library('splines')
library('boot')
library('rpart')
set.seed(42)
col1 <- c("#882255","#332288", "#44AA99", "#CC6677", "#007733")
dat <- read.csv("nonlinear-bagging.csv")
## linear predictor (b-splines)
fit_bs <- function(dat, idx=1:nrow(dat),
knots=c(0.638, 1.020, 1.948, 2.498),
bknots = c(0.01, 2.99)) {
pxv <- seq(min(dat$x),max(dat$x),length.out=100)
dat <- dat[idx,]
fit <- lm(y ~ bs(x, knots=knots, Boundary.knots=bknots), data=dat)
#fit <- lm(y ~ x, data=dat)
pre <- suppressWarnings(predict(fit, data.frame(x=pxv)))
attr(pre, 'x') <- pxv
return(pre)
}
boo_bs <- boot(dat, fit_bs, R=1000)
## tree-based (nonlinear) predictor
fit_tr <- function(dat, idx=1:nrow(dat)) {
pxv <- seq(min(dat$x),max(dat$x),length.out=100)
dat <- dat[idx,]
fit <- rpart(y ~ x, method='anova', data=dat,
control=rpart.control(minsplit=5))
pre <- predict(fit, data.frame(x=pxv))
attr(pre, 'x') <- pxv
return(pre)
}
boo_tr <- boot(dat, fit_tr, R=1000)
plot(dat)
pre_tr <- fit_tr(dat)
lines(attr(pre_tr, 'x'), pre_tr, lwd=2, col=col1[3])
lines(attr(pre_tr, 'x'), colMeans(boo_tr$t), lwd=2, col=col1[4])
legend("topleft", c("Tree original",
"Tree bagged (B=2000)"),
lwd=2, col=col1[3:4], bty="n")
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)
plot(dat)
pre_bs <- fit_bs(dat)
lines(attr(pre_bs, 'x'), pre_bs, lwd=2, col=col1[1])
lines(attr(pre_bs, 'x'), colMeans(boo_bs$t), lwd=2, col =col1[2])
legend("topleft", c("Splines original",
"Splines bagged (B=2000)"),
lwd=2, col=col1[1:2], bty="n")
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABUAAAAPACAMAAADDuCPrAAAA21BMVEUAAAAAADoAAGYAOjoAOmYAOpAAZmYAZpAAZrYzIog6AAA6OgA6Ojo6OmY6OpA6ZmY6ZpA6ZrY6kJA6kNtmAABmOgBmOjpmZjpmZmZmZpBmkJBmkLZmkNtmtttmtv+IIlWQOgCQOjqQZgCQZjqQZmaQkLaQtraQttuQtv+Q2/+2ZgC2Zjq2kDq2kGa2kLa2tpC2tra2ttu225C227a229u22/+2///bkDrbkGbbtmbbtpDbtrbb25Db27bb29vb2//b/7bb////tmb/25D/27b/29v//7b//9v///+AndHNAAAACXBIWXMAAB2HAAAdhwGP5fFlAAAgAElEQVR4nO3dC3sbVYKgYRnCbpKBbRgShl4GnF1mmmmzmaFnATfpDT25gPX/f9GqdK1SXVR1VJdzqt73ebqxZVk6LtlfTl21WgMQZDX1AABSJaAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgUNwBXQH0pv9E9f6IPZp6aQPz0nuj+n7APg3wDwawWAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBSYhaEuMNf8nL0/Yt8P2CcBhZka7hKdjU/a+yP2/YB9ElCYp2M4Ry2ogALpy2VTQAcjoDBL+T/tEf/MUw3ow99++Mvfu3+bgMIsCehFv/16SOar59ttxTefven4EAIKsySgl/z+bPXBz9kHD98fd7fdfNPtMQQUZklALzkG9C4r5x++/PKLLKHdCiqgMEsCeskhoG832dytu79/sdo3tS0BhVkS0EsOAd1MQB/vb3rYFPTzLo8hoDBLDmO6ZB/QLJrH9fbNbPSjLjuSBBTmyYH0F+wDetwUmrutbigVhhodMCmncjZLOqAPr754unn2D//4U+09Xhwm2N0263YcR83Dt3/agQcIoVxMpNFpG+jNnw+3vXva7a95qoD+8vRY8I9qEiqgkJzEApqV821ux1Ei20Df5ufANfkRUEhOWgHNVoL/54//+zgFzW5KYC98NsxH32Wh//Xl07rkpxKmVMYJI0guoLlZ3MNfn6ZxHOh9LprvntYc/J9KmFIZJ4wgoYBu/nZfv/zi6SmgWVFPm0NbmSag+a22WU0fV90plTClMk4YQVIB3dpW9BDQR7U7tatFENDNFPTx4T/vv8iuiLK7REpxG+j2Pw8v/2Hz9U+PP+PDLx9v/vH45Ls3hc8//Kp8WaqHV1/k73m3mQG/2jzWJz+d8vd+e4+fNgsxmx03Pe1vL7Onufnku/w4gRQDevLw7x3zOeEqfGlLbRbQd7vp9K6u5YD+52HX/TfHb9nZ/7Nx/Lz06O+fF++5Cegvu2c65u9+f49/LAX0/GkP99xvhxBQOEo5oAEu/Li3oZqfNSvdZ38v3fbfX+zDtC1oKaAnu8KeennagnFQ3Kqa+8rh8isfbr/58TF/+eMCigE9f9r73C2frwUUcgT0JDifFwu6jdDNH/6Ui+g2h9kEMTtE9PG6MqA3X7/ZXbsvC9duV3623r7/hs2DPvpxvbukSnHH/t3mW7/afOvL/T2316/aHX+6f/jtg+2fvBTQ0tNu4//6eeGegIDmDRfQ04H0x82S747HM20+yuZ65YDuO7Xf63Q65HXTtOwb7g4Tz/Ok7R8w99Hd8Xv3973PPfl5QEtP+/j4sCMcqAopEdCTAQO6fnh12CyZzQ3X+cplefu8KqD7LZube2aJy+2J2p1KcF93VlNuP//uoQ//WR8f/i6/hfMsoMWnPTldzEVAYUdAx/P65RenfTG5Pu0meaWAHnq5u+d+b/nhlsf7zZg3f/jX0mH5pzoedvmfbtk9fO4SAvtx1D3twW9/+5f9QbcCCkcCOq733+63Le7Ttj5+eDmgebs56WFOW9hBlfvW8uz1GNBDHEuHMZUCur8OymGXlIDCkYCObb8psRjQTaouBDS3D/645/xl5XFM+cLt83ge0Nzs8mJA808soFAgoMO7Kx5mtPu06wy0tEly69W35YL2OwPdX4Hgkz/+6b9sA4UzAjq8s5M37w8B7boNtLpbv/3Ht6vicUy5YO/3oVcEtO020Pvj0fh2IsE5AR1e8aKl+0blbtwF70JAC+9ksn+cwwOcxbVqL3wxoLkHK+2FLz3t4Ya3VuHhjIAOL8vV6aT9+9VhG+g+c8XjK5umgh/8dHyIz/PHJp0FtOo40GJAT8eBZmvo7QL6/pmAwhkBHcF2P8ynP745HA76+fG2n04nFl0K6PbaU19vPvjt+91Zltu3dz6cI/Q4/3z5M5G2nSwF9HAm0qvymUhnT3u3u+Nuh1XugH9AQMfxS2EP+uPspk2fPswfHXQxoIXT17dTz7vT58WkVZwLfxbQhnPhz562cDF9AYUCAR3Fu+enCP3z7panq8f7OD3a9uhiQNdvz45aOl3549HZVVHLV2M6D2j91ZjOn/b7w7i/epHfVgsI6Ghef7u7qObhxKHtsUtZVz/8enfD5YBu1qPPrv/5+tusqacLhB4drge6/7QioIfrge4Pp2p42u1DffjVm+LRAoCATiZ3HOikYhkHpEhAJzJtuE6Hit51fFs+4ERAJzJ5QG+y9ftsj74VcggloBOZNqD5E9xNQCGUgE5k4m2Pv1RehwToREAnMvXOm9+yt96sfEdPoC0BBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEdBwPr77Izj7/8I8/1d7jRV/v2TbwWaK5N5XPud8+5/3pGiUfN58lur849Ke55fE+uzz0TZdbNgur8E6lMDIBHcXp2h2rj2oSmnZA3z3djjoX0Owt8Oof5LRAPju/af+eJ61u2T8tTERAx1B4Z7aaP/mkA3qYChYCuqqfHuYXyOPSTd+0v+W+ajYMYxHQEWzfRHj7xkW/Ht9puKS/9xqaIKCHjt0fy7Z9A+e6uG0XyI/r3Tsy796E6fBGy9ktu+XQ5pbsJtfjYzoCOoL7XEqySxlXTsxSDujmGXc/033uh9vc7+bs3UIP3h7nndk7iz7ef+fuUbNbPm97S3ablXimI6AjuMuX5H5VnbeUA3p3uCUf0NwbL53LfWX/5p/ltwNtc8vaFJRpCegICgHd5237n+ythW8+2+2tLr2t8Qc/P2QXPc7thH745ePCuxjvPi9dFPn40Nl7Ee/99nL3rsqHNzo+vKvxqYalG86fbf3+22y0b8oB3TzhcT5YCOj2xy5sAF6dz0r3j5Z70H0n29yye0pTUCYjoCO4r3jjjKxy+3cm2qWgHND/fFrcYXJ8I6NHPxU/P3v00kPnd+6cpopb//jstPWyeMP5sx3u8dF/lQJ6n3+e/Cr89n6tAvo2Ny/fzU/b3LIfpykoUxHQvCehmp81a9Fn5Wnif3