CINXE.COM

<!doctype html><html><head><title>View article</title><meta http-equiv="Content-Type" content="text/html;charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="referrer" content="always"><meta name="viewport" content="width=device-width,initial-scale=1,minimum-scale=1,maximum-scale=2"><meta name="format-detection" content="telephone=no"><link rel="shortcut icon" href="/favicon.ico"><meta name="description" content="‪L Breiman‬, ‪The Annals of Statistics, 1996‬ - ‪Cited by 1,773‬"><meta property="og:description" content="‪L Breiman‬, ‪The Annals of Statistics, 1996‬ - ‪Cited by 1,773‬"><meta property="og:title" content="‪Heuristics of instability and stabilization in model selection‬"><meta property="og:image" content=""><meta property="og:type" content="website"><meta name="twitter:card" content="summary"><style>html,body,form,table,div,h1,h2,h3,h4,h5,h6,img,ol,ul,li,button{margin:0;padding:0;border:0;}table{border-collapse:collapse;border-width:0;empty-cells:show;}html,body{height:100%}#gs_top{position:relative;box-sizing:border-box;min-height:100%;min-width:964px;-webkit-tap-highlight-color:rgba(0,0,0,0);}#gs_top>*:not(#x){-webkit-tap-highlight-color:rgba(204,204,204,.5);}.gs_el_ph #gs_top,.gs_el_ta #gs_top{min-width:320px;}#gs_top.gs_nscl{position:fixed;width:100%;}body,td,input,button{font-size:13px;font-family:Arial,sans-serif;line-height:1.24;}body{background:#fff;color:#222;-webkit-text-size-adjust:100%;-moz-text-size-adjust:none;}.gs_gray{color:#777777}.gs_red{color:#dd4b39}.gs_grn{color:#006621}.gs_lil{font-size:11px}.gs_med{font-size:16px}.gs_hlt{font-weight:bold;}a:link{color:#1a0dab;text-decoration:none}a:visited{color:#660099;text-decoration:none}a:hover,a:hover .gs_lbl{text-decoration:underline}a:active,a:active .gs_lbl,a .gs_lbl:active{color:#d14836}.gs_el_tc a:hover,.gs_el_tc a:hover .gs_lbl{text-decoration:none}.gs_pfcs a:focus,.gs_pfcs button:focus,.gs_pfcs input:focus,.gs_pfcs label:focus{outline:none}.gs_a,.gs_a a:link,.gs_a a:visited{color:#006621}.gs_a a:active{color:#d14836}a.gs_fl:link,.gs_fl a:link{color:#1a0dab}a.gs_fl:visited,.gs_fl a:visited{color:#660099}a.gs_fl:active,.gs_fl a:active{color:#d14836}.gs_fl{color:#777777}.gs_ctc,.gs_ctu{vertical-align:middle;font-size:11px;font-weight:bold}.gs_ctc{color:#1a0dab}.gs_ctg,.gs_ctg2{font-size:13px;font-weight:bold}.gs_ctg{color:#1a0dab}a.gs_pda,.gs_pda a{padding:7px 0 5px 0}.gs_alrt{background:#f9edbe;border:1px solid #f0c36d;padding:0 16px;text-align:center;box-shadow:0 2px 4px rgba(0,0,0,.2);border-radius:2px;}.gs_alrt:empty{display:none;}.gs_spc{display:inline-block;width:12px}.gs_br{width:0;font-size:0}.gs_ibl{display:inline-block;}.gs_scl:after{content:"";display:table;clear:both;}.gs_ind{padding-left:8px;text-indent:-8px}.gs_ico,.gs_icm{display:inline-block;background:no-repeat url(/intl/en/scholar/images/1x/sprite_20161020.png);background-position:-23px -161px;background-size:169px;width:21px;height:21px;}@media(-webkit-min-device-pixel-ratio:1.5),(min-resolution:144dpi){.gs_ico,.gs_icm{background-image:url(/intl/en/scholar/images/2x/sprite_20161020.png);}}.gs_el_ta .gs_nta,.gs_ota,.gs_el_ph .gs_nph,.gs_oph{display:none}.gs_el_ta .gs_ota,.gs_el_ph .gs_oph{display:inline}.gs_el_ta div.gs_ota,.gs_el_ph div.gs_oph{display:block}.gs_sth_g{visibility:hidden;max-height:0;}.gs_sth_vis .gs_sth_g{max-height:1000px;}.gs_sth_vis .gs_sth_b{position:fixed;top:0;}.gs_sth_trk .gs_sth_b{position:absolute;top:auto;}@keyframes gs_anm_spin{0%{transform:rotate(0deg);}100%{transform:rotate(360deg);}}.gs_invis{visibility:hidden;}.gs_rimg{display:block;background-color:#e5e5e5;border-radius:50%;overflow:hidden;position:relative;z-index:1;}.gs_rimg>img{position:absolute;margin:auto;left:0;top:0;bottom:0;right:0;}.gs_in_txtw{display:inline-block;vertical-align:middle;}.gs_in_txtb{display:block;}.gs_in_txt{color:#000;background-color:#fff;font-size:16px;box-sizing:border-box;height:29px;line-height:23px;border:1px solid #d9d9d9;border-top-color:#c0c0c0;padding:3px 6px 1px 8px;border-radius:1px;outline:none;-webkit-appearance:none;-moz-appearance:none;}.gs_el_tc .gs_in_txt{font-size:18px;}.gs_in_txtb .gs_in_txt{width:100%;}.gs_in_rnd .gs_in_txt{border-radius:14.5px;padding:3px 12px 1px 12px;}.gs_in_txt:hover{border-color:#b9b9b9;border-top-color:#a0a0a0;box-shadow:inset 0 1px 2px rgba(0,0,0,.1);}.gs_in_txte .gs_in_txt{border-color:#dd4b39;}.gs_in_txt:focus{border-color:#4d90fe;box-shadow:inset 0 1px 2px rgba(0,0,0,.3);}.gs_in_txt:disabled{color:#b8b8b8;border-color:#f1f1f1;box-shadow:none;}.gs_in_txtm .gs_in_txt{font-size:13px;height:24px;line-height:16px;padding:3px 6px;}.gs_in_txtm.gs_in_rnd .gs_in_txt{border-radius:12px;}.gs_el_tc .gs_in_txtm .gs_in_txt{height:29px;line-height:21px;}.gs_el_tc .gs_in_txtm.gs_in_rnd .gs_in_txt{border-radius:14.5px;}.gs_in_txtl .gs_in_txt{height:41px;padding:9px 43px;}.gs_in_txtl.gs_in_rnd .gs_in_txt{border-radius:20.5px;}.gs_in_txts{font-size:13px;line-height:18px;color:#666;}.gs_in_txts:not(:empty){margin-top:2px;}.gs_in_txte .gs_in_txts{color:#dd4b39;}button{position:relative;z-index:1;box-sizing:border-box;font-size:13px;cursor:pointer;height:29px;line-height:normal;min-width:72px;padding:0 8px;color:#444;border:1px solid rgba(0,0,0,.1);border-radius:3px;text-align:center;background-color:#f5f5f5;-ms-user-select:none;user-select:none;}button.gs_btn_rnd{border-radius:14px;padding:0 12px;}button.gs_btn_rnd.gs_btn_rndci{padding-left:4px;}button.gs_btn_lrge{height:41px;min-width:82px;padding:0 9px;}button.gs_btn_lrge.gs_btn_lrge_asym{padding-left:5px;padding-right:8px;}button.gs_btn_lrge.gs_btn_rnd{border-radius:20px;padding:0 16px;}button.gs_btn_lrge.gs_btn_rnd.gs_btn_rndci{padding-left:10px;}button.gs_btn_cir{border-radius:14.5px;min-width:29px;}button.gs_btn_lrge.gs_btn_cir{border-radius:20.5px;min-width:41px;}button.gs_btn_mini{padding:0;border:0;}.gs_el_ph button.gs_btn_mph,.gs_el_ta button.gs_btn_mta{height:41px;}button .gs_wr{position:relative;display:inline-block;width:100%;height:100%;}button .gs_wr:before{content:"";width:0;height:100%;}button .gs_wr:before,button .gs_ico,button .gs_rdt,button .gs_lbl,button .gs_icm{display:inline-block;vertical-align:middle;}button .gs_wr{font-size:13px;text-transform:none;}.gs_btn_lrge .gs_wr{font-size:15px;}.gs_btn_lsb .gs_wr{font-size:11px;font-weight:bold;}.gs_btn_lsu .gs_wr{font-size:11px;text-transform:uppercase;}.gs_btn_lrge.gs_btn_lsb .gs_wr,.gs_btn_lrge.gs_btn_lsu .gs_wr,.gs_btn_lrge.gs_btn_lrge_asym .gs_wr{font-size:13px;}.gs_btn_half,.gs_el_ta .gs_btn_hta,.gs_el_ph .gs_btn_hph{min-width:36px;}.gs_btn_lrge.gs_btn_half,.gs_el_ta .gs_btn_lrge.gs_btn_hta,.gs_el_ph .gs_btn_lrge.gs_btn_hph,.gs_el_ta .gs_btn_mta,.gs_el_ph .gs_btn_mph{min-width:41px;}.gs_btn_slt{border-radius:3px 0 0 3px;}.gs_btn_srt{margin-left:-1px;border-radius:0 3px 3px 0;}.gs_btn_smd{margin-left:-1px;border-radius:0;}button:hover{z-index:2;color:#222;border-color:rgba(0,0,0,.2);background-color:#f8f8f8;}button.gs_sel{background-color:#dcdcdc;}button:active{z-index:2;background-color:#f1f1f1;}button:focus{z-index:2;}button::-moz-focus-inner{padding:0;border:0}button:-moz-focusring{outline:1px dotted ButtonText}.gs_pfcs button:-moz-focusring{outline:none}a.gs_in_ib{position:relative;display:inline-block;line-height:16px;padding:6px 0 7px 0;-ms-user-select:none;user-select:none;}a.gs_btn_lrge{height:40px;padding:0;}a.gs_in_bgcw{min-width:41px;}a.gs_btn_lrge.gs_in_bgcw:before{position:absolute;content:"";height:29px;width:29px;top:6px;left:6px;background-color:#fff;box-shadow:0 1px 3px rgb(0,0,0,.4);border-radius:50%;}a.gs_in_bgcw:hover:before{background-color:#f5f5f5;}a.gs_in_bgcw:active:before{background-color:#e5e5e5;}a.gs_in_bgcw.gs_dis:before{background-color:#fff;}a.gs_in_ib .gs_lbl{display:inline-block;padding-left:21px;color:#222;}a.gs_in_ib.gs_in_gray .gs_lbl{color:#444;}a.gs_in_ib .gs_lbl:not(:empty){padding-left:29px;}button.gs_in_ib .gs_lbl:not(:empty){padding-left:4px;}a.gs_in_ib:active .gs_lbl,a.gs_in_ib .gs_lbl:active,a.gs_in_ib :active~.gs_lbl{color:#d14836;}.gs_el_ta .gs_btn_hta .gs_lbl,.gs_el_ph .gs_btn_hph .gs_lbl,.gs_el_ta .gs_btn_mta .gs_lbl,.gs_el_ph .gs_btn_mph .gs_lbl,.gs_el_ta .gs_btn_cta .gs_lbl,.gs_el_ph .gs_btn_cph .gs_lbl{display:none;}a.gs_in_ib .gs_ico{position:absolute;top:3px;left:0;}.gs_in_ib.gs_md_li .gs_ico{left:14px;}.gs_el_tc .gs_in_ib.gs_md_li .gs_ico{top:11px;}.gs_in_ib.gs_md_li.gs_md_lix .gs_ico{top:10px;left:16px;}a.gs_btn_lrge .gs_ico{top:50%;left:50%;margin:-10.5px 0 0 -10.5px;}.gs_in_ib .gs_ico{opacity:.55;}.gs_in_ib:hover .gs_ico{opacity:.72;}.gs_in_ib:active .gs_ico,.gs_in_ib .gs_ico:active,.gs_in_ib :active~.gs_ico{opacity:1;}.gs_in_ib:disabled .gs_ico,.gs_in_ib.gs_dis .gs_ico{opacity:.28;}.gs_in_ib.gs_btn_act .gs_ico,.gs_in_ib.gs_btn_cre .gs_ico{opacity:1;}.gs_btn_act:disabled .gs_ico,.gs_btn_cre:disabled .gs_ico{opacity:.72;}.gs_rdt{position:relative;width:0;height:21px;}a.gs_in_ib .gs_rdt{left:21px;}.gs_rdt:before{content:"";position:absolute;top:1px;right:0;width:5px;height:5px;border:1px solid #fff;border-radius:50%;background-color:#dd4b39;}.gs_notf{display:inline-block;vertical-align:top;margin-left:8px;width:16px;line-height:16px;background-color:#d14836;border-radius:50%;color:#fff;text-align:center;font-size:9px;font-weight:bold;}.gs_notf:empty{display:none;}.gs_ind .gs_notf{text-indent:0;}button.gs_btn_flat{border-color:transparent;background-color:transparent;}button.gs_btn_olact{color:#4d90fe;background-color:transparent;}button.gs_btn_flat:hover,button.gs_btn_olact:hover{background-color:rgba(0,0,0,.05);}button.gs_btn_flat:active,button.gs_btn_olact:active{background-color:rgba(0,0,0,.1);}button.gs_btn_flat.gs_btn_flact{color:#1a0dab;}button.gs_btn_act{color:#fff;background-color:#4d90fe;}button.gs_btn_act:hover{color:#fff;background-color:#3983fe;}button.gs_btn_act.gs_sel{background-color:#2f6bcc;}button.gs_btn_act:active{background-color:#357ae8;}button.gs_btn_cre{color:#fff;background-color:#d14836;}button.gs_btn_cre:hover{color:#fff;background-color:#c53727;}button.gs_btn_cre.gs_sel{background-color:#992b1e;}button.gs_btn_cre:active{background-color:#b0281a;}button.gs_btn_hov_nobg:hover,button.gs_btn_hov_nobg:active{border:none;background:transparent;}button:disabled,button:disabled:hover,button:disabled:active{cursor:default;color:#b8b8b8;border-color:rgba(0,0,0,.05);background-color:transparent;z-index:0;}button.gs_btn_flat:disabled{color:#b8b8b8;border-color:transparent;}button.gs_btn_act:disabled{color:#fff;background-color:#a6c8ff;}button.gs_btn_cre:disabled{color:#fff;background-color:#e8a49b;}a.gs_in_ib.gs_dis{cursor:default;pointer-events:none}a.gs_in_ib.gs_dis .gs_lbl{color:#b8b8b8;text-decoration:none}.gs_ttp{position:absolute;top:100%;right:50%;z-index:10;pointer-events:none;visibility:hidden;opacity:0;transition:visibility 0s .13s,opacity .13s ease-out;}button:hover .gs_ttp,button:focus .gs_ttp,a:hover .gs_ttp,a:focus .gs_ttp{transition:visibility 0s .3s,opacity .13s ease-in .3s;visibility:visible;opacity:1;}.gs_md_tb.gs_sel .gs_ttp{transition:none;visibility:hidden;}button.gs_btn_lrge.gs_btn_cir .gs_ttp{top:75%;}.gs_ttp .gs_aro,.gs_ttp .gs_aru{position:absolute;top:-2px;right:-5px;width:0;height:0;line-height:0;font-size:0;border:5px solid transparent;border-top:none;border-bottom-color:#595959;z-index:1;}.gs_ttp .gs_aro{top:-3px;right:-6px;border-width:6px;border-top:none;border-bottom-color:white;}.gs_ttp .gs_txt{display:block;position:relative;top:2px;right:-50%;padding:4px 6px;background:#595959;color:white;font-size:11px;font-weight:bold;line-height:normal;white-space:nowrap;border:1px solid white;border-radius:3px;box-shadow:inset 0 1px 4px rgba(0,0,0,.2);}.gs_press,.gs_in_se,.gs_tan{touch-action:none;}.gs_in_se .gs_lbl:not(:empty){padding-right:14px;}.gs_in_se .gs_icm{position:absolute;top:50%;margin-top:-5.5px;right:0;width:7px;height:11px;background-position:-21px -88px;opacity:.55;}.gs_in_se:hover .gs_icm{opacity:.72;}.gs_in_se:active .gs_icm{opacity:1;}.gs_in_se:disabled .gs_icm{opacity:.28;}.gs_el_ta .gs_btn_hta .gs_icm,.gs_el_ph .gs_btn_hph .gs_icm,.gs_el_ta .gs_btn_mta .gs_icm,.gs_el_ph .gs_btn_mph .gs_icm,.gs_el_ta .gs_btn_cta .gs_icm,.gs_el_ph .gs_btn_cph .gs_icm{display:none;}.gs_btn_mnu .gs_icm{margin-top:-3.5px;height:7px;background-position:0 -110px;}.gs_in_se.gs_btn_act .gs_icm,.gs_in_se.gs_btn_cre .gs_icm{margin-top:-3.5px;height:7px;background-position:-42px -44px;opacity:1;}.gs_btn_act:disabled .gs_icm,.gs_btn_cre:disabled .gs_icm{opacity:.72;}button.gs_btnG .gs_ico{width:21px;height:21px;background-position:-92px -253px;}button .gs_bs{position:absolute;top:50%;left:50%;margin-top:-10px;margin-left:-10px;box-sizing:border-box;width:20px;height:20px;border-radius:50%;border:2px solid #eee;border-top-color:#4d90fe;visibility:hidden;animation:gs_anm_spin .8s linear infinite;}button.gs_bsp .gs_bs{visibility:visible;transition:visibility 0s .4s;}.gs_md_d{text-transform:none;white-space:nowrap;position:absolute;top:0;left:0;border:1px solid #ccc;border-color:rgba(0,0,0,.2);background:#fff;box-shadow:0 2px 4px rgba(0,0,0,.2);z-index:1100;text-align:left;visibility:hidden;max-height:0;margin-top:-1000px;opacity:0;transition:opacity .13s,visibility 0s .13s,max-height 0s .13s,margin-top 0s .13s;}.gs_md_d.gs_vis{visibility:visible;max-height:10000px;margin-top:0;opacity:1;transition:all 0s;}.gs_el_tc .gs_md_d{transform-origin:100% 0;transform:scale(1,0);transition:opacity .218s ease-out,transform 0s .218s,visibility 0s .218s,max-height 0s .218s,margin-top 0s .218s;}.gs_el_tc .gs_md_d.gs_ttzi{transform-origin:50% 50%;transform:scale(0,0);}.gs_el_tc .gs_md_d.gs_ttzr{transform:scale(0,0);}.gs_el_tc .gs_md_d.gs_vis{transform:scale(1,1);transition:transform .218s ease-out;}.gs_md_r{position:relative;display:inline-block;}.gs_md_rmb>.gs_md_d{top:29px}.gs_md_rmbl>.gs_md_d{top:41px}.gs_md_ul{list-style-type:none;word-wrap:break-word;display:inline-block;vertical-align:top;}.gs_md_ul.gs_md_ul_tb{display:block;}.gs_md_li,.gs_in_cb.gs_md_li,.gs_md_li:link,.gs_md_li:visited{display:block;padding:6px 44px 6px 16px;font-size:13px;line-height:16px;color:#222;cursor:pointer;text-decoration:none;position:relative;z-index:0;}a.gs_md_li:hover .gs_lbl,a.gs_md_li:active .gs_lbl{text-decoration:none}.gs_el_tc .gs_md_li{padding-top:14px;padding-bottom:10px;}.gs_md_li.gs_md_lix{font-size:16px;line-height:20px;padding:12px 16px 8px 16px;}.gs_md_li:before{content:"";background-color:#f1f1f1;position:absolute;left:0;right:0;top:0;bottom:0;opacity:0;transition:opacity .13s;z-index:-1;}.gs_md_li:hover:before,.gs_md_li:focus:before{opacity:1;transition:all 0s;}a.gs_in_ib.gs_md_li .gs_lbl{color:#222}a.gs_in_ib.gs_md_li.gs_in_gray .gs_lbl{color:#444}.gs_md_li:active:before{background-color:#ddd}.gs_md_li.gs_sel,a.gs_in_ib.gs_md_li.gs_sel .gs_lbl{color:#d14836}.gs_md_d:focus,.gs_md_li:focus{outline:none}a.gs_md_lix .gs_lbl,a.gs_md_lix .gs_lbl:not(:empty){padding:0 0 0 40px;}a.gs_in_cb:link,a.gs_in_cb:visited,a.gs_in_cb:active,a.gs_in_cb:hover{cursor:pointer;color:#222;text-decoration:none;}.gs_in_cb,.gs_in_ra{position:relative;line-height:16px;display:inline-block;-ms-user-select:none;user-select:none;}.gs_in_cb.gs_md_li{padding:6px 44px 6px 16px;}.gs_in_cb input,.gs_in_ra input{position:absolute;top:1px;left:1px;width:15px;height:15px;margin:0;padding:0;opacity:0;z-index:2;}.gs_in_ra input{top:0;left:0}.gs_el_tc .gs_in_cb input{top:9px}.gs_el_tc .gs_in_ra input{top:8px}.gs_in_cb.gs_in_cbj input{top:15px;left:15px}.gs_in_cb label,.gs_in_cb .gs_lbl,.gs_in_ra label{display:inline-block;padding-left:21px;min-height:16px;}.gs_in_ra_lrge{font-size:15px;}.gs_in_cb label:empty:before,.gs_in_cb .gs_lbl:empty:before,.gs_in_ra label:empty:before{content:"\200b";}.gs_el_tc .gs_in_cb label,.gs_el_tc .gs_in_cb .gs_lbl,.gs_el_tc .gs_in_ra label{padding-top:8px;padding-bottom:5px;}.gs_in_cb.gs_in_cbj label,.gs_in_cb.gs_in_cbj .gs_lbl{padding:13px 0 12px 41px;}.gs_in_cbb,.gs_in_cbb label,.gs_in_cbb .gs_lbl{display:block;}.gs_in_cb .gs_cbx,.gs_in_ra .gs_cbx{position:absolute}.gs_in_cb .gs_cbx{top:2px;left:2px;width:11px;height:11px;border:1px solid #c6c6c6;border-radius:1px;}.gs_md_li .gs_cbx{top:8px;left:18px}.gs_el_tc .gs_in_cb .gs_cbx{top:10px}.gs_el_tc .gs_md_li .gs_cbx{top:16px}.gs_in_cb.gs_in_cbj .gs_cbx{top:15px;left:15px}.gs_el_tc .gs_in_ra .gs_cbx{top:8px}.gs_in_ra .gs_cbx{top:0;left:0;border:1px solid #c6c6c6;width:13px;height:13px;border-radius:7px;}.gs_in_cb:hover .gs_cbx,.gs_in_ra:hover .gs_cbx{border-color:#666;box-shadow:inset 0 1px 1px rgba(0,0,0,.1);}button.gs_in_cb:hover .gs_cbx{border-color:#c6c6c6;}.gs_in_cb :focus~label,.gs_in_ra :focus~label{outline:1px dotted #222;}.gs_pfcs .gs_in_cb :focus~label,.gs_pfcs .gs_in_ra :focus~label{outline:none;}.gs_in_cb:active .gs_cbx,.gs_in_ra:active .gs_cbx,.gs_in_cb .gs_cbx:active,.gs_in_ra .gs_cbx:active,.gs_in_cb :active~.gs_cbx,.gs_in_ra :active~.gs_cbx{border-color:#666;background-color:#ebebeb;}button.gs_in_cb:active .gs_cbx{border-color:#a6a6a6;}.gs_in_cb :disabled~.gs_cbx,.gs_in_ra :disabled~.gs_cbx,button.gs_in_cb:disabled .gs_cbx{border-color:#f1f1f1;box-shadow:none;}.gs_in_cb :disabled~label,.gs_in_ra :disabled~label{color:#b8b8b8;}.gs_in_cb.gs_err .gs_cbx{border-color:#eda29b;}.gs_in_cb .gs_chk,.gs_in_ra .gs_chk{position:absolute;z-index:1;top:-3px;left:-2px;width:21px;height:21px;}.gs_md_li .gs_chk{top:3px;left:14px}.gs_el_tc .gs_in_cb .gs_chk{top:5px}.gs_el_tc .gs_md_li .gs_chk{top:11px}.gs_in_cb.gs_in_cbj .gs_chk{top:10px;left:11px}.gs_in_ra .gs_chk{top:4px;left:4px;width:7px;height:7px;border-radius:4px;}.gs_el_tc .gs_in_ra .gs_chk{top:12px}.gs_in_cb input:checked~.gs_chk,.gs_in_cb.gs_sel .gs_chk{background:no-repeat url(/intl/en/scholar/images/1x/sprite_20161020.png) -69px -67px;opacity:.62;}.gs_in_ra input:checked~.gs_chk{background-color:#666}.gs_in_cb.gs_par .gs_chk{background:no-repeat url(/intl/en/scholar/images/1x/sprite_20161020.png) -21px -44px;opacity:.55;}@media(-webkit-min-device-pixel-ratio:1.5),(min-resolution:144dpi){.gs_in_cb input:checked~.gs_chk,.gs_in_cb.gs_sel .gs_chk,.gs_in_cb.gs_par .gs_chk{background-image:url(/intl/en/scholar/images/2x/sprite_20161020.png);background-size:169px;}}.gs_in_cb input:checked:disabled~.gs_chk{opacity:.22}.gs_in_ra input:checked:disabled~.gs_chk{background-color:#f1f1f1}.gs_in_cb.gs_bsp .gs_cbx{top:6px;left:16px;border-radius:6px;border-width:3px;animation:gs_cbx_spn .5s infinite linear;}.gs_el_tc .gs_in_cb.gs_md_li.gs_bsp .gs_cbx{top:14px}.gs_in_cb .gs_csp{background:url('/intl/en/scholar/images/spinner.gif') no-repeat;position:absolute;height:25px;width:25px;top:2px;left:12px;display:none;animation:gs_cbx_ah 9s infinite;}.gs_in_cb.gs_bsp .gs_csp{display:block}.gs_el_tc .gs_md_li .gs_csp{top:10px}@keyframes gs_cbx_spn{0%,100%{border-color:#4d90fe #c6c6c6 #c6c6c6 #c6c6c6}40%{border-color:#c6c6c6 #4d90fe #c6c6c6 #c6c6c6}50%{border-color:#c6c6c6 #c6c6c6 #4d90fe #c6c6c6}60%{border-color:#c6c6c6 #c6c6c6 #c6c6c6 #4d90fe}}@keyframes gs_cbx_ah{0%,100%{visibility:hidden}}.gs_ico_x{background-position:-113px -22px;opacity:.55;}.gs_ico_x:hover{opacity:.72;}.gs_ico_x:active{opacity:1;}.gs_ico_X{background-position:-71px 0;opacity:.55;}.gs_ico_X:hover{opacity:.72;}.gs_ico_X:active{opacity:1;}.gs_btnX .gs_ico{background-position:-71px 0;}.gs_el_tc .gs_ico_Xt{background-origin:content-box;background-clip:content-box;padding:10px 6px 10px 14px;}.gs_ico_P{background-position:0 0;opacity:.55;}.gs_ico_P:hover{opacity:.72;}.gs_ico_P:active{opacity:1;}.gs_btnP .gs_ico{background-position:-21px 0;}.gs_btnC .gs_ico{background-position:0 -66px;}.gs_btnL .gs_ico{background-position:-92px -44px;}.gs_ico_LB{background-position:-50px -44px;height:16px;}.gs_btnJ .gs_ico{background-position:-92px -22px;}.gs_btnM .gs_ico{background-position:-92px 0;}.gs_btnMW .gs_ico{background-position:-21px -22px;}.gs_btnSB .gs_ico{background-position:0 -44px;}.gs_btnTSB .gs_ico{background-position:-115px -253px;}.gs_btnPL .gs_ico{background-position:-148px -66px;}.gs_btnPR .gs_ico{background-position:-21px -66px;}.gs_btnPLW .gs_ico{background-position:-0 -230px;}.gs_btnPRW .gs_ico{background-position:-23px -230px;}.gs_btnZI .gs_ico{background-position:-148px -22px;}.gs_btnZO .gs_ico{background-position:-127px -44px;}.gs_btnDE .gs_ico{background-position:-134px 0;}.gs_btnFI .gs_ico{background-position:-50px -66px;}.gs_btnAD .gs_ico{background-position:-141px -88px;opacity:.55;}.gs_btnAD:hover .gs_ico{opacity:.72;}.gs_btnAD:active .gs_ico,.gs_btnAD .gs_ico:active,.gs_btnAD :active~.gs_ico{opacity:1;}.gs_btnBA .gs_ico{background-position:-50px -22px;}.gs_btnADD .gs_ico{background-position:-92px -66px;}.gs_btnMRG .gs_ico{background-position:-113px 0;}.gs_btnLBL .gs_ico{background-position:0 -161px;}.gs_btnCNCL .gs_ico{background-position:-71px 0;}.gs_btnDWL .gs_ico{background-position:-28px -88px;}.gs_btnMNU .gs_ico{background-position:0 -88px;}.gs_btnMNT .gs_ico{background-position:-46px -161px;}.gs_btnALT .gs_ico{background-position:-92px -161px;}.gs_btnART .gs_ico{background-position:-115px -161px;}.gs_btnGSL .gs_ico{background-position:-69px -161px;}.gs_btnCLS .gs_ico{background-position:-138px -161px;}.gs_btnXBLU .gs_ico{background-position:-138px -253px;}.gs_btnSSB .gs_ico{background-position:0 -276px;}.gs_btnSSW .gs_ico{background-position:-23px -276px;}.gs_btnFLT .gs_ico{background-position:0 -184px;}.gs_btnXT .gs_ico{background-position:-46px -184px;}.gs_btnPD .gs_ico{background-position:-69px -184px;}.gs_btnPU .gs_ico {background-position:-92px -276px;}.gs_btnCP .gs_ico{background-position:-92px -184px;}.gs_btnTP .gs_ico{background-position:-138px -184px;}.gs_btnML .gs_ico{background-position:-115px -276px;}.gs_btnCHK .gs_ico{background-position:-71px -66px;}.gs_btnDNB .gs_ico{background-position:-115px -230px;}.gs_btnDNW .gs_ico{background-position:0 -207px;}.gs_btnACA .gs_ico{background-position:-23px -207px;}.gs_btnAPT .gs_ico{background-position:-46px -207px;}.gs_btnAPTW .gs_ico{background-position:-92px -230px;}.gs_btnAFL .gs_ico{background-position:-69px -207px;}.gs_btnAN .gs_ico{background-position:-46px -276px;}.gs_btnAI .gs_ico{background-position:-69px -276px;}.gs_btnPBL .gs_ico{background-position:-92px -207px;}.gs_btnUCT .gs_ico{background-position:-115px -207px;}.gs_btnVRF .gs_ico{background-position:-138px -207px;}.gs_btnLSI .gs_ico{background-position:-46px -230px;}.gs_btnLSG .gs_ico{background-position:-69px -230px;}.gs_btnMOR .gs_ico{background-position:-23px -253px;}.gs_btnADV .gs_ico{background-position:-46px -253px;}.gs_btnPRO .gs_ico{background-position:-69px -253px;}.gs_ico_star{background-position:-71px -44px;width:13px;height:13px;}.gs_btnPLSW .gs_ico{background-position:-138px -230px;}.gs_btnPDF .gs_ico{background-position:0 -253px;}.gs_btnS .gs_ico{background-position:-138px -276px;}.gs_btnUNS .gs_ico{background-position:0 -299px;}.gs_btnMORR .gs_ico{background-position:-23px -299px;}.gs_btnTW .gs_ico{background-position:-46px -299px;}.gs_btnIN .gs_ico{background-position:-69px -299px;}.gs_btnFB .gs_ico{background-position:-92px -299px;}.gs_btnET .gs_ico{background-position:-115px -299px;}.gs_btnARC .gs_ico{background-position:-138px -299px;}.gs_btnOL .gs_ico{background-position:0px -322px;}.gs_btnFA .gs_ico{background-position:-23px -322px;}.gs_btnFAD .gs_ico{background-position:-46px -322px;}.gs_btnHP .gs_ico{background-position:-69px -322px;}.gs_btnPLM .gs_ico{background-position:-92px -322px;}.gs_btnPRM .gs_ico{background-position:-115px -322px;}.gs_btnRN .gs_ico{background-position:-138px -322px;}.gs_btnVF .gs_ico{background-position:0px -345px;}.gs_btnVP .gs_ico{background-position:-23px -345px;}.gs_btnSRT .gs_ico{background-position:-46px -345px;}#gs_md_s.gs_hdr_drs{transition:opacity .15s,visibility 0s .15s;}#gs_md_s.gs_hdr_drs.gs_vis{transition:opacity .15s,visibility 0s;}.gs_el_tc #gs_md_s.gs_hdr_drs{transition:opacity .218s,visibility 0s .218s;}.gs_el_tc #gs_md_s.gs_hdr_drs.gs_vis{transition:opacity .218s,visibility 0s;}#gs_hdr_drw{position:fixed;top:0;left:0;height:100%;z-index:1200;visibility:hidden;overflow:auto;width:228px;background-color:#fff;box-shadow:2px 2px 4px rgba(0,0,0,.15);outline:none;transform:translate(-100%,0);transition:transform .15s ease-in-out,visibility 0s .15s;}#gs_hdr_drw.gs_vis{visibility:visible;transform:translate(0,0);transition:transform .15s ease-in-out,visibility 0s;}.gs_el_tc #gs_hdr_drw{transition:transform .3s cubic-bezier(.4,0,.6,1),visibility 0s .3s;}.gs_el_tc #gs_hdr_drw.gs_vis{transition:transform .225s cubic-bezier(0,0,.2,1),visibility 0s;}#gs_top #gs_hdr_drw.gs_abt,#gs_top #gs_md_s.gs_abt{transition:none;}#gs_hdr_drw_in{position:relative;box-sizing:border-box;min-height:100%;padding:0 0 8px 0;}.gs_el_ta #gs_hdr_drw_in,.gs_el_ph #gs_hdr_drw_in{padding:0 0 65px 0;}#gs_hdr_drw_top{position:relative;height:63px;border-bottom:1px solid #e5e5e5;margin-bottom:8px;}.gs_el_ta #gs_hdr_drw_top,.gs_el_ph #gs_hdr_drw_top{height:57px;}#gs_hdr_drw_mnu,#gs_hdr_drw_lgo{position:absolute;top:0;height:100%;}#gs_hdr_drw_mnu{left:0;width:55px;}#gs_hdr_drw_lgo{left:56px;}.gs_hdr_drw_sec:before{display:block;content:" ";height:0;border-bottom:1px solid #e5e5e5;margin:8px 0;}.gs_hdr_drw_sec:first-child:before{display:none;}#gs_hdr_drw_bot{display:none;}.gs_el_ta #gs_hdr_drw_bot,.gs_el_ph #gs_hdr_drw_bot{display:block;position:absolute;left:0;bottom:0;width:100%;height:65px;}#gs_hdr_drw_bot .gs_md_li:before{opacity:0;}#gs_hdr_drw_bot .gs_hdr_pp{display:block;position:absolute;bottom:14px;left:15px;pointer-events:none;}#gs_hdr_drw_bot .gs_lbl{display:block;white-space:nowrap;overflow:hidden;text-overflow:ellipsis;}#gs_hdr{position:relative;height:63px;background-color:#f5f5f5;border-bottom:1px solid #e5e5e5;display:flex;}.gs_el_ta #gs_hdr,.gs_el_ph #gs_hdr{height:57px;}#gs_hdr_mnu,#gs_hdr_bck,#gs_hdr_lgo,#gs_hdr_lgt,#gs_hdr_md,#gs_hdr_sre,#gs_hdr_act{display:inline-block;vertical-align:top;position:relative;height:100%;flex:0 0 auto;}#gs_hdr_md{flex:1 1 auto;}#gs_hdr .gs_hdr_mbo,#gs_hdr .gs_hdr_mbo,.gs_el_ta #gs_hdr .gs_hdr_dso,.gs_el_ph #gs_hdr .gs_hdr_dso{display:none;}.gs_el_ta #gs_hdr .gs_hdr_mbo,.gs_el_ph #gs_hdr .gs_hdr_mbo{display:inline-block;}#gs_hdr_mnu,#gs_hdr_bck,#gs_hdr_sre{width:55px;margin-right:1px;}#gs_hdr_lgo,#gs_hdr_drw_lgo{width:149px;background:no-repeat url('/intl/en/scholar/images/1x/scholar_logo_24dp.png') 0% 50%;background-size:149px;}@media(-webkit-min-device-pixel-ratio:1.5),(min-resolution:144dpi){#gs_hdr_lgo,#gs_hdr_drw_lgo{background-image:url('/intl/en/scholar/images/2x/scholar_logo_24dp.png');}}#gs_hdr_lgo{margin-right:31px;}.gs_el_ph #gs_hdr_lgo{margin-right:0;}#gs_hdr_lgt{min-width:164px;margin-right:16px;}#gs_hdr_md{margin-right:16px;min-width:1px;}#gs_hdr_lgt,#gs_hdr_md h1{padding:19px 0 0 0;white-space:nowrap;overflow:hidden;text-overflow:ellipsis;font-size:20px;line-height:25px;font-weight:normal;color:#666;max-width:100%;text-align:left;}.gs_el_ta #gs_hdr_md h1,.gs_el_ph #gs_hdr_md h1{padding:16px 0 0 0;}#gs_hdr_srch{padding:14px 0 0 0;max-width:600px;}.gs_el_ta #gs_hdr_srch,.gs_el_ph #gs_hdr_srch{padding:10px 0 0 0;max-width:none;}#gs_hdr_frm{position:relative;padding-right:39px;}#gs_hdr_tsi{height:38px;border-radius:2px 0 0 2px;}#gs_hdr_tsi::-ms-clear{display:none;}#gs_hdr_tsc{display:none;position:absolute;top:3px;right:41px;width:21px;height:21px;padding:6px 10px 7px 10px;}.gs_in_acw[dir="rtl"]~#gs_hdr_tsc{right:auto;left:1px;}#gs_hdr_tsb{position:absolute;top:0;right:0;width:40px;height:38px;border-radius:0 2px 2px 0;}#gs_hdr_frm_ac{top:37px;right:40px;}.gs_el_ph #gs_hdr_frm_ac{right:0;}.gs_el_ph .gs_hdr_ifc #gs_hdr_mnu,.gs_el_ph .gs_hdr_ifc #gs_hdr_bck,.gs_hdr_src #gs_hdr_srch,.gs_hdr_src #gs_hdr_lgt,.gs_hdr_srx #gs_hdr_sre,.gs_hdr_srx #gs_hdr_md h1,.gs_hdr_srx #gs_hdr_md h1.gs_hdr_mbo,.gs_hdr_srx #gs_hdr_md h1.gs_hdr_dso,.gs_el_ta .gs_hdr_srx #gs_hdr_lgo,.gs_el_ph .gs_hdr_srx #gs_hdr_lgo,.gs_el_ph .gs_hdr_srx #gs_hdr_mnu,.gs_el_ph .gs_hdr_srx #gs_hdr_bck{display:none;}.gs_el_ph .gs_hdr_ifc #gs_hdr_md,.gs_el_ph .gs_hdr_srx #gs_hdr_md{margin-left:16px;}.gs_el_tc .gs_hdr_tsc #gs_hdr_tsi[dir="ltr"]{padding-right:41px;}.gs_el_tc .gs_hdr_tsc #gs_hdr_tsi[dir="rtl"]{padding-left:41px;}.gs_el_tc .gs_hdr_tsc .gs_in_acw~#gs_hdr_tsc{display:block;}#gs_hdr_act{min-width:64px;max-width:200px;text-align:right;float:right;}.gs_el_ta #gs_hdr_act,.gs_el_ph #gs_hdr_act{display:none;}#gs_hdr_act_i,#gs_hdr_act_s{display:inline-block;padding:23px 24px 23px 16px;max-width:100%;box-sizing:border-box;font-size:13px;line-height:17px;white-space:nowrap;overflow:hidden;text-overflow:ellipsis;color:#444;}#gs_hdr_act_s{text-transform:uppercase;}.gs_el_sm #gs_hdr_act_i,.gs_el_sm #gs_hdr_act_s{padding:23px 16px;}.gs_el_ta #gs_hdr_act_i,.gs_el_ta #gs_hdr_act_s,.gs_el_ph #gs_hdr_act_i,.gs_el_ph #gs_hdr_act_s{padding:20px 16px;}#gs_hdr_act_i:active,#gs_hdr_act_s:active{color:#d14836;}#gs_hdr_act_i,.gs_el_sm #gs_hdr_act_i{padding-top:15px;padding-bottom:16px;}.gs_el_ta #gs_hdr_act_i,.gs_el_ph #gs_hdr_act_i{padding-top:12px;padding-bottom:13px;}#gs_hdr_act_i .gs_hdr_pp{vertical-align:top;}#gs_hdr_act_d{top:63px;left:auto;right:24px;min-width:288px;max-width:400px;}.gs_el_sm #gs_hdr_act_d{right:16px;}.gs_el_ta #gs_hdr_act_d{top:57px;}.gs_el_ph #gs_hdr_act_d{top:57px;min-width:280px;max-width:280px;max-width:90vw;}/* Account dialog body. */#gs_hdr_act_aw,#gs_hdr_act_ap,.gs_hdr_act_am,#gs_hdr_act_ab{display:block;padding:10px 20px;word-wrap:break-word;white-space:normal;}#gs_hdr_act_aw{background-color:#fef9db;font-size:11px;}#gs_hdr_act_ap,.gs_hdr_act_am{border-bottom:1px solid #ccc;}#gs_hdr_act_ap{padding:20px;}.gs_el_ph #gs_hdr_act_ap{padding:10px;}#gs_hdr_act_apb{margin-top:12px;}#gs_hdr_act_aa:link,#gs_hdr_act_aa:visited{float:right;margin-left:8px;color:#1a0dab;}#gs_hdr_act_aa:active{color:#d14836}.gs_hdr_act_am:link,.gs_hdr_act_am:visited{color:#222;text-decoration:none;background:#fbfbfb;}.gs_hdr_act_am:hover,.gs_hdr_act_am:focus{background:#f1f1f1;}.gs_hdr_act_am:active{background:#eee;}#gs_hdr_act_ab{background:#fbfbfb;padding:10px 0;display:table;width:100%;white-space:nowrap;}#gs_hdr_act_aba,#gs_hdr_act_abs{display:table-cell;padding:0 20px;}#gs_hdr_act_abs{text-align:right;}.gs_el_ph #gs_hdr_act_aba,.gs_el_ph #gs_hdr_act_abs{display:block;padding:10px;text-align:center;}.gs_el_ph #gs_hdr_act_aba button,.gs_el_ph #gs_hdr_act_abs button{width:100%;}#gs_hdr_act_a1,#gs_hdr_act_a2{position:absolute;top:-9px;right:7.5px;width:0;height:0;z-index:1;border:8.5px solid transparent;border-top:none;border-bottom-color:#333;border-bottom-color:rgba(0,0,0,.2);}#gs_hdr_act_a2{top:-8px;border-bottom-color:#fff;}.gs_hdr_act_mw #gs_hdr_act_a2{border-bottom-color:#fef9db;}.gs_hdr_pp{border-radius:50%;overflow:hidden;}#gs_hdr_act_ap .gs_hdr_pp,.gs_hdr_act_am .gs_hdr_pp{float:left;}#gs_hdr_act_ap .gs_hdr_pm{margin-left:116px;}.gs_hdr_act_am .gs_hdr_pm{margin:6px 0 0 58px;}#gs_ab{position:relative;height:41px;border-bottom:1px solid #e5e5e5;display:flex;white-space:nowrap;background-color:#fff;z-index:1000;}.gs_el_ta #gs_ab.gs_nta,.gs_el_ph #gs_ab.gs_nph{display:none;}.gs_sth_vis #gs_ab{position:fixed;}#gs_ab_ico,#gs_ab_ttl,#gs_ab_md,#gs_ab_btns{display:inline-block;vertical-align:top;position:relative;height:100%;flex:0 0 auto;}.gs_el_ph #gs_ab_md{display:block;}#gs_ab_ico{width:55px;margin-right:1px;}#gs_ab_ico .gs_ico{position:absolute;top:50%;left:50%;margin:-10.5px 0 0 -10.5px;}#gs_ab_ttl{min-width:172px;padding-right:8px;}.gs_el_sm #gs_ab_ttl{min-width:68px;}.gs_el_ta #gs_ab_ttl,.gs_el_ph #gs_ab_ttl{min-width:0;}#gs_ab_ttl,#gs_ab_ttll{font-size:18px;color:#666;text-transform:none;}.gs_el_sm #gs_ab_ttl,.gs_el_sm #gs_ab_ttll{font-size:16px;}#gs_ab_ttll{overflow:hidden;text-overflow:ellipsis;max-width:200px;}#gs_ab_md{flex:1 0 auto;}.gs_ab_st #gs_ab_md{flex:1 1 auto;font-size:13px;line-height:17px;padding:0 8px;color:#999;overflow:hidden;text-overflow:ellipsis;}.gs_el_ph .gs_ab_st #gs_ab_md{visibility:hidden;padding:0;}#gs_ab_btns{margin-right:8px;}.gs_el_sm #gs_ab_btns{margin-right:0;}.gs_el_ta #gs_ab_btns,.gs_el_ph #gs_ab_btns{margin-right:4px;}#gs_ab_ttl:before,#gs_ab_md:before,#gs_ab_btns:before{content:"";display:inline-block;width:0;height:100%;vertical-align:middle;}#gs_ab_md>button,#gs_ab_btns>button,#gs_ab_md>.gs_in_ib,#gs_ab_btns>.gs_in_ib,#gs_ab_md>.gs_md_r,#gs_ab_btns>.gs_md_r,#gs_ab .gs_ab_mdw,#gs_ab .gs_ab_btw{margin:0 8px;vertical-align:middle;}#gs_ab .gs_ab_mdw,.gs_ab_btw{display:inline-block;margin:0;}#gs_ab_btns>.gs_in_ib{margin:0 16px 0 8px;}#gs_ab .gs_ab_btw{margin:0 12px 0 16px;}.gs_el_ta .gs_ab_sel #gs_ab_ico,.gs_el_ph .gs_ab_sel #gs_ab_ico,.gs_el_ta .gs_ab_sel #gs_ab_ttl,.gs_el_ph .gs_ab_sel #gs_ab_ttl,.gs_el_ta .gs_ab_sel #gs_ab_btns,.gs_el_ph .gs_ab_sel #gs_ab_btns{display:none;}#gs_bdy{display:table;table-layout:fixed;width:100%;}#gs_bdy_sb{vertical-align:top;width:228px;word-wrap:break-word;display:table-cell;}.gs_el_sm #gs_bdy_sb{}.gs_el_ta #gs_bdy_sb,.gs_el_ph #gs_bdy_sb{display:none;}.gs_bdy_sb_sec{margin:0 40px 0 56px;}.gs_bdy_sb_sec:before{display:block;content:" ";height:0;margin:13px 0;border-top:1px solid #eee;}.gs_bdy_sb_sec:first-child:before{margin:21px 0 0 0;border:none;}#gs_bdy_sb ul{list-style-type:none;}.gs_bdy_sb_sec a:link,.gs_bdy_sb_sec a:visited{color:#222;}.gs_bdy_sb_sec a:active{color:#d14836;}.gs_bdy_sb_sel a:link,.gs_bdy_sb_sel a:visited{color:#d14836;text-decoration:none;}.gs_el_tc .gs_bdy_sb_sec li.gs_ind,.gs_el_tc .gs_bdy_sb_sec li.gs_ind a{padding-top:8px;padding-bottom:5px;}.gs_el_tc .gs_bdy_sb_sec:first-child li.gs_ind:first-child{margin-top:-8px;}#gs_bdy_sb .gs_ind,#gs_bdy_sb .gs_inw{margin-bottom:6px;}.gs_el_tc #gs_bdy_sb .gs_ind,.gs_el_tc #gs_bdy_sb .gs_inw{margin-bottom:0;}#gs_bdy_ccl{display:table-cell;vertical-align:top;padding:0 24px 0 16px;}.gs_el_sm #gs_bdy_ccl{padding:0 16px;}.gs_el_ta #gs_bdy_ccl,.gs_el_ph #gs_bdy_ccl{padding:0 16px 0 56px;}.gs_el_ph #gs_bdy_ccl{padding:0 16px;padding:0;}#gs_ftr_sp{height:62px;}.gs_el_sm #gs_ftr_sp{height:57px;}#gs_ftr{position:absolute;bottom:0;left:0;width:100%;white-space:nowrap;border-top:1px solid #e4e4e4;background-color:#f2f2f2;display:flex;}#gs_ftr.gs_pfix{position:fixed;}#gs_ftr_rt{box-sizing:border-box;max-width:100%;overflow-x:auto;margin-left:auto;padding:0 12px;}.gs_el_sm #gs_ftr_rt{padding:0 8px;}.gs_el_ph #gs_ftr_rt:after{content:" ";position:absolute;top:0;right:0;width:16px;height:100%;background-image:linear-gradient(to right,rgba(242,242,242,0),rgba(242,242,242,1) 80%);}#gs_ftr_rt>a{display:inline-block;line-height:16px;padding:12px;white-space:nowrap;}.gs_el_sm #gs_ftr_rt>a{padding:12px 8px;}#gs_ftr_rt>a:link,#gs_ftr_rt>a:visited{color:#666}#gs_ftr_rt>a:active{color:#d14836}#gs_ftr_mnu{top:auto;bottom:48px;left:auto;right:24px;padding:8px 0;}.gs_el_sm #gs_ftr_mnu{right:16px;}#gsc_sb_ui{text-align:center;margin-bottom:16px;}#gsc_sb_ui img{max-width:120px;height:auto;}.gs_el_sm #gsc_sb_ui img{max-width:100px;}.gsc_sb_addl{text-align:right;padding:0 8px;color:#777777;min-width:60px;}#gsc_ccl{max-width:862px;margin:21px 0 0 0;}.gs_el_sm #gsc_ccl{margin:16px 0 0 0;}.gsc_art_mm{font-size:24px;line-height:16px;display:inline-block;margin:-10px 0 0 4px;position:relative;top:8px;}.gs_pp_tn,.gs_el_ta .gs_pp_mo_tn,.gs_el_ph .gs_pp_mo_tn{width:32px;height:32px;}.gs_pp_sm,.gs_el_ta .gs_pp_mo_sm,.gs_el_ph .gs_pp_mo_sm{width:56px;height:56px;}.gs_pp_nm,.gs_el_ta .gs_pp_mo_nm,.gs_el_ph .gs_pp_mo_nm{width:128px;height:128px;}#gsc_vcpb{max-width:870px;padding-top:21px;}.gs_el_ph #gsc_vcpb{padding:16px 8px;}#gsc_vcpb_btns{padding-bottom:16px;}#gsc_vcpb_btns:empty{display:none;}#gsc_vcpb_btns>button{margin-right:16px;}.gs_el_ph #gsc_vcpb_btns>button{margin-right:8px;}#gsc_oci_title_wrapper{font-size:16px;margin:0 0 16px 0;}#gsc_oci_title{font-size:20px;}.gs_el_sm #gsc_oci_title{font-size:18px;}#gsc_oci_title_gg{float:right;padding:0 0 8px 16px;}.gs_el_ph #gsc_oci_title_gg{float:none;text-align:right;padding:0;margin:-4px 0 8px 0;}.gsc_oci_title_ggt{font-size:13px;font-weight:bold;}.gsc_oci_title_ggut{font-size:13px;color:#777;padding-bottom:8px;}.gsc_oci_field{float:left;width:100px;text-align:right;color:#777;}.gs_el_ph .gsc_oci_field{float:none;width:auto;text-align:left;margin-bottom:4px;font-size:16px;color:black;}.gsc_oci_value{margin-left:116px;max-width:512px;margin-bottom:16px;}.gs_el_ph .gsc_oci_value{margin-left:0;}.gsc_oci_merged_snippet{margin-bottom:1em;}#gsc_oci_graph_wrapper{height:100px;overflow-x:auto;overflow-y:hidden;direction:rtl;}#gsc_oci_graph{position:relative;min-width:100%;}#gsc_oci_graph_x{position:absolute;top:57px;left:0;width:100%;height:13px;border-top:1px solid #777;}.gsc_oci_g_t{position:absolute;top:60px;color:#777;font-size:11px;}#gsc_oci_graph_bars{position:absolute;top:0;right:0;width:100%;height:100px;}.gsc_oci_g_a{position:absolute;bottom:13px;width:15px;background:#777;}.gsc_oci_g_a:hover{background:#1a0dab;text-decoration:none;}.gsc_oci_g_a:active{background:#d14836;}.gsc_oci_g_al{position:absolute;bottom:15px;left:7px;color:#222;background:white;text-align:center;font-size:11px;min-width:11px;padding:1px;border:1px solid #777;border-radius:1px;visibility:hidden;opacity:0;}.gsc_oci_g_a:hover .gsc_oci_g_al{visibility:visible;opacity:1;}.gsc_oci_g_a{transition:all .218s;}.gsc_oci_g_al{transition:opacity .218s,visibility 0s .218s;}.gsc_oci_g_a:hover,.gsc_oci_g_a:hover .gsc_oci_g_al{transition:all 0s;}a.gsc_oci_lbx:link,a.gsc_oci_lbx:visited{white-space:nowrap;display:inline-block;vertical-align:middle;font-size:11px;background-color:#e5e5e5;color:#777;padding:2px 6px;text-decoration:none;}a.gsc_oci_lbx:hover{color:#e5e5e5;background-color:#777;}a.gsc_oci_lbx:active{color:#d14836;}.gsc_oms_mm{font-size:24px;line-height:16px;display:inline-block;margin:-10px 0 0 4px;position:relative;top:8px;}.gsc_oms_link{white-space:nowrap;margin-right:12px;}.gsc_oms_link:last-child{margin-right:0;}.gs_fsvg line{stroke:#222222}a:link .gs_fsvg{fill:#1a0dab;}a:link .gs_fsvg line{stroke:#1a0dab;}a:visited .gs_fsvg{fill:#660099;}a:visited .gs_fsvg line{stroke:#660099;}a:active .gs_fsvg{fill:#d14836;}a:active .gs_fsvg line{stroke:#d14836;}a .gs_fsvg{border-bottom:1px solid transparent;}a:hover .gs_fsvg,a:focus .gs_fsvg{border-bottom-color:inherit;}.gs_fsml{font-size:13px}.gs_fscp{font-variant:small-caps}.gsh_clim{display:table-row}.gsh_clil,.gsh_clic{display:table-cell;padding-bottom:8px}.gsh_clil{padding-right:8px;}.gsh_lla{list-style-type:lower-alpha}.gsh_lua{list-style-type:upper-alpha}.gsh_llr{list-style-type:lower-roman}.gsh_lur{list-style-type:upper-roman}.gsh_l>li{margin-left:32px;}.gs_fma .gsh_l>li{margin-left:16px;}.gsh_h3{font-size:inherit;font-weight:normal}.gsh_h3,.gsh_csp{margin:16px 0}.gsh_h3+.gsh_csp{margin-top:-8px}.gs_fma .gsh_h3{margin:12px 0 0 0;font-size:15px;font-weight:bold;}.gs_fma_abs .gsh_csp{margin:0 0 12px 0;}.gs_fma b,.gs_fma .gsh_h3{color:#444;}.gs_fma .gsh_h3+.gsh_csp{margin:4px 0 0 0;}.gs_fma .gsh_csp:last-child,.gs_fma .gsh_h3.gsh_flh{margin:0;}.gs_fma ul .gsh_clim:last-child .gsh_clic{padding-bottom:0;}.gs_fma ul,.gs_fma ol{margin:12px 0;}.gsh_ovln{text-decoration:overline}.gsh_small .gsh_l .gsh_csp{margin:8px 0}.gsh_small .gsh_csp:first-child,.gsh_small .gsh_h3.gsh_flh{margin-top:0}.gsh_small .gsh_csp:last-child{margin-bottom:0}.gsh_dspfr{text-align:center}.gsh_dspfr svg{margin:8px 0}</style><script>!function(GSP){var aa=function(a){var b=0;return function(){return b<a.length?{done:!1,value:a[b++]}:{done:!0}}},ba=typeof Object.defineProperties=="function"?Object.defineProperty:function(a,b,c){if(a==Array.prototype||a==Object.prototype)return a;a[b]=c.value;return a},ca=function(a){a=["object"==typeof globalThis&&globalThis,a,"object"==typeof window&&window,"object"==typeof self&&self,"object"==typeof global&&global];for(var b=0;b<a.length;++b){var c=a[b];if(c&&c.Math==Math)return c}throw Error("Cannot find global object"); },da=ca(this),h=function(a,b){if(b)a:{var c=da;a=a.split(".");for(var d=0;d<a.length-1;d++){var e=a[d];if(!(e in c))break a;c=c[e]}a=a[a.length-1];d=c[a];b=b(d);b!=d&&b!=null&&ba(c,a,{configurable:!0,writable:!0,value:b})}}; h("Symbol",function(a){if(a)return a;var b=function(f,g){this.ba=f;ba(this,"description",{configurable:!0,writable:!0,value:g})};b.prototype.toString=function(){return this.ba};var c="jscomp_symbol_"+(Math.random()*1E9>>>0)+"_",d=0,e=function(f){if(this instanceof e)throw new TypeError("Symbol is not a constructor");return new b(c+(f||"")+"_"+d++,f)};return e});var ea=typeof Object.create=="function"?Object.create:function(a){var b=function(){};b.prototype=a;return new b},fa; if(typeof Object.setPrototypeOf=="function")fa=Object.setPrototypeOf;else{var ha;a:{var ia={a:!0},ka={};try{ka.__proto__=ia;ha=ka.a;break a}catch(a){}ha=!1}fa=ha?function(a,b){a.__proto__=b;if(a.__proto__!==b)throw new TypeError(a+" is not extensible");return a}:null} var la=fa,ma=function(a,b){a.prototype=ea(b.prototype);a.prototype.constructor=a;if(la)la(a,b);else for(var c in b)if(c!="prototype")if(Object.defineProperties){var d=Object.getOwnPropertyDescriptor(b,c);d&&Object.defineProperty(a,c,d)}else a[c]=b[c];a.qa=b.prototype};h("Symbol.dispose",function(a){return a?a:Symbol("Symbol.dispose")}); h("Math.trunc",function(a){return a?a:function(b){b=Number(b);if(isNaN(b)||b===Infinity||b===-Infinity||b===0)return b;var c=Math.floor(Math.abs(b));return b<0?-c:c}});var na=function(a){a=Math.trunc(a)||0;a<0&&(a+=this.length);if(!(a<0||a>=this.length))return this[a]};h("Array.prototype.at",function(a){return a?a:na});var n=function(a){return a?a:na};h("Int8Array.prototype.at",n);h("Uint8Array.prototype.at",n);h("Uint8ClampedArray.prototype.at",n);h("Int16Array.prototype.at",n); h("Uint16Array.prototype.at",n);h("Int32Array.prototype.at",n);h("Uint32Array.prototype.at",n);h("Float32Array.prototype.at",n);h("Float64Array.prototype.at",n);h("String.prototype.at",function(a){return a?a:na});/* Copyright The Closure Library Authors. SPDX-License-Identifier: Apache-2.0 */ var oa=function(a,b){var c=Array.prototype.slice.call(arguments,1);return function(){var d=c.slice();d.push.apply(d,arguments);return a.apply(this,d)}};var t=function(){this.C=this.C;this.H=this.H};t.prototype.C=!1;t.prototype.isDisposed=function(){return this.C};t.prototype.dispose=function(){this.C||(this.C=!0,this.K())};t.prototype[Symbol.dispose]=function(){this.dispose()};t.prototype.K=function(){if(this.H)for(;this.H.length;)this.H.shift()()};var pa=function(){};function u(a,b){a.classList.add(b)}function v(a,b){a.classList.remove(b)}function w(a,b){return a.classList?a.classList.contains(b):!1}function x(a,b,c){c=c!==void 0?c:!w(a,b);(c?u:v)(a,b)};function z(a){return(navigator.userAgent||"").indexOf(a)>=0}var qa=z("iPhone")||z("iPad")||z("iPod"),ra=z("iPhone")||z("Android")&&z("Mobile");function sa(){if(b===void 0){var a=window.screen;a={width:window.innerWidth,height:window.innerHeight,pa:a.width,oa:a.height}}else a=b;var b=a;a=b.width;var c=b.height,d=b.pa;b=b.oa;var e=4;if(a<600||d*b<48E4||ra)e=1;else if(a<982)e=2;else if(a<1136||c<590)e=3;return e}var ta,ua=/[?&]tc=([01])/.exec(location.search||""); ta=ua?+ua[1]>0:z("Android")?!0:window.matchMedia&&window.matchMedia("(pointer)").matches?window.matchMedia("(pointer:coarse)").matches:!z("Firefox")||z("Mobile")||z("Tablet")?qa||"ontouchstart"in window||(navigator.msMaxTouchPoints||0)>0:!1;function va(){if(wa==void 0){wa=!1;try{var a=Object.defineProperty({},"passive",{get:function(){wa=!0}});window.addEventListener("testPassive",pa,a);window.removeEventListener("testPassive",pa,a)}catch(b){}}return wa}var wa;var xa=new function(){this.aa="INPUT"};function D(a){return document.getElementById(a)}function E(a){return a.id||(a.id="gs_id"+ya++)}function za(a){a=(a===void 0?null:a)||document.body;return(a?window.getComputedStyle(a,null):null).direction=="rtl"}function Aa(a){var b=[];a=a.elements;for(var c=a.length,d=0;d<c;d++){var e=a[d],f=encodeURIComponent(e.name||""),g=e.type;!f||e.disabled||!(g!="checkbox"&&g!="radio"||e.checked)||b.push(f+"="+encodeURIComponent(e.value||""))}return b.join("&")} function Ba(a,b){var c=a.elements[b];c||(c=document.createElement(xa.aa),c.type="hidden",c.name=b,a.appendChild(c));return c}var ya=100,Ca=/\S+/g,Da=/^(?:https?:|[^:/?#]*(?:[/?#]|$))/i,Ea=/^(?:#|\/[a-z0-9_-]*(?:[?].*)?$)/i;function F(a){return a.hasOwnProperty("gs_uid")?a.gs_uid:a.gs_uid=++Ga}var Ga=0;var G=function(){this.o=[];this.F={};this.S=this.I=0};G.prototype.add=function(a){var b=F(a);this.F[b]||(this.o.push(a),this.F[b]=this.o.length,++this.I)};G.prototype.remove=function(a){a=F(a);var b=this.F[a];b&&(this.o[b-1]=null,delete this.F[a],--this.I*2<this.o.length&&!this.S&&Ha(this))};G.prototype.notify=function(a){var b=this.o;try{++this.S;for(var c=0;c<b.length;c++){var d=b[c];d&&d.apply(null,arguments)}}finally{!--this.S&&this.I*2<b.length&&Ha(this)}};G.prototype.getSize=function(){return this.I}; var Ha=function(a){var b=a.o,c=b.length;a=a.F;for(var d=0,e=0;e<c;e++){var f=b[e];f&&(b[d]=f,a[F(f)]=++d)}b.length=d};function H(a,b,c,d,e){Ia(a,b,c,d===void 0?!1:d,e===void 0?!1:e,Ja)}function I(a,b,c,d){Ia(a,b,c,d===void 0?!1:d,!1,Ka)}function La(a,b,c,d){function e(g){I(f,a,e,c);b(g)}var f=document;c=c===void 0?!1:c;H(f,a,e,c,d===void 0?!1:d)}function Ma(a){Na?Na.add(a):a()}var Oa=window.requestAnimationFrame?function(a){window.requestAnimationFrame(a)}:function(a){setTimeout(function(){return a(window.performance&&performance.now?performance.now():Date.now())},33)}; function Pa(a){a.stopPropagation();a.preventDefault()}function Qa(a){return(a.ctrlKey?1:0)|(a.altKey?2:0)|(a.metaKey?4:0)|(a.shiftKey?8:0)}function Ja(a,b,c,d,e){var f=a.addEventListener;e=e&&va();f.call(a,b,c,e?{passive:e,capture:d}:d)}function Ka(a,b,c,d){a.removeEventListener(b,c,d)}function Ia(a,b,c,d,e,f){if(typeof b==="string")f(a,b,c,d,e);else for(var g=b.length,m=0;m<g;m++)f(a,b[m],c,d,e)}function Ra(){Na.notify();Na=null} function Sa(){document.readyState=="complete"&&(I(document,"readystatechange",Sa),Ra())}var Na,Ta=!!document.attachEvent,Ua=document.readyState;if(Ta?Ua!="complete":Ua=="loading")Na=new G,Ta?H(document,"readystatechange",Sa):La("DOMContentLoaded",Ra);function Va(){La(["mousedown","touchstart"],function(){x(document.documentElement,"gs_pfcs",!0);H(document,"keydown",Wa,!0)},!0,!0)}function Wa(a){a.keyCode==9&&(x(document.documentElement,"gs_pfcs",!1),I(document,"keydown",Wa,!0),Va())}Va();function Xa(a,b,c,d,e){var f=D(a);Ya(f,function(){u(f,"gs_vis");b&&b()},function(){v(f,"gs_vis");c&&c()},d,e)}function Za(a){a=J[a]||[0];return a[a.length-1]} function Ya(a,b,c,d,e,f){f=f===void 0?"":f;var g=E(a),m=Za(g);if(!m||m<Za(f)){var k=document.activeElement;f=D(f);$a(ab(f||a),!0);b&&b();K.push(function(l){J[g].pop();J[g].length||delete J[g];if(!l){(l=e)||k==document.body||(l=k);var p=document.activeElement;if(l)try{l.focus()}catch(A){}else p&&a.contains(p)&&p.blur()}c&&c()});J[g]||(J[g]=[]);J[g].push(K.length);k&&a.contains(k)||setTimeout(function(){var l=d,p=l&&l.type=="text";if(!l||p&&ta)l=a;try{l.focus(),p&&(l.value=l.value)}catch(A){}},0)}} function L(a){$a((Za(a)||1E6)-1,!1)}function bb(a){a=a===void 0?!1:a;K.pop()(a)}function $a(a,b){for(b=b===void 0?!1:b;K.length>a;)bb(b||K.length>a+1)}function ab(a){for(var b=0;a&&!(b=Za(a.id));)a=a.parentNode;return b}var K=[],J={};H(document,"click",function(a){var b=K.length;b&&!Qa(a)&&b>ab(a.target)&&bb(!0)});H(document,"keydown",function(a){a.keyCode==27&&!Qa(a)&&K.length&&bb()}); H(document,"focus",function(a){var b=K.length;if(b)for(var c=ab(a.target);c<b;){var d="",e;for(e in J)if(Za(e)==b){d=e;break}a:{d=(D(d).getAttribute("data-wfc")||"").match(Ca)||[];for(var f=0;f<d.length;f++){var g=D(d[f]);if(g&&g.offsetWidth){d=g;break a}}d=void 0}if(d){Pa(a);d.focus();break}else bb(!0),--b}},!0);var cb={},db={},eb;try{eb=window.sessionStorage}catch(a){};function M(a){return typeof a=="object"?a:null}function fb(){var a=gb(),b=hb();b=ib(b);a=jb(a);a=kb(a)||"#";N=M(b);lb?window.history.replaceState(b,"",a):window.location.replace(a)}function kb(a){var b=[],c;for(c in a)b.push(encodeURIComponent(c)+"="+encodeURIComponent(a[c]));return(a=b.sort().join("&"))?"#"+a:""} function mb(a){var b={};a=a.split("&");for(var c=0;c<a.length;c++){var d=a[c],e=d.indexOf("=");if(e+1){var f=d.substr(0,e);d=d.substr(e+1)}else f=d,d="";f&&(b[decodeURIComponent(f)]=decodeURIComponent(d))}return b}function nb(){var a=window.location.hash,b=a.indexOf("#")+1;return mb(b?a.substr(b):"")}function ob(a,b){for(var c in b){var d=b[c];d!==void 0?a[c]=d:delete a[c]}}function jb(a){var b=nb();ob(b,a);return b} function ib(a){var b=N||M(window.history.state),c={},d;for(d in b)c[d]=b[d];ob(c,a);return c}function pb(){setTimeout(function(){if(!qb){var a=window.history.state;qb=!0;N=M(a);rb.notify()}sb=!1},0)}var rb=new G,N,qb=!1,sb=!0,lb="pushState"in window.history,tb; if(typeof GSP=="undefined")tb=!1;else{var ub=.001*Date.now(),vb=GSP.eventId,wb=!1,O,xb=eb;if(!("nh"in cb)){var yb=xb&&xb.getItem("nh"),zb;if(yb)try{zb=JSON.parse(yb)}catch(a){}db.nh=zb}O=db.nh;O instanceof Array||(O=[]);for(var Ab=O.length,Bb=0,Cb=0;Cb<Ab;Cb++){var Db=O[Cb];if(Db instanceof Array&&Db.length==2){var Eb=Db[1]==vb;wb=wb||Eb;Ab-Cb<=10&&+Db[0]>ub-86400&&!Eb&&(O[Bb++]=Db)}}O.length=Bb;O.push([ub,vb]);var Fb=O,Gb=eb;db.nh=Fb;try{Gb&&Gb.setItem("nh",JSON.stringify(Fb))}catch(a){}tb=wb} var Hb=tb;"onpageshow"in window?H(window,"pageshow",pb):Ma(pb);H(window,lb?"popstate":"hashchange",function(a){document.readyState!="loading"&&(a=a.state,qb=!0,N=M(a),rb.notify())});function Ib(){Jb&&(I(D("gs_alrt_l"),"click",Jb),Jb=void 0)}function Kb(){var a=Lb();u(a,"gs_anm");u(a,"gs_vis");H(document,"click",Mb);clearTimeout(Nb);Nb=setTimeout(Mb,4E3);++Ob;setTimeout(Pb,0)}function Mb(){Ob||(I(document,"click",Mb),clearTimeout(Nb),Nb=void 0,Ib(),v(Lb(),"gs_vis"))}function Lb(){return D("gs_alrt")}function Pb(){Ob=0}var Nb,Ob=0,Jb;Ma(function(){var a=D("gs_alrt_m");a&&(a.innerHTML&&!Hb&&Kb(),H(window,"pagehide",function(){Ob=0;Mb();v(Lb(),"gs_anm")}))});function Qb(a,b,c){var d=new XMLHttpRequest;d.onreadystatechange=function(){if(d.readyState==4){var e=d.status,f=d.responseText,g=d.getResponseHeader("Content-Type"),m=d.responseURL,k=window.location,l=k.protocol;k="//"+k.host+"/";m&&m.indexOf(l+k)&&m.indexOf("https:"+k)&&(e=0,g=f="");c(e,f,g||"")}};d.open(b?"POST":"GET",a,!0);d.setRequestHeader("X-Requested-With","XHR");b&&d.setRequestHeader("Content-Type","application/x-www-form-urlencoded");b?d.send(b):d.send();return d} function Rb(a){a&&(a.onreadystatechange=function(){},a.abort())};var Sb=function(a,b,c){this.type=a;this.currentTarget=this.target=b;this.i=c===void 0?null:c;this.U=!1};Sb.prototype.stopPropagation=function(){this.i&&this.i.stopPropagation();this.U=!0};var P=function(a){a.i&&Pa(a.i);a.U=!0};var Q=function(a,b){this.V=a;this.na=b},Tb=function(a,b,c){this.V=a;this.types=b;this.listener=c};function Ub(a,b){var c=b.length;if(c){var d=F(a),e=Vb[d];if(!e){e=Vb[d]=[];d=Wb(b[0].V);for(var f in d){var g=Xb[f];g||(g=Xb[f]=Object.create(null));for(var m in d[f]){var k=g[m];k||(k=g[m]=[]);k.push(a)}}Yb(a,e,b[0],Zb);for(f=1;f<c;f++)Yb(a,e,b[f],$b)}}}function S(a,b,c){ac(new Sb(a,b,c===void 0?null:c))} function T(a,b,c){var d=bc;typeof b==="string"&&(cc[0]=b,b=cc);var e=b.length;a=Wb(a);for(var f in a)for(var g in a[f])for(var m=0;m<e;m++)d(f,g,b[m],c)}function Wb(a){typeof a==="string"&&(dc[0]=a,a=dc);for(var b=a.length,c=Object.create(null),d=0;d<b;d++){var e=a[d],f=e.charAt(0),g=e.substr(1);if(f!="#"&&f!="."||!g)throw Error("bad selector: "+e);(e=c[f])||(e=c[f]=Object.create(null));e[g]=!0}return c} function bc(a,b,c,d){var e=ec[c];e||(c!="touchstart"&&c!="mouseover"&&c!="mouseout"&&H(document,c,fc,c=="focus"||c=="blur"),e=ec[c]=Object.create(null));(c=e[a])||(c=e[a]=Object.create(null));(a=c[b])||(a=c[b]=new G);a.add(d)}function fc(a){var b=a.target;b&&b.nodeType==3&&(b=b.parentNode);ac(new Sb(a.type,b,a))} function ac(a){for(var b=a.target;b&&b!=document&&!b.disabled&&!w(b,"gs_dis");){a.currentTarget=b;var c=b.id;if(c&&!gc("#",c,a))break;c=b.classList||[];for(var d=c.length,e=0;e<d;e++)if(!gc(".",c[e],a))return;b=b.parentNode}}function gc(a,b,c){var d=ec[c.type];(b=(a=d&&d[a])&&a[b])&&b.notify(c);return!c.U}function Yb(a,b,c,d){var e=c.V;c=c.na;for(var f in c){var g=oa(d,a,c[f]);T(e,f,g);b.push(new Tb(e,f,g))}}function Zb(a,b,c){var d=c.currentTarget;a=hc(a,d)||a;a=ic(a,d);b.call(a,c)} function $b(a,b,c){a:{for(var d=c.currentTarget;d&&d!=document;){var e=hc(a,d);if(e){a=ic(e,d);break a}d=d.parentNode}a=void 0}a&&b.call(a,c)}function ic(a,b){var c=jc(b),d=kc[c];d||(d=kc[c]=[]);for(var e=d.length,f=0;f<e;f++){var g=d[f];if(g instanceof a)return g}b=new a(b);d.push(b);a=F(a);(d=lc[a])||(d=lc[a]=[]);d.push(c);return b}function hc(a,b){var c,d=b.id;d&&(c=mc(a,c,"#",d));b=b.classList||[];d=b.length;for(var e=0;e<d;e++)c=mc(a,c,".",b[e]);return c} function mc(a,b,c,d){c=(d=(c=Xb[c])&&c[d])?d.length:0;for(var e=0;e<c;e++){var f=d[e];!(f===a||f.prototype instanceof a)||b&&!(f===b||f.prototype instanceof b)||(b=f)}return b}function jc(a){var b=a.getAttribute("data-duid");b||a.setAttribute("data