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%!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: ICA2003.dvi %%CreationDate: Fri Feb 21 11:23:02 2003 %%Pages: 6 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Times-Bold Times-Italic Times-Roman Courier CMMI10 %%+ MSBM10 CMMI7 CMR10 CMR7 CMSY7 CMSY10 CMEX10 CMR5 CMMI5 MSAM10 CMSY5 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: DVIPS.EXE -t letter ICA2003 %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.02.21:1122 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. 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All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /asteriskmath put dup 62 /latticetop put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /defines put dup 54 /lessorequalslant put dup 62 /greaterorequalslant put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 59 /comma put dup 84 /T put dup 87 /W put dup 106 /j put dup 107 /k put dup 109 /m put dup 117 /u put dup 118 /v put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec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B59744399378C5347228E57082E3A486A333655AC64506B15CEF64C1B2C5F515 AC9789C5C3A402CA60EE4ADD00DE26AEF003386289D0C2109EB013C071E81002 90F2833F431C4DAC89DCF3FBDBFEC2A0B20176B90980B3601AEE94A0D1BF8CF5 4E32477A9F3F44E52C4500CDDF283176C2143B7482657595CAA66B4942D5E006 7B8B2C083CD9D65EEFB4C297D68B6E0230D702089851122F106EF79524F4A813 D5DDAB31704CE944CD4E2081F2F4DED37EF5AA17B86983AA3EC3ABBAD82528E5 7F3E22880DD104400A5A07C93042CE255EC9804CBCB283DD7FC5540890363640 780309CF229C7A507A9D7702045ECC85EB64B13933B6A60A2C3EFFF13ACAF30E 934E4F04B510167C534144BA5D4F7F780BE9CE6BA2B75718093110616BF8FCF7 1DC8B9DF4EBCDC06A891C6F12F094D6C3F11D0D263764E7D0B619D37BACB708A 008E996BE9C57B6A48A1E80A225A598834903AF87B95505B602F98A0981B9B08 98DF9340C858B71AD03C56C7B69D5F11135A78AC8A2E6AA46E25300C7CDD20AD 4B409517BB76CCF2B134C0E75135C9E0D0D83B815BDB0D8382094E6A88555B9A 46E6F1F8A1DC74E7663FD795F436AADA352D2DE4568D2B021FECE9BB95DA19FD 66CAAF24E001F81BEE3BDCE052F03FF920BBCF7B6B3B5DB61A912886E4BF21E0 DF129BF6145802801293DE15F99B2A5FF3C2EF0FA6880342B4B8D66975484C21 A5282631A54E642B41E89D756AB0FA0924FCB344D4C2D8A0CCFDFF3BB8CB8E20 7C4E226F0B057043CCECCD0B8560DC21BEC25743EF9D3358EB1603482C6B2BCB C1F63A0B816FAC326E61C85DE616708746E5D345EEEAF244A1473D19CEAE7C07 2FF46EA48F8B112EE4051256C708E9C084F5C7C5FE19ED6EBC551038760EB916 39043B29ECF89BF370BE2BB5987AB634A980C1452069EED578B3BF4A57D57FEB DB12E58C15C188EC21EE2E2C335AE8987A8871B5DEEB9222730D285037453116 4FA80744C9AE0C4B598B8DA975192800CF0D2C294A09D7AC62F5C8FF3B973773 13F7121DDCF1FC2DE89EB5AA4A9CF0E7FE4474746AE5CF16C46AAE27BCAB783C F7C0C0C0E98812E130DCC5FD1017B87D22CC76348E2D7AE1446C593B52934DFA C23DB762CD0906570D34E5A6554CE8D4E5DA2C1D344CC63CC01B1A2EB2236768 0C987B390A9BC6A420BEC776B5EEFDE22DCBA640A8810A54AA2E88150B529D30 B5A79C46B00F17897B667370D08E1B58BB36F04D4012B9703AC5FC3D43B8E9C0 EB78423EC5AF48ED064F18EAE6A4E8BCA47EFBAC3087FACE332B5740C25C9A00 122F43066967E3B2737F16769E4364E3B71515E407C58262E032CEAF3FD99306 6EB27FC78159A9D06DD05E64573E82CD4F0C3B97C8AA4E71866225B3BE396BDF E3935550A6DCF936A345C2E524D70C4CBCB98DE5175BBEB45D8684E4D1992C18 3AC510E0D5E9B11A9CC23DC8F467F45E8F111D3762207AB750F7381A37532291 B425A3724E438DDECD3B8A78BBAE9EB75F54970CC98B8389F9C55D26BF0BC4E5 06DA731FC97D4D0C0E453F4F4445B64CCF3C6B3E93ACAE378E7E17968D08498F 14112FE49EDCF722CC8ADF3F68C0ABD6EE8D79756CD37CA32F9C4F27CE47B369 DF2BE78FE7F75DF35EB8BE335B66D91CD3FA8594DF239E974D791C7BB582169A 01A772C77269D93A99A7E61A7B50394A0B8FA666F0A2E9C9F1602448791AA8EC 29DBCF1CDE0182095AC0D084E17410041ED67DF32824F9A9A6D8B2730B1D950C F852244ADDC670960B05FB498AF73B14AA6CF45B4731798D5C1049CDA81C32F1 40D88E6E248EE0787D19109AE3EA1EEB22EA1F929C4CBCFA1F1C720DF9D7C342 6E55711ABC0E5A6E99F435AFD122337B8EB7F46F1F2BF31DCF8D14B867B0FBCE CC802CF9806B474C5E96165C8EA8C42A8BC6068EA2DC25CC4DC5A8A1CBB8F53E D2165F4822A46C00B48978CC02957E678239A3A7CA46FB3D9DB450DECE88B8DB B53D06938C3664D7A5977984D2FAF64C7F3C729710680952D8527E3EDCD2A8E0 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 16 /parenleftBig put dup 17 /parenrightBig put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 80 /summationtext put dup 81 /producttext put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 25 /approxequal put dup 32 /arrowleft put dup 33 /arrowright put dup 47 /proportional put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 68 /D put dup 91 /union put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 6 /plusminus put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 62 /latticetop put dup 68 /D put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 61 /equal put dup 100 /d put dup 101 /e put dup 116 /t put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 6 /Sigma put dup 35 /numbersign put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 52 /four put dup 53 /five put dup 56 /eight put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex put dup 97 /a put dup 100 /d put dup 101 /e put dup 103 /g put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 116 /t put dup 120 /x put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec 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5CA1CF3B56B15EBD258CABB5E85FC0E364E9019B7A5D1FFA1FC354EA8381C300 64CC9E026745EBB9470A67E1ED085482D2764394805EF9D1A279669932A6C70B 16C8DD6DD334852ECC65058C6C74EBF25DA4B9C411EEBD63243C9027C9A22F80 E536F0DAC3EABBD04A7CBA0CAEE87350FCEFC56878E6C02E61A8BADFD6F90DDF 5E24A4FA3E9E05348B0D08D9FD08276904348B31E59554F24BF63990A6A96455 65A508B23CA81532A5D519CA5CF219EE1FB4A803BC0896B48FCE0ED511D56F8D A03E7FCCBE82E7DA64 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 25 /pi put dup 27 /sigma put dup 33 /omega put dup 59 /comma put dup 65 /A put dup 67 /C put dup 69 /E put dup 78 /N put dup 83 /S put dup 84 /T put dup 87 /W put dup 97 /a put dup 100 /d put dup 102 /f put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 112 /p put dup 113 /q put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 63 /emptyset put dup 82 /R put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 22 /mu put dup 25 /pi put dup 27 /sigma put dup 33 /omega put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J put dup 78 /N put dup 79 /O put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 97 /a put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 112 /p put dup 113 /q put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec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1359 y Fn(u)3394 1334 y Fp(p)p Fm(\()p Fp(x)3515 1346 y Fn(u)3558 1334 y Fm(\))p Fq(.)60 b(In)32 b(addi-)1975 1455 y(tion,)i Fp(q)46 b Fm(=)e Fp(p)2394 1467 y Fn(T)2477 1455 y Fq(minimizes)32 b Fp(D)r Fm(\()p Fp(p)14 b Fj(jj)g Fp(q)s Fm(\))32 b Fq(o)o(ver)g Fp(q)46 b Fj(2)e(D)3591 1425 y Fn(T)3644 1455 y Fq(,)34 b(and)d(we)1975 1553 y(have:)2191 1696 y Fp(I)2234 1662 y Fn(T)2286 1696 y Fm(\()p Fp(x)p Fm(\))84 b Ff(,)102 b Fm(min)2629 1755 y Fn(q)r Fk(2D)2760 1739 y Fg(T)2819 1696 y Fp(D)r Fm(\()p Fp(p)14 b Fj(jj)g Fp(q)s Fm(\))23 b(=)g Fp(D)r Fm(\()p Fp(p)14 b Fj(jj)g Fp(p)3482 1708 y Fn(T)3534 1696 y Fm(\))285 b Fr(\(1\))2481 1895 y Fm(=)55 b Fp(I)7 b Fm(\()p Fp(x)2723 1907 y Fl(1)2761 1895 y Fp(;)14 b(:)g(:)g(:)g(;)g(x)2993 1907 y Fn(m)3056 1895 y Fm(\))19 b Fj(\000)3194 1816 y Fi(X)3135 1998 y Fl(\()p Fn(u;v)r Fl(\))p Fk(2)p Fn(T)3387 1895 y Fp(I)7 b Fm(\()p Fp(x)3509 1907 y Fn(u)3553 1895 y Fp(;)14 b(x)3637 1907 y Fn(v)3677 1895 y Fm(\))p Fp(:)119 b Fr(\(2\))1975 2145 y(W)-7 b(e)32 b(refer)e(to)h Fp(I)2442 2115 y Fn(T)2494 2145 y Fm(\()p Fp(x)p Fm(\))i Fr(as)e(the)g Fp(T)12 b Fq(-mutual)28 b(information)p Fr(:)45 b(it)32 b(is)f(the)1975 2243 y(minimum)c(possible)h(loss)h(of)f(information)e(when)h(encoding)f (the)1975 2341 y(distrib)n(ution)d Fp(p)p Fm(\()p Fp(x)p Fm(\))i Fr(with)f(a)g(distrib)n(ution)e(that)i(f)o(actorizes)f(in)g Fp(T)12 b Fr(.)35 b(It)1975 2438 y(is)22 b(equal)d(to)h(zero)g(if)h (and)e(only)h(if)g Fp(p)h Fr(does)f(f)o(actorize)f(in)h Fp(T)12 b Fr(.)2100 2536 y(In)24 b(order)f(to)h(\002nd)g(the)g(best)h (forest)e Fp(T)12 b Fr(,)25 b(we)f(need)g(to)g(minimize)1975 2634 y Fp(I)2018 2603 y Fn(T)2071 2634 y Fm(\()p Fp(x)p Fm(\))e Fr(in)f(Eq.)f(\(2\),)g(with)h(respect)f(to)h Fp(T)12 b Fr(.)25 b(W)m(ithout)20 b(an)o(y)g(restriction)1975 2731 y(on)27 b Fp(T)12 b Fr(,)29 b(since)e(all)h(mutual)f(information)e (terms)i(are)g(nonne)o(gati)n(v)o(e,)1975 2829 y(the)17 b(minimum)f(is)i(attained)e(at)h(a)h(spanning)d(tree)i(and)f(thus)h (the)g(min-)1975 2926 y(imization)k(is)h(equi)n(v)n(alent)d(to)i(a)h (maximum)d(weight)i(spanning)e(tree)1975 3024 y(problem)d(with)h (weights)g Fp(I)7 b Fm(\()p Fp(x)2833 3036 y Fn(u)2877 3024 y Fp(;)14 b(x)2961 3036 y Fn(v)3001 3024 y Fm(\))p Fr(,)k(which)e(can)h(easily)g(be)g(solv)o(ed)1975 3122 y(in)k(polynomial)d(time)i(by)g(greedy)f(algorithms)f(\(see)j(e.g.)f ([14)n(]\).)1975 3334 y Fs(3.2.)49 b(Prior)20 b(on)g(f)n(or)o(ests)1975 3464 y Fr(In)k(order)e(to)i(model)e(forests,)i(we)g(include)f(a)h (prior)e(term)i Fp(w)r Fm(\()p Fp(T)12 b Fm(\))29 b(=)1975 3562 y(log)14 b Fp(p)p Fm(\()p Fp(T)e Fm(\))26 b Fr(where)g Fp(p)p Fm(\()p Fp(T)12 b Fm(\))25 b Fr(is)i(a)f(prior)f(probability)f (on)h(the)h(forest)g Fp(T)1975 3659 y Fr(which)e(penalizes)g(dense)f (forests.)37 b(In)24 b(order)e(to)j(be)f(able)g(to)g(mini-)1975 3757 y(mize)g Fp(I)2204 3727 y Fn(T)2256 3757 y Fm(\()p Fp(x)p Fm(\))e Fj(\000)f Fp(w)r Fm(\()p Fp(T)12 b Fm(\))p Fr(,)25 b(we)f(restrict)g(the)f(penalty)g Fp(w)r Fm(\()p Fp(T)12 b Fm(\))24 b 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b(The)19 b(o)o(v)o(erall)f(comple)o(xity)g(of)h(e)n(v)n(al-) 1975 181 y(uation)h(of)g(the)g(contrast)f(function)g(is)i Fp(O)r Fm(\()p Fp(m)3243 151 y Fl(2)3281 181 y Fp(N)9 b Fm(\))p Fr(.)2100 278 y(In)32 b(the)g(second)f(approach,)i(we)g(e)o (xtend)e(the)h(contrast)g(func-)1975 376 y(tion)16 b(of)f([2)o(],)h (based)f(on)g(the)h Fq(k)o(ernel)f(g)o(ener)o(alized)g(variance)f Fr(\(KGV\),)1975 474 y(which)i(is)h(a)g(Mercer)e(k)o(ernel-based)f (approximation)f(to)j(the)g(mutual)1975 571 y(information.)23 b(The)d(e)n(v)n(aluation)e(can)i(be)g(performed)e(in)i Fp(O)r Fm(\()p Fp(mN)9 b Fm(\))p Fr(.)2100 669 y(Finally)-5 b(,)34 b(in)f(the)f(third)g(approach,)h(we)f(use)h Fq(Gr)o(am-Charlier) 1975 766 y(e)n(xpansions)g Fr(for)g(one-dimensional)e(and)i(tw)o (o-dimensional)f(en-)1975 864 y(tropies,)e(as)f(laid)g(out)f(in)h([1)o (].)50 b(The)28 b(resulting)f(contrast)h(function)1975 962 y(in)m(v)n(olv)o(es)18 b(fourth-order)d(cumulants)i(and)h(is)i (easily)e(computed)f(and)1975 1059 y(minimized.)22 b(Although)14 b(cumulant-based)e(contrast)j(functions)f(are)1975 1157 y(usually)h(less)h(rob)n(ust)f(to)g(outliers)g(and)g(source)f (densities)i(\(see)f(e.g.)g([2)o(]\),)1975 1255 y(the)o(y)20 b(pro)o(vide)e(a)j(f)o(ast)f(good)f(initialization)h(for)f(the)h (lengthier)f(opti-)1975 1352 y(mizations)h(using)g(KDE)g(or)g(KGV)-11 b(.)2165 1578 y Fs(4.)49 b(ST)-7 b(A)f(TION)n(AR)m(Y)21 b(GA)l(USSIAN)g(PR)n(OCESSES)1975 1750 y Fr(In)j(this)h(section,)g(we)g (assume)f(\002rst)h(that)g(the)f(sources)g(are)g(doubly)1975 1847 y(in\002nite)31 b(sequences)f(of)h(real)g(v)n(alued)f(observ)n (ations)f Fj(f)p Fp(s)3648 1859 y Fn(k)3688 1847 y Fm(\()p Fp(t)p Fm(\))p Fp(;)14 b(t)44 b Fj(2)1975 1945 y Fo(Z)p Fj(g)p Fr(,)23 b Fp(k)29 b Fm(=)d(1)p Fp(;)14 b(:)g(:)g(:)f(;)h(m)p Fr(.)30 b(W)-7 b(e)23 b(model)e(this)h(multi)n(v)n(ariate)f(sequence)g (as)1975 2042 y(a)31 b(zero-mean)d(multi)n(v)n(ariate)g(Gaussian)i (stationary)f(process)g(\(we)1975 2140 y(assume)34 b(that)g(the)g(mean) f(has)h(been)f(remo)o(v)o(ed\).)63 b(W)-7 b(e)35 b(let)g Fm(\000\()p Fp(h)p Fm(\))p Fr(,)1975 2238 y Fp(h)30 b Fj(2)f Fo(Z)p Fr(,)c(denote)e(the)h Fp(m)c Fj(\002)h Fp(m)j Fr(matrix)f(autoco)o(v)n(ariance)d(function,)1975 2335 y(de\002ned)g(as)2520 2419 y Fm(\000\()p Fp(h)p Fm(\))k(=)e Fp(E)5 b Fm([)p Fp(s)p Fm(\()p Fp(t)p Fm(\))p Fp(s)p Fm(\()p Fp(t)20 b Fm(+)e Fp(h)p Fm(\))3301 2385 y Fk(>)3357 2419 y Fm(])p Fp(:)1975 2571 y Fr(W)-7 b(e)31 b(assume)e(that)2542 2509 y Fi(P)2629 2529 y Fk(1)2629 2596 y(\0001)2765 2571 y Fj(jj)p Fm(\000\()p Fp(h)p Fm(\))p Fj(jj)40 b Fp(<)f Fj(1)p Fr(,)32 b(so)d(that)h(the)f(spectral)1975 2669 y(density)20 b(matrix)g Fp(f)9 b Fm(\()p Fp(!)s Fm(\))20 b Fr(is)h(well-de\002ned,)e(as)2454 2858 y Fp(f)9 b Fm(\()p Fp(!)s Fm(\))23 b(=)2769 2802 y(1)p 2744 2839 92 4 v 2744 2915 a(2)p Fp(\031)2905 2755 y Fl(+)p Fk(1)2903 2780 y Fi(X)2859 2958 y Fn(h)p Fl(=)p Fk(\0001)3081 2858 y Fm(\000\()p Fp(h)p Fm(\))p Fp(e)3284 2824 y Fk(\000)p Fn(ih!)3446 2858 y Fp(:)1975 3098 y Fr(F)o(or)17 b(each)g Fp(!)s Fr(,)h Fp(f)9 b Fm(\()p Fp(!)s Fm(\))18 b Fr(is)g(an)g Fp(m)8 b Fj(\002)g Fp(m)17 b Fr(Hermitian)f(matrix.)24 b(In)17 b(addition)1975 3196 y(the)k(function)d Fp(!)26 b Fj(7!)d Fp(f)9 b Fm(\()p Fp(!)s Fm(\))20 b Fr(is)i Fm(2)p Fp(\031)s Fr(-periodic.)1975 3412 y Fs(4.1.)49 b(Entr)o(opy)19 b(rate)h(of)g(Gaussian)g(pr)o(ocesses)1975 3542 y Fr(The)g(entrop)o(y)f(rate)h(of)g(a)h(process)e Fp(s)i Fr(is)g(de\002ned)e(as)i([15)o(]:)2291 3705 y Fp(H)7 b Fm(\()p Fp(s)p Fm(\))24 b(=)55 b(lim)2581 3759 y Fn(T)9 b Fk(!1)2795 3649 y Fm(1)p 2786 3686 61 4 v 2786 3762 a Fp(T)2856 3705 y(H)e Fm(\()p Fp(s)p Fm(\()p Fp(t)p Fm(\))p Fp(;)14 b(:)g(:)g(:)g(;)g(s)p Fm(\()p Fp(t)k Fm(+)g Fp(T)12 b Fm(\)\))p Fp(:)1975 3886 y Fr(In)32 b(the)g(case)h(of)f(Gaussian)g(stationary)f(processes,)k(the)d(entrop)o (y)1975 3984 y(rate)20 b(can)g(be)g(computed)d(using)j(the)f(spectral)h (density)f(matrix)g(\(due)1975 4081 y(to)d(an)f(e)o(xtension)f(of)h (Sze)o(g)7 b(\250)-35 b(o')-5 b(s)14 b(theorem)g(to)i(multi)n(v)n (ariate)d(processes,)1975 4179 y(see)21 b(e.g.)46 b([18)n(]\):)2305 4326 y Fp(H)7 b Fm(\()p Fp(s)p Fm(\))24 b(=)2631 4270 y(1)p 2605 4307 92 4 v 2605 4383 a(4)p Fp(\031)2721 4213 y Fi(Z)2804 4234 y Fn(\031)2767 4402 y Fk(\000)p Fn(\031)2878 4326 y Fm(log)14 b(det[4)p Fp(\031)3229 4292 y Fl(2)3266 4326 y Fp(ef)9 b Fm(\()p Fp(!)s Fm(\)])p Fp(d!)s(:)1975 4528 y Fr(Note)21 b(that)g(this)h(is)f(an)g(analog)f(of)h(the)g(e)o (xpression)e(for)h(the)h(entrop)o(y)1975 4625 y(of)34 b(a)f(Gaussian)h(v)o(ector)e Fp(z)37 b Fr(with)d(co)o(v)n(ariance)d (matrix)i Fm(\006)p Fr(,)k(where)1975 4723 y Fp(H)7 b Fm(\()p Fp(z)t Fm(\))23 b(=)2279 4690 y Fl(1)p 2279 4704 34 4 v 2279 4752 a(2)2336 4723 y Fm(log)14 b(det[2)p Fp(\031)s(e)p Fm(\006])p Fr(.)2100 4821 y(By)33 b(the)g(usual)f(linear) h(combination)d(of)i(entrop)o(y)g(rates,)j(the)1975 4918 y(mutual)24 b(information)e(between)h(process)h(can)h(be)f(de\002ned.) 36 b(Also,)1975 5016 y(we)c(can)f(e)o(xpress)g(the)h(entrop)o(y)d(rate) j(of)f(the)h(process)f Fp(x)44 b Fm(=)f Fp(V)19 b(s)p Fr(,)1975 5114 y(where)h Fp(V)40 b Fr(is)21 b(a)f Fp(d)f Fj(\002)f Fp(m)j Fr(matrix,)e(using)h(the)g(spectral)g(density)f(of)h Fp(s)2177 5261 y(H)7 b Fm(\()p Fp(V)19 b(s)p Fm(\))k(=)2569 5205 y(1)p 2544 5242 92 4 v 2544 5318 a(4)p Fp(\031)2660 5148 y Fi(Z)2743 5169 y Fn(\031)2706 5337 y Fk(\000)p Fn(\031)2816 5261 y Fm(log)14 b(det)q([4)p Fp(\031)3168 5227 y Fl(2)3205 5261 y Fp(eV)k(f)9 b Fm(\()p Fp(!)s Fm(\))p Fp(V)3546 5227 y Fk(>)3602 5261 y Fm(])p Fp(d!)s(:)p eop end %%Page: 4 4 TeXDict begin 4 3 bop -186 83 a Fs(4.2.)48 b(Graphical)20 b(model)g(f)n(or)g(time)h(series)-186 213 y Fr(The)k(graphical)f(model) g(frame)n(w)o(ork)f(can)i(be)g(e)o(xtended)e(to)i(multi-)-186 311 y(v)n(ariate)f(time)h(series)g([7)o(,)g(16)o(].)39 b(The)24 b(dependencies)f(that)h(are)h(con-)-186 409 y(sidered)g(are)g(between)g(whole)g(time)h(series,)h(that)f(is)g (between)f(the)-186 506 y(entire)32 b(sets)i Fj(f)p Fp(s)275 518 y Fn(i)302 506 y Fm(\()p Fp(t)p Fm(\))p Fp(;)14 b(t)46 b Fj(2)h Fo(Z)p Fj(g)p Fr(,)35 b(for)d Fp(i)46 b Fm(=)g(1)p Fp(;)14 b(:)g(:)g(:)f(m)p Fr(.)62 b(If)33 b(the)f(pro-)-186 604 y(cess)25 b(is)g(jointly)f(Gaussian)g(stationary)-5 b(,)23 b(then)h(most)g(of)g(the)g(graph-)-186 702 y(ical)j(model)f (results)g(for)g(Gaussian)h(v)n(ariables)e(can)i(be)f(e)o(xtended.)