From 21e6ab4d640d0e5af6e1094cd4b9baf880e44a97 Mon Sep 17 00:00:00 2001 From: j-hartling Date: Mon, 15 Jun 2026 18:20:33 +0200 Subject: [PATCH] Progress with cleaning up "IntInv vs SNR". --- main.pdf | Bin 33850967 -> 33850878 bytes main.tex | 147 +++++++++++++++++++++++++++++++------------------------ 2 files changed, 83 insertions(+), 64 deletions(-) diff --git a/main.pdf b/main.pdf index 493383d778006a17ae41832fff10bfb580ff1995..81040ed30ef116c5c68628cfcdd3fab40b1dfc99 100644 GIT binary patch delta 25443 zcmW*RRX|qF76xE8-Q8VM(%m7AfFLE^($XO1M{J}v-Hm{xbT<;xA=2F)0!j*;pK~$K z<=joIwca@>0rxQ~0XGl?KzI-VL=30i^H;Cs*pv<2-zd(Z)N1f9SS zpfl(Kx`J+?JLmy=f?l9E_!0C0eL+9a9}ECLfiN%-3<86}5D)}I!OvhA7!F2&kzf=E zfzelL zz(H^b90o_gQE&_#2PeQu@FzG0{sO1L8E_Vy1Lwg7a1mSrm%$Zq6oP8vwlo zAa(%a03c2P;sPLU0OA24UI5|)AbtQ603bmC5&|G$01^QpQ2-JHAaMYa03b;Kk^&%U z0FnWqR{$gnKym;i4?qe4qzFJt0Hh2+Dgg8vfK&lU4S>`E=nVjA0FWjCy#*jG0MZ5^ z9RSh=AUyzj2SEA&WB@>h0AvI}#sFjjK&Aj>20-QjWC1{y0AvL~)&TS#fNTKB7J%#k z$R2<6Z0C@w@M*#8xAYTCT10a6@3IL!_ z00aY|KmZB?pkM$B0U!{7LILPA0EGciH~>WeP$U3F0T2X0(Etf<;1_;h4T^|G5Sci2O1{xd62qKlvWhhLavb20 z*|=9jB`Q(YIVDb|AR_|*THC?L3;FlBd=LAdE#4;>?Fu%%b~*J@<%13vSTlJ9Yi&50 zERWesrmlde21wW+eME`l_ePR?WYcb36MhC2m#98ei)U^2P2hqky?a}%m<7{*zi755 z{k%sl-b7dAleq|tYn=)9d^Iz$vs`@akxs&RTvWJR=Vi0Z*zjU7lHk==b6GR@-%R)6 z)iu4I$LoHeml}2JoI^OxU@V=3;V5y$@Hq?fK|=xFsswL>rna13jdBU7PIxk%GMjaV>=?Ik*{azhazkJSlJ>&x>a&vzrl@-fw@?QgJrJu6`%N|y z+|X@p?utrI6Wnh^beYhJ4f%Tx7Z|kQB%<*fyyM?0x2J>_G}3rN)e)4bsto=P$_cyS zV>#U~G4A?kF`)Jz{%n48lj&DM)Xlv>b{p`^EC0ds2({EK??=WqXqqx|p=Qq4!g_`x zPBAw(-}2??WA2GKT%TP3tpeU$6#wmzy9o^54@Q1uk#0}kd(C>G_B}hCvdIfD4R~AV;4af zL^2Vm!Hl9eHuZNfY zqNyn)2ac>1k+j$l-3fUy~<)RZ+$URDr7Cw;g{1s;81q{ z-b!V3o)UOGtS`5A(|x6Rwg;nTJ&>+3CE8^y)E6J@&^y-l9QfU2g)cyweoBU)A`hA4 zw7}`!PY$k@2Lg@za*?KkmQ!$8v78u~XVJA8@e`x{h##e4#F(@i<{gR{#aLTT*fz17 zN?VjfdO=}9vYg^HgC7oLn@}@ouia!A-?0=qWn8`2NFtpqMvt{6MQd;;k}xOYG$U2! z9Uz_dJgiClZSaPnEo$#ribZCUAYB-fN;HRBp;^M`)jvet<+gaUaz#Fm#AGs_Xa#(V zKZB94KjC(>z@DTa-`cLmR1)^Hu6Sah75Tb}>M@LzI%35_(OjMaT9&T00*gA!-Hs{T z9-++b4~dw9Xb3-Z{Jj>GwLi2okBjVvbW3}2xD$MLq!cFqPGWkeTZ_3YvxyRObd^dA z{S|K0UPiO(bfBsGoA)K|k*Kd!YB+ms=nSWI3$;e@Gfdp=hepck*~@So(rr|)T38qu|I3~I%Q~%cp)Af0@bA_qB%Hk33@@#Ro@vy739doqH8uAqo1D3n@8P@h zWS?0yzjXfi_hKYa)Kb&!X2#r=Jba&H03E=|oJiW9P5K8HCmfAX_KnnG+GdkVUHK(y z{9J7foRH|kw~W&mpks22+SuLxXF{5+3w=WxPA%-)J5mZodgE^WQvT8RRXAHOE7PGJ z{elQH%5fjQ>NS5Gjq&;g2t?bDZ_Y8hj>)9AxW`p;KSdkjR)S$^JW5)@K<2kN zP|o_ep2Oqk-rg&+hXy*$913VJ(j#xw!_M43s|!VaNJ;Qr63?RN_R;>~PKl`>sgZX7~ zVWmpGI6iLPpUNz{jmin)7z`W@*`6%6n#$fJ9`u@beemV!@!{djy(PJ<9JtCC65n8O zo_KpK3NnjOjlilo?GHEd72u~W6jY#9d;q22>vvo zi#&A7&-)`e#7|8;7^k}cD`Xx4E??|qwBtMaro$Mn4K>48#QHW$E_Bp5HFXd!h9>Y= ziLvI@+i9J{qO$&u|Ni(qt3I>Zm@i?NhN>9};=8tIhrQ;l{Nf*8%-OzhEy=sEOHLv- z(x}9bzkho!R_dzv)n4Z7q2NZGWO?76*<1^!LbAqK*IVx#&7wL|olQ5)zOX-tZfOQ1 zzH`f2*O95Z=uUL{!jwT+=(&j#&TGr^ttxSWSYp8oQ6C~k0*6Hq*rcw`*3gY$y3O4f zc@@ZXa_1AthpIokv5-j7={`~-(vDuLE9ZQ4W{2(8a{kcpE1Id1Tk9|k;EevcTodg2 z+m$+28f_vx>a;L~we8||I9yI|_mSNKJGh1b2k)O|D_Zqmc{$}?9kzD8>_~e?tC`=4 zV@Mcnk{W06@3P|DRUHkEzf9VZIGsnE zerp4MXiLQ(4|T*3Q6xn<{@J(uDS}V0VH4MmpzE#=H;+)PGR5YVeLEA;>u&ZG^`8U6 z;)O9-{~G@&xp9fy)mrMI?zzp*cgWc#%MZwR4l9{kFs*AM>vI`%YDwlL+%GD(q7Zb-Gn4a$hUmq;!rl&k_{X2c z`cN%vw`&vF_GvZ0;yOHe^PX?5d6Ua;>yB#PUgIN-3R+p=F_p>;FtCE1!|=(_9YRZ_ zwC~;vVaBw7(6J=D75=lCRC92;=jxFf;7-8*m;bigvrQ_#ko=Qkz|Jg-%}~VApBH2~ z$`fkK1EHn%g?Et5~%&{urYQG85$ zT^H*5lpJmK31E3C=PN<(P5;xVvH10ZIxw_T4{1yNJzUhy?AG?DOhdn>m(eWAn^apy z-|CLNIOZf*rZ#H+7$ZAg7qwEPu5pa)4oX$JI3i37%IdwQGi>gG`F=v*cq(20A^9nV zEyK4x)rV*fL0Y_%&V=>*I{y7*^NPvHdo6#rxZ*L7Uw&a(wM!4FG4m5Cu!E2D4f*sK zLNcdZ&bjC4tjl(xd+yp@4zfGTpCeTugUXh6zlOos+A912y8@!sC}Y^>p52uWX?!=g zLGD09y+c9|+G9u#gKpB8!AJe;%Y%nE zuNNp@jUpC{G)eA0If%-+9-_Rs`OW+H*DIFDEv%_r>dsrCMufcS$kgu(0AVi6ejY%G zz$e0=>+)ZD!Um%piP>&EKdnm3%18FHI{%6iOzGIIPPuI^>>lMl>EY0dRQ|QGaP==d zaB);>LG;(&zIZA9{M4j~HGy8g-&fDB)Bk3}&$a2SGyL?*`{zpT=d~)D&YKHEhEotb zIc8_2_g8jAudtSPM5Ju;s>Jc>BhkKw^J!=t(@o_n3m)u`{7UkJ!qED|uE`4~7N_ea zHTIBpj!R!djVHrn&czQ5!S0I2Pyg<5rU%Q5R<-J+e*d#X=;ECxB9h3xcnn->@AY*1 zclqh^EUe4_wqp1cMCG$QjxT8QW0l2Y_E@g^ZB6A7V0b#Nvzl5Ti+$y^>KV4{vA8^f zINskOZ(I-aG4=S9cDWSocVvtf7MMc*`S$}qOXE&#{G{O_yF+(4>TtW;1jT#^4^qW- zrZ%#(8GCeycbHpL07}kc3j)b)@qJOtJ7kmioP$^Ivp}NP5$bJ#l}ZG{up2{!~U`UepA{?8C{ls zdAXQLMtf@;oi1!^F5G_NfD5lG8GF&fFv-~!#ZST7HCD>lz0!M`{aPSz+N3qzxOGsD z#R}eVf#cJL$dEDqdu2u!bPe9o4ia;CL?@dDX*s;O#ISG>o$t#jQz9NxXSQcJ)@svr z#aCGoSPtgTzsTo|MI^D^$?ny$;r*s}?uL`@mvUVm`oljN8ym;sT^6QKXT?#H4L&nz zp3-KYl`!$YdJ}W^7T1usc}^LhEty+@l-vsw3C`)V?6;GxYMS~S!LXn8(rGJX$1a9ShoUOa(c zr{eyS*va;hk!OZM^^83e@V_#!Dw6#&nxz~x;9YOA>yobKQ!jszth~w*9ekRmN7TMy zIWCN0&6e9CO{TzPVq}I4A7(yCX{)ax@DUZhz!-{G4*oBWCpmeki7x(;UP2!ts>9xorV{)w{6dFBJxL^KEUKQq9NdR< za9YVy3-?GPL4jhyrvo`MO^YL5O&?nNO<;lxFXZHgK~df#1r#z(vtIFr{s|ki$tiNx zQuGY>wdA&7>NGQ=Nn@S%71HX5y)B#{P%^7mliOceW6B5Nw2w+u5HgKhOXU1fI+nV#7II!uqz zm1TX`G$E!|&k`Nn3Q?u&74D4xuWaP)?#k_d(SBtyS%_g=%GYbfx4NDun&;4bf70Td zI3CEO(c<#&TIKJ=F}nG3lEdKvS`2?g z?CUE-N%yFSAA$&XtN^dhS;DVLF#VFPo5YSC40*Ded}vT0DmXy-*yLU?0_!GxS0s}$ z2!kr7=iONOqgggH4HDy*j}iAMD0CQ>NLpX}YqI_7rVivlsJU8cd;!TO_|i-aP$SHvHI*u(+ACaxW^CvJ}Ha591g&p*8KR zjI__MsBkq8hB+c0WfOnv6_Wg^`l!mte$t3aDVb&Pv989&DXOw=N=FgTx4$^1$Yl^N zvzJ^@ZXI(ui=SNWgO9>WcTf9JrF7Vo=w!1}uhtOj%czaxY1l#U5`m@=i;#qzn7D>y zj-OllQaiIcv?oSAZY8P_-3_aDBzbiLlYRaT+d))V8exBV*q17P`ohyv}yP! zZYt8S;2X|$3#tR2gpDV&z83{Qu|wy>?VTwKF`(`}f@zi1q!&83P z(TrwreHZlnyoq%+?^<9h??TX1xd>deniRwN6RnRizrTx{D*mX#J{OMP9;Nz%=4JB^ zvx-Q=k(6sbgoO9PteJ6`Txa0nt%ER(w6vrV5u-{%fWvd=kGtJ8o)0-yWZx)4nbiU7 z7QH!>F~bDEc6=)bE;0(7T~irvC057-y1g!C*{g1K(g8NFZTB}Yz!*`?D66U9XK|y* zodi`k7%8<7XV#j>6*yld_~ItFsmC=N?>E~QHE>H>63ck9kA^G=QI<2Z7ZIAk3H6A3 zlXVv@fe%}h5L&2)$>SE8X}=g!j2AuhDkW$k&5<|pX2}&+7m`;^y|(!+!`&h`>=4eB zTEG&C`x*yULgqlv=<-{&zPen3*YI_{aeP^W72Rj7)U3WMVz0(a?hlC;%kNPaCto@Ngu}6I z`CN;Z`b+o-FxDSL14gWpEm#AX9XK<*Xvw;{VP4Xd z*Ox7h6-B`&310>C^pbBa`}ebv?;6KC8x!uMEnlD+z}QR_S{wx;1i#~T0G!)D-*4Ob z4<4Y%R>-e@;p`spMj=`0tJytY{@cyfo`scQzs1IMjO}wx&~GC^Qe&IBSFqOUeCcG0 zEnXU3A#cIlk?UxUVPqD;pcllxWn!qIfN(nx(bAz*?Pk_W{_`&2Gh4ZgK*&J)rDqa4 z4K#iuh4qHSGjo;{x*|{EzN&baqs`y`>Ju-z`Cq+6Boo2eU6M{YGMRcmzy4r9 zEN@Z!W6YHrjrq5PgU=;o-BB@4$?GOi#TFB`C}p_AhAHw2OIMLB5z$nrQ54SBg? zg3mRIsEU9JugyN*HF1Q5)A&>XuRMqu{~-byCYc&k`tdi4uyiR8ZC*b;iON(XO~8H6 z`|du-mR-Vf@12=i|LdL?!