Discovery of Biorhythmic Stories behind Daily Vital

&KUEQXGT[QH$KQTJ[VJOKE5VQTKGUDGJKPF&CKN[8KVCN5KIPUCPF+VU#RRNKECVKQP

:

&KUEQXGT[QH$KQTJ[VJOKE5VQTKGUDGJKPF&CKN[ 8KVCN5KIPUCPF+VU#RRNKECVKQP

:HQ[L&KHQ

%LRPHGLFDO,QIRUPDWLRQ7HFKQRORJ\/DERUDWRU\WKH8QLYHUVLW\RI$L]X -DSDQ

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·VEHKDYLRXU6DFUHG/RWXV $UWV )ROORZLQJWKHSKLORVRSK\RI\LQDQG\DQJWKHHDUOLHVWH[LVWLQJPHGLFDOERRN´7KH0HGLFDO &ODVVLFRI(PSHURU+XDQJµZDVIRUPXODWHGIURPDGLDORJXHEHWZHHQ(PSHURU+XDQJDQG DPHGLFDOSURIHVVLRQDO8QFOH4LEDVHGRQWKHWKHRU\RI\LQDQG\DQJDQGFRPSLOHGIURPD VHULHV RI PHGLFDO DFKLHYHPHQWV E\ PDQ\ PHGLFDO SUDFWLWLRQHUV EHWZHHQ ² %& 7KH ILUVW SXEOLFDWLRQ RI WKH ERRN ZDV FRQILUPHG WR KDYH RFFXUUHG QR ODWHU WKDQ %& DQG QR HDUOLHUWKDQ%&:DQJ 7KH ERRN ZDV D PHGLFDO WUHDWLVH FRQVLVWLQJ RI D FROOHFWLRQ RI SDSHUV LQ WZR SDUWV ´0LUDFXORXV0HULGLDQDQG$FXSXQFWXUHµDQG´0HGLFDO,VVXHVDQG)XQGDPHQWDO3ULQFLSOHVµ (DFKSDUWKDVQLQHYROXPHVDQGHDFKYROXPHKDVQLQHSDSHUVEHFDXVHWKHQXPEHUQLQHLV WKHKLJKHVWQXPEHULQ&KLQHVHFXOWXUHDQGKHUHLPSOLHVWKDWWKHERRNFRYHUVDOODVSHFWVRI PHGLFDOPDWWHUV=KDQJHWDO

4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI

7KLVERRNSURYLGHGDV\VWHPDWLFPHGLFDOWKHRU\DQGLQVLJKWVLQWRWKHSUHYHQWLRQGLDJQRVLV DQGWUHDWPHQWPHWKRGRORJLHVIRUGLVHDVHV$WWKHVDPHWLPHWKHLQWHUUHODWLRQVKLSEHWZHHQ PHWHRURORJLFDO IDFWRUV JHRJUDSKLFDO FRQGLWLRQV DQG WKH KHDOWK RI KXPDQ EHLQJV ZDV HVWDEOLVKHG DQG UDWLRQDOL]HG DV WKH WKHRU\ RI ´7KH XQLW\ RI KHDYHQ DQG KXPDQLW\µ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² $' :LNLSHGLD J ZKR LV NQRZQ DV WKH &KLQHVH $HVFXODSLXV DQG ZKRVH ZRUNV ´7UHDWLVHRQ&ROG3DWKRJHQLF'LVHDVHVµDQG´(VVHQWLDO3UHVFULSWLRQVRIWKH*ROGHQ&RIIHUµ HVWDEOLVKHG PHGLFDWLRQ SULQFLSOHV DQG SURYLGHG D VXPPDU\ RI KLV PHGLFLQDO H[SHULHQFH EDVHG RQ KLV FOLQLFDO SUDFWLFH DQG KLV LQWHUSUHWDWLRQ RI ´7KH 0HGLFDO &ODVVLF RI (PSHURU +XDQJµ 7KHUH DUH WKUHH LPSRUWDQW KLVWRULFDO SHULRGV LQ WKH GHYHORSPHQW DQG PDWXUDWLRQ RI 7&0 IROORZLQJ=KDQJ·VSLRQHHUZRUN7KHILUVWSHULRGLVIURPWKHUGWRWKHWKFHQWXU\ZKHUH WKHPDLQZRUNVIRFXVHGRQLQKHULWDQFHFROODWLRQDQGLQWHUSUHWDWLRQRIWKHH[LVWLQJWKHRULHV GHVFULEHG LQ ´7KH 0HGLFDO &ODVVLF RI (PSHURU +XDQJµ 6HYHUDO PLOHVWRQHV LQ WKH 7&0 V\VWHP ZHUH UHDFKHG LQ WKH VHFRQG SHULRG IURP WKH WK WR WKH WK FHQWXU\ ZKLFK LV WKH PRVWLPSRUWDQWSHULRGLQWKHGHYHORSPHQWRI7&00DQ\PHGLFDOSUDFWLWLRQHUVVWXGLHGDQG DQQRWDWHGWKHDQFLHQWFODVVLFDQGDFFXPXODWHGWKHLURZQFOLQLFDOH[SHULHQFHVDQGSURSRVHG WKHLU RZQ GRFWULQHV 7KH PRVW HPLQHQW UHSUHVHQWDWLYHV ZHUH NQRZQ DV ´WKH IRXU JUHDW PDVWHUVµ /LX :DQVX ² =KDQJ &RQJ]KHQJ ² /L *DR ² DQG =KX =KHQKHQJ ² 7KHLU FRQWULEXWLRQV JUHDWO\ HQULFKHG DQG DFFHOHUDWHG WKH GHYHORSPHQW RI 7&0 )XUWKHU GHYHORSPHQW DQG PDQ\ SUDFWLFDO PHGLFDWLRQ DSSURDFKHV ZHUHPDWXUHGLQWKHWKLUGSHULRGIURPWKHWKWRWKHWKFHQWXU\ :XDDDăăăD0@cLQWHUPV RIWKHLQSXWGDWDYHFWRU\ >\ïQ/\Q5@cFDQEHZULWWHQLQPDWUL[QRWDWLRQDVEHORZ

$ D

7KHSRO\QRPLDOFRHIILFLHQWVYHFWRUDEHFRPHV

D

$

7

$

\

$

7

\


:HDOVRKDYHWKHVSHFLILFIRUPV

^$

7

`

$

LM

Q5

¦$

N Q/

NL

Q5

¦N

$NM

L M

N Q/

DQG

^$ \` 7

M

Q5

Q5

¦ $NM \N

¦N

N Q/

N Q/

M

\N

6LQFHWKHILOWHUFRHIILFLHQWFNLVWKHFRPSRQHQWDZKHQ\LVUHSODFHGE\WKHXQLWYHFWRUHN ZHKDYH

FN

^$

7

$

$

7

HN

` ¦ ^$ 0

P

7

$

`

P

NP

²Q/NQ5

:KHQWKHILOWHUFRHIILFLHQWYHFWRUF >FQ/«FQ5@ZDVREWDLQHGXVLQJ(TXDWLRQ WKHVLJQDO VKRZQLQWKHEODFNWUDFHLQ)LJXUHFRXOGEHVPRRWKHGXVLQJ(TXDWLRQ DQGWKHUHVXOWLV WKHUHGWUDFHVKRZQLQ)LJXUH $IWHUWKHVHWZRILOWHULQJVWHSVWKHQRLVHVXSSUHVVHG+5GDWDZHUHXVHGIRUWKHGHWHFWLRQRI WKUHHGLIIHUHQWELRUK\WKPVDVGHVFULEHGLQWKHIROORZLQJWKUHHVHFWLRQV

5NGGRE[ENGGUVKOCVKQP 6OHHSLVFOLQLFDOO\FODVVLILHGLQWRWZRGLVWLQFWVWDWHVWKHUDSLGH\HPRYHPHQW5(0 VWDWHDQG WKH QRQUDSLG H\H PRYHPHQW 15(0 VWDWH 7KH 15(0 VWDWH LV IXUWKHU GLYLGHG LQWR IRXU VWDJHV²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²RIVOHHSLV15(0VOHHSDQGDOPRVWKDOIRIWKHWRWDOVOHHSWLPHLVLQ6WDJH 15(0 5(0 VOHHS HSLVRGHV DFFRXQW IRU ² RI WKH WRWDO VOHHS SHULRG 7KH UHODWLYH DPRXQW RI 5(0 VOHHS YDULHV FRQVLGHUDEO\ ZLWK DJH $V DJH LQFUHDVHV WKH WRWDO VOHHS WLPH EHFRPHVVKRUWHUOHDGLQJWRVKRUWHU15(0VOHHSEXWQRVLJQLILFDQWFKDQJHLQ5(0VOHHS%\ FRQWUDVWLQIDQWVVSHQGDERXWKDOIRIWKHLUVOHHSWLPHLQ5(0VOHHS 5K\WKPLF DOWHUQDWLRQ RI 5(0 DQG 15(0 VWDWHV GXULQJ VOHHS LV UHIOHFWHG LQ GLIIHUHQW SK\VLRORJLFDO DFWLYLWLHV VXFK DV H\H PRYHPHQW PXVFXODU WRQH HOHFWURHQFHSKDORJUDP


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uZ IURPDJJUHJDWHGSL[HOGDWD 7KLV VWXG\ GHDOV ZLWK RQHGLPHQVLRQDO +5 GDWD VHTXHQFHV DQG GHILQHV WKH :/9L DW GDWD SRLQWLDVVKRZQLQ(TXDWLRQ

:/9L

Z

LZ

¦ [ M L

M

§ LZ · ¨¨ ¦ [ M ¸¸ Z© M L ¹

ZKHUHZLVWKHZLQGRZOHQJWKDQG[MLVWKHLQSXWGDWDZLWKLQWKHZLQGRZ )LJXUHVKRZVWKHQRLVHVXSSUHVVHG+5GDWDLQWKHUHGWUDFHDQGWKHHVWLPDWHGUHVXOWRID ELSKDVLF VOHHS F\FOH LQ WKH EOXH WUDFH 7KH ORZOHYHO SKDVH LQGLFDWHV WKH SHULRG ZLWK ORZHU +5 SHUWXUEDWLRQ DQG WKH KLJKOHYHO SKDVH FRUUHVSRQGV WR D SHULRG ZLWK LQFUHDVHG +5 IOXFWXDWLRQ$OWKRXJKLWLVQRW\HWDFRQFOXVLRQWKDWWKHUHLVDUHODWLRQVKLSEHWZHHQWKH5(0² 15(0F\FOHDQGWKHHVWLPDWHGELSKDVLFF\FOHEHFDXVHQRFRQFRPLWDQW((*ZDVUHFRUGHGLW LVLQIHUUHGWKDWWKHORZOHYHOSKDVHPD\LPSO\WKH15(0VWDWHZKLOHWKHKLJKOHYHOSKDVH UHIHUVWRWKH5(0VWDWH $VVKRZQLQ)LJXUHWKHSHULRGOHQJWKRIWKHKLJKOHYHOSKDVHJUDGXDOO\LQFUHDVHGGXULQJ WKHFRXUVHRIVOHHSLHLWZDVVKRUWDWWKHEHJLQQLQJRIWKHVOHHSSHULRGDQGORQJHUWRZDUGV WKHHQGRIWKHVOHHSSHULRGDEHKDYLRXUVLPLODUWRWKH5(0VWDWHDOWKRXJKFRQILUPDWLRQRI WKLVLVUHTXLUHGIURPDQ((*


+5

(VWLPDWHG6OHHS&\FOH

+5ESP

6OHHSVWDWXV

7LPHKKPPVV

)LJ+5SURILOHRIDVLQJOHQLJKW·VVOHHSDQGWKHHVWLPDWHGVOHHSF\FOH'DWDZHUHFROOHFWHG IURPDPDOHVWXGHQWLQKLVWZHQWLHV7KHUHGOLQHLVWKHSURILOHRIWKHQRLVHVXSSUHVVHG+5 7KHEOXHOLQHLVWKHHVWLPDWHGVOHHSF\FOHLQZKLFKWKHORZOHYHOSKDVHLQGLFDWHVWKHSHULRG ZLWK ORZ +5 SHUWXUEDWLRQ DQG WKH KLJKOHYHO SKDVH FRUUHVSRQGV WR WKH SHULRG ZLWK PRUH +5IOXFWXDWLRQV

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`ZLWKGDWDOHQJWK0DQGWKHWHVWSDWWHUQ7 ^WW1`ZLWKGDWDOHQJWK1DVVKRZQ LQ )LJXUH 7KH YDOXH RI HDFK EODFN GRW GLM LQGLFDWHV WKH GLIIHUHQFH GLVWDQFH EHWZHHQ WKH UHIHUHQFHSDWWHUQGDWDULDQGWHVWSDWWHUQGDWDWMDVGHVFULEHGE\(TXDWLRQ

G LM

L M UL WL L

«0M «1

7KXVDWZRGLPHQVLRQDO1u0GLVWDQFHPDWUL['1ð0LVFRQVWUXFWHGZKHUHWKHHOHPHQWGLM LV WKH GLVWDQFH EHWZHHQ WKH LWK GDWD LQ WKH UHIHUHQFH SDWWHUQ DQG WKH MWK GDWD LQ WKH WHVW SDWWHUQ


$VDVLPLODULW\PHDVXUHWKHVKRUWHVWSDWKIURPWKHVWDUWWKHORZHUOHIWKDQGFRUQHURIWKH GLVWDQFHPDWUL[ WRWKHHQGWKHXSSHUULJKWKDQGFRUQHURIWKHGLVWDQFHPDWUL[ RIWKHGDWD VHTXHQFHPXVWH[LVWDPRQJPXOWLSOHSRVVLEOHSDWKV 7KHVKRUWHVWSDWKLVGHWHUPLQHGXVLQJWKHIRUZDUGG\QDPLFSURJUDPPLQJDSSURDFKZLWKD PRQRWRQLFLW\FRQVWUDLQW

3LM

PLQ^G MN 3L N ` Nt M

+HUH3LMGHQRWHVWKHGLVWDQFHIURPWKHLWKDQGMWKGDWDQRGHWRWKHWHUPLQDWLQJQRGH 7KHRYHUDOOPLQLPXPGLVWDQFH'75 XVHGDVWKHVLPLODULW\PHDVXUHIRUWZRSDWWHUQVD VPDOOHUGLVWDQFHYDOXHLQGLFDWHVDKLJKHUVLPLODULW\ LVGHWHUPLQHGIURP

'7 5 3

7KH 6OHHS ,QGH[ 6, LV REWDLQHG E\ QRUPDOL]LQJ '7 5 EHWZHHQ WKH YDOXHV RI DQG DV EHORZ

6,

'7 5 'PLQ 'PD[ 'PLQ

ZKHUH'PLQDQG'PD[LQGLFDWHWKHPLQLPXPDQGPD[LPXPVLPLODULW\YDOXHVUHVSHFWLYHO\ 7KHVPDOOHUWKH6,YDOXHWKHPRUHUHJXODUWKHVOHHSLV

)LJ 7KH PLQLPXP GLVWDQFH WUDFH UHG OLQH IURP WKH EHJLQQLQJ WR WKH HQG RI WZR GDWD VHTXHQFHV7KHEODFNGRWLQGLFDWHVWKHGLVWDQFHEHWZHHQWKHLWKGDWDLQWKHUHIHUHQFHSDWWHUQ DQGWKHMWKGDWDLQWKHWHVWSDWWHUQ7KHYDOXHRIWKHPLQLPXPGLVWDQFH'75 LVWKHVXP RIDOOWKHEODFNGRWVDORQJWKHUHGOLQHDQGLQGLFDWHVWKHVLPLODULW\EHWZHHQWKHWZRSDWWHUQV 7KHVPDOOHUWKHYDOXHRI'75 WKHQWKHJUHDWHUWKHVLPLODULW\LVEHWZHHQWKHWZRSDWWHUQV $OO WKH GDWD LQ WKH WZR GDWD VHTXHQFHV ZHUH FDOFXODWHG WR EXLOG D WZRGLPHQVLRQDO1 u 0 GLVWDQFH PDWUL[ %HFDXVH WKH HQGSRLQW KDG FRQVWUDLQWV WKH JUH\FRORXUHG GRWV FDQ EH LJQRUHG


7KHUHIHUHQFHSDWWHUQZDVFUHDWHGE\VHOHFWLQJRQHZHHN·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

L

L

J]L @

ZKHUHQLVWKHGDWDOHQJWK 7RPLQLPL]HWKHYDOXHRI566(TXDWLRQ LVSDUWLDOO\GLIIHUHQWLDWHGZLWKUHVSHFWWR0 E DQGJ7KHIROORZLQJQRUPDOVLPXOWDQHRXVHTXDWLRQVFDQEHHVWDEOLVKHG

4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI Q § Q · § Q · Q0 [ E ] J \L ¨ ¸ ¨ ¸ ¦ ¦ ¦ L L ° L L L © ¹ © ¹ ° Q § Q · § Q · °§ Q · [ 0 [ E [ ] J [L \L ¨¦ L ¸ ¨¦ L L ¸ ®¨ ¦ L ¸ ¦ L L L L © ¹ © ¹ © ¹ ° Q °§ Q · § Q · § Q · ] 0 [ ] E ] J ]L \L ¨ ¸ ¨ ¸ ¨ ¸ ¦ ¦ ¦ ¦ L L L L ° L ©L ¹ ©L ¹ ¯© L ¹

$IWHUWKHSDUDPHWHUVHW0 E J LVGHULYHGIURPWKHVLPXOWDQHRXVHTXDWLRQV WKHYDOXH RI566FDQEHFDOFXODWHGXVLQJ(TXDWLRQ 7KHYDOXHVRI$DQG MFDQEHFDOFXODWHGXVLQJ (TXDWLRQ DVEHORZ

$

E J

M

§J · DUFWDQ¨¨ ¸¸ ©E ¹

%HFDXVHWKHYDOXHRI566GHSHQGVRQWKHSURSRVHGYDOXHRIZWKHRSWLPDOYDOXHRI ZZKLFK KDVWKHPLQLPXPYDOXHRI566LVFKRVHQDVWKHHVWLPDWHGF\FOHOHQJWK )LJXUH VKRZV WKH +5 PRGH YDOXH DQG VWDQGDUG GHYLDWLRQ SURILOHV RYHU D SHULRG RI VL[ PRQWKVXSSHUVXESORW DQGWKHPHQVWUXDOF\FOHHVWLPDWLRQSURFHGXUHORZHUVXESORW 7KH+5GDWDZHUHFROOHFWHGIURPDIHPDOHVXEMHFWLQKHUWKLUWLHVGXULQJGDLO\VOHHSIURP 2FWREHUWR0DUFK7KHGDWDFROOHFWLRQUDWHZDVLHGD\VFROOHFWHGRXWRIDWRWDO GD\ SHULRG 7KH VWDUWLQJ GDWHV RI WKH VXEMHFW·V PHQVWUXDWLRQ ZHUH UHFRUGHG E\ WKH VXEMHFW DV 2FWREHU 1RYHPEHU 'HFHPEHU -DQXDU\ )HEUXDU\ 0DUFK DQG 0DUFK(DFKPHQVWUXDOF\FOHRYHUWKHVL[PRQWKSHULRGFRXOGEHGHGXFHGDVEHLQJ DQGGD\VUHVSHFWLYHO\DQGWKHDYHUDJHOHQJWKrWKHVWDQGDUGGHYLDWLRQRIWKHVHOI UHFRUGHGPHQVWUXDOF\FOHVZDVrGD\V 7KH GDLO\ +5 PRGH YDOXH DQG VWDQGDUG GHYLDWLRQ ZHUH FDOFXODWHG IURP PRUH WKDQ +5 GDWD SRLQWV GXULQJ WKH ²KRXU PHDVXUHPHQWV RI D VLQJOH QLJKW·V VOHHS HSLVRGH $V VKRZQ LQWKHXSSHU VXESORWRI )LJXUH WKH IOXFWXDWLRQ RI WKH UDZ +5PRGH YDOXH SURILOH 093 VKRZVQRDSSDUHQWUHJXODULW\DORQJWKHWLPHD[LV 7KHORZHUVXESORWVKRZVWKHVPRRWKHG+5093GDWDEROGEOXHOLQH REWDLQHGE\DSSO\LQJ WKH6DYLW]N\²*ROD\VPRRWKLQJILOWHUWRWKHUDZ+5093GDWD$VORZZDQGHULQJEDVHOLQHLQ WKHVPRRWKHG+5093GDWDZDVH[WUDFWHGXVLQJWKHPXOWLUDWHILOWHUDQGVXEWUDFWHGIURPWKH VPRRWKHG +5 093 GDWD WR SURGXFH WKH GHWUHQGHG +5 093 GDWD GRWWHG EODFN OLQH 7KH FRVLQRUDQDO\VLVPHWKRGZDVXVHGWRFDOFXODWHWKHEHVWDSSUR[LPDWLRQEROGUHGOLQH RIWKH GHWUHQGHG +5 093 GDWD DQG WR REWDLQ WKH EHVWILWWHG PHQVWUXDO F\FOH OHQJWK RI GD\V 7KLV FRPSDUHV ZLWK WKH DYHUDJH VHOIUHFRUGHG PHQVWUXDO F\FOHOHQJWK RI GD\V LH WKH PDWKHPDWLFDOO\ HVWLPDWHG PHQVWUXDO OHQJWK LQGXFHG DQ HVWLPDWLRQ HUURU RI ,W ZDV REVHUYHG WKDW WKH WLPLQJ RI WKH VHOIUHFRUGHG PHQVWUXDWLRQ VWDUWLQJ GDWHV FRUUHVSRQGHG WR WKHGHFUHDVHSKDVHLQ+5093GDWDDSSUR[LPDWHO\DVLPLODUFKDUDFWHULVWLFZKLFKLVVKRZQ LQ%%7ELSKDVLFGDWD