-186 799 y(In)35 b(particular)m(,)j(maximum)c(lik)o(elihood)h(estimation)g (of)g(spectral)-186 897 y(density)22 b(matrices)h(in)g(decomposable)e (models)h(decouples)g(and)g(is)-186 994 y(equi)n(v)n(alent)27 b(to)i(equating)e(local)i(spectral)f(density)g(matrices.)50 b(As)-186 1092 y(we)30 b(sho)n(w)g(in)g(the)h(ne)o(xt)e(section,)j (this)e(enables)g(Theorem)e(1)j(and)-186 1190 y(Theorem)18 b(2)j(to)f(be)g(e)o(xtended)e(to)j(the)f(time)g(series)h(case.)-186 1410 y Fs(4.3.)48 b(Contrast)20 b(function)-186 1540 y Fr(Let)32 b Fp(x)g Fr(be)g(a)f(multi)n(v)n(ariate)g(time)g(series)h Fj(f)p Fp(x)1134 1552 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4700 y Fr(In)h(the)g(presence)g(of)g(a)g(\002nite)h(sample)f Fj(f)p Fp(x)p Fm(\()p Fp(t)p Fm(\))p Fp(;)14 b(t)26 b Fm(=)e(0)p Fp(;)14 b(:)g(:)g(:)g(;)g(N)g Fj(\000)5 b Fm(1)p Fj(g)p Fr(,)-186 4798 y(we)26 b(use)g(the)g Fq(smoothed)e (periodo)o(gr)o(am)g Fr([8)o(])i(in)g(order)e(to)i(estimate)-186 4895 y(the)35 b(spectral)g(density)f(matrix)h(at)g(points)g Fp(!)1159 4907 y Fn(j)1217 4895 y Fm(=)22 b(2)p Fp(\031)s(j)5 b(=)-5 b(N)9 b Fr(,)39 b Fp(!)1660 4907 y Fn(j)1731 4895 y Fj(2)-186 4993 y Fm([)p Fj(\000)p Fp(\031)s(;)14 b(\031)s Fm(])p Fr(.)47 b(At)28 b(those)f(frequencies,)g(the)h(periodogram)c(is) k(de\002ned)-186 5091 y(as)-89 5285 y Fp(I)-53 5297 y Fn(N)10 5285 y Fm(\()p Fp(!)94 5297 y Fn(j)129 5285 y Fm(\))c(=)295 5252 y Fl(1)p 282 5266 59 4 v 282 5313 a Fn(N)365 5193 y Fi(\020)414 5223 y(P)502 5243 y Fn(N)502 5310 y(t)p Fl(=1)629 5285 y Fp(x)676 5297 y Fn(t)706 5285 y Fp(e)745 5255 y Fk(\000)p Fn(it!)887 5263 y Fg(j)922 5193 y Fi(\021)13 b(\020)p 1056 5193 508 4 v 1056 5223 a(P)1143 5243 y Fn(N)1143 5310 y(t)p Fl(=1)1270 5285 y Fp(x)1317 5297 y Fn(t)1347 5285 y Fp(e)1386 5259 y Fk(\000)p Fn(it!)1528 5267 y Fg(j)1584 5193 y Fi(\021)1634 5207 y Fk(>)1975 83 y Fr(\(we)23 b(assume)f(the)g(means)g(ha)n(v)o(e)f (been)h(pre)n(viously)e(remo)o(v)o(ed)f(from)1975 181 y(the)h(data\),)e(and)h(can)g(readily)f(be)h(computed)f(using)g Fp(m)i Fr(f)o(ast)g(F)o(ourier)1975 278 y(transforms)k(\(FFT\).)h(W)-7 b(e)26 b(use)g(the)f(follo)n(wing)f(estimated)h(spectral)1975 376 y(density)20 b(matrices)2410 505 y Fm(^)2392 527 y Fp(f)9 b Fm(\()p Fp(!)2526 539 y Fn(k)2566 527 y Fm(\))24 b(=)2736 471 y(1)p 2719 508 76 4 v 2719 584 a Fp(N)2819 424 y Fn(N)6 b Fk(\000)p Fl(1)2831 448 y Fi(X)2833 625 y Fn(j)s Fl(=0)2976 527 y Fp(W)12 b Fm(\()p Fp(j)5 b Fm(\))p Fp(I)3205 539 y Fn(N)3269 527 y Fm(\()p Fp(!)3353 539 y Fn(j)s Fl(+)p Fn(k)3476 527 y Fm(\))p Fp(;)320 b Fr(\(4\))1975 755 y(where)26 b Fp(W)12 b Fm(\()p Fp(j)5 b Fm(\))27 b Fr(is)h(a)e(smoothing)f(windo)n(w)g(that)h(is)i(required)c (to)i(be)1975 852 y(symmetric)21 b(and)g(sum)h(to)f(one.)29 b(In)21 b(our)g(simulations,)g(we)h(took)e(the)1975 950 y(windo)n(w)32 b Fp(W)12 b Fm(\()p Fp(j)5 b Fm(\))46 b(=)f(\(2)p Fp(p)27 b Fm(+)g(1\))2932 920 y Fk(\000)p Fl(1)3054 950 y Fr(for)32 b Fj(j)p Fp(j)5 b Fj(j)46 b Ff(6)f Fp(p)p Fr(,)36 b(and)c Fm(0)g Fr(other)n(-)1975 1048 y(wise.)26 b(Note)18 b(that)h(if)f(the)h(number)d(of)j(samples)f Fp(N)28 b Fr(tends)18 b(to)h(in\002nity)1975 1145 y(with)j Fp(p)p Fm(\()p Fp(N)9 b Fm(\))23 b Fr(tending)d(to)i(in\002nity)f(such) g(that)h Fp(p)p Fm(\()p Fp(N)9 b Fm(\))p Fp(=)-5 b(N)34 b Fj(!)26 b Fm(0)p Fr(,)c(then)1975 1243 y(Eq.)c(\(4\))f(pro)o(vides)e (a)j(consistent)g(estimate)g(of)f(the)h(spectral)f(density)1975 1340 y(matrix)j([8)o(].)2100 1438 y(Our)g(contrast)f(function)g(in)m(v) n(olv)o(es)g(inte)o(grals)g(of)h(the)g(form)2676 1507 y Fi(R)2731 1528 y Fn(\031)2715 1604 y Fk(\000)p Fn(\031)2826 1574 y Fp(B)t Fm(\()p Fp(f)9 b Fm(\()p Fp(!)s Fm(\)\))p Fp(d!)s(:)1975 1711 y Fr(The)o(y)16 b(can)h(be)f(estimated)h(by)f (Riemannian)g(sums)g(using)h(estimated)1975 1809 y(v)n(alues)27 b(of)g Fp(f)36 b Fr(at)27 b Fp(!)2526 1821 y Fn(j)2596 1809 y Fm(=)35 b(2)p Fp(\031)s(j)5 b(=)-5 b(N)9 b Fr(,)29 b Fp(!)3042 1821 y Fn(j)3112 1809 y Fj(2)36 b Fm([)p Fj(\000)p Fp(\031)s(;)14 b(\031)s Fm(])p Fr(,)29 b(from)d(Eq.)g(\(4\).) 