Teorik 4. Do ğ al seçilim teorisi

4. Do

ğal seçilim teorisi

Teorik

4. Do

ğal seçilim teorisi

Uygulama





1RWHKHUHWKDWZKHQGHIඈQඈQJRXUYHFWRUƒZHDOVRDFWXDOO\QDPHGHDFKHOHPHQWRIඈW1DPHVZRUNDOඈWWOH

GඈIIHUHQWO\ඈQYHFWRUVWRKRZWKH\GRඈQD†ƒ–ƒŜˆ”ƒ‡)RUH[PDSOHƒɛɨɨZඈOOQRWZRUN+RZHYHU ƒƃɑɨɨɑƄGRHV 5HWXUQඈQJWRWKHSRSXODWඈRQJHQHWඈFVZHIRUPXODWHGWKඈQJVDOඈWWOHGඈIIHUHQWO\WRKRZ\RXIඈUVWHQFRXQWHUHGWKඈV H[DPSOHඈQWKHPDඈQWH[WඈQRUGHUWRGHPRQVWUDWHVRPH5FRGH1RQHWKHOHVVWKHUHVXOWVDQGWKHJHQHUDO SURFHVVDUHWKHVDPH(VVHQWඈDOO\ZHGHIඈQHIඈWQHVVUHODWඈYHWRWKHPD[ඈPXPIඈWQHVV6ඈQFHERWK DQG SURGXFHWKHKඈJKHVWQXPEHURIRIIVSUඈQJWKHඈUIඈWQHVVඈVZKHUHDV KDVDORZHUUHODWඈYHIඈWQHVV :HPඈJKWDOVRZDQWWRFDOFXODWHWKHPHDQSRSXODWඈRQIඈWQHVVGHQRWHGDV 7KඈVඈVHVVHQWඈDOO\WKHVXPRI WKHUHODWඈYHIඈWQHVVRIHDFKJHQRW\SHPXOWඈSOඈHGE\WKHJHQRW\SHIUHTXHQF\:ඈWK5FDOFXODWඈQJWKඈVඈVVඈPSOH ZHVඈPSO\PXOWඈSO\DYHFWRURIJHQRW\SHIUHTXHQFඈHVZඈWKWKHUHODWඈYHIඈWQHVVDQGVXPWKHUHVXOW:HGRWKඈV EHORZ ɪ†‡ˆ‹‡–Š‡‰‡‘–›’‡ˆ”‡“—‡…‹‡•Ş‘–‡†‹ˆˆ‡”‡–™ƒ›–‘†‡ˆ‹‡Š ‰‡‘ɏˆ”‡“ʳŞ…ſɨɨʰɥŜɭɬřɨɩʰɥŜɨɬřɩɩʰɥŜɩƀ ɪ…ƒŽ…—Žƒ–‡‡ƒ’‘’—Žƒ–‹‘ˆ‹–‡•• ™ɏ„ƒ”ʳŞ•—ſ”‡Žɏˆ‹–Ƌ‰‡‘ɏˆ”‡“ƀ 6RIDUZHKDYHGHDOWZඈWKIඈWQHVVIRUJHQRW\SHV7KඈVPDNHVVHQVHEHFDXVHVHOHFWඈRQDFWVRQJHQRW\SHVDQG WKHSKHQRW\SHVWKH\FRQYH\%XWZKDWඈIZHZDQWWRGHIඈQHWKHIඈWQHVVRIDVSHFඈIඈFDOOHOH",QWKඈVFDVHWKඈQJV EHFRPHDEඈWPRUHFRPSOඈFDWHGEHFDXVHDOOHOඈFIඈWQHVVGHSHQGVRQWKHJHQRW\SHWKHDOOHOHIඈQGVඈWVHOIඈQ,QRXU SUHYඈRXVH[DPSOH KDVDKඈJKIඈWQHVVZKHQඈWඈVඈQWKHKHWHUR]\JRXV JHQRW\SHEXWQRWZKHQඈWඈV KRPR]\JRXV

7RDFFRXQWIRUWKඈVZHHVWඈPDWHPDUJඈQDOIඈWQHVVIRUDJඈYHQDOOHOH DV 6RIRUWZRDOOHOHVWKHPDUJඈQDO IඈWQHVVඈV

:KHUH DQG DUHWKHIUHTXHQFඈHVIRU DQG UHVSHFWඈYHO\,QRWKHUZRUGVPDUJඈQDOIඈWQHVVඈVD FRPSRQHQWRIWKHIඈWQHVVRIWKHJHQRW\SHVDQDOOHOHRFFXUVඈQ$1'WKHIUHTXHQF\RIWKRVHJHQRW\SHV/HW¶V FDOFXODWHWKHIඈWQHVVRIRXUDOOHOHVXVඈQJ5 ɪɪˆ‹”•–…ƒŽ…—Žƒ–‡–Š‡ƒŽŽ‡Ž‡ˆ”‡“—‡…‹‡• ɪ†‡ˆ‹‡–Š‡–‘–ƒŽ—„‡”‘ˆƒŽŽ‡Ž‡• ʳŞɩƋ•—ſƒƀ ɪ…ƒŽ…—Žƒ–‡’ ’ʳŞſſƒƃɑɨɨɑƄƋɩƀʫƒƃɑɨɩɑƄƀŵ ɪ…ƒŽ…—Žƒ–‡“ “ʳŞɨŞ’ ɪɪ‘™…ƒŽ…—Žƒ–‡–Š‡ƒ”‰‹ƒŽˆ‹–‡•• ™ɨʳŞſ’Ƌ”‡Žɏˆ‹–ƃɑɨɨɑƄƀʫſ“Ƌ”‡Žɏˆ‹–ƃɑɨɩɑƄƀ ™ɩʳŞſ’Ƌ”‡Žɏˆ‹–ƃɑɨɩɑƄƀʫſ“Ƌ”‡Žɏˆ‹–ƃɑɩɩɑƄƀ 1RWHDJDඈQWKDWZHDUHH[SOඈFඈWO\QDPඈQJHOHPHQWVRIWKHYHFWRUWRPDNHWKHPDWKHPDWඈFVKHUHFOHDUHUWR\RX +RZHYHUWKඈVFDQFDXVHVRPHDQQR\ඈQJQDPHVWRIROORZDURXQG\RXUGDWD7DNHDORRNDW™ɨDQG™ɩ\RX VKRXOGVHHWKH\KDYHJHQRW\SHQDPHV7KHFRGHEHORZඈVH[DFWO\WKHVDPHDVWKHFRGHEORFNDERYHEXWWKඈV WඈPHZඈWKQXPHUඈFDOඈQGH[HVRQFHDJDඈQ\RXVHHWKHUHDUHPXOSWඈOHZD\VWRGRWKඈQJVඈQ57KHQDPHVVWඈOO KDQJDERXWEHFDXVHZHXVHGWKHPUඈJKWIURPWKHVWDUWVRZHDOVRUHPRYHWKHPKHUHE\DVVඈJQඈQJD   



   





 

 

 





_

_

_

 

 





_

_

_

_







  ɪɪ…ƒŽ…—Žƒ–‡–Š‡ƒ”‰‹ƒŽˆ‹–‡•• ™ɨʳŞſ’Ƌ”‡Žɏˆ‹–ƃɨƄƀʫſ“Ƌ”‡Žɏˆ‹–ƃɩƄƀ ™ɩʳŞſ’Ƌ”‡Žɏˆ‹–ƃɩƄƀʫſ“Ƌ”‡Žɏˆ‹–ƃɪƄƀ ɪ•–”‹’ƒ‡• ƒ‡•ſ™ɨƀʳސƒ‡•ſ™ɩƀʳŞ ƒ‡•ſ’ƀʳސƒ‡•ſ“ƀʳŞ 1RZWKDWZHKDYHWKHEDVඈFVඈQSODFHඈQWHUPVRIFDOFXODWඈQJIඈWQHVVZHFDQJRRQWRFUHDWHDRQHORFXVPRGHO RIYඈDEඈOඈW\VHOHFWඈRQ