`v_0WK%DkTEw)*GDuZIC)bh4rin(9n|j$eV#i(!)Z)EN^Oe4Z+to3Y*B zv-gk_$MD&6G{@7?a}3{Ip+8$CsWfT(dh8dR%beBpKql?5u**yrEcso-RW7B<66Kqv z?Zg0`om9gzleHuG6(bUEESd4ZsqCt(RRQ*3f8fs{iSdNEs}*lH7kvIX8Y$&u zK8@V=^5M6NLoXVYgg8+PN9#2bqLxcTzLkua>z^-oIa4V4=sIks99bb6H@yM}quI>G zxH1a&xD+q#nD{TbEb7V?3PxYKP$|zyU zG;Mj6pbs$2)PB6?(@$eL|MwXVFq#jh)SE^8NkhREQNWT_nJ&kN|CFuw zAx(oRWR9?fZPz1x<)Da2NRMPwTzwY?9pL&O8WT-UbNB9jHGj_>i(EVwI`2T@vgTUb zd~HL(h)$|Jpyxki@xvE~jY=!h$-?m@(#ddpcJ_xN{@rl0+{*@Xtz!GnB=M$I`c)1_ z9h`x@|26b{>>a9P%K}y9?@C|WBj#LK;NxV~mdy~2!SQ%JD;0pHO>XZfAedQKZjCxVe7f9s=%z#Fsn?O84b)p58 z{gVTPEk;>L(uM>n3BR=MkOJP-Ez~Qj=nsDl!@9ij)3K$BYB#xep%+LjlO%)Pvoroq zXUf(4N6K1rp=rfSK8$xV%IY0)>$67*^d!iuJGb|ZzmC)=jrcNo$vhF=Z=O`d#m+NR zRZ`_?ARVb6uB~uHCHeKl}sU$4)Jz_l>xxIUl#9-k#oalICs^bT+E6S;z3FIwqlTU&-=$*LpaBEJd8@M#}QGpn0zWv0s z)LZ&GF?EBjJ!GrfpVZMYNW89jp1u~wy2sEocFCv3=pH<=GMMr`7LB4V8wr%qNn6k; z*rW|hkb2^A1)CPDZGJ?@NN9DR!4c%jvAua>xGEQlGdBoj+HlTE%2B&T+uewI0#5#{ z^5ybSegTMbGjH+$0t69W{#4B(Tvk|vu3GG}AZEu|6}Q_3T+QrV?Xg2pksXdq{CLGu z$ZP=>#&0EpkyXZrzhC8iYE4GzDQG*sDRat4#>P%BpGrL{M_D$PMp7V^>fy^x+w=#$^OR&~Vxh&v?6D0j^2fX1ct}sM>U*1~ zffKP7H2HMeV6DNV9;@6UPQn9iH7&t>ZB5O5T5Gr3{rV1qu=2^xh&f}9BL_01_=Kw4 zU577-=BgFcxStb@XQsdXlb9365zL!DGFuIv7r=un8m_YSUe$TZ7%I3j`_rz9oIH?C z_?0@9iX$;pRv2p-8YUNEH=mt_rORS(FcW&TbLY{KZeT^huk&D3h+S-OBeXU-jGWf7R%haa0qDXg~hyx2@`oGvd|i z^I*Ty%qj`sAGJCvle){r?>GvzB`mWW}Y zCQcLs4(#QdvXyEIN9Tu_VB?AGf2|(yCj&81pev8hXdrvqp;fi)f?DhlvxX5gIOxxyd_Lk{n(tF9wz?b1~UbJZiBkygkP%J>DoOf1C^G zf<^NC*KO5{(dy=JNC#mij~0$;vCVBDnai3?Hf={Yo_>|*psUBPf*DS4>O>j*!^Cf# zP(qb|f!{NCYZQNre}strhflC%Ox&J;*%c+&^xdiX5k0YPEcXch``eB#+#c~CPwA{b zW%`>7n&SD0TR;qCp?V9sX}6J8lUz?6l#AEjP2df^;S2(!SBa4x{-v363x&?#{=)F09JADD`ngeMB0~ ze;XNox_}NdzY=|=mDq`3C2Q~_7oP04cTrqlGtf9uS#WF?k^hGpP1hi=6wU;8XmYAc z{#{XD+5K^Rqju8fw~)NfY%jaCfp3L-3=ys?g#Hca-~qII()X%2b@fp zqZ;noalTUjl5++H70juv)>X&5VCL#%OuhKLk^XmPrkqn$BU?tm&~G7BPD5`3CqJR= zL+|iPugPBQr}l?mQK_P9a++}iJlPz}$4Th(r*vhSK3uEmi}L+L~?>sMpeF|i3U&qYzC-oZ>(=VJi17Ow0Nk%n*V z*eD2KJL?TIz7X@8PMEiPpPw>J6y zeoR6=@J+5t&aE+N`mE=2x;ZH0ba2<|-j3e*;=f%4vJZpa^wa8jeEiB`c8cZ}hn?p0;GNw#6uL z-NPYF+ZBeJxnF82Pciv}@fKO&^>@cUV`M|21az4>xWb2J=)963ayFa*95{ovS7|-hXvsBJTTwJV=Q46&_1P;Y|{= zVEa{n<6I|gTz;S$DZ+WXOF=6$LXa6hZga_c?ssXJl@+b+QR#BnoNxMsCVv!x&x33N z9uVxwKkzuJ6vs2DjMKA9<@PSYZz+z;QC7ib@CK7?=`-c2?? z=41V1488sPVddE{LaZv4bovOQhCb=` zYd+T>5gn+f>b=KdhtiRF8BTx+laRb(4~kgcuc6iiziqNx0*kGwU|B=zvfaUlvs*?i zSE*Bd(Rg~7`js-qebk76$CuR^ff^bA{BYmoNgK=yAv-mv)21_^qiB@rT2!kg#12+TnuP=>UpYi>1CI<;$|%Af?}`Xt%;e&1qtQk z&##Q?2g+ExKe~;>OOJGuN_R`A9g$Lo@56?>H9=}k+R%b-*}~{AEnL#Y^j8Ji{Je0m zeHjLwq(w70#Jdt-pPHRD6kVP8Act3h8xq!8Jes^O&#zZG@tF*akLbYouNp(X^gSVA za)>!8Z>8ZF4a3}}C4zm+tV3A_k&99ar^@noktpd(`k1*Ad~`uA`aHa~)=I>)SFjIX zyN?+~)(&5Yc2pqI==Reow|!qf_CFBI$M}S%DEEHptuEyh`VF=?wfZoJGv6j^oA-9O{X@TS_$}WA2K-EW?JAazC<|Z1KBvYbcp|V3a}7 zQa$qKf%wM#&xb!(x=h8192*zrl53X}Yn3Z-89Zio>g(Y=f3TTNzKi^UdFJNAHZ=YH zg{c(jiZtgExqV7tz2FOL!t&C0F49=scmqFAAAq?01D0cJ1L(p=C%@;9RNS4!G z9vAd^)5qL8sVI%}d1;+^y&ycXvLn}eC~hXV>M#)%KJ{kEMu52F09^(XhGL2r{_0aQ zjlC00e4*1&*ds}kG56{wD_b(APb3;37>t%^?ys#BjncY>qpRAP_dVrnv^FO4_B`u#@%y&c-Z<>wm)t%7cxzMWP}T+(7PDp~A%V>D z3zQHzJx8R1*jxO?G+KdMnDg{@J2Rayh7_!b>m1EA!h^RaDiOquiop(1<&sl8rY|~C zj%Jal%N-SgGxF>HEI?>9C=7H{^J50VMN*kBzH zK5m|&kZ*}%2h6lf7#-Ptd&S0xe_b5)Q=VX*D@oeNytGoK!2oj2$(ejQA?)B~7vrP9%;2%^7mnPFMx zMXTO5k4AjQqv`tCaOFwvk^DlZkUf|JqfA5jhjj8NiN6c^``Q>ZX`6GzxSlwjb42_Y zx`Wu4!=h*j@5Z(Xei4)hzaUF}LlCG8pqJFlcrVN&Mi>mj4hgVcT-z}aAAKQd4V)dc#V5+yT$hzaG+!<`As&u=#@N~ zOgZa4ak#J_Ou?nn1Ae3Z!sXR68sUozz-yn3vSBE)F`-*iag<}8C9}g;VYZe$YLx90 z<+qwsY&xwsU)YdX_GaEz1!4IJ_7&|M^1_^#8!4x%dA~}S`Oq|--Ci5zO<);NXsvu% z?W~NkF{CmZ8uo1MG;c@`#y(ln6e~K|tS>7}fVrj@>MBR(Np*?6syvO6R#z<^ z^=ijT$EvR-saKe-8^{YXm#Zbz^K^`^ON-X&ZjkdWli%)4g>wvgqZBbUSkIiySn3xF5>awi8HhS|5z+U9M1s= zgu-t_pb&MfsJjW)MOYKLf;1x`PUL>F(>B&5g%{^-;E(b^sfU4DyRxm{o(zZ1x`b_s z#@^)YIKj>Ag6GyXHZIy%g;Ry2$vQqNw|0a-VOlbOE0R&PqOFI~Y;WxLH)@FIspmr; z)c2E($P9s&iFw_lLvKy;dy*ri+QgUFp9_iP>^@$8SJvt6I$p-1Nld_`JTH6o5uu58 z;?HR9Y_<4>N%5w7Qu+^@_bJqlzhcrDMN&DU0@ZJCGgd2CG8|Xxc<0iS#HNisOAiol z*nMVS= zX2SPu|9pFg-p$NT(a_c}H2IKbLxI+oZUI~K4pp-19DJhA>F+%`>gv3}z503Sq>nlL z-@Ti(CrLr~PDFfZO>QYj4H##_(YuRvWnXd$({kkIBa%m})>3{G-)!(IHp_(a@6GaD zwf^{px2^Ygn~zjZXP?6+(q2}F(f7NwUC=XsonfMEq9o+~`>$YkJh1e(@$dP#$!r)b zFrh$O^7HB&-cFMM`!!7K1HIE%Uys-r`a^hTD3nv_1{YedgOcMXSyRFZ3|$z~{C0Uw zlO3MIUphP2hv(KEAoRt~Z*Fpz4)s|uFU(^*kh=UGk18-(HKQycHjGHXRb*TIRO6)> zQ3!XEg$8{#Aernbgkv0zOc=^`%@9A<+U$Nu6*h660^?#(R_V%-XIDvY#QXZM`X1Ar zv#s(bN7jHch^2l*CCGKe!lkxbk(}mf!=P8n&N1n;G*ei!YB6y0)&F(&C{uvv{Q?Xw zr1aa$|2s6S2;74I)p(SM@T@T1*Re~2xSeNJlbY}r1HP||>4Ahlq51QFD^7wMZ6n?p z5GoBFx$RK^+Vd0{K0TN@fY)BAg>oW}N$EqmfT(jH`7YSn8LU+iD%R7-(^ZrBJWi+={zV5#`Fgyb&x(Y^tPQpskK8DH=-+Att8Gn@BgGU>+; zkT_H-5%H{j9@RwmdquLQG;O%CY*wV9qGMkh=E zSf4jdMxc_-717Sl{5~0pKL?}LX5r$)akXC%zfX^%??Xvk}xV_4y?O=f0kM=KK zh-!IxhP9$^yhZ$?>lY;nXTx z?=;1XQt$<8fXYTW&F=TpYL~WZSav=(z_D6hE%1e>FoctBO8ik$x(~(j+VoYG-;ZFoyy9S`YtW7OIe`A}SIGDX&4f~+%dex3w=TrL z3X?qw|Ep|1t@h9;0YBI=8J3fz)=>WXAG5UyLO)BqruNPpyxxxoIz!wW$zl|=a z$;qG?32!m344JIzkM|W7H}IZkx9U8#ZzhljR5TFoso>?jl=#*k>yzWxj$z6{XMF;; ze7d3U&H`Q5ipGcsNd&Ml>r^w$7*SaMd=gM^f=m?_Jn778%g%J|mIO0nXp$)yTdvD~ zc-xh5Y)*_Eb!SJ(_IIf&RpBTeY0gQtvy6;9d>P9()||U$-1{q5!8K6)1UQ=3>-|4| z6|4VW=;}Z6pDB2z@R_gA6g^Y?Ovy8)&y+n={>-;$DxRr)rs|pMXKJ3QeWvc2`ez!R zX?&*XndWC&o@sri?V0vxI-co#rt6vRXTCqv^GxqEeb4ki^W&L;X9k}cdS>{Uk!MDq z8GB~@nTcm6pZWRB)HA=HnSN&Gnb~LNo|%7U;hDu}mY!LDX62dHXV#use`e#E&1bfr z*?wl{ncZjhp4orq;F-f`j-EMw=H!{vXU?Aa{ml6@7tdS*UHWu?0QLoVA;HXzEO>Sp z#X!xcy{h@9z8!{>WiD2|G7FvrEh70^A~DIG3k0PgLW@=Sz?dylSf{fWd7Cs#XdEK2 zu@FY*%jJG_aBy|0VN7;Wz{+xm0(zj#DM2I%aFNeej{ZBlJf_ik%gYud_fh=SY(YoxBm)g+Y?P1`Ha z-`1ZyG%`AtE+3na$ioafH*>uKiAb9ufg{O|eo&w}U$!lZ8p> zM48_Rmq>mqvhHapOPeN}d%I~f@`=6Sv>S=p3umjJb2N}+-IqG6?Pbb;*cUT^g>(8Q zY$vHiGDg-Q{}YHbs{5YC5XUmNOX@@NLbw*05#3wHF2O7#$`(N>>4+!;2j3XomO@z@ zPnDCg47Kw2nyZF$_w&r3lW9 zf)gPXwCQx--ao~i{9A%L?a!#}VI#I(r)6dlEWsV!q@+qnb>?|$co=avmQ?O}gUHvI zFX{P=roVA8C!