1975 1906 y(Ho)n(we)n(v)o(er)m(,)32 b(in)f(lar)o(ge)f(samples,)k(we)d (subsample)f(\(using)g(a)i(linear)1975 2004 y(\002lter\))22 b(the)f(estimated)g(density)f(matrix)h(to)g(a)h(grid)e(of)h(size)h Fp(d)j Fm(=)f(50)p Fr(,)1975 2102 y(and)c(use)g(the)h(follo)n(wing)d (approximation:)2298 2171 y Fi(R)2353 2191 y Fn(\031)2337 2267 y Fk(\000)p Fn(\031)2448 2238 y Fp(B)t Fm(\()p Fp(f)9 b Fm(\()p Fp(!)s Fm(\)\))p Fp(d!)26 b Fj(\031)2967 2205 y Fl(2)p Fn(\031)p 2967 2219 75 4 v 2986 2266 a(d)3064 2176 y Fi(P)3152 2196 y Fn(d)3152 2263 y(i)p Fl(=1)3278 2238 y Fp(B)t Fm(\()p Fp(f)9 b Fm(\()p Fp(!)3511 2250 y Fn(i)3538 2238 y Fm(\)\))p Fp(:)2589 2463 y Fs(5.)49 b(OPTIMIZA)-8 b(TION)1975 2647 y(5.1.)49 b(Identi\002ability)1975 2777 y Fr(F)o(or)35 b(the)f(ICA)i(model,)h(it)e(is)h(well)f(kno)n(wn)e (that)i(in)g(the)g(tempo-)1975 2874 y(rally)28 b(independent)d(case)j (the)g(model)e(is)j(identi\002able)e(up)g(to)h(per)n(-)1975 2972 y(mutation)k(and)g(scaling,)k(if)d(and)f(only)g(if)h(there)f(is)i (at)f(most)g(one)1975 3070 y(Gaussian)28 b(source,)g(and)e(that)i(in)f (the)h(Gaussian)f(stationary)f(case,)1975 3167 y(the)31 b(model)f(is)h(identi\002able)f(up)g(to)h(permutation)d(and)i(scaling)g (if)1975 3265 y(and)f(only)g(if)h(the)g(sources)f(ha)n(v)o(e)g (linearly)g(independent)e(autoco-)1975 3362 y(v)n(ariance)33 b(functions)f([20)n(].)66 b(It)34 b(is)g(possible)f(to)h(sho)n(w)g (that\227for)1975 3460 y(a)29 b(gi)n(v)o(en)d(forest)i Fp(C)6 b Fr(\227a)29 b(necessary)e(condition)f(for)h(identi\002ability) 1975 3558 y(up)22 b(to)f(permutation)f(and)h(scaling)g(of)h(the)f (demixing)f(matrix)h Fp(W)34 b Fr(is)1975 3655 y(that)21 b(the)g(components)d(are)j(non-Gaussian)d(in)j(the)g(temporally)e(in-) 1975 3753 y(dependent)24 b(case,)j(and)f(ha)n(v)o(e)f(linearly)g (independent)e(autoco)o(v)n(ari-)1975 3851 y(ance)31 b(functions)f(in)i(the)f(Gaussian)h(stationary)e(case.)59 b(Ho)n(we)n(v)o(er)1975 3948 y(this)26 b(condition)e(is)j(not)e(suf)n (\002cient)g(because)f(there)h(are)h(additional)1975 4046 y(in)m(v)n(ariances)e(be)o(yond)f(permutation)h(and)h(scaling.)40 b(Indeed,)25 b(for)g(a)1975 4144 y(gi)n(v)o(en)f(set)i(of)f(clusters,)h (as)f(pointed)f(out)h(in)g([9)o(],)h(only)e(those)h(sub-)1975 4241 y(spaces)h(spanned)e(by)h(the)h(corresponding)c(ro)n(ws)j(of)g Fp(W)38 b Fr(are)25 b(iden-)1975 4339 y(ti\002able,)f(namely)f(if)g (the)h(subspace)e(has)i Fp(p)f Fr(dimensions,)g(the)o(y)g(can)1975 4436 y(be)e(premultiplied)d(by)h(an)o(y)h(linear)g(transform)e(on)i Fp(p)h Fr(dimensions.)2100 4534 y(W)-7 b(e)25 b(deal)e(with)h(the)g (scaling)f(in)m(v)n(ariance)f(by)h(imposing)g(a)h(unit)1975 4632 y(norm)30 b(constraint)g(on)g(the)h(ro)n(ws)g(of)f Fp(W)12 b Fr(,)34 b(while)d(we)g(ignore)e(dur)n(-)1975 4729 y(ing)21 b(the)f(optimization)f(\(b)n(ut)i(not)f(during)f(the)i(e) n(v)n(aluation)e(stage,)h(in)1975 4827 y(Section)c(6\))f(the)h(in)m(v)n (ariance)e(by)h(permutations)f(or)i(by)f(global)g(linear)1975 4925 y(transform)k(of)h(clusters.)1975 5111 y Fs(5.2.)49 b(Algorithm)1975 5241 y Fr(Our)19 b(model)f(is)i(estimated)e(by)h (minimizing)e(the)i(contrast)f(function)1975 5339 y Fp(F)12 b Fm(\()p Fp(W)n(;)i(T)e Fm(\))39 b(=)g Fp(J)8 b Fm(\()p Fp(x;)14 b(W)n(;)g(T)e Fm(\))25 b Fj(\000)f Fp(w)r Fm(\()p Fp(T)12 b Fm(\))p Fr(,)32 b(where)d Fp(w)r Fm(\()p Fp(T)12 b Fm(\))29 b Fr(is)h(the)f(log-)p eop end %%Page: 5 5 TeXDict begin 5 4 bop -131 3 1862 4 v -81 73 a Fs(Input)p Fr(:)26 b(data)20 b Fj(f)p Fp(x)p Fj(g)j Fm(=)g Fj(f)p Fp(x)656 43 y Fl(1)693 73 y Fp(;)14 b(:)g(:)g(:)f(;)h(x)924 43 y Fn(N)988 73 y Fj(g)p Fr(,)20 b Fj(8)p Fp(n;)34 b(x)1271 43 y Fn(n)1340 73 y Fj(2)23 b Fo(R)1478 43 y Fn(m)-81 230 y Fs(Algorithm)p Fr(:)-1 327 y(1.)i(Initialization:)f Fp(T)34 b Fm(=)23 b Fo(?)p Fr(,)d Fp(W)33 b Fr(random)-1 425 y(2.)25 b(F)o(or)20 b Fp(i)i Fm(=)h(0)d Fr(to)h Fp(m)d Fj(\000)g Fm(1)58 523 y Fr(a.)25 b(While)c Fp(F)12 b Fm(\()p Fp(W)n(;)i(T)e Fm(\))20 b Fr(is)h(decreasing)176 620 y(1.)k(Find)20 b(best)h(tree)f Fp(T)32 b Fr(with)20 b Fp(i)g Fr(edges,)g(for)f(\002x)o(ed)h Fp(W)176 718 y Fr(2.)25 b(Compute)19 b(gradient)g(of)h Fp(F)33 b Fr(with)20 b(respect)g(to)g Fp(W)176 816 y Fr(3.)25 b(Perform)i(line)h(search)g (in)h Fp(W)12 b Fr(,)31 b(in)d(direction)f(of)264 913 y(the)20 b(gradient)58 1000 y(b)m(.)25 b Fp(W)221 1012 y Fn(i)272 1000 y Fm(=)d Fp(W)12 b Fr(,)21 b Fp(T)540 1012 y Fn(i)590 1000 y Fm(=)i Fp(T)12 b Fr(,)19 b Fp(J)825 1012 y Fn(i)876 1000 y Fm(=)k Fp(J)-1 1097 y Fr(3.)i(Find)20 b Fp(i)289 1067 y Fk(\003)350 1097 y Fm(=)i(arg)14 b(max)722 1109 y Fn(i)764 1097 y Fp(J)810 1109 y Fn(i)-81 1254 y Fs(Output)p Fr(:)25 b(demixing)19 b(matrix)g Fp(W)35 b Fm(=)23 b Fp(W)1077 1266 y Fn(i)1100 1250 y Fe(\003)1140 1254 y Fr(,)d(forest)g Fp(T)34 b Fm(=)23 b Fp(T)1611 1266 y Fn(i)1634 1250 y Fe(\003)p -131 1287 V 349 1435 a Fs(Fig)o(.)c(3)p Fr(.)25 b(The)20 b(TCA)h(algorithm)-186 1733 y(prior)i(on)h(the)h(tree)f Fp(T)36 b Fr(and)24 b Fp(J)8 b Fm(\()p Fp(x;)14 b(W)n(;)g(T)e Fm(\))25 b Fr(is)g(the)g(contrast)f(function)-186 1830 y(that)16 b(depends)e(on)h(the)h(forest)f Fp(T)d Fr(,)k(the)f(demixing)f(matrix)h Fp(W)28 b Fr(and)15 b(the)-186 1928 y(data)23 b Fp(x)p Fr(,)h(de\002ned)e(in)h(Theorem)f(2)h(or)f(Theorem)g(3,)h(using)f(the)h (esti-)-186 2026 y(mation)28 b(methods)f(presented)g(in)h(Section)g (3.4)g(and)g(Section)g(4.4.)-186 2123 y(The)20 b(algorithm)e(is)k (presented)d(in)h(Figure)f(3.)-61 2224 y(In)31 b(order)f(to)i(perform)e (the)i(optimization)e(of)h Fp(F)12 b Fm(\()p Fp(W)n(;)i(T)e Fm(\))p Fr(,)35 b(we)-186 2322 y(alternate)19 b(minimization)g(with)h (respect)g(to)g Fp(T)12 b Fr(,)19 b(using)h(a)g(greedy)f(al-)-186 2419 y(gorithm)h(for)h(the)h(maximum)e(weight)h(spanning)g(tree)g (problem)f(as)-186 2517 y(presented)k(in)h(Section)g(3.2,)g(and)f (minimization)g(with)h(respect)g(to)-186 2615 y Fp(W)12 b Fr(,)22 b(using)f(steepest)i(descent)e(with)h(line)f(search.)29 b(Note)22 b(that)g(since)-186 2712 y(we)i(constrain)f(each)g(ro)n(w)g (of)g Fp(W)36 b Fr(to)24 b(ha)n(v)o(e)f(unit)h(norm,)f(our)f(search) -186 2810 y(space)g(for)f Fp(W)34 b Fr(is)23 b(a)f(product)e(of)i Fp(m)g Fr(spheres.)29 b(On)22 b(each)g(sphere)f(we)-186 2907 y(perform)g(line)j(search)f(along)f(the)h(geodesic,)g(as)h (detailed)f(in)g([17)o(].)-186 3005 y(T)-7 b(o)27 b(compute)e(the)h (gradient)g(with)g(respect)h(to)f Fp(W)12 b Fr(,)29 b(we)e(use)f (either)-186 3103 y(\002rst-order)20 b(dif)n(ferences)f(\(KGV)-11 b(,)21 b(KDE,)g(CUM\))g(or)g(e)o(xact)g(compu-)-186 3200 y(tations)h(\(ST)-8 b(A)f(T\),)22 b(b)n(ut)h(in)f(principle,)g(e)o (xact)f(computations)g(can)h(be)-186 3298 y(carried)d(through)f(for)i (all)h(four)e(methods.)-61 3399 y(The)27 b(procedure)f(con)m(v)o(er)o (ges)g(to)i(a)h(local)f(minimum)f(with)h(re-)-186 3497 y(spect)21 b(to)g Fp(W)12 b Fr(.)28 b(In)21 b(order)e(to)i(deal)g(with) g(multiple)g(local)f(minima)h(for)-186 3594 y(the)d(pair)f Fm(\()p Fp(W)n(;)d(T)e Fm(\))p Fr(,)19 b(an)f(ef)n(\002cient)f (heuristic)g(is)i(to)f(start)h(from)e(an)g(ICA)-186 3692 y(solution)26 b(\(zero)g(edges\))g(and)h(incrementally)e(increase)h (the)h(num-)-186 3789 y(ber)20 b(of)h(allo)n(wed)f(edges)g(from)g(zero) g(to)h Fp(m)d Fj(\000)h Fm(1)p Fr(,)h(as)i(we)f(describe)f(in)-186 3887 y(Figure)g(3.)453 4104 y Fs(6.)49 b(SIMULA)-8 b(TIONS)-186 4282 y Fr(In)31 b(all)h(of)f(our)f(simulations,)j(data)f(were)f (generated)e(from)h Fp(q)35 b Fr(in-)-186 4379 y(dependent)26 b(clusters)j Fp(C)526 4391 y Fl(1)563 4379 y Fp(;)14 b(:)g(:)g(:)g(;)g(C)807 4391 y Fn(q)844 4379 y Fr(,)30 b(and)e(then)g(rotated)f(by)h(a)h(ran-)-186 4477 y(dom)d(b)n(ut)g(kno)n (wn)f(matrix)g Fp(B)t Fr(.)44 b(W)-7 b(e)28 b(measure)e(the)g(demixing) e(per)n(-)-186 4575 y(formance)18 b(by)i(comparing)e Fp(W)33 b Fr(to)20 b Fp(V)42 b Fm(=)22 b Fp(B)1068 4545 y Fk(\000)p Fl(1)1158 4575 y Fr(.)-186 4812 y Fs(6.1.)48 b(P)n(erf)n(ormance)19 b(metric)-186 4948 y Fr(In)24 b(the)g(case)h(of)f(ICA,)g(the)g(only)g(in)m(v)n(ariances)e(are)i(in)m (v)n(ariances)e(by)-186 5046 y(permutation)15 b(or)i(scaling,)g(which)g (can)g(be)g(tak)o(en)g(care)g(of)f(by)h(a)h(sim-)-186 5143 y(ple)h(metric.)24 b(Indeed,)17 b(what)i(needs)f(to)h(be)g (measured)e(is)j(ho)n(w)e(much)-186 5241 y Fp(A)24 b Fm(=)f Fp(W)12 b(V)145 5211 y Fk(\000)p Fl(1)255 5241 y Fr(dif)n(fers)20 b(from)f(a)i(diagonal)e(matrix,)h(up)g(to)h (permuta-)-186 5339 y(tion.)36 b(In)24 b(our)f(case,)j(ho)n(we)n(v)o (er)m(,)c(we)j(need)e(to)h(measure)f(ho)n(w)h(much)1975 83 y Fp(A)d Fr(dif)n(fers)f(from)f(a)i(block)e(diagonal)f(matrix,)i(up) g(to)g(permutation.)2100 181 y(W)-7 b(e)23 b(\002rst)g(b)n(uild)f(the)h Fp(m)c Fj(\002)h Fp(m)j Fq(cost)f(matrix)h Fp(B)k Fr(as)c(follo)n(ws:) 29 b(for)1975 278 y(an)o(y)20 b Fp(i)i Fj(2)i(f)p Fm(1)p Fp(;)14 b(:)g(:)g(:)f(;)h(m)p Fj(g)20 b Fr(and)f Fp(j)28 b Fj(2)c Fp(C)2988 290 y Fn(k)3029 278 y Fr(,)c(we)h(ha)n(v)o(e)2261 420 y Fp(B)2324 432 y Fn(j)s(i)2405 420 y Fm(=)i(1)18 b Fj(\000)g Fm(\()2668 358 y Fi(P)2756 445 y Fn(p)p Fk(2)p Fn(C)2883 454 y Fg(k)2937 420 y Fj(j)p Fp(A)3022 432 y Fn(pi)3084 420 y Fj(j)p Fm(\))p Fp(=)p Fm(\()3213 358 y Fi(P)3301 378 y Fn(m)3301 445 y(p)p Fl(=1)3437 420 y Fj(j)p Fp(A)3522 432 y Fn(pi)3584 420 y Fj(j)p Fm(\))p Fp(;)1975 571 y Fr(which)f(is)g(the)g(cost)g(of)g(assigning)e (component)g Fp(i)i Fr(to)g(the)f(cluster)h Fp(C)3886 583 y Fn(k)3927 571 y Fr(.)1975 668 y(F)o(or)h(each)g(permutation)d Fp(\033)22 b Fr(o)o(v)o(er)17 b Fp(m)h Fr(elements,)g(we)h(de\002ne)e (the)h(cost)1975 766 y(of)29 b(the)f(assignment)g(of)g(components)e(to) j(clusters)g(de\002ned)e(by)h Fp(\033)1975 863 y Fr(to)22 b(be)g Fp(e)p Fm(\()p Fp(\033)s Fm(\))k(=)2433 801 y Fi(P)2520 888 y Fn(i)2562 863 y Fp(B)2625 878 y Fn(\033)r Fl(\()p Fn(i)p Fl(\))p Fn(i)2768 863 y Fr(.)k(Finally)-5 b(,)22 b(the)f(performance)e(metric)i(is)1975 961 y(de\002ned)f(as)h (the)f(minimum)e(of)i Fp(e)p Fm(\()p Fp(\033)s Fm(\))i Fr(o)o(v)o(er)d(all)h(permutations:)2406 1103 y Fp(e)j Fm(=)f(max)2612 1153 y Fn(\033)2724 1103 y Fp(e)p Fm(\()p Fp(\033)s Fm(\))h(=)g(max)3045 1153 y Fn(\033)3156 1024 y Fi(X)3205 1201 y Fn(i)3290 1103 y Fp(B)3353 1118 y Fn(\033)r Fl(\()p Fn(i)p Fl(\))p Fn(i)3497 1103 y Fr(,)1975 1327 y(which)e(can)h(be)f(computed)f(in)i(polynomial)d(time)j(by)f(the) g(Hungar)n(-)1975 1425 y(ian)k(method)e([6)o(].)39 b Fp(e)24 b Fr(is)i(al)o(w)o(ays)f(between)f Fm(0)g Fr(and)g Fp(m)h Fr(and)g(is)g(equal)1975 1522 y(to)c Fm(0)f Fr(if)h(and)e(only)h (if)g Fp(V)40 b Fr(is)21 b(equi)n(v)n(alent)d(to)j Fp(W)12 b Fr(.)1975 1738 y Fs(6.2.)49 b(Comparisons)1975 1868 y Fr(F)o(or)31 b(temporally)e(independent)62 b(sources,)70 b(we)65 b(compare)e(our)1975 1966 y(algorithm\227with)14 b(the)h(three)g(dif)n(ferent)e(contrast)i(functions)f(CUM,)1975 2064 y(KDE,)27 b(KGV)-8 b(\227to)66 b(tw)o(o)h(ICA)g(algorithms)37 b(J)-5 b(ADE)27 b([10)o(],)68 b(and)1975 2161 y(F)o(astICA)21 b([20)o(].)2100 2259 y(F)o(or)i(Gaussian)g(stationary)g(sources,)g(we)h (compare)e(our)g(algo-)1975 2356 y(rithm)33 b(to)g(three)f(ICA)h (algorithms)f(for)g(time)h(series,)j(SOBI)d([5)o(],)1975 2454 y(TDSEP)26 b([24)o(])f(and)g(an)g(algorithm)e(that)j(minimizes)e (with)i(respect)1975 2552 y(to)i Fp(W)40 b Fr(the)27 b(contrast)g(function)e(used)j(by)f(Pham)g([22)n(].)47 b(This)27 b(con-)1975 2649 y(trast)i(function)d(corresponds)f(e)o (xactly)i(to)h(our)f(contrast)g(function)1975 2747 y Fp(J)2029 2717 y Fn(S)s(T)9 b(AT)2256 2747 y Fr(when)32 b(no)f(edges)h(are)g(allo)n(wed)f(in)h(the)g(graph;)37 b(that)32 b(is,)1975 2845 y Fp(J)2029 2814 y Fn(S)s(T)9 b(AT)2224 2845 y Fm(\()p Fp(f)t(;)14 b(W)n(;)g Fo(?)p Fm(\))p Fr(.)1975 3061 y Fs(6.3.)49 b(T)-8 b(emporally)20 b(independent)h(sour)o(ces)1975 3191 y Fr(W)-7 b(e)27 b(generated)c(patterns)h(of)h(components)e(as)j(follo)n(ws:)34 b(gi)n(v)o(en)24 b Fp(m)1975 3288 y Fr(v)n(ariables)19 b(and)h Fp(q)j Fr(components,)18 b(we)i(generated)e(component)f(sizes) 1975 3386 y(from)29 b(a)h(multinomial)e(distrib)n(ution.)52 b(F)o(or)29 b(each)g(component)e(we)1975 3484 y(generated)h Fp(N)38 b Fr(iid)29 b(samples)g(from)f(a)h(mixture)f(of)g(tw)o(o)i (Gaussian)1975 3581 y(with)i(means)f Fp(\026)2449 3593 y Fl(+)2537 3581 y Fr(and)g Fp(\026)2739 3593 y Fk(\000)2827 3581 y Fr(and)g(co)o(v)n(ariance)e(matrices)j Fm(\006)3741 3593 y Fl(+)3828 3581 y Fr(and)1975 3679 y Fm(\006)2035 3691 y Fk(\000)2091 3679 y Fr(,)j(where)30 b Fp(\026)2431 3691 y Fk(\006)2530 3679 y Fm(=)43 b Fj(\006)p Fp(au)31 b Fr(\()p Fp(u)g Fr(is)h(a)g(random)d(unit)i(norm)f(v)o(ector)1975 3776 y(and)f Fp(a)g Fr(is)h(sampled)f(from)f(a)h(Gamma)g(distrib)n (ution\))e(and)i Fm(\006)3788 3788 y Fk(\006)3883 3776 y Fm(=)1975 3874 y Fp(U)2032 3886 y Fk(\006)2088 3874 y Fp(D)2157 3886 y Fk(\006)2213 3874 y Fp(U)2279 3844 y Fk(>)2270 3895 y(\006)2356 3874 y Fr(\(the)20 b(diagonal)f(elements)i (of)f Fp(D)3289 3886 y Fk(\006)3366 3874 y Fr(are)h(sampled)e(from)1975 3972 y(a)g(Dirichlet)e(distrib)n(ution)g(and)g(the)h(orthogonal)e (matrices)h(are)h(both)1975 4069 y(random\).)28 b(Then)21 b(the)g(data)h(were)g(rotated)f(by)g(a)h(random)e(orthogo-)1975 4167 y(nal)h(matrix.)2100 4265 y(W)-7 b(e)54 b(performed)c(simulations) 25 b(with)52 b(v)n(arious)25 b(numbers)52 b(of)1975 4362 y(sources,)34 b(from)d Fp(m)44 b Fm(=)f(4)32 b Fr(to)g Fp(m)44 b Fm(=)f(8)p Fr(.)59 b(W)-7 b(e)33 b(report)d(results)i(ob-) 1975 4460 y(tained)26 b(from)f(20)h(replications)f(in)h(T)-7 b(able)26 b(1.)43 b(The)25 b(FCA)j(methods)1975 4558 y(reco)o(v)o(er)f(the)i(components)e(better)i(than)f(the)h (\223plain\224)g(ICA)g(algo-)1975 4655 y(rithms.)63 b(Note)33 b(that)f(if)h(the)g(distrib)n(ution)f(of)g(a)h(component)e(can)1975 4753 y(itself)26 b(be)g(modeled)e(by)h(a)g(local)h(ICA)g(model,)f(then) g(such)g(a)h(com-)1975 4850 y(ponent)f(should)g(be)h(retrie)n(v)o(ed)e (perfectly)g(by)i(an)g(ICA)g(algorithm.)1975 4948 y(Since)i(the)f(sets) h(of)f(random)e(distrib)n(utions)h(that)i(we)f(use)g(contain)1975 5046 y(such)c(distrib)n(utions,)f(the)g(a)n(v)o(erage)g(performance)d (of)k(all)g(the)f(algo-)1975 5143 y(rithms)29 b(\(both)f(ICA)i(and)f (FCA\))g(is)h(relati)n(v)o(ely)e(good.)51 b(These)29 b(re-)1975 5241 y(marks)f(also)g(apply)f(to)i(the)f(simulations)f(with) i(stationary)e(Gaus-)1975 5339 y(sian)21 b(processes.)p eop end %%Page: 6 6 TeXDict begin 6 5 bop -186 140 a Fs(T)-8 b(able)22 b(1)p Fr(.)27 b(\(T)-7 b(op\))19 b(Results)j(for)e(temporally)g(independent)e (sources.)-186 238 y(\(Bottom\))h(Results)i(for)f(Gaussian)g (stationary)f(sources.)p -130 303 1860 4 v -132 401 4 98 v -80 371 a Fp(m)p 41 401 V 100 w Fr(Jade)99 b Fd(F)o(astICA)93 b(FCA-Cum)65 b(FCA-Kde)46 b(FCA-Kgv)p 1729 401 V -130 404 1860 4 v -132 501 4 98 v 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Fr(and)22 b(the)h(demixing)e(matrix)h Fp(W)35 b Fr(are)22 b(determined)f(by)h(minimiz-)-186 3108 y(ing)30 b(contrast)g(functions)g(within)g(a)h(semiparametric)e(estimation)-186 3206 y(frame)n(w)o(ork,)c(for)g(temporally)f(independent)f (non-Gaussian)h(data)-186 3303 y(or)e(for)g(stationary)g(Gaussian)g (processes.)32 b(Searching)21 b(for)h(the)h(op-)-186 3401 y(timal)18 b(forest)g(enables)g(us)h(to)f(determine)f(the)h (number)e(and)i(sizes)h(of)-186 3498 y(components,)e(which)h(w)o(as)i (not)f(feasible)g(in)g(pre)n(viously)e(proposed)-186 3596 y(approaches)h(to)j(\002nding)e(clusters)h([9)o(,)h(19)o(].)-61 3694 y(Although)g(we)i(ha)n(v)o(e)f(limited)h(ourselv)o(es)f(to)h(a)g (generalization)-186 3791 y(of)e(ICA)g(that)g(allo)n(ws)g (forest-structured)d(dependenc)o(y)g(among)h(the)-186 3889 y(sources,)27 b(it)f(is)h(clearly)e(of)h(interest)g(to)g(mak)o(e)f (use)i(of)e(the)h(general)-186 3987 y(graphical)16 b(model)g(toolbox)f (and)i(consider)f(broader)f(classes)k(of)d(de-)-186 4084 y(pendenc)o(y)-5 b(.)