%PDF-1.5 % 1 0 obj << /S /GoTo /D (section.1) >> endobj 4 0 obj (Introduction) endobj 5 0 obj << /S /GoTo /D (section.2) >> endobj 8 0 obj (Preliminaries) endobj 9 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 12 0 obj (The coarea formula) endobj 13 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 16 0 obj (Background on subanalytic sets) endobj 17 0 obj << /S /GoTo /D (section.3) >> endobj 20 0 obj (The density of expected persistence diagrams) endobj 21 0 obj << /S /GoTo /D (section.4) >> endobj 24 0 obj (Proof of Theorem 7) endobj 25 0 obj << /S /GoTo /D (section.5) >> endobj 28 0 obj (Examples) endobj 29 0 obj << /S /GoTo /D (subsection.5.1) >> endobj 32 0 obj (Rips-Vietoris filtration) endobj 33 0 obj << /S /GoTo /D (subsection.5.2) >> endobj 36 0 obj (Cech filtration) endobj 37 0 obj << /S /GoTo /D (section.6) >> endobj 40 0 obj (Persistence surface as a kernel density estimator) endobj 41 0 obj << /S /GoTo /D (section.7) >> endobj 44 0 obj (Numerical illustration) endobj 45 0 obj << /S /GoTo /D (section.8) >> endobj 48 0 obj (Conclusion and further works) endobj 49 0 obj << /S /GoTo /D (appendix.A) >> endobj 52 0 obj (Proofs of the subanalytic elementary lemmas) endobj 53 0 obj << /S /GoTo /D (appendix.B) >> endobj 56 0 obj (Proof of Theorem 8) endobj 57 0 obj << /S /GoTo /D (appendix.C) >> endobj 60 0 obj (Proof of Corollary 9) endobj 61 0 obj << /S /GoTo /D (appendix.D) >> endobj 64 0 obj (Proof of Theorem 10) endobj 65 0 obj << /S /GoTo /D (appendix.E) >> endobj 68 0 obj (Proof of Corollary 11) endobj 69 0 obj << /S /GoTo /D (appendix.F) >> endobj 72 0 obj (Bandwidth selection on accelerometer data) endobj 73 0 obj << /S /GoTo /D [74 0 R /Fit] >> endobj 93 0 obj << /Length 3979 /Filter /FlateDecode >> stream xڭ:ks6+SIm:V&l@@9e_7!)J^Jnt_h Zݮ՛:{ZʕHB)^]ݬ(RJevޮ7*Nڢ[+|~춳;Q`h;[m="mCKڭ?^u4a&fOH6-D]qȻˋZ0F"' BcBzῦy*u (#US Tpo|-[=Ltdikys@<9a⦱; Ʌ7g(4B {Q^ޯ PVuQ|^֥%V7::a/aa$67q]-a/& i ׅ;X/.JƌBqv5y쇫`o,T l=v ,սyX,Sruy$ 5- DI~ j0aƮnC<0B:L#0R,mΉqtHFr1ڬq®zw^ǡ'VZoDoyIAw~pkRo{we_aԻۆt{ZށEAlmnxsY!RqO}Qv<!`zGW $u @vzV_v-dQL$ޖ gbA[U;V t;hJ^V|)ji\pIֲMyG5o=߱>_˵cRrfh$lނ[92))0AҡLĄ-MAc)B}9"]?Xj!W~ɀs VeG`(dԑ$uk' |0uC7J"]+\A络2x]4m_e<9 An}c-Sq6'D t812%\֢ nHY 4䅍wh7<!98e4^cozo:;aSylss(*dN3z6NFӘX !ixN?Rl@HW9ɲ=1h& .AI>e^Bg1 ~w\ԽK!#\U;얠=8;Gq774e0 {>)iR~~ߋ0{x/_/wI3>Q8Q>v]g=VAp<-k|my$mS|__ǀ/-=0mC;\e5X&8nThGBqgk(K|!3 ؞~H<а`T AROQ:yBPŜHHqWMdI*MX' !ZBR7X qwӓI"Ȗk],ymaj[TsJmC+c ' ww{;3NB&O.S^Nn(QId~_k Gf7:sݾClc-;Σ!rv=ځu$! j_@g}F)uaemTm<-{Hm$U⧷?ݶeMD 9HM+} 8u {z9˛K9w 0v`&/dGθo ,)A{ndyE{y4 d5}-pu/o!2RC0Krr1~R)d!h2fy~5~);ҁ[돨QǦooj0n洣O.JAg}Fj2gY*Z$El!