Page 108 - First special issue on The impact of Artificial Intelligence on communication networks and services
P. 108
,78 -2851$/ ,&7 'LVFRYHULHV 9RO 0DUFK
JHQHUDWLQJ VXLWDEOH DFWLRQV IRU ERWK SUHGLFWHG DQG 0RVW EXW QRW DOO VLPSOH HYHQWV DUH XQRVWHQWDWLRXV DQG
XQSUHGLFWHG UHOHYDQW FKDOOHQJHV > @ VKRZ WKH VDPH RU VLPLODU EHKDYLRU DW GLIIHUHQW SODFHV
7KLV SUREOHP KDV EHHQ DWWHPSWHG LQ WKLV SDSHU DQG ODWHU DQG RU GLIIHUHQW WLPHV
LW VKDOO EH VHHQ KRZ $, FDQ EH DQ LQHYLWDEOH VWDLUZD\ WR
DWWDLQ WKLV VHHPLQJO\ LPSRVVLEOH FOLII 6HFWLRQ UHIOHFWV 2.2. Place-Time Events
WKH QHHG LQIOXHQFH RI DUWLILFLDO LQWHOOLJHQFH $, RQ WKH
SODFH DQG WLPH HYHQWV ,Q )LJ ZH UHYLVLW WKH IDPRXV 6FKURGLQJHU¶V FDW
H[DPSOH > @ H[FHSW ZLWK D FKDQJH ZKHUH WKLV WLPH WKH
2. BACKDROP: OSTENTANEITY OF AN FDJH LV D ODUJH ZDOOHG FLUFXODU SDUN DQG QXFOHDU
EVENT UDGLDWLRQ LV VRPHZKHUH ZLWKLQ WKH FRQWRXU RI WKH SDUN ,Q
WKLV H[DPSOH DV ZH FDQ LPDJLQH WKH SUREDELOLW\ RI
%HIRUH ZH JHW LQWR WKH EURDGHU GLVFXVVLRQV OHW XV WDNH KDYLQJ WKH FDW DOLYH LV QRW ò DOO WKH WLPH DQG
D PRPHQW WR XQGHUVWDQG WKH EDFNJURXQG RI ZK\ WKLQJV LWV OLNHOLKRRG LV GLVWULEXWHG DFURVV SODFH DQG WLPH 7KH
DUH QRW DV VLPSOH DV WKH\ VHHP GHDWK RI WKH FDW LV GLUHFWO\ SURSRUWLRQDO WR LWV FORVHQHVV
WR WKH UDGLDWLRQ DQG WKH WLPH LW VSHQGV LQ WKH SDUN DW D
2.1. Unostentatious Events SDUWLFXODU SRVLWLRQ
,Q RXU SUHYLRXV ZRUN > @ ZH KDYH GHILQHG VXFK HYHQWV
DV WKH Place-Time Events (PTE)s, whose one or more
outcomes depend on at what time and at what position
the incidence took place. 7KLV PHDQV WKDW DQ HYHQW FDQ
KDYH GLIIHUHQW SUREDELOLWLHV RI RXWFRPHV DW YDULRXV
WLPHV ZKLOH EHLQJ DW WKH VDPH ORFDWLRQ 7KH YLFH YHUVD
RI WKLV KRZHYHU LV QRW WUXH DV ZKHQHYHU WKH SRVLWLRQ
FKDQJHV WKHUH LV DOZD\V VRPH ODSVH LQ WLPH
%\ WKH WHUP µWLPH¶ ZH PHDQ ERWK NLQGV RI WLPH L
absolute time VD\LQJ WKH OHQJWK RI WLPH IRU ZKLFK WKH
SURFHVV LV RQJRLQJ DQG LL WKH event time LQGLFDWLQJ
WKH WLPH DW ZKLFK WKH HYHQW KDSSHQHG $V DQ H[DPSOH ,
GURYH D FDU IRU KRXUV LV WKH DEVROXWH WLPH DQG , SDUNHG
P\ FDU DW DP LV WKH HYHQW WLPH
1RQHWKHOHVV LQ WKH SUHVHQW H[DPSOH WKH SUREDELOLW\ RI
DQ RXWFRPH LV GHILQLWH FRQFHUQLQJ SODFH DQG WLPH
PHDQLQJ WKDW LI WKH SRVLWLRQ RI WKH FDW DQG WKH WLPH LW
VSHQGV DW WKDW ORFDWLRQ DUH NQRZQ ZH FDQ GHWHUPLQH WKH
SUREDELOLW\ RI WKH FDW EHLQJ GHDG RU DOLYH +HQFH WKLV LV
D partially unostentatious event DV ZH VHH KRZ WKH
)LJ 8QRVWHQWDWLRXV (YHQW V\VWHP EHKDYHV DQG SODFH DQG WLPH DUH FRQYROYHG ZLWK
HDFK RWKHU
$Q µ(YHQW¶ E\ GHILQLWLRQ LQ PDWKHPDWLFV LV DQ
H[SHULPHQW SURFHVV RU DFWLRQ WKDW JHQHUDWHV VRPH
PHDVXUDEOH RXWFRPH )LJ VKRZV D FRQYHQWLRQDO GLH
ZKLFK SURGXFHV RQH RI WKH VL[ UHVXOWV ZKHQ UROOHG RQ D
IODW VXUIDFH DQG ZKHQ VDPSOH VSDFH LV SORWWHG DJDLQVW
SODFH DQG WLPH WKH JUDSK LV OLQHDU
7KLV LQGLFDWHV WKDW QR PDWWHU KRZ PDQ\ WLPHV ZH UROO D
GLH RQ D IODW VXUIDFH DQG DQ\ZKHUH DFURVV VSDFH ZH
DOZD\V KDYH D SUREDELOLW\ RI IRU HYHU\ RXWFRPH > @
6XFK HYHQWV ZKHUH WKH EHKDYLRU UHPDLQV XQFKDQJHG
ZLWK WLPH DQG SODFH DUH GHILQHG DV DQ Unostentatious
Event 8( LQ RXU ZRUN LQ > @ 8(V DV LOOXVWUDWHG LQ > @
DUH ³Events whose probabilities of all outcomes, or
sample space, remain unchanged no matter at what
places and at what times theevent takes place.”
)LJ ([DPSOH RI D SODFH WLPH HYHQW 6FKURGLQJHU¶V
WKRXJKW H[SHULPHQW
,QWHUQDWLRQDO 7HOHFRPPXQLFDWLRQ 8QLRQ