2QHORFXVPRGHORIYඈDEඈOඈW\VHOHFWඈRQ

:KHQZHWDONDERXWYඈDEඈOඈW\ZHVඈPSO\PHDQWKDWඈQGඈYඈGXDOVZඈWKGඈIIHUHQWJHQRW\SHVZඈOOYDU\ඈQWKHඈU SUREDEඈOඈW\RIVXUYඈYQJXQWඈOWKH\DUHDEOHWRUHSURGXFH9DUඈDWඈRQඈQYඈDEඈOඈW\ZඈOOWKHUHIRUHHIIHFWWKHDEඈOඈW\RI ඈQGඈYඈGXDOVWRUHSURGXFHDQGWKXVSDVVRQWKHඈUJHQHVWRWKHQH[WJHQHUDWඈRQ,QRWKHUZRUGVDOOHOHIUHTXHQFඈHV ZඈOOFKDQJHDVDUHVXOWRIVHOHFWඈRQ

7RPRGHOWKඈVZHZඈOOXVHDORFXV ZඈWKDOOHOHV DQG HDFKZඈWKDIUHTXHQF\ DQG )URPWKHODVW VHFWඈRQZHKDYHWKHUHODWඈYHIඈWQHVVRIWKHJHQRW\SHVZඈWK  DQG )RUVඈPSOඈFඈW\ZHZඈOODVVXPH WKDWIඈWQHVVUHPDඈQVFRQVWDQWDQGWKDWWKHIUHTXHQF\RIWKH]\JRWHVDWHDFKJHQHUDWඈRQDUHඈQOඈQHZඈWKWKH +DUG\:HඈQEHUJH[SHFWDWඈRQ/ඈNHඈQWKHERRNZHVXPPDUඈVHWKHEDVඈFVඈQWKHWDEOHEHORZ

*HQRW\SH =\JRWHIUHTXHQF\ )ඈWQHVV

,QRXUPRGHOZHZඈOOFDOFXODWH WKHIUHTXHQF\RIDOOHOH DIWHUDVඈQJOHJHQHUDWඈRQRIVHOHFWඈRQ7KඈV GHSHQGVRQWKUHHWKඈQJV WKHDOOHOHIUHTXHQF\EHIRUHVHOHFWඈRQ WKHPDUJඈQDOIඈWQHVVRIWKH DOOHOH DQGWKHGඈIIHUHQFHEHWZHHQWKඈVDQG WKHPHDQSRSXODWඈRQIඈWQHVV6RRXUPRGHOඈVEDVඈFDO\

:HZඈOOXVHRXUSUHYඈRXVUHVXOWVWRFDOFXODWHKRZ FKDQJHVDIWHUDURXQGRIVHOHFWඈRQ

’ɏ–ʳŞſ’Ƌ™ɨƀŵ™ɏ„ƒ”

,I\RXFRPSDUH’DQG’ɏ–\RXZඈOOVHHKRZWKHIUHTXHQF\ඈQ’FKDQJHGDVDUHVXOWRIVHOHFWඈRQ,QIDFWWKඈV

ඈV ,Q5ZHFDQHDVඈO\FDOFXODWHඈWDV †‡Ž–ƒɏ’ʳŞ’ɏ–Ş’ ,IHYHU\WKඈQJZRUNHGFRUUHFWO\\RXU†‡Ž–ƒɏ’VKRXOGEHɥŜɥɪɮɩɥɰɪ

6ඈPXODWඈQJVHOHFWඈRQXQGHUWKHRQHORFXVPRGHO

6RIDUZHKDYHUHFUHDWHGWKHPRGHOIRUDVඈQJOHJHQHUDWඈRQWRWU\DQGXQGHUVWDQGKRZඈWZRUNV%XWWKHEHDXW\ RI5ඈVWKDWZHFDQHDVඈO\FKDQJHWKHSDUDPHWHUVWRVHHKRZWKඈVZඈOOYDU\WKHFKDQJHඈQIUHTXHQF\RIRXU DOOHOH7KHHDVඈHVWZD\WRGRWKඈVඈVඈIZHZUඈWHDIXQFWඈRQWKDWQHDWO\VXPPDUඈVHVWKHFRGHZHKDYHDOUHDG\ H[SORUHGWKHQDOOZHQHHGWRGRWRVHHKRZWKHSDUDPHWHUVKDYHDQHIIHFWඈVVඈPSO\DOWHUWKHDUJXPHQWVZH JඈYHRXUIXQFWඈRQ 





 











_







  





















 













 





  :HZඈOOQRZZUඈWHDIXQFWඈRQWKDWWDNHVWKHඈQඈWඈDOIUHTXHQF\RISDQGDYHFWRUFRQVඈVWඈQJRIWKHUHODWඈYHIඈWQHVVRI HDFKJHQRW\SH7KඈVIXQFWඈRQZඈOOWKHQFDOFXODWHWKHDOOHOHIUHTXHQFඈHVWKHPHDQSRSXODWඈRQIඈWQHVVDQGWKH PDUJඈQDOIඈWQHVVRIWKHDOOHOHV ɪƒ•‹’Ž‡ˆ—…–‹‘–‘†‡‘•–”ƒ–‡–Š‡‘‡Ž‘…—••‡Ž‡…–‹‘‘†‡Ž •‡Ž‡…–‹‘ɏ‘†‡Žʳވ—…–‹‘ſ’ř”‡Žɏˆ‹–ƀƇ ɪ†‡ˆ‹‡“ “ʳŞɨŞ’ ɪ…ƒŽ…—Žƒ–‡‰‡‘–›’‡ˆ”‡“—‡…‹‡•ſ—†‡”ƀ ‰ˆʳŞ…ſ’ɋɩřɩƋſ’Ƌ“ƀř“ɋɩƀ ɪ…ƒŽ…—Žƒ–‡‡ƒ’‘’ˆ‹–‡•• ™ɏ„ƒ”ʳŞ•—ſ”‡Žɏˆ‹–Ƌ‰ˆƀ ɪ…ƒŽ…—Žƒ–‡ƒ”‰‹ƒŽƒŽŽ‡Ž‡ˆ”‡“—‡…‹‡• ™ɨʳŞſ’Ƌ”‡Žɏˆ‹–ƃɨƄƀʫſ“Ƌ”‡Žɏˆ‹–ƃɩƄƀ ™ɩʳŞſ’Ƌ”‡Žɏˆ‹–ƃɩƄƀʫſ“Ƌ”‡Žɏˆ‹–ƃɪƄƀ ɪ…ƒŽ…—Žƒ–‡ˆ”‡“‘ˆ’‹–Š‡‡š–‰‡‡”ƒ–‹‘ ’ɏ–ʳŞſ’Ƌ™ɨƀŵ™ɏ„ƒ” ɪ”‡–—”–Š‡”‡•—Ž–• ”‡–—”ſ’ɏ–ƀ ƈ :ඈWKWKඈVVඈPSOHIXQFWඈRQZHFDQSOD\DURXQGZඈWKWKHඈQඈWඈDOIUHTXHQF\RIWKH DOOHOHDQGWKHUHODWඈYHIඈWQHVV RIWKHJHQRW\SHV7U\DIHZGඈIIHUHQWYDOXHVIRU\RXUVHOIWRVHH ɪ‡‡’‹‰–Š‡‹‹–‹ƒŽˆ”‡“—‡…›…‘•–ƒ– •‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰɥŜɬř”‡Žɏˆ‹–ʰ…ſɨřɨřɥŜɮɬƀƀ •‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰɥŜɬř”‡Žɏˆ‹–ʰ…ſɨřɨřɥŜɬƀƀ •‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰɥŜɬř”‡Žɏˆ‹–ʰ…ſɨřɨřɥŜɪƀƀ 7RJHWDJRRGඈGHDRIKRZWKHPRGHOZRUNVZKDWZHUHDOO\ZDQWWRGRඈVH[DPඈQHඈWVFKDQJHඈQIUHTXHQF\RYHU WඈPH:HFDQGRWKඈVQHDWO\XVඈQJWKHYHFWRUඈVDWඈRQVNඈOOVZHOHDUQHGඈQWKHODVWVHVVඈRQ KWWSVHYROXWඈRQDU\JHQHWඈFVJඈWKXEඈR&KDSWHUKWPO:HZඈOOඈQඈWඈDOඈVHWZRYDOXHVWKHඈQWඈDOIUHTXHQF\’DQG WKHQXPEHURIJHQHUDWඈRQVZHZDQWWRVඈPXODWHVHOHFWඈRQIRUɏ‰‡ ɪˆ‹”•–‹‹–‹ƒŽ‹•‡–Š‡˜ƒŽ—‡• ’ʳŞ’ɏ‹‹–ʳŞɥŜɬ ɏ‰‡ʳŞɨɥɥ ɪ—•‡•ƒ’’Ž›–‘”‡’‡ƒ–‡†Ž›”—–Š‡•‡Ž‡…–‹‘‘†‡Ž ’ɏ˜‡…ʳŞ•ƒ’’Ž›ſɨśɏ‰‡řˆ—…–‹‘ſ›ƀƇ ’ɏ–ʳŞ•‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰ’ř”‡Žɏˆ‹–ʰ…ſɨřɨřɥŜɮɬƀƀ ’ʳʳŞ’ɏ– ƈƀ ɪ…‘„‹‡–Š‡‹‹–‹ƒŽ’ƒ†–Š‡˜ƒŽ—‡•‘ˆ’ƒ…”‘••‡ƒ…Š‰‡‡”ƒ–‹‘ ’ɏ˜‡…ʳŞ…ſ’ɏ‹‹–ř’ɏ˜‡…ƀ