-186 4268 y Fs(Ackno)o(wledgements)-186 4387 y Fr(W)e(e)20 b(w)o(ould)d(lik)o(e)i(to)f(ackno)n(wledge)e (support)h(from)h(NSF)h(grant)e(IIS-)-186 4484 y(9988642,)22 b(ONR)j(MURI)f(N00014-00-1-0637)o(.)31 b(The)24 b(MA)-9 b(TLAB)-186 4582 y(codes)25 b(for)f(the)h(ICA)g(algorithms)f(that)h(we) g(used)g(for)f(comparison)-186 4679 y(were)19 b(do)n(wnloaded)d(from)i (the)h(webpages)f(of)h(their)g(respecti)n(v)o(e)e(au-)-186 4777 y(thors,)j(e)o(xcept)g(for)h(SOBI,)g(for)f(which)h(we)g(used)g (the)g(implementa-)-186 4875 y(tion)f(in)g(ICALAB)h([12)o(].)499 5082 y Fc(8.)44 b(REFERENCES)-149 5249 y Fd([1])e(S.)15 b(Akaho,)j(Y)-10 b(.)16 b(Kiuchi,)h(and)g(S.)f(Ume)o(yama.)22 b(Multimodal)17 b(indepen-)-20 5339 y(dent)i(component)i(analysis.)27 b(In)19 b Fb(Pr)m(oc.)g(IJCNN)p Fd(,)e(1999.)2013 83 y([2])41 b(F)-6 b(.)18 b(R.)h(Bach)g(and)h(M.)e(I.)h(Jordan.)28 b(K)n(ernel)19 b(independent)i(component)2141 173 y(analysis.)28 b Fb(J)n(.)18 b(of)h(Mac)o(hine)h(Learning)g(Resear)m(c)o(h)p Fd(,)f(3:1\22648,)h(2002.)2013 291 y([3])41 b(F)-6 b(.)30 b(R.)g(Bach)h(and)g(M.)g(I.)f(Jordan.)65 b(T)m(ree-dependent)33 b(component)2141 381 y(analysis.)28 b(In)19 b Fb(Pr)m(oc.)f(U)m(AI)p Fd(,)g(2002.)2013 500 y([4])41 b(A.)17 b(J.)f(Bell)g(and)i(T)-6 b(.)16 b(J.)h(Sejno)n(wski.)22 b(An)17 b(information-maximization)2141 589 y(approach)g(to)d(blind)h(separation)h(and)f(blind)g(decon)m(v)o (olution.)k Fb(Neur)o(al)2141 679 y(Computation)p Fd(,)h (7\(6\):1129\2261159,)i(1995.)2013 798 y([5])41 b(A.)48 b(Belouchrani,)56 b(K.)48 b(Abed)h(Meraim,)55 b(J.-F)-6 b(.)47 b(Cardoso,)56 b(and)2141 887 y(E.)22 b(Moulines.)40 b(A)23 b(blind)g(source)g(separation)h(technique)g(based)f(on)2141 977 y(second)18 b(order)e(statistics.)k Fb(IEEE)15 b(Sig)o(.)h(Pr)m (oc.)p Fd(,)g(45\(2\):434\22644,)j(1997.)2013 1095 y([6])41 b(D.)23 b(Bertsimas)g(and)h(J.)e(Tsitsiklis.)40 b Fb(Intr)m(oduction)24 b(to)f(Linear)g(Opti-)2141 1185 y(mization)p Fd(.)k(Athena)20 b(Scientic,)e(1997.)2013 1304 y([7])41 b(D.)16 b(Brillinger)l(.)k (Remarks)d(concerning)h(graphical)f(models)g(for)f(time)2141 1393 y(series)j(and)h(point)f(processes.)28 b Fb(Re)o(v)-6 b(.)19 b(de)g(Econ.)p Fd(,)g(16:1\22623,)h(1996.)2013 1512 y([8])41 b(P)-8 b(.)24 b(J.)g(Brockwell)h(and)h(R.)e(A.)g(Da)o (vis.)46 b Fb(T)l(ime)24 b(Series:)35 b(Theory)26 b(and)2141 1602 y(Methods)p Fd(.)i(Springer)o(-V)-8 b(erlag,)18 b(1991.)2013 1720 y([9])41 b(J.-F)-6 b(.)34 b(Cardoso.)79 b(Multidimensional)37 b(independent)g(component)2141 1810 y(analysis.)28 b(In)19 b Fb(Pr)m(oc.)f(ICASSP)p Fd(,)g(1998.)1975 1929 y([10])42 b(J.-F)-6 b(.)20 b(Cardoso.)32 b(High-order)22 b(contrasts)f(for)f(independent)j(compo-)2141 2018 y(nent)d(analysis.)27 b Fb(Neur)o(al)19 b(Computation)p Fd(,)h(11\(1\):157\226192,)h(1999.)1975 2137 y([11])42 b(C.)24 b(K.)f(Cho)n(w)h(and)h(C.)e(N.)h(Liu.)42 b(Approximating)26 b(discrete)e(proba-)2141 2227 y(bility)19 b(distrib)o(utions)g(with)f (dependence)j(trees.)27 b Fb(IEEE)17 b(Inf)o(.)i(Theory)p Fd(,)2141 2316 y(14:462\226467,)j(1968.)1975 2435 y([12])42 b(A.)23 b(Cichocki,)h(S.)f(Amari,)g(and)h(K.)f(Siwek.)40 b(ICALAB)22 b(toolbox)o(es.)2141 2524 y Fa (http://www.bsp.brain.riken.go.jp/ICALAB)p Fd(.)1975 2643 y([13])42 b(P)-8 b(.)17 b(Comon.)27 b(Independent)20 b(component)g(analysis,)f(a)f(ne)n(w)g(concept?)2141 2733 y Fb(Signal)i(Pr)m(ocessing)p Fd(,)f(36\(3\):287\226314,)j(1994.) 1975 2852 y([14])42 b(T)-6 b(.)15 b(H.)g(Cormen,)h(C.)f(E.)f (Leiserson,)i(and)g(R.)f(L.)f(Ri)n(v)o(est.)19 b Fb(Intr)m(oduction) 2141 2941 y(to)g(Algorithms)p Fd(.)27 b(MIT)19 b(Press,)f(1989.)1975 3060 y([15])42 b(T)-6 b(.)17 b(M.)f(Co)o(v)o(er)h(and)g(J.)f(A.)g (Thomas.)22 b Fb(Elements)16 b(of)h(Information)g(The-)2141 3149 y(ory)p Fd(.)28 b(John)19 b(W)m(ile)o(y)g(&)f(Sons,)h(1991.)1975 3268 y([16])42 b(R.)24 b(Dahlhaus.)44 b(Graphical)24 b(interaction)h(models)g(for)e(multi)n(v)n(ariate)2141 3358 y(time)c(series.)27 b Fb(Metrika)p Fd(,)19 b(51:157\226172,)i (2000.)1975 3477 y([17])42 b(A.)28 b(Edelman,)j(T)-6 b(.)28 b(A.)g(Arias,)i(and)f(S.)e(T)-6 b(.)28 b(Smith.)56 b(The)29 b(geometry)2141 3566 y(of)c(algorithms)f(with)g(orthogonality) i(constraints.)44 b Fb(SIAM)24 b(J)n(.)g(Mat.)2141 3656 y(Anal.)19 b(Appl.)p Fd(,)f(20\(2\):303\226353,)k(1999.)1975 3774 y([18])42 b(E.)18 b(Hannan.)28 b Fb(Multiple)19 b(T)l(ime)f(Series)p Fd(.)27 b(W)m(ile)o(y)-5 b(,)18 b(1970.)1975 3893 y([19])42 b(A.)f(Hyv)t(\250)-29 b(arinen)42 b(and)g(P)-8 b(.)39 b(Ho)o(yer)l(.)99 b(Emer)o(gence)41 b(of)g(phase)h(and)2141 3983 y(shift)26 b(in)m(v)n(ariant)h(features)f (by)g(decomposition)i(of)e(natural)g(images)2141 4072 y(into)31 b(independent)h(feature)f(subspaces.)65 b Fb(Neur)o(al)31 b(Computation)p Fd(,)2141 4162 y(12\(7\):1705\2261720,)23 b(2000.)1975 4281 y([20])42 b(A.)23 b(Hyv)t(\250)-29 b(arinen,)25 b(J.)e(Karhunen,)j(and)e(E.)e(Oja.)40 b Fb(Independent)26 b(Com-)2141 4370 y(ponent)20 b(Analysis)p Fd(.)27 b(John)20 b(W)m(ile)o(y)e(&)h(Sons,)g(2001.)1975 4489 y([21])42 b(S.)18 b(L.)g(Lauritzen.)27 b Fb(Gr)o(aphical)20 b(Models)p Fd(.)28 b(Clarendon)19 b(Press,)g(1996.)1975 4608 y([22])42 b(D.)15 b(T)-6 b(.)15 b(Pham.)k(Mutual)d(information)g (approach)h(to)e(blind)h(separation)2141 4697 y(of)26 b(stationary)g(sources.)49 b Fb(IEEE)24 b(Inf)o(.)h(Theory)p Fd(,)i(48\(7\):1935\2261946,)2141 4787 y(2002.)1975 4906 y([23])42 b(B.)19 b(W)-7 b(.)18 b(Silv)o(erman.)28 b Fb(Density)19 b(Estimation)f(for)i(Statistics)e(and)i(Data)2141 4995 y(Analysis)p Fd(.)27 b(Chapman)20 b(and)g(Hall,)e(1985.)1975 5114 y([24])42 b(A.)22 b(Ziehe)g(and)h(K.-R.)e(M)6 b(\250)-31 b(uller)l(.)38 b(TDSEP)21 b(-)h(an)g(ef)n(\002cient)g(algorithm)2141 5203 y(for)k(blind)f(separation)h(using)g(time)f(structure.)47 b(In)26 b Fb(Pr)m(oc.)e(ICANN)p Fd(,)2141 5293 y(1998.)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF