From 9f4218ad1a47436a98ffb0a49dda30b07d487916 Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Mon, 25 Aug 2025 09:02:59 +0200
Subject: [PATCH] small update

---
 .../_build/.doctrees/environment.pickle       | Bin 224640 -> 224640 bytes
 .../_build/.doctrees/week35.doctree           | Bin 334628 -> 334984 bytes
 .../_build/html/_sources/week35.ipynb         | 751 +++++++++---------
 doc/LectureNotes/_build/html/week35.html      |   6 +-
 .../_build/jupyter_execute/week35.ipynb       | 751 +++++++++---------
 doc/LectureNotes/week35.ipynb                 | 751 +++++++++---------
 6 files changed, 1131 insertions(+), 1128 deletions(-)

diff --git a/doc/LectureNotes/_build/.doctrees/environment.pickle b/doc/LectureNotes/_build/.doctrees/environment.pickle
index e4d56df2c50d5045fb73a239bd191c4ede8d960c..3d0ad279321f88859daac5a79c6cd69016903b03 100644
GIT binary patch
delta 7910
zcmY+Jd0<UP7r@P2@`Mn1Nrc)Z_7W6HY_(Rt#8O&IsfsL3@<b9@YX79xmnXi^d3Ehe
z)lRE@m?}l-XNg#%sHKUPYN=X^;#13a&Y8KX{4?`AXU@z!_uMn*-a9YnQk9%bRkkG#
z>D$Jg=arJ2IyxoMo#!2wG&(&iA*0P}?!1bc!(n`ULc*BW+QE2M!i22Yw6rmqFrFEg
zln|etlJJjdJJDchjcKhxk(DqSMl;Y%FBA3;zO;B-cV30$)U1rOe@5H8^D4!qWM_gK
z$*C{<1h&><5$-(R8{|@d;UcUtdj}lEt0J#qIe+nIguh4|8q&46e7SOY6??aBm7G2?
zHP-F8h;miyqAl%V)cRW5)|UE|C>mP5#-%cYr7N8mFNRicdGzJ=O2^K;tbNT|?t9T=
zSc{(LULNaUjs5ttHq6qVepwrCX$!=*VS)TYd2uVEuHm>`UJUFM*wOI=+E%2{wi+An
zcAQ1oN8M*@<`L9Ywr(St9WO6Vh6e^ZPSTKd7ip+SjDE+zSs|^X^1)i?*gv}VmaarB
zf2Y<ojJM+oHW+EgRctW2j$g1jh0Qf=FsP1Su{n>;Z`fcg9oMnJ_&IK1^F21dV{-zV
zo7i9k9e-ehQFGkF1|#LTU49z01&DXBxq!`GY%XK-CpH)+$31K?K#u#^U|1XvusM#+
zU)W$g91pQ6!sZb+7z)Q@Y%l<h|6x;t%@b&{vtyIGdv*?g#wiFcTg`yaLt1q4qCmK8
zwKA22!Eo8`4*inGFd#15qQxGPFeolt$93CD!oav}P5pP0gu!vy?l+MnVSrq=pq{%(
z!XUY9zj}6)bYdEb??>$+5u@d@y_x+DNf<Ggt+?r4k}zs6Ti^{PVc=Z0*LLrtF$|u|
z=F|OKk}!ZS+xcG(kc2^mc^waugn@L~#?DpJk@6!^j2QYI4Pr!Hwprtpgi&?bX7@Wp
zV;EVNEyblIjIPVpZikXE!Y<pru%l#&QFht#1{H?15LHJ-vSKlG)Gb!*=^ZnSv5TG+
zqdPEmSe%WmCj#OFM8!BCArb;aQ|SGnkAyxG`XuPzjtdY@=pV%Ui}i6W#dfg24stu3
z7w;q7&^LuX3;Iat+kt&jybrr9vg7NCERZ&UbXM#D>1~_~HfQ4ey`w*NjHpnqTr?94
z;)1--`Y5TI@B`^nt|UVg#Rqw>W=i7X&)A@j^Fx#rnw?3xG}Y}G2J1|9H+2k$zTehb
zYCJeQGds^KD>*AAA=8bc#p2t9Q({$Su*jQTPkjG=H!(XUSae%dPYg~RC>o3n7F+hV
z6VDQ(L}6C2a3r}zd`7St?#o(;9?4PS6;OVjJVWFq2aCau3~_B-u=#W#t1l{zIWOGl
z!DinHEKGDxi4rehsf{TU#9wK_rq5<JPV5*PB_cq0ewg(X38_)yK~k_doth{XydNyy
zO<OG5I)X)w^eMtWG1yEC;o;&=dN=WTYOq<*ng2^H9Tz38j0rY3_T{xjNJckt7|iEn
zxJ4gWrfX)b2nAO<rSc$gF|(Ukml!O%WaYCGu{yJ%xRbS3m6&x98&zWVAyJ7bM4}RN
z35iO~4J0ZtkC3RuRPX|#6623VC8hxqm6%W@DluJ<sKi7gQHgoStF*)<qLNBXHWHPX
z8Aw!O79dfHS&2j?W(yLPn6Htj#2iMV5_1-bO3W1`DlvDEsKh)4%FZjFl~yrM-+#}N
z4?>vPFNTMBu8eO<<mahBae$_rNwJDVuel980aH$E{iCTaO&?8Lt10rsHJYAIpRY))
za#!_io|(bS!m+%L88eO#f<#L+m!!h)1<mQiko-Jx&XI~l&ZJ<^gWT7(zSrEUTwBcB
zqjjzGztnVp{xMA_KiaQpmD{bU_rg48R?KB-kj;r^|0T@Ne4fiHdiF1B!BDh&o-LlF
zDR-$uk$GngZ|(_Qo}>phu4rzMu^F_Bw-Y6@vM1z|P;L9o9$wuudClM2*16W7tA)3&
zU#@lUZtS9Un>VktbX#*ZJ^JiZMP~hKMi<ZT+aRXsnc2LS(b;q0%i-Ft)%JW%CwIVw
zlF8q3tg>f|govXkR?MvIN!c}5n|beE_>z9lo)4M1d=o@s%ibww?X6ZMy6@}AP_%pI
z?H{A5(gFA>(rrH2mMgmRU#HgP9tPKGG~_7wO0>UVqNeD=v6>2wTXqR2;eL=^<)R!-
z%TGhxN!RR*m;R0J=OAN9clCz_nr2@ZugUk)6iv&2w5UbN9IgBA@+M6=KSMldmG)O5
zD~bO2<s(h=f1ReO!Sz&4t8b)es(150n)dwx8Afww-2Q}_2Y%;iQ2DxvGj}7+yAQd}
zqxOGBFcj^coO`o1)p#&f)B3;QYH2j$QGuqw|1DJ{a_&{~6h86g%Hq~j@Re*oeGapZ
zz2Np89awEOD&sjDriSGSgF&p(Qod7xRnrEOZ49o9v_9Uf8#iM*8v!z=GTWiGO{y@s
zj7R-=8W!$Mv+iJh4e~o*)`6jHmp*=Mrp8a~3=)R4?E@IxQ^M_mtXSikAoee=w9jj@
z8Col9F~|wB4XwitX|&a2kO8FKTEBGNZVlPTTKiitdqpqi-xv*gj)O{3&COmh@Alyl
z@OX(ZyEJ8yX8J74?G;TK>_L$2@^Ui<2|+lv1>2~xX-l?C<Na1FfSav1@c>z?4I84h
zGukrPdNeJf9fRFY=xNUkZn~Q=RjJHI;Vj)e-c0Wo`B^x7o1tu%0UhzT2v2rmknDtx
zE(|i8@L^X5n~_j-W2-g3(SvPMXr63ubdX(pG1z!ywYxW)u5myg3q^|(UwJRG^atie
zv2V3eOkei7#s>Y_R~l~)z+2s^FYiFX!)I}lS*0KMU+7|9a_S(~f}!YVZtKcx%F}PL
z_mnKV4`%<?cxng>Q@FmyFviJVHXDvfhEwIP5p1%?-XrnmlJ@uaN-;mCbgjCv?3gkT
ztE7+gif2XI{(1ttqVZB9yP(hn^pQo$3^p{anm2|G^jR1JnF}ux)66>|`bvJ8z`~ii
zvI%5Bt4VBxLNWhWFS&X$?hzOXkgcY&K(34iPh(KmNc%VkGlr(lo{m{a*m5S`FES{c
z#h@0EHgyhL!p!``P&zlJv@+M`LK=2C#rz~ZNgzgmcG+hx%hGr}kHP*W?Wq5-K^hO{
zV^))P$O7E8gcAgd*V@}|woK!)g{-MIIJbyR(At<Kr3O`(;f25o0rHFGn1i%f%1Rcd
zr|npc8<Mn9YuFbWtE^=;v_aVVQqPudV4Rx~^&!0QO18@!+tAu!C7W4ShBCx=D<(DJ
z*Pk({mW1KkFp7kSzF@C%LUZJgtfKVU&fsZILz8!~#%f4<BqlX!`|M)-HP+mXSxnlC
zd)Pp2+hrd+thDCw18}9yzh&@DAS;kpXq@^TRxHx`A3|>$K4oe6Iyu)&e{SvBPmZv+
zV0S-<hidHzBg|}li+RgF1#GxhE_&Svlt+%SWF^a<$8k%bz4V;GdPX?l6x9>dzH*v%
z=1QA%hHcRXjnA>o%#2}>b=Q8t?5Anj7uZ0J=P$BMjSwVw`jA0!F?&cDAb-1zyXt6F
zNVU_cb<Ep8L#oZUTbD853hTsBw##K#8NApKcD#m_0Wd)R@GFLwv}3N9;)@$BQEMmM
z#Ka+knzxuASJ?RuW(#SH?y`5a_VxR0p4OH;z$7Ds#ScsI?Z<c*NL&61tII{5*=g|3
zKEV9xDT@^QbJZhKc7FzS8brIC{+wkK?eOM93C#C;a+{n83CPJ}p224;+eQ`m$BGKQ
z_<BXND)Lo|!Yc73MPF3rRn**5Rd_F@YwXKYkOJhoYW$(1ZFW9Ujdlv)la;O@kf$o@
z8^q_U(c3lnSBk!Rg)di>Sey4!zwu374k@-X3{q@EeLl(b?Qh+iP7QclhO%8wYsf!j
zqR33c50)H}Fa35l;>{R<T|8UtE2A3o!6cctKH`n!xh8x7i88DipQ#4mapEPvZ_X3c
zK-8;xK>pN{-&eY8p?JBlrtH*)rzzUg7F=d$<?wbq7JBoW_WUM@8$0kGDE<+KqIo`?
z-vaHS2;LNp?{tJ{nXx~^HNiL40(0M8>zcB<aClOHjDFXUN4xTDCCWG91w)|;kGsmU
zd=DO}<n?ezIn9yjz2Rmmtk{P`Va1i?+DH!BNLV+D*WqUIc-CQ|oky6P`tmrl_9W)F
zuo3q++w|jy%y|Q0C(Ox+GPm{Tk!I_`mS=tgI8=U+?Q+DM5N(CG2Xc6xllIfMIMge`
z)`L0hV8X&798#Ka%rL$|W25059+#+9rR(Pr9BMgPC62`GYIHXZJ|-KQ6=Ha#*!G0{
zljCA|eFl<Ut{Kf|C<>3m)B>IPnVnabr{eh_CD!~muO$b(&;6BMRwBQqXiPF6sOW@)
zk5Lqzf>$)6vw8s<gx{~D%#~fa`rW;${C#*Zb%mnbA)QxYqRZYi_^KUXvJCJp^qjI9
zn}Obip0mr9nLM2d-|GP~I2#FdYd?THN%ZOj?ohO0B7av=^~rpkqQz5igXG_Ux2Atv
zqq);CD`AzLAL1Uwg{MsCnQ8)?iK&P`F?|;9Rit)v_&y>N(zv^PBbWD7BII(2+~<PK
z0Xz7KJly*@!!wU>Q8X@}f2*k10?0TTg-xT~OLy}LO84YryahNn-{dP5bz96AD!RUe
zpHft?j2}?6Vg<jV=%ZD9yP{#A@L7uB15m9eHm(SgOV{G9!PRT5hXf*$8?c^$&V=pP
zNG5LLQA&h8*h1dkj9VOM4BpCf72W-euT!*Po4ytkwurxs|B??;1BD(8DNcK12ai$o
z)lS}zlMX&Ui<Iuk*Zd0=`h9!&RMM^QzZYsKPL0{mg)*yf04pcz_8zo!asTBXDBaCN
ze7vHpBYcyh)&=~SqAG>_xS~If^MgbtBx{g7f0FlA109NBW6|=bPxD2JrkvqRl<|PS
z;ASVE)0bgFdI!mSKUh~4e}RuxGp=5=Tyy@&L+KL4*7bq1q=Xylg6{vsy%klxYEiRm
z7WMkgqER<^9AhQs>ai>pPIulmXWfJy;X6_7h(B-g+7Ppec3JNhe?!su+x%}uGw)*Z
z;b`r9m;^|k`*?jwa4oBeR0wK5!p(pKa~{L<fGF?@PgXSlZ`>d-Y8JoXm89P@Ebpb_
zl;>KMFgjh$7{`n`iYgh#TxCr0+FRa$H1eGoAe(p@+Lwbi18y(=c#^lVj7V(W94ea3
z@RLI-8za=%L7!5qss^MT+QabzY$2qhe#Rt4gZ&Li2h<e@Si0oumOH$L0d)dLb88y;
zir`dY2ayS%KjE@j9Rq4y+N1!PU)Oj~nY^fHWGEAOjs?qg4XlCc!3LxpuD3G8qNa@v
z*dU-Y5A`>E<>@9ymJ;E?QbVRUGh)?@Uz+Oy>3G$^!UHoNc7>Oo$1ROf$|O0|S_(d~
zn#)#gEZ5v^tzWCt&VaIn9>AxUTde{gU3JV5!|;=9!i+>U3a^POwz8n30c8YdWOTM-
z;NR7Nf`>YIbJSPVpt}{_f*uAG3G@%X;eupNF9WtW8ei{ijN?ROA`N)oz#HouW$1KU
z7i~aALAy5n45&Ux5R&DLPAQ|k>4-AA5}i**2h!nWbX_``jP|2r$>^$dCJB~!AQ|mT
zr;*Xs=qNJUi_RfoIvzqs`_l;|jNv&wSmMzmba?IvOXHzqG^Z0sm~f;yir#eC7|rOU
z5wv*B2ueI-1XDa<jE;1aNS}d52pnmfZAKa^r{R(1d`EiAa^>>jkXcC?Wu%#9q}gR8
zQAYZ>jAWLP7MGEhS`z+uG2gM=5=q)rM%q$F+Eqr{T}C=mMk**H6_$}sluEtv=TDW2
zC>58HE|-yhE+bvFB-4MC5elzqJx3XB)ZalP)nAX$;ZZeocuox+9#TVxC)Cj4@icUp
z3ee%fG<0|>4ILgyLx-sV9UewQhp7M^rUG=B3eaIHK!^7ZI!XoT@!T0YJamQ*Qvo_m
z1?Vspper%!#2QhQy1A6OPV&}C&N|6gC%Nh*Po3nbll*j&n@;l5NlrS+M<==HBoCeB
zpp*P_l6$#yF771Xa>+HPqsR`<<dSE(<d_pu^l_}gIV+Zb#~YP-U=f2;@$a!Yjm;Ts
MPRUw{MuOM>0ngdLuK)l5

delta 8006
zcmZ9RcR*Cf*1(;)%8H=KvWN}aV!?(O6)YIL1XN-YjWHUP5@10(u|JG;S@EG6;<aJ#
zmAElCMx&-YHHcBM#He74i9TyA(Pu2*IcH{xeE-b+PMO)c=bkzD-r4CFYEHjUvnYOe
z-7W=r)ngLIrDersbS=npn-CY5^hT$GJRk9ASD(0oJa=Ua?f}N*#FTN#@&63y{13tq
z*EDbZgCVa?5L}Q~BPKaJ6MiT$1t-ajNr;QhPL31l!|OzYwOV3IRz~VSgFC{2%&c))
ziJ4i6F`2K;1P1r4xQSWOsi{ezmur4)Euk<+R@^w4J_F3WKg`YhcND4b2lOnjTBS-}
z_5K~(C#FqGi7v2RLb;af8eQ5msP%GbJGj(G#mV>U)IC|rSTWPD;??_g+MRxVz6#qf
zuWR3MO?O=M8PTTivDa-~T(-lnYeQVx6R&GSUD}JHXoN36QdQjP+DNk%R~19M`*yRH
zqHlEyY5Vc91-7#&d&)cL8d-um57&Jlw^LQc@lao1+c`41qDZDPG42DO!1FYZOcU2U
zKmDWY?9yEjg&#D?!Fb!QVuO*kUBd>WYx@nGqu5->27_w*9h+aV`2!n_rR@eb7(d%h
zY>s2|Uu=HH<`y;>LECL?Flx3t*kGh=cdO<=dlB&-Hb=0zk4-T)e`14SvOT~C17v%M
z4Ti<`2%A&bJjMp&Vfzc4GHjk;gQ2iJ#Rdal`yVzJuz3bec6M|^Z|7GdUvLV7!}Q#_
z_*Gz-8wJ8)I%Hl#5(dLzTJ?AtNf;1^X=kTGk}xO^)6rflNW#E4Oy6u>NfHLfVS2WI
z6-gK%hiUr7H6&q>!1mU9l77x1@%$wzVzeBl9QTc6#E3aeHTFsgqvkN}n!Jf@7&wRN
zgF%}~!r(bfStquTgaLGzcBgM634`b`tv@0q45Y*KW8ikOl~f&#;;DyH#E3dfUz&E1
z5u@rb*{|#*2_x$;EpJpr5=Pfynh-7}jIhHLe0UexFv<?oo#VS-1&Uf@!dba^f6N_L
z?(9Ey1Y?(+E5>zU?2I@Q-B@JCSw!_1Pw@uyt)PD|)*`~8&x)~#1n3JuwnOg&_DwNu
z#iLjs@kdNec33=)X)GQ^!>CwK@d&)bp+61Y3D9@KQP5kU--LRwAA$Z|nB@la1u;JE
zk)PW>tX8E;Boo0ges7)elv3^NOv<2X1-21jomSAwHWK>5>$tRQV8<)}|Mt~P+PN4S
z<LAC0KuSTvJI1g6ss>WBW@l#Sxn(70CC6nJ;LPRXySNjgYpPY`&1o!7ecVeFq*+C;
z#f`<V_@SbHmQ`%q-$}fPj}Q$qt-_Yz5Ia+>dZ-s`Bl;vph>kX^*qJy}JcbE|*)l|I
zhE;z)lr<4GlFo_i=~jKvL>3}?Bu5CJc&pf)JW*_jx9Xl-S-RLgK0?e%w(2hrv%VrO
zB|-$HTSaL~ym&R<Dn_L)5lx}5n>JNkO|t5#0X$UPOY0?8Wm@&(9{eq_EImRTwpsPf
zgLp#`kkLy#O0bH#83n9Ntj=sEdS*t8g&$k>?kU_)oX_kf@)E5gEGu6O1h;!x>t)&5
z0CAON=KvCwof0G}I~S0s?A%16vhxIq%1$*mASydPNK|&3B2n21LZY%0hD2p25{b&r
z2W}N*CmxklcCwME?94=>va=A0%Faq8Dm&YdsO)@$L}lkN5|y1ZNK|&NB2n47heT!P
zIZ$?9)vVO&@VKP=?_Byx0MqaP#l06b=RVG>6WWnvb~c?fgz3{eY8G)iw~2G@<Ts^W
z^q<$nX_;E8yq-?WRU~rODSGSEHHu!$$OrP%>NwZTn!@yE&si$uS-hV1lF6U*o7<hC
zWOl~dM=2`J9jB=Oyqa8D=kHaz;QTKXJz7w#=)`9SB#9NXYC3lm%u)IQi{`OK0X!A*
zIbOdPz<m}un49z9;x<fQ*^--`FP2PJl)KC(Nx!$2w{`{<CMd(^6|FUL*8TSIPNLlK
za0aXiQoi5r<8_=<*8Z)0?dyHGoOt`jLZutEIZWxcZe8ipZHJiA0-o%Em?7y+YHMN6
z{}wrv*t&t%!}<NLk;<?Amk>u9aeVhd<??q7^Kfo6)=Cks+{2l?XP$C%-@E8F{l0yl
zGQDp)1Y+C%se0OM?ybMfW!0U%4|Ib_&4x(KKbWMb#`o}3q}%#KM~FUJ@BPQFbh(FN
z>7)zz3D!z<uy~T9$dd6)@34hioF&KRDqY<10!1Dtrz<Kfg}Bq$z|(H(H+r94pmf)M
zS*U2vuM>zYPVWn@5rr40Dr=i^*KhoIX^YZLzXI_%SPCl$xduePar?K=6fO8YM^V!o
zDT-F#Ojc`ddMi)q4&2_QXy#o=<*YFfIa@+6ar%C^K6tE3qt1VJWhi+&a~{A#i2NS?