}!D@zLT92Js-IcSypQD%W}-EeL4VWSUVa5zMoMIkE&Uh*uU2GzZBw zrs*(7C@>LVM6?g3eyI5x!H2?VKd`M?g2ii1+qAQS$m*TZAj4jP9?4i%4`X|a%B>MS zqnt<)r&-Q-pHEjv{LKo@thga`#HzNzmS+eKzwTm?bh}}kwH;0{M(DiREO|KU`cR~H@8%{cVV`Sc z%2BL0g46(p-rek$JiKp(HFsv`s*_}MvR>!BF`ZyCHF=u)m*;}eASpOWG;}b)`t%X3 z-DLrLl85iRo+Mt{Yuxq!{WmkV?Xj5DqkrTkl5Hwb)b?+SYs981C2^;ol}JGGM2o-V zb~CCdAo6tkw4xaIL0cIU{*Qtp%D7qiHd@-r4%$0P^ys2`uD!WpSXI%;F3L3QU%lOv z=!5mbzjubWx?X)^^BYYTinBEFR4=L9y<*ae3BZ=+_`vv-qzS*B;n^TA@%f)|MBn1frrG>*iqfCmD}B~KZgy3=lT_9 zUICt}IsdM1ytTWAEnz>*8rdFNc)K(Yg>wIkU$TqYcV)2`h5DSNPINuq-Ly@_7Q=G= zz3=Va8sPM7F8eQrGKbnV6;E=RlLaU9UtFJixQgbkRNL$@yc7O&cx9zOY{PL?@-VXP z=Igz|vN6&#yo;CA{DE4;7J=$^gKze6z9Xn|!p2`wLN~IY!WV{KRV_nl6%${P_&Zjw zc&^GuZ%=Jauf=nkdSZOMh?Eig2qzljWXwad?Njtw!2OZOrxg=ZwWS@Ys->OGTaU#Y z894H@MWl>%S+VTwE`8#2yC*@v4*$A+$v+|SotX_2kJn4iUAK3a%&Dn-`(r2b_G|sK zW5Fow{mhr~=UK4Z$!Lwsv+r-31fM!%C2bEB;vJU zsyt+8txK8H@!(1H(UDTjT5refX{X76Te8cIn2ijf{XXu5uOJ}p#)rsVWRWGnzn6S84w3{$;aDtalbs(W(^f01~we;lLlSFALsP-hQ357RbLA~qLi zdN7ENZfYDtT&*q=4$~?k4^jE6U&6olVG$BN4JTa|aQyTReirz;Bu^Y{;>_kuZ2szE zN+=~?%p}#O0j}~lqb9B>+0C`~e+};V2y^`OIBl!1!+q~9+R&r@d$qS;xf+#WF2}p^ zW*gad!BXUy7(Ht>tSuOlYf|6vc7 zkF7lIh2=byFc;6&eAXcfgWt%EmuZu@ap<38{3wX?XV0tA{AJSejnmm z!BxNt_sV_~2r7CM{g!w&mlz9Nd~azRCK9nZ$CSu#7j{Dt?fV&!@*QoTFREX1jpLT6 zImqpH+44B8*d=tXl6`|V>|f)7x8Yw zao&uI_zPnvIr6~Hj4+bIa#y9^1-;&CzGhe0363J2fhvNga~A#uMfn~6UplsL%M{xS zx>S)W9@?Zznti4+RIl{q(tNaifKf=B#gTysI$i9ulil+X;;{5-N|HfB_>sbEzb5>l z9OKjV*Pp#>I*M`Wmj<6WcAJ*DvUeK}R=J>y2lv&cbg#UlG@Y{=o`2SC);Q61vYKHq zN;Nkfg>3YA^lEV-PjJ+%@GyX_bxLz>M@@%K7b<_CnCd}fjrI6k+c#B5(jsd<$~+T( ze?BXcSpVzi_Px(hj>PTKwS&W*BG-RM_o+Gi!yXITZuaR{Z|&M$!9e1`m8cyhmd@R{ zM(-@d`^T8X)o2ond&HDC_n4pc@ACs-`u=PuXvMzwt=Ww>CnB0%Ub7;4iz5mSD<(}s zH=ZZ$#`PmtUcC$W%P=pUfV@lon*gylvNv#7Rrl&mzb!+Xwf5|k{M>Usw+l#xd>|o7 z?9b$AFVQ@iiX#8p*a zDk7ao4}x$D0@A?%p$3uOAt)Hyu~3w1APK$qUPFhdNDW0==uHS9RYDE*!F%5Syfg3f z&OGycIKR2}%vA9nXTdvTDwD&}9J`JI0S9#zahLuXOA^*i7-v)g0K=w+b|y}*UA z*X*qx{rdRc=k-&MwQ*DG{W!R{J+x>q==Ip2lWb$@Eb)S=hFN&`Q2h zJu_SJ+^53u_OXAV{)gCSyIw^7o^2t}C+my{Oc#?=_`cJIUhT;LQ_39nEJXF)YEb+G-##C|67w&AS(0ev^4 zf0jkQn507}BsBb7;D&kPk)QXN{(cVO`f-+{dyUmwgBEzk+Y&k5u*xa>fcX4A(h@n2_}?D(acj@XfyKFZcWY=(^TvuJ5&|s%y-xyY*k^ zspU+p{9(Ng;t{%+BGas@e)Bi{>~>|H&|b(-%x?x&G3!^sp0yp|(`)Cow*@ZETz*V9 zV~<{q_E&vOe-=1_W$zUo0yHQm@O-{X)$OyBvE%f;s)zm(^NM&@vhF$U=F&fOZ$I=< zy=7${WS#lUR%b5Rk<8A3UX5q+@^d?mQj^5EF)_Es#`Hnusgk*7C^P4@m#TQ*@hlAr zEIhixE1tiO;eTxCDamyDW9Xl>)~kW6lRv@C$ML;<5yo!@^SMr>e*r0sOs8S)pMciN z2%vLU{+oO>>t-+0Dd;c0*HD2vb{|PitCkD>rn@2@fk_jeq$6VI{-r5{wv0n()Fwra z?=f~LE!EP9lm9WcyQi+Fy1Zx#*&?CQ=x`%V%J_MtCFlo0Vhp=Q~lM z_Z+>?$C-7qt)biM{r)s)`%wlzg~!E$wr6=vA=WIwHr4v}th9Y2Rc9qUY5e?H@mU*_ zOC_p@7>QzQ`m}S_#=A^CsyP^Q7(w{^^6*f3v>TvmT=Guz$%Hbb?zKwH`XzMuKcm#= zJ9YZ#cn1*e?tOv!X`bA3#_1PB{Q_4Y6AML}tiK$_=Hb?adtYIh!FLj>Y!r1(#szFg ztyQQQVg6?N1dHOy+2k4y7v|w|k%Eu&mE9R996NiLI>Nt9G@ljOo>nng{fp0~yW@Ze zvoVe-B}%f<@!KeqA=`W0zckWp6$Ne-(dnwd5!YdYF-?=rMhM9x(}aW-+Km<)-5Yw=Z#CbPuuSARL{>U%c*;TD$AwE ze93pF5NftgfHD2X7O+Oj&b(N!_~`|0HTaY0{@#yb27^uI8ki(S2<%4L!SRy}-AvNN!i zkB)Fm7y!bY-UJCwQe;a`saa{QN*znq>AEuo`23(o(A>Mzt(_!7Dc zRH{m}5+V>0h?scFsrCgb(0@w!`#Kk>;J0-ZlqAHYl_eC!l$0P65Rpd^h=`adP^x0mZ5&~`xeQ(|Dx^U^i1*!|!>r??c)B#gI z!9RUm;e&>{_H^m@pKn~EyAbp8Y-90G#B~YSaMXy>4a-_@?q#16p;11pSMqe9d{fGn zv`pOSldVKi+ei2A9c_SR?xpo`em10b40@Pp82d7isGZs*wfkKd@>A`3J-(Lm`cfND zI{S$}K&Cr(uGYUi80$g2MA#I_(?J97IlkoerLO$66$`53H` z`Y=J;qm(Cwcv-&D>0@#1X<&l`x?$lw(##Cm%wM~pSlfhe_#H6uHfN#|HdUwT(xmTF zt2^c1IN_f)L1C=*DVvZ{Sx@0-jED(VY3HH_NPXI*$raM(C)v#~S!t80tpwRO&y&~r zHvF`wdZm0zn|zlRM}-)v)|TWUG*4gM4rA@OgFjfTCY8Vl`R<}x z2{pH~fQqBzrxaMXj(|md<(rEI%0h9O<__G89eOy-(4QBhHC16CRQI+?;T5yVPFX13OP3BsD&w4%)M)94LqY&=SWZddiWCvBP=tHpi!;%r95^p_t zMxtTCdepGI5G3C)C5-8%L!dC9DN9Be*X;V7BBlO0Yq#p zjo3!1*f-Ztq1(_bE07|;Ux~7LGFFonrpmqT(4)G6x*THTA<3_Dht%;2E1E(wrr2IOR_50}i&|D6tEmtyc2u42-wuGN362Kv%nCxg)qve0_UXYE8fO%2y;qZ{g zYgb^$d}Zad-L;P3Y92L>EJvgrCA;oe<{h1lTdIw{2U*cam@s{3lzY!icgzWa>^1g> zQSP|FA~z{j#&Nt33V5cEbrz>3j^oxbe07JOW=Y?){GJn`a%0);c8A-AE6!4iRWQeKc5%^>q@d28 zLo2Po)$GC1$(@3=WFhMkphIqOTYtKYRvb%B>G}93ay88q@Txf|c|w+x&R2`jomwrU zorg?<_9zi|TK7UWM7sx!l^Xa)p}% za)?^l*0{)mjS-rydDR^Q8Sh}(JVO|{c zShMX2^ME%M>bCm_9vFXMf}!xd&rqThP#=fcS8*2+7-ma>NHMcI6(d zb134=F}kdJoRK|oR}c^#L9-cO#=(ljNXizJ5iO_|Bcbdx4l!2>0)C(q3@^VC71aQw zuVZ=EL`m5eNJTKzrv3&cm$!;_xC_{A`6x?Bmq%S zdXz$)JuyaC;vU0SeVLHq|AbpY)bz#Hq5v540rAG=VzG`~H^yJIVwW5H!-)ow+ ziiR9FVi9en4U)ZRnLyHqMa^0dz|j9t3EFd+Fg5Mm-=g-s+jkIMA4F=vpH`U|HZ_f* zJ(|e_IL+F6j1IUWf^Y84EvTJ7g+F3vv%C@Z z66zGxT}ET`QoZYk!3gX4%Ue|~PENsVWz?QOv_@DwO6fgYTw+5f%Tf$nE>Q9F$R-9v zyVGg4*hAQDXEYK6E8H1+T96RV+cOHL0io`fgCc9psQb{478J+BQ zfyyLh>r5co{Q{K>wL#10l%HpjTT0KF#=y%6%$Hpa+vtE=3rhGxwk%i>Xdt2&gGr&& z38F~)c9VamsK~dzRKIJWnHRe2dLBtHYylfx75ZPk;~zeWHH$UPtfamsm9ZPt^G0iy znMgv{2H+6x{D{8Ub|`A(pDlafN{YsS|FpyIEbU9F)%Rv)@}6ySNBXp@pOQ+&f_n2& zntKUbUf+sGu6mTo?0!uiq4&v<2FzD)C$HUF6IOOP)^H(msLy+@y;G{POW`k_xV)V@n#zN47fRQ)Ri**jf-y_MfQB4Vm%s4G6od)=sHne2brSMTIPqV$|Mtz{UWIAf$*D~43 z{h&r`-nI1VJ6UEK3sWL8kT>7sP1m-u5x~%(7!<;1(f#E*bl?^MZH{LG$Ftg83ugIY zanU{YDahtp4ho~Q>yDF-LjJJeaF101EieWD_b}0*U1RnU6k;?>k=I?p_~j?Xmp2nh_cm6eA`lId~qQJ6RE#V&4&4s)Dzm&=dM z6_87ma=kv0u*zu&lRN?K!8>p`bd*=Sf4rJJrsj$)KTtx3?9LOQ5((%WJ|EImm5eD) zj8y-4Be}KF`bMKOU*ysgKmqB|NW<&;IgZO(pj(vWEY6R$weJGE7L*k?_38V5uQS@w!qP(jeLg zGScm)tB-EWOcn-&;z44zFO@xGQS3HW!7QT||2Lck)*6~Szp=dQGU&N$74{}5VDVJn z)l>K++sCiWc;gnhwM`ASaRKb@9qQgUoIni4JIdDX2T$pk9(hC_6)-M0DqAaXEU!6d z6-lXKK6^JC8Y#Mt@;feTLakrGj7&Ce2t@BFXOs)45TPw6BFEOfdIdJT^kbaHspLr0+*n%1t3xWd%}+%s#SF{2Qa+gFG<7+(;Mt(O!mWIE-l|=%G(D|rK#95Lf~9t& zqg^M zsR0#(!1-Xz+3v`%7Thy}3dC~^j^~0U-Zis+wYWM{cnQDQr+851B^A?lt9_1^bb0-I z$3=3o5E(5*AK5-|H00MzI=(#*e1vrb3uS6@_^Bqxg>!bam7ugu(b|*zy$@%4$sm~Y zUY760l(~ULsgB#pXt05*?KyvL^ItOfn=#-LtWsVq*t|%{JmG#QtYdhOaAy%&pnzTd zvOx}&o00Or(;lft;yFd7p#G5A>vC{oCb{t`-;-UGsM+m#PG8DtK9d0oRSoSN;$McB zw)#&G4*oEX4ZxK}Sd%11Uq-05-Yg8wGh|$`WR?6HG;(R6%>8ZE^BRY8a=e^yLY_7W zr=zwditWJe5xUr{S8kPePl~QM$0a=+@BTh*eJD|`sHg|-S@}Vc`8`DWMI_@%3%;K_Y-T)@pyh*ZD27^l*Z2yI}(BNxwJ{s+zUp4`T#;kOC)P1X3_D z?mYyFs(I(_?n(O)RO!Q02{E>a)Q7YQfjf@030w)5^j%-Ev4Fi11;^hlQdBBY^-a(z z^lWe1xaGg|y~o?C2Rq$IkAznPU=)M~hfySBG-=`?cT zKPyijwY!$*^(SkGkWIExEUflhViNuf)x=NnDOsoo@+KLt{SOJ&JUjJAi3wIQm&*$d zwET;&W2T`1m#;sV^Z*~Jyl~WXqz_ng0q0;WsqS*XPYY?QT+m~4hB>cr(0vs%0TquE zkxs*t5obh$^4!s90V|GahY;n+qr6V!Nu>w5KW#zyb&Ie?cUW1rjkqVhBlgJN0r8(S z#l+xS;wuj;&ehQ4QhA22?;)3H=dOW5ngKURylMCk-C4?_gPc(8Vh7EE5Dk4vbSMWl z6o^t6pJoS2yeRK%f3R(n`%i`g zD)URW31L_7M*U4_f&V9?ogMXr=Xi?@ZZ*fA#0v<^s#^D z&@WKla0%$t*p4*@dz;36zLhJbr0uX8K9%7as@&EIHOFy^&?){p#f?%@x8xcRJeF=j+uOM?Noe;ZXw%q~fnz#eARZoxS1wff1rEYGL z`N6js*6s)AZQP8|>E#FIA&cB94Za6jO4Qwo7+9`$dnFLJSDaXAZU(WwgT2#Bq#MWAhD4q4t=Q?CqbF{pM7@#Vx|!uL&zFzCBOhZQuNlHBtfC_M z{k5DmhhWGmMsqr*8=@_?gG;|veNUxokUy6fiWGJzLRRsr&%t#~xT|=91iW(&96I=P z1)Hwr&A`80*q4{AhYCfjomy=s^;IE7CF2@sF%k1&( zhba<5@(dNt+O!ek5^JSTJikVa@EsL&z3|Ym?fND>!d!15?AgXKa>K{Mb@fJa(U7uV zG|`ynM|mZGsI^IMp9~Rzd-xU3@#e8#7QklM1{>bSDHfXW3<_Q&=$Ayk8Ge3!CC|6j z+uk>Hr|HG6(St(-#=q`%*$L#GHm$)~-hlWtCMH=axvbR^WZgMyJlUdb_aH2M(C!9X z7UjOAa@^-|C}*VR&pXTs?bBNQ70yl}-kMI!D%mXuujE%Fsom}Z4Bx*&E(HI21d8Bt zdl2!x4|1_BXxKQ5Ny0NJ>RSC%$Ker&ZcLek@!}8S<_gjAV&r6|gtL<++aUkrDpkLG zo&;7sD$8oV=CW~$k_r0jh(XcuE3ZHGRqmLzP7^2E_4xra9@6^W{8TG~bMFcE zFY}7lp7N2k%rY1aY>mu1>N@U^po+-F;`0%l1Kway-#Xbe4tANmoKi!yqA?nEK1^cAx`FvWYz;v_kw;y_XM)(Q%BfDapR{DAy$|`l^jpCy=nf) zN%lnA5o{Ioz{?#o86P9CI|G-S%&9GZg-_NNU|@(2uJm}}4xxRs!M_fA?|o1Vd3+la z9a1k&4+9NA;VqYo5ih*(ziv)%RoZNY9Kxd+?IsG|>IgK31aqQoEB%Y#$^yNWi&Unc zLfu4ywtl-#33_zBFbyKO)4;#`iF*wwu-z!TNc>?u>!)o{Rq#UG*dU9aM}MaYvxCQ8 ztyC*?$Xp!Ff4$bKC(-xZgt?E`cu0_W=%IeM1hoO~=SIFm-ehLJ#*+#duD@7I-!WWF z-?>H&oBS$&?3H9nm5++2jyaIKoXeD&A3Y_Z_hvnUu_Li87p^n(hH3f4;LRbl#7BEc zSnmx?K7Y9b=RM7Hxamx5N1NgBg($192uCU6)Jjr zDJY45Unes(Y?oQoWU!L5tbexlRWd9KZ#4E{7+M+JD;Rd1E<8{UXB=Y7Cv~&>6u9zoBt)8NH349J)KjC`5IXd83M@+0IE_E>Gt&H7k(M z=c}pV=uzafgP_zrVMM@A2Ao*_*KFuv8-R_s@WU~h4XJ#;|`es zm9-n-zDw5tSg*w9-caN(PQc+xB#McJ#r(U{hN{^oRVwfLenF%Wj=rz^3+* z-Ix`BP;dKYh;nwefM>JmYQz&k!tsiuhlciQU}G8MZj1j2C+*BXpn#9=&-XR24^BT( zKOU@*fckva)YX0rzlzI&LAhdM(1MPRMJwEnyW20&|CA)}rZyZb7XfhU9rqGca%$si zT*SWAM_<2C?EJ9@hAEI){h;^xZ)@pp%gZ7@l1@$wo(9W4FnXQx?f-T@8TUO1Lm^r$JfP#dLROd;RY6m^} zxz4uXPM&BIRF%9sK%RJz=jS9dTPs1P#F1N)??j&_-c2eY5kluF(^h>Bluk7YKMd)N z6>J4If3M)%4P_`cO};B(zCM!JcCX?eq2=3>N2X1~22JwH{_Xm5$q&Ja(J4vj0|5B7 z8qho30T!Kyh0hO9&P&md$5-ZCKomc3yKwuMyrX8n?4rk(LK@%43~8f9XjWeF6PpiW zgRYj|JDca6!ZaUUhwruFPifSlgevbU36hNkC1@^tLROG-*``zIJDGkj9-(Y_f-K{! zu5_x0m+{#KktW(SYV{4Lrh3sPKrjiMoq%8?XcboUqbt56f}67^Bn5lroI6L)R#ij( zE`zG9#3Bw$kCy$R>({WrxK$^6GdYD`qZT@nA0C#LGODuZP-Q6Xjf`p`WOG3_AT|qa{9rOS_K`+o7^Z|WAKkyUi4+elRFc1s^gTW9G1Vh0vFdU2kBf%&z z8ic?YFcyphQfnUI{;5V=tYyrQ6tzaA24t9V)z)r9W>;`+lUa$}R z3HE~n;2<~z4ud1$C^!a=gA?E+I0a6FzrY!A7Mug;!3A&;{0%OF%is#Q3a)|c;0Cw} zZh_n24!8^Mf&1VAcnBVW$KVNg3Z8-I;01UIUV+!(4fqGV1@FLn@Bw@TpTNK1zX$*V z00mgbP5g0SFI( z@BxSbfCvGI2!MzIhy;L00f-EM$N`7~fG7co3V^5qhz5XY0f-KO=mF>r05Jg2TL5AN zASM7}1|SvyVg(>J0AdFq4glf=AT9vn1|S{);sqc+0OAKA0RR#NARzz}1|Sgt5(OYJ z01^iv2>_A=ASnQn1|S&#k_8|+0FnnF1prb6pmzYI1VG9Fqyj*y0Hg*$>HwqxK$-xg z1wiisNE?8307w^r^Z-a7fD8c05P*yT$QXc30LT=8%mBz7fGhyW5`e4#=mP+K1R!ew zvH>7l0I~xhdjN6(AV&al0w8AqaseP$0CEE$cL4GLAWs1D0w8Yy@&O=U0P+K%PXOc( zKmh;*1E4?v3Id>D015#h5P(7fC=7tY0Vo21A^|80fT95i0-zWGiUpuJ0E!2o1OQ3| zpdk*BVN2+xq0_d6dz zhSk8FfZ z-)mc+hi;$CvmWFxLYQ@h%RU6he~)0RqHVsHtZ%&(L#=Sm;%~lIHqvRU ze_^odgYe5H2kz0pDuo0jzE^R5*%opQ;2A`V7r^G|1Htm>t7|I1ATrg^yYRVB_O;9aSL~+Wl2>&?aF~t`+2jV0|;f&-_*vTlB z1{U1&zcN%)7y7xFpmA2Z_jk&DC)+kG&*zo0A^~O~aZijNy*ARp1dU8^3$Vr!8?ptd zTZkw4OQ(fdBYcdGDTmHzTk%Y8LY<0_JI$#XXV6b+Mt(fLG36RJgWe?QsiPyYSx0&1~Oe5DsyA9~accuPvp zwtX4+(en<9`7<5|Z}ZUx{yQvOKRJ-1V@7oS@NzIVP$@sEpLF(j9!7>2omt+r0wj+2hFLsHPXE*ykOW|F(-u=UP0 zg>55X3chHVZl5uk{>`;F;*3saRS*A9i}gwT>ji7^Em}_dt1(c5eJtdaK05rl=wl6f z3qWY5m2mth^_Uqk+dp%@<-GQ}Anz#mkz$-EcC12(dpVNj5ErLqA0aF^`-37Y?d1XL zL29bZ8HNb2FTJ$2pz|Z_$S{!^pB^CHOWac(LzL*TF0;*+$J!u$Iqi_))V`1Xt95hm z%sP>pU#V7FP7+3JVED3i*&29)}- z-jm~^`3)d_UJQ@UZbuiTCX>C zt$gD5do7pwy1bcK7|qai$4Axk-K%3}>)@qfqy*EV^c!azM}#OGgnO-ZJOWwCV?$}x z`A`x<*+gdc7hh@u?CIKOldQbX6QAVhP<*Lz!waPPf4_(Nliu{wecl+0K{OD<@E3~V zq$!=0HxH?=Zr(x$V9>?C5T5BPLDy5!~b;NVn;jNiAx)> z*6bJnX_;4hRe0kJe3}+*yUs6&|4SCB2}|aKC9a+-4`Z9#z|drlpaSNQRUIq}_JJ?S zV+maHABK%H2NIMK-A{(5_0d$xCwMK(O7ZLm%5Jgj_-$$8$*!hTPcKet(#mXKMooJY zuu@)W#YD3k8!Ys_vvwgCsm_)e^A&0%g~O3&2>+11l%OCTNgiC+jt8O|O4@atakj!M zS`)nNrt}jMfF+91LfN?%FOdiosB7SpkU5Qa?`UWE}oEiUcEuZ_}d!lIdIpm~8HzQK)A-eAsbr_w8w zov4jPeQIR^I5xTJ@+=!6_?jKz8;O3gmLEaQmS@=sfiVk>LCWR{tZU3##2;1;dv2rr zO3k(w`mnnAuY9Mx{;$X?mNFZ-r6oxljd z{bLS)2aD+a6}l=jNc1@mBg(i^uWfEFX+|{KWTlq}*=lD@;(PbwM@NZf9CCA6HszNu zsv9J6a8l~0zfZ`_*>R-hGA%~~Z#@XfHaPnaI{T(uEYyO3yX`w6Jn$C(+%0o)ZoSIC zzJGPBG}Em~@MEi@ef)miJhOI&T5Ji4XmnEGyd0KahoPyNIv(Q`f9M0%^971{+%yp(voFNt|}y z>oW}D*D;G_C&6cl1afESI=lu|{D=3_q0qk5YD(iRpY=8(-HYi>6NO`J=adbi?ONno zbG*H8-#Fzx-wYG#V4U!rqu>Y1F}*E^R%#Kgneu*^DuJt%_j|EQ%@I z0W({g2P3!Xyp)le*MgD_&du;7uc_YTt+xG$c2A)MNO%z&@s>5xfD};##=M6=PKc~9 zA;UGK3H=bP!n<8X5Bkm4FnF|3tTqgItR0{5Ci##*G;D5qX{O~OlPA)Jr?XWZsXynv zs!d5n#y7DU)`?subDG$#bWZXh`76tlaq16jge2!!UE@>Afh-i%ik0{kXWAZ&l?jRO zdsI(e;d}b$ucYecB+}N(#y?ur3uH*ZnlfYsLc5(AcM=8Ny1K$L%Pi}L2gZc120kv; zUdwEwj0sV!~OrV>95M&TJ#ThM1AFXnNjRu1!-;PJR^f z3w@nMHWjeKR8OUcuf&hXm#x^hsefV6U>L=Y ztq-JxZa<$U<&ml=<6a=08=?JUQ*7lQ>_#EISudBQyHH8Q8_Od{Hhw~ujvv=b>skO_ z=h5!v1FsReIXL1F2NPjyXeLWX3S>Lfi&wekhQB3=qWdcqii&{RU*U5pxvgQb{ za9DPVykA1JgDbnhvGh}0MNW2`_aK#wOPJg4K;H7FKQ+zYPsLu=oz!(#{fPUKxBBT~ zAx+;fl0hvYL5I&vXAzP9y-q!6kYcSPhR(kg8434x0?C7AozX8iu+{?Wd)H=d*FWCv zI`u0l_>X@V2aIM@^pXe=VR37Phjo1?OSpRvP93d(Pe;YX9yCgHBoQlSZ)(#xR$!Irq8=PL^3E1b~|5O>0Pp>w_-|f@0 zc(ERjZT5{Nus<+x188jf7Ly4WWCBIFa4e!zadAzzSbA&q)l|Bk@GAnqI}D_{bt;;` zL+ZnEqaXv!o@Je3qw+|mwQN!gdEw@rz$FneYvqWEBI*pRK+k1QH2;Pe5%vA2FR_7m zK_uc)%nK`2ez4GHW2v}UrU$jIG%UtnJ`7b+`u@DxLevOXa0D;%)|HfvIS=2T*&3G( zefMK~SFL+5BMj(D=ZliZmLwfA{Av{zx}N6*Uk8)6e2%H?<_$~zVD+f``wAf`oKpJh z!AP{F&)kipRp%Z`;kK0{-ivx~Y_Dh{FA~!OSXXRocms@$kW04HTcyvnHHv#cy@7Vw zTZ>UC!K&{>+=2fnyUWuIPXz+S-w`2B-BFj@UtpwemK}Vx39>bxOQu|yp^>0aR0|dr zw8kqY7;aWl_<79QdZcz_@KC)>crem?Fk(5CA^nmjSiW{Epn|4aUt_TXgWpJ`kx4(E zxbFov{0Eq4ADLny5_RkRDvc^K(!|zw1tY02$zBBnFqOo87T%Oq-%!_Vt)6_nz(S=c zihkN7O&_2H7wcMXT0C|u@%RNx5}o+R87hK@nT7LLM4=``npZR3`-_f0d!*suuJlGv zNro0}1yVZK3ncs21^myH+c7z~opuFVYY1spq`$)sRV^tlabm@WURsaC!D?<>zH;TW zu&5Ihqc@Zu9p=*4bL2UQ84x{v^$77P-t7pPnpOkK*<;;g(5zFKQLT8|=In z=E7qUgPn*xk3eU$fkjVpi9Ny`Ap8+em-^uD35isIGE!?2PsN8So`tuTUx(ak64|j) z1Mw%UxM`v8x8GX+x^9}hEpCt?xIE)6EaJk}DKGxnWk4mw!j6kbfmA5dd^`I@RohN!ryHZcatijefKjVC=sF0J_qan0Kw zxTOyavr}Cd7%N67=N}@T)D9q5X_)RsmNkD&DzJ)=7$~!T6LYWx6nyGv4yAb`O}z-a z*6yR+vVthPRN2o5JlZks$gI!t?ZqERMTmm}RJIL%4^V2DQ;Fv9Y@gJvT=Gib#5Uj; zl9qh<6X&U+XTRQwD}yN~K!AQD*)$rRP?|e>lmf3L+3tx4Gr*RlKqOtjS-x@It9bX9 ziyQSF4g1-h8qQbc$xB+2aN6>XcVW6PgOtxT8!7skO*aJ;ckKokO^IgtY})Q?T=j#c z$Ck>cHxVCDg0ecwP`kC*9CF90A|+)~X;4cpJIZd+H(7!$5k`@i(6)+r4LC?^(|s5Z zNkYEOPA4NT8L7V?a4==)5KD*~2tZiWz0$(1-`t%q)8_S*P;oCrqfA|Nje_5Ty%8U)E-u-r2S~Cf$FyYM-6WDu;DEOtM~-r1~CTO(Wltkf;$nVK8v2OdBoI_ z@H8W@Mqd;~KsoSr-p*L4mO5?ZBD3^r^y|X5w4XBIc4G~YEv0r!cT5M7sh5NcaQWZs z^(E^kzBFVed%>ufHX?};`i1c0Axzz@vCWCO?mk{gyiULGc$G3ZCoAT3*tb`Tp@Gd4HZ;CI2`@uveTC}KFI5Kid(wlc5n+R0f0b3& zPa#TqsMEYz3XY3=iCwW7I?>Iwz#i`-{84HW_oy}m3tl*K3f`3H%)<{N-(yK0Lhs6w z3JLbKy_l%IiNr8Z@s&c$a5jFeH0Y1~$;)1KY`Iw79nQ~AQ)*0;-u~>f1g~~;Hi`Jj z7+GHuiZLC4!EH5CD(UC^&J(t05bv>BZPq>binL~6xgl}=WqPVBj#G=i;7ds=la!J~ zz9dW@tA?iwV24(jO=`z#cK;d)@m8)sVLC5j9^&Z4nbAzf3<(d`n;>TJ%O?EtbA$zD zU_4|vADCC@FXE$C=q%CP^gIy;;qM{{+=s^h;_^wLVRYFSqNm@f1i>_}1MSi5TbwC( zm+Zc@ZR#96Ns1LA)hxcnoA(jHMKTkoH4f9b5?17l_gybGV`mw$OklrW_Y{PeOZv7h zsDLL8!y1poYS@1(LB;2O`p$gh1JkEpX(m^J2pqC8kQJ&*m*XGX4z931r~8euX!9^GRn8QPfVN!nZ?ed|16xKsd(pOjVmN$9v$KQ zcLOsqY54=amnIYrOOUmc)-a$9G8#$$Ko%Zk!>ySyk+IxkJ{Lv9I_YwY=3tf-!{`x! zTWuJ^;kn51rH|H=zU{-B$e9Cm-45^6)fSbq)8(GbMc=XP-3sCth2{}Pc4O~Qa|`S} zv6f1Sd^eKMBC6VHCvW|L(3t821IK~}xz&MDJzvR=FDrMfu!;Pllg!5WvEd`d*E@hen7CTU|pL$I^+sgxD%B5RIY(JO4Lxmo+4JJODMWf&6N1wZPAzM!TSvic0KI4>@<|d?|VXvy(eAorF%ao z@Wiz|KH<_J@an#)dwutkW>;%qzK6Q@YYE-N@XrTF&)=}H?&VAmUZV)S7gAnhZ{Lmc zAQwxU-n<@IJYm2{*E<;F88!BC{GgbFm6Gd>s9Vdg@)ye{F3>{((d=!TrArpf4G|Fh ziucyDI;-dvA$DDbeSc|_X4-OGT(cne?-nLC9fH5rL1-J!IXvv^Zf%OVs+WY#cd~RZE4 z!}?MIDicg}9R9c+XwiOxu0c=k60L$qFWcIpWp0n{Rbb4gFBk)IP0Yv1 zxQ^<`xH`(nqf5RcY-j#~AN$=~mpe$mvr>UN*afEAesHRqLu4<%l zKV$`4`=wn;Vi+h+awm9ySTiEVDMY#z(_^zPC0 z)UV~zXcQ}WND+j2=Z|DD!Jvg>ab)E;-={e4Pmck$2|)>UUZvCCb)D#cz5i$8mSZX_xrOF-hlXl+x@1o{m$yBCevg#yLnTUh8bY zYPJ&XOarMmYN>dbv<)fG)RRk> z_q&^zvkn1`+_~^0lF!twFl|HzHP}Z3y*)E=R0`5)JMsSC1ru^T+gSoBQmve54X_8bC zp(E3UGnjpn1PeHxm_NR+^w8&CM~kC+TmYvYWw%!XXZljpDNj1>K$Lno2}GRiI|r-zcYf(nDxjN2rj5G)4B65yix6jAKZ8# zQ8oh1DB6f7L)c;D`PU`?sBgI*FUi--5Z5M*9F6;AE)`E!2jW@`YckX>(g+d{i|bQ9 z-emEo5ZBK6(t1zxKIBE$maMqHfK9kCPA*r_Shy||c`gk-we;5&G4xRB1>-(OM8hx2 z2UAv$nWkWMe^0gaO5fnv+df|SAe+BHu*^U{@x?_tdy&~c7yZVc111!S&bp-V0q=bN z_nAt`3w(~cOZ1>eyu8Ff*6J_|zYZ}@PXseQ^Mr3t?B?Q{+4@Q$-bTbib+CLruvzki zq35^jJkM-~YsRR?0!rnK!RrlSCj_g?&h_^cdH5GvYsrQrDc4UerNnwNp>&dCjy$36 zddqU9);aGDBm4+)Jcn>zDtZMYdJl^=WzPKhCa7C z8Zy#e- zf5Mys|7pR^${2UTK4Q5{8OcQJnJj&}5Zf|kZT?@Vu=(e|PyvCPpFa;M8Uz?&$z8Eo z>{wx^KByEDjIj>vVRj{sRpgbn!!`R|R4SiAXIrIj{tvN4Z(8+A4y@Ql<{!Co?+6=@ z$$z-IX7WMVC^QsxH~!xiM3Y(8v%hMfPLV}c+bpL_r|__lOpy)zv1iwGx+qLm#t+*X z5o9(-KBPCyyOiY4Xw<}@?``LWx%EHF{qcFAbi!C`C`_qbd*tz%`UNp8GX9(+F4rht z(~_X78YtZRI)#I}wH0dHPuuEcE>n~=_Uezud##9_!a#1)tOl;d!IIdK)A_O?C5jO$ zY!~Z4x9}d94S6B5_}X#YY?gzKs;tO^nxE25&U4OB#Z9Wxz1(@Xgd3+{!Zf9))ZUt^ z1#2q>BP>-C+Z|o&{lS8(_#0^a`0A^DMRnFUGnSRuFTQ=m2V#P8u{VAsZ8x4uIp{as z`G1awX#`ahat(eWu=;I=e4VE2%*uj@s^HDN-aYJwV~XB0$9UCa;O0~;_n4)9Fw>@Q6&~y^o)`Jm3PTc9 zIz8FcE$K=-Ho`%M71|dVE-Cqwr5nZso@q=B8ULTyEDe%idO+>zU3O3OPA3mUH=hYMSE7{$SHohwVrh z!0UIEQ#p&V3z(@-klpg>;sxNC=U=x4zM`a`8TQ07_7ZM`9m~FG`rs4>I1>};&G7Ki zQ|@$+s-sljazXxcIBF&dEX}oyfbmy<2X>wr*qn6T{_T`0@`p42&M5`6!~0J zq^-)Q5eH}*FrXxvR$=B#2Kp~3m!uJxZWHK|4WfXu_($<9{A#B{?u!}}#xK=;_oY(> z8ZAA6Hs&jRNpuDI(=Es+!xFzfa6c`4l~r-uBc2w9ImKd+Q=}&#MC#AS58Zob3$hY$ zbYXB5V}%8pZo35EtNw_2Bjjus=Zfku;bsj7YtkMD?f#nn;9y=x_fogQ3<&GINqQV5 zEQEzo*?#N3e;Zc*%?jlth)7ay@=JKFm_?asO<7W6(fomPJv$=0e*MfVwd_f`V#OY< z{?msF7%g!%hfRm zr+FT9;q%9Bk|?FzzgiX>cAlEh^Kl-5UQe9_0icFufcb zj)?`@J*l>59g3}Vx9%4eseUJ-A-$AsWR~#ip>-$4!WSKBwi}e6Vj3hQ9E1%qzUxLY zhfV!Eefy(bGZ0i{RL;Q4FpcGg(-3VFsRFie4(#YCD_(5+-1CI)@2Ikq!Uec$sGY8QZy z=Tc6In0$FV+f&F4MQwaTr|B(viu@-1Q8=M(crvQ!4tqQ&*(#lW@U+V#1d>^c(1l^u zxKuC!=bB5jrf}4GP{N-fy{^D4)0d{j7b%pVOQoc^iDYb5(){W9RC_p80_Z%nPt|fP zLJyV(Zo*EEmQ~5a)wSCG1Q2_gb_gxVMU$qIEi^h*8lz!Hc^L%j{cgpTt@}^|zY5nAVNVh*}fFO&=97_Z1|1 zInGh5Zy@mKvFc#Qom<)Yg-R*8neo<_i3&qlNAfd{G!Fw@VxtV{=kcU$q$^rKM_?vi z`OEtr1b!Ldbw#e_?*_Cv%T5Df%%Y$(S>F84Q!6^BwLC%(1Tr%GcJ2xHqbisgzen1z zdF#{{bv}fjdosk#`ZgI_y(9}3hupxwSTk055?1PS=?QYeg8J3k6g>x!SE@&>EH2Nq zo?$q|4OvK$hEULZyAg$kC;IHwYOfVxNk-4DVd-&M&sLsVxVkng?$poL6+RB7V#%7J zn*JwL9XO0DT+S0$^KTj`3sp}mlnOM*_p#}*;htQe~T1%hGfVMknX;-=&wj+ZLMDx(fmYaWuQ?SaXV7u zkR1^}nOlFKCP}*4g!h7fPNE&tPxl(*a&t2rO;0^&*-frnE}ZHBtuqQnr&#*BBu-ed zzTh)Q&zh!V8NBvvAzJ%?+i^s!_zAy4If!;xXrz~DLGwqgm+UPUaXmm4I$oAKLGcIx(4|qG*c^M4&nCI z=&}>!xHoCFCWVG2Yx#0?~bjlAWpMdBHznBW{V?B;xsT3=xZ!?v(ti~I?tQ{me z3b7{dNXHehj%@MzH^~KJ`|)KZ!+tA!NfQa?DE!?>$9NH37_==KTf!ZPzLcqnvNxw0 z_Y!B0ftrk7?_@AKNy9=AX-eiI`VV5ZcFJ4b>;nddkAA`}rZvB+VA-UC(tP=Rrea%O zYs(C|W}z#!B7|tBn6iy=Hz>uI-M$5A$h27Z9HMDv6$+t7af`Jqp{&BGk``-St1s{z zw&0Dh*ND=)KCjZ-M==&M+?v1V!;uO`Lt>*ZX*2h`X$F5hYE-h1Cap@F!z4VKoM+S{ zXLJqT6MgV$xOT^Lg~@M6#cFRW1bX04$EBo*>ihpBym=qOOZ;2xtc=(EmQt*je|Nyb zoAvFK1wvsx#&(cj_=>pj+({nNgLA0JmoNKS9~0jm<%tKg%}~B8qU0_5=Xr=6*&|;c zxU6k1bXMpW*|hf|rtoXOtoUB(c{D2HhG=}lKHa#V!MzbM~ef`Kwd!ue(ZB!`$~O_7~Q7LmbK)1bdKX9*Z{`(F5zG#?2jXq-d+p5=J`zPMM>4>D>rs`mjDj7Br7oFYTu*75C40bK3z}2Pf z_`dQ(jr9?&o(cTosY=Q+l!um=(wG#{jFDHbssX?10R{R0cbv(rK*rXc4a!E7w#7o3 zo3gRx!`=F|2h$>Qc^^+B$E>8T9b6-|I|}QJfPF6{h*7A&L0QMB7U0oklpWCLVAfl2 za=t31`xraF$E3KA_UG%hI4Ng(3-22S{}?uoeYwPdz?>?JcX}c&ib!=w=SvHV=tO0+ z?*$7Tbid`@)A3IG8t0h=(h8PPcP3`a55lt>`AUkC-hYB`$%d13RDlaJ?3=sVkuDW* zQ-{F~Gv_45->HZXw~8489}ez6Qpn+-9MXN%63lVJDG!bl`yMPe!~Yd7{_$AnpLgWL z->qpeMZ_Xbx=7@Fd+mISxx^EywHxC=lnh%T>b_r_elMI}%#G_cT7FwS9!0VzrBg?w zLM^lC^LELQp>VsrthG7n#J@%gF&@3)!TbyJOZ%zE9(B5XPNp+*bH{CC z_Kzn>T=)$)hT$7!{iHHG$;<0*+nO?}2{j1QZu7!)gCVN#_&&sRQc6$^1elMX(R_FX zBNekSxN~Uq>tmL?{N_km=FNn$CGYlG;6#Hkq5KNL#MAH6{KEGI4BIYfT+O#fb7FIk ziz(9(<-)M+K>bKBSm!WX#4L-A(>Zxx?-g8g8}}LhOHBK%BuV2^?xJ>XX^9q>N^1vd z)_Ez~39fF}Wd5L!UXKVF?&4|RDsB(DVOKYPE8UOQk!rukFv7B88(hbXtW>?1xvu@V z9(B7ELpa42V|}XYar)_P6bxJbSSsj#*%J*a$LDl?kIPN8VcOLRXK2he_2jQDI%M({8#TwVfdBHwK1z6g?J?g>_2%G|txlw<;)7pcuKV>*MA*Yo zxM{KJLWyjTb8NSBu>n-o&f?|#W21dR8(!%kkl*)auU74tJd!o{PEJwWJ$KUK(>|LK z`-Ov%&r8H* z3@763UFiE1_DI?Vr3Un=GE9m`%u@u#ANKzXCXz`D06YXvj{iTHdT76M`pu8kv8#h3 zGAMqe@3gPgB;KmZj34RL>X%O^OD!4wLZKvU`tNnlI%G+w#>RU$`k>%1Eb^Ek-QFrB z>+cQ)=>PqZeIgn#oXMbop{!m!x&M}NNNT}SJtZZ)I#$K#N=KOZ$L}%^>{pM&n*?-Y z`Z!xqZW||!dK=X*80OIAzAgHhv8Tc(O!1_?kG&QPQG*Kj#Kjg4l0s6ZuNbEpZ?tpX zjB7dJ1Mp}KZEJB&k|F5Ix7NR^&rdBh@^$e@{N|4@xg*6+{|Y>zuAe47#_!VgdDD^a zYN4>at6Y0)O)mYp5G@lpI7L7!3Eybf{ ze>=gr?U5MPHuX>S#czyVMVTACl@>T#mNd+4Y@|d!CbRWfC<&gidM@mAhPe^@!9#D3 zsmczBae@<%yoerE7APpw`zUO#nal>%L!Kr_rz$B5I@G{I>kV9M4CUbBQ>xdBGz?{| z;@vYt1X?tMORx{%Jer>JogauZA)Pzb2;Cltp7n z80yal1a(fBRk4a8pR4KB7PR*pl3GlD{prcL)m-^j25)wCN|6)NfzUybC=LJ0DnSlKXMz^*`rMTw)dH zlM*EdeyP{qMdCYwN}D;lj}=A)(>}axJx+P;N+_-aTbTq_Lal7^Qh%V6l&F~1AQO>` zW&b|bb+Rz%bj>lc8}g1PRMwpu^-be541G~!=l>huY=)=r0ey9eR~So5aowbDr|YEN z`M(3+PqRAlbzxt8aDfK2o=Gp54pi)zk2X3wIHa2(7_hPm~EUx*h=n=Vg^ zI2YU$u=J;6RLNjsq3go$kzRr$Lu|tan@D{CQSi_j^RMmEtckVYD!5EDE+_jw55}Eb zdCf2rPo&~mMvgFDK&;N2{GWFx!Y9n~U4xP})>@sKVj5QB8juDNZqa{*XX4r!EyiTp zS4M@&&rFDgY_%r|KKNTK8r`dSGa7Eq&c_gCSi@6F5W?ZP^4`L-tB?8AHEzf!gd z!pY#nuhNSH0~V()vYwpMHicX=TJ&@xzppTK`)B5BVf@e<`=`$wJ*1t}s}MlSM+At~cu%kIkyXKsnZ3m5VdJr{mn zo2K#0d$rdBdV`gGh9;_B{}A|=nersQ{Q+>}(5MQ4|0sN>=$YbYN}efwrtF#WXDXhl ze5UG|>St=6sePvIna|JEKhy9`<1UGvA(Rex~J_@6WV8)AmgJGab+Tc&782 zu4lTR>3OF2nZ9R!KGXlqz%zr-3_Uaa%*ZpN&x}1Y{>;QPlg~^&GyTl3XJ($6eP-^N z`DYfMS$yXAGfU4bKeO`8>N9K4tUt5y%;qy&&ul-l^UUrud(Z4YbMVaJGe^%HKXdZT z=`&}~oIi8%%q8#xjp_AWp7lDR?VDe zwjEOnX0mW<#vZDIRpZ_D1Nn_z2vPn$zA%^!f#6%_b#h+;n zi-PIRNXXz(N=R^hWEOt@bnoL?k;fr-y2f13i^Wcs^)$XmQ2Qk9ZLArCvlu@Gi^0#O z+t6alIw_=OnQE=&(B~36Cb4+$OT+#1CGybspMp6ItGcH&L!S#=rY_M*NIv3atx0bN zDt;f(azXz4L%l%9{(bAQZQ(=5udlZ=SGP<|bC?KYr=a;S!qhd&gLT>X7wOZ)2f z&6o8?a-w%tx;$}Z#i{}fhVNHUn_xNLw9s;C1?Z>+3ghdvtwqyA2%4sM;EHLPq_*B~ znGR&;`u$W;#=+wOJm4Zf)rdbx1gEGdO5w=xv*1KhXLHc%X*$7I^^76l3M+CkbU$bz z^Rj!V<;vKY%KN6;W4~?eEYrn}$HEOFP`JpuZo|?|m^YCrne^SkI#<=-RfFkEmspt~ z3d9q?!l{|+KK~M7puj9%$nAh+K$_4}FIc)H;oCPw8BM9oi2IEayE$AGA@Z*%T;vGZ zeSGy#G1alRHfPEG6bfxS9=-+Ue-%b(<;CQ=q&S&B;|PYUqH<9sGH*Q_-Ir}`{@X}y&Tx`uHNOH zQ3^hp(k@c<%QvRLz)I~XkFP!;V2VAWXNd~LOjCI(#UD)C}2=-21h5)UvBz8}q*WL}rX zX~lMN-*=}6cL{#*iJ=;Po?Lk!pJ=+Zj0F=EH|DaG6nM3Nrz&P8f$l2So-WdwP3omQ zlwHD#zkJlD{3vMxqn)*3zT78dl)^y!%yf=kEtUaE;{;NxF+(4r`#YPQCQw+ zT*a@#sB)jVJlK-@V!?XSFxzyxY1$)uya@|^+4Sc4n5v3UuBd_g$JGRH?mH14AT>|D z*(j_yRle&62ZDG%z20DLtN!PD=|rpzZOz_J=gI%*V#PH*lJq#X~6Q`kpI__$~S6VqOazA zS&jBuG<(;+J2q~TqLo_MdnO{i(Wx4WR!EPxw;^#$5UHDP&jvpF(Wztk65YBfw#8Bn z_VVLpFuWa9OpUzm^`#>|jnPbe)fF(v>8ufoX(!sI7vj7AlUQr9{)IAMGzO3Cs&sVWWiUD#8`E)rAyYZP`L%AyZFRQ`=J6g5f`rHXr(Tk^a%b8LR1RwNx1B-iJ zq=eeZL9M9?YMM!3VJj_ZgeOj~N zbF3D7Lmh57I@$iy=d1mNWMn)v!mNt{2a6vps<+E*DdZGs=v~94bKB({9mChZtaGdW z-t{sFE$w=c*&t`;>fI4D_0VVz`PpY5N5cdyof4}`<|?o%;HLdk{N!VN8BNLx-=Tkb zYNdMDm*~>sZ}FYIU`tLAM-a;utHs}J#BU~|^?a5HuQ5IT-~JaY2nakP zy@-kt2u(x?9R&fUBal!-liq`Zp~XT`kRZKEq!?-fgbqRkq$L!k_aX$OLm*(N7oXp~ zYyI!KFa9s)v-a$n^XAN~nc3etXAftJ_a0RhuZVxj@7)-OuS{B&A%+6#Ukeba7zG3C z(X^exwixR2Gey-;-8Npc8Wj5ssEK3%NrU3%2MLu7`|}LIU0EL@b&P3U!W_f6j_1o+ zUbC&kRW}gZGrkKoc)LFZd$BKMSM??_r32|*!N`p}2Y#YnkcQ`6lgzOI}JhKT!@7E4fQ{J`$A$KM}vA$S%Mn zpG3-RdUu8!Yv*!x9|}Wy4pT)RoWi=1Q z&+JAul9pUV?*f`Q~*qkc{*=%=@+)1zj%Oyqhm5__gIRgMeVOc28fkr7wn22DE zeN41dGfC!z4I7`~ua)(&y49nz-cI&e2#wN1PF1C4v$KaX&1jT-A2JW1aZZu^rr;j7 zfJW)o#3C`^+-<^8YRXDs=_}`pO5Xglg^!?*E=e;y=VGhirDFrejc5b-t-!KZPrr{n z&OVR{U+Ec@B&|pFbwMx|RS35>RnZeT@3z5a$De$b;y=#jCy=ea8^9Cu?Y<}k_-F_G zh(j$q27TzrFP*=52ItXclkReRB)eZp>O3}=PDPEcit=bbLvE7w=sVgMc&MJf&HEfmvo)fEdEvx)J6Wm(;;!e0H ztrK8&w(-0ZE)3*B3yRqL2dsB^uA*YE3y6Bg99!%8AWiJ`b(SZq0K+@PoZmuu>#V{F zj`F)#UGbHfU$~CSaV58cY3fUEDcuxLd61S!3{iaWZ(r6H#(sa-7$PpL?3^R6L@+as zSqG05E52NTuz@5eg)#QS=o7oP@3pM-V(}q_LC>uUT~KvB(a+pb>pY9Izo}_TkJVw1vabph zC_!u~xgMXO06w;+1cWaDZwDOSkaq=kf*)2h;7k!8*JWRMM4GsaX$C*AV8UL^6)gk5 zu3{)Lwe@sv4i=pY5`7&4Vp^PM!HLveS=7PzeVGBK8YIhw8{I{TNiiYtwkr7xhhd^$ zs)A@C+N*nP*u-IPUTmW58rK=TXs}{-A&nVp?d2i;?>&FT^>t7^Nr zM`1ouMlBD2Lqz6oocZrw4jBY+g+Z5CFP}Arz0S--QTcx8Y|=qqn%~vi#fc@O-`1}s zY46_al*xZ-?(&%aiXa{QZn4BR&K1~*pg0bg9(N)1b+SjK~EjaOPD zOmJdq-M^oi)2IIIlCv;;I^0Eh_sqPa+N8;G-UK*_iz*hLtbHTjZrUvc?k;zmijoI+ zZ*$lqwXYl=7vi{gCG#rml^e8GeQaKLG3bJAakL3F=Tg_0o|q;ppyH|piALgx{m?t> z5RUvp+^jrzRFN2bgGmFR5iTQIVs6*N;J(pO%A~NZg7Ez3pl_4@T>i6B<8%65wVvnn zMamt{P^Wq>^Ql|L83G|^aEd;I|6h1%o#7;e#z#BclKxvE>oxK}&)?I-buA=l3O>1Q(i>eZ|NyZiv%jx za0rwEd5fOX_RO+?orVNT2#eW_{jIU=!p7FkL+n;GwG7{;RL(~X}gorR73OeJXEH&p&S-irkXH&8- z(6YtaGf-&Gu=f}HfAQxpsDE+r7l(gw^cTl}aq<_ZG|~19v}Xp*U(o)=d0M9FfTSO3Jd~EYD}VQ)tdyqI{fFxEckfB7 zse|rnXsFy!`u}#ZW{}i%^m2agasvdCzW3kKhWJE4FuQ3>`*!#3${%XJ9SmOcBa{mSPw<)#{+mK8Fi3LWb_3s-2-h-x)oDFR8^fQJP#lFqo z0yBNoOvSXi{cb-(W^-8B7G8BdEG!T&WY0RxpjY5+_lA93?)8DnC~w2B8=^N!&BKcW z*$6(=JO4kBF45hZDG0#Op*M|fxYC7l7*u#%RapAAs`a4SJ8fsdPIXP-Oh1luSc&L( zZl3x;j{~)6FR6mz3=O1SvM!(1fm2-I>+0l#OE3x$KCeYa)4+}!Ve_BJ$;U9_I(b+e zHqis?V1g}~!uDqtrrThrd~n-zrTd77*SSSvnd3WDQUYdf$7(G!_H|vWAcf$&5+X^3 zQ1Zz>>1}Z9Kn$rhmZ+8ADXrSovEM0lDvC-2phBQcKQyx@#B4n8I2^5wTYmWY!3)>8yI zi3w#v>6tk5gI=(I_FA5|`wQa?GkAleK~=?&C4O+_5Y6{PjrqWg*_3G3Iv78ExhhL$ z<)XY(A>S&2z77_@@kvHrT_0|!A7s*75?6sp+M%-RBr3a)S;9!Pa93Suxh}L00u9lG z7H66jZ^VN#liUfUp5O@t698shK6#`HcjvG3jQiSHH(6!0QD-&X%*}jm&?%8A|yy8XZhQkzZIGGHEqw z0PVHW6n~SZ+)0bm-;z4i7mj(qLPDqLDyfm|WCx1i>NSehYQ-vPNq|5u$Ek@_0qgKK zFlRjYwCaQ^N%dr*P7%pL24L|-)h$dYFyZv3t7`GSIsSPvKEC{qta&T; z)EB{o4ed`;>iF@EB#9vW&BLby1|c2SQ-O5bpAeD1uaC9XZd|6=1Pz{tJ-0%dPOtgW zkzP(o2H9t2=5bW-$RNjzYYBs*q{>aw71D54;lgOjT71Q+;1U$L%W=dE2h*}n!JZMnm4-&p_7jWt{x5rATP7+LY<4Zk@SVlXHy-h=o{wnhtX_!@>s>5te53l>UBQ zdDdj1O({~c9bDbp*o!?mcO(_ITE<7bN0POpE=8a-odCB%!R?6ytz<`MJ$XSfRVxRA zXDb=coDNeI{n~Dgo>UQwJ^7g^-Aa~W)U8uDo1Pg>tY{(E*&AJGQZK@;ZcD>>gEe_3q$|;{6}Jz`cwWWIXPIw|eR=ddxaF=n&jAo}yi2oInUOobG!ox6 zYPnKopISu_eJ^6K=-s~gUWQ{l_1zOQMt2APl4#0Z?p25L9`9nxq|mn4JfeEa zea|s}e<;TlIcvy=;`h2hdrjm?YHWfpgMOQ<9KZ9dZf1DOtViZsKi})U9T#i=;heL# zdZXjZEz!aL7&Uj+-w}1g`vUEq|3fa+{F&bfReHwof60mR^|?S>hB7>(@`WfkfG@iQStBx4$o~)p@9Y^v2Hexhp7L zV+k+N;nw+b#l7!da_53e--C6eroRhB7H8Z*h?}Aq9lnTDc0+YetHW%r zyWv4FIs}DoI)Sbs$KU!^WK}-DJh@6K{hdH(LzNJ>JeEKIvE2;=7gZscz|75qT(SO) z@Xq5d@=Yb>M=B-O8=ZpVQqh^q!U6-+whQ#@^;%hjSnmbTiOPu^d|bmyFN*6V-}-V< zjD39mEQ?BJ%%2VU{f;XgSHWss=@Z>j|ISXt|C*i)TOJ^{k;-Qne~QkqYe4bBqSD|7 zxGQj7HpRn`G0~$x)TB$?ptHx%2w(HeU3F03y9+aJCs7x3u~1ok+{9iSyVGsfSSF{8+oA0gARmnM53fw_M^Ka!%6-yK)s z<7Boo7;G%fD@pGT{pp41a<(zrOl=ZC>I1&$^vLTe_O-#~1UP5atl0KyYxdHlCEEeD zY$N)E*~7+PShfAupoCIF9B*X@$Q zO~Ux6EjsvNM6dHQXxv!*I2nJSzbUAVhfE}cUHj^G>DHZ6P701!`Vlq}c;e~rW25Ch zZP@bZ?q2rph<-t+(Lsj)SDoTI?W#Qu9d|YH;-?|igCs7ShRH9l_quf?SFlMZSSa|Q zgVrQR`_zP$P!drPaLw_3Aki@SzUgrPAr7ZdA83wHUN=hy7{pVmu0e+%G!PtPqMs2& z#!Q0h9DDv0FS@1SOd9!xqkrq!m=gtYFO<{JQ$KOfs|?H|rfCzahECkf6|3CL(FZTh zliMfm`Ogv+mYE#Po!396kXFRi%^{6#!mAuI`^d58LeAj@*Zdlf7I$=3T1%n8@D*_x z8Gb~WotZQlVBC7;*WI^r-8Yz}-<_HFD_9Atg|b@rV&%F8nRni`D*d|qf6W1oG!Z^0 z1|eys(|or^a$nT|^d#J$LL?3qk=O$T!O$^iXyLHvsl}!?;k2+ujWn|bnJKhMIn}8H z;y;7zNviiBBBpZ5s7iI{$)?V>B6Y@cp)c^7(Mj}%2enj$3~D?D#`-1w>BI3@t59}1 zawj1y;&?Mg8OFrZteDa+RnF|`n_x4ZaG=K*>@6dQmm1=ZxjD$`CeuOFK+*UiN#KgR zK~qk)Q$iG*V`ByL=*`o~0a)Vpbfph@Mh<*TUY-CTePx8y>XQls)) z#txwxbTKd3$LQ~AdFuidR;RQyu+u4~&p$bCxN3DXxYvgi9~8Esv*btUmsX?ZR`r;2 z8wW&6xKFdV<1`IhKdjvqRIKZ?TD!}sIE4vg#7{c(e*4$i-N`JC`%n9SOvD5{GU=`K zKWUiE=1#8FD@=W-#nWq6fAsbb)T*Y%p#|JR){WP`&Mu3$U$pVIkhB_n37ZRO%&y() zP@y{83%X-G9pS*C`X(2FRHAd6)yozU@Kh~`T zURP9j&wR*gUe~l}`i-f^E@BT;WSZ`Qxrzf?d;cgJ2X>jRCnXdy2R2wFy#Tm*8YW=^ zI!xv3B~7g>?-i~T)##W`?Izb1DN>Yo_lk=0r&~-Y{Vv8sTHfNt2d?5qG7mO|i!Zs} zFHYaa)-f((nONK}Ev55FGk&<@PIgY^S@epmo3PvPPi^2|^l}cCL-gN44!*Qh)sl@R z?0P%)a;5F(^Ob2KYai+#8TAqpqBlOK=*N!)-zsg?gYJK{q9DJX;9)PM>(KbGzS&j{ z=2%65ccAffcN*w^GH(!3&yOU|yRdk;kUX+5yh-w;kYt;>_RL`&3h+bUx*hhqRo=RM zcAb~(dTT>yeNVoO@pW!e3jE~y1T4oa$`{FwY-Q+3`%qGvS=b3| zNkf+KWu|qeH`iS-7nk$7{*bfe|{9deT=IZr$qNiaSdIxo2J7S)9qfDpCB^7MMYiV0-I2oQy^ zNe0l52HtUfw`WfmDy&Fjr3-$4Xi-fsqm}j(gGD4hz5Y`boVIxciwSm&5%YR?kz7?z zrWE3yB?a%i`rw-t0CZfIpkBxSRu7%mdVN%@8+sr~y+~g=`X$IhaYAkAh;Q$?=t`uh zKT-eWXK*^=oxfQ^*^j}>Z+T_yC*KAKTgJ`kR_&FE1n=@@zJ&j~ueMfbw3sF&&5-HG zv_pXSn5XHeYF)Idu(Vh5`grGF0I@s35gfJlk{+5k1|npl3!s@ZX*&VKjl{n78x2LI zorc2Ar6pxx5H_*#1t%GCs3LecBT6?V8L1=@=@s89ZFH8TQP}YgqT2w*w2F4QJmlijtvuL=OZn}Q9x!a6#?7Y_;%)|Y(yW>L21@<~<IKJcw0X1^CPH? zF%)xX`BKkMNw{?N&C&wJVLR{ZYj2$9yyjet-@vvI1hrM#wW>A zhL+6>fzY20g>DRvKCNwtoy?Ul@Ik>WUv>zPf7}?nV*1idUh-?greC5>V9GtimwcN; zJfF)9{S4>md)C5#o~Z=qpT)77{dsj(Y+0xuog!NXoEKVo>=;g`rzd;Pz5*(N56a5y zNLewmtAJVub-%rrqu=p`$!V=+=BL?@JoQ^(Lu5t`_$c&#OOs=iY#x)NTl)2N%cDVZ zKz=`1V!u#GbKhN@tx;XtWB2nx=&lb4o@aJ_i2wa{<6_NCuLy$f?)56@ZtcBm;wIiv zSwBX38x7VuVvq?!b=q+U4!dmAefccG!UFx5xs{K-3lZ*Ygl%UpO-Gr7RHv}t^Mgv} zmI#%kXl;jG*Dt~cA2!r>OWNmtSFFtcT)Mxgg&NToJa_|R4>9sH-_3N|`aM&J-AQvD z3a`CU0;fWx?_@wLxH!Wpo9J}Glwa{>=-~1~b0o1PopB891c-3YDb5@b z{#HH8JmKKpBsF>^Y3cOGrow6daB>^H#cR%qbjhfMO0XFAi+oP4zOy-`c>huh(#+K$Q6*W0&MH4^b+$z76y;2iGKO@?y2=8kYC=w z9m5bc;nHZ5*&erSLE>eKdqxMja)@s9NUkfY?+paj)}E>^oQrWN=U%BRkMtNI&r69OJ^!I%JaDx_ z>MUSb+A1BdmhE`nY_%3ORi?OT$Flamu?)1=+@z4PxM~&@(_h}r`D_^RY|O|3Ce~o# zKQ7te0^lGH0Y!&R*Z*0?$^?s*sW zZDU~NH&ck&ZhfO=<^_uEyjU4GkGvS21z`-xK6mD$LsHu4pMBEzDi|w5(Y)fRM^T`j zN1)<>{c)Kp^S9S>m+27m|L{e%`p6-_#mO;f&2#ZZ&$qZ^#tTHrkN7Mxre15Bj556K z!`rJ~*TqNNH;|r#6=og@S)~pcin&fhqa1*{)u!CYsdmY6^o90n8$iHTgVz#JF{x%$ zVzMVcsA!?-ew~e9z}mU}U*9IkhJtydvs6J`it$K`o8LDEcY+XWzk|rw@J@cb){fCy zZPrEm{UWUneU~2Y=>A2aDrrM%Vix#U0t(_ja{T?n$7?MH1{B$K)vH2wD*Ejrb2Hez zZmIt#qW+(Ny0rrH^Ri(bIQJ1rVf~!RbP2T>))*KS@trj8}uV;xmu~apiLFO?*ESc7gW+4T(e`|r-oIP`M;b=kQwRV zbxC{&8U%d+f$_+Emzb;GIhEftmTNkUWkTC6T_U2i28*`A(S|ds(-w!a+xIaq=a&!G zx2w4ei~!U6#|l|pruWVU@k|*&If?FU^R1tLS9DFefekScokloHyOH?%hNj*J3|R?m zqEEOsv13A6AdS+XO;gw}<@<~sLB1H3z^thKr3vO>GiFzjNSWr%h08H3+do%~x62i9 z2l~gJJ)q6hVPcz4)jt9=t%HOASvTzd)Ig3p_y#WXIxxsKqerh~H~_1^U9SGVHCA2! zK-z+mG`@r=Y|`#CAA&e%XVDgwo~0CM0v|U9CV_c|M%){%8!e*N_BUSx2}j(f%jQ1&XO>pH>5gakW-j(_9m4y4m zQ_a9n_pko&zl0~Bf?o8=##mYbyhG!oqnxxuU-p^ zhLIeX$A(u6nr2Cv4{ZFw6M@#lY5rUht-cqK-;L}TZTuqTo$e!>%jK9m<}YNvOSmf_ zG|!gFleIp6v)+AVx#qA~A$xf1gp&I)sNTY0^@NAQj5yWAFdV&bvpaR_xqNczOWRDr z_5fbP?=@ay_0}mELpbuRA*}ao(ZCxtA0w7lVJWz!&Edy=s-HvTPd^{v z5RY>+5s%JFeirgLH+}iYK_J6fSXxq-#eHMh&P_L?`+v50AwKWeAT(gj0D&JTiZz4&>|)~XRckgKzX@K-3EmH-#y(dP(m5pJ z_7{SzNr#|L7G!5^EkS6%tB>081YvVz2_Eb`4N?z1bA)LJ;Gw7E@s#odqng|v0K{S{<>kXnXy`3=}|nw zgq{S7m7X*wT1JvuGj!|p%vAPABpzCroy>3>>(_WR`1%?5UM9j3Q~T9+2>24Su@`4D z{zEz}h^Su@FnlJW!g@jI$(v$*CvAU4)QF4dNvX5w#F;Q=N3D|7lNS;@-D5G{U`sxI zIhv>#iAlHkQtdgU@76J-PmsGafl4&j)_;oJaCpk8<$tKLcXsCFAf7}nd>9O5$^;G*aLjC8&Y$3$!;G0$. However, the presence of $\noc(t)$ -limits the effectiveness of this mechanism to sufficiently large $\sca$. This -means that intensity invariance and SNR interact at the input level, as well. -Specifically, the saturation point of $\adapt(t)$ is determined by the input -SNR of $\env(t)$, which in turn depends on the initial SNR of the sound signal -$\raw(t)$. This initial SNR is presumably improved by the bandpass filtering of -$\raw(t)$ into $\filt(t)$ at the tympanal membrane, which attenuates -frequencies outside the relevant range of grasshopper songs. The SNR is then -further improved by the rectification and lowpass filtering of $\filt(t)$ into -$\env(t)$. This improvement depends on the cutoff frequency $\fc$ of the -lowpass filter --- the lower $\fc$, the higher the SNR of $\env(t)$ at a given -$\sca$. However, $\fc$ must not be too low to avoid the attenuation of relevant -amplitude dynamics of the song pattern. The saturation level of $\adapt$, +% Building a sufficient SNR "buffer": +A stridulating grasshopper generates a song with a specific initial intensity, +which is steadily attenuated as the song propagates through the +environment~(\bcite{michelsen1978sound}). A listening grasshopper receives a +sound signal $\raw(t)$, which is a mixture of the song component $\soc(t)$ with +scale $\sca$ and the environmental noise component $\noc(t)$. The greater the +distance between sender and receiver, the smaller $\sca$ and hence the lower +the SNR of $\raw(t)$ at the position of the receiver. The tympanal bandpass +filtering of $\raw(t)$ into $\filt(t)$ likely improves the SNR by attenuating +frequencies outside the relevant range of grasshopper songs. The SNR is further +improved by the rectification and lowpass filtering of $\filt(t)$ into +$\env(t)$. The lower the cutoff frequency $\fc$ of the lowpass filter, the +higher the SNR of $\env(t)$ at a given $\sca$, although $\fc$ must also be +sufficiently high to preserve the amplitude dynamics of the song pattern. +Overall, the first processing steps along the pathway are not designed to +achieve intensity invariance but rather to improve the SNR of the song +representation beyond the initial SNR of $\raw(t)$. + +The first mechanism of intensity invariance consists of logarithmic compression +and adaptation of $\env(t)$ into $\adapt(t)$. In the absence of $\noc(t)$, +$\adapt(t)$ is a perfectly intensity-invariant representation of $\soc(t)$. In +the presence of $\noc(t)$, $\adapt(t)$ is intensity-invariant only for a +sufficiently high SNR of $\env(t)$. The preceeding SNR improvements from +$\raw(t)$ to $\env(t)$ thus serve to improve the intensity invariance of +$\adapt(t)$ by shifting the saturation point towards lower $\sca$. However, +this effect is limited --- if the SNR of $\raw(t)$ at the receiver's position +does not allow for a sufficiently high SNR of $\env(t)$, $\adapt(t)$ will not +be intensity-invariant. The initial song intensity that the sender can achieve +therefore determines the distance at which $\adapt(t)$ is intensity-invariant +to the receiver. + +Assuming that intensity invariance of $\adapt(t)$ is required for reliable song +recognition, + + +This might be a reason why robustness to noise masking is an +attractive property of male calling songs~(\bcite{einhaupl2011attractiveness}). + +The saturation level of $\adapt$, unlike its saturation point, is independent of the SNR of $\env(t)$ because the influence of $\noc(t)$ is negligible for sufficiently large $\sca$. The output SNR of $\adapt(t)$ saturates at a comparably low value of around 10. This might @@ -1798,35 +1818,34 @@ the saturation level of $f_i(t)$ will be determined by the second mechanism. The saturation points of $f_i(t)$ across the set are distributed over a much wider range than those of the preceeding kernel responses $c_i(t)$, which suggests that the interaction between the two mechanisms is specific to -individual kernels $k_i(t)$. A number of $f_i(t)$ achieve a lower saturation -point than the respective $c_i(t)$, while some $f_i(t)$ exhibit similar or only -marginally lower saturation points. This raises the question whether two -consecutive mechanisms of intensity invariance are actually beneficial for the -overall system. +individual kernels. A number of $f_i(t)$ achieve a lower saturation point than +the respective $c_i(t)$, whereas some $f_i(t)$ exhibit similar or only +marginally lower saturation points. In these cases, the question arises to what +extent two consecutive mechanisms of intensity invariance are actually +beneficial for the overall system. -Various grasshopper species, especially those with longer songs like \textit{C. -mollis}, \textit{G. rufus}, or \textit{O. rufipes}, tend to stridulate softly -at first and then continuously increase the amplitude of their song over time. -This slow "ramping" amplitude modulation makes the overall song less periodic -despite its temporal regularity. The "ramping" appears more pronounced in -$\env(t)$ compared to $\adapt(t)$, which suggests that the logarithmic -compression and adaptation during the preprocessing stage might be at least -partially beneficial for mitigating the effect of this amplitude modulation on -later representations. However, the adaptation of $\adapt(t)$ can only act on -certain time scales --- depending on the cutoff frequency of the underlying -highpass filter --- and is hence not able to compensate for "ramping" across -the entire duration of a song. +From a computational perspective, the answer could be that logarithmic +compression and adaptation is a necessary preprocessing step towards robust +$f_i(t)$ because it works towards a more consistent distribution $\pci$ of +$c_i(t)$. If $\pci$ is consistent between different songs of the same species, +a static threshold value $\thr$ is sufficient to generate a consistent +species-specific feature representation. If $\pci$ is consistent over the +course of a song, $f_i(t)$ is constant throughout the song, which extends the +time window for reliable recognition~(Section\,\ref{sec:constant_feat}). -From a purely functional perspective, the answer could be that logarithmic -compression and adaptation is a necessary preprocessing step towards a robust -feature representation, even if thresholding and temporal averaging alone would -be sufficient to render $f_i(t)$ intensity-invariant. This preprocessing likely -improves the temporal regularity of the song pattern in $\adapt(t)$ and -$c_i(t)$, which is required for constant $f_i(t)$ across the duration of a -song~(Section\,\ref{sec:constant_feat}). It also ensures consistency between -the distribution $\pci$ of $c_i(t)$ across songs of different intensity, which -is essential for the generation of consistent species-specific $f_i(t)$ under a -static $\thr$. From a physiological perspective, the answer is likely that + +First, the preprocessing results in a more consistent +distribution $\pci$ of $c_i(t)$ between songs of different intensity and in +turn allows for the generation of consistent $f_i(t)$ under a static threshold +value $\thr$. Second, this preprocessing improves the temporal regularity of +the song pattern by mitigating the slow "ramping" amplitude modulation that is +common to many grasshopper songs. + +This preprocessing likely improves the temporal regularity of the song pattern +in $\adapt(t)$ and $c_i(t)$, which is required for constant $f_i(t)$ across the +duration of a song~(Section\,\ref{sec:constant_feat}). + +From a physiological perspective, the answer is likely that neurons possess only a limited firing rate for encoding stimulus intensities that can range over several orders of magnitude. Sigmoidal tuning curves over logarithmically compressed stimulus intensities are a common property of