6RDOOZHGඈGKHUHZDVZUDSRXU•‡Ž‡…–‹‘ɏ‘†‡ŽIXQFWඈRQඈQDQ•ƒ’’Ž›FRPPDQG:HDOVRWRRNDPRPHQW

WRFRPEඈQHRXUඈQඈWඈDOYDOXHRIS’ɏ‹‹–WRWKHWKH’ɏ˜‡…RXWSXW1RWHDJDඈQWKDWZHXVHGWKHʳʳŞQRWDWඈRQ

WKඈVVඈPSO\WHOOV5WRUHSHDWHGO\XSGDWHWKHYDOXHRI’ZඈWKඈQRXUIXQFWඈRQ:K\GRZHQHHGWRGRWKඈV":HOO

\RXFDQUXQWKHIROORZඈQJ•ƒ’’Ž›ZUDSSHGYHUVඈRQRI•‡Ž‡…–‹‘ɏ‘†‡ŽWRVHH

  ɪˆ‹”•–‹‹–‹ƒŽ‹•‡–Š‡˜ƒŽ—‡• ’ʳŞɥŜɬ ɏ‰‡ʳŞɨɥɥ ɪ—•‡•ƒ’’Ž›–‘”‡’‡ƒ–‡†Ž›”—–Š‡•‡Ž‡…–‹‘‘†‡Ž •ƒ’’Ž›ſɨśɏ‰‡řˆ—…–‹‘ſ›ƀƇ •‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰ’ř”‡Žɏˆ‹–ʰ…ſɨřɨřɥŜɮɬƀƀ ƈƀ 7KHUHඈVQRDVVඈJQPHQWඈQWKHDERYHEORFNRIFRGHRQSXUSRVHVR\RXGRQ¶WZUඈWHRYHU\RXU’ɏ˜‡…EXWWKH RXWSXWPDNHVඈWFOHDUDOOZHGඈGKHUHZDVUHUXQWKHVHOHFWඈRQPRGHOWඈPHV:HQHHGWRXSGDWH’RUHOVH ZHDUHQRWSURSHUO\VඈPXODWඈQJVHOHFWඈRQ

9ඈVXDOඈVඈQJVHOHFWඈRQZඈWKGඈIIHUHQWSDUDPHWHUV

:HDOUHDG\NQRZWKDW5¶VYඈVXDOඈVDWඈRQFDSDEඈOඈWඈHVDUHH[WUHPHO\ඈPSRUWDQWIRUGHYHORSඈQJDQXQGHUVWDQGඈQJRI GDWDDQGFRQFHSWV6ROHW¶VFRPEඈQHRXUSURJUDPPඈQJDQGYඈVXDOඈVDWඈRQVNඈOOVWRGHPRQVWUDWHKRZYDU\ඈQJWKH SDUDPHWHUVUHDOO\HIIHFWWKHRXWFRPHRIRXUPRGHO )ඈUVWWKඈQJVIඈUVWZHZඈOOWDNHRXUYHFWRUඈVHGVඈPXODWඈRQIURPWKHSUHYඈRXVVHFWඈRQDQGPDNHඈWඈQWRඈW¶VRZQ IXQFWඈRQ•‡Ž‡…–‹‘ɏ•‹ ɪɪƒ‡ƒ•‹—Žƒ–‘”ˆ—…–‹‘ •‡Ž‡…–‹‘ɏ•‹ʳވ—…–‹‘ſ’ř”‡Žɏˆ‹–řɏ‰‡ƀƇ ɪ‹‹–‹ƒŽ‹•‡˜ƒ”‹ƒ„Ž‡• ’ɏ‹‹–ʳŞ’ ›ɏ”‡Žɏˆ‹–ʳŞ”‡Žɏˆ‹– ɪ—•‡•ƒ’’Ž›–‘”‡’‡ƒ–‡†Ž›”—–Š‡•‡Ž‡…–‹‘‘†‡Ž ’ɏ˜‡…ʳŞ•ƒ’’Ž›ſɨśɏ‰‡řˆ—…–‹‘ſ›ƀƇ ’ɏ–ʳŞ•‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰ’ř”‡Žɏˆ‹–ʰ›ɏ”‡Žɏˆ‹–ƀ ’ʳʳŞ’ɏ– ƈƀ ɪ…‘„‹‡–Š‡‹‹–‹ƒŽ’ƒ†–Š‡˜ƒŽ—‡•‘ˆ’ƒ…”‘••‡ƒ…Š‰‡‡”ƒ–‹‘ ’ɏ˜‡…ʳŞ…ſ’ɏ‹‹–ř’ɏ˜‡…ƀ ɪ”‡–—”–Š‡‘—–’—– ”‡–—”ſ’ɏ˜‡…ƀ ƈ 7KඈVඈVWKHVDPHFRGHMXVWZUDSSHGඈQDIXQFWඈRQ7KHRQO\WKඈQJ\RXQHHGWRQRWHKHUHඈVWKDWඈQRUGHUWR GඈVWඈQJXඈVKEHWZHHQWKH”‡Žɏˆ‹–DUJXPHQWVPDGHWRWKH•‡Ž‡…–‹‘ɏ•‹DQG•‡Ž‡…–‹‘ɏ‘†‡ŽIXQFWඈRQVZH

UHQDPHඈWDV›ɏ”‡Žɏˆ‹–ZඈWKඈQWKHIXQFWඈRQ7KඈVඈVDXVHIXOH[DPSOHRIFRGඈQJEHFDXVHKHUHZHKDYHEXඈOWD PRUHFRPSOH[IXQFWඈRQXVඈQJDQRWKHUVඈPSOHRQHZHZURWHHDUO\WKඈVඈVWKHSUඈQFඈSOHRIPRGXODUSURJUDPPඈQJ KWWSVHQZඈNඈSHGඈDRUJZඈNඈ0RGXODUBSURJUDPPඈQJ,WPDNHVඈWPXFKHDVඈHUWRGඈDJQRVHඈVVXHVDV\RXFDQIඈ[ WKHඈQGඈYඈGXDOIXQFWඈRQVVHSDUDWHO\ $Q\ZD\QRZZHFDQHDVඈO\VඈPXODWHVHOHFWඈRQRYHUPXOWඈSOHJHQHUDWඈRQV)RUH[DPSOH ɪ‡•––Š‡•‡Ž‡…–‹‘•‹—Žƒ–‘” •‡Ž‡…–‹‘ɏ•‹ſ’ʰɥŜɬř”‡Žɏˆ‹–ʰ…ſɨřɨřɥŜɮɬƀřɏ‰‡ʰɨɥɥɥƀ

  6RQRZZHZඈOOSHUIRUPVඈPXODWඈRQVIRUJHQHUDWඈRQVNHHSඈQJRXUඈQඈWඈDOIUHTXHQF\RI’DW+RZHYHU ZHZඈOODOWHUWKHUHODWඈYHIඈWQHVVRIWKH JHQRW\SHIURPWR:HFDQDOVRGRWKඈVYHU\HDVඈO\ZඈWK YHFWRUඈVDWඈRQ ɪ•‡––Š‡˜‡…–‘”ˆ‘”–Š‡”‡Žƒ–‹˜‡ˆ‹–‡••‘ˆɯɯ ɩɩɏ”ˆʳŞ•‡“ſˆ”‘ʰɥŜɩř–‘ʰɥŜɯř„›ʰɥŜɩƀ ɪ”—•‹—Žƒ–‹‘•ˆ‘”‡ƒ…Š •‡Žɏ•‹•ʳŞ•ƒ’’Ž›ſɩɩɏ”ˆřˆ—…–‹‘ſœƀƇ •‡Ž‡…–‹‘ɏ•‹ſ’ʰɥŜɬř”‡Žɏˆ‹–ʰ…ſɨřɨřœƀřɏ‰‡ʰɩɥɥƀ ƈƀ ɪƒ••‹‰ƒ‡•–‘–Š‡ƒ–”‹š …‘Žƒ‡•ſ•‡Žɏ•‹•ƀʳŞ’ƒ•–‡ɥſɑ™ɩɩʰɑřɩɩɏ”ˆƀ 1RWHWKDWWKHODVWWKඈQJZHGඈGKHUHZDVXVH’ƒ•–‡ɥWRFUHDWHVRPHFROXPQQDPHVIRURXUPDWUඈ[RIVHOHFWඈRQ

VඈPXODWඈRQV:HXVHG’ƒ•–‡ɥWRFRPEඈQH™ɩɩʰZඈWKWKHYDOXHRIUHODWඈYHIඈWQHVVIRUWKH JHQRW\SH7KඈV

ZඈOOPDNHVHQVHඈQDPRPHQWZKHQඈWඈVXVHGඈQRXUSORWWඈQJ1H[WXSZHVKRXOGJHWHYHU\WKඈQJWRJHWKHUඈQD –‹„„Ž‡DQGXVH‰ƒ–Š‡”WRSUHSDUHIRUSORWWඈQJ ɪ…”‡ƒ–‡ƒ‰‡‡”ƒ–‹‘•˜‡…–‘” ‰ʳŞ•‡“ſɥřɩɥɥřɨƀ ɪ…‘„‹‡–‘‰‡–Š‡”–‘ƒ‡ƒ–‹„„Ž‡ •‡Žɏ•‹•ʳރ•Ŝ–‹„„Ž‡ſ…„‹†ſ‰ř•‡Žɏ•‹•ƀƀ ɤɤƒ”‹‰śļƒ•Ŝ–‹„„Ž‡ſƀļ‹•†‡’”‡…ƒ–‡†ř—•‡ļƒ•ɏ–‹„„Ž‡ſƀļſ„—–‹†–Š‡‡™•‡ƒ–‹…•ƀŜ ɤɤŠ‹•™ƒ”‹‰‹•†‹•’Žƒ›‡†‘…‡’‡”•‡••‹‘Ŝ ɪ—•‡‰ƒ–Š‡”–‘”‡ƒ””ƒ‰‡ˆ‘”’Ž‘––‹‰ •‡Žɏ•‹•ɏ‰ʳމƒ–Š‡”ſ•‡Žɏ•‹•ř‡›ʰɑ”‡Žɏˆ‹–ɑř˜ƒŽ—‡ʰɑ’ɑřމƀ

-XVWWRPDNHFOHDUZKDWZHGඈGKHUHZHXVHG‰ƒ–Š‡”WRUHDUUDQJHRXU–‹„„Ž‡VRWKDWHDFKYDOXHRI‰KDVD

URZIRUWKHGඈIIHUHQWYDOXHVRI”‡Žɏˆ‹–7KඈVPDNHVඈWYHU\VWUDඈJKWIRUZDUGWRSORWWKHGඈIIHUHQWDOOHOHIUHTXHQF\ FKDQJHVRYHUWඈPHXVඈQJ‰‰’Ž‘–ɩ/ඈNHVR ɪ‹‹–‹ƒŽ‹•‡’Ž‘– ƒʳމ‰’Ž‘–ſ•‡Žɏ•‹•ɏ‰řƒ‡•ſ‰ř’ř…‘Ž‘—”ʰ”‡Žɏˆ‹–ƀƀʫ‰‡‘ɏŽ‹‡ſƀ ƒʳރʫšŽƒ„ſɑ‘Ŝ‘ˆ‰‡‡”ƒ–‹‘•ɑƀʫ›Žƒ„ſɑ’ɑƀʫ›Ž‹ſɥřɨƀ ƒʫ–Š‡‡ɏŽ‹‰Š–ſƀʫ–Š‡‡ſŽ‡‰‡†Ŝ’‘•‹–‹‘ʰɑ„‘––‘ɑřŽ‡‰‡†Ŝ–‹–Ž‡ʰ‡Ž‡‡–ɏ„Žƒſƀƀ









  6R\RXFDQVHHIURPWKඈVSORWWKDWDVWKHGඈIIHUHQFHEHWZHHQWKHPDUJඈQDOIඈWQHVVRI DQGWKHPHDQ SRSXODWඈRQIඈWQHVV GHFUHDVHVWKHSURSRUWඈRQDOඈQFUHDVHඈQDOOHOHIUHTXHQF\SHUJHQHUDWඈRQVORZVGRZQ0RUH SODඈQO\ZHFDQVHHWKDWZKHQ ඈVWKHඈQFUHDVHඈQSSHUJHQHUDWඈRQඈVVORZHUWKDQZKHQ ඈV

*HWWඈQJPRUHIURPRXUVHOHFWඈRQPRGHOIXQFWඈRQZඈWKOඈVWV

/HW¶VWDNHDQRWKHUORRNDWRXU•‡Ž‡…–‹‘ɏ‘†‡ŽIXQFWඈRQ ɪ‡‡’‹‰–Š‡‹‹–‹ƒŽˆ”‡“—‡…›…‘•–ƒ– •‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰɥŜɬř”‡Žɏˆ‹–ʰ…ſɥŜɯřɨřɥŜɮƀƀ <RXZඈOOUHFDOOWKDWZKHQZHGHIඈQHGWKHFRGHIRUWKඈVIXQFWඈRQZHDFWXDOO\FDOFXODWHGTXඈWHDORWRIVWXIIඈQVඈGHඈW  WKHIUHTXHQF\RIWKH DOOHOHWKHJHQRW\SHIUHTXHQFඈHVPHDQSRSXODWඈRQIඈWQHVVDQGPDUJඈQDOIUHTXHQFඈHV %XWWKHRQO\WKඈQJZHXVHG”‡–—”WRZUඈWHRXWZDVWKHIUHTXHQF\RI ඈQWKHQH[WJHQHUDWඈRQ

:KDWඈIZHZDQWWRH[WHQGRXUIXQFWඈRQWRJඈYHXVHYHU\WKඈQJZHFDOFXODWHG"7KඈVZඈOOEHYHU\XVHIXOIRUWKH XSFRPඈQJVHFWඈRQVZKHUHZHZඈOOQHHGDOOWKHVHSDUDPHWHUV+RZHYHUZHFDQ¶WMXVWZUඈWHWKHPDOORXWDVD YHFWRUVRWRDFKඈHYHWKඈVZHQHHGWROHDUQDERXWDQHZ5GDWDVWUXFWXUHDOඈVW /ඈVWVDUHDFWXDOO\IDඈUO\VWUDඈJKWIRUZDUG<RXFDQWKඈQNRIWKHPDVYHFWRUVZKඈFKDUHDEOHWRVWRUHRWKHUYHFWRUV RUREMHFWV7KH\DUHඈPSRUWDQWEHFDXVHWKH\FDQVWRUHGDWDRIGඈIIHUHQWW\SHV6RIRUH[DPSOHZHZඈOOFUHDWHD ඈVWEHORZWKDWVWRUHVDFKDUDFWHUYHFWRUDQXPHUඈFDOYHFWRUDQGDORJඈFDOYHFWRU ɪ…”‡ƒ–‡˜‡…–‘”• ƒʳŞɨśɨɥ „ʳŞ…ſɑ‹’Ž‡›ɑřɑƒ„‡”–ɑřɑ•Šɑřɑƒ‡ɑƀ …ʳŞ…ſřř ř ř ƀ ɪ…”‡ƒ–‡Ž‹•– ›Ž‹•–ʳŞŽ‹•–ſƒʰƒř„ʰ„ř…ʰ…ƀ



 ? ???





  2QHWKඈQJWRQRWHIURPWKHDERYHFRGHඈVWKDWWKHYHFWRUVZHVWRUHGDVƒ„DQG…DUHDOVRDOORIGඈIIHUHQW OHQJWKV$Q\ZD\QRZZHFDQORRNDWRXUOඈVW)ඈUVWRIDOOVඈQFHZHH[SOඈFඈWO\QDPHGHDFKRIRXUYHFWRUVඈH ƒʰƒZKHQZHXVHGWKHŽ‹•–IXQFWඈRQZHFDQDFFHVVREMHFWVඈQWKHOඈVWE\QDPH ɪƒ……‡••Ž‹•–‘„Œ‡…–• ›Ž‹•–ɛƒ ›Ž‹•–ɛ„ ›Ž‹•–ɛ… %XWZHFDQDOVRXVHQXPEHUHGඈQGඈFHVWRGRWKHVDPHWKඈQJ ɪƒ……‡••Ž‹•–‘„Œ‡…–• ›Ž‹•–ƃɨƄ ›Ž‹•–ƃɩƄ ›Ž‹•–ƃɪƄ 6WUඈFWO\EHFDXVHඈW¶VDOඈVWZHVKRXOGUHDOO\XVHGRXEOHVTXDUHEUDFNHWV&RPSDUHWKHIROORZඈQJFRGHZඈWKWKH DERYH ɪƒ……‡••Ž‹•–‘„Œ‡…–• ›Ž‹•–ƃƃɨƄƄ ›Ž‹•–ƃƃɩƄƄ ›Ž‹•–ƃƃɪƄƄ 1RZZKDWඈIZHZDQWHGWRJHWWKHIඈUVWHOHPHQWRIWKH„ඈQRXUOඈVW":HFRXOGGRWKඈVVHYHUDOZD\V ɪ„‘–Š‘ˆ–Š‡•‡ƒ”‡‡“—‹˜ƒŽ‡– ›Ž‹•–ƃƃɩƄƄƃɨƄ ›Ž‹•–ɛ„ƃɨƄ 7KHSRඈQWKHUHඈVWKDWOඈVWVXVHIXOIRUVWRUඈQJඈQIRUPDWඈRQ6ROHW¶VඈQWHJUDWHRQHඈQWRRXU•‡Ž‡…–‹‘ɏ‘†‡Ž IXQFWඈRQVRZHFDQJHWVRPHRIWKRVHFDOFXODWඈRQVIURPRXWRIඈW

  ɪƒ•‹’Ž‡ˆ—…–‹‘–‘†‡‘•–”ƒ–‡–Š‡‘‡Ž‘…—••‡Ž‡…–‹‘‘†‡Ž •‡Ž‡…–‹‘ɏ‘†‡Žʳވ—…–‹‘ſ’ř”‡Žɏˆ‹–ƀƇ ɪ†‡ˆ‹‡“ “ʳŞɨŞ’ ɪ…ƒŽ…—Žƒ–‡‰‡‘–›’‡ˆ”‡“—‡…‹‡•ſ—†‡”ƀ ‰ˆʳŞ…ſ’ɋɩřɩƋſ’Ƌ“ƀř“ɋɩƀ ɪ…ƒŽ…—Žƒ–‡‡ƒ’‘’ˆ‹–‡•• ™ɏ„ƒ”ʳŞ•—ſ”‡Žɏˆ‹–Ƌ‰ˆƀ ɪ…ƒŽ…—Žƒ–‡ƒ”‰‹ƒŽƒŽŽ‡Ž‡ˆ”‡“—‡…‹‡• ™ɨʳŞſ’Ƌ”‡Žɏˆ‹–ƃɨƄƀʫſ“Ƌ”‡Žɏˆ‹–ƃɩƄƀ ™ɩʳŞſ’Ƌ”‡Žɏˆ‹–ƃɩƄƀʫſ“Ƌ”‡Žɏˆ‹–ƃɪƄƀ ɪ…ƒŽ…—Žƒ–‡ˆ”‡“‘ˆ’‹–Š‡‡š–‰‡‡”ƒ–‹‘ ’ɏ–ʳŞſ’Ƌ™ɨƀŵ™ɏ„ƒ” ɪƒ‡Ž‹•–ˆ‘”‘—–’—– ‘—–’—–ʳŞŽ‹•–ſ’ʰ’ř“ʰ“ř‰‡‘ɏˆ”‡“ʰ‰ˆř™ɏ„ƒ”ʰ™ɏ„ƒ”ř ™ɨʰ™ɨř™ɩʰ™ɩř’ɏ–ʰ’ɏ–ƀ ɪ”‡–—”–Š‡”‡•—Ž–• ”‡–—”ſ‘—–’—–ƀ ƈ $OOZHGඈGKHUHZDVFRPEඈQHVRPHRIWKHඈQQHUZRUNඈQJVRIRXUIXQFWඈRQඈQWRYHFWRUVඈHWKHƒ”‰‹ƒŽɏˆ‹–

REMHFWDQGSXWHYHU\WKඈQJWRJHWKHUඈQDOඈVWZHFDOOHG‘—–’—–6ROHW¶VWU\RXU•‡Ž‡…–‹‘ɏ‘†‡ŽIXQFWඈRQRQFH

PRUH ɪ‡‡’‹‰–Š‡‹‹–‹ƒŽˆ”‡“—‡…›…‘•–ƒ– •‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰɥŜɬř”‡Žɏˆ‹–ʰ…ſɥŜɯřɨřɥŜɮƀƀ :KHQZHUXQWKHPRGHOWKඈVWඈPHZHJHWDOඈVWZඈWKORWVRIGඈIIHUHQWRXWSXWV$OORIZKඈFKZඈOOEHYHU\XVHIXOඈQ WKHFRPඈQJVHFWඈRQV«

&DQDUDUHPXWDQWHVWDEOඈVKඈQDSRSXODWඈRQ"

7RXQGHUVWDQGDVHOHFWඈRQPRGHOOඈNHWKHRQHZHKDYHMXVWGHYHORSHGඈWFDQEHXVHIXOWRVHHZKHWKHUDUDUH PXWDQWඈVDEOHWRHVWDEOඈVKඈQDSRSXODWඈRQZKHUHWKHDOWHUQDWඈYHDOOHOHඈVQHDUO\Iඈ[HG7KඈVඈVWKHEDVඈVRI ඈQYDVඈRQIඈWQHVVDQDO\VඈV :HFDQGRWKඈVXVඈQJDVඈPSOHFDVHZKHUHKHWHUR]\JRWHVKDYHDJUHDWHUDGYDQWDJHWKDQKRPR]\JRWHV8VඈQJ RXUQHZO\PRGඈIඈHG•‡Ž‡…–‹‘ɏ‘†‡ŽIXQFWඈRQZHFDQWHVWWKඈVE\VHWWඈQJRXUUHODWඈYHIඈWQHVVWRVKRZDKඈJKHU UHODWඈYHIඈWQHVVඈQKHWHUR]\JRWHVDQGVHWWඈQJ’WRDKඈJKIUHTXHQF\FORVHWR ɪ‡‡’‹‰–Š‡‹‹–‹ƒŽˆ”‡“—‡…›…‘•–ƒ– •‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰɥŜɰɰř”‡Žɏˆ‹–ʰ…ſɥŜɮřɨřɥŜɯƀƀ :HVHHKHUHWKDW™ɏ„ƒ”ඈVDURXQGZKඈFKZHZRXOGH[SHFWJඈYHQWKHIUHTXHQF\RI ඈH’DQGWKH UHODWඈYHIඈWQHVV,QYDVඈRQIඈWQHVVRI ඈVHTXඈYDOHQWWRWKHPDUJඈQDOIඈWQHVVIRUWKHDOOHOHVRKHUHFORVHWR WKHUHODWඈYHIඈWQHVVIRUWKH KHWHUR]\JRWH :KHQඈQYDVඈRQIඈWQHVVඈVJUHDWHUWKDQUHVඈGHQWPHDQSRSXODWඈRQIඈWQHVVWKHPRGHOඈVQRWDWDVWDEOHHTXඈOඈEUඈXP DVDQDOOHOHFDQHDVඈO\ඈQYDGHDQGඈQFUHDVHඈQIUHTXHQF\:KDWZRXOGKDSSHQඈIWKHIUHTXHQF\RI ZDV DOPRVWIඈ[HG"



















ɪ‡‡’‹‰–Š‡‹‹–‹ƒŽˆ”‡“—‡…›…‘•–ƒ–

•‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰɥŜɥɨř”‡Žɏˆ‹–ʰ…ſɥŜɮřɨřɥŜɯƀƀ

,QWKඈVFDVH™ɏ„ƒ”WKHUHVඈGHQWIඈWQHVVඈVKඈJKHUWKDQZKHQWKH DOOHOHඈVIඈ[HGKRZHYHUWKHPDUJඈQDO

IඈWQHVVRIWKH DOOHOHWKHඈQYDVඈRQIඈWQHVVඈVKඈJKHUWKDQWKඈVVRඈQWKඈVVFHQDUඈRQ FRXOGHDVඈO\ඈQYDGH DQGඈQFUHDVHඈQIUHTXHQF\WRR ,QRUGHUIRUWKHHTXඈOඈEUඈXPWREHVWDEOHZඈWKKHWHUR]\JRWHDGYDQWDJHWKHPDUJඈQDOIඈWQHVVRIWKHWZRDOOHOHV VKRXOGHTXDORQHDQRWKHU:HZඈOOUHWXUQWRWKඈVඈQDVKRUWZKඈOH

'ඈUHFWඈRQDOVHOHFWඈRQ

(DUOඈHUZHVඈPXODWHGVHOHFWඈRQඈQRUGHUWRXQGHUVWDQGRXUPRGHO7KඈVZDVDQH[DPSOHRIGඈUHFWඈRQDO VHOHFWඈRQ1RZZHDUHJRඈQJWRH[SORUHWKDWඈQPRUHGHWDඈOඈQSDUWඈFXODUZHZDQWWRVHHKRZJHQRW\SඈFIඈWQHVV FDQDOWHUWKHRXWFRPHRIVHOHFWඈRQ:HFDQYඈVXDOඈVHWKඈVXVඈQJDQDGDSWඈYHODQGVFDSH+HUHZHZඈOOXVHD VඈPSOඈIඈHG'ODQGVFDSHඈHDSORWRIPHDQSRSXODWඈRQIඈWQHVV DJDඈQVWWKHDOOHOHIUHTXHQF\  :ඈWKRXUQHZO\XSGDWHG•‡Ž‡…–‹‘ɏ‘†‡ŽZHFDQGRWKඈVDJDඈQEXWZHQHHGWRIඈUVWXSGDWHWKHVඈPXODWඈRQ IXQFWඈRQWRRXWSXWWKHGDWDඈQDPRUHVWDQGDUGZD\&RS\DQGSDVWHWKHFRGHEHORZWRXSGDWH\RXU •‡Ž‡…–‹‘ɏ•‹IXQFWඈRQ •‡Ž‡…–‹‘ɏ•‹ʳވ—…–‹‘ſ’ř”‡Žɏˆ‹–řɏ‰‡ƀƇ ɪ‹‹–‹ƒŽ‹•‡˜ƒ”‹ƒ„Ž‡• ’ɏ‹‹–ʳŞ’ ›ɏ”‡Žɏˆ‹–ʳŞ”‡Žɏˆ‹– ɪ—•‡•ƒ’’Ž›–‘”‡’‡ƒ–‡†Ž›”—–Š‡•‡Ž‡…–‹‘‘†‡Ž •‹ʳŞ•ƒ’’Ž›ſɨśɏ‰‡řˆ—…–‹‘ſ›ƀƇ ‘—–ʳŞ•‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰ’ř”‡Žɏˆ‹–ʰ›ɏ”‡Žɏˆ‹–ƀ ’ʳʳŞ‘—–ɛ’ɏ– ɪ”‡–—”Ž‹•– ”‡–—”ſ‘—–ƀ ƈř•‹’Ž‹ˆ›ʰ ƀ ɪ—•‡ƒ’†ƒ–ƒŜˆ”ƒ‡–‘‡š–”ƒ…–†ƒ–ƒ™‡™ƒ– •‹ɏ†ƒ–ƒʳŞ•‹ʩʴʩ ƒ’ɏ†ˆ”ſƒ‰”‹––”śś‡š–”ƒ…–ř…ſɐ’ɐřɐ“ɐřɐ™ɏ„ƒ”ɐř ɐ™ɨɐřɐ™ɩɐřɐ’ɏ–ɐƀƀ ɪ”‡–—”–Š‡‘—–’—– ”‡–—”ſ•‹ɏ†ƒ–ƒƀ ƈ -XVWWRJඈYHVRPHඈQVඈJKWDERXWZKDWඈVGඈIIHUHQWKHUH2XU•‡Ž‡…–‹‘ɏ‘†‡ŽIXQFWඈRQQRZRXWSXWVDŽ‹•–VR •ƒ’’Ž›QRORQJHUSURGXFHVDYHFWRURI’ɏ–EXWUDWKHUDOඈVWRIOඈVWV7KඈVඈVTXඈWHDFRPSOඈFDWHGVWUXFWXUHEXW XVඈQJWKHƒ’ɏ†ˆ”IXQFWඈRQIURPWKH’—””SDFNDJHSDUWRIWKHWඈG\YHUVHZHFDQHDVඈO\H[WUDFWYHFWRUVRIWKH YDUඈDEOHVZHDUHඈQWHUHVWHGඈQ,WඈVEH\RQGWKHVFRSHRIWKඈVWXWRUඈDOWRH[SORUHWKඈVඈQWRRPXFKGHWDඈOEXWZHZඈOO UHWXUQWRඈWඈQDIXWXUHVHVVඈRQZඈWKVRPHPRUHDGYDQFHG5WDVNV

:KDWHYHUWKHFDVHඈIZHUHUXQRXU•‡Ž‡…–‹‘ɏ•‹IXQFWඈRQZHJHWDQඈFH–‹„„Ž‡RIWKHRXWSXW/ඈNHVR

ɪ‡‡’‹‰–Š‡‹‹–‹ƒŽˆ”‡“—‡…›…‘•–ƒ– •‡Ž‡…–‹‘ɏ•‹ſ’ʰɥŜɥɨř”‡Žɏˆ‹–ʰ…ſɥŜɮřɨřɥŜɯƀřɨɥɥƀ













3

? ???

_,

  7RVඈPSOඈI\RXUDQDO\VHVZHZඈOOXVHWKUHHGඈIIHUHQWVFHQDUඈRV,QHDFKRIWKHPZHZඈOOVWDUWZඈWKD RI DQGZHZඈOOVඈPXODWHJHQHUDWඈRQV,QDOOFDVHV ZඈOOKDYHWKHKඈJKHVWUHODWඈYHIඈWQHVVRIDQG WKHORZHVWRI7KHRQO\WKඈQJZHZඈOOYDU\ඈVWKHUHODWඈYHIඈWQHVVRIWKHKHWHUR]\JRWH 7KHUHIRUHZHDUH VඈPXODWඈQJWKUHHW\SHVRIJHQRW\SඈFIඈWQHVV GRPඈQDQFH  DGGඈWඈYHඈQKHUඈWDQFH  UHFHVVඈYH  ɪ•‡–‰‡‡”ƒ–‹‘• ɏ‰‡ʳŞɬɥ ɪ”—•‹—Žƒ–‹‘• †‘ʳŞ•‡Ž‡…–‹‘ɏ•‹ſ’ʰɥŜɥɨř”‡Žɏˆ‹–ʰ…ſɨřɨřɥŜɩƀřɏ‰‡ƀ ƒ††ʳŞ•‡Ž‡…–‹‘ɏ•‹ſ’ʰɥŜɥɨř”‡Žɏˆ‹–ʰ…ſɨřɥŜɭřɥŜɩƀřɏ‰‡ƀ ”‡…ʳŞ•‡Ž‡…–‹‘ɏ•‹ſ’ʰɥŜɥɨř”‡Žɏˆ‹–ʰ…ſɨřɥŜɩřɥŜɩƀřɏ‰‡ƀ :H¶OOWDNHDEUඈHIEUHDNIURPWKHWඈG\YHUVHDSSURDFKQRZDQGSORWWKඈVඈQEDVH57KඈVඈVMXVWEHFDXVHZHZDQW \RXWRIRFXVRQZKDWZHDUHPRGHOOඈQJUDWKHUWKDQUHVKDSඈQJWKHGDWDWRRPXFK$OVRඈW¶VJRRGWROHDUQQHZ DSSURDFKHVIRUSORWWඈQJ ɪ‹–‹ƒŽ‹•‡’Ž‘– ’Ž‘–ſřšŽ‹ʰ…ſɥřɨƀř›Ž‹ʰ…ſɥřɨƀř šŽƒ„ʰɑ ”‡“—‡…›Ş’ɑř›Žƒ„ʰɑ‡ƒ’‘’ˆ‹–‡••ɑřŽƒ•ʰɨƀ ɪƒ††…—”˜‡•ˆ‘”‡ƒ…Š…ƒ•‡ Ž‹‡•ſ†‘ɛ’ř†‘ɛ™ɏ„ƒ”řŽ™†ʰɩř…‘Žʰɑ„Ž—‡ɑƀ Ž‹‡•ſƒ††ɛ’řƒ††ɛ™ɏ„ƒ”řŽ™†ʰɩř…‘Žʰɑ”‡†ɑƀ Ž‹‡•ſ”‡…ɛ’ř”‡…ɛ™ɏ„ƒ”řŽ™†ʰɩř…‘Žʰɑ‰”‡‡ɑƀ









 











































:KDWGRHVWKඈVVKRZXV":HOOIඈUVWO\\RXPඈJKWUHPHPEHUWKDWWKඈVIඈJXUHඈVPRUHRUOHVVඈGHQWඈFDOWR)ඈJXUH ඈQWKHPDඈQWH[WERRN7KHEOXHOඈQHඈVRXUFDVHRIGRPඈQDQFHඈHERWK DQG ඈGHQWඈFDOKඈJKHU UHODWඈYHIඈWQHVVFRPSDUHGWR ,QWKඈVFDVHWKHIUHTXHQF\RIWKH DOOHOHTXඈFNO\ඈQFUHDVHVEXWVORZV GRZQDVWKHDOOHOHUHDFKHVIඈ[DWඈRQKHQFHWKHSODWHDXDWKඈJKHUYDOXHVRI 7KHJUHHQFXUYHVKRZVWKH UHFHVVඈYHFDVH7KHඈQFUHDVHඈQ ඈVORZHUZKHQ ඈVORZEHFDXVHWKHQWKHQHZPXWDQWJHQRW\SHඈVPRUH OඈNHO\WRRFFXUඈQKHWHUR]\JRWHV+RZHYHUDVWKHIUHTXHQF\ඈQFUHDVHVඈH JRHVXSWKHPHDQSRSXODWඈRQ IඈWQHVVඈQFUHDVHVUDSඈGO\WZR,QFRQWUDVWWKHDGGඈWඈYHFDVHඈQUHGඈVMXVWDOඈQHDUඈQFUHDVHZඈWKIUHTXHQF\ :HFDQWU\ORRNඈQJDWWKHUHVXOWVRIWKHVHVඈPXODWඈRQVඈQDVOJඈWKO\GඈIIHUHQWZD\WRVHHKRZWKHIUHTXHQF\RI DOWHUVRYHUWKHJHQHUDWඈRQVZHVඈPXODWHGඈWIRU$JDඈQZHZඈOOXVHEDVH5FRGHWRDFKඈHYHWKඈV ‰ʳŞ•‡“ſɨřɏ‰‡řɨƀ ɪ‹–‹ƒŽ‹•‡’Ž‘– ’Ž‘–ſřšŽ‹ʰ…ſɥřɏ‰‡ƀř›Ž‹ʰ…ſɥřɨƀř šŽƒ„ʰɑ‹‡ſ‰‡‡”ƒ–‹‘•ƀɑř›Žƒ„ʰɑ ”‡“—‡…›Ş’ɑřŽƒ•ʰɨƀ ɪƒ††…—”˜‡•ˆ‘”‡ƒ…Š…ƒ•‡ Ž‹‡•ſ‰ř†‘ɛ’řŽ™†ʰɩř…‘Žʰɑ„Ž—‡ɑƀ Ž‹‡•ſ‰řƒ††ɛ’řŽ™†ʰɩř…‘Žʰɑ”‡†ɑƀ Ž‹‡•ſ‰ř”‡…ɛ’řŽ™†ʰɩř…‘Žʰɑ‰”‡‡ɑƀ $OORIWKHVHFXUYHVDUH6VKDSHGWRVRPHH[WHQWVRWKHWUDQVඈWඈRQIURPKඈJKWRORZIUHTXHQF\ඈVUDSඈWEXWWKH DSSURDFKWRIඈ[DWඈRQඈVPXFKVORZHU7KHPRVWPDUNHGGඈIIHUHQFHඈVඈQWKHJUHHQOඈQHWKHUHFHVVඈYHFDVH +HUHඈWWDNHVWඈPHIRU DOOHOHVWRRFFXUඈQ KRPR]\JRWHVVRWKHQHZPXWDWඈRQUHPDඈQVDWORZ IUHTXHQF\IRUTXඈWHDQXPEHURIJHQHUDWඈRQV

2YHUDQGXQGHUGRPඈQDQFH















































(DUOඈHURQZHOHDUQHGDEඈWDERXWKHWHUR]\JRWHDGYDQWDJH7KඈVDOVRUHIHUUHGWRDVRYHUGRPඈQDQFHඈHZKHQ WKHIඈWQHVVRIWKHKHWHUR]\JRWHඈVKඈJKHUWKDQHඈWKHUKRPR]\J\RWH+RZHYHUZHDOVRWRXFKHGXSRQWKHIDFWWKDW WKඈVFDQRQO\EHVWDEOHඈQXQGHUFHUWDඈQFRQGඈWඈRQVඈH :HDOVROHDUQHGWKDWZKHQ RU ZHUH ඈHWKHSRSXODWඈRQඈVIඈ[HGIRUHඈWKHUDOOHOHWKHVHHTXඈOඈEUඈDDUHXQVWDEOH6RDWZKDWDOOHOHIUHTXHQF\ඈVWKH SRSXODWඈRQඈQDVWDEOHHTXඈOඈEUඈD" 3UHYඈRXVO\ZHVඈPXODWHGGDWDEXWWKඈVWඈPHZHDUHJRඈQJWRUXQRXUVHOHFWඈRQPRGHOIRUDUDQJHRIYDOXHVRI DQGVHHZKHUHPHDQSRSXODWඈRQIඈWQHVV ඈVPD[ඈPඈVHG7KHQZH¶OOYඈVXDOඈVHඈWPDNHඈWFOHDUHUWRRXUVHOYHV $VZඈWKWKHERRNZHZඈOOVHWUHODWඈYHIඈWQHVVDVDQGIRUWKH  DQG JHQRW\SHV ɪ•‡––Š‡”ƒ‰‡‘ˆ’ ’ɏ”ƒ‰‡ʳŞ•‡“ſɥřɨřɥŜɥɨƀ ɪ—•‡•ƒ’’Ž›–‘ˆ‹––Š‡‘†‡Žˆ‘”ƒŽŽ˜ƒŽ—‡•‘ˆ’ƒ†…”‡ƒ–‡ƒŽ‹•– ‡•–‹ƒ–‡•ʳޏƒ’ſ’ɏ”ƒ‰‡řˆ—…–‹‘ſœƀ•‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰœř”‡Žɏˆ‹–ʰ…ſɥŜɩřɨřɥŜɫƀƀƀ ɪ‡š–”ƒ…–™Šƒ–™‡ɖ”‡‹–‡”‡•–‡†‹ˆ”‘–Š‡Ž‹•– ‘˜‡”†‘ʳޏƒ’ɏ†ˆ”ſ‡•–‹ƒ–‡•řƒ‰”‹––”śś‡š–”ƒ…–ř…ſɐ’ɐřɐ™ɏ„ƒ”ɐƀƀ 6RZඈWKWKඈVVKRUWSඈHFHRI5FRGHZHIඈUVWVHWWKHUDQJHRIDOOYDOXHVRI ZඈWK•‡“WKHQZHXVHGWKHƒ’

IXQFWඈRQWRUXQRXU•‡Ž‡…–‹‘ɏ‘†‡ŽIXQFWඈRQRQHDFKYDOXH)ඈQDOO\ZHXVHGƒ’ɏ†ˆ”WRH[WUDFWWKHYHFWRUVRI ’DQG™ɏ„ƒ”1RZZHFDQYඈVXDOඈVHWKHVHWRVHHWKHVWDEOHHTXඈOඈEUඈXP ɪ‹‹–‹ƒŽ‹•‡’Ž‘– ƒʳމ‰’Ž‘–ſ‘˜‡”†‘řƒ‡•ſ’ř™ɏ„ƒ”ƀƀʫ‰‡‘ɏŽ‹‡ſ…‘Ž‘—”ʰɑ„Ž—‡ɑř•‹œ‡ʰɨŜɬƀ ƒʳރʫšŽ‹ſɥřɨƀʫ›Ž‹ſɥřɨƀ ƒʳރʫšŽƒ„ſɑ ”‡“—‡…›‘ˆɨŞ’ɑƀʫ›Žƒ„ſɑ‡ƒ’‘’—Žƒ–‹‘ˆ‹–‡••ɑƀ ƒʫ–Š‡‡ɏŽ‹‰Š–ſƀ :HFDQVHHPHDQSRSXODWඈRQIඈWQHVVඈVPD[ඈPඈVHGDW7KඈVඈVWKHVWDEOHSRඈQWRQRXU'DGDSWඈYH ODQGVFDSH



Ç Ç

 



c ccc



























  8QGHUGRPඈQDQFHඈVWKHRSSRVඈWHRIRYHUGRPඈQDQFHඈHඈWඈVKHWHUR]\JRWHGඈVDGYDQWDJH,QVKRUWUHODWඈYH IඈWQHVVRIWKHKHWHUR]\JRWHඈVORZHUWKDQHඈWKHUKRPR]\JRWH2QFHDJDඈQZHFDQYඈVXDOඈVHWKHVWDEOH HTXඈOඈEUඈXPIRUDPRGHORIRYHUGRPඈQDQFHXVඈQJPRUHRUOHVVH[DFWO\WKHVDPHFRGHDVEHIRUH$OOZHUHDOO\ QHHGWRFKDQJHඈVWKHUHODWඈYHIඈWQHVVZKඈFKZHZඈOOVHWWRDQGIRUWKH  DQG JHQRW\SHV )ඈUVWZHUXQWKHPRGHORYHUGඈIIHUHQWYDOXHVRI  ɪ•‡––Š‡”ƒ‰‡‘ˆ’ ’ɏ”ƒ‰‡ʳŞ•‡“ſɥřɨřɥŜɥɨƀ ɪ—•‡•ƒ’’Ž›–‘ˆ‹––Š‡‘†‡Žˆ‘”ƒŽŽ˜ƒŽ—‡•‘ˆ’ƒ†…”‡ƒ–‡ƒŽ‹•– ‡•–‹ƒ–‡•ʳޏƒ’ſ’ɏ”ƒ‰‡řˆ—…–‹‘ſœƀ•‡Ž‡…–‹‘ɏ‘†‡Žſ’ʰœř”‡Žɏˆ‹–ʰ…ſɥŜɰřɥŜɪřɨƀƀƀ ɪ‡š–”ƒ…–™Šƒ–™‡ɖ”‡‹–‡”‡•–‡†‹ˆ”‘–Š‡Ž‹•– —†‡”†‘ʳޏƒ’ɏ†ˆ”ſ‡•–‹ƒ–‡•řƒ‰”‹––”śś‡š–”ƒ…–ř…ſɐ’ɐřɐ™ɏ„ƒ”ɐƀƀ 7KHQZHSORWඈWXVඈQJ‰‰’Ž‘–ɩ ɪ‹‹–‹ƒŽ‹•‡’Ž‘– ƒʳމ‰’Ž‘–ſ—†‡”†‘řƒ‡•ſ’ř™ɏ„ƒ”ƀƀʫ‰‡‘ɏŽ‹‡ſ…‘Ž‘—”ʰɑ„Ž—‡ɑř•‹œ‡ʰɨŜɬƀ ƒʳރʫšŽ‹ſɥřɨƀʫ›Ž‹ſɥřɨƀ ƒʳރʫšŽƒ„ſɑ ”‡“—‡…›‘ˆɨŞ’ɑƀʫ›Žƒ„ſɑ‡ƒ’‘’—Žƒ–‹‘ˆ‹–‡••ɑƀ ƒʫ–Š‡‡ɏŽ‹‰Š–ſƀ +HUHZHVHHDVFHQDUඈRZKHUHXQGHUGRPඈQDQFHඈVDWDVWDEOHHTXඈOඈEUඈDDW  

6WXG\TXHVWඈRQV

)RUVWXG\TXHVWඈRQVRQWKඈVWXWRUඈDOGRZQORDGWKH…Šƒ’–‡”ɫɏɏ“—‡•–‹‘•ŜIURP&DQYDVRUIඈQGඈWKHUH KWWSVHYROXWඈRQDU\JHQHWඈFVJඈWKXEඈRFKDSWHUB5BTXHVWඈRQV5



















,

,