zOVNhM5OUImJ~^t$^1tPhM9u>bXUQ`!E<J8P-=I9!zJyWxY}~xN3u`E?Mhs^kNV9QF
zV-N<M)fiEYc`Jv>CI*2et%p17t+b;(*w;$iq9%h_L|<X4ShzFw1NWIs0OLn5)`g*L
zHaxxAEQM>#43<IK&K3r@l<-SmR;F;RAA5^S?aO*>rqYTA3{rx8gZ$Ycg{H;~5`eVZ
zn^er(s~P)TY5%aY`f4(t7U=L*2=mu#7qI&J{eiqIJYKr$VXauW?lr`<>=msTY(bFC
z#-%_8`9L_n4cn}+RXesv;luXK!lgsKU^YT&XLe+;^JrMtP7F3Xp|dm7xZbr1Pt}`;
zvNU~sGqqEU9ii+!hO*hPbi<z^Jl>tbb|AEc;jJP3t0#kPNGN)-)d~mnVMP-4<DIoG
zM$di>wj6ow?ayWqTJ)rTny+5tP39r^WglbKKsH$Vh&JV3#)I&RpPL`SzEh*e4q`hM
zHXVZZoaVe0#UOK^42DaA=W&AGXqf9#roF@3FqF;W#ge*4>AUPBDH?r-v1!VJKX-XJ
zYpE>tMzB{3TaRRr<2c;-=0m(@!U3b1P<ZR33S2POHKEZsniVStC|nm6-i%{c6kd#H
z=OpTY9>&Q;2Ai5DpP$6u_SCx%;$0{s@SP$@uQ^!mL*uuJER><>ZM2)rMoAR;znhHJ
zQy5exvb34T>T-$i<uIr;q<uV{K|vs#J%d5TBy2m2K_MXgX*OO9;rO|1851Y<RCtSN
zudmN#;UeGgHlU7%Fd(xra30H&bSw`xB<aTdo4q6HhkQtF(hXn8YICBAg2hVR-2%2;
z((*;Dm9(B+%qB|R*rhIOt>r9V>UI{gt&);gvJg39_iEUSG;_pS_5~ABdn|_6dR9kT
zLpHkBvTPIMT!igU#TT(XBIvBD2IX5>PX?mdXuloqtjND<G4}0XHmM6Of}KXzLtn7A
z97!L2kyST5zhrRtaoCjItOXeirvWKVx`BJxK}q%YLZXuH{602R`h^`}he@X&`<_{h
z*59#((gnm7lBWF#g^7mw9KyX`Js0X2yfn_!hb(m!gf&Oly9{Ns-mt3{qIbB%+>L?7
zY@|{yepB-`jvQr)Qa1V?!=y)l!}&8-EyAc1STzXim$DvQV!~;*O=(-4g`i9AwO_F4
zl5h5}Y^cI>=UJvg2n{@9$f2x^{iX2wCEO7o_J9XUX^Ovo_X^atl|5ZsGwLdX*CCM2
z#`0^JgoNF$<F+R}^E(!4!lWBmGzeeaWbq0o-hu>?+In~J2|*4$?qQK8Jb9muQrb5k
zviV9|{s?OtIV}0B0^fTI_dsf^K4Xozo_`qL-$tcI>6f3wy2DPm!r%J^)?<*(#*CLN
zTjFka{=OvrqrTi^OoF82(rLcN;T4Vin^)uTARsJp;~N#uuFh8}45`7PJd?v09vt2W
z2~X7I{gk$a7f)8Wt~P(FaEF;sQP|y5fk%9Kn$kx2ad<7D$?n$WP&Ns_uFv7kjWE6;
z@27t4+eRD`uW$<_-lisevfgmJ>&m+~<sBKyW+SH=hlf|$1aN|{mFarJ$;|t!<~$J0
zlNr`pFC(G_A0|cp&S$*2akeFolClvJ$l=bSrw&gQH{(=m9>?@ib74~qYRlnHqsh43
zjz3g*JqRN}+U~(TRpGvluzq&d7}<$OL$80^nco6&a~IwR#oHk$>gPiF9nc=?%3GoH
zy>1x6lJVSMADhnK!SAbu`qC6tU$eqEJTE}>Hi~-ke=CgY#TQG|6T_INQMC^bSEkW@
zIpZ`ye|s0V7&H5G*c3E@X&{HJCR`Ve_m$8;f<to6AIiFj%OVuN=wkH_!{ir&9z2*I
z(toN2i8nVRLN6M^!}SGbSNOf7IMjZSEyn1#In;7MvvGGQU#D>0yBr=-r0p<_!$v18
z8O|Z|36n<fO$wWj<nYKut*mQTKIB=-6h9g=kCo}G$Fmgpv}~qV8_UCm*ChIgG1ABK
zCJZFAv34AX3XBvQ14$=RCtLI)Gj}&m#Bz8LfI+YKFW$h2`k4DjzpQwET~bmaA1di*
z8&8rHnG884{O8d7&^!1sJ4PJLmA|?_g@4RIG8<jecul4kw1n3txPLeGV}UYu#`p|a
z7>Z_NWhQ1mVbg4$p>X{t9Cj;d+fL**g_|aEc#M*^&J>=maLH5-1&y?D4NyJ-EylbY
z9wW71eTp}f?2~6yOv`3rZjyG!Y~0j@o#yfb67`6-ytgqRm-i*vViY=D>(Cec&8r&z
zdAKoXlyg4crZ7F9!}||u`z_?ULfBNU)ut8jiAwwIbGRweH(%!~74}-f;ek&x+*ry_
zC@fyizgM_o1;48BvsL^{g(KGR*$UxHQOzqhukbULt%tiNC#<^>^NZ#-HgR|dLDXTJ
zHaFt8@CYTtUTtIC-HIiFT!(GvQ0EEn@8IxBK)9($U7p2wcNd2`Pudb^MX(3#=3|xi
z>#z7=E*;=&^`z21`-Xp^5I$I8li&;+hwO)HOmmGr$c3_3`yNX$Y4`t7p^f<u|3qnT
z9pdmwMh;m=_!fm7iuqB6HB0z0g}0CKA0+CK+kVEm<9v`ZbvcQ9k)|mv#X>?j^)z3q
z21GrEtVlfTx-uQMgrD)?7nf|r{>sOzQP<8_EYyCH2g!>P+c)|e<>ee+=V|JPm$|#b
zTGuKt@OlOI`=bKK+=P@C&F`neInjIi>|3zYi=N3n_vbC%kbz`28sFgqBu%)>|CTiC
zK0MaQ+VBBn36b+5TqzM;(rO|Zje1XDlaXQWQ+T=%`99-`k|6ctq;uITUc>Ny0S^jv
z(Mg>8Qi%qL@ScSWN@v<!Ni{TWo^+<D?XRj0lZNJQTArjIOq!6C;I1tv5?i+hiIy|H
zjo}{Jhsw*d!mF0HLF(X~LYMTDw+8Qs_|wCDv`-|JSzNlrI<DpLx>~lh=GN2T?G;DB
z@y2c<9loYQjX-}5sv{caH`2yRdevCVkS_2%v>F?lYVciwE_JNh1W79cT-2(CmMfhP
z4bi-e(v}*$ii5KbpJjE8v_LIdj`*#$G8neDT7q<e&oztjw4F9ax+Dg<rh+fF)<*ka
z*U~=gs7;bC{++Z{lHg0OK+Xc+aQ=FLrg<A{L$r8lg;!A-Tcfy}wn*wSdbncX(^Jco
zI(R!(SJbq(E4syfwE1%8sDaGSnBGqtE}d`m*U~u!A}L&3Aayk(T*2ND=~`s)U=1Ec
z7%&J)A*1uoNOwByjI2Q?osqtD%o*8;&Nw5z>3}n`7M*T_CmwA^deOONWNkXsjC7+D
zO&E^HnUOwpmI*fe7XUo*5ED8)!Gx*t_%f2y*(D4pX^o;g9a}~+I<o{V9$11BPb<L{
zk18X>Z5IsBp;~|^yru+?)>h`=;pYNdTDvM$^5M8zN*R@;S(T(Yl_XI~`n-~)SCW=g
zl9st7{AXl=t<WWsw55`?t&+5-lC-yybfl70TuCaaB>h|=^~aw-Q6ZvKR!O>4NxD)=
zy5^E}pD|hxyy^8FqXo-9n?}n&Hlf2qZ|LyE8#+Ahh7QlVp~Hi2=r9$a!y|6!@O&FO
zJluv3Qvo_W)`kvK0Xj?t=r9$a!&HC{?;UiM3ee*THgtG=4IQQebeIazVJbj(LHCc=
zA}DopDRb?#T01S)PHVN(Qth--J1x{s>$KA{?X*feEz(YFw9^vpv_d;A&`#^K)ADlZ
zgxyYS%cZ5+ZDnRyOfIb~mlkG+6nz@4an8z(zhgBI?t7ZS`T8krO0hYC%}Jv{ycXy7
Ee{EbCasU7T

diff --git a/doc/LectureNotes/_build/.doctrees/week35.doctree b/doc/LectureNotes/_build/.doctrees/week35.doctree
index 28f58c1ae71eadf3725eaeba59d478b6535298fa..72605c4d9587969b4853c8861ef764efcd5c9138 100644
GIT binary patch
delta 11179
zcmbVSc|cUv{`V~70)wK03d-UNA}T1F2naJEATTQG%Ox}1N1h5OE^QA;O>u=r{YGlI
z<&tD-<(MUESr(?Cl^PO?sW0tmZds=0`<`=V=Fafz{qy6Gd%5Skf4=8@&-b1?Tlae{
z`PeIeAz4U2WI41UZ$KI}Xt3rs^Rup|>_8qF3)y+BEd(uK#>VDG&#yK&U#<<k*KT>m
zJoB`P=D=yQ17~LC2IiV42hJWpV{+j5*@2xPCy(`pW~X_JW}QL<72l*elLK?J;B-D~
z1;1`&o+AV2WzCsBDbPHA?&QF!)8<Z|88~M)su{0z&B&TGd3xaFoH^sCi_yt}S#xr;
z=j8TSEnEpkUwr<DdAPWgbt3~c7c94+vCH$}OYZdYGmx{4rT)EpSy|j2{<D<%L;hwS
zPVXz;XZrsCJchcZ2;;B5v?I)1$-H1sK69g^HbGn|_qP7BfUP3%{USDk>ib#93;uY6
z)Yn;8qKEX=%+InS-ay(x^FkKkvG82y2IgRMS97aOWb$6j`e-tioGC3KZ!wEjav_$C
zQ=LfPzmrQ_!h{i<Eh$&JgmtjVfu|?yM21SiU>Ac88koD8*_;UoJ?#;=deQ2F)vsbA
zq%Z9)#0Oq4WW&h>AsGrq7NYC?Kg7)qon`GY4_(S4$-KXF_{37y-i8LaEn|~O;oouX
zUB<%dh1F^~>*W&GmcJ7uUaXA}Og|h(7oLMVudtSuhhgs46__hRzEttt9!neQ|8l_p
zc|S1dNlUo5isg{+WTGHr5=|#H(t>`q#`+z26|?U2J88hfiST(pOL0ak>&q|j-Gtun
zXE}Y`;IX-L7kh^7Cf?e}`aq3^<q{5t5;mCXBVp5OHh}U-s9Vh<?8E-ruzNNS5ajWh
zEL@-Fq)`|Ik1e<W!`8AZv~MKbIZKWD*-k7fuFS2hGpq+zOA>`qKd8#%eaK)aDq*oW
zM7ANYk}{ZN*axdhaPryMB^I+Jg(gNqP8Dr~q_4NLvG^#E)}MJxGYZ-3*pGB&Bplt%
zjryY+!G`jl_3Q)kwsHhDH-n-L%t*H({{<SM|JlL+cBJL#gFuQmwBT`9BPgf=q4tEV
zQg#?dm9mSpJW^l|FKuM*)CujK<diTKB3A-E8wn(jN5G2BxM)w=Aa`c?xgG<8A4sGJ
zaAUL7Y)Ac1(f|xQnGsU9Y8I^sH6zrszvWK<c554Q4|ww(7EIc}(RWxZ4nwmN7B0x?
zzjYNJb#@R=m#`?oK(@0PB-$}7uolA=+u3tc4#DoVD9ACb1lZl7Xb0OvMhSOJBKA#t
zNlWXNo$Mz<&HX{H=1sd;ILQ)fLm|H_Z|MH5Lx&kW%UHDFtUE_dq(Cr5KvfxYCuXQA
zW9^Y7mo;(}ui>5H;xOV*z=dtgdu*s+!>FP8Zq||PbRo~#&3XxP!9zdzayJVkpSX~N
z-e(JheT=;u6n({wF!n>{303bPJ~ltb>|t*S4Pq(`(|orFo4A*)B=oBElU#-0_OTai
zPvRzuY2gQmjbgA5xqryg>kSou$TGx`F!QXl8OxopmJt6D`-}QVLHI-xrl0Vq1Hrb?
z{tWH}mi_Dz4UMv-o5J9T72&guU$U}a2uAlct~{}ns4>b?oYEVzK1QDY@bbr4qA^Ve
zSpeRSe9SVmC&NJ&N&BP9!(mW%5a(H26vZ-Ad64xZG!q}Hjga~&bF<m9W`4>Dp)V;X
zHXPENICO~ZqD$2HTjdT-aHyQ+(zQ|0zA-VnX9e3QR$JI~jComCA7=Xq*`}P^22+o+
zN!k-S=e71THrRCp7JSBv=r-xIe)C#Qqc#0=)`HM;HvIM-a*)2WqOmUsCQgEI6&8QV
zw$rOB?2O|W#CHne{NwB>d8D`=2|zo-qOX`AZ4@m5b+5p<9z|I$)wDw{B*#%77Yg*?
z%nwPMzQ)bAn?}N+))j1k67sWbtn`5V3f756yRclXU|ocIk&KuVXzIHtOWn3s){GNu
zA*CatW%+f#qJ^cLPCCV&p_8KJwAgb>iHXYn?J4#LorOys%Oo_b!W`P7>`}!^=xa*g
zVU;G(?ljv^i=suD)6;^k_Ebr!d32)^s5qlJcJmBNrgXQG=uqh-A(Q*&_v}+j%cJ4+
zOzI2S=dqFa0)v=OaQdD{(97YQ^Q;TrHeJG*>-hs~OV24lGJcTc=|A8mUk=-T!2RpG
zpoBt;YRqvtbgpL8@z%T+=X5#jt7a3lr|?=_D}ydDUmQZsal{=AH?ZQ^lwQ4n-BLL;
zt6^h^pP+Pwtn0KPl+>^^9KTk>{Ojq8{E?;C8#-Kn=mm{ouX5^iEgM9J2m`9WkueK2
zNDXZ(?y_#Ky2yga_<CHZ>;6R+uc?$FO}~WOw=JZXwUDGr(Ug>9f^g={sFU*<7lW5|
zMIF-<u@?#_uqn~OiOZP2bup@h|8kklBcu$*Uu6NbEC!B#%)FuG3QMt#;jQ2*g4yOO
zOLiHW<nrVNzSmeFDv<W4Uy~MO8Ci9WjU}`?M(&(Fes(fF_-DkF+<=YO*+z0#I2emh
z1vhZ?hV%z-_inJ!^ag7Et*fQ7v=jDbcm5PR$1kYoMvQ6`P)2y@_8;acSerjFkq$0w
zmV$ryN+novC;T(SKB?EmNC$myvT8#64-j=u|ArG)H8vxEWu-J_fJ&7$mbWLvgmRTo
zkJmnS2q2GW3`q(U|Hi`MliLadEb7}Y+{TJIM~R8P5Sre_-eA@MWug0B_K+^HSuosV
z2C_`E0ORhX9;C`CW9Rz)9_vFk)Z_A9FhJ|Lom=Jw1H|4+7Qp8FEMDl6oA7=i9s$#S
zlllcl$bqg$qhqq>ge9^C1hS{FCf1zaSrMV92FSXwxluPegtM$eA2J_8YX`v5)3hJt
z<>LIx=iJ?rvd9NwO}v?S@+Q}WtyoeE;g7IT)egW-ye+s-<UZsNJLTddETu>hp4LL#
zW2}QVzGm&24{aW6$=Ms>-os(K7Jht;{kxJ7H?ad7pRi|9S|*_42?mCth`sFQ6BbHH
z*qS?H-+wB{751+@#g-^8Ru<0diXa5m==l{g7}<mQ8q$EkN~#O+xV*(-98)J7py7lE
z6Ie+305T4Uj{C!q0Nxn#I&*(IC02Hu5W~0|9T%(S>NuFd_#}Lk-45P_*N+%)spS1E
z{)<{TaI1$RUFf6{`Ok75qQnyDS|^f|v5h)zv}wjpu@5b)$0qkG>A4^5Ysh=ka#se6
z;bw@(-3q6;<;=)!#IH0WXC$2KnsEWMg7cGRd=R}X;q++X6Y7{IYC?_n<oZVBwh;5^
z5a&!4ozGXT`CaNB2S=aB)pN5Ag4Q@rp{)1evk3KxQ){rqm$#?w<J2b7)StWKi{u}^
z+<**n^7z1*w!AA2h6ixJwduSgjf#_7_XWkPYsWj;sA|J8xsbQC<NY*MB!GK?ryoyo
z8EOeD{kY!Y(MNtfh|YBN$k(4IDJys+;Lp3ze9ejwlrK0wfckqXHq4<bN9=GCVDnRU
z3nY+tqB~r8WO^c|I*>%b<V)t>Kz@>b8mHQU_L!f>D2B`6+xC1ep%rnm7BBB82@2w}
zj=YSJYJpi7HGMB*CMIHiSQ*USkWky1htO(;uw-*;Vg7JsJ<x@RA*;$33*w!rn?Yr3
zOb}+P8m0vCXib-d_*@Y0rOf+Tj$8|;oeVD4OM-c5J&8Yqv945uXICCi2e|4l?#dJD
zal3^`_mxjWLU5*!a+Ns}!aE2V(UlMT$O%zv`)>Rap>quoK8qNdOsGLxtIXL3$j>5)
zdhw*rSF#P@$!HQ>>&}w}-m;nR!4J~SD2dHH^z4avml_n_LwfQTDA@ys-aG(r;W0SP
zehTM9wW0C7amd_@r`H?0)r${v8Ty*;L8T?sPpduTJY+}kSY+E1!A(e)yK>Jy%7KC|
zEZRE150B8%2Qn%n-0sgC(t8Go8;{3cF;U2O+ZIl76o!Ldi+N?e6~#Lc+S(|KS8F5m
zis2KrM_J1%VtASu5;(q*-rbIlO#_$*@O;|GsM<jui)Av#sOE-S9L|kCkP(Y>0~usz
zB(_^R#EC&r<R;q(!s3vz)F5##h~uBpSw{8Jw0XY6Y8Dh2_}4VwS=|z)PQO)S%ZFn|
zEROloYv>k_;b$2^!jv1&&r-S#Rb%pDMIvuRw-^;n)02>IqfuqOXA;7cWfb06mnU&b
z=o#e>97)EwDup9na4DJJq?e3x|D``8j5j0nUpl<KWR#5x-qH_;!>$ypfR#pQUd4T^
zRVf@_`5VN`{rAjGhlovY-!#6Bdd55L!GleB9@)jjWAI!ceGHHAxa`%#o(s=-Q8%Cx
zS<rwi40laDh0su`AM%E19+wW`Z_{WL80QCLhjL$%Al1RHp~w>r)}g$cAd8a-thD4=
zjoL0cUh77dldew3e<&cj)c4ah2hODP^MuY64jAFqa4b2t&^$(9f&7<H8)}JrwIO7U
zkg&*YsCWd1O_wXLUmEG~+WOW=k%9HnFE}`ge@wOt4Y6cBd^nn~C;RMA#bdBCua6g}
z0)B9I3?B-kpXZ*CF@}dB@6_jTcV7=h&+%xxJ9W=-pf%1&|4p}ZMWW!5@YDf0O2|XQ
z8Ws7n=T+pQM(lc?-=d8YRE;<>4hcL#Rq<cO@hIw@AgZ{>h%P<t>Ej79W$F~LV*;E$
zj7`mq@d%4uaQS$Ci1tnpMIoL>Av+!fjGl<_^oGg_c+l57!O?$FlM8wBL_SuK#p<1v
zTi;}>NqjS*lM>|i@o2J>t8J(7a+)jDwu9fN@KpMWQhVEsR&!y&RNf28%Au7mq$o3w
z5u~F-h`*&OS_d1<SQIw8@H{qS89?n~(hQj<&C2}Gn#NzF^nmooWAk+<cNKsmr=#w#
z6oC6Y!(0J`>(luudNx76QNyDdPWbuG<m>3Q1SrnM;&}`2CAbeh%|Z?w6ep+-VuOJi
z5u02$Jjp|vbaZUCa#XyA=VkLNw9P<uTDi#C5itY4%;CFf?}2g#c-$>>ki!P5FziRG
zJ;8T2f1er#N|?p@DjhUXCf9#1+A<83Cx2L`igNj2`kX6C_8SI>oP&)LaypK|XpY8*
zq9Jp!buvJ49!?W9B)Zcjb9torU(AX7F5cy=V>PsRpqvf?^U($LShmHn^U*iDX`p)1
z*ts?jm)<7eFY_*V6T0!1`Z6CNSR9^^&ux5>ukh|RK4g$Stb2vG#UT+G`O(If_$n?^
zhq}F}RUN3`v(c0P#S`n%vlD1IZGxxKdDyVy=af9$aGf=bpaBkIV!nfD_u@o8_Ib9b
z;QIwwD4OMAt0RICFW=~^n4u>N6cTdByjg%}yCfaz7Glup&|?ALPSX=5mcEbvPo{$w
zVyT*{n5P0+gge|+$qZSGq*Af+;f+Q7UHWRGggx(dC)i70=T8Y;k*M~UHHmU=<SoY~
zxB_|<V)wWrQ7(M>LbY8Zw_B0uRH|uUuv4vGp}biEd?_D;dPE>XkC+*jrP!6(&3&cm
zL$)Eyu%C0~-oFexLF9HMoL+VjS+<-9JG9-`NMbDi5N<uL>MSepJDc5j(<J9uN36t2
z?8?1wr4x6s#w{HZ$-|ID^2%2!oW;7VUB!=(RH!TFGwJXo%ieDz^x5I|B9fYfn`jp(
z+KXRPUMxnT<RrCPONz1a#~h**9)=Hn1E>B}D0%}c*wiGM_XJHzGCG0@wSQ#*7_yo-
zg|H0X5>8q8HM%%SB-vvaILz9uv|hvK<M}vR!M4xDf@mo!UmO8$Yq3f}lKiTHH?d|X
zlsiewy18sEf1Oe*8m~6GU)89PQGx~YIEvxva%G7Ms(2A?W4&L(vkCn^Ngm<qd-t-V
zV0Y*EIzA7NR;4@g1L#c&v3~Oy2kTWhwVo%@tI8=S0_u=9rf(27bjhlmlq&10oRsnx
z3H44EQ)dSCOU7JB!0oLVDUMCsgq^*2vTRB5@uN+Ay!I%kY3gR)S`68~hjgN`nuey{
z$xc(>2dcI)9}lPLZ#SB*i3GTa@WAmiC%FjNJ!!s`j}Z=v!xq@NjeA;3Q@S|ZmK8%d
zg&F#6hXW-Wpw=nx@OVNO$guEOreYiKk56i0TZAvY;p7fn*b89wc0Sz3C~jh1w%ftG
z3vRi8y{B=DF=-e1(60WtlU-}rPE<#$l2s!z<6V3@38z2fUe*=w@}qdfqkO4_tTNmW
z@JTF}>M~5zNwk13mru(0XN25`BfGiDCJHm=(pX#|NB8qki2D&gi2C)mPaT`o{`dJl
zLR$=yS>LtSVHHm7<;8f8Cqyk(nL1dx&tVE4zetN{n3U0XuxKh_(--LPuP@OoLgNO>
zM8pk()6bHTBu!|FC2?@_BitMvM2XkX{WwAFj8p84#EM%bGK!ui!-~!Ad`S_Eo_W;Q
zrh~+-J;47V9z-U49n_prsJwfCZzc3i<*TtyBP(nl7f^3PcSv8!4*2&c*iYk=uo?C#
zuBijUW(3rHioxS}_fG>9xh<SsM}0_zMn>tpL%gj`m$-?kP<aTGh5w6W^)HtQT5+{4
zA>=w#9o7={%3}H)c__3gv=1L~pluCZLN^lHC`F`5|Jth&jtq(rZqn8%vR>T&T+5y3
zF+Q4hR^#iAIW$4}F}|AiR*E*C&=grQZxbnrhq?;fUE)*V{dZ}Mcsz^cO@0|3jvq^S
ztRQXJMZ4QL@kUPIYt_?TbXdKiCtq`eLxD)%9H{_@j#S`|tSsRT<%iq&Ecpph5LAh~
z`l<@-EaKtT2`rOnQG674zpHtxGWX>-VrSnjd<<C|jvsQ~Pm#-VS0%=~Jw+YxY=@##
z9LtvA8ce@%;gBzT+YuyOi3gn2TRp3|AE7^{sBb+!eO&PNf}+!WB)zG?^*N)!6`zQr
z&+yBXK1z{Yru)?TVg=vx4b(kVOfC7*c+gpVxoHVu=MYx+RQTX5)(j-uizMmnAmyCH
z;}T?%r^e4XhGiuY5;(Q;&MQB}wpn@}{TP#~+F82a;m62SwLyOS1J*^eu;dS>YTlD(
zBkwR4;jXco;ZQY?lT4_*=LJ+gGF5Js!!GbybV({sMWg;lXVr3}2&&;`Tx_Z08vxyy
zYAJXS0Wp{GW%5l3sKs6dDdKqfO_*MbeH%X6qooI3m_sjO=cSnO2KYl0f7o#mPi(4O
z*pe?{Q{iBf>uvWX+(B_jEZ`<}d=Pwp1q=VG2VJBeLYah3n8wIz>ttlAY5uE@4<wXg
zp>lZ@a!Zrb>XV<4m8Mz0`iXl8E+Ov`%=_9W2jU~Z54y^~q}@@6I7AJ+hM|W*-LJSt
zVz2QpXcUT>!t@c{9AY8R{yJ|BqyLQuD1*{u5gzw5E@Ye3zkcSE>1ZW2>_tt=ic*n;
zPE7;(_WAY=&CsD6ScK-KK~6jg2lrnjLD;Z%|Aj9nbdfUh_&*LK)^;~}D?-<#sY9&v
zTlh-8K?PlQ3%S<7fm_@U>9U^VE!~1YN%<9znY1BM>Q?^By~U7NPj7fXV+Te?@`QdN
zg8<Jvn%%HFJe<&P)4;QawS&C7c#wD@4VqWd9+shDZ7gNon^;16x`Y2cJnH>6&0^@;
zSKP!8uJBgUGuSR_x!BV{A2=jKo2I;}nMc+oVWC1oB+Q8rk|q;&?>?`lz9zNnKK%`o
z+}fnpNx%clSg=W*ggt$L5QLf3QQ6?%F^FIo^E)<`!6u;?-oqi3lpAr?@BAx5lT9+4
z7alsPeDn~T%26h{Bhn1y#y%?h5vFJqy!?nSMw0aMv!xF7TAQqf$9Vif=PPwbo;azy
z^n|}mm!J%`i!1)p9N6=h*z?v(36Hx^os`MQ)>w50y3J%E9$o#`{NaN?A;dp(ka?&%
zB!vd`vnS3Ljfv>I2>nnfGs14Fb8`T6lIrs5F_UA1rr((4il51KZsZtLGF=!swwCMq
z(OMV6i(D5i<U~R`%yG5X2J|}JWBNcvo7zw(^C64NKO5?1Q`&GaTxzU~p-l(NnF6LJ
zx^80dr6#(U#J%`A9<Kk~NhyTy#GWL{P4^8W6RloNbw4rRetqO`67hF&{FyL(P`_@&
zW93cIyoIhWDTU+~I)Abernb;^B74PP8`#=H7l@QETIl-lw+A<90O>7s-gw08)lwJI
zurCf|hFcR_>V6=3NBZHzA#rIFg%@veIV~=y#O2KxysQzIEc{-WIbB?Iad@HPvfhA~
z5^<Ss#LF~s`9@s678jC$m%s2}FSGkVyo89$z$CmF#ias!>CEHF(Rdw^ikEb82};9D
zCvovI;ib8_gbHuF;$_bACNuFDpt&z*Po6D)8<^P_&U@=RVqf#vTlbR;q)-M?C<7>z
z&KF9@3#HSA(&0ksY@u|tP&!#C9W0d26-vhnrB8*@pF-(Nq4cA0j@d_84o7#)F_~@@
zZ*OE$yk%O)wbp$=@+6Ym`{IB^5|e8~vaNtqBKe*8Pa?Ta04tH4C4iMkHWt82BufRb
z63Hw9r$n++{3ns*0$qt@m;m;;fHOHM7_Sn^lj2z-IZ^;Ckqi;Q3M4bJY#i{>-6uKl
Jp094+e*s(unyUZ+

delta 11024
zcmZu%dtlAw|KD>t#&(urn9Xhs+pr76W}EFCmob}d^(`f}xn(V8V?xE|?wA;dy-Q(A
za%YMY=9*MOo665EjBbiTh{AsF_wzYd_0Q)y&-1=K@AvC@Kkw)Lc|K>}E}u0!eM)Ds
zS^Q&B#2auo=H}+M?1l)iEal>p5^nN<x>=$xRDLVn;p7aF)F{vWg{65-7CcT^$De&*
zxj09xVO@g%m-q67;1R<Lf`^S6KWf;>DZ#@>c}&V1RS-OBRPfk|V~Src95W@jI1f9+
zipRe^V$=kv^AXJ<w^B5P>GQ-huwahxHaE`kRzJYqB>c6ZlHQs8*B(&RoX5iG*`g(!
zFo_5kZV&U6mpq~Ke37UP2R%&YGR{dtS0<YMheSr1XrqRqq)a69KxYxp1>y;f7G-9h
z5W7G;#iQfk=42KPUFM(_XYL3+6wh+l>;VuWT0qcH;m`XztD5yD4lD2Kdp-f5yeUTU
z!Oryjg`%CSb+BupNOH2Q$cep0^T_|g8m7+?{x<j&Ak72+3x3GC&YRn<VeNo5Mr>#m
z8ZEW1veTH?(%DO=FP*wHEU!g=nUfKq_Yq#CCDnXC+S77#k?>)BOB^)$ipS_5wR6i0
z%L_-5jd5Vmvt}@OF~(VS9K`GvWBK7YsCxm|a_kb}!Kz{M644oH=Is5^UQ3-t&5Lte
zST5$uEsUR!GuM7@fZvu1Pj1usXtn4DDa%ALzlOqh!r|gF5z24JnTx7o;ZcR~z;W16
zC}Umd4dPws<BDVu@eRutF)$QRXk#4B3)4XS%>(1%<|%H3>bDd@^X0?`qFu$?;sT3=
zqIX09RQ{jzf=0_l80!v~-oY@6jE9##6fsu1x$<i-Wg6>mCx@*Q2^zV84Y7|F)o@=D
zj$ALE$5sJya(R0PmddaT>oJ(hC(CX8)p&@h6-Lj44wj0Q;&V2K?CJ#N>x7XnjE95g
z5bH6k(1SVg=7V>GsX?sa=qd%KQi>>hL)J10kb9Hsp|Vo^!`H?u%rC5V#e6;6srh|i
zg^c0*;?0ZGy26e3k!feVg4=~&<4RX>BOjY7V<2;l3*0T>Vh#6(0|C4NtXLyX@Lx0o
zwtV0)z=Gfl#_rjX_lEklq8)eZ35(B)SZKWtRo=7WZ{<>UHhqjit$<>%0u}lggIWyK
zq!t6))t50qs@FR##&tNtQ+mSmtJ0|7)WNYzu)2yhv$$^*R~XOg2_a_I3Ur%A3?JN6
zWe@$6-`Kgcpm?)LWLZ$PSqx$?S8Nf<*h$$ULa;fwLj-B009ds}bYLY`y8Bj<Wg|@7
zD%!HeR>GOBqKl0Xz73VUZzYs%6Ekgu+>tz+?XVK|Rf*+jr3#4o+clt-{TsH6g^V57
zj5rR@eJpYuy}BL32d;lCG9DWmw?kyR3>EX^O1IZD4xe#@-HdJqAMO;7c!LCp8Ns5x
zhW~AcL?me2>@N$(pihE1J0n^@(uoYwyF@)}1JS!h0gp(a@YBEKptpgGyD<&4Nr0P4
zA_zkFh+JETC76p|Y6iRZV8FCN#kdE&tI=hFN-)!Otrl^NKZ%{QM%cO+SK4Zd<-}f$
zIW`<>_K8H>AcX7}8+oC!4<7BetATr6STUcL03i*TQ9mxs78j^X;d<|Y*v|OE1T)JC
zWDDV|Lt><(m-VR_ZtYP+*8cpdD5u|K?fS#oGz8z5hY`O08hmj7GbB`7XJ~aqR55;B
zo8dV8_PO|wdZ<AE@m{+<)ll<=_>NyuY}DNB*&42VDcbTs6s9olE7XbOm(I7gk!Ku5
zGD}oD-b#i@DFQUQKQs;zt#~sBon3*~zY@KOO!?W;L5A{B7xI8(qCIjI9z$TO6U=pM
zTUZVs6SFu^Ow=;(g0FEM&@*+4Z2VgE;OU7fBu;vU+n}ws1lNeh3^QqTt;n!*FR2x8
z^L)h(FPu~Wsa#ijQtafD6IF7X@{I<ZQvdchVg#S32}FLY36MqE--`a6S7;LFPiYcr
zF&~@~)ts+QgxUh`2j89%fqXL>P9?&&OTv?_h3K=QJu;XLF9yJYZ0X1LL-|?U<ZGek
ztcb_P;~WB1OQ3XuSI>#2IAl5}#*osOPceX7oX3!`b`W|BiOuJQAL*nO`|&((|37Uy
z2YfHWiSk-xYbgI-Byn95H2IoG!o%-HI%-b4fEKzcTX8{TKQ`3%;=hL0Ulao!TyQB+
z2BNxdm&5?xBgx?~v9R;ppIVjo{=6hQ@BvO7DD`Ze=<U#@JgTV^u{dP+h>u93eBMjx
z^AWx%Re4zp5sZDy&C5d1_?#q_J0R)@T#=bc+V;x)K}=$NX_DGrOX24qar<jMY6!hI
ze!|tX4?*qQ%m@DdNn|?46x+0)MKBG~zN`6J&7iWxpFfMCj2(iks~BpwS+`%syvI&L
z)itaKLVgo7`Pn33*F`TJ`|&qK^Q30bNf>-hJf|@Z;<q&(B!W6^kckW|xGuakmI!n1
ziBRSNi|>d|=HR4;aOO8O1lguP?MDsS_WbV-+ot_4&NAMnm&#!8-oTxM2CC5Bb3?3R
zUBGZh_<_GchA=$s?uZz#8M`8EyQoVqU<ftGw$6{oK=3UkPr3TT<Xe~kUm%grP+rBP
z*OE(ixgou@DHi`J?z304DL%L@3~U1NC-PTNFNTCh%4D<EDE3a=5iOCZ7U~sfa2JCD
zS?m6fXRwvTqj`M%F1m+Y<S{ms#FjeE4F?;_mX_##c)CI1OQMnGyL+OX@twVBcYD3(
z-qGfr)k@13e+wPsM|#1*S{?@%by)UP>tqr;p{9iB3egDWKft>52rPSm+2%+u3`&0(
zH&V7@m;TMu`=Ll79!lm%V9i6^>{bcNh3x*nB@B;5v{ix{TJW`x#54F?t3jjcaq=PL
zR|`v4z39xiZ?Z~-`llavX4xf~z`}q%Lab`?b&$cNr&ScjG5I6!o~#N){rk?6Dsdg)
zGK@7^)<C`Zxw*kFLiXbQl414RJODO#lkM3c(i;nvQhE|0<XzDUjz~EYJLD}jWP6TI
zHY56DaE@_EvwqOCfs7y~)ZUv-bC76^6f;eiue*#Sy_DBfQC;MYRxWkrSLcnDsYOHC
z6;p$=p=QJN2>q?24u>s><Uj6wce2X&_1@@?En<V3$N}sqiEH>RZ(_r*rDbmusdwk6
zH7R{7C8f%iPOaoE_NNkp8$-Dcviy*E1D&I)uh379XPl*I+3%r0?zBc=2$G46!O+&y
zfFu<w4ED8_;ncGy@wUX*2@WKqL`tyqK#7+F@W4bK`{B{;-#qStGR~njH&DLl=v@rN
zmm8Zgt%76+_KeM#X+biTNNT}<2*L%=drUV`Ra!y=Xr-qFOMklrhDbx$6O5<8wEqxG
zeu~k&>d+q*B12jEznN&EykbXpvTaaAP-Uv-ZRBybhWI;!cU##Qp|ymxl?xc(o}$&-
z3!P;Y>fY_-CdLn0y;0$NRGYDIxM<|L!!B?Lj2$o(52;0<##WZ#-d5=Ui@$Z4j3&+M
zG#ecz+p$~383X&mFjx-3(J-0l&<9luu`o^y#}^|_x%ul=p<Hi(gCj(&iyaTcWhaN6
z0{F!U+1xsnA1sQHVZ6OTJ6f%C-HDKW9+N5PsNB)a`>3Pr%2QlrLOaPe$`*XNe$oL1
z#p_L$2unK4qfpjao@FmWlSFB3IQ%?<)gu3S*cK_X*|XI6!T}Q&G-*+?KQ4w=yGP00
ze7-@e-N%d0wndz4(6+%x(K3hgw+v8qQ3gTRu9!Bg9cECz9_uQz9YatX#eLwZSm!at
zb|zNtAU1ni;s+4RW{9O@&bPp)yUai?Ivl);9RxIHdV7&*Ip1Bz>evPHZvZ<-9`)1D
zh_Ksy+R4W|iRdHBQ6yTPOp<LFuQ#Z4S8srdUUGz^tL%$RmgzJ^2l1w4%mY?gIF>9+
zSpYDD^n=kUG6=6(rVqs3U2bMNC@^5?1i;}GObd!9f%SNd%ma+tX&hiwXI@3N-QKxS
zYmlcf&nty01)VXX!od*pg7ks=M!5s`GR~a93Z1mJ?t?se5Y|U_<9SA?yN5Ac-bZ@y
z!A1?H(|zPA&KDXXW;`=A+P(@W#48^oR7J|ZklY`go2NQ0wQw-^N2mrHDI6>}`b*B(
zZihwsLr3iPS~R=*q{-|23!In^_!?qOW?#U;ftXajARl9(aXMOKF{&ynCS5jQ{1>B2
z+OK7x=~gw%Gvr!+&#0X@CB>M3O9sjQ%nepQjqsMX=Z)auAk=fus1nR&pGaG5S~WkD
zDbpC1e5<o$hE1u+mMd8(7zW7z*q<%^Stq4Vm0XRV#K}X!|4G@=#-eKOUal;yLwmcq
z<#o&x6Nlq9DGPVHHVf^oB9o7J+?4K5$<qu|GMZx4H=XYwYlsy+Eu+{=G)*GGLT@5>
zo<{Fkv66rb&)Q+JJbIQ^U>2|;7#a&S(<*Bk!GWQ8kjw(#=jFR>x$CgUEW5?#=xqVW
zrTmW{iu-<(D=X5z8jAU7mhwbztamkaBg`L4*GGe76l5La4Plo~rm$m52b8~v1;XLp
zDw-9aIcI+x_~S*4Cv=M5WE<zm-`O9;treFLm5an{y|wcoGZzE-AyM)AMI)#P(e4F3
z`=|)18SW%;W4PSQ{rjkDgSYLY-d6XHl%8$;`#3F;d#B(@FBj(pJ1vxdAA7CGyE){T
zKYTe-4n>t}9mf|(*+S}CZ)M7BqvU&xr)#F<jCL}mWVGDJhmzXX@O+*e$VNhNJ_i0!
z_&HB@L5fxqy=og>^|DN&(Sw;R&|H(KgJVD75j)RD&drx0q>d8Zl0(jBP;i{emoqr8
z)XaEitdkjg#-iG7D3=ip5e14shC@byJi+(%(cZLk#^JWHp+0S#e21Sv3EQ>msXkEm
z4%UM!3o)Qh!1_W=BhK_+T<HZxGFZ_uF&-##%y^|p{(zg+Fhv@{V}dqLF%U5UZ+ZP;
z`b6BsDy4Z8Bhk0776aBB*C?1)EVuITz6wvrwQCH?C9`liI1xcbvdwDNTTyUGRWiu2
z;#I7{uuJ#Q>^Ym<!bw<*p&Zq<*if}|ZIX<q-vssTP0_X$_wB2Iv){q8DdbBAS*j|L
z_opB(+|*Y~bBk#Ltf5PAqnaS^4cQ(^s{S*<);F-?Mn+}HMi<5vQ)Oo>BQ<1B{Z!18
z_}lK;XD$*OreT$$sm2Btg@`~<*L>$(*fy2Oey(gCD`G?_yXnHUrc`FRas@i>xVd{j
zwV|v&ZJ6%Nt4xiWAv=%}l<0YggPX?a1(TU7W@1LOuB|0|rVM8A!3?Q=`k^1NdX{`k
z4OJ|bZQzyJPN7gXTkhhS{S=6qFlr7Sp_y>AT*i0>{PXxK-JK&huu-sjuG0dEd9t4I
ziTyP5ruNgWjW;jCsGbN*=3~7*v7gEU>Mm=ME4_1>^dmaG?M;NdGC9QBqlT90uQIIa
zNckf^2;Y0um9$m&M+-1EHCY?C-<z@>ajTCaM_t+fcoXxj&CK&oG#WfQi`(q5>H2FS
z)|@u}yH5OQ=qHOXyj`bmfr#1Jy;B{Q(x6(UiG(UGlgiP?#qt2}no6d2)IKaEq?)U~
ziPaaz*tSO3R6KFptLp*yehDsFbgH&{A1=XHjZA0R!KoBO`aTZfOt@{v+?JWDHk=b7
z8d)(@*}hNghw4hPg}zoj0YS^KxN2M>8}V_ekbPAcVQ2-WFx#}RSIEh{Bvq>&voi3_
zd@gFA8w&-1TqUXMQwTOxyBz~%uR3G@06B;ARXFciqy9&`dp5PFmm`>4Q=xXBh|%l2
z*t|#b;@RBS^6WdZknz2#>iQS-E1V4KxI#|i$5WxG3~!FU(;#?nh+V^R=&}-lI<8r?
zaixZ!Qd+Z;lwMC&mm1rr+eL6vE$dXuDU3gKhFI4hA&!MkAD{t9IQ|~KCp=7584kOx
z-j~Cix~nZ%IBt7iwjfqzUI$n4!D}$Txaf~}Fa$kJbvjpN@UViBPKT;v(vUB)>@t0T
zDF`*G?C_LB35}`iC*-FU*|63TL6)OyWpBn`>9024D-gL(_Qam1<8{)}6|Swr9Qz8~
zTPL5gGEzf(vUELWQ~Yg9oqU-?g0!eviH@26^L0+xs=!~jLH@-)fy#}TXm$XrmOhr#
zMf@OMAt`IHfjtv=9CgX;UR%)Y9XJ7gPv~FF4>5Kg43${kUA}AAtf_&qukvJm4aG8|
zy>10`wFQz@*sn@%XY6k!42?fR=d5B;AIZgdC3x^7+?*OOJeb1Ex$gjq4t*Q5Llc?X
z%<}td9D^rpfLi;o0Z{u48_Z(i=1x2^!yv{Y2U&^OtF*|D*wc6hDIV%(OyeoUL}ko@
zuVh=6YbSY^U@EdJSAge~a05xHFJ{+vVE|fvdSbU+!+7Zc^&0P4=P=ZQhK4g<J^&0a
zu^<?@7p*AQrh9!RpTsI@x>!irhv4FP=jtGh><^}WcrUlzg{);qt1dP`nbc}Fk0%jY
zqLusA5?OF(&11Y)gKc<JtbGC0D#IId`SYxfaE|dB|BQpGt!<}yypr)hlrV%Jc3PhK
z{0ysCV)`X(9AcW%A!YnI?v<trvHH*Kp#lvT@TJ^8P1UmZkJz*|v-p0F$1Crcrq-@w
z8f@Lbld!9u7zt_WOZJ$fh%k<=*vLCOvC=Db#U`HZ7*a^g*@TOO3T;ctUvSluwwVV#
zCbDuf1}aWKfx{=cvQOT^XA@0*KKDF<r>J$4M4Z55oi9q$HYud3P1?8?UB)rGR$`0b
z_SX_rmlEP;7Z!Ejy9j~8P5H?!2aFo}WwrEn_*t4NTs>QLdu-`$pOl07cN)r5ztK>p
z0=e=Vd71Mo2p@elAMGSodrDUEKQ&aauI$GDNz*=?zj+41{WA?(p2j4CEhR_h1$E~z
z92cBH)j0OuX}os9R=wE<xzbc}LB-_9t%Z&m`>W(4&dSRSUy09It6nd@)6SASP&++)
zoRdTF%PqTv7b#We@Qv_U;-{~~A?NWeD+`)j!3dSkg6hQFd0vj^g#$69j4<YV^a2&C
z!=mhana5ZuY1F<i%+pM+tdpKkln!)C<vvi=lKD9Q1Eh4IO2MU2b5TZXItH=#9P&6+
zehCwk#)pkoit6iR4kl5B8cl<2o9eItv9qbrY<d~*;gwwhF!nOu)tq!lkSbM{l#;)R
zc4vlPk$oBLyo^Po_a*s+`9z|-_Re%mlMVV2*XY-QmQFuPFDqa06{;zJ!tvyRY8A?U
zl1F&+bU63|p6DIB+k&ZSIy4Ez6Kl=S@-T0kuJ-KmUr?-Rx&nCbFY*wJfzqp3T_Uf#
zyu5r>j^YN5cgnAJUdy|`(p6Gsx;nszS31w3<U+1td7qOGMZHnuxNEpt+9a06*XZVR
ztP+IW-<3u+m8JA|*@E$@=~{iW;}3kdn4JzG`7+kCc@LWpQ=#<@8Gu|WfnbwuZUIF%
z@Y2dLL}%o!8+i3dWXzB8HyyLUb2sHxzF9e>uW;yXYAL;iz_UHj<c<t5S48$^pF-gs
znF<BB@x^aXy4eubof>+h!shL$Fpc*`yoW=+(bzkE2e%Z`XluOXq&i(K%HX?rC&^*@
zJ?o`_*L#U}uj;L6&-_b%#=SGN%g+(_WB~IefkfsF`|jb*yEk0I9<NvHWr@8nzhFE%
zLnYbdf6z&ro}7Q=Pdp_<JN5dL3ia(te`vma$`rWxK+Z)bWv&y!s(jBwyg}!=O1am`
zD!Uv`5mPT0(oGzCVon(-y)K`2qEaO7@X_J1I88I`AEt8{=FfEo{EvWLly``;t*mw4
z-CT$NyLy*oJIG~=ecfO>mqA`l2RSinp&27}rF>I{J@K=T9gen{XlLI9U3I!>Vx*4_
zGjuvX{H|q3#D(#Doi33WDQE^ZP-de$zEIde_kdr}+}Y}`xuY`A*Y3Irod2GoK2PU*
z=t9_CQXLLiw`BvU^3ZieB3$s$y+%x=cD|>kmM$4Lc<PP|HqbJ;vF?iS>(RybXEoU)
z8auPqztr%?(gZh}>3reMX1YK&7dBBd558)q3uSK;B@PF}eRSRMPf|HPI$!n{O!m=5
zGzc8z=9b^evd%|$hLx;~!_Eiva7)0)!=CuqMZb2^qcjO0Q|U3d7e4++kL$_!_>~^B
z4EUH%kN+9*kxh?}=}|?Gt9a#>{}Vl$_r*t3dUVF>IX{9P+xz2VYyU)iCSo4WkEciD
zbbRRP@qixp>ET1xHo?cl1&s=ZjU81yrEt^)`jcLMASAZbwZ)1kx25jNSaQUqoG>W|
zOv-qZGTfw$HYtNm%2<;!)TE3wDFaQ)IFmBWq--)NdrZm}ld{7!F|QTP+{&`eSN9n!
zQMi5B9Su~tZ6p{KZi2v5xK-0Hh1*PmQQ<a(U{tu>AQ%;Ha|uR;+h77u;bx&<3b$(n
vqr%OXVBAXJMW=@0Q{lFQ`U<yXf>Ghtl)xk0@^N3b_SfCUE1)K=b(8)d+=-V|

diff --git a/doc/LectureNotes/_build/html/_sources/week35.ipynb b/doc/LectureNotes/_build/html/_sources/week35.ipynb
index 35f134d71..01ae64c94 100644
--- a/doc/LectureNotes/_build/html/_sources/week35.ipynb
+++ b/doc/LectureNotes/_build/html/_sources/week35.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "82c2f725",
+   "id": "f0622ebb",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2fc786b",
+   "id": "3fe98f20",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77512f33",
+   "id": "8e604e3c",
    "metadata": {
     "editable": true
    },
@@ -49,7 +49,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41516757",
+   "id": "c7f0b40a",
    "metadata": {
     "editable": true
    },
@@ -69,7 +69,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3703d2f",
+   "id": "507709a4",
    "metadata": {
     "editable": true
    },
@@ -102,7 +102,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f22b90af",
+   "id": "bb3b5f67",
    "metadata": {
     "editable": true
    },
@@ -118,7 +118,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3fe305bb",
+   "id": "14444be5",
    "metadata": {
     "editable": true
    },
@@ -130,7 +130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2f38355",
+   "id": "4edc5258",
    "metadata": {
     "editable": true
    },
@@ -140,7 +140,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3d9a4b6",
+   "id": "4d6f9c43",
    "metadata": {
     "editable": true
    },
@@ -152,7 +152,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff3ba043",
+   "id": "fb52f7f5",
    "metadata": {
     "editable": true
    },
@@ -173,7 +173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5de294d5",
+   "id": "4fff6b39",
    "metadata": {
     "editable": true
    },
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5721942a",
+   "id": "54a4cabb",
    "metadata": {
     "editable": true
    },
@@ -198,7 +198,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b2aa843",
+   "id": "d383a507",
    "metadata": {
     "editable": true
    },
@@ -210,7 +210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b12c06f",
+   "id": "498fe31e",
    "metadata": {
     "editable": true
    },
@@ -222,7 +222,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "276d4eba",
+   "id": "7bbbdcd2",
    "metadata": {
     "editable": true
    },
@@ -232,7 +232,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4751c9b4",
+   "id": "405a61ac",
    "metadata": {
     "editable": true
    },
@@ -244,7 +244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd00bf4b",
+   "id": "e7c07f57",
    "metadata": {
     "editable": true
    },
@@ -257,7 +257,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc9028f0",
+   "id": "6054782f",
    "metadata": {
     "editable": true
    },
@@ -269,7 +269,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6a27e54",
+   "id": "7b55104f",
    "metadata": {
     "editable": true
    },
@@ -279,7 +279,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82f1494a",
+   "id": "4635525e",
    "metadata": {
     "editable": true
    },
@@ -291,7 +291,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6427a35",
+   "id": "11f6ffc7",
    "metadata": {
     "editable": true
    },
@@ -303,7 +303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38c78421",
+   "id": "820ddc3f",
    "metadata": {
     "editable": true
    },
@@ -314,7 +314,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f23ac12e",
+   "id": "9aa4b864",
    "metadata": {
     "editable": true
    },
@@ -326,7 +326,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88fd9c03",
+   "id": "c542e149",
    "metadata": {
     "editable": true
    },
@@ -345,7 +345,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a953b1a3",
+   "id": "7be13194",
    "metadata": {
     "editable": true
    },
@@ -358,7 +358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19eb0838",
+   "id": "aad2641f",
    "metadata": {
     "editable": true
    },
@@ -368,7 +368,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a4f910a4",
+   "id": "9dfe7e22",
    "metadata": {
     "editable": true
    },
@@ -380,7 +380,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5060e089",
+   "id": "852c82a9",
    "metadata": {
     "editable": true
    },
@@ -390,7 +390,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8542c5a3",
+   "id": "84163c68",
    "metadata": {
     "editable": true
    },
@@ -402,7 +402,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "475e1436",
+   "id": "5bfb8965",
    "metadata": {
     "editable": true
    },
@@ -412,7 +412,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88abf4ad",
+   "id": "3822fa25",
    "metadata": {
     "editable": true
    },
@@ -424,7 +424,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62f558d9",
+   "id": "2c0f9f09",
    "metadata": {
     "editable": true
    },
@@ -435,7 +435,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99cc5104",
+   "id": "7ce9a08c",
    "metadata": {
     "editable": true
    },
@@ -447,7 +447,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29043759",
+   "id": "3efb75ba",
    "metadata": {
     "editable": true
    },
@@ -457,7 +457,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9d0f067",
+   "id": "8c4ceb9d",
    "metadata": {
     "editable": true
    },
@@ -469,7 +469,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c34bfdd2",
+   "id": "53a5a827",
    "metadata": {
     "editable": true
    },
@@ -479,7 +479,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3533f92e",
+   "id": "12d309d7",
    "metadata": {
     "editable": true
    },
@@ -491,7 +491,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "135631d4",
+   "id": "16fdbfbe",
    "metadata": {
     "editable": true
    },
@@ -511,7 +511,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf25f4a7",
+   "id": "b5651e23",
    "metadata": {
     "editable": true
    },
@@ -538,7 +538,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d82400a",
+   "id": "e3289213",
    "metadata": {
     "editable": true
    },
@@ -550,7 +550,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00d8d123",
+   "id": "db9c8386",
    "metadata": {
     "editable": true
    },
@@ -562,7 +562,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cce17e14",
+   "id": "ea7d7d7e",
    "metadata": {
     "editable": true
    },
@@ -578,7 +578,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65efb775",
+   "id": "7dace63c",
    "metadata": {
     "editable": true
    },
@@ -596,7 +596,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2df9efd6",
+   "id": "b00b4a82",
    "metadata": {
     "editable": true
    },
@@ -608,7 +608,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37b621d8",
+   "id": "26392bc2",
    "metadata": {
     "editable": true
    },
@@ -620,7 +620,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "297be9c9",
+   "id": "f5214ffc",
    "metadata": {
     "editable": true
    },
@@ -631,7 +631,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe288c99",
+   "id": "0eec52de",
    "metadata": {
     "editable": true
    },
@@ -643,7 +643,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d4333779",
+   "id": "077e4fe0",
    "metadata": {
     "editable": true
    },
@@ -653,7 +653,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7e72c3d",
+   "id": "e3ff215c",
    "metadata": {
     "editable": true
    },
@@ -665,7 +665,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3423b702",
+   "id": "6cb9ae59",
    "metadata": {
     "editable": true
    },
@@ -679,7 +679,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe66f713",
+   "id": "7a02062e",
    "metadata": {
     "editable": true
    },
@@ -691,7 +691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43eed51b",
+   "id": "45f73c0f",
    "metadata": {
     "editable": true
    },
@@ -703,7 +703,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f943ccb",
+   "id": "6c9d24a2",
    "metadata": {
     "editable": true
    },
@@ -715,7 +715,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5df09c55",
+   "id": "241fed59",
    "metadata": {
     "editable": true
    },
@@ -725,7 +725,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b92d9f2a",
+   "id": "1c67de99",
    "metadata": {
     "editable": true
    },
@@ -737,7 +737,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6cf49ab",
+   "id": "36af470a",
    "metadata": {
     "editable": true
    },
@@ -749,7 +749,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e000448",
+   "id": "38f9d9cf",
    "metadata": {
     "editable": true
    },
@@ -761,7 +761,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbaa984b",
+   "id": "b20c89a1",
    "metadata": {
     "editable": true
    },
@@ -775,7 +775,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4e444ea",
+   "id": "e56ba6c5",
    "metadata": {
     "editable": true
    },
@@ -787,7 +787,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "454ba5ba",
+   "id": "1481f969",
    "metadata": {
     "editable": true
    },
@@ -799,7 +799,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0434cd9",
+   "id": "fbd29e7c",
    "metadata": {
     "editable": true
    },
@@ -811,7 +811,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2bcda9d",
+   "id": "889c22f1",
    "metadata": {
     "editable": true
    },
@@ -821,7 +821,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aea0ba73",
+   "id": "5a753c31",
    "metadata": {
     "editable": true
    },
@@ -833,7 +833,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a58d6e8",
+   "id": "4fed4676",
    "metadata": {
     "editable": true
    },
@@ -843,7 +843,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "927428aa",
+   "id": "e1894902",
    "metadata": {
     "editable": true
    },
@@ -855,7 +855,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "372ad443",
+   "id": "ddca93b1",
    "metadata": {
     "editable": true
    },
@@ -865,7 +865,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37a99489",
+   "id": "5f9d8901",
    "metadata": {
     "editable": true
    },
@@ -877,7 +877,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4872a1cd",
+   "id": "726c169c",
    "metadata": {
     "editable": true
    },
@@ -889,7 +889,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b21e9cb2",
+   "id": "7d7715d5",
    "metadata": {
     "editable": true
    },
@@ -901,7 +901,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "442375d1",
+   "id": "057fedd9",
    "metadata": {
     "editable": true
    },
@@ -916,7 +916,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aabab237",
+   "id": "4c06fecd",
    "metadata": {
     "editable": true
    },
@@ -928,7 +928,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "106f09df",
+   "id": "490e6469",
    "metadata": {
     "editable": true
    },
@@ -938,7 +938,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "73d8f824",
+   "id": "b6259635",
    "metadata": {
     "editable": true
    },
@@ -950,7 +950,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2626be7",
+   "id": "0fda0191",
    "metadata": {
     "editable": true
    },
@@ -960,7 +960,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "81d89d86",
+   "id": "797e356f",
    "metadata": {
     "editable": true
    },
@@ -972,7 +972,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59c2576a",
+   "id": "46bdaee6",
    "metadata": {
     "editable": true
    },
@@ -982,7 +982,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b7bf3f9",
+   "id": "cb1f5f36",
    "metadata": {
     "editable": true
    },
@@ -994,7 +994,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea1e8943",
+   "id": "fa70c555",
    "metadata": {
     "editable": true
    },
@@ -1006,7 +1006,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0425d72",
+   "id": "2fdb367f",
    "metadata": {
     "editable": true
    },
@@ -1018,7 +1018,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38386834",
+   "id": "ced6532f",
    "metadata": {
     "editable": true
    },
@@ -1028,7 +1028,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bfbc4bd3",
+   "id": "49c27708",
    "metadata": {
     "editable": true
    },
@@ -1040,7 +1040,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ced3cec",
+   "id": "27da1de0",
    "metadata": {
     "editable": true
    },
@@ -1053,7 +1053,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc6f1dec",
+   "id": "9ddef35d",
    "metadata": {
     "editable": true
    },
@@ -1065,7 +1065,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "699662d2",
+   "id": "ae006a7e",
    "metadata": {
     "editable": true
    },
@@ -1075,7 +1075,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0991592c",
+   "id": "904d2486",
    "metadata": {
     "editable": true
    },
@@ -1087,7 +1087,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "450dd961",
+   "id": "525eda84",
    "metadata": {
     "editable": true
    },
@@ -1097,7 +1097,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a13de0fa",
+   "id": "7eadfb46",
    "metadata": {
     "editable": true
    },
@@ -1109,7 +1109,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c64bc916",
+   "id": "8ee45bc9",
    "metadata": {
     "editable": true
    },
@@ -1119,7 +1119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab1e18bc",
+   "id": "73b41248",
    "metadata": {
     "editable": true
    },
@@ -1131,7 +1131,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1e74f34",
+   "id": "dc4356aa",
    "metadata": {
     "editable": true
    },
@@ -1141,7 +1141,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ad3ebd9",
+   "id": "3e2b94a9",
    "metadata": {
     "editable": true
    },
@@ -1153,7 +1153,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37d1b4ca",
+   "id": "b9716f36",
    "metadata": {
     "editable": true
    },
@@ -1163,7 +1163,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d5fc67a",
+   "id": "01341a5b",
    "metadata": {
     "editable": true
    },
@@ -1175,7 +1175,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d98472d9",
+   "id": "83a3f463",
    "metadata": {
     "editable": true
    },
@@ -1191,7 +1191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d859f20",
+   "id": "c2c42203",
    "metadata": {
     "editable": true
    },
@@ -1203,7 +1203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7bb91ec",
+   "id": "94f060b9",
    "metadata": {
     "editable": true
    },
@@ -1213,7 +1213,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1553864b",
+   "id": "d0e5c32c",
    "metadata": {
     "editable": true
    },
@@ -1225,7 +1225,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8cc9c71",
+   "id": "0b464ed4",
    "metadata": {
     "editable": true
    },
@@ -1243,7 +1243,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1f01477",
+   "id": "5c952119",
    "metadata": {
     "editable": true
    },
@@ -1255,7 +1255,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2dea7e1",
+   "id": "25e4a5f3",
    "metadata": {
     "editable": true
    },
@@ -1267,7 +1267,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "76b0f99e",
+   "id": "4f774737",
    "metadata": {
     "editable": true
    },
@@ -1277,7 +1277,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cfa3ca25",
+   "id": "59c91b82",
    "metadata": {
     "editable": true
    },
@@ -1289,7 +1289,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a9163d8",
+   "id": "33ceec0f",
    "metadata": {
     "editable": true
    },
@@ -1299,7 +1299,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6b54a1e",
+   "id": "931da8ef",
    "metadata": {
     "editable": true
    },
@@ -1311,7 +1311,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "659c98d0",
+   "id": "2f2516b6",
    "metadata": {
     "editable": true
    },
@@ -1321,7 +1321,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "209b5b37",
+   "id": "bcb56a20",
    "metadata": {
     "editable": true
    },
@@ -1335,7 +1335,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b325d0c3",
+   "id": "86333a6f",
    "metadata": {
     "editable": true
    },
@@ -1347,7 +1347,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c49a2fcd",
+   "id": "1513e73c",
    "metadata": {
     "editable": true
    },
@@ -1358,7 +1358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6978ef70",
+   "id": "c8c47d9a",
    "metadata": {
     "editable": true
    },
@@ -1371,7 +1371,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "01530c39",
+   "id": "8ec18f31",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1398,7 +1398,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90ff28d4",
+   "id": "b7255330",
    "metadata": {
     "editable": true
    },
@@ -1409,7 +1409,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "1d052cbe",
+   "id": "9d5f3a70",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1422,7 +1422,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3362efd4",
+   "id": "8daa4681",
    "metadata": {
     "editable": true
    },
@@ -1436,7 +1436,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "3e9e681f",
+   "id": "de91ca73",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1449,7 +1449,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78e4427f",
+   "id": "442ef680",
    "metadata": {
     "editable": true
    },
@@ -1460,7 +1460,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "20aab659",
+   "id": "9b329ab4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1472,7 +1472,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "326f641d",
+   "id": "d7ded522",
    "metadata": {
     "editable": true
    },
@@ -1483,7 +1483,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "c8e80cf1",
+   "id": "34c18b8f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1499,7 +1499,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aba7b289",
+   "id": "229d94fa",
    "metadata": {
     "editable": true
    },
@@ -1510,7 +1510,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "7235bf1b",
+   "id": "afb92eb9",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1524,7 +1524,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3eaf5f8d",
+   "id": "8a02aaaf",
    "metadata": {
     "editable": true
    },
@@ -1545,7 +1545,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6fc5dc26",
+   "id": "b64b7d81",
    "metadata": {
     "editable": true
    },
@@ -1556,7 +1556,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "98ca5627",
+   "id": "094eed3e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1609,7 +1609,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "09f0c1c6",
+   "id": "76119de5",
    "metadata": {
     "editable": true
    },
@@ -1620,7 +1620,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "02220d97",
+   "id": "dff69c9a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1645,7 +1645,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5494af4d",
+   "id": "02285c48",
    "metadata": {
     "editable": true
    },
@@ -1657,7 +1657,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "048560ee",
+   "id": "71fab9ce",
    "metadata": {
     "editable": true
    },
@@ -1686,7 +1686,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "85b56c79",
+   "id": "424914f7",
    "metadata": {
     "editable": true
    },
@@ -1711,7 +1711,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60937483",
+   "id": "e486c793",
    "metadata": {
     "editable": true
    },
@@ -1731,7 +1731,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d0ea6a3",
+   "id": "1c6a9f34",
    "metadata": {
     "editable": true
    },
@@ -1758,7 +1758,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8f6fc4e6",
+   "id": "28f4300e",
    "metadata": {
     "editable": true
    },
@@ -1771,7 +1771,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bd392ed",
+   "id": "deb48c69",
    "metadata": {
     "editable": true
    },
@@ -1783,7 +1783,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e33d3e3",
+   "id": "127f4812",
    "metadata": {
     "editable": true
    },
@@ -1794,7 +1794,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e1c73ac",
+   "id": "305b4349",
    "metadata": {
     "editable": true
    },
@@ -1810,7 +1810,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "2c315558",
+   "id": "9dacf721",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1844,7 +1844,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aaa58775",
+   "id": "63596c47",
    "metadata": {
     "editable": true
    },
@@ -1854,7 +1854,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "02b198ed",
+   "id": "e663049c",
    "metadata": {
     "editable": true
    },
@@ -1869,7 +1869,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4cef197d",
+   "id": "e2b36261",
    "metadata": {
     "editable": true
    },
@@ -1881,7 +1881,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23b34528",
+   "id": "69fa292f",
    "metadata": {
     "editable": true
    },
@@ -1891,7 +1891,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2847956",
+   "id": "23b3dece",
    "metadata": {
     "editable": true
    },
@@ -1907,7 +1907,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "b8dacc33",
+   "id": "e1630ab8",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1924,7 +1924,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd89705f",
+   "id": "c2d3b936",
    "metadata": {
     "editable": true
    },
@@ -1937,7 +1937,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "d35541fd",
+   "id": "355c6a66",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1984,7 +1984,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36014ec9",
+   "id": "ab553d39",
    "metadata": {
     "editable": true
    },
@@ -1998,7 +1998,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16fb5f8f",
+   "id": "f439180e",
    "metadata": {
     "editable": true
    },
@@ -2010,7 +2010,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1ec698e",
+   "id": "7ba7386d",
    "metadata": {
     "editable": true
    },
@@ -2022,7 +2022,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "787f58f5",
+   "id": "7e0a1440",
    "metadata": {
     "editable": true
    },
@@ -2034,7 +2034,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e23435fd",
+   "id": "2e7611f3",
    "metadata": {
     "editable": true
    },
@@ -2044,7 +2044,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ccaad283",
+   "id": "414e53ca",
    "metadata": {
     "editable": true
    },
@@ -2056,7 +2056,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be8092da",
+   "id": "31ed8899",
    "metadata": {
     "editable": true
    },
@@ -2066,7 +2066,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e055e08",
+   "id": "a66641fb",
    "metadata": {
     "editable": true
    },
@@ -2078,7 +2078,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff86c9bc",
+   "id": "28a50f9e",
    "metadata": {
     "editable": true
    },
@@ -2089,7 +2089,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4f2e747",
+   "id": "b8c5f507",
    "metadata": {
     "editable": true
    },
@@ -2101,7 +2101,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a9a9f87",
+   "id": "445744c8",
    "metadata": {
     "editable": true
    },
@@ -2113,7 +2113,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1232e11a",
+   "id": "ef90b7cb",
    "metadata": {
     "editable": true
    },
@@ -2123,7 +2123,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a807825b",
+   "id": "9d4c2ac7",
    "metadata": {
     "editable": true
    },
@@ -2135,7 +2135,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4fa9855c",
+   "id": "84e62cfc",
    "metadata": {
     "editable": true
    },
@@ -2147,7 +2147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcffefcf",
+   "id": "41c2ba4b",
    "metadata": {
     "editable": true
    },
@@ -2157,7 +2157,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c08ff3a",
+   "id": "beb557ef",
    "metadata": {
     "editable": true
    },
@@ -2169,7 +2169,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c2483a13",
+   "id": "b3fdffce",
    "metadata": {
     "editable": true
    },
@@ -2179,7 +2179,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a82a8c5",
+   "id": "8005292a",
    "metadata": {
     "editable": true
    },
@@ -2191,7 +2191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "743f7309",
+   "id": "92d9f94b",
    "metadata": {
     "editable": true
    },
@@ -2201,7 +2201,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6d7b31a",
+   "id": "17940c71",
    "metadata": {
     "editable": true
    },
@@ -2241,7 +2241,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "518d6bb4",
+   "id": "6ffb31dd",
    "metadata": {
     "editable": true
    },
@@ -2258,7 +2258,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "056673c8",
+   "id": "cc767251",
    "metadata": {
     "editable": true
    },
@@ -2281,7 +2281,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63daba59",
+   "id": "347029b1",
    "metadata": {
     "editable": true
    },
@@ -2298,7 +2298,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "89b74667",
+   "id": "a77dda49",
    "metadata": {
     "editable": true
    },
@@ -2317,7 +2317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "588dd662",
+   "id": "25a0d7d6",
    "metadata": {
     "editable": true
    },
@@ -2328,7 +2328,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb8348c6",
+   "id": "70462fa0",
    "metadata": {
     "editable": true
    },
@@ -2340,7 +2340,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62027bc1",
+   "id": "f8421c8e",
    "metadata": {
     "editable": true
    },
@@ -2358,7 +2358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c73c4b7",
+   "id": "d4ef09ac",
    "metadata": {
     "editable": true
    },
@@ -2374,7 +2374,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3a2d330",
+   "id": "fc6f8651",
    "metadata": {
     "editable": true
    },
@@ -2386,7 +2386,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "374b88cc",
+   "id": "ece72dfe",
    "metadata": {
     "editable": true
    },
@@ -2396,7 +2396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5aa42e6",
+   "id": "3f900d15",
    "metadata": {
     "editable": true
    },
@@ -2409,7 +2409,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c01a816",
+   "id": "3cb45c74",
    "metadata": {
     "editable": true
    },
@@ -2421,7 +2421,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f556eddc",
+   "id": "81b8790f",
    "metadata": {
     "editable": true
    },
@@ -2431,7 +2431,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcf14a16",
+   "id": "9d42c98f",
    "metadata": {
     "editable": true
    },
@@ -2444,7 +2444,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08c37095",
+   "id": "ab036419",
    "metadata": {
     "editable": true
    },
@@ -2454,7 +2454,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6815fa1b",
+   "id": "bba11ff3",
    "metadata": {
     "editable": true
    },
@@ -2466,7 +2466,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "daf50946",
+   "id": "6518184d",
    "metadata": {
     "editable": true
    },
@@ -2479,7 +2479,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7a60cb3",
+   "id": "ba89e5b0",
    "metadata": {
     "editable": true
    },
@@ -2492,7 +2492,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38105bfd",
+   "id": "47325cf5",
    "metadata": {
     "editable": true
    },
@@ -2504,7 +2504,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d697464",
+   "id": "8d9036c1",
    "metadata": {
     "editable": true
    },
@@ -2516,7 +2516,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c298d7ba",
+   "id": "889f801b",
    "metadata": {
     "editable": true
    },
@@ -2526,7 +2526,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45265b59",
+   "id": "8a803d4a",
    "metadata": {
     "editable": true
    },
@@ -2539,7 +2539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab6ce408",
+   "id": "ec92b840",
    "metadata": {
     "editable": true
    },
@@ -2551,7 +2551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca0350a7",
+   "id": "6de4ce40",
    "metadata": {
     "editable": true
    },
@@ -2563,7 +2563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8146e6f",
+   "id": "22e97024",
    "metadata": {
     "editable": true
    },
@@ -2575,7 +2575,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05d97a86",
+   "id": "9cd0a124",
    "metadata": {
     "editable": true
    },
@@ -2587,7 +2587,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f84e7118",
+   "id": "29b31bed",
    "metadata": {
     "editable": true
    },
@@ -2601,7 +2601,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28be9ec4",
+   "id": "d1145ae7",
    "metadata": {
     "editable": true
    },
@@ -2613,7 +2613,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b9f5a5d8",
+   "id": "f1479849",
    "metadata": {
     "editable": true
    },
@@ -2623,7 +2623,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "86b43b21",
+   "id": "0c51f5eb",
    "metadata": {
     "editable": true
    },
@@ -2635,7 +2635,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58744172",
+   "id": "2cbb0f42",
    "metadata": {
     "editable": true
    },
@@ -2647,7 +2647,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd515e6f",
+   "id": "406c4098",
    "metadata": {
     "editable": true
    },
@@ -2659,7 +2659,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8c98bfe",
+   "id": "70966948",
    "metadata": {
     "editable": true
    },
@@ -2671,7 +2671,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08cc9626",
+   "id": "627f3d38",
    "metadata": {
     "editable": true
    },
@@ -2683,7 +2683,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "725df93e",
+   "id": "129105f7",
    "metadata": {
     "editable": true
    },
@@ -2706,7 +2706,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "8d0397cd",
+   "id": "bce32748",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2782,7 +2782,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbc56c2b",
+   "id": "62eccb26",
    "metadata": {
     "editable": true
    },
@@ -2794,7 +2794,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cfab477f",
+   "id": "675cc7de",
    "metadata": {
     "editable": true
    },
@@ -2809,7 +2809,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc176ed4",
+   "id": "ff36cd09",
    "metadata": {
     "editable": true
    },
@@ -2821,7 +2821,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9eef8e3",
+   "id": "7ae7a42a",
    "metadata": {
     "editable": true
    },
@@ -2831,7 +2831,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c33552ec",
+   "id": "607325f0",
    "metadata": {
     "editable": true
    },
@@ -2843,7 +2843,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9465d4f6",
+   "id": "cfb328b4",
    "metadata": {
     "editable": true
    },
@@ -2853,7 +2853,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cd89a35",
+   "id": "bc44d844",
    "metadata": {
     "editable": true
    },
@@ -2865,7 +2865,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "13a9f453",
+   "id": "17ddbfda",
    "metadata": {
     "editable": true
    },
@@ -2877,7 +2877,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6c909f72",
+   "id": "f5658751",
    "metadata": {
     "editable": true
    },
@@ -2892,7 +2892,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b32ee709",
+   "id": "2b01e674",
    "metadata": {
     "editable": true
    },
@@ -2903,7 +2903,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5d3f72c",
+   "id": "c18a65c6",
    "metadata": {
     "editable": true
    },
@@ -2923,7 +2923,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18f488f0",
+   "id": "04258de2",
    "metadata": {
     "editable": true
    },
@@ -2935,7 +2935,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "93618783",
+   "id": "e10d0aad",
    "metadata": {
     "editable": true
    },
@@ -2945,7 +2945,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "02f57528",
+   "id": "d198578b",
    "metadata": {
     "editable": true
    },
@@ -2957,7 +2957,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "762833f4",
+   "id": "2aec2fc1",
    "metadata": {
     "editable": true
    },
@@ -2986,7 +2986,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ab8ec4f",
+   "id": "81fed6f5",
    "metadata": {
     "editable": true
    },
@@ -3013,7 +3013,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e526d1f",
+   "id": "fe7d1d49",
    "metadata": {
     "editable": true
    },
@@ -3024,7 +3024,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "f5d258ce",
+   "id": "0b32041d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3064,7 +3064,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e4bf198",
+   "id": "db224b5b",
    "metadata": {
     "editable": true
    },
@@ -3081,7 +3081,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33a42ac4",
+   "id": "6b988f39",
    "metadata": {
     "editable": true
    },
@@ -3104,7 +3104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b5d1bbb",
+   "id": "1214012e",
    "metadata": {
     "editable": true
    },
@@ -3118,7 +3118,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1fee5f54",
+   "id": "c7a8cd85",
    "metadata": {
     "editable": true
    },
@@ -3137,7 +3137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "235f2975",
+   "id": "0f2a2211",
    "metadata": {
     "editable": true
    },
@@ -3147,7 +3147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fd7415b7",
+   "id": "e9863a0f",
    "metadata": {
     "editable": true
    },
@@ -3159,7 +3159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c265b5d",
+   "id": "d88c8316",
    "metadata": {
     "editable": true
    },
@@ -3173,7 +3173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "976c31a2",
+   "id": "643f1b6d",
    "metadata": {
     "editable": true
    },
@@ -3185,7 +3185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8dc8acd7",
+   "id": "0769ec85",
    "metadata": {
     "editable": true
    },
@@ -3195,7 +3195,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1dc8e8e",
+   "id": "f0d61e66",
    "metadata": {
     "editable": true
    },
@@ -3207,7 +3207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb688af0",
+   "id": "0d7c9d9e",
    "metadata": {
     "editable": true
    },
@@ -3224,7 +3224,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eeadd85e",
+   "id": "335fb5ed",
    "metadata": {
     "editable": true
    },
@@ -3234,7 +3234,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9375ad7",
+   "id": "1dbb3e05",
    "metadata": {
     "editable": true
    },
@@ -3250,7 +3250,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "025f1ca1",
+   "id": "4a535424",
    "metadata": {
     "editable": true
    },
@@ -3260,7 +3260,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d44951a1",
+   "id": "512418d2",
    "metadata": {
     "editable": true
    },
@@ -3276,7 +3276,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ecc9216b",
+   "id": "baa56321",
    "metadata": {
     "editable": true
    },
@@ -3286,7 +3286,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28e2ff44",
+   "id": "1fd5881c",
    "metadata": {
     "editable": true
    },
@@ -3302,7 +3302,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "935324af",
+   "id": "546a2bf3",
    "metadata": {
     "editable": true
    },
@@ -3312,7 +3312,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a15e7526",
+   "id": "4e356417",
    "metadata": {
     "editable": true
    },
@@ -3329,7 +3329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d3cef55",
+   "id": "1f3c787b",
    "metadata": {
     "editable": true
    },
@@ -3341,7 +3341,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0fab1783",
+   "id": "72018911",
    "metadata": {
     "editable": true
    },
@@ -3353,7 +3353,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9a8450e",
+   "id": "7d741e98",
    "metadata": {
     "editable": true
    },
@@ -3365,7 +3365,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "485d1023",
+   "id": "f2e4a67f",
    "metadata": {
     "editable": true
    },
@@ -3375,7 +3375,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a2da5dbe",
+   "id": "302c8edf",
    "metadata": {
     "editable": true
    },
@@ -3387,7 +3387,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "13959099",
+   "id": "def3ec8a",
    "metadata": {
     "editable": true
    },
@@ -3399,7 +3399,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23f0b903",
+   "id": "37150ee7",
    "metadata": {
     "editable": true
    },
@@ -3411,7 +3411,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c344e77",
+   "id": "e937a396",
    "metadata": {
     "editable": true
    },
@@ -3421,7 +3421,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8064053",
+   "id": "07e76c7b",
    "metadata": {
     "editable": true
    },
@@ -3433,7 +3433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "714ab01f",
+   "id": "99f80e22",
    "metadata": {
     "editable": true
    },
@@ -3443,35 +3443,36 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3ff6988",
+   "id": "7a917bf2",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_i\\boldsymbol{u}^T_i\\boldsymbol{y},\n",
+    "\\tilde{y}_{\\mathrm{OLS}}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_i\\boldsymbol{u}^T_i\\boldsymbol{y},\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5c204f79",
+   "id": "c11ae5fe",
    "metadata": {
     "editable": true
    },
    "source": [
+    "which is not the same as $\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}$, which due to the orthogonality of $\\boldsymbol{U}$ would have given us that the model equals the output.\n",
+    "\n",
     "It means that the ordinary least square model (with the optimal\n",
     "parameters) $\\boldsymbol{\\tilde{y}}$, corresponds to an orthogonal\n",
     "transformation of the output (or target) vector $\\boldsymbol{y}$ by the\n",
     "vectors of the matrix $\\boldsymbol{U}$. **Note that the summation ends at**\n",
     "$p-1$, that is $\\boldsymbol{\\tilde{y}}\\ne \\boldsymbol{y}$. We can thus not use the\n",
-    "orthogonality relation for the matrix $\\boldsymbol{U}$. This can already be\n",
-    "when we multiply the matrices $\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T$."
+    "orthogonality relation for the matrix $\\boldsymbol{U}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "78c51f10",
+   "id": "f300aa1b",
    "metadata": {
     "editable": true
    },
@@ -3483,7 +3484,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c432ed4",
+   "id": "8bd1e2a6",
    "metadata": {
     "editable": true
    },
@@ -3495,7 +3496,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68a7b505",
+   "id": "62502292",
    "metadata": {
     "editable": true
    },
@@ -3505,7 +3506,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14268cd5",
+   "id": "efca6f6c",
    "metadata": {
     "editable": true
    },
@@ -3517,7 +3518,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3207844",
+   "id": "e2cbd6f5",
    "metadata": {
     "editable": true
    },
@@ -3528,7 +3529,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c7f5556",
+   "id": "5cc9aea6",
    "metadata": {
     "editable": true
    },
@@ -3540,7 +3541,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01bd8826",
+   "id": "61ad8f4c",
    "metadata": {
     "editable": true
    },
@@ -3550,7 +3551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb083248",
+   "id": "b1cc9449",
    "metadata": {
     "editable": true
    },
@@ -3562,7 +3563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "66bd1ec9",
+   "id": "a9b28652",
    "metadata": {
     "editable": true
    },
@@ -3572,7 +3573,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b92a06bb",
+   "id": "f26b69cc",
    "metadata": {
     "editable": true
    },
@@ -3584,7 +3585,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dad0b409",
+   "id": "53acde0e",
    "metadata": {
     "editable": true
    },
@@ -3595,7 +3596,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75d85fa8",
+   "id": "512b9f17",
    "metadata": {
     "editable": true
    },
@@ -3607,7 +3608,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0918773",
+   "id": "a1c49f5f",
    "metadata": {
     "editable": true
    },
@@ -3625,7 +3626,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65592b3b",
+   "id": "db70d623",
    "metadata": {
     "editable": true
    },
@@ -3641,7 +3642,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "442404b8",
+   "id": "95b18b06",
    "metadata": {
     "editable": true
    },
@@ -3653,7 +3654,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50eca816",
+   "id": "db07fa1e",
    "metadata": {
     "editable": true
    },
@@ -3665,7 +3666,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a27e487e",
+   "id": "9856cea3",
    "metadata": {
     "editable": true
    },
@@ -3677,7 +3678,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49c74d48",
+   "id": "7f6cba4c",
    "metadata": {
     "editable": true
    },
@@ -3690,7 +3691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "214feab7",
+   "id": "581565a5",
    "metadata": {
     "editable": true
    },
@@ -3706,7 +3707,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e61c0669",
+   "id": "22b63d08",
    "metadata": {
     "editable": true
    },
@@ -3720,7 +3721,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9f3db006",
+   "id": "cd6032aa",
    "metadata": {
     "editable": true
    },
@@ -3730,7 +3731,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6dfeb8ca",
+   "id": "25b7936a",
    "metadata": {
     "editable": true
    },
@@ -3742,7 +3743,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da47505d",
+   "id": "9c4ad4d2",
    "metadata": {
     "editable": true
    },
@@ -3752,7 +3753,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87c1a756",
+   "id": "75bcfcea",
    "metadata": {
     "editable": true
    },
@@ -3764,7 +3765,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5028dae1",
+   "id": "95c9cc40",
    "metadata": {
     "editable": true
    },
@@ -3774,7 +3775,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98da161b",
+   "id": "33c19ed1",
    "metadata": {
     "editable": true
    },
@@ -3788,7 +3789,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69065ef4",
+   "id": "c28b0a97",
    "metadata": {
     "editable": true
    },
@@ -3805,7 +3806,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3455143e",
+   "id": "d4ece056",
    "metadata": {
     "editable": true
    },
@@ -3821,7 +3822,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e322fdc8",
+   "id": "22360ee3",
    "metadata": {
     "editable": true
    },
@@ -3833,7 +3834,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f50b583d",
+   "id": "77e8998d",
    "metadata": {
     "editable": true
    },
@@ -3846,7 +3847,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b12b62dc",
+   "id": "8ef4225d",
    "metadata": {
     "editable": true
    },
@@ -3860,7 +3861,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40355c87",
+   "id": "627eac2b",
    "metadata": {
     "editable": true
    },
@@ -3870,7 +3871,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee70666b",
+   "id": "f7ac0db1",
    "metadata": {
     "editable": true
    },
@@ -3883,7 +3884,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc6d0cc7",
+   "id": "e93eae5d",
    "metadata": {
     "editable": true
    },
@@ -3902,7 +3903,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6b6f792",
+   "id": "58364673",
    "metadata": {
     "editable": true
    },
@@ -3914,7 +3915,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39c76bf5",
+   "id": "30541096",
    "metadata": {
     "editable": true
    },
@@ -3926,7 +3927,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2d754e5",
+   "id": "101bb217",
    "metadata": {
     "editable": true
    },
@@ -3936,7 +3937,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77a984ab",
+   "id": "ba8e52b1",
    "metadata": {
     "editable": true
    },
@@ -3948,7 +3949,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33060c1a",
+   "id": "67d4335e",
    "metadata": {
     "editable": true
    },
@@ -3961,7 +3962,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ed1e8279",
+   "id": "06416768",
    "metadata": {
     "editable": true
    },
@@ -3980,7 +3981,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22b40263",
+   "id": "dd2f405a",
    "metadata": {
     "editable": true
    },
@@ -3990,7 +3991,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b02469c",
+   "id": "40ded798",
    "metadata": {
     "editable": true
    },
@@ -4009,7 +4010,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0660e456",
+   "id": "d3044a01",
    "metadata": {
     "editable": true
    },
@@ -4027,7 +4028,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a40e5c0",
+   "id": "d612ad97",
    "metadata": {
     "editable": true
    },
@@ -4041,7 +4042,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82d7e99d",
+   "id": "52f27c53",
    "metadata": {
     "editable": true
    },
@@ -4056,7 +4057,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "6f4b429b",
+   "id": "ca5ce77c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4077,7 +4078,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a38f8430",
+   "id": "1c02019d",
    "metadata": {
     "editable": true
    },
@@ -4094,7 +4095,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "87d44fdf",
+   "id": "58381fbe",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4126,7 +4127,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f08f4dc",
+   "id": "a647044e",
    "metadata": {
     "editable": true
    },
@@ -4140,7 +4141,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a25b356f",
+   "id": "d7bea0a6",
    "metadata": {
     "editable": true
    },
@@ -4153,7 +4154,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "928ae649",
+   "id": "81d407da",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4178,7 +4179,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cab70377",
+   "id": "7998701a",
    "metadata": {
     "editable": true
    },
@@ -4190,7 +4191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22ac4a6d",
+   "id": "e4f65917",
    "metadata": {
     "editable": true
    },
@@ -4202,7 +4203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd0697a9",
+   "id": "73ecb476",
    "metadata": {
     "editable": true
    },
@@ -4212,7 +4213,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5043405",
+   "id": "f4f10483",
    "metadata": {
     "editable": true
    },
@@ -4229,7 +4230,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a4edab6",
+   "id": "9e173ba2",
    "metadata": {
     "editable": true
    },
@@ -4239,7 +4240,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1b67496",
+   "id": "6b6f3d02",
    "metadata": {
     "editable": true
    },
@@ -4254,7 +4255,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47a041cb",
+   "id": "69a2c9b4",
    "metadata": {
     "editable": true
    },
@@ -4264,7 +4265,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "575264b7",
+   "id": "41dedd73",
    "metadata": {
     "editable": true
    },
@@ -4278,7 +4279,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b049c58",
+   "id": "a7b2bb8c",
    "metadata": {
     "editable": true
    },
@@ -4290,7 +4291,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9780789f",
+   "id": "dba35fc4",
    "metadata": {
     "editable": true
    },
@@ -4302,7 +4303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da396c4a",
+   "id": "0e30a645",
    "metadata": {
     "editable": true
    },
@@ -4314,7 +4315,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87a74417",
+   "id": "6fa482d3",
    "metadata": {
     "editable": true
    },
@@ -4324,7 +4325,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5ca565a",
+   "id": "ae9f30ae",
    "metadata": {
     "editable": true
    },
@@ -4336,7 +4337,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "10944fc5",
+   "id": "67907a60",
    "metadata": {
     "editable": true
    },
@@ -4346,7 +4347,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b985955",
+   "id": "3a21fe71",
    "metadata": {
     "editable": true
    },
@@ -4363,7 +4364,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b748051",
+   "id": "3b91b5d8",
    "metadata": {
     "editable": true
    },
@@ -4373,7 +4374,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40c1c1eb",
+   "id": "86de4409",
    "metadata": {
     "editable": true
    },
@@ -4385,7 +4386,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e44c9e87",
+   "id": "d0c0608f",
    "metadata": {
     "editable": true
    },
@@ -4395,7 +4396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28abe46c",
+   "id": "98f544a6",
    "metadata": {
     "editable": true
    },
@@ -4407,7 +4408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "178bc776",
+   "id": "24587410",
    "metadata": {
     "editable": true
    },
@@ -4421,7 +4422,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f0ead95",
+   "id": "61fb4275",
    "metadata": {
     "editable": true
    },
@@ -4433,7 +4434,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fcce3bb5",
+   "id": "6d2404eb",
    "metadata": {
     "editable": true
    },
@@ -4455,7 +4456,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f9a7281",
+   "id": "22615b7e",
    "metadata": {
     "editable": true
    },
@@ -4467,7 +4468,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3ea695c",
+   "id": "bee48c87",
    "metadata": {
     "editable": true
    },
@@ -4482,7 +4483,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "edfff9e0",
+   "id": "7f12f53a",
    "metadata": {
     "editable": true
    },
@@ -4494,7 +4495,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3c83244",
+   "id": "a6acb75c",
    "metadata": {
     "editable": true
    },
@@ -4506,7 +4507,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00df5ee5",
+   "id": "131e9d9c",
    "metadata": {
     "editable": true
    },
@@ -4516,7 +4517,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4661cbd7",
+   "id": "85812d77",
    "metadata": {
     "editable": true
    },
@@ -4528,7 +4529,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07b95265",
+   "id": "35007c74",
    "metadata": {
     "editable": true
    },
@@ -4538,7 +4539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8c9aeba4",
+   "id": "0100935a",
    "metadata": {
     "editable": true
    },
@@ -4550,7 +4551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "03690a72",
+   "id": "7b6ff86e",
    "metadata": {
     "editable": true
    },
@@ -4560,7 +4561,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "478e2a9d",
+   "id": "1f452dfb",
    "metadata": {
     "editable": true
    },
@@ -4572,7 +4573,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e997196a",
+   "id": "05600fbd",
    "metadata": {
     "editable": true
    },
@@ -4589,7 +4590,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "770e587e",
+   "id": "a2af3e04",
    "metadata": {
     "editable": true
    },
@@ -4602,7 +4603,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5cb701c2",
+   "id": "0342c08c",
    "metadata": {
     "editable": true
    },
@@ -4614,7 +4615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dee9d948",
+   "id": "bdd5faeb",
    "metadata": {
     "editable": true
    },
@@ -4624,7 +4625,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "121cd014",
+   "id": "35873dc6",
    "metadata": {
     "editable": true
    },
@@ -4637,7 +4638,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2ee745b4",
+   "id": "6ff6ab78",
    "metadata": {
     "editable": true
    },
@@ -4647,7 +4648,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94a15fb9",
+   "id": "77286b5f",
    "metadata": {
     "editable": true
    },
@@ -4659,7 +4660,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6341fe06",
+   "id": "0ade2616",
    "metadata": {
     "editable": true
    },
@@ -4672,7 +4673,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5bef6925",
+   "id": "da22a168",
    "metadata": {
     "editable": true
    },
@@ -4685,7 +4686,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4539e82b",
+   "id": "caa18da2",
    "metadata": {
     "editable": true
    },
@@ -4697,7 +4698,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f496d16",
+   "id": "f31c8084",
    "metadata": {
     "editable": true
    },
@@ -4709,7 +4710,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee78adfa",
+   "id": "53dc71a2",
    "metadata": {
     "editable": true
    },
@@ -4719,7 +4720,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47a0c860",
+   "id": "753442d5",
    "metadata": {
     "editable": true
    },
@@ -4732,7 +4733,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b452b5d",
+   "id": "e0b2f58a",
    "metadata": {
     "editable": true
    },
@@ -4744,7 +4745,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3331a79",
+   "id": "e4af8e7e",
    "metadata": {
     "editable": true
    },
@@ -4756,7 +4757,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9befd0e3",
+   "id": "6e353a3a",
    "metadata": {
     "editable": true
    },
@@ -4773,7 +4774,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d8f2ba3",
+   "id": "66a4056b",
    "metadata": {
     "editable": true
    },
@@ -4785,7 +4786,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da712e9d",
+   "id": "ea5b3d9f",
    "metadata": {
     "editable": true
    },
@@ -4795,7 +4796,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d91cd5f7",
+   "id": "db50585a",
    "metadata": {
     "editable": true
    },
@@ -4807,7 +4808,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18940f72",
+   "id": "afd3cd57",
    "metadata": {
     "editable": true
    },
@@ -4817,7 +4818,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51fe3527",
+   "id": "6606774b",
    "metadata": {
     "editable": true
    },
@@ -4829,7 +4830,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e85d1eb",
+   "id": "bcfd3adb",
    "metadata": {
     "editable": true
    },
@@ -4841,7 +4842,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96c47485",
+   "id": "46d7227b",
    "metadata": {
     "editable": true
    },
@@ -4857,7 +4858,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1adcbbc",
+   "id": "a214b881",
    "metadata": {
     "editable": true
    },
@@ -4869,7 +4870,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9693074c",
+   "id": "727c87de",
    "metadata": {
     "editable": true
    },
@@ -4881,7 +4882,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46b05531",
+   "id": "5083858e",
    "metadata": {
     "editable": true
    },
@@ -4891,7 +4892,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e4ce02b",
+   "id": "973ad2fa",
    "metadata": {
     "editable": true
    },
@@ -4903,7 +4904,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbd3f781",
+   "id": "4fbd0028",
    "metadata": {
     "editable": true
    },
@@ -4913,7 +4914,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "779e1ac5",
+   "id": "bee26901",
    "metadata": {
     "editable": true
    },
@@ -4925,7 +4926,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ef53f2a5",
+   "id": "da771d96",
    "metadata": {
     "editable": true
    },
@@ -4942,7 +4943,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57adfaff",
+   "id": "8ecb8a62",
    "metadata": {
     "editable": true
    },
@@ -4954,7 +4955,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8f94cba",
+   "id": "5cf08e3d",
    "metadata": {
     "editable": true
    },
@@ -4966,7 +4967,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d60431ff",
+   "id": "d984ce12",
    "metadata": {
     "editable": true
    },
@@ -4976,7 +4977,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f78d1dfd",
+   "id": "837a69b7",
    "metadata": {
     "editable": true
    },
@@ -4988,7 +4989,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "445800de",
+   "id": "21dde5ad",
    "metadata": {
     "editable": true
    },
@@ -4998,7 +4999,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c54c49c",
+   "id": "4d49c112",
    "metadata": {
     "editable": true
    },
@@ -5010,7 +5011,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11366dc1",
+   "id": "5b4eabcf",
    "metadata": {
     "editable": true
    },
@@ -5020,7 +5021,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d68d3ac1",
+   "id": "28dcb3c8",
    "metadata": {
     "editable": true
    },
@@ -5032,7 +5033,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63fedbd6",
+   "id": "f315a306",
    "metadata": {
     "editable": true
    },
@@ -5042,7 +5043,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "470b20a8",
+   "id": "7b4f990c",
    "metadata": {
     "editable": true
    },
@@ -5054,7 +5055,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3277c65",
+   "id": "197daa81",
    "metadata": {
     "editable": true
    },
diff --git a/doc/LectureNotes/_build/html/week35.html b/doc/LectureNotes/_build/html/week35.html
index 15c73ed19..0c1161977 100644
--- a/doc/LectureNotes/_build/html/week35.html
+++ b/doc/LectureNotes/_build/html/week35.html
@@ -1802,15 +1802,15 @@ decomposition of the design matrix.</p>
 <p>which gives us, using the orthogonality of the matrix <span class="math notranslate nohighlight">\(\boldsymbol{V}\)</span>,</p>
 <div class="math notranslate nohighlight">
 \[
-\tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y},
+\tilde{y}_{\mathrm{OLS}}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y},
 \]</div>
+<p>which is not the same as <span class="math notranslate nohighlight">\(\tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y}\)</span>, which due to the orthogonality of <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span> would have given us that the model equals the output.</p>
 <p>It means that the ordinary least square model (with the optimal
 parameters) <span class="math notranslate nohighlight">\(\boldsymbol{\tilde{y}}\)</span>, corresponds to an orthogonal
 transformation of the output (or target) vector <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> by the
 vectors of the matrix <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span>. <strong>Note that the summation ends at</strong>
 <span class="math notranslate nohighlight">\(p-1\)</span>, that is <span class="math notranslate nohighlight">\(\boldsymbol{\tilde{y}}\ne \boldsymbol{y}\)</span>. We can thus not use the
-orthogonality relation for the matrix <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span>. This can already be
-when we multiply the matrices <span class="math notranslate nohighlight">\(\boldsymbol{\Sigma}^T\boldsymbol{U}^T\)</span>.</p>
+orthogonality relation for the matrix <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span>.</p>
 </section>
 <section id="further-properties-important-for-our-analyses-later">
 <h2>Further properties (important for our analyses later)<a class="headerlink" href="#further-properties-important-for-our-analyses-later" title="Link to this heading">#</a></h2>
diff --git a/doc/LectureNotes/_build/jupyter_execute/week35.ipynb b/doc/LectureNotes/_build/jupyter_execute/week35.ipynb
index f83c664a9..d1052d6cf 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week35.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week35.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "82c2f725",
+   "id": "f0622ebb",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2fc786b",
+   "id": "3fe98f20",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77512f33",
+   "id": "8e604e3c",
    "metadata": {
     "editable": true
    },
@@ -49,7 +49,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41516757",
+   "id": "c7f0b40a",
    "metadata": {
     "editable": true
    },
@@ -69,7 +69,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3703d2f",
+   "id": "507709a4",
    "metadata": {
     "editable": true
    },
@@ -102,7 +102,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f22b90af",
+   "id": "bb3b5f67",
    "metadata": {
     "editable": true
    },
@@ -118,7 +118,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3fe305bb",
+   "id": "14444be5",
    "metadata": {
     "editable": true
    },
@@ -130,7 +130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2f38355",
+   "id": "4edc5258",
    "metadata": {
     "editable": true
    },
@@ -140,7 +140,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3d9a4b6",
+   "id": "4d6f9c43",
    "metadata": {
     "editable": true
    },
@@ -152,7 +152,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff3ba043",
+   "id": "fb52f7f5",
    "metadata": {
     "editable": true
    },
@@ -173,7 +173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5de294d5",
+   "id": "4fff6b39",
    "metadata": {
     "editable": true
    },
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5721942a",
+   "id": "54a4cabb",
    "metadata": {
     "editable": true
    },
@@ -198,7 +198,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b2aa843",
+   "id": "d383a507",
    "metadata": {
     "editable": true
    },
@@ -210,7 +210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b12c06f",
+   "id": "498fe31e",
    "metadata": {
     "editable": true
    },
@@ -222,7 +222,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "276d4eba",
+   "id": "7bbbdcd2",
    "metadata": {
     "editable": true
    },
@@ -232,7 +232,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4751c9b4",
+   "id": "405a61ac",
    "metadata": {
     "editable": true
    },
@@ -244,7 +244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd00bf4b",
+   "id": "e7c07f57",
    "metadata": {
     "editable": true
    },
@@ -257,7 +257,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc9028f0",
+   "id": "6054782f",
    "metadata": {
     "editable": true
    },
@@ -269,7 +269,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6a27e54",
+   "id": "7b55104f",
    "metadata": {
     "editable": true
    },
@@ -279,7 +279,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82f1494a",
+   "id": "4635525e",
    "metadata": {
     "editable": true
    },
@@ -291,7 +291,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6427a35",
+   "id": "11f6ffc7",
    "metadata": {
     "editable": true
    },
@@ -303,7 +303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38c78421",
+   "id": "820ddc3f",
    "metadata": {
     "editable": true
    },
@@ -314,7 +314,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f23ac12e",
+   "id": "9aa4b864",
    "metadata": {
     "editable": true
    },
@@ -326,7 +326,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88fd9c03",
+   "id": "c542e149",
    "metadata": {
     "editable": true
    },
@@ -345,7 +345,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a953b1a3",
+   "id": "7be13194",
    "metadata": {
     "editable": true
    },
@@ -358,7 +358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19eb0838",
+   "id": "aad2641f",
    "metadata": {
     "editable": true
    },
@@ -368,7 +368,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a4f910a4",
+   "id": "9dfe7e22",
    "metadata": {
     "editable": true
    },
@@ -380,7 +380,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5060e089",
+   "id": "852c82a9",
    "metadata": {
     "editable": true
    },
@@ -390,7 +390,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8542c5a3",
+   "id": "84163c68",
    "metadata": {
     "editable": true
    },
@@ -402,7 +402,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "475e1436",
+   "id": "5bfb8965",
    "metadata": {
     "editable": true
    },
@@ -412,7 +412,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88abf4ad",
+   "id": "3822fa25",
    "metadata": {
     "editable": true
    },
@@ -424,7 +424,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62f558d9",
+   "id": "2c0f9f09",
    "metadata": {
     "editable": true
    },
@@ -435,7 +435,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99cc5104",
+   "id": "7ce9a08c",
    "metadata": {
     "editable": true
    },
@@ -447,7 +447,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29043759",
+   "id": "3efb75ba",
    "metadata": {
     "editable": true
    },
@@ -457,7 +457,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9d0f067",
+   "id": "8c4ceb9d",
    "metadata": {
     "editable": true
    },
@@ -469,7 +469,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c34bfdd2",
+   "id": "53a5a827",
    "metadata": {
     "editable": true
    },
@@ -479,7 +479,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3533f92e",
+   "id": "12d309d7",
    "metadata": {
     "editable": true
    },
@@ -491,7 +491,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "135631d4",
+   "id": "16fdbfbe",
    "metadata": {
     "editable": true
    },
@@ -511,7 +511,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf25f4a7",
+   "id": "b5651e23",
    "metadata": {
     "editable": true
    },
@@ -538,7 +538,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d82400a",
+   "id": "e3289213",
    "metadata": {
     "editable": true
    },
@@ -550,7 +550,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00d8d123",
+   "id": "db9c8386",
    "metadata": {
     "editable": true
    },
@@ -562,7 +562,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cce17e14",
+   "id": "ea7d7d7e",
    "metadata": {
     "editable": true
    },
@@ -578,7 +578,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65efb775",
+   "id": "7dace63c",
    "metadata": {
     "editable": true
    },
@@ -596,7 +596,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2df9efd6",
+   "id": "b00b4a82",
    "metadata": {
     "editable": true
    },
@@ -608,7 +608,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37b621d8",
+   "id": "26392bc2",
    "metadata": {
     "editable": true
    },
@@ -620,7 +620,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "297be9c9",
+   "id": "f5214ffc",
    "metadata": {
     "editable": true
    },
@@ -631,7 +631,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe288c99",
+   "id": "0eec52de",
    "metadata": {
     "editable": true
    },
@@ -643,7 +643,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d4333779",
+   "id": "077e4fe0",
    "metadata": {
     "editable": true
    },
@@ -653,7 +653,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7e72c3d",
+   "id": "e3ff215c",
    "metadata": {
     "editable": true
    },
@@ -665,7 +665,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3423b702",
+   "id": "6cb9ae59",
    "metadata": {
     "editable": true
    },
@@ -679,7 +679,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe66f713",
+   "id": "7a02062e",
    "metadata": {
     "editable": true
    },
@@ -691,7 +691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43eed51b",
+   "id": "45f73c0f",
    "metadata": {
     "editable": true
    },
@@ -703,7 +703,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f943ccb",
+   "id": "6c9d24a2",
    "metadata": {
     "editable": true
    },
@@ -715,7 +715,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5df09c55",
+   "id": "241fed59",
    "metadata": {
     "editable": true
    },
@@ -725,7 +725,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b92d9f2a",
+   "id": "1c67de99",
    "metadata": {
     "editable": true
    },
@@ -737,7 +737,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6cf49ab",
+   "id": "36af470a",
    "metadata": {
     "editable": true
    },
@@ -749,7 +749,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e000448",
+   "id": "38f9d9cf",
    "metadata": {
     "editable": true
    },
@@ -761,7 +761,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbaa984b",
+   "id": "b20c89a1",
    "metadata": {
     "editable": true
    },
@@ -775,7 +775,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4e444ea",
+   "id": "e56ba6c5",
    "metadata": {
     "editable": true
    },
@@ -787,7 +787,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "454ba5ba",
+   "id": "1481f969",
    "metadata": {
     "editable": true
    },
@@ -799,7 +799,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0434cd9",
+   "id": "fbd29e7c",
    "metadata": {
     "editable": true
    },
@@ -811,7 +811,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2bcda9d",
+   "id": "889c22f1",
    "metadata": {
     "editable": true
    },
@@ -821,7 +821,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aea0ba73",
+   "id": "5a753c31",
    "metadata": {
     "editable": true
    },
@@ -833,7 +833,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a58d6e8",
+   "id": "4fed4676",
    "metadata": {
     "editable": true
    },
@@ -843,7 +843,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "927428aa",
+   "id": "e1894902",
    "metadata": {
     "editable": true
    },
@@ -855,7 +855,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "372ad443",
+   "id": "ddca93b1",
    "metadata": {
     "editable": true
    },
@@ -865,7 +865,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37a99489",
+   "id": "5f9d8901",
    "metadata": {
     "editable": true
    },
@@ -877,7 +877,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4872a1cd",
+   "id": "726c169c",
    "metadata": {
     "editable": true
    },
@@ -889,7 +889,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b21e9cb2",
+   "id": "7d7715d5",
    "metadata": {
     "editable": true
    },
@@ -901,7 +901,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "442375d1",
+   "id": "057fedd9",
    "metadata": {
     "editable": true
    },
@@ -916,7 +916,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aabab237",
+   "id": "4c06fecd",
    "metadata": {
     "editable": true
    },
@@ -928,7 +928,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "106f09df",
+   "id": "490e6469",
    "metadata": {
     "editable": true
    },
@@ -938,7 +938,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "73d8f824",
+   "id": "b6259635",
    "metadata": {
     "editable": true
    },
@@ -950,7 +950,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2626be7",
+   "id": "0fda0191",
    "metadata": {
     "editable": true
    },
@@ -960,7 +960,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "81d89d86",
+   "id": "797e356f",
    "metadata": {
     "editable": true
    },
@@ -972,7 +972,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59c2576a",
+   "id": "46bdaee6",
    "metadata": {
     "editable": true
    },
@@ -982,7 +982,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b7bf3f9",
+   "id": "cb1f5f36",
    "metadata": {
     "editable": true
    },
@@ -994,7 +994,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea1e8943",
+   "id": "fa70c555",
    "metadata": {
     "editable": true
    },
@@ -1006,7 +1006,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0425d72",
+   "id": "2fdb367f",
    "metadata": {
     "editable": true
    },
@@ -1018,7 +1018,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38386834",
+   "id": "ced6532f",
    "metadata": {
     "editable": true
    },
@@ -1028,7 +1028,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bfbc4bd3",
+   "id": "49c27708",
    "metadata": {
     "editable": true
    },
@@ -1040,7 +1040,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ced3cec",
+   "id": "27da1de0",
    "metadata": {
     "editable": true
    },
@@ -1053,7 +1053,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc6f1dec",
+   "id": "9ddef35d",
    "metadata": {
     "editable": true
    },
@@ -1065,7 +1065,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "699662d2",
+   "id": "ae006a7e",
    "metadata": {
     "editable": true
    },
@@ -1075,7 +1075,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0991592c",
+   "id": "904d2486",
    "metadata": {
     "editable": true
    },
@@ -1087,7 +1087,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "450dd961",
+   "id": "525eda84",
    "metadata": {
     "editable": true
    },
@@ -1097,7 +1097,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a13de0fa",
+   "id": "7eadfb46",
    "metadata": {
     "editable": true
    },
@@ -1109,7 +1109,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c64bc916",
+   "id": "8ee45bc9",
    "metadata": {
     "editable": true
    },
@@ -1119,7 +1119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab1e18bc",
+   "id": "73b41248",
    "metadata": {
     "editable": true
    },
@@ -1131,7 +1131,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1e74f34",
+   "id": "dc4356aa",
    "metadata": {
     "editable": true
    },
@@ -1141,7 +1141,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ad3ebd9",
+   "id": "3e2b94a9",
    "metadata": {
     "editable": true
    },
@@ -1153,7 +1153,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37d1b4ca",
+   "id": "b9716f36",
    "metadata": {
     "editable": true
    },
@@ -1163,7 +1163,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d5fc67a",
+   "id": "01341a5b",
    "metadata": {
     "editable": true
    },
@@ -1175,7 +1175,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d98472d9",
+   "id": "83a3f463",
    "metadata": {
     "editable": true
    },
@@ -1191,7 +1191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d859f20",
+   "id": "c2c42203",
    "metadata": {
     "editable": true
    },
@@ -1203,7 +1203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7bb91ec",
+   "id": "94f060b9",
    "metadata": {
     "editable": true
    },
@@ -1213,7 +1213,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1553864b",
+   "id": "d0e5c32c",
    "metadata": {
     "editable": true
    },
@@ -1225,7 +1225,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8cc9c71",
+   "id": "0b464ed4",
    "metadata": {
     "editable": true
    },
@@ -1243,7 +1243,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1f01477",
+   "id": "5c952119",
    "metadata": {
     "editable": true
    },
@@ -1255,7 +1255,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2dea7e1",
+   "id": "25e4a5f3",
    "metadata": {
     "editable": true
    },
@@ -1267,7 +1267,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "76b0f99e",
+   "id": "4f774737",
    "metadata": {
     "editable": true
    },
@@ -1277,7 +1277,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cfa3ca25",
+   "id": "59c91b82",
    "metadata": {
     "editable": true
    },
@@ -1289,7 +1289,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a9163d8",
+   "id": "33ceec0f",
    "metadata": {
     "editable": true
    },
@@ -1299,7 +1299,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6b54a1e",
+   "id": "931da8ef",
    "metadata": {
     "editable": true
    },
@@ -1311,7 +1311,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "659c98d0",
+   "id": "2f2516b6",
    "metadata": {
     "editable": true
    },
@@ -1321,7 +1321,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "209b5b37",
+   "id": "bcb56a20",
    "metadata": {
     "editable": true
    },
@@ -1335,7 +1335,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b325d0c3",
+   "id": "86333a6f",
    "metadata": {
     "editable": true
    },
@@ -1347,7 +1347,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c49a2fcd",
+   "id": "1513e73c",
    "metadata": {
     "editable": true
    },
@@ -1358,7 +1358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6978ef70",
+   "id": "c8c47d9a",
    "metadata": {
     "editable": true
    },
@@ -1371,7 +1371,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "01530c39",
+   "id": "8ec18f31",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1398,7 +1398,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90ff28d4",
+   "id": "b7255330",
    "metadata": {
     "editable": true
    },
@@ -1409,7 +1409,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "1d052cbe",
+   "id": "9d5f3a70",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1422,7 +1422,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3362efd4",
+   "id": "8daa4681",
    "metadata": {
     "editable": true
    },
@@ -1436,7 +1436,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "3e9e681f",
+   "id": "de91ca73",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1449,7 +1449,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78e4427f",
+   "id": "442ef680",
    "metadata": {
     "editable": true
    },
@@ -1460,7 +1460,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "20aab659",
+   "id": "9b329ab4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1472,7 +1472,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "326f641d",
+   "id": "d7ded522",
    "metadata": {
     "editable": true
    },
@@ -1483,7 +1483,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "c8e80cf1",
+   "id": "34c18b8f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1499,7 +1499,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aba7b289",
+   "id": "229d94fa",
    "metadata": {
     "editable": true
    },
@@ -1510,7 +1510,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "7235bf1b",
+   "id": "afb92eb9",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1524,7 +1524,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3eaf5f8d",
+   "id": "8a02aaaf",
    "metadata": {
     "editable": true
    },
@@ -1545,7 +1545,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6fc5dc26",
+   "id": "b64b7d81",
    "metadata": {
     "editable": true
    },
@@ -1556,7 +1556,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "98ca5627",
+   "id": "094eed3e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1609,7 +1609,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "09f0c1c6",
+   "id": "76119de5",
    "metadata": {
     "editable": true
    },
@@ -1620,7 +1620,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "02220d97",
+   "id": "dff69c9a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1645,7 +1645,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5494af4d",
+   "id": "02285c48",
    "metadata": {
     "editable": true
    },
@@ -1657,7 +1657,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "048560ee",
+   "id": "71fab9ce",
    "metadata": {
     "editable": true
    },
@@ -1686,7 +1686,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "85b56c79",
+   "id": "424914f7",
    "metadata": {
     "editable": true
    },
@@ -1711,7 +1711,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60937483",
+   "id": "e486c793",
    "metadata": {
     "editable": true
    },
@@ -1731,7 +1731,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d0ea6a3",
+   "id": "1c6a9f34",
    "metadata": {
     "editable": true
    },
@@ -1758,7 +1758,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8f6fc4e6",
+   "id": "28f4300e",
    "metadata": {
     "editable": true
    },
@@ -1771,7 +1771,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bd392ed",
+   "id": "deb48c69",
    "metadata": {
     "editable": true
    },
@@ -1783,7 +1783,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e33d3e3",
+   "id": "127f4812",
    "metadata": {
     "editable": true
    },
@@ -1794,7 +1794,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e1c73ac",
+   "id": "305b4349",
    "metadata": {
     "editable": true
    },
@@ -1810,7 +1810,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "2c315558",
+   "id": "9dacf721",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1844,7 +1844,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aaa58775",
+   "id": "63596c47",
    "metadata": {
     "editable": true
    },
@@ -1854,7 +1854,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "02b198ed",
+   "id": "e663049c",
    "metadata": {
     "editable": true
    },
@@ -1869,7 +1869,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4cef197d",
+   "id": "e2b36261",
    "metadata": {
     "editable": true
    },
@@ -1881,7 +1881,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23b34528",
+   "id": "69fa292f",
    "metadata": {
     "editable": true
    },
@@ -1891,7 +1891,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2847956",
+   "id": "23b3dece",
    "metadata": {
     "editable": true
    },
@@ -1907,7 +1907,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "b8dacc33",
+   "id": "e1630ab8",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1924,7 +1924,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd89705f",
+   "id": "c2d3b936",
    "metadata": {
     "editable": true
    },
@@ -1937,7 +1937,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "d35541fd",
+   "id": "355c6a66",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1984,7 +1984,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36014ec9",
+   "id": "ab553d39",
    "metadata": {
     "editable": true
    },
@@ -1998,7 +1998,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16fb5f8f",
+   "id": "f439180e",
    "metadata": {
     "editable": true
    },
@@ -2010,7 +2010,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1ec698e",
+   "id": "7ba7386d",
    "metadata": {
     "editable": true
    },
@@ -2022,7 +2022,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "787f58f5",
+   "id": "7e0a1440",
    "metadata": {
     "editable": true
    },
@@ -2034,7 +2034,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e23435fd",
+   "id": "2e7611f3",
    "metadata": {
     "editable": true
    },
@@ -2044,7 +2044,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ccaad283",
+   "id": "414e53ca",
    "metadata": {
     "editable": true
    },
@@ -2056,7 +2056,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be8092da",
+   "id": "31ed8899",
    "metadata": {
     "editable": true
    },
@@ -2066,7 +2066,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e055e08",
+   "id": "a66641fb",
    "metadata": {
     "editable": true
    },
@@ -2078,7 +2078,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff86c9bc",
+   "id": "28a50f9e",
    "metadata": {
     "editable": true
    },
@@ -2089,7 +2089,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4f2e747",
+   "id": "b8c5f507",
    "metadata": {
     "editable": true
    },
@@ -2101,7 +2101,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a9a9f87",
+   "id": "445744c8",
    "metadata": {
     "editable": true
    },
@@ -2113,7 +2113,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1232e11a",
+   "id": "ef90b7cb",
    "metadata": {
     "editable": true
    },
@@ -2123,7 +2123,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a807825b",
+   "id": "9d4c2ac7",
    "metadata": {
     "editable": true
    },
@@ -2135,7 +2135,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4fa9855c",
+   "id": "84e62cfc",
    "metadata": {
     "editable": true
    },
@@ -2147,7 +2147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcffefcf",
+   "id": "41c2ba4b",
    "metadata": {
     "editable": true
    },
@@ -2157,7 +2157,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c08ff3a",
+   "id": "beb557ef",
    "metadata": {
     "editable": true
    },
@@ -2169,7 +2169,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c2483a13",
+   "id": "b3fdffce",
    "metadata": {
     "editable": true
    },
@@ -2179,7 +2179,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a82a8c5",
+   "id": "8005292a",
    "metadata": {
     "editable": true
    },
@@ -2191,7 +2191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "743f7309",
+   "id": "92d9f94b",
    "metadata": {
     "editable": true
    },
@@ -2201,7 +2201,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6d7b31a",
+   "id": "17940c71",
    "metadata": {
     "editable": true
    },
@@ -2241,7 +2241,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "518d6bb4",
+   "id": "6ffb31dd",
    "metadata": {
     "editable": true
    },
@@ -2258,7 +2258,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "056673c8",
+   "id": "cc767251",
    "metadata": {
     "editable": true
    },
@@ -2281,7 +2281,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63daba59",
+   "id": "347029b1",
    "metadata": {
     "editable": true
    },
@@ -2298,7 +2298,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "89b74667",
+   "id": "a77dda49",
    "metadata": {
     "editable": true
    },
@@ -2317,7 +2317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "588dd662",
+   "id": "25a0d7d6",
    "metadata": {
     "editable": true
    },
@@ -2328,7 +2328,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb8348c6",
+   "id": "70462fa0",
    "metadata": {
     "editable": true
    },
@@ -2340,7 +2340,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62027bc1",
+   "id": "f8421c8e",
    "metadata": {
     "editable": true
    },
@@ -2358,7 +2358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c73c4b7",
+   "id": "d4ef09ac",
    "metadata": {
     "editable": true
    },
@@ -2374,7 +2374,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3a2d330",
+   "id": "fc6f8651",
    "metadata": {
     "editable": true
    },
@@ -2386,7 +2386,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "374b88cc",
+   "id": "ece72dfe",
    "metadata": {
     "editable": true
    },
@@ -2396,7 +2396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5aa42e6",
+   "id": "3f900d15",
    "metadata": {
     "editable": true
    },
@@ -2409,7 +2409,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c01a816",
+   "id": "3cb45c74",
    "metadata": {
     "editable": true
    },
@@ -2421,7 +2421,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f556eddc",
+   "id": "81b8790f",
    "metadata": {
     "editable": true
    },
@@ -2431,7 +2431,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcf14a16",
+   "id": "9d42c98f",
    "metadata": {
     "editable": true
    },
@@ -2444,7 +2444,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08c37095",
+   "id": "ab036419",
    "metadata": {
     "editable": true
    },
@@ -2454,7 +2454,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6815fa1b",
+   "id": "bba11ff3",
    "metadata": {
     "editable": true
    },
@@ -2466,7 +2466,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "daf50946",
+   "id": "6518184d",
    "metadata": {
     "editable": true
    },
@@ -2479,7 +2479,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7a60cb3",
+   "id": "ba89e5b0",
    "metadata": {
     "editable": true
    },
@@ -2492,7 +2492,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38105bfd",
+   "id": "47325cf5",
    "metadata": {
     "editable": true
    },
@@ -2504,7 +2504,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d697464",
+   "id": "8d9036c1",
    "metadata": {
     "editable": true
    },
@@ -2516,7 +2516,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c298d7ba",
+   "id": "889f801b",
    "metadata": {
     "editable": true
    },
@@ -2526,7 +2526,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45265b59",
+   "id": "8a803d4a",
    "metadata": {
     "editable": true
    },
@@ -2539,7 +2539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab6ce408",
+   "id": "ec92b840",
    "metadata": {
     "editable": true
    },
@@ -2551,7 +2551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca0350a7",
+   "id": "6de4ce40",
    "metadata": {
     "editable": true
    },
@@ -2563,7 +2563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8146e6f",
+   "id": "22e97024",
    "metadata": {
     "editable": true
    },
@@ -2575,7 +2575,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05d97a86",
+   "id": "9cd0a124",
    "metadata": {
     "editable": true
    },
@@ -2587,7 +2587,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f84e7118",
+   "id": "29b31bed",
    "metadata": {
     "editable": true
    },
@@ -2601,7 +2601,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28be9ec4",
+   "id": "d1145ae7",
    "metadata": {
     "editable": true
    },
@@ -2613,7 +2613,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b9f5a5d8",
+   "id": "f1479849",
    "metadata": {
     "editable": true
    },
@@ -2623,7 +2623,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "86b43b21",
+   "id": "0c51f5eb",
    "metadata": {
     "editable": true
    },
@@ -2635,7 +2635,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58744172",
+   "id": "2cbb0f42",
    "metadata": {
     "editable": true
    },
@@ -2647,7 +2647,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd515e6f",
+   "id": "406c4098",
    "metadata": {
     "editable": true
    },
@@ -2659,7 +2659,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8c98bfe",
+   "id": "70966948",
    "metadata": {
     "editable": true
    },
@@ -2671,7 +2671,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08cc9626",
+   "id": "627f3d38",
    "metadata": {
     "editable": true
    },
@@ -2683,7 +2683,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "725df93e",
+   "id": "129105f7",
    "metadata": {
     "editable": true
    },
@@ -2706,7 +2706,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "8d0397cd",
+   "id": "bce32748",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2782,7 +2782,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbc56c2b",
+   "id": "62eccb26",
    "metadata": {
     "editable": true
    },
@@ -2794,7 +2794,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cfab477f",
+   "id": "675cc7de",
    "metadata": {
     "editable": true
    },
@@ -2809,7 +2809,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc176ed4",
+   "id": "ff36cd09",
    "metadata": {
     "editable": true
    },
@@ -2821,7 +2821,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9eef8e3",
+   "id": "7ae7a42a",
    "metadata": {
     "editable": true
    },
@@ -2831,7 +2831,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c33552ec",
+   "id": "607325f0",
    "metadata": {
     "editable": true
    },
@@ -2843,7 +2843,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9465d4f6",
+   "id": "cfb328b4",
    "metadata": {
     "editable": true
    },
@@ -2853,7 +2853,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cd89a35",
+   "id": "bc44d844",
    "metadata": {
     "editable": true
    },
@@ -2865,7 +2865,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "13a9f453",
+   "id": "17ddbfda",
    "metadata": {
     "editable": true
    },
@@ -2877,7 +2877,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6c909f72",
+   "id": "f5658751",
    "metadata": {
     "editable": true
    },
@@ -2892,7 +2892,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b32ee709",
+   "id": "2b01e674",
    "metadata": {
     "editable": true
    },
@@ -2903,7 +2903,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5d3f72c",
+   "id": "c18a65c6",
    "metadata": {
     "editable": true
    },
@@ -2923,7 +2923,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18f488f0",
+   "id": "04258de2",
    "metadata": {
     "editable": true
    },
@@ -2935,7 +2935,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "93618783",
+   "id": "e10d0aad",
    "metadata": {
     "editable": true
    },
@@ -2945,7 +2945,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "02f57528",
+   "id": "d198578b",
    "metadata": {
     "editable": true
    },
@@ -2957,7 +2957,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "762833f4",
+   "id": "2aec2fc1",
    "metadata": {
     "editable": true
    },
@@ -2986,7 +2986,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ab8ec4f",
+   "id": "81fed6f5",
    "metadata": {
     "editable": true
    },
@@ -3013,7 +3013,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e526d1f",
+   "id": "fe7d1d49",
    "metadata": {
     "editable": true
    },
@@ -3024,7 +3024,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "f5d258ce",
+   "id": "0b32041d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3064,7 +3064,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e4bf198",
+   "id": "db224b5b",
    "metadata": {
     "editable": true
    },
@@ -3081,7 +3081,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33a42ac4",
+   "id": "6b988f39",
    "metadata": {
     "editable": true
    },
@@ -3104,7 +3104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b5d1bbb",
+   "id": "1214012e",
    "metadata": {
     "editable": true
    },
@@ -3118,7 +3118,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1fee5f54",
+   "id": "c7a8cd85",
    "metadata": {
     "editable": true
    },
@@ -3137,7 +3137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "235f2975",
+   "id": "0f2a2211",
    "metadata": {
     "editable": true
    },
@@ -3147,7 +3147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fd7415b7",
+   "id": "e9863a0f",
    "metadata": {
     "editable": true
    },
@@ -3159,7 +3159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c265b5d",
+   "id": "d88c8316",
    "metadata": {
     "editable": true
    },
@@ -3173,7 +3173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "976c31a2",
+   "id": "643f1b6d",
    "metadata": {
     "editable": true
    },
@@ -3185,7 +3185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8dc8acd7",
+   "id": "0769ec85",
    "metadata": {
     "editable": true
    },
@@ -3195,7 +3195,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1dc8e8e",
+   "id": "f0d61e66",
    "metadata": {
     "editable": true
    },
@@ -3207,7 +3207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb688af0",
+   "id": "0d7c9d9e",
    "metadata": {
     "editable": true
    },
@@ -3224,7 +3224,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eeadd85e",
+   "id": "335fb5ed",
    "metadata": {
     "editable": true
    },
@@ -3234,7 +3234,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9375ad7",
+   "id": "1dbb3e05",
    "metadata": {
     "editable": true
    },
@@ -3250,7 +3250,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "025f1ca1",
+   "id": "4a535424",
    "metadata": {
     "editable": true
    },
@@ -3260,7 +3260,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d44951a1",
+   "id": "512418d2",
    "metadata": {
     "editable": true
    },
@@ -3276,7 +3276,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ecc9216b",
+   "id": "baa56321",
    "metadata": {
     "editable": true
    },
@@ -3286,7 +3286,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28e2ff44",
+   "id": "1fd5881c",
    "metadata": {
     "editable": true
    },
@@ -3302,7 +3302,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "935324af",
+   "id": "546a2bf3",
    "metadata": {
     "editable": true
    },
@@ -3312,7 +3312,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a15e7526",
+   "id": "4e356417",
    "metadata": {
     "editable": true
    },
@@ -3329,7 +3329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d3cef55",
+   "id": "1f3c787b",
    "metadata": {
     "editable": true
    },
@@ -3341,7 +3341,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0fab1783",
+   "id": "72018911",
    "metadata": {
     "editable": true
    },
@@ -3353,7 +3353,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9a8450e",
+   "id": "7d741e98",
    "metadata": {
     "editable": true
    },
@@ -3365,7 +3365,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "485d1023",
+   "id": "f2e4a67f",
    "metadata": {
     "editable": true
    },
@@ -3375,7 +3375,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a2da5dbe",
+   "id": "302c8edf",
    "metadata": {
     "editable": true
    },
@@ -3387,7 +3387,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "13959099",
+   "id": "def3ec8a",
    "metadata": {
     "editable": true
    },
@@ -3399,7 +3399,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23f0b903",
+   "id": "37150ee7",
    "metadata": {
     "editable": true
    },
@@ -3411,7 +3411,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c344e77",
+   "id": "e937a396",
    "metadata": {
     "editable": true
    },
@@ -3421,7 +3421,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8064053",
+   "id": "07e76c7b",
    "metadata": {
     "editable": true
    },
@@ -3433,7 +3433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "714ab01f",
+   "id": "99f80e22",
    "metadata": {
     "editable": true
    },
@@ -3443,35 +3443,36 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3ff6988",
+   "id": "7a917bf2",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_i\\boldsymbol{u}^T_i\\boldsymbol{y},\n",
+    "\\tilde{y}_{\\mathrm{OLS}}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_i\\boldsymbol{u}^T_i\\boldsymbol{y},\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5c204f79",
+   "id": "c11ae5fe",
    "metadata": {
     "editable": true
    },
    "source": [
+    "which is not the same as $\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}$, which due to the orthogonality of $\\boldsymbol{U}$ would have given us that the model equals the output.\n",
+    "\n",
     "It means that the ordinary least square model (with the optimal\n",
     "parameters) $\\boldsymbol{\\tilde{y}}$, corresponds to an orthogonal\n",
     "transformation of the output (or target) vector $\\boldsymbol{y}$ by the\n",
     "vectors of the matrix $\\boldsymbol{U}$. **Note that the summation ends at**\n",
     "$p-1$, that is $\\boldsymbol{\\tilde{y}}\\ne \\boldsymbol{y}$. We can thus not use the\n",
-    "orthogonality relation for the matrix $\\boldsymbol{U}$. This can already be\n",
-    "when we multiply the matrices $\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T$."
+    "orthogonality relation for the matrix $\\boldsymbol{U}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "78c51f10",
+   "id": "f300aa1b",
    "metadata": {
     "editable": true
    },
@@ -3483,7 +3484,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c432ed4",
+   "id": "8bd1e2a6",
    "metadata": {
     "editable": true
    },
@@ -3495,7 +3496,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68a7b505",
+   "id": "62502292",
    "metadata": {
     "editable": true
    },
@@ -3505,7 +3506,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14268cd5",
+   "id": "efca6f6c",
    "metadata": {
     "editable": true
    },
@@ -3517,7 +3518,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3207844",
+   "id": "e2cbd6f5",
    "metadata": {
     "editable": true
    },
@@ -3528,7 +3529,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c7f5556",
+   "id": "5cc9aea6",
    "metadata": {
     "editable": true
    },
@@ -3540,7 +3541,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01bd8826",
+   "id": "61ad8f4c",
    "metadata": {
     "editable": true
    },
@@ -3550,7 +3551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb083248",
+   "id": "b1cc9449",
    "metadata": {
     "editable": true
    },
@@ -3562,7 +3563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "66bd1ec9",
+   "id": "a9b28652",
    "metadata": {
     "editable": true
    },
@@ -3572,7 +3573,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b92a06bb",
+   "id": "f26b69cc",
    "metadata": {
     "editable": true
    },
@@ -3584,7 +3585,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dad0b409",
+   "id": "53acde0e",
    "metadata": {
     "editable": true
    },
@@ -3595,7 +3596,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75d85fa8",
+   "id": "512b9f17",
    "metadata": {
     "editable": true
    },
@@ -3607,7 +3608,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0918773",
+   "id": "a1c49f5f",
    "metadata": {
     "editable": true
    },
@@ -3625,7 +3626,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65592b3b",
+   "id": "db70d623",
    "metadata": {
     "editable": true
    },
@@ -3641,7 +3642,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "442404b8",
+   "id": "95b18b06",
    "metadata": {
     "editable": true
    },
@@ -3653,7 +3654,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50eca816",
+   "id": "db07fa1e",
    "metadata": {
     "editable": true
    },
@@ -3665,7 +3666,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a27e487e",
+   "id": "9856cea3",
    "metadata": {
     "editable": true
    },
@@ -3677,7 +3678,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49c74d48",
+   "id": "7f6cba4c",
    "metadata": {
     "editable": true
    },
@@ -3690,7 +3691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "214feab7",
+   "id": "581565a5",
    "metadata": {
     "editable": true
    },
@@ -3706,7 +3707,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e61c0669",
+   "id": "22b63d08",
    "metadata": {
     "editable": true
    },
@@ -3720,7 +3721,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9f3db006",
+   "id": "cd6032aa",
    "metadata": {
     "editable": true
    },
@@ -3730,7 +3731,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6dfeb8ca",
+   "id": "25b7936a",
    "metadata": {
     "editable": true
    },
@@ -3742,7 +3743,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da47505d",
+   "id": "9c4ad4d2",
    "metadata": {
     "editable": true
    },
@@ -3752,7 +3753,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87c1a756",
+   "id": "75bcfcea",
    "metadata": {
     "editable": true
    },
@@ -3764,7 +3765,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5028dae1",
+   "id": "95c9cc40",
    "metadata": {
     "editable": true
    },
@@ -3774,7 +3775,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98da161b",
+   "id": "33c19ed1",
    "metadata": {
     "editable": true
    },
@@ -3788,7 +3789,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69065ef4",
+   "id": "c28b0a97",
    "metadata": {
     "editable": true
    },
@@ -3805,7 +3806,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3455143e",
+   "id": "d4ece056",
    "metadata": {
     "editable": true
    },
@@ -3821,7 +3822,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e322fdc8",
+   "id": "22360ee3",
    "metadata": {
     "editable": true
    },
@@ -3833,7 +3834,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f50b583d",
+   "id": "77e8998d",
    "metadata": {
     "editable": true
    },
@@ -3846,7 +3847,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b12b62dc",
+   "id": "8ef4225d",
    "metadata": {
     "editable": true
    },
@@ -3860,7 +3861,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40355c87",
+   "id": "627eac2b",
    "metadata": {
     "editable": true
    },
@@ -3870,7 +3871,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee70666b",
+   "id": "f7ac0db1",
    "metadata": {
     "editable": true
    },
@@ -3883,7 +3884,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc6d0cc7",
+   "id": "e93eae5d",
    "metadata": {
     "editable": true
    },
@@ -3902,7 +3903,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6b6f792",
+   "id": "58364673",
    "metadata": {
     "editable": true
    },
@@ -3914,7 +3915,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39c76bf5",
+   "id": "30541096",
    "metadata": {
     "editable": true
    },
@@ -3926,7 +3927,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2d754e5",
+   "id": "101bb217",
    "metadata": {
     "editable": true
    },
@@ -3936,7 +3937,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77a984ab",
+   "id": "ba8e52b1",
    "metadata": {
     "editable": true
    },
@@ -3948,7 +3949,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33060c1a",
+   "id": "67d4335e",
    "metadata": {
     "editable": true
    },
@@ -3961,7 +3962,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ed1e8279",
+   "id": "06416768",
    "metadata": {
     "editable": true
    },
@@ -3980,7 +3981,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22b40263",
+   "id": "dd2f405a",
    "metadata": {
     "editable": true
    },
@@ -3990,7 +3991,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b02469c",
+   "id": "40ded798",
    "metadata": {
     "editable": true
    },
@@ -4009,7 +4010,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0660e456",
+   "id": "d3044a01",
    "metadata": {
     "editable": true
    },
@@ -4027,7 +4028,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a40e5c0",
+   "id": "d612ad97",
    "metadata": {
     "editable": true
    },
@@ -4041,7 +4042,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82d7e99d",
+   "id": "52f27c53",
    "metadata": {
     "editable": true
    },
@@ -4056,7 +4057,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "6f4b429b",
+   "id": "ca5ce77c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4077,7 +4078,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a38f8430",
+   "id": "1c02019d",
    "metadata": {
     "editable": true
    },
@@ -4094,7 +4095,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "87d44fdf",
+   "id": "58381fbe",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4126,7 +4127,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f08f4dc",
+   "id": "a647044e",
    "metadata": {
     "editable": true
    },
@@ -4140,7 +4141,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a25b356f",
+   "id": "d7bea0a6",
    "metadata": {
     "editable": true
    },
@@ -4153,7 +4154,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "928ae649",
+   "id": "81d407da",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4178,7 +4179,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cab70377",
+   "id": "7998701a",
    "metadata": {
     "editable": true
    },
@@ -4190,7 +4191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22ac4a6d",
+   "id": "e4f65917",
    "metadata": {
     "editable": true
    },
@@ -4202,7 +4203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd0697a9",
+   "id": "73ecb476",
    "metadata": {
     "editable": true
    },
@@ -4212,7 +4213,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5043405",
+   "id": "f4f10483",
    "metadata": {
     "editable": true
    },
@@ -4229,7 +4230,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a4edab6",
+   "id": "9e173ba2",
    "metadata": {
     "editable": true
    },
@@ -4239,7 +4240,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1b67496",
+   "id": "6b6f3d02",
    "metadata": {
     "editable": true
    },
@@ -4254,7 +4255,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47a041cb",
+   "id": "69a2c9b4",
    "metadata": {
     "editable": true
    },
@@ -4264,7 +4265,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "575264b7",
+   "id": "41dedd73",
    "metadata": {
     "editable": true
    },
@@ -4278,7 +4279,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b049c58",
+   "id": "a7b2bb8c",
    "metadata": {
     "editable": true
    },
@@ -4290,7 +4291,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9780789f",
+   "id": "dba35fc4",
    "metadata": {
     "editable": true
    },
@@ -4302,7 +4303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da396c4a",
+   "id": "0e30a645",
    "metadata": {
     "editable": true
    },
@@ -4314,7 +4315,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87a74417",
+   "id": "6fa482d3",
    "metadata": {
     "editable": true
    },
@@ -4324,7 +4325,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5ca565a",
+   "id": "ae9f30ae",
    "metadata": {
     "editable": true
    },
@@ -4336,7 +4337,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "10944fc5",
+   "id": "67907a60",
    "metadata": {
     "editable": true
    },
@@ -4346,7 +4347,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b985955",
+   "id": "3a21fe71",
    "metadata": {
     "editable": true
    },
@@ -4363,7 +4364,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b748051",
+   "id": "3b91b5d8",
    "metadata": {
     "editable": true
    },
@@ -4373,7 +4374,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40c1c1eb",
+   "id": "86de4409",
    "metadata": {
     "editable": true
    },
@@ -4385,7 +4386,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e44c9e87",
+   "id": "d0c0608f",
    "metadata": {
     "editable": true
    },
@@ -4395,7 +4396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28abe46c",
+   "id": "98f544a6",
    "metadata": {
     "editable": true
    },
@@ -4407,7 +4408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "178bc776",
+   "id": "24587410",
    "metadata": {
     "editable": true
    },
@@ -4421,7 +4422,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f0ead95",
+   "id": "61fb4275",
    "metadata": {
     "editable": true
    },
@@ -4433,7 +4434,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fcce3bb5",
+   "id": "6d2404eb",
    "metadata": {
     "editable": true
    },
@@ -4455,7 +4456,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f9a7281",
+   "id": "22615b7e",
    "metadata": {
     "editable": true
    },
@@ -4467,7 +4468,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3ea695c",
+   "id": "bee48c87",
    "metadata": {
     "editable": true
    },
@@ -4482,7 +4483,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "edfff9e0",
+   "id": "7f12f53a",
    "metadata": {
     "editable": true
    },
@@ -4494,7 +4495,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3c83244",
+   "id": "a6acb75c",
    "metadata": {
     "editable": true
    },
@@ -4506,7 +4507,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00df5ee5",
+   "id": "131e9d9c",
    "metadata": {
     "editable": true
    },
@@ -4516,7 +4517,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4661cbd7",
+   "id": "85812d77",
    "metadata": {
     "editable": true
    },
@@ -4528,7 +4529,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07b95265",
+   "id": "35007c74",
    "metadata": {
     "editable": true
    },
@@ -4538,7 +4539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8c9aeba4",
+   "id": "0100935a",
    "metadata": {
     "editable": true
    },
@@ -4550,7 +4551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "03690a72",
+   "id": "7b6ff86e",
    "metadata": {
     "editable": true
    },
@@ -4560,7 +4561,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "478e2a9d",
+   "id": "1f452dfb",
    "metadata": {
     "editable": true
    },
@@ -4572,7 +4573,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e997196a",
+   "id": "05600fbd",
    "metadata": {
     "editable": true
    },
@@ -4589,7 +4590,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "770e587e",
+   "id": "a2af3e04",
    "metadata": {
     "editable": true
    },
@@ -4602,7 +4603,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5cb701c2",
+   "id": "0342c08c",
    "metadata": {
     "editable": true
    },
@@ -4614,7 +4615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dee9d948",
+   "id": "bdd5faeb",
    "metadata": {
     "editable": true
    },
@@ -4624,7 +4625,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "121cd014",
+   "id": "35873dc6",
    "metadata": {
     "editable": true
    },
@@ -4637,7 +4638,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2ee745b4",
+   "id": "6ff6ab78",
    "metadata": {
     "editable": true
    },
@@ -4647,7 +4648,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94a15fb9",
+   "id": "77286b5f",
    "metadata": {
     "editable": true
    },
@@ -4659,7 +4660,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6341fe06",
+   "id": "0ade2616",
    "metadata": {
     "editable": true
    },
@@ -4672,7 +4673,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5bef6925",
+   "id": "da22a168",
    "metadata": {
     "editable": true
    },
@@ -4685,7 +4686,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4539e82b",
+   "id": "caa18da2",
    "metadata": {
     "editable": true
    },
@@ -4697,7 +4698,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f496d16",
+   "id": "f31c8084",
    "metadata": {
     "editable": true
    },
@@ -4709,7 +4710,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee78adfa",
+   "id": "53dc71a2",
    "metadata": {
     "editable": true
    },
@@ -4719,7 +4720,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47a0c860",
+   "id": "753442d5",
    "metadata": {
     "editable": true
    },
@@ -4732,7 +4733,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b452b5d",
+   "id": "e0b2f58a",
    "metadata": {
     "editable": true
    },
@@ -4744,7 +4745,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3331a79",
+   "id": "e4af8e7e",
    "metadata": {
     "editable": true
    },
@@ -4756,7 +4757,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9befd0e3",
+   "id": "6e353a3a",
    "metadata": {
     "editable": true
    },
@@ -4773,7 +4774,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d8f2ba3",
+   "id": "66a4056b",
    "metadata": {
     "editable": true
    },
@@ -4785,7 +4786,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da712e9d",
+   "id": "ea5b3d9f",
    "metadata": {
     "editable": true
    },
@@ -4795,7 +4796,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d91cd5f7",
+   "id": "db50585a",
    "metadata": {
     "editable": true
    },
@@ -4807,7 +4808,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18940f72",
+   "id": "afd3cd57",
    "metadata": {
     "editable": true
    },
@@ -4817,7 +4818,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51fe3527",
+   "id": "6606774b",
    "metadata": {
     "editable": true
    },
@@ -4829,7 +4830,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e85d1eb",
+   "id": "bcfd3adb",
    "metadata": {
     "editable": true
    },
@@ -4841,7 +4842,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96c47485",
+   "id": "46d7227b",
    "metadata": {
     "editable": true
    },
@@ -4857,7 +4858,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1adcbbc",
+   "id": "a214b881",
    "metadata": {
     "editable": true
    },
@@ -4869,7 +4870,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9693074c",
+   "id": "727c87de",
    "metadata": {
     "editable": true
    },
@@ -4881,7 +4882,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46b05531",
+   "id": "5083858e",
    "metadata": {
     "editable": true
    },
@@ -4891,7 +4892,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e4ce02b",
+   "id": "973ad2fa",
    "metadata": {
     "editable": true
    },
@@ -4903,7 +4904,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbd3f781",
+   "id": "4fbd0028",
    "metadata": {
     "editable": true
    },
@@ -4913,7 +4914,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "779e1ac5",
+   "id": "bee26901",
    "metadata": {
     "editable": true
    },
@@ -4925,7 +4926,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ef53f2a5",
+   "id": "da771d96",
    "metadata": {
     "editable": true
    },
@@ -4942,7 +4943,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57adfaff",
+   "id": "8ecb8a62",
    "metadata": {
     "editable": true
    },
@@ -4954,7 +4955,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8f94cba",
+   "id": "5cf08e3d",
    "metadata": {
     "editable": true
    },
@@ -4966,7 +4967,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d60431ff",
+   "id": "d984ce12",
    "metadata": {
     "editable": true
    },
@@ -4976,7 +4977,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f78d1dfd",
+   "id": "837a69b7",
    "metadata": {
     "editable": true
    },
@@ -4988,7 +4989,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "445800de",
+   "id": "21dde5ad",
    "metadata": {
     "editable": true
    },
@@ -4998,7 +4999,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c54c49c",
+   "id": "4d49c112",
    "metadata": {
     "editable": true
    },
@@ -5010,7 +5011,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11366dc1",
+   "id": "5b4eabcf",
    "metadata": {
     "editable": true
    },
@@ -5020,7 +5021,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d68d3ac1",
+   "id": "28dcb3c8",
    "metadata": {
     "editable": true
    },
@@ -5032,7 +5033,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63fedbd6",
+   "id": "f315a306",
    "metadata": {
     "editable": true
    },
@@ -5042,7 +5043,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "470b20a8",
+   "id": "7b4f990c",
    "metadata": {
     "editable": true
    },
@@ -5054,7 +5055,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3277c65",
+   "id": "197daa81",
    "metadata": {
     "editable": true
    },
diff --git a/doc/LectureNotes/week35.ipynb b/doc/LectureNotes/week35.ipynb
index 35f134d71..01ae64c94 100644
--- a/doc/LectureNotes/week35.ipynb
+++ b/doc/LectureNotes/week35.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "82c2f725",
+   "id": "f0622ebb",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2fc786b",
+   "id": "3fe98f20",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77512f33",
+   "id": "8e604e3c",
    "metadata": {
     "editable": true
    },
@@ -49,7 +49,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41516757",
+   "id": "c7f0b40a",
    "metadata": {
     "editable": true
    },
@@ -69,7 +69,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3703d2f",
+   "id": "507709a4",
    "metadata": {
     "editable": true
    },
@@ -102,7 +102,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f22b90af",
+   "id": "bb3b5f67",
    "metadata": {
     "editable": true
    },
@@ -118,7 +118,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3fe305bb",
+   "id": "14444be5",
    "metadata": {
     "editable": true
    },
@@ -130,7 +130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2f38355",
+   "id": "4edc5258",
    "metadata": {
     "editable": true
    },
@@ -140,7 +140,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3d9a4b6",
+   "id": "4d6f9c43",
    "metadata": {
     "editable": true
    },
@@ -152,7 +152,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff3ba043",
+   "id": "fb52f7f5",
    "metadata": {
     "editable": true
    },
@@ -173,7 +173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5de294d5",
+   "id": "4fff6b39",
    "metadata": {
     "editable": true
    },
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5721942a",
+   "id": "54a4cabb",
    "metadata": {
     "editable": true
    },
@@ -198,7 +198,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b2aa843",
+   "id": "d383a507",
    "metadata": {
     "editable": true
    },
@@ -210,7 +210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b12c06f",
+   "id": "498fe31e",
    "metadata": {
     "editable": true
    },
@@ -222,7 +222,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "276d4eba",
+   "id": "7bbbdcd2",
    "metadata": {
     "editable": true
    },
@@ -232,7 +232,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4751c9b4",
+   "id": "405a61ac",
    "metadata": {
     "editable": true
    },
@@ -244,7 +244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd00bf4b",
+   "id": "e7c07f57",
    "metadata": {
     "editable": true
    },
@@ -257,7 +257,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc9028f0",
+   "id": "6054782f",
    "metadata": {
     "editable": true
    },
@@ -269,7 +269,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6a27e54",
+   "id": "7b55104f",
    "metadata": {
     "editable": true
    },
@@ -279,7 +279,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82f1494a",
+   "id": "4635525e",
    "metadata": {
     "editable": true
    },
@@ -291,7 +291,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6427a35",
+   "id": "11f6ffc7",
    "metadata": {
     "editable": true
    },
@@ -303,7 +303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38c78421",
+   "id": "820ddc3f",
    "metadata": {
     "editable": true
    },
@@ -314,7 +314,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f23ac12e",
+   "id": "9aa4b864",
    "metadata": {
     "editable": true
    },
@@ -326,7 +326,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88fd9c03",
+   "id": "c542e149",
    "metadata": {
     "editable": true
    },
@@ -345,7 +345,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a953b1a3",
+   "id": "7be13194",
    "metadata": {
     "editable": true
    },
@@ -358,7 +358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19eb0838",
+   "id": "aad2641f",
    "metadata": {
     "editable": true
    },
@@ -368,7 +368,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a4f910a4",
+   "id": "9dfe7e22",
    "metadata": {
     "editable": true
    },
@@ -380,7 +380,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5060e089",
+   "id": "852c82a9",
    "metadata": {
     "editable": true
    },
@@ -390,7 +390,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8542c5a3",
+   "id": "84163c68",
    "metadata": {
     "editable": true
    },
@@ -402,7 +402,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "475e1436",
+   "id": "5bfb8965",
    "metadata": {
     "editable": true
    },
@@ -412,7 +412,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88abf4ad",
+   "id": "3822fa25",
    "metadata": {
     "editable": true
    },
@@ -424,7 +424,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62f558d9",
+   "id": "2c0f9f09",
    "metadata": {
     "editable": true
    },
@@ -435,7 +435,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99cc5104",
+   "id": "7ce9a08c",
    "metadata": {
     "editable": true
    },
@@ -447,7 +447,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29043759",
+   "id": "3efb75ba",
    "metadata": {
     "editable": true
    },
@@ -457,7 +457,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9d0f067",
+   "id": "8c4ceb9d",
    "metadata": {
     "editable": true
    },
@@ -469,7 +469,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c34bfdd2",
+   "id": "53a5a827",
    "metadata": {
     "editable": true
    },
@@ -479,7 +479,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3533f92e",
+   "id": "12d309d7",
    "metadata": {
     "editable": true
    },
@@ -491,7 +491,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "135631d4",
+   "id": "16fdbfbe",
    "metadata": {
     "editable": true
    },
@@ -511,7 +511,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf25f4a7",
+   "id": "b5651e23",
    "metadata": {
     "editable": true
    },
@@ -538,7 +538,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d82400a",
+   "id": "e3289213",
    "metadata": {
     "editable": true
    },
@@ -550,7 +550,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00d8d123",
+   "id": "db9c8386",
    "metadata": {
     "editable": true
    },
@@ -562,7 +562,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cce17e14",
+   "id": "ea7d7d7e",
    "metadata": {
     "editable": true
    },
@@ -578,7 +578,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65efb775",
+   "id": "7dace63c",
    "metadata": {
     "editable": true
    },
@@ -596,7 +596,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2df9efd6",
+   "id": "b00b4a82",
    "metadata": {
     "editable": true
    },
@@ -608,7 +608,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37b621d8",
+   "id": "26392bc2",
    "metadata": {
     "editable": true
    },
@@ -620,7 +620,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "297be9c9",
+   "id": "f5214ffc",
    "metadata": {
     "editable": true
    },
@@ -631,7 +631,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe288c99",
+   "id": "0eec52de",
    "metadata": {
     "editable": true
    },
@@ -643,7 +643,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d4333779",
+   "id": "077e4fe0",
    "metadata": {
     "editable": true
    },
@@ -653,7 +653,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7e72c3d",
+   "id": "e3ff215c",
    "metadata": {
     "editable": true
    },
@@ -665,7 +665,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3423b702",
+   "id": "6cb9ae59",
    "metadata": {
     "editable": true
    },
@@ -679,7 +679,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe66f713",
+   "id": "7a02062e",
    "metadata": {
     "editable": true
    },
@@ -691,7 +691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43eed51b",
+   "id": "45f73c0f",
    "metadata": {
     "editable": true
    },
@@ -703,7 +703,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f943ccb",
+   "id": "6c9d24a2",
    "metadata": {
     "editable": true
    },
@@ -715,7 +715,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5df09c55",
+   "id": "241fed59",
    "metadata": {
     "editable": true
    },
@@ -725,7 +725,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b92d9f2a",
+   "id": "1c67de99",
    "metadata": {
     "editable": true
    },
@@ -737,7 +737,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6cf49ab",
+   "id": "36af470a",
    "metadata": {
     "editable": true
    },
@@ -749,7 +749,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e000448",
+   "id": "38f9d9cf",
    "metadata": {
     "editable": true
    },
@@ -761,7 +761,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbaa984b",
+   "id": "b20c89a1",
    "metadata": {
     "editable": true
    },
@@ -775,7 +775,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4e444ea",
+   "id": "e56ba6c5",
    "metadata": {
     "editable": true
    },
@@ -787,7 +787,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "454ba5ba",
+   "id": "1481f969",
    "metadata": {
     "editable": true
    },
@@ -799,7 +799,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0434cd9",
+   "id": "fbd29e7c",
    "metadata": {
     "editable": true
    },
@@ -811,7 +811,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2bcda9d",
+   "id": "889c22f1",
    "metadata": {
     "editable": true
    },
@@ -821,7 +821,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aea0ba73",
+   "id": "5a753c31",
    "metadata": {
     "editable": true
    },
@@ -833,7 +833,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a58d6e8",
+   "id": "4fed4676",
    "metadata": {
     "editable": true
    },
@@ -843,7 +843,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "927428aa",
+   "id": "e1894902",
    "metadata": {
     "editable": true
    },
@@ -855,7 +855,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "372ad443",
+   "id": "ddca93b1",
    "metadata": {
     "editable": true
    },
@@ -865,7 +865,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37a99489",
+   "id": "5f9d8901",
    "metadata": {
     "editable": true
    },
@@ -877,7 +877,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4872a1cd",
+   "id": "726c169c",
    "metadata": {
     "editable": true
    },
@@ -889,7 +889,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b21e9cb2",
+   "id": "7d7715d5",
    "metadata": {
     "editable": true
    },
@@ -901,7 +901,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "442375d1",
+   "id": "057fedd9",
    "metadata": {
     "editable": true
    },
@@ -916,7 +916,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aabab237",
+   "id": "4c06fecd",
    "metadata": {
     "editable": true
    },
@@ -928,7 +928,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "106f09df",
+   "id": "490e6469",
    "metadata": {
     "editable": true
    },
@@ -938,7 +938,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "73d8f824",
+   "id": "b6259635",
    "metadata": {
     "editable": true
    },
@@ -950,7 +950,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2626be7",
+   "id": "0fda0191",
    "metadata": {
     "editable": true
    },
@@ -960,7 +960,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "81d89d86",
+   "id": "797e356f",
    "metadata": {
     "editable": true
    },
@@ -972,7 +972,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59c2576a",
+   "id": "46bdaee6",
    "metadata": {
     "editable": true
    },
@@ -982,7 +982,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b7bf3f9",
+   "id": "cb1f5f36",
    "metadata": {
     "editable": true
    },
@@ -994,7 +994,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea1e8943",
+   "id": "fa70c555",
    "metadata": {
     "editable": true
    },
@@ -1006,7 +1006,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0425d72",
+   "id": "2fdb367f",
    "metadata": {
     "editable": true
    },
@@ -1018,7 +1018,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38386834",
+   "id": "ced6532f",
    "metadata": {
     "editable": true
    },
@@ -1028,7 +1028,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bfbc4bd3",
+   "id": "49c27708",
    "metadata": {
     "editable": true
    },
@@ -1040,7 +1040,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ced3cec",
+   "id": "27da1de0",
    "metadata": {
     "editable": true
    },
@@ -1053,7 +1053,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc6f1dec",
+   "id": "9ddef35d",
    "metadata": {
     "editable": true
    },
@@ -1065,7 +1065,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "699662d2",
+   "id": "ae006a7e",
    "metadata": {
     "editable": true
    },
@@ -1075,7 +1075,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0991592c",
+   "id": "904d2486",
    "metadata": {
     "editable": true
    },
@@ -1087,7 +1087,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "450dd961",
+   "id": "525eda84",
    "metadata": {
     "editable": true
    },
@@ -1097,7 +1097,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a13de0fa",
+   "id": "7eadfb46",
    "metadata": {
     "editable": true
    },
@@ -1109,7 +1109,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c64bc916",
+   "id": "8ee45bc9",
    "metadata": {
     "editable": true
    },
@@ -1119,7 +1119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab1e18bc",
+   "id": "73b41248",
    "metadata": {
     "editable": true
    },
@@ -1131,7 +1131,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1e74f34",
+   "id": "dc4356aa",
    "metadata": {
     "editable": true
    },
@@ -1141,7 +1141,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ad3ebd9",
+   "id": "3e2b94a9",
    "metadata": {
     "editable": true
    },
@@ -1153,7 +1153,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37d1b4ca",
+   "id": "b9716f36",
    "metadata": {
     "editable": true
    },
@@ -1163,7 +1163,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d5fc67a",
+   "id": "01341a5b",
    "metadata": {
     "editable": true
    },
@@ -1175,7 +1175,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d98472d9",
+   "id": "83a3f463",
    "metadata": {
     "editable": true
    },
@@ -1191,7 +1191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d859f20",
+   "id": "c2c42203",
    "metadata": {
     "editable": true
    },
@@ -1203,7 +1203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7bb91ec",
+   "id": "94f060b9",
    "metadata": {
     "editable": true
    },
@@ -1213,7 +1213,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1553864b",
+   "id": "d0e5c32c",
    "metadata": {
     "editable": true
    },
@@ -1225,7 +1225,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8cc9c71",
+   "id": "0b464ed4",
    "metadata": {
     "editable": true
    },
@@ -1243,7 +1243,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1f01477",
+   "id": "5c952119",
    "metadata": {
     "editable": true
    },
@@ -1255,7 +1255,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2dea7e1",
+   "id": "25e4a5f3",
    "metadata": {
     "editable": true
    },
@@ -1267,7 +1267,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "76b0f99e",
+   "id": "4f774737",
    "metadata": {
     "editable": true
    },
@@ -1277,7 +1277,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cfa3ca25",
+   "id": "59c91b82",
    "metadata": {
     "editable": true
    },
@@ -1289,7 +1289,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a9163d8",
+   "id": "33ceec0f",
    "metadata": {
     "editable": true
    },
@@ -1299,7 +1299,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6b54a1e",
+   "id": "931da8ef",
    "metadata": {
     "editable": true
    },
@@ -1311,7 +1311,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "659c98d0",
+   "id": "2f2516b6",
    "metadata": {
     "editable": true
    },
@@ -1321,7 +1321,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "209b5b37",
+   "id": "bcb56a20",
    "metadata": {
     "editable": true
    },
@@ -1335,7 +1335,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b325d0c3",
+   "id": "86333a6f",
    "metadata": {
     "editable": true
    },
@@ -1347,7 +1347,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c49a2fcd",
+   "id": "1513e73c",
    "metadata": {
     "editable": true
    },
@@ -1358,7 +1358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6978ef70",
+   "id": "c8c47d9a",
    "metadata": {
     "editable": true
    },
@@ -1371,7 +1371,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "01530c39",
+   "id": "8ec18f31",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1398,7 +1398,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90ff28d4",
+   "id": "b7255330",
    "metadata": {
     "editable": true
    },
@@ -1409,7 +1409,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "1d052cbe",
+   "id": "9d5f3a70",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1422,7 +1422,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3362efd4",
+   "id": "8daa4681",
    "metadata": {
     "editable": true
    },
@@ -1436,7 +1436,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "3e9e681f",
+   "id": "de91ca73",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1449,7 +1449,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78e4427f",
+   "id": "442ef680",
    "metadata": {
     "editable": true
    },
@@ -1460,7 +1460,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "20aab659",
+   "id": "9b329ab4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1472,7 +1472,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "326f641d",
+   "id": "d7ded522",
    "metadata": {
     "editable": true
    },
@@ -1483,7 +1483,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "c8e80cf1",
+   "id": "34c18b8f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1499,7 +1499,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aba7b289",
+   "id": "229d94fa",
    "metadata": {
     "editable": true
    },
@@ -1510,7 +1510,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "7235bf1b",
+   "id": "afb92eb9",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1524,7 +1524,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3eaf5f8d",
+   "id": "8a02aaaf",
    "metadata": {
     "editable": true
    },
@@ -1545,7 +1545,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6fc5dc26",
+   "id": "b64b7d81",
    "metadata": {
     "editable": true
    },
@@ -1556,7 +1556,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "98ca5627",
+   "id": "094eed3e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1609,7 +1609,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "09f0c1c6",
+   "id": "76119de5",
    "metadata": {
     "editable": true
    },
@@ -1620,7 +1620,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "02220d97",
+   "id": "dff69c9a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1645,7 +1645,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5494af4d",
+   "id": "02285c48",
    "metadata": {
     "editable": true
    },
@@ -1657,7 +1657,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "048560ee",
+   "id": "71fab9ce",
    "metadata": {
     "editable": true
    },
@@ -1686,7 +1686,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "85b56c79",
+   "id": "424914f7",
    "metadata": {
     "editable": true
    },
@@ -1711,7 +1711,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60937483",
+   "id": "e486c793",
    "metadata": {
     "editable": true
    },
@@ -1731,7 +1731,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d0ea6a3",
+   "id": "1c6a9f34",
    "metadata": {
     "editable": true
    },
@@ -1758,7 +1758,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8f6fc4e6",
+   "id": "28f4300e",
    "metadata": {
     "editable": true
    },
@@ -1771,7 +1771,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bd392ed",
+   "id": "deb48c69",
    "metadata": {
     "editable": true
    },
@@ -1783,7 +1783,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e33d3e3",
+   "id": "127f4812",
    "metadata": {
     "editable": true
    },
@@ -1794,7 +1794,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e1c73ac",
+   "id": "305b4349",
    "metadata": {
     "editable": true
    },
@@ -1810,7 +1810,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "2c315558",
+   "id": "9dacf721",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1844,7 +1844,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aaa58775",
+   "id": "63596c47",
    "metadata": {
     "editable": true
    },
@@ -1854,7 +1854,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "02b198ed",
+   "id": "e663049c",
    "metadata": {
     "editable": true
    },
@@ -1869,7 +1869,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4cef197d",
+   "id": "e2b36261",
    "metadata": {
     "editable": true
    },
@@ -1881,7 +1881,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23b34528",
+   "id": "69fa292f",
    "metadata": {
     "editable": true
    },
@@ -1891,7 +1891,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2847956",
+   "id": "23b3dece",
    "metadata": {
     "editable": true
    },
@@ -1907,7 +1907,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "b8dacc33",
+   "id": "e1630ab8",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1924,7 +1924,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd89705f",
+   "id": "c2d3b936",
    "metadata": {
     "editable": true
    },
@@ -1937,7 +1937,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "d35541fd",
+   "id": "355c6a66",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1984,7 +1984,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36014ec9",
+   "id": "ab553d39",
    "metadata": {
     "editable": true
    },
@@ -1998,7 +1998,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16fb5f8f",
+   "id": "f439180e",
    "metadata": {
     "editable": true
    },
@@ -2010,7 +2010,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1ec698e",
+   "id": "7ba7386d",
    "metadata": {
     "editable": true
    },
@@ -2022,7 +2022,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "787f58f5",
+   "id": "7e0a1440",
    "metadata": {
     "editable": true
    },
@@ -2034,7 +2034,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e23435fd",
+   "id": "2e7611f3",
    "metadata": {
     "editable": true
    },
@@ -2044,7 +2044,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ccaad283",
+   "id": "414e53ca",
    "metadata": {
     "editable": true
    },
@@ -2056,7 +2056,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be8092da",
+   "id": "31ed8899",
    "metadata": {
     "editable": true
    },
@@ -2066,7 +2066,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e055e08",
+   "id": "a66641fb",
    "metadata": {
     "editable": true
    },
@@ -2078,7 +2078,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff86c9bc",
+   "id": "28a50f9e",
    "metadata": {
     "editable": true
    },
@@ -2089,7 +2089,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4f2e747",
+   "id": "b8c5f507",
    "metadata": {
     "editable": true
    },
@@ -2101,7 +2101,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a9a9f87",
+   "id": "445744c8",
    "metadata": {
     "editable": true
    },
@@ -2113,7 +2113,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1232e11a",
+   "id": "ef90b7cb",
    "metadata": {
     "editable": true
    },
@@ -2123,7 +2123,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a807825b",
+   "id": "9d4c2ac7",
    "metadata": {
     "editable": true
    },
@@ -2135,7 +2135,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4fa9855c",
+   "id": "84e62cfc",
    "metadata": {
     "editable": true
    },
@@ -2147,7 +2147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcffefcf",
+   "id": "41c2ba4b",
    "metadata": {
     "editable": true
    },
@@ -2157,7 +2157,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c08ff3a",
+   "id": "beb557ef",
    "metadata": {
     "editable": true
    },
@@ -2169,7 +2169,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c2483a13",
+   "id": "b3fdffce",
    "metadata": {
     "editable": true
    },
@@ -2179,7 +2179,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a82a8c5",
+   "id": "8005292a",
    "metadata": {
     "editable": true
    },
@@ -2191,7 +2191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "743f7309",
+   "id": "92d9f94b",
    "metadata": {
     "editable": true
    },
@@ -2201,7 +2201,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6d7b31a",
+   "id": "17940c71",
    "metadata": {
     "editable": true
    },
@@ -2241,7 +2241,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "518d6bb4",
+   "id": "6ffb31dd",
    "metadata": {
     "editable": true
    },
@@ -2258,7 +2258,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "056673c8",
+   "id": "cc767251",
    "metadata": {
     "editable": true
    },
@@ -2281,7 +2281,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63daba59",
+   "id": "347029b1",
    "metadata": {
     "editable": true
    },
@@ -2298,7 +2298,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "89b74667",
+   "id": "a77dda49",
    "metadata": {
     "editable": true
    },
@@ -2317,7 +2317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "588dd662",
+   "id": "25a0d7d6",
    "metadata": {
     "editable": true
    },
@@ -2328,7 +2328,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb8348c6",
+   "id": "70462fa0",
    "metadata": {
     "editable": true
    },
@@ -2340,7 +2340,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62027bc1",
+   "id": "f8421c8e",
    "metadata": {
     "editable": true
    },
@@ -2358,7 +2358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c73c4b7",
+   "id": "d4ef09ac",
    "metadata": {
     "editable": true
    },
@@ -2374,7 +2374,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3a2d330",
+   "id": "fc6f8651",
    "metadata": {
     "editable": true
    },
@@ -2386,7 +2386,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "374b88cc",
+   "id": "ece72dfe",
    "metadata": {
     "editable": true
    },
@@ -2396,7 +2396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5aa42e6",
+   "id": "3f900d15",
    "metadata": {
     "editable": true
    },
@@ -2409,7 +2409,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c01a816",
+   "id": "3cb45c74",
    "metadata": {
     "editable": true
    },
@@ -2421,7 +2421,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f556eddc",
+   "id": "81b8790f",
    "metadata": {
     "editable": true
    },
@@ -2431,7 +2431,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcf14a16",
+   "id": "9d42c98f",
    "metadata": {
     "editable": true
    },
@@ -2444,7 +2444,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08c37095",
+   "id": "ab036419",
    "metadata": {
     "editable": true
    },
@@ -2454,7 +2454,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6815fa1b",
+   "id": "bba11ff3",
    "metadata": {
     "editable": true
    },
@@ -2466,7 +2466,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "daf50946",
+   "id": "6518184d",
    "metadata": {
     "editable": true
    },
@@ -2479,7 +2479,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7a60cb3",
+   "id": "ba89e5b0",
    "metadata": {
     "editable": true
    },
@@ -2492,7 +2492,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38105bfd",
+   "id": "47325cf5",
    "metadata": {
     "editable": true
    },
@@ -2504,7 +2504,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d697464",
+   "id": "8d9036c1",
    "metadata": {
     "editable": true
    },
@@ -2516,7 +2516,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c298d7ba",
+   "id": "889f801b",
    "metadata": {
     "editable": true
    },
@@ -2526,7 +2526,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45265b59",
+   "id": "8a803d4a",
    "metadata": {
     "editable": true
    },
@@ -2539,7 +2539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab6ce408",
+   "id": "ec92b840",
    "metadata": {
     "editable": true
    },
@@ -2551,7 +2551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca0350a7",
+   "id": "6de4ce40",
    "metadata": {
     "editable": true
    },
@@ -2563,7 +2563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8146e6f",
+   "id": "22e97024",
    "metadata": {
     "editable": true
    },
@@ -2575,7 +2575,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05d97a86",
+   "id": "9cd0a124",
    "metadata": {
     "editable": true
    },
@@ -2587,7 +2587,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f84e7118",
+   "id": "29b31bed",
    "metadata": {
     "editable": true
    },
@@ -2601,7 +2601,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28be9ec4",
+   "id": "d1145ae7",
    "metadata": {
     "editable": true
    },
@@ -2613,7 +2613,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b9f5a5d8",
+   "id": "f1479849",
    "metadata": {
     "editable": true
    },
@@ -2623,7 +2623,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "86b43b21",
+   "id": "0c51f5eb",
    "metadata": {
     "editable": true
    },
@@ -2635,7 +2635,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58744172",
+   "id": "2cbb0f42",
    "metadata": {
     "editable": true
    },
@@ -2647,7 +2647,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd515e6f",
+   "id": "406c4098",
    "metadata": {
     "editable": true
    },
@@ -2659,7 +2659,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8c98bfe",
+   "id": "70966948",
    "metadata": {
     "editable": true
    },
@@ -2671,7 +2671,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08cc9626",
+   "id": "627f3d38",
    "metadata": {
     "editable": true
    },
@@ -2683,7 +2683,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "725df93e",
+   "id": "129105f7",
    "metadata": {
     "editable": true
    },
@@ -2706,7 +2706,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "8d0397cd",
+   "id": "bce32748",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2782,7 +2782,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbc56c2b",
+   "id": "62eccb26",
    "metadata": {
     "editable": true
    },
@@ -2794,7 +2794,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cfab477f",
+   "id": "675cc7de",
    "metadata": {
     "editable": true
    },
@@ -2809,7 +2809,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc176ed4",
+   "id": "ff36cd09",
    "metadata": {
     "editable": true
    },
@@ -2821,7 +2821,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9eef8e3",
+   "id": "7ae7a42a",
    "metadata": {
     "editable": true
    },
@@ -2831,7 +2831,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c33552ec",
+   "id": "607325f0",
    "metadata": {
     "editable": true
    },
@@ -2843,7 +2843,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9465d4f6",
+   "id": "cfb328b4",
    "metadata": {
     "editable": true
    },
@@ -2853,7 +2853,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cd89a35",
+   "id": "bc44d844",
    "metadata": {
     "editable": true
    },
@@ -2865,7 +2865,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "13a9f453",
+   "id": "17ddbfda",
    "metadata": {
     "editable": true
    },
@@ -2877,7 +2877,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6c909f72",
+   "id": "f5658751",
    "metadata": {
     "editable": true
    },
@@ -2892,7 +2892,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b32ee709",
+   "id": "2b01e674",
    "metadata": {
     "editable": true
    },
@@ -2903,7 +2903,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5d3f72c",
+   "id": "c18a65c6",
    "metadata": {
     "editable": true
    },
@@ -2923,7 +2923,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18f488f0",
+   "id": "04258de2",
    "metadata": {
     "editable": true
    },
@@ -2935,7 +2935,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "93618783",
+   "id": "e10d0aad",
    "metadata": {
     "editable": true
    },
@@ -2945,7 +2945,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "02f57528",
+   "id": "d198578b",
    "metadata": {
     "editable": true
    },
@@ -2957,7 +2957,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "762833f4",
+   "id": "2aec2fc1",
    "metadata": {
     "editable": true
    },
@@ -2986,7 +2986,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ab8ec4f",
+   "id": "81fed6f5",
    "metadata": {
     "editable": true
    },
@@ -3013,7 +3013,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e526d1f",
+   "id": "fe7d1d49",
    "metadata": {
     "editable": true
    },
@@ -3024,7 +3024,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "f5d258ce",
+   "id": "0b32041d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3064,7 +3064,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e4bf198",
+   "id": "db224b5b",
    "metadata": {
     "editable": true
    },
@@ -3081,7 +3081,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33a42ac4",
+   "id": "6b988f39",
    "metadata": {
     "editable": true
    },
@@ -3104,7 +3104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b5d1bbb",
+   "id": "1214012e",
    "metadata": {
     "editable": true
    },
@@ -3118,7 +3118,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1fee5f54",
+   "id": "c7a8cd85",
    "metadata": {
     "editable": true
    },
@@ -3137,7 +3137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "235f2975",
+   "id": "0f2a2211",
    "metadata": {
     "editable": true
    },
@@ -3147,7 +3147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fd7415b7",
+   "id": "e9863a0f",
    "metadata": {
     "editable": true
    },
@@ -3159,7 +3159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c265b5d",
+   "id": "d88c8316",
    "metadata": {
     "editable": true
    },
@@ -3173,7 +3173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "976c31a2",
+   "id": "643f1b6d",
    "metadata": {
     "editable": true
    },
@@ -3185,7 +3185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8dc8acd7",
+   "id": "0769ec85",
    "metadata": {
     "editable": true
    },
@@ -3195,7 +3195,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1dc8e8e",
+   "id": "f0d61e66",
    "metadata": {
     "editable": true
    },
@@ -3207,7 +3207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb688af0",
+   "id": "0d7c9d9e",
    "metadata": {
     "editable": true
    },
@@ -3224,7 +3224,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eeadd85e",
+   "id": "335fb5ed",
    "metadata": {
     "editable": true
    },
@@ -3234,7 +3234,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9375ad7",
+   "id": "1dbb3e05",
    "metadata": {
     "editable": true
    },
@@ -3250,7 +3250,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "025f1ca1",
+   "id": "4a535424",
    "metadata": {
     "editable": true
    },
@@ -3260,7 +3260,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d44951a1",
+   "id": "512418d2",
    "metadata": {
     "editable": true
    },
@@ -3276,7 +3276,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ecc9216b",
+   "id": "baa56321",
    "metadata": {
     "editable": true
    },
@@ -3286,7 +3286,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28e2ff44",
+   "id": "1fd5881c",
    "metadata": {
     "editable": true
    },
@@ -3302,7 +3302,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "935324af",
+   "id": "546a2bf3",
    "metadata": {
     "editable": true
    },
@@ -3312,7 +3312,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a15e7526",
+   "id": "4e356417",
    "metadata": {
     "editable": true
    },
@@ -3329,7 +3329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d3cef55",
+   "id": "1f3c787b",
    "metadata": {
     "editable": true
    },
@@ -3341,7 +3341,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0fab1783",
+   "id": "72018911",
    "metadata": {
     "editable": true
    },
@@ -3353,7 +3353,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9a8450e",
+   "id": "7d741e98",
    "metadata": {
     "editable": true
    },
@@ -3365,7 +3365,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "485d1023",
+   "id": "f2e4a67f",
    "metadata": {
     "editable": true
    },
@@ -3375,7 +3375,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a2da5dbe",
+   "id": "302c8edf",
    "metadata": {
     "editable": true
    },
@@ -3387,7 +3387,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "13959099",
+   "id": "def3ec8a",
    "metadata": {
     "editable": true
    },
@@ -3399,7 +3399,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23f0b903",
+   "id": "37150ee7",
    "metadata": {
     "editable": true
    },
@@ -3411,7 +3411,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c344e77",
+   "id": "e937a396",
    "metadata": {
     "editable": true
    },
@@ -3421,7 +3421,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8064053",
+   "id": "07e76c7b",
    "metadata": {
     "editable": true
    },
@@ -3433,7 +3433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "714ab01f",
+   "id": "99f80e22",
    "metadata": {
     "editable": true
    },
@@ -3443,35 +3443,36 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3ff6988",
+   "id": "7a917bf2",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_i\\boldsymbol{u}^T_i\\boldsymbol{y},\n",
+    "\\tilde{y}_{\\mathrm{OLS}}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_i\\boldsymbol{u}^T_i\\boldsymbol{y},\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5c204f79",
+   "id": "c11ae5fe",
    "metadata": {
     "editable": true
    },
    "source": [
+    "which is not the same as $\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}$, which due to the orthogonality of $\\boldsymbol{U}$ would have given us that the model equals the output.\n",
+    "\n",
     "It means that the ordinary least square model (with the optimal\n",
     "parameters) $\\boldsymbol{\\tilde{y}}$, corresponds to an orthogonal\n",
     "transformation of the output (or target) vector $\\boldsymbol{y}$ by the\n",
     "vectors of the matrix $\\boldsymbol{U}$. **Note that the summation ends at**\n",
     "$p-1$, that is $\\boldsymbol{\\tilde{y}}\\ne \\boldsymbol{y}$. We can thus not use the\n",
-    "orthogonality relation for the matrix $\\boldsymbol{U}$. This can already be\n",
-    "when we multiply the matrices $\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T$."
+    "orthogonality relation for the matrix $\\boldsymbol{U}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "78c51f10",
+   "id": "f300aa1b",
    "metadata": {
     "editable": true
    },
@@ -3483,7 +3484,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c432ed4",
+   "id": "8bd1e2a6",
    "metadata": {
     "editable": true
    },
@@ -3495,7 +3496,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68a7b505",
+   "id": "62502292",
    "metadata": {
     "editable": true
    },
@@ -3505,7 +3506,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14268cd5",
+   "id": "efca6f6c",
    "metadata": {
     "editable": true
    },
@@ -3517,7 +3518,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3207844",
+   "id": "e2cbd6f5",
    "metadata": {
     "editable": true
    },
@@ -3528,7 +3529,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c7f5556",
+   "id": "5cc9aea6",
    "metadata": {
     "editable": true
    },
@@ -3540,7 +3541,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01bd8826",
+   "id": "61ad8f4c",
    "metadata": {
     "editable": true
    },
@@ -3550,7 +3551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb083248",
+   "id": "b1cc9449",
    "metadata": {
     "editable": true
    },
@@ -3562,7 +3563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "66bd1ec9",
+   "id": "a9b28652",
    "metadata": {
     "editable": true
    },
@@ -3572,7 +3573,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b92a06bb",
+   "id": "f26b69cc",
    "metadata": {
     "editable": true
    },
@@ -3584,7 +3585,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dad0b409",
+   "id": "53acde0e",
    "metadata": {
     "editable": true
    },
@@ -3595,7 +3596,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75d85fa8",
+   "id": "512b9f17",
    "metadata": {
     "editable": true
    },
@@ -3607,7 +3608,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0918773",
+   "id": "a1c49f5f",
    "metadata": {
     "editable": true
    },
@@ -3625,7 +3626,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65592b3b",
+   "id": "db70d623",
    "metadata": {
     "editable": true
    },
@@ -3641,7 +3642,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "442404b8",
+   "id": "95b18b06",
    "metadata": {
     "editable": true
    },
@@ -3653,7 +3654,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50eca816",
+   "id": "db07fa1e",
    "metadata": {
     "editable": true
    },
@@ -3665,7 +3666,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a27e487e",
+   "id": "9856cea3",
    "metadata": {
     "editable": true
    },
@@ -3677,7 +3678,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49c74d48",
+   "id": "7f6cba4c",
    "metadata": {
     "editable": true
    },
@@ -3690,7 +3691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "214feab7",
+   "id": "581565a5",
    "metadata": {
     "editable": true
    },
@@ -3706,7 +3707,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e61c0669",
+   "id": "22b63d08",
    "metadata": {
     "editable": true
    },
@@ -3720,7 +3721,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9f3db006",
+   "id": "cd6032aa",
    "metadata": {
     "editable": true
    },
@@ -3730,7 +3731,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6dfeb8ca",
+   "id": "25b7936a",
    "metadata": {
     "editable": true
    },
@@ -3742,7 +3743,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da47505d",
+   "id": "9c4ad4d2",
    "metadata": {
     "editable": true
    },
@@ -3752,7 +3753,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87c1a756",
+   "id": "75bcfcea",
    "metadata": {
     "editable": true
    },
@@ -3764,7 +3765,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5028dae1",
+   "id": "95c9cc40",
    "metadata": {
     "editable": true
    },
@@ -3774,7 +3775,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98da161b",
+   "id": "33c19ed1",
    "metadata": {
     "editable": true
    },
@@ -3788,7 +3789,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69065ef4",
+   "id": "c28b0a97",
    "metadata": {
     "editable": true
    },
@@ -3805,7 +3806,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3455143e",
+   "id": "d4ece056",
    "metadata": {
     "editable": true
    },
@@ -3821,7 +3822,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e322fdc8",
+   "id": "22360ee3",
    "metadata": {
     "editable": true
    },
@@ -3833,7 +3834,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f50b583d",
+   "id": "77e8998d",
    "metadata": {
     "editable": true
    },
@@ -3846,7 +3847,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b12b62dc",
+   "id": "8ef4225d",
    "metadata": {
     "editable": true
    },
@@ -3860,7 +3861,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40355c87",
+   "id": "627eac2b",
    "metadata": {
     "editable": true
    },
@@ -3870,7 +3871,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee70666b",
+   "id": "f7ac0db1",
    "metadata": {
     "editable": true
    },
@@ -3883,7 +3884,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc6d0cc7",
+   "id": "e93eae5d",
    "metadata": {
     "editable": true
    },
@@ -3902,7 +3903,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6b6f792",
+   "id": "58364673",
    "metadata": {
     "editable": true
    },
@@ -3914,7 +3915,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39c76bf5",
+   "id": "30541096",
    "metadata": {
     "editable": true
    },
@@ -3926,7 +3927,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2d754e5",
+   "id": "101bb217",
    "metadata": {
     "editable": true
    },
@@ -3936,7 +3937,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77a984ab",
+   "id": "ba8e52b1",
    "metadata": {
     "editable": true
    },
@@ -3948,7 +3949,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33060c1a",
+   "id": "67d4335e",
    "metadata": {
     "editable": true
    },
@@ -3961,7 +3962,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ed1e8279",
+   "id": "06416768",
    "metadata": {
     "editable": true
    },
@@ -3980,7 +3981,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22b40263",
+   "id": "dd2f405a",
    "metadata": {
     "editable": true
    },
@@ -3990,7 +3991,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b02469c",
+   "id": "40ded798",
    "metadata": {
     "editable": true
    },
@@ -4009,7 +4010,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0660e456",
+   "id": "d3044a01",
    "metadata": {
     "editable": true
    },
@@ -4027,7 +4028,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a40e5c0",
+   "id": "d612ad97",
    "metadata": {
     "editable": true
    },
@@ -4041,7 +4042,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82d7e99d",
+   "id": "52f27c53",
    "metadata": {
     "editable": true
    },
@@ -4056,7 +4057,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "6f4b429b",
+   "id": "ca5ce77c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4077,7 +4078,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a38f8430",
+   "id": "1c02019d",
    "metadata": {
     "editable": true
    },
@@ -4094,7 +4095,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "87d44fdf",
+   "id": "58381fbe",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4126,7 +4127,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f08f4dc",
+   "id": "a647044e",
    "metadata": {
     "editable": true
    },
@@ -4140,7 +4141,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a25b356f",
+   "id": "d7bea0a6",
    "metadata": {
     "editable": true
    },
@@ -4153,7 +4154,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "928ae649",
+   "id": "81d407da",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4178,7 +4179,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cab70377",
+   "id": "7998701a",
    "metadata": {
     "editable": true
    },
@@ -4190,7 +4191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22ac4a6d",
+   "id": "e4f65917",
    "metadata": {
     "editable": true
    },
@@ -4202,7 +4203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd0697a9",
+   "id": "73ecb476",
    "metadata": {
     "editable": true
    },
@@ -4212,7 +4213,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5043405",
+   "id": "f4f10483",
    "metadata": {
     "editable": true
    },
@@ -4229,7 +4230,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a4edab6",
+   "id": "9e173ba2",
    "metadata": {
     "editable": true
    },
@@ -4239,7 +4240,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1b67496",
+   "id": "6b6f3d02",
    "metadata": {
     "editable": true
    },
@@ -4254,7 +4255,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47a041cb",
+   "id": "69a2c9b4",
    "metadata": {
     "editable": true
    },
@@ -4264,7 +4265,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "575264b7",
+   "id": "41dedd73",
    "metadata": {
     "editable": true
    },
@@ -4278,7 +4279,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b049c58",
+   "id": "a7b2bb8c",
    "metadata": {
     "editable": true
    },
@@ -4290,7 +4291,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9780789f",
+   "id": "dba35fc4",
    "metadata": {
     "editable": true
    },
@@ -4302,7 +4303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da396c4a",
+   "id": "0e30a645",
    "metadata": {
     "editable": true
    },
@@ -4314,7 +4315,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87a74417",
+   "id": "6fa482d3",
    "metadata": {
     "editable": true
    },
@@ -4324,7 +4325,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5ca565a",
+   "id": "ae9f30ae",
    "metadata": {
     "editable": true
    },
@@ -4336,7 +4337,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "10944fc5",
+   "id": "67907a60",
    "metadata": {
     "editable": true
    },
@@ -4346,7 +4347,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b985955",
+   "id": "3a21fe71",
    "metadata": {
     "editable": true
    },
@@ -4363,7 +4364,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b748051",
+   "id": "3b91b5d8",
    "metadata": {
     "editable": true
    },
@@ -4373,7 +4374,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40c1c1eb",
+   "id": "86de4409",
    "metadata": {
     "editable": true
    },
@@ -4385,7 +4386,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e44c9e87",
+   "id": "d0c0608f",
    "metadata": {
     "editable": true
    },
@@ -4395,7 +4396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28abe46c",
+   "id": "98f544a6",
    "metadata": {
     "editable": true
    },
@@ -4407,7 +4408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "178bc776",
+   "id": "24587410",
    "metadata": {
     "editable": true
    },
@@ -4421,7 +4422,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f0ead95",
+   "id": "61fb4275",
    "metadata": {
     "editable": true
    },
@@ -4433,7 +4434,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fcce3bb5",
+   "id": "6d2404eb",
    "metadata": {
     "editable": true
    },
@@ -4455,7 +4456,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f9a7281",
+   "id": "22615b7e",
    "metadata": {
     "editable": true
    },
@@ -4467,7 +4468,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3ea695c",
+   "id": "bee48c87",
    "metadata": {
     "editable": true
    },
@@ -4482,7 +4483,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "edfff9e0",
+   "id": "7f12f53a",
    "metadata": {
     "editable": true
    },
@@ -4494,7 +4495,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3c83244",
+   "id": "a6acb75c",
    "metadata": {
     "editable": true
    },
@@ -4506,7 +4507,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00df5ee5",
+   "id": "131e9d9c",
    "metadata": {
     "editable": true
    },
@@ -4516,7 +4517,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4661cbd7",
+   "id": "85812d77",
    "metadata": {
     "editable": true
    },
@@ -4528,7 +4529,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07b95265",
+   "id": "35007c74",
    "metadata": {
     "editable": true
    },
@@ -4538,7 +4539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8c9aeba4",
+   "id": "0100935a",
    "metadata": {
     "editable": true
    },
@@ -4550,7 +4551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "03690a72",
+   "id": "7b6ff86e",
    "metadata": {
     "editable": true
    },
@@ -4560,7 +4561,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "478e2a9d",
+   "id": "1f452dfb",
    "metadata": {
     "editable": true
    },
@@ -4572,7 +4573,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e997196a",
+   "id": "05600fbd",
    "metadata": {
     "editable": true
    },
@@ -4589,7 +4590,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "770e587e",
+   "id": "a2af3e04",
    "metadata": {
     "editable": true
    },
@@ -4602,7 +4603,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5cb701c2",
+   "id": "0342c08c",
    "metadata": {
     "editable": true
    },
@@ -4614,7 +4615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dee9d948",
+   "id": "bdd5faeb",
    "metadata": {
     "editable": true
    },
@@ -4624,7 +4625,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "121cd014",
+   "id": "35873dc6",
    "metadata": {
     "editable": true
    },
@@ -4637,7 +4638,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2ee745b4",
+   "id": "6ff6ab78",
    "metadata": {
     "editable": true
    },
@@ -4647,7 +4648,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94a15fb9",
+   "id": "77286b5f",
    "metadata": {
     "editable": true
    },
@@ -4659,7 +4660,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6341fe06",
+   "id": "0ade2616",
    "metadata": {
     "editable": true
    },
@@ -4672,7 +4673,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5bef6925",
+   "id": "da22a168",
    "metadata": {
     "editable": true
    },
@@ -4685,7 +4686,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4539e82b",
+   "id": "caa18da2",
    "metadata": {
     "editable": true
    },
@@ -4697,7 +4698,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f496d16",
+   "id": "f31c8084",
    "metadata": {
     "editable": true
    },
@@ -4709,7 +4710,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee78adfa",
+   "id": "53dc71a2",
    "metadata": {
     "editable": true
    },
@@ -4719,7 +4720,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47a0c860",
+   "id": "753442d5",
    "metadata": {
     "editable": true
    },
@@ -4732,7 +4733,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b452b5d",
+   "id": "e0b2f58a",
    "metadata": {
     "editable": true
    },
@@ -4744,7 +4745,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3331a79",
+   "id": "e4af8e7e",
    "metadata": {
     "editable": true
    },
@@ -4756,7 +4757,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9befd0e3",
+   "id": "6e353a3a",
    "metadata": {
     "editable": true
    },
@@ -4773,7 +4774,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d8f2ba3",
+   "id": "66a4056b",
    "metadata": {
     "editable": true
    },
@@ -4785,7 +4786,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da712e9d",
+   "id": "ea5b3d9f",
    "metadata": {
     "editable": true
    },
@@ -4795,7 +4796,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d91cd5f7",
+   "id": "db50585a",
    "metadata": {
     "editable": true
    },
@@ -4807,7 +4808,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18940f72",
+   "id": "afd3cd57",
    "metadata": {
     "editable": true
    },
@@ -4817,7 +4818,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51fe3527",
+   "id": "6606774b",
    "metadata": {
     "editable": true
    },
@@ -4829,7 +4830,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e85d1eb",
+   "id": "bcfd3adb",
    "metadata": {
     "editable": true
    },
@@ -4841,7 +4842,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96c47485",
+   "id": "46d7227b",
    "metadata": {
     "editable": true
    },
@@ -4857,7 +4858,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1adcbbc",
+   "id": "a214b881",
    "metadata": {
     "editable": true
    },
@@ -4869,7 +4870,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9693074c",
+   "id": "727c87de",
    "metadata": {
     "editable": true
    },
@@ -4881,7 +4882,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46b05531",
+   "id": "5083858e",
    "metadata": {
     "editable": true
    },
@@ -4891,7 +4892,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e4ce02b",
+   "id": "973ad2fa",
    "metadata": {
     "editable": true
    },
@@ -4903,7 +4904,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbd3f781",
+   "id": "4fbd0028",
    "metadata": {
     "editable": true
    },
@@ -4913,7 +4914,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "779e1ac5",
+   "id": "bee26901",
    "metadata": {
     "editable": true
    },
@@ -4925,7 +4926,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ef53f2a5",
+   "id": "da771d96",
    "metadata": {
     "editable": true
    },
@@ -4942,7 +4943,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57adfaff",
+   "id": "8ecb8a62",
    "metadata": {
     "editable": true
    },
@@ -4954,7 +4955,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8f94cba",
+   "id": "5cf08e3d",
    "metadata": {
     "editable": true
    },
@@ -4966,7 +4967,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d60431ff",
+   "id": "d984ce12",
    "metadata": {
     "editable": true
    },
@@ -4976,7 +4977,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f78d1dfd",
+   "id": "837a69b7",
    "metadata": {
     "editable": true
    },
@@ -4988,7 +4989,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "445800de",
+   "id": "21dde5ad",
    "metadata": {
     "editable": true
    },
@@ -4998,7 +4999,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c54c49c",
+   "id": "4d49c112",
    "metadata": {
     "editable": true
    },
@@ -5010,7 +5011,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11366dc1",
+   "id": "5b4eabcf",
    "metadata": {
     "editable": true
    },
@@ -5020,7 +5021,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d68d3ac1",
+   "id": "28dcb3c8",
    "metadata": {
     "editable": true
    },
@@ -5032,7 +5033,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63fedbd6",
+   "id": "f315a306",
    "metadata": {
     "editable": true
    },
@@ -5042,7 +5043,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "470b20a8",
+   "id": "7b4f990c",
    "metadata": {
     "editable": true
    },
@@ -5054,7 +5055,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3277c65",
+   "id": "197daa81",
    "metadata": {
     "editable": true
    },