)LJ+5PRGHYDOXHDQGVWDQGDUGGHYLDWLRQSURILOHVXSSHUVXESORW DQGPHQVWUXDOF\FOH HVWLPDWLRQSURFHGXUHORZHUVXESORW 'DWDDUHSORWWHGEDVHGRQWKHGD\E\GD\GDWDDORQJ WKH [D[LV 7KH \D[LV GHQRWHV +5 LQ XQLWV RI ESP ,Q WKH XSSHU VXESORW WKH GDWD PDUNHUV ´RµDQGYHUWLFDOEDUV´_µWHUPLQDWHGDWWKHXSSHUDQGORZHUHQGVE\VKRUWKRUL]RQWDOOLQHV ´µ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

%%7

/+

%%7͠

/7+

)+

+RUPRQHFKDQJH

)6+

0HQVWUXDWLRQSHULRG

2YXODWLRQSHULRG

'DWH

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

&CVCEQNNGEVKQP 7KUHHIRUPVRIERG\WHPSHUDWXUHGDWDZHUHFROOHFWHGIURPHDFKVXEMHFW$VVKRZQLQ)LJXUH ERWKWKH6%7DQGWKH&%7ZHUHFROOHFWHGDXWRPDWLFDOO\E\DWWDFKLQJWZRVHQVRUGHYLFHV 42/&R/WG RQWZRVLGHVRIDGUDZHUVVWUDSGXULQJVOHHS 7KH 6%7 GHYLFH RUDQJH HOOLSVH LQ )LJXUH ZDV SURJUDPPHG WR PHDVXUH WKH VNLQ ERG\ WHPSHUDWXUHDWPLQXWHLQWHUYDOVIURPPLGQLJKWWRDP0HDVXUHPHQWRXWOLHUVDERYH q& RU EHORZ q& GXH WR SRRU FRQWDFW RU PRYHPHQW DUWHIDFWV ZHUH DXWRPDWLFDOO\ GLVUHJDUGHG ,Q WKH HQG GDWD SRLQWV DW PRVW FDQ EH FROOHFWHG GXULQJ D VL[KRXU SHULRG 7KH FROOHFWHG WHPSHUDWXUH GDWD ZHUH HQFRGHG DV D WZRGLPHQVLRQDO EDU FRGH NQRZQ DV D ´4XLFN5HVSRQVHµ45 FRGH'HQVR:DYH,QF DQGGLVSOD\HGRQDQ/&'ZLQGRZ$ PRELOHSKRQHEXLOWLQFDPHUDZDVXVHGWRFDSWXUHWKH45FRGHLPDJH)LJXUHD RQWKH GHYLFHGLVSOD\PLGGOHF\FOH 2QFHWKH45FRGHZDVFDSWXUHGRQWKHPRELOHSKRQH)LJXUH E WKH RULJLQDO WHPSHUDWXUH GDWD )LJXUH F ZHUH UHFRYHUHG IURP WKH FDSWXUHG LPDJHDQGWUDQVPLWWHGWRDGDWDEDVHVHUYHUYLD+773SURWRFROWKURXJKDPRELOHQHWZRUNIRU GDWDVWRUDJHDQGDQDO\VLV 7KH&%7GHYLFHEODFNFXEHLQ)LJXUH ZDVGHYHORSHGXVLQJWKH]HURKHDWIORZSULQFLSOH .RED\DVKLHWDO7RJDZD1HPRWR 7RJDZD