RYv e ueF R R W Re V D R H gUaHVhRGHeWIIdXsIXBgCsxDGVgeII`pBgDGaISdqgfqdFGbgheGHUaGHgheGHgXaIFUkGaghe`s UiHvDgfeIFIBVIn hXhqHaxDV hGHDsIFIBV`pe`UWa9UBeUHhqeIFhBUHpCiDsEI`XWVD aeP H D RY a a H D aWP b D H H H D H Hv aB mgGehRH9XB'IFgG`QCiUDI'SF1XarfGFQ hGHDsfXHIeghWg`WGVreXtIg9`CWnmxhqGHIFD b D V H D W RW HB H D V De D a a qP b e W B D VBe R a H q R De D HP RP DB RWP V H DWBe De HT V H i DPeF `WRuaxDIGYUaGHrIFCsDhRp`WIu9geD`pURIFgSgqhuGHr9GVDUa`9BQVhRGHSgfpCBA hhI`XWtTIhFpDggIGFhHIUBIfXB'XsIUPhHIgheIgIgWgSglghVQpUR``SWage RY V e Hv H Re H D b HY V q Hu B bkHB qekuBe DF H i H Vv e q H eF a RW HB H Vv HF V eBsu Vu D H D V RY V e Hv q V R VF H gtTI1lGgpCiDIuUR``SS1UhhabgfS'SBIgGeRIGFBS`WTfhFprebSdFGbgGehRHSIFD W bB RWP V H D DYW D VWP q R HF h Deu q VP H uBe HuW H H gvhHIgeD`pIF`9B`paxDIGYUaGHGHhaSSdewfghebVRIhqIghqIehBUHpCiDsv D H Re uWW H D HT RP a qeBe q b qY H D q HP RP B D 9UBeUhHGHgg`'SFhagWIvXaGVXsrfggdeDgeRxVxDI'IGFjGWXauhhhaXHVgDhRp`GWI`WGVrneUqGHR gm`UWQXRhVIGFpgsqhqQQrIGBSYUDHuIGFgdgWVDIIY`WGVSIXvGVRgDaICsXDVXqIgfgGWIIFBpgIB%i R b H D ae H i ae a R R H DW B bB B DY Vu Vvev RP H D V a V ineehRQtisiIFg@dFIYerf%geHiSFgaDgeUuhHXtVCsDiIFggD`haUHIIGWIUPGHR q H WP H D ae b a Deu q R H D W b q a H D W aW bYu R ky}fIIXBj`gIGFgUaGHIY`WUqqXsqrf%gUaHGVURGHeXViDIXBg9gUuHgDhaHSdew`GWSge Hu V H D W R a b Veu W a H D e a Vee D k De DY R q b H D W RY V eFevq V eBsu HF a b H R q H D aWP b D H geIYXqhqhHEIGFgrI`XWTfrfghebgfSvShhahRHgDIYUqrDhagGge1IGFIBV`s`UWGalUB`ge H D W aW sv b a e a RW sYv D B Hu H D V k V HF RWkB D VB R SFpr1gD`9dWgDiqUqGH`SIWq`XWGVaUVhbIIGFXBISBIuhRI`c`XWVrhetIgGWIdFb mB a H DW q R e ae b qP H D B b H a b H q aB De bY H R qk ae b gsIFcg%xDIGYUaGH%ghHrneIgrde'geUkhaIFgeURgXVfhkS`WGVrfYDIfqgGgeIgXbVDrfdFGWDa aIBlge`XWGVXahVhbS%gvahahHGWSIGF`IgIFxDujUhhRQtsIBSgeGReIGFB9dFGbgGehRXHIie V Ve B Hu W b RP H D FYW q H iWP Vu D H D V s R VF UaIfUSUuGHgIGFa`WGVreG`WSXBIGFdFbI%IuVIB%UkGahRSgeGRgdIS`GW`iIFrjhHXtGVa HB Hu k Re a V B De R V H D VF i H a V Hu D W aPY R H D W HF y  d y ~ H D D R R R n e BW H H H D He Vu D W Ih9wvgfdiSF'IBGV9hBGHUaGHIUPGHXuGV`0qg`GUReUa9hBgg'IXBIgeGRgGaURHD gmIXYhqpgeXbegIUDSBVgDaIhkUaHIY`XWVre`hWbhRpXHIeXGVSBGVSQhhUDrGgeedWgDIGFBV a bq V eBsu b Vu q R B D q HP qP a aY s H Re b a H D hugThRHI`S`WGVrfYDIf `GgeIFQ`WuHSvGVS`sPhaHsGW'hu`THXVhqpI`XWTfUFsSBIuhRIF H avW aB De bY H R q H D R q aBW R Hv D H Hv RY V e Hv V H H D R DP b D H RW V aY V De DYe R q b ae b a e DPeF SFGHSYSghedWhRIu`BqUuGHIaeere`WSrugeIYXqhqUHbGVDgfdFWgDddhRGHSgfpCBA hhS`WGVrneXqqhVb`IFgW aB D aW H D UaHhVShBIlhHRrSFhR`tTaVXsgfrev`19hBIShBphPIIXBerlEGWXagehuGfSghW%GHgQaxDIGYUaGHR b HY H D H W a qeBe v W D Hu H Hu V Be sv qe H RB b Re q HhaI & gjXWVrGejIXBVgheGbhuHGRURHUGHSjFxD%hGHDsIF%ghHIrneGVrg9XBdHgheGba HF h W D R q a RP e V i a a H D W bB ReT V q GHUDHhRGbXaIdIXBXsGqURIIIjge `GWRXDIYhaHuIWVhRpGHUaIFvUHtVhRHDgerfdFdFbS%I`WGVrneXqqUVGb`W Vu V HuBY B q R au HP H D b Re b VF i aB D a XbIXWGVURsoPr`WGHUaIFrfGFhuIgGguphkhRgtThWGHgiUhhhaXbGV9IBI`XWVXDVIgGeRHgfI1WgeqV Vu H m q H D De D HY Re H i H RW asFP V aB aB D aeFP D R m ak D aq b bYu a e D HYu Hv B b b RP A h VB V Hv H XGVgHwdeDfrebGVXDVhRUuhHISIBoVnmXhqH1vWSIupdghehHIUBGHhaHIpGaoDSg`gvIBISB`UsIFD qGVlSg`g `GWRaDggGBURHDUapS`WVgrBqII`WqhBUHsgIUkhaGHSYUDSGYRgDUuIIUusv DBY H Re H i aY ReT V uBY Hv aeF R b a Hu H