+Rb0opoOfNyb0R3HbOle1SOdsnfXzo//as8K35nePb2uSjVqrc9obzZzs9xn87D2huZljcibR78uaA7qv4NvevwP0hlxdvOXt2GJuAngTn82JBt/G5+cOfchHdBiqb3GWHNj5eVwb05us364fv99Hb7crP1qz333C/35P9/sXZ7u7SQ2ffug346/2e8cPu7O1hlfU35J+tdI/C8x3CVjiM6VHtSQMnhz1N+anrLpRtbtm6q91XBUMT0JPhAno6bvy4SfHd8XimzUdZAcoB3W/buz/O0U77TbJvOK7Fnu9+Kj30ad13c0N21/vcHbYflW4oPVvpHie5sLU+kH7v4e60Ez40oPcNx5vCsAT0ZMCA7g6L3GXlq3zbMnfbGJQDui/Efo9zbqJ17En1WU2lhz7Z1DB79Lvcgej7By/dUHy2wl6bs4Dm7nt2IP3jS0vlLreBIDSgb701M5MR0PG8fvlFYRvjIUO7CWIpoMVDdvKb+nY78t/utgv8a8VplWcPvffb3/7l6TZY+4wWHrx0Q/HZSvc4yU+Ac9tAX3+7ulS27F+J/U95RUCnfoNolkxAx/X+kJXcn/3uw8sBzdtPG/dz2uIOqtJDH69lst8llMvj7sOqG4rPVrrHSXVAd59kX6jdifT++apy972AkgwBHdt+M2SxcpsiXQhobq/4IaAPL6uPYyo9dOGbN4+em0Pualh1Q/HZSvc4qQ1oVuFv6gOabRd+dPjG8L3wpRkxjEdAh3d2Rs7u064z0OpMvPq2oqClh97NJz/85I9/+q9n7WagpWcLmYFma+j1Ac02l352fJzw40DNQJmQgA7v7OTN+0NAu24DrT7j5rf/+HZV3K1Teuj74yFFvz9rvQ20+Gydt4GujwGt9n2x+uFnIgkoExLQ4e1X2vf2f/u5G3ezqQsBLdUo162z3J0/dO6x3m5X4XOPtdul3nTD8dnO9tOfFPfCF1bha4/QvD87oj74XHh74ZmSgA4vi8/poPL9rpV3Tw/z0n3vLgR0+32nkyo/zx+iVA7o/qHfbjN1eqz3z1bF40CzlfvCcaC5G4rPVrrHSfE40NJOpCpvTw9/unPQ1ZgcB8qUBHQE210yn/745nA46OfH2346nepzKaBZuLJTk9a/fb86HB5/Or/ocenp/r7byZR94W4X8N1Op/3K8PaWV+dnIhVuKDzb4RKex3sUnq/ioPb3DYcxVcxND49/dvXPC7es185EYkoCOoZfCrtRHmc3barzYe7IossBLeyM2Ybp7vT5+ZlIx3Pht18o7MYpXSGp+lz40rMdb/jH5nPh8+omoMW7lU6Z73BFeufCMykBHcW756dc7N7OJ9v1se/B7lieiwFdvz07aul0wZFHhSlY7mpM+y0H3x+e+6sXq+J7b9Rfjen82Q6no166GlPOo5p+Fq6UctwY+tfSOyC1ucUmUKYkoCN5/e3ugpyHE4e2+46zrn64P2P8ckAP72R5Om7+dfYelflLdp4eOjtK/XQ90FdfrHafHg8F2l/+87QLu3RD6dmyd8S8fD3Qgw8//bFuWZwdpn/4Qbu/K2fmzvVAmY6ATiSSg29Kwwga1910a9GuSM+UBHQikwb0dBj6fld+6YZuju+JND4XpGdKAjqRqQN6k725R7aLfduf0g0dTfbuwiagTEpAJzJpQPOnun9eeUNHm45NMwX1vvBMSkAnMu020F9qdrEH9jP7cSZZk3731DGgTElAJzLxTqTfsjf8zO9iL93Q0f0UP87DCychMSkBBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIHSDejD3374S+frSAgo0J90A1r7RulNBBToj4ACBEopoL/9mvd6E9AfN//tdPkgAQX6k1BAz96K7KDTNFRAgf4IKECghAK6vWr6zZcH//R0dfOHzX//2GVXvIAC/UkpoOv3L1arR4e3BG+xE6lqwjrc6IClSSqg6/VfN9POf959KKDAxBIL6Pr989Xqo+0k1GFMwMRSC+j64f+sVjdfrwUUmFxyAV2v320moZ++EVBgagkGdP3w/WYS+p2AAhNLMaC7A5r+8FRAgUmlGdDtAU0dj6HfElCgP4kGdHtAk4ACk0o2oOv3/9LtJKQtAQX6k25Agwgo0B8BBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIBObrU39TiArgR0aquVgkKiBHRix3AqKCRHQKeVy2Z0YwMuENBp5QcU3eCAZgI6LQGFhAnotAQUEiag0xJQSJiATktAIWECOi0BhYQJ6LQcxgQd3OZMPZaMgE7MgfTQ0m2FiYckoFNzKie0UZXPySsqoJPTT7ikoppPYkiogAKRy1Xz3MQFFVAgavX1LFR0krEJKBCxy/mcMqECCsSrTT2PDR1/eAIKxKqcz7M7TJ1QAQXiVMpnzf0KDR11hAIKxKllPjP5hI42voyAAhE6y+fF+09TUAEF4tMxn5lu9+6HgAKTqjoXr3s+t0YvqIACU6q4GkRgPtenWWjfg6wjoMCEKq5Hlu9n58cbN6ECCkwn38/dNDS/9TPkEUctqIAC0znv5+rKfGZGLKiAshSuGxij/euxfV2y//XQz82DjFZQAWUhXLk6SruXY/eqFKafV+VvtIIKKMvgvVPidAjo9v97mX5ujVVQAWURvHtfpPIBvb6fp5WMkQoqoCyC94+OVC6g108/85tpximogLIIAhqpw9bPnvqZ+2CUggooiyCgsTrsfz/1M/TlOdtMcztGQQWURRDQaB0P/9z37vzlaX3wxPlrPEZBBZRFENB4tevn5Vet9BqPUFABZREENGr5fhZfnQ6Hn5Vf4+ELKqAsgsOYYnbsZ2mi2eV1qwro0AUVUJbBgfQRq+1npzWHivsOXlABZSGcyhmthspdGdDBCyqgLIV+Rqqpcd0CWl7dvx24oOkG9PUPf/l752/y1wORaSxcp51/VZtpjgW9dph1T9n7I/b9gEW/vsn+/+Hl02wu8ei7jt8toBCX5hlit6MnqjbTDFvQtAL6/tusmn9er+8Oy+mzbg8goDC6po0nF9awOx5+VvVMgxY0qYC+2047Vzd/frv5/0++/DL79PNOjyCgMLam3XeXtlD2cPjZoJtBUwro7882S/Pjf9jMQZ9vIrq54eH71e6D1gQURtZ0ANnltPVw+NmQU9CUAnq/Wn3w034e+s32locXHaegAgrjappDtpka9nD42YAFTSigWS233dyE9KM3u9venj5sRUBhXA1bMdutWl9/+NntcAVNKKCbNfgPfs4+2ExBH5/fVj2UCkONDqhSH9BRrje3f6ahnivFgG4+eHx+W/VQBBQm1hDQsfo5YEHTCuhuj9HD//r4f+zX2zeT0YaAlgkojKs2oCP2c7iV+IQCmh38eb7H6H51nIy2IqAwrrqADnqCUMlQBU0poG9LBy29f2YvPEStJqDj9nMX0PWyA5rthl/9j9NO9+35nJ12wgsojKz6MKaR+znYFDSlgK5/f77Kb/LMDqzvdhy9gMLYKg+FH3MD6P4ZByloUgHN5pzFgD76qdsDCCiMreIYmPH7KaAlD//eMZ8CChOIoZ8DFTTlgAYQUJjcJP3MFbTHxxRQYFxX9POaE2KGmIIKKDCqHvoZTUEFFBjTdf08+6AbAb2SgMK0+uhn6F9y/1NQAQXGc83+o47v71Gh9/ORBBQYzzXzv34C2usUVECB0TTH68IeousDepqC9lRQAQXG0q6fdX+mXQJa80gCehUBhek0bwC9uI+9Q0DrWnzbc0EFFBhJu37W/p22D2h9i7cB7W8/koAC47i0Al/9cf7WlocxNdyx5ymogAKjuFCtFvPLtgfSNz1Uv1NQAQVGcX1A257KeSmg/U1BBRQYw6VmtdrC2e5U+MaH6nUKKqDACC7O+Xo4yrPVQ/U6BRVQYHiXT+EcK6C9TkEFFBje5Rnf1ZcKyT9U9cc7fU5BBRQYXJtcXXuxuopHqv6T73EKKqDA0NpN9667XPLZI519kHcK6NUFFVBgaC1j1Vc/L7T4tr8pqIACA5vgPeQaW9zfFFRAgWFN0M9m/U1BBRQY1DUXoR9Ib1NQAQUGFV8/+5uCCigwpAj72d8UVECBAW0jdTv1KM7tAnr9FFRAgQFFOQHNr8NfNTgBBYYTZz97m4IKKDCYOFfg171NQQUUGEqERzAd9DMFFVBgKPH2Mx/QK0YooMBAol2BXx/X4a+cggooMIyY+9nTFFRAgWFEvAK/7mkKKqDAIOKegPazG0lAgSHE3s9e1uEFFBhC3Cvw637W4QUUGED0E9BepqACCvRv18/e3qJjEPuAXjMFFVCgf9uA9vYmccO4vX4KKqBA7/YT0N0nURc0+6+AthTrCwmzUuhnvH93109BBRTo2e4aIrk/tlj/8K6eggoo0LOzCWi8f3gC2k2sryPMyGEP/OmWWP/wrl6HF1CgV/sjQFMI6NVTUAEFerWfziUT0GumoAJKG3Efz0dMDqcgJRHQa6egAkoLq8iPiCYex1M4c78tEf/e5AMaUFAB5bLjn4KCcsmpREn82txeNwUVUC5KYypBFPLXEElixeW6KaiAclEaG7OIQfEaTAn08xjQsCmogHKRgNJW9BcBLbluHV5AuUhAaSmBi4CWXLUOL6BcJKC0lGA/r1uHF1AuElDaSXECWlyH71pQAeUiAaWVJPt53RRUQLnIYUy0kt4epC0Bbc3ff5AkjohmaolOQK9ahxdQWkjiiGimlWo/r5qCCiht6CeXCGgvov4bUwAYRrr9vGYdXkCBHqTbz2umoAIKXC/hCaiAtiagMISk+3nFOryAAldLO6DhU1ABBa6VeD/DL8kkoMC1Eu9n+CWZBBS4UuoT0PB1eAEFrpN+P4PX4QUUuM4MAhq6Dp9YQB9efvHxH/71zfHz35+tPvi5w/cLKPRtDv0MXYdPK6B/fbo9Ifvmq0NCBRSmtu3nHAIaMAVNKqD3x2sCfbQvqIDCxGYxAQ2dgqYU0Heb+eej73799fvsv7tsCihMayb9XEBA7w8zz/fPDwUVUJjWnALafR0+oYA+vFitvjl9uG2pgMKk5tLPwCloQgHNxzIr6OP1pYCuKgw1OlikWexB2lpSQLNPVp8LKExrPhPQsHX4VAOa7VG6+bNVeJjSjPoZNgVNKKC5baCZt6vVBz8JKExIQNMJaLYX/nHx0w/+r4DCZObUz9Vquw6fFaLDOnxKAc2OA/3076fP77YbNQUUJjKfPUjbHSbbgB4K2vbbeh9I3w94cn/Wy+8FFKYzownodv/yLqCr2QZ0/cvTYi83nwsoTGNu/dxtBI0voA9/6e3BH1798U3h8++fCihMYlYBzf7/Nl/QLt/Y61BKt/z+bPXJj30/TRgBhZ7MqJ+HMBwD2vUb+xxK6ZbsoPfV6tMYGiqg0JMZ7UGKO6DrV893l/H89Ke+n6wrAYV+zGkCmg/obXwBza4k/w/7SyH/verLoxFQ6MWs+nkMQ6wBXZ8a+uFXb2ruMQIBhV4IaOEbexxK/Zd+e7l7S45H303VUAGFPsyrn+tVbh2+UyPGPg5039CbiaahAgp9mFc/jwU9XpGp/ff1PpKmL7769nBZuZs/9/3EbQgo9GBmE9D18dqXMQf01Rf7FfjX305VUAGF682vn4eCRhvQ/dxzv+5+uKL82AQUrtftrX9T0nUdfpyAvt6vuZ8OBH33tNtJ7D0RULjaHCegBxEGdHcm0mbVvXibgEKSZtzPWAN6vtt9c9tHE+yIF1C41pwnoHEGtOIczl/7ft5WBBSuNOt+dt0Imtb1QK8moHCl+e5B2hLQBgIK15n3BFRAGwkoXGfm/RTQJgIK4Var1cxX4LtuBBVQoJ1DP7tdbyM1AlpPQCFUdsGNbUBXs/47EtB6s37hYUjHfnZ814vUdFqHF1CgjcP7/d6uZ/6HJKC1Zv26w5AOE9D9x/MloLVm/brDkA57kHYfTz2aAQlorVm/7jCk/CFMs/5D6rIRVECBNnIT0Jn/IQlonXm/7jCgVe4cpHn/IQlonXm/7jCgxUxAu6zDCyjQQqGfs/472r0zUrufUUCBFvYnce5MPZghrQ4BbfNTCihw2ZL6udsI2urnFFDgsrlfxe5gm83dNlABLRHQAKsFTDu4YO6XUT7a/Z7vdiK1+J0XUC5YrRSUpfSzkAgBPScCnR3DqaALtpgJqIA20oCuctm08BZrOf0U0EYa0FXH3ydmSUDb3L2nAfT9gH2SgK4ElCX1U0AbSUBXAspuD9JiAtppm5WA0khAWdIEtOteUwGlkYCyqH52PG5PQGkkoIu3rAnoutuZIwJKI4cxLd7S+tmJgNLMgfQLt7gJaCcCygVO5Vw0/WwkoFyin0smoI0EFKiln80EFKi1pGPoQwgoUMcE9AIBBQ7Ot3fr5wUCCuydH3FhAnqJgAI758f86udFAgpslc46E9CLBBTYOr/ugX5eJqDReHJyezT1oFiQqoD6FWwmoNN6csGtljKWs4CagLYgoJO51E4VZVzFgOpnGwI6hfbtrMzo1MNnngS0OwEdXW0hL99DRRlQIaD62YqAjqqmiOU77geqooyncBiTfrYioONp2c6t/EBVlHHkDqQ3AW1HQEdSWb/6u5ffiuhCRf2uc73jmZz62ZKAjqGqes3fUfNebs0VHWj0LEchoFMPJgUCOrxOU8+9pjfDbFyl73nsLJIJaFsCOrDAxl18N2ENZTj62ZaADqpiRbvdN7Z7N+GG9fmrh85ymYC2JqADuiZr7d9NuH6baOHpvDUcLelnewI6mCtnhV3eTfiw1b+iobenuygorWx/haYeRCIEdCDHlq1DV6o79bPwlBUT0fYT2mGpePxMQDsQ0EFcn88uao9zyk1E22xSHZ55cAL0swMBHUA5n8P+PlZcBKJhdX7CeMUyD6aBFfguBLR/x3yOMv1cVxzzVNqvlM/odO1qd2gBk7IC34mA9m7sfNYcNFoR0anPn794cCvTMwHtRED7dsjnerxU1YWpqqFTVlRA42cC2o2A9uvJBP1sDlNEFRXQ+OlnNwLaq/PV92Gf7eDytsXSnqWzio4zUAGNnhX4jhIK6O/PVlU++LnL4Ib9s52mny32bq/q9i2NWh0iYDAAABfDSURBVFEBjZ4JaEcC2qOzfI74i3jx+MpTYidcpRfQ2JmAdpVQQNfvn3cMaNXdBxvdZNPPrYs/XnEJVFd06JQ6jCl2JqBdpRTQ9cOL1erzDvcfNaCT9rOF8gJoqOhAK/cXNzUwKRPQzpIK6Lag31zzAMP93Z71c6in6d2liuZa2sOzjbEmQKgnJqCdpRXQbDtop22e54b6wz3mM7V+7rXLaA/zE/2MmAlod4kFdP2220r8uYH+clPvZ84YFSVKJqABUgvoZiX+minoIAHNZSX5fubI6MLoZ4DUArp+9+WX/xb+3UMENJeTOfUzT0oXwCsZIrmAXmeAgC6gnzkqmqqLW59NQEMI6JXO87mEX0EVTc/F4x+8fEEE9DpL7Oeeiibk8hG4JqBBBPQqC+5njozG7vI5YF6yMAJ6jTQ3fw5xLObtrYZG7OJVCJ6YgIYR0Cuk3c/eX/rbyor2/CSEaBfQ0YYzIwIaLrl+FsN5oaBBld0uBw2NzqWAmoCGEtBgyfbzVNAOd+7gtpzRsAHTlzYBjf8XOEYCGirFfm7/f92moNdfN0lDI3IhoF6gYAIaKNF+bpfA5YA27LXtMDE9m4gGDJp+NAfUCnw4AQ2TXD8PP/phGpq7qf7OFffqumqvoTFoPozJSxNOQIOk18+eAhqyal9cl28/YvrT9LqZgF5BQIOcUpBKP/sJaOCbcpiGTq5hzUE/ryCgIRLsZ18Brf74MtPQiTX20wsSSkADpNjPUzSPe5Ead8J3+7iNWw2NkRX4qwhodwluAF3nd72vDtPQfUYrZiZDBHRtVT5GXoqrCGhnub/+hPpZ2I2Qa2b1trG6bZ1XBnR9tiof8gD0ygT0OgLaVaL9rCjo+Y11dy7cXP1xF4VpaNhD0Bv9vI6AdpVqPysnm/V71etmptUfd5RvaPCD0AMvwZUEtKOzfqYU0IrNnQ1BrNk2GnQYUwUJjYEV+GsJaDcp97NC5xnltefI57IsodOz9K8loJ0kuwG0RvdV8iuu0lT6bgmdmAno1QS0i7n1M2Sb5pX9LH4goVPSz+sJaAez62dfO4VaP1t5C6qETsdSv56AdjCzDaDr8QNa9bGETsQEtAcC2l7ub3y4fl6zhhz0bKcPR3i2yo8d1DQJ/eyDgLY2aj9HL+gYz1g735XQCVjafRDQtkbZADpqzw5PNFqxGzYYSOjYTEB7IaBtjTEBHXeN+vicY814m7a45t/+Y4ShoJ+9ENCWRlqBr/54Jpp/PAkdk8XcDwFtZ5R+zj+gzRNsCR2NFfieCGgrTwS0Dxc38doUOhJLuCcC2so4/Zx9QFvssjIJHYMJaF8EtI2R+jn/gLbYZWU9fnj62RsBbSH/xyygg8sldOqhzJRl2xsBrbxXcZo01gR0ksOYYqSggzIB7Y+AVt2pWNDR+jnFgfSRktDh6GePBLTiPsWIjbYCv3/OUU/ljJaCDma7VP2G9UNAy3cprkaPdART7unn0M8efgz7koaxm4DO4HcsCgLadJfs49p+ziR1g+hlIm0SOoTVYQXer24fBLTpLpuPa1fgrWzX62lTrgOa+rX9bT0tTr+5PRDQprvsA7r/7LyfZx9w0N/BBCahPTr18/Zww7QDmgMBbbpL/t/rmn76NSzr8XBWBe3N6rRJ//hv/6QDmgUBbbpLvp/nAe30oMvS68KR0H7k+nkroL0R0Ka71E5A+2rEPDej9vuvi4L2ItfPw4syt9+7KQho+S6nlfPzCWj1A4Uvw5nuiOp7em5fUg9OAV0LaH8EtOI+xzWc+kPoe2nEXHdE9b59wyT0esdD8m4FtEcCWnWnvYZD6PtoxGx3RPW/gdgBTVc7BDTbALp7Ueb1SzcRAa2813k/Bwro9Y8RpSH+ZTAJvdLhmObsxdm+KjNb7ZmIgNZrOoezj0bMNqClbRN9bOk1Cb3O8RDQmW54n4iA1jqfgBZ/63rYfjnfgJ79kfb0Jyuh1zitUelnjwS01vkK/KpU0Ct/EWcc0MIfaW/7yhT0GsdzkLSzRwJa53wFvhSBq/8hn3NAc/rcIiqhwfaH0Jt79ktAa7Q6B6m/wcz4l7rv85LsTApy2IOkn70S0Br1e5B6W2SzPYypqOd/JxQ0yHEFnl4JaLXSHqSAx2gxmnkeSF803GH1PTzWYujnMAS0WmkPUsBjtBnOAvaIDnlYfR+PtgiW1kAEtNr5HqSBNlcuoJ+DbOpV0G6swA9FQKuVDmEKeAy2Bll2CtqJRTUUAb1gtwdJQMMNtK/MhtD2LKjBCOgFuz3wC9lhPoyB9pWZhLZlBX44AtrscAjTMnaYD2SgfWUK2pKFNBwBbXacgC5ih/lQhlp0TktqwxIakIA2OmwB1c84mYS2YAV+QALa6NDPw3dH/cMtkoJeYvEMSUCbHK7CFPjtjMAktJllMygBbeIQpgQoaCOLZlAC2sAxoElwibuG3XQLXy6DE9AGh13wod/PSBY/Ca3dx7nopTIGAa13K6CpWHhBa3dzLnmhjENA6x2PoQ/8fsaz6As01e7mXOwSGY+A1roV0IQsuaC1v6ELXR5jEtBah+vQO4wpDcvdl1QX0EUujJElGNCHX//2ww8//OXXNwHf2+HHPb2RhwPp07DYSWhNQLeLwvlzw0otoK+/zZ1V+emPXb+9Y0CP3+U8zhQstaDVAX2SD6jf3IGkFdD3z1dFj/7c7QHa/7hn78TptzAJy0xoQ0CtOw0sqYC+fZpV7OMvd/4h++Tmm06P0C2gnQfI1BZZ0MqA5vtp6/1gUgro7882wfwud8OrTVA/+LnLQ7T+cW8FNFELLGjVbs5iPxV0KCkF9L6Uyyypn3d5iE4B7fLAxGHTkgW+63F5N+cTAR1HQgF9eLFana+wv12tPuqyN15A5227pXqBq/HnuzkPO5Dy95hmZHOXUEA3083S+nrVbbmhVGj5ZPqZosPru9yC7j/d/fACOjwBZTZOL+/yClqw/9EFdHgJBXSzCn9zftTSYKvwJCj/6i5vQ+jJ4QcX0OElFND1XamW2WbRx10ewq/RnBWCsdxJ6JNTQB3GNLSUAvru6aagP+VueL/pZ2lS2sjv0ZwVZ1yLLejph3YS8uBSCmh2HNOmmF/+6YfMf+yOpO90FJOAztr5KusyC5r/kW37H1pSAV3/8vRsl9DN190ewC/SnJW2+S1xQ2jxB9bPgaUV0PXDy3xCb77qekUmv0lzVrHTZHmT0IX9uFNLLKAbD69/ePnll19+9cOPAdezE9A5q9ppsrSCLuqHjUB6Ab2KgM5a1U6TZRV0QT9qHASUGanaabKkDaHL+UljIaDMSeVOk+VMQhfyY0ZEQJm/pRR0ET9kXASUBVjG+83N/yeMj4CyBIs4LWn2P2CEBJRlmP8kdN4/XaQElIWY+/vGz/hHi5iAshizLuh8f7KoCSjLMeNJ6Ex/rOgJKEsy151Js/yhUiCgLMs8CzrDHykNAsrCzPHUztn9QMkQUBYn7UloxdmqCf80qRNQliflglZcLyXdHyZ9AsoCpVvQiiv2pfqjzIKAskSpbgituGZ0mj/IXAgoy5TmJLT8riUp/hQzIqAsVJIFLQU0wZ9hVgSUpUrxtKTzgCb3A8yNgLJYCZ6WdBbQ1IY/PwLKgiVX0GJAExv8HAkoS5baJLQQ0KRGPlMCyrKlVdD8YUwpjXu2BJSFS2tf0ulA+oQGPWMCytKltRp/OJEzoSHPmYBCUpNQ/YyJgEJik9Bj8aceBgIKmaQmofoZDQGFrXQSqp/xEFDYS6Sg+hkRAYWDJCah+hkTAYWT+Hcm6WdUBBTyIp+E6mdcBBSKYk6ofkZGQOFMvAXVz9gIKJREmlD9jI6AQoUYExrhkBZPQKFKfAWNbkAIKNSJK6HxH2C1SAIKdSJKqM2fcRJQqBVNQWMZB2cEFBpEkdDD6vvuUqCTDoUiAWV5Dld1b3Xn6RNa7Kff4ZgIKDPUnJrVKqigEyX0cLHn45sh+SWOiIAyP82FXHVO0ZMJG3qafh5u8UscEQFldpoLuQpJ0VQJPV5gr/CG8H6LoyGgzM2FQgamaIqE3p6eU0DjJKDMzYXWBKdo9ITmr+8soHESUOZmqICux92fVLw8voDGSUCZmwEDOmJCz55HQOMkoMzNoAEdJ6G3pScR0DgJKHMzcECHT2g5n4HHDjA4AWVuLgb0+hQdC3cb+AD1bqvyuQ45epURCChzc6mQvaTotEv+ts+I1uVz3fn8KUYhoMzOpUL2k6J8Qvtp6G1DPtcdz+BnHALK/FwqZE8pelJo6LURzdXTZeuSIaDM0FiTtSdPihENfqBb+UyTgMI1zhsaEtF8PeUzKQIK13nypBTR1hXd3lk+0yWgcLUn51pU9Dyd6pkiAYVelCK6q2it0t2n/gEIIKDMzXSH+5Qb2tr4g6UPAsrMTHzAuXwuioAyL1Gc8iidSyGgzEpEF93QzgUQUGbFZd8Yk4AyKwLKmASUWRFQxiSgzIqAMiYBZVYElDElFNDfn62qfPBzl8H5k5o5AWVMAsqsRHQYEwuQUEDX758LKJdEcSA9S5FSQNcPL1arz696BH9T83fFqZzeNIOOkgrotqDfXPMA/jYW4Op++i2hrbQCmm0H7bTKfs6fBrXarvyrLEeJBXT99rqVeL/11Gm7+8k8lZPUArpZiW8/Ba3a5zTk4EhZywOg7KQiJ7WArt99+eW/tb2vgNJeu4A6TIq85AJ6Hb/z1Gkb0Db3YikEFLYElO4EFLYElO4EFLYElO5SDejvX3z8ScABoX7lqdNu95CAkpdsQMOOqPcrT61WBygJKHkCCnttDnZzGBN5AgoHbQ4WdiA9OQIKnTgpgxMBhW70kyMBBQgkoACBBBQgUKoBDSSgQH8EFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoDMfV62dOQGEw3j9p7gQUhuIdPGdPQGEg3kN+/gQUBpL/bfObN08CCgMR0PkTUBiIgM6fgMJABHT+BBQGIqDzJ6AwEAGdPwGFgTiMaf4EFIbiQPrZE1AYjFM5505AYTj6OXMCChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgRaXEAB+tN7o/p+wD5NvbCBeem9UX0/4OhSWs831mEY6zASGutUQ01nCdVJ6EU21oEY6zASGquAhkroRTbWgRjrMBIaq4CGSuhFNtaBGOswEhqrgIZK6EU21oEY6zASGquAhkroRTbWgRjrMBIaq4CGSuhFNtaBGOswEhqrgIZK6EU21oEY6zASGquAhkroRTbWgRjrMBIaq4CGSuhFNtaBGOswEhqrgIZK6EU21oEY6zASGquAhkroRTbWgRjrMBIaq4CGSuhFNtaBGOswEhqrgIZK6EU21oEY6zASGquAhkroRTbWgRjrMBIaq4CGSuhFNtaBGOswEhqrgIZK6EU21oEY6zASGquAhkroRTbWgRjrMBIaq4CGSuhFNtaBGOswEhqrgAIkRkABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQKDkAvr+26er1c2nP3X70jRqB/TwYnX0zQQDq/H7sw9+rrg5uuWaqRxrfMv14eXHm7F8mMTva/1Y41uur77IhvrVm4ovjbtYUwvoL093L+PNP3f50jTqB/T7s9h+ITObP5OqgEa3XDPVY41uuR6W3Wr1We3XYlmuDWONbbkeg35THs3IizWxgL6tfyEbvjSNdmONZLAbD3erqihFt1wzl8caxWDz43lc/7UYhtp2rDEMtmlCPPZiTSug2b+EjzZz89fPS38/DV+aRtOA7qP4PSza/laWl1x0yzVTM9bYlut22f243i28mz+XvxbRcm0aa2zLdTOcm2zt/f9thvpRcS1+9MWaVkDvDwss+wv6vO2XptE0oLso/mYKXm3XfMrDim65ruvHGttyfXucy2UL73Hha7Et16axRrZcNwPcF36Ty7PWj75Ykwroacmt3z0t/tvT8KVpNA1o87UIRpj3fvMP9urT5+W/k+iWa8NYo1uud6eJW/S/rw1jjW25bsb3eP/h+dR4/MWaVEA3/+AclkluSV360jSaBrT52uMJhtQgWyn6umrHTHTLtWGsES7Xo9xyPP88luV6dD7WiJfr3VlAx1+sSQX0bW7d4mzRNXxpGk0D2nztm/fZcRiffDf6uKrd33z2pnLPdnTLtWGsES7Xo/MoRbhcj0oBjXa5bkZa/C0Yf7GmFtDjZo37UkDrvjSNpgHdr27+ab+n8NM4Vo1+y4ZRE9C4lmvDWCNcrkdvz7YrRrhcj87HGutyfXj59HzJjb9YkwpofpG8LW4jbvjSNJoGdJc7KiSijUtVUYpuue5VBjTS5bqu2NsR63JdV+2ZiXK5bgd183XxxvEXq4AOpGFA2Q7C7WEY779dxTDUg9QDGuty3R22+rhwS6zLtWqscS7XbUA//LrYcwFtNJOA5v6Jv4/jIMCd1AMa63KtOuw/1uVaNdYol+vD//r4i6elGbGANppJQHOyf9yj2f6VekCLX45quTYemh7Zcm3aeR3Vct0d0fY4f4OANppfQLO7TT/WvRkFNKbl+r7i1J5Yl2vlWPMiWq6Z8+21AtpoLnvha+42tUT2wm9dCmg8yzW7uMWjqiOuIlyu1WPNi2e57pwF3V74RnM5DrR4t2h+IRM5DnQrmYBu/oxXn5X3XEe5XGvGmhfNct17Wwro48PHjgMtmcuZSDnxzD5qd8zEtVz3WqzCR7Fcv6/Zbx3jcq0ba14sy/WgvH/WmUj1ZnIufG61o3zM3YRqDg2Ka7nu1WyvjW253tdtUoxwudaONbblml9tP5tmOhe+2TyuxrR5afd//OVj7qZUc3ZPZMt1p2qs8S3Xzfzog5oro0e3XOvHGtty3Yyn9rAqV2NqdLhoYd31QKu/NI36AW0PFcmOAK669OKE6i7QEddy3ak9kD6m5do0X4ttuTaMNbblehxPxYH9oy/WtAJavt706XWP7QrfDWN99/T0pRgmH3v5KEW8XLcqxxrbcr1f5W3HGO1ybRprbMv1fe4dRh5vb5lusSYW0PVfz97xJPcP5/mXJlc/1nfPV5GNNVMd0PiWa6Z6rHEt1/w7T5QDGtdybR5rXMt1f0nYrf1BA9Mt1tQCev6ee/k1j9je5bBhrA/7dxX8+2Rjq1AT0PiW67p2rFEt1/xbsVUENKrlemGsUS3XzG48EWQguYACxEJAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoKTs7Wr1wc/ZBw8vVqvHEw+G5RFQUnbs5rGkMCIBJWnvnq5u/rxe//5stfpm6rGwPAJK2u5Wq4/e7P8fRiagpG0799yswGfzUBiZgJK4TTw/fLpafT71OFgiASVx2X4kK/BMQ0BJ3bunVuCZiICSumwK6hAmJiGgpO4+W4W3CZQpCCiJ+/3Z6uapdXgmIaAk7m4z/bx3HieTEFDS9jbbA+9EJKYhoCQt24P0jVPhmYiAkrT73SGgWUftR2J0AkrK3h12HzmZkykIKCm7O+49urMfifEJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKEAgAQUIJKAAgQQUIJCAAgQSUIBAAgoQSEABAgkoQCABBQgkoACBBBQgkIACBBJQgEACChBIQAECCShAIAEFCCSgAIEEFCCQgAIEElCAQAIKEEhAAQIJKECg/w/8wAFOlv4tBwAAAABJRU5ErkJggg==)