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%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: bach03a.dvi %%Pages: 29 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Times-Roman Times-Bold Times-Italic Symbol MSBM10 CMR10 %%+ CMMI10 CMSY10 ZapfChancery-MediumItalic CMEX10 Courier %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -Ppdf -N0 -G0 -t letter bach03a -o bach03a.ps %DVIPSParameters: dpi=8000, compressed %DVIPSSource: TeX output 2003.12.09:2158 %%BeginProcSet: tex.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/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]{Ci}imagemask restore}B/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: alt-rule.pro %! % Patch by TVZ % Makes dvips files draw rules with stroke rather than fill. % Makes narrow rules more predictable at low resolutions % after distilling to PDF. % May have unknown consequences for very thick rules. % Tested only with dvips 5.85(k). 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202 3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4d81cf7fbc8de5 2d2e7bb57142033993f9c08c315abade8dbc4a732e84e142d3bee51557910e12 cd8aa37c459a5e6b7f5269f59078aba3be4641a11ac48d0b625c8325b38ec08e 4c9e5e7fed976a5650d99d82114f449b9ca14c4ec957702295a39a93ef93f618 99b8ea06b092c3c1e503e6e436e0a9fa22576c8930ab3dc8c20f5d82b69cddf8 ff4dacfa9c54bed5a3aa3ea5b129fe96be632843b9b6bc91b615581a985db56b 1e01ca60ee69ca92cf5c0882ece62edad3e106d835348822400f0b66af658f2a e56ed08f8b0010571807009b73ab12a8cf14ca6c71f03c2a48c500f9d62266af 154a6375ff600d9bac3f05ce34142d6867a79581c533176bb2f3117336671e2e 44638a97167e2ea9644e31ea16c2ad2990ea33c54001e0c8156e6de8ab6a4d40 a7137ba275f39589fea2e2db8256adc103d6f9cc038037a47e8fd469c5f98a5e 3c15bd4ace40d340018b1cff7d1ed8abb0ac57b5b5a2c20a51957b96c453edb7 dae5affd91a46d938fe0a13363001d844ded4323f1ee6d30012aea19b024a552 315505535c85dc26bad31e09c50e6512802976d298c4e90d0044c362e6bf3ab3 62a454ee93de25ce54411090c29e9d75c80ce26a84404bd9de3aee0e3f921ac5 87f907572b8354a5c3165eea7e8b2ba4e4f834663063e9a307d8ff6f8b61acd8 799bc105cddcf8f95f2160494fc01f7ec3effb95de571b8d7f27a2f9ad203c09 cd4cffd98a119a507460e7fef5c910405e877aa1f8da68d1272e59e3adccef8d 82e692b3229926fbe621080b7831a2ee248948dd3ae55082a939f02875a7a0eb 7ae7d50270a576fbdfde7109c670f51be75b80b6fe3045ea50e2121021e62adf 47101df97d95a5a98efbf72e0a8772e90ee5ae28f88d9a1875c5c5203e3a3887 6df75ef7e65b98d215ad7084756b5f9e3768a329d0fb8c16dfa2bee83072549f b9a3ac5854a3ed9e0ccc35aa8da23d88b893ef9c777e8e0bf28eb6aac5dfdda1 35cb1519d7dd0d7d75235a4f38527400355e1accf05ecf8b80913f368b3edff6 5780be402670efad2ddbce83807f546965184b38e118bbfb363b6ecc5d09a687 938259ca0324c3ff53acbffa20c7c60eb2ea03f660a0cd67556d03dd6ead467a 40525fc22f3afbf7594ff34117b008590b4da385739f8839212c9f87184739e7 54a663c0b0b5e4a763e2278f5f60692cb9c96967af48a195ad9137f196b85966 688268e647e192a7ebadac7f170e8096e31b8e55da0e77a6146164f5a9056b9c 8799cd5a9c16bb5fca6793c5c082421bc2d27eddc260e766458866bfd538d169 b32b85ebe300ad36100995cd379af49efede570cb3bb7431869eca6bbc352ee6 22e3053946a256d54123201a11ee52efbb8bad115a52a520b1787187d2d9d279 9e7437e11c1069162ed9d38080e58332b84cbc497362541413f482de123a575b 60b1c4b98bac5860d0c0d01d20f638bf1fd9530fe862be0233fbe34dd926aff7 6c64d1666b4dae6564dd7cc2a3193c26a102207ab011788193fbbdc72ab661b5 a0c62d59fef021fa2a83c8a6853d24786c50c6ecceef5faf19be33a4b0ebf12d 56de0803fb6af6319ac559901b70918f1f605643558b513e63beef42586f34a3 92e31169e636a8b8ecd1b47527aee083ff27dd538bf8c25a0689dc13d48be24b e38751bc54e507efcb7b6e6d1aa4c3a5cf535a4263004ece158332e565b09e86 d125747b99bed87b34eaccd173e0f0f6a56371bc17d9694f03b5988109fa3a80 50a4872c9079b2b23d6e9723bc5d4b646133dd699790cea95428e065a29c77b7 47dde2b8d34bb3fe2c4df6368f13b80f75b79152dc81b73f9989cbaf1bd677cd dd2d22c6cc941f835b0f82fa0ae737be83385c4d974e2328f93a8dfab1a48efc b07304f608c338ae6bed7b78fefaf8c790ce0d1c74d3cfad7aa29bb02f537c97 e0a57a086ad379198092d05092462a47332f337b 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 5087385 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b310b58348c4b42393988fef4925cf984423aaf65fea9f0e6 4629953bcf50b919d968d99bd185f83112b2759cc411764e9bde677f57c5ee5a c555448d5f81a16259ded1e11bf4119d53e8ab07a802df900d3a2d5ccc1c6876 d29c5e9effb7af3ef83400b0910c07873a8c56fa7b1eb1ba426043b00cc95dbe dc6e136cbbbcb3f67509964f9f281ebf81fe5b018122eaf66c4a838487e82e18 6e006093042848a903efb3469ab6b4049767aadb95c30408dfd58d8a10f4cb22 168decd9f3ee100f07b49aa44c92139b669cc312ba20192454eb2375be6284b0 26659d964b96ae82d4942e758027fcf23c25ed01115af27ce7f20efe2a822bb6 84004f20243a49c9e93301fc21b80815c033c3e2ba58ef53da2157d524b395f2 b37abca13bc6a2f42e824ab7e47106176b0d6db267fbb795ac7425582df2e3dc 55863468a9200742bd7b552c48f8cf58bc21343bd3b95abfa140f33f37c6f3f7 8b0d8a5154eb7c1f62ec598267f13e841a3e64172663935ac8b665d86540d316 ddece329c008049c5e74b27d59022c5515059bc3b89370b1bc6a169c888bb325 e0b74282d6f053a50da4024ed1e433271a32ab8c17d41c632b41cf9f3ecd5fe1 24daf7aea7ce8a63047b245822930d517df7baaafa69d2d17f7d93cebd45416d f3459365434123a76ccf883a4973bab19807e1f0c4bab03a45f7ed69ff2660ff 3963e4def11001eec4238c368a39d874fd30b3c14f4186ec7700fbce22abe468 eb32baf7b0164f8f21a9b5e706b91411faaa44467cb2180ab03de375c1ab93e9 76e11ab92fdd4a7280a6d1a8dc65c4c89d04c8ed6988045a2a3de9a4c7b1efd3 75b3a4105c3d10ef7781c955b819182c6c351e3c2708d2ecc18fd84117d28415 be070709c783ddb1cd03727712191ed4941ba27bad26580e23c680cbbc337b56 06365f2f02db2309c21dc4d2da178840100307fbd9f3dc9a661d9bc485e8e74d 3d8f2fd45388634a5e86f57f0ae8bc28118fc87f7b8bc566a1199397cfe149b0 58b2e6e52319db5c018b294489b186bda76e5e5c35bb29fc43572172605dd05e 757ec6c5a2ce63f5a83ddb05d6b24b4172cab58a7a0ddd54774d26bb8404c072 aa973093d94798ff0f51fff769205cf238acc860a4bdf8fb7880deb3469627a9 ce754c40004cc9b0604059066751702c85285f007a378598002eb19d0a817abb 91d9764cc1808ef87a7f506f11cb80097700a5d5cc1e7d9ff7c2b328ecee45d9 ebfc1bbf871cb3550832132e853dc7c80bda47d837ef058797e1e6e683bdce1e 81d6ffcf5f15c0f6bd69612fed7c6357d2f550553dfdb898f893beabf218b6b5 b89a9c6ae405e458aed2ae9f400de59dbf8a04d3b08681fe0169a69a6888d83e a508f326d06e3963560e16cf906cd07dc587442492e7db815ee391d8b34e9282 dab4c3428e53a161a4f9d3c26b75f7fb10cc7f4b15be20cc82bbae4d81684708 53bbaafe949a8a6094777743f3df061a1f324efacd72d43f4f66558c72e82cfc fa9bfd62bede98415844a41ca75ea11a778f5dacfa692b718541aff824ee99af 1f50e2c26ca07b88e6b6f2beaacbd0a7db2571a6392668227a8548704e227d3a eea0724b974bf6ad4e4727af5a109c1b0b85c7e12602b8b9f7192cfbe63fbf53 2ad112b959a340f8242b8d9e4e528107ddb362f39f9c3ebf655e445ee3fd5097 47832c531e9e934da51171154b1ea2d4e6d901e206ad35cf2f871ad675e1 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 13 /circlecopyrt put dup 15 /bullet put dup 25 /approxequal put dup 26 /propersubset put dup 32 /arrowleft put dup 33 /arrowright put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 62 /latticetop put dup 91 /union put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 110 /backslash put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c4301d3b93ae93f58c5699e2d50dcec6ff1a9f8468dafdac6874a7f56ba9a 578aa4182a73bb06fc8dfd963262c42647a48d946040521e5110a0796ec7b48c 8ee1ef3a761d2c69592abfc78290d5b599bc5552559cbda6954b7f5c53c6d3c0 33d585a646caa9f3af65d138720ed881e76e3cfaff527a35cf06e2d4bbbff057 36741dc324f7bf14fff00e0b573837f910ec2e405e7134203eef7943bbb54873 7d1322da3fda8678e23d149e22e8c977772ec507a39acf4f955c27c06bd4ae72 6939060ae086c5e11f240964281930179b88eb89325e19fd2e479a0647b283b4 f2471852711d2c8dfe43bd9968ed8cb6abf15e0208330013a23a2c96a5a1b530 c101a95362e5c96a5c50783468188ef94110e6b0a5317b5650cd4578fe165cdc 5de00b1507a903d40b9a9504ab7e74a208de9b1a840c8a2de0582449e7422ed1 bb56ac6974baee6314c1954946d53d5670ff3d873e38ad869d9734f6d0490700 98136ba29423814da1fbf8f303398c0b1bbfefca02aad13d36cff71487810f4f bcd4bea3707573e7ee157da1fe10355823fecc208b30fcc15060420f2c9290a2 e55d4c0d8f64a9ce39af0dacf5ffd40f6c799d21fa5251a6efe0bd27e813f2e6 6e7b16db53e84e4cf994410c3ae90e81a65f41346a7d11c2d9da2f5d44150f6a c6117fe56271fcc8bd510cbf7f3a7169830f1aa44ba26afff2b8caed5a91df47 3f4083064cdf4a8f38f8f7e37b58c5c1303d4c70728f075e9a725e98995ad4f7 2ee998f5608f29428f3bf92a622d069757e0a47943e18be02bccae603d26b230 d69208d4124bf8c7218e8371a538dfced727cb6650776c212cab93ccaa637867 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808134cbaa8c66411da3557201939761922c2021348fa1b8b939349b10e27695 fc4c563a50ac3427091c66c15d658575828751956cf6ea7fc403d5eb7344281f 632f85a349f5aef8f8e73f0081937207b493aed41cbb377be4c11f43e0a6d3a7 c496dac5fdad3b46d2b4dc3e4310b2f5de1fbe209f01de2c8fb74be7eab4dc4e 79b80dfee22965e10c87abba933ef0968ef08939779a524b22e2bb80682f16fc a8214eb73336b52513ed9e9fdb65023a7c256496052761c0b21bc7e7933a2750 ccc3dad28c478e99983206a017ae8e603f205fa45f07091e1c92d4d2890ecbb0 b117aa097528d01cc1f787a46e98322b761fa20c6151116b169c3ecebfc8a08a 3b0a5e8394f07270b7f09d00dc48098af1dbae040e9faf1eb2075884e1d7ed0d c36677b6b0e93f4ec2044c0101971a25f153bdf463e9f392f195240c2e014c11 fd4e0eb94cd50dc53b3bd173812dc3b97740e227b36853e048c115576e26370f 2de0415a3bb993e2459b600fde844030151f0a30315dc310d891e1feb87efc2a 244e5b24e2cc3c519e108ae3babe6b5f2d3ba0bbed27fec6eab44a565fac86ea e15f110425b6a8cd6969d994f430110e0fd92d1756a02c74f02cd11e3597b777 7bf3a909b4d9e80c4dd567ed3eb29bed2adc6a353785c717e3200629e5d83d5b 818b92f0162870bff026ce9ebbf9e74e13e8be06be4215e7ce05848d1ccf0ea2 076c0c9291131f778dc1f2f7ae9859b88f991981b37292478d3b7f69df46d64c e990de8ee28756431ef0afde4b311f597ad50cbf3c811374a11295ff2598aa73 af6f3c281b4daf126a6b2f12711548658ce41ebbc7ede0cbcf58e1c621147aa8 b7d6d798cf82b8a5c1a0efc88850bd1066f255a4e1b05910f3d776d15213ba2c 9f19c64cdf2baec18eacff7e45624e66d70d8efdcc559bf00a14e860f3e39721 ab5b5e2bbc47221aa4d73cf8ba01edf41dfca9de7beabb0d3850fce807ca652c 51cdc7b7b60d8ea2ca3aebeffeffbd5a92fe41debace94f5520ddcdc8fcc0c21 ffff8e1a629b2d453804ef97a9825f54d0520a523be78caa7b8f80764da125aa 6dee2b91a4dba8511edc1b6f2389fd57479812149812570c8fe7ccde5af88e68 b06c06bc412d6944091d6d9294593ab504f1475f9258431548eabe56226d7b51 49a0a6a6e56064eb847e4938e65110263cbeadc603f20fb8e7cd8e9aae0f932a 337a6ab18d336ade108055 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 /UniqueXX 5031982 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d56491bdecdcafdc988206c5a457a19270b 37d0ab776e03eaa7eb568eeab6b5e79dec03b0dcbf923a2aa8e4f4deda2cb043 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FD(T)154 b FF(,)312 b(and)e(de\002ne)h(the)g (error)e FD(e)36650 60434 y Fz(T)37621 60252 y FF(as)h(this)g(number)g (multiplied)2000 61758 y(by)3920 61280 y FM(100)p 3699 61479 1771 49 v 3699 62176 a Fz(m)p Fv(\000)p FM(1)5957 61758 y FF(\(if)353 b(tw)-12 b(o)355 b(components)f(are)g(assigned)g (to)h(the)f(same)g(true)g(component,)368 b(which)355 b(can)g(only)f(occur)h(when)2000 63416 y(the)372 b(demixing)g(is)f (especially)h(bad,)390 b(then)372 b(some)f(edges)h(of)27821 63175 y(\210)27549 63416 y FD(T)525 b FF(become)373 b(tri)-30 b(vial)371 b(when)h(estimated)g(components)2000 64921 y(are)303 b(assigned)g(to)g(true)f(component,)i(simply)f(making)g FD(e)25768 65103 y Fz(T)26731 64921 y FF(lar)-22 b(ger\).)3882 66427 y(W)-97 b(e)347 b(report)g(results)f(\(a)-24 b(v)-18 b(eraged)346 b(o)-18 b(v)g(er)347 b(20)g(replications\))f(in)h(T)-97 b(able)347 b(1.)508 b(W)-97 b(e)348 b(also)e(ran)h(tw)-12 b(o)347 b(ICA)h(algorithms,)2000 67932 y(J)-73 b(ADE)322 b(\(Cardoso,)g(1999\))g(and)g(F)-18 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w(3.4)p 21971 32806 V 1632 w(2.9)p 25387 32806 V 2372 w(2.3)p 29745 32806 V 3225 w(2.1)p 34868 32806 V 3540 w(1.0)p 39854 32806 V 3404 w(0.5)p 44706 32806 V 7250 34312 V 7936 33860 a FF(8)p 9790 34312 V 1934 w(2)p 11724 34312 V 1851 w(3.1)p 15612 34312 V 2169 w(4.3)p 19094 34312 V 1665 w(3.2)p 21971 34312 V 1632 w(2.7)p 25387 34312 V 2372 w(1.8)p 29745 34312 V 3225 w(1.6)p 34868 34312 V 3540 w(1.7)p 39854 34312 V 3404 w(1.0)p 44706 34312 V 7250 35817 V 7936 35366 a(8)p 9790 35817 V 1934 w(3)p 11724 35817 V 1851 w(2.9)p 15612 35817 V 2169 w(4.2)p 19094 35817 V 1665 w(3.0)p 21971 35817 V 1632 w(2.5)p 25387 35817 V 2372 w(1.6)p 29745 35817 V 3225 w(1.9)p 34868 35817 V 3540 w(1.9)p 39854 35817 V 3404 w(1.2)p 44706 35817 V 7250 37323 V 7936 36871 a(8)p 9790 37323 V 1934 w(4)p 11724 37323 V 1851 w(3.0)p 15612 37323 V 2169 w(4.2)p 19094 37323 V 1665 w(3.1)p 21971 37323 V 1632 w(2.6)p 25387 37323 V 2372 w(1.6)p 29745 37323 V 3225 w(2.1)p 34868 37323 V 3540 w(2.1)p 39854 37323 V 3404 w(1.3)p 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2169 w(6.9)p 19094 43389 V 1665 w(5.4)p 21971 43389 V 1632 w(4.1)p 25387 43389 V 2372 w(3.2)p 29745 43389 V 3225 w(3.3)p 34868 43389 V 3540 w(3.5)p 39854 43389 V 3404 w(2.1)p 44706 43389 V 7272 43433 37457 45 v 2000 45699 a(T)-97 b(able)303 b(2:)606 b(Density)341 b(estimation)f(for)g (increasing)h(number)g(of)f(components)h FD(m)g FF(and)g(tree)-30 b(width)340 b FE(t)h FF(of)g(the)f(gener)-24 b(-)6515 47204 y(ating)303 b(model)h(\(all)e(results)g(are)h(a)-24 b(v)-18 b(eraged)303 b(o)-18 b(v)g(er)303 b(20)g(replications\).)1939 53267 y FD(W)524 b FF(and)376 b FD(T)529 b FF(v)-18 b(ery)375 b(accurately)-79 b(,)394 b(with)376 b(the)f(contrast)g(based)g(on)h(k) -12 b(ernel)375 b(density)g(estimation)g(leading)h(to)f(the)g(best)2000 54772 y(performance.)483 b(Moreo)-18 b(v)g(er)-48 b(,)347 b(using)339 b(an)g(ICA)g(algorithm)g(for)f(this)h(problem)g(leads)g(to) g(signi\002cantly)f(w)-12 b(orse)339 b(per)-24 b(-)2000 56278 y(formance.)374 b(An)298 b(interesting)f(f)-12 b(act)298 b(that)g(is)f(not)h(apparent)g(in)g(the)g(table)g(is)f(that)h (our)g(results)e(are)i(quite)g(insensiti)-30 b(v)-18 b(e)2000 57783 y(to)358 b(the)g(\223density\224)g(of)g(the)g(tree)g (that)g(w)-12 b(as)357 b(used)h(to)g(generate)g(the)g(data:)486 b(b)-24 b(ush)-6 b(y)358 b(trees)f(yield)h(roughly)g(the)g(same)2000 59289 y(performance)303 b(as)g(sparse)f(trees.)2000 62914 y FK(9.2)606 b(Density)303 b(Estimation)2000 65579 y FF(Here)310 b(we)f(focus)g(on)h(density)f(estimation,)i(comparing)f (the)f(follo)-30 b(wing)309 b(models:)389 b(Gaussian)309 b(\(GA)-67 b(U\),)309 b(Gaussian)2000 67085 y(mixture)376 b(\(GMM\),)f(independent)h(Gaussian)g(mixtures)f(\(IND\),)h(Cho)-30 b(w-Liu)375 b(with)i(Gaussian)e(mixtures)h(\(CL\),)2000 68590 y(ICA)275 b(using)g(mar)-22 b(ginal)275 b(Gaussian)g(mixtures)f (\(ICA\),)h(and)h(TCA)f(using)g(Gaussian)f(mixtures)h(\(T)-112 b(-CUM,)274 b(T)-112 b(-KDE,)2000 70096 y(T)g(-KGV\).)24893 73417 y FJ(1225)p eop %%Page: 1226 22 1226 21 bop 21244 -2672 a FJ(B)22 b 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b(the)g(tree)-30 b(width)365 b FE(t)g FF(is)f(equal)h(to)g (1)g(\(lines)f(in)h(bold)g(in)f(T)-97 b(able)365 b(2\),)380 b(the)365 b(data)g(e)-18 b(xactly)365 b(follo)-30 b(w)365 b(the)g(TCA)2000 12418 y(model)335 b(and)h(it)f(is)f(no)h(surprise)f (that)h(our)g(TCA)g(algorithm)g(outperforms)f(the)h(other)g(models.)471 b(Ho)-30 b(we)g(v)-18 b(er)-48 b(,)343 b(when)2000 13923 y FE(t)396 b FF(is)f(greater)g(than)h(one,)419 b(the)395 b(TCA)h(model)g(assumptions)e(do)i(not)g(hold,)418 b(b)-24 b(ut)396 b(our)f(models)g(still)g(e)-18 b(xhibit)396 b(good)2000 15429 y(performance,)311 b(especially)e(with)g(the)h (contrast)e(function)i(based)f(on)g(k)-12 b(ernel)309 b(density)g(estimation)g(\(KDE\).)g(Note)2000 16934 y(that)423 b(when)f(the)h(generating)g(model)g(becomes)f(too)h(connected)g (\(e.g.,)452 b FD(m)336 b Fx(=)f FF(8)p FC(;)135 b FE(t)334 b Fx(=)g FF(4\),)452 b(the)423 b(performance)f(of)2000 18440 y(the)315 b(TCA)g(models)f(starts)g(to)g(de)-18 b(grade,)318 b(which)d(simply)g(illustrates)e(the)i(f)-12 b(act)315 b(that)f(in)h(those)g(conditions)f(the)h(tree)2000 19945 y(approximation)303 b(is)g(too)g(loose.)2000 23122 y FK(9.3)606 b(Finding)303 b(Clusters)f(in)h(ICA)2000 25340 y FF(In)426 b(this)g(section,)457 b(we)427 b(study)f(the)h (problem)f(of)g(\002nding)h(clusters)e(in)i(independent)g(component)g (analysis.)745 b(In)2000 26845 y(all)377 b(of)g(our)f(simulations,)395 b(data)377 b(were)g(generated)h(from)e FD(q)h FF(independent)h (clusters)315 b FD(C)38289 27027 y FM(1)38787 26845 y FC(;)135 b(:)g(:)g(:)129 b(;)74 b FD(C)41858 27027 y Fz(q)42355 26845 y FF(,)395 b(and)378 b(were)f(then)2000 28351 y(rotated)294 b(by)g(a)h(random)f(b)-24 b(ut)294 b(kno)-30 b(wn)294 b(matrix)g FD(A)p FF(.)373 b(W)-97 b(e)294 b(measure)g(the)h(demixing)f(performance)g(by)g(comparing)h (the)2000 29856 y(results)302 b(of)h(our)f(algorithms)14535 29615 y(\210)14127 29856 y FD(W)452 b FF(to)242 b FD(W)418 b Fx(=)269 b FD(A)20155 29416 y Fv(\000)p FM(1)21340 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b(.)416 b(Ef)-30 b(\002cient)292 b(multiscale)i(re)-18 b(gularization)293 b(with)h(applications)3212 57856 y(to)303 b(the)g(computation)h(of)f(optical)g(\003o)-30 b(w)-79 b(.)436 b FD(IEEE)302 b(T)-67 b(r)-18 b(ansactions)302 b(on)h(Ima)-12 b(g)g(e)303 b(Pr)-55 b(ocessing)p FF(,)302 b(3\(1\):41\22664,)h(1994.)2000 60431 y(E.)357 b(G.)g(Miller)g(and)h (J.)e(W)-112 b(.)359 b(Fisher)d(III.)609 b(ICA)358 b(using)f(spacings)f (estimates)h(of)g(entrop)-12 b(y)-79 b(.)610 b(In)357 b FD(Pr)-55 b(oceedings)357 b(of)h(the)3212 61936 y(F)-127 b(ourth)302 b(Symposium)h(on)g(Independent)h(Component)g(Analysis)e (and)h(Blind)g(Sour)-45 b(ce)303 b(Separ)-18 b(ation)p FF(,)303 b(2003.)2000 64510 y(S.)345 b(A.)g(Murph)-6 b(y)345 b(and)g(A.)g(W)-112 b(.)346 b(v)-30 b(an)345 b(der)g(V)-135 b(aart.)571 b(On)346 b(pro\002le)f(lik)-12 b(elihood.)571 b FD(J)-30 b(ournal)344 b(of)h(the)h(American)e (Statistical)3212 66016 y(Association)p FF(,)302 b(95:449\226485,)i (2000.)2000 68590 y(H.)387 b(C.)g(Ombao,)408 b(J.)386 b(A.)g(Raz,)409 b(R.)387 b(L.)f(Stra)-18 b(wderman,)407 b(and)387 b(R.)g(V)-156 b(on)387 b(Sachs.)703 b(A)387 b(simple)f(GCV)h(method)g(of)f(span)3212 70096 y(selection)303 b(for)g(periodogram)f(smoothing.)437 b FD(Biometrika)p FF(,)302 b(88:1186\2261192,)i(2001.)24893 73417 y FJ(1232)p eop %%Page: 1233 29 1233 28 bop 10897 -2672 a FJ(B)56 b FM(E)g(Y)29 b(O)56 b(N)g(D)327 b FJ(I)56 b FM(N)g(D)g(E)g(P)g(E)g(N)g(D)g(E)g(N)g(T)320 b FJ(C)56 b FM(O)g(M)g(P)g(O)g(N)g(E)g(N)g(T)g(S)g FJ(:)389 b(T)56 b FM(R)e(E)i(E)g(S)328 b(A)56 b(N)g(D)330 b FJ(C)56 b FM(L)g(U)g(S)g(T)g(E)g(R)e(S)2000 3313 y FF(J.)303 b(Pearl.)436 b FD(Causality:)375 b(Models,)303 b(Reasoning)f(and)i (Infer)-45 b(ence)p FF(.)436 b(Cambridge)304 b(Uni)-30 b(v)-18 b(ersity)302 b(Press,)g(2000.)2000 5815 y(D.)375 b(T)-90 b(.)375 b(Pham.)667 b(Blind)375 b(separation)g(of)g (instantaneous)g(mixture)f(of)h(sources)f(via)h(an)h(independent)f (component)3212 7321 y(analysis.)436 b FD(IEEE)301 b(T)-67 b(r)-18 b(ansactions)302 b(on)i(Signal)f(Pr)-55 b(ocessing)p FF(,)302 b(44\(11\):225\226229,)h(1995.)2000 9822 y(D.)284 b(T)-90 b(.)284 b(Pham.)396 b(Blind)285 b(separation)e(of)h (instantaneous)g(mixture)g(of)g(sources)f(via)h(the)h(Gaussian)e (mutual)i(informa-)3212 11328 y(tion)303 b(criterion.)436 b FD(Signal)303 b(Pr)-55 b(ocessing)p FF(,)302 b(81:850\226870,)i (2001a.)2000 13830 y(D.)287 b(T)-90 b(.)287 b(Pham.)403 b(Contrast)287 b(functions)f(for)h(blind)g(separation)g(and)g(decon)-48 b(v)-24 b(olution)288 b(of)f(sources.)401 b(In)287 b FD(Pr)-55 b(oceeding)287 b(of)3212 15335 y(the)303 b(ICA)g(2001)g (Confer)-45 b(ence)p FF(,)304 b(2001b.)2000 17837 y(D.)295 b(T)-90 b(.)294 b(Pham.)418 b(Mutual)294 b(information)g(approach)g(to) h(blind)f(separation)g(of)g(stationary)g(sources.)417 b FD(IEEE)293 b(T)-67 b(r)-18 b(ansac-)3212 19342 y(tions)303 b(on)g(Information)f(Theory)p FF(,)h(48\(7\):1935\2261946,)g(2002.)2000 21844 y(D.)385 b(T)-90 b(.)385 b(Pham.)699 b(F)-18 b(ast)385 b(algorithm)g(for)f(estimating)h(mutual)g(information,)405 b(entropies)385 b(and)g(score)g(functions.)698 b(In)3212 23349 y FD(Pr)-55 b(oceedings)448 b(of)h(the)f(F)-127 b(ourth)447 b(Symposium)i(on)f(Independent)h(Component)g(Analysis)e (and)i(Blind)f(Sour)-45 b(ce)3212 24855 y(Separ)-18 b(ation)p FF(,)303 b(2003.)2000 27357 y(J.)g(Rissanen.)436 b(Modeling)303 b(by)g(Shortest)f(Data)i(Description.)436 b FD(A)-24 b(utomatica)p FF(,)303 b(14:465\226471,)g(1978.)2000 29858 y(B.)h(Sch)5334 29852 y(\250)5233 29858 y(olk)-12 b(opf)302 b(and)i(A.)f(J.)g(Smola.)436 b FD(Learning)303 b(with)g(K)-42 b(ernels)p FF(.)436 b(MIT)302 b(Press,)g(2001.)2000 32360 y(B.)i(W)-112 b(.)303 b(Silv)-18 b(erman.)436 b FD(Density)303 b(Estimation)g(for)f(Statistics)g(and)i(Data)f(Analysis) p FF(.)435 b(Chapman)304 b(and)f(Hall,)h(1985.)2000 34862 y(M.)291 b(W)-97 b(elling)292 b(and)f(M.)g(W)-97 b(eber)-67 b(.)412 b(A)291 b(constrained)g(EM)g(algorithm)g(for)f(independent)i (component)g(analysis.)411 b FD(Neu-)3212 36367 y(r)-18 b(al)302 b(Computation)p FF(,)i(13\(3\):677\226689,)f(2001.)2000 38869 y(A.)356 b(S.)g(W)-48 b(illsk)-18 b(y)-79 b(.)604 b(Multiresolution)355 b(statistical)g(models)g(for)g(signal)h(and)g (image)g(processing.)604 b FD(Pr)-55 b(oceedings)356 b(of)3212 40374 y(the)303 b(IEEE)p FF(,)f(90\(8\):1396\2261458,)h (2002.)2000 42876 y(A.)238 b(Ziehe)g(and)h(K.-R.)f(M)12513 42870 y(\250)12412 42876 y(uller)-67 b(.)296 b(TDSEP\227an)237 b(ef)-30 b(\002cient)238 b(algorithm)g(for)g(blind)g(separation)g (using)g(time)g(structure.)3212 44382 y(In)303 b FD(Pr)-55 b(oceedings)303 b(of)g(the)g(International)f(Confer)-45 b(ence)304 b(on)g(Arti\002cial)e(Neur)-18 b(al)303 b(Networks)p FF(,)g(1998.)24893 73417 y FJ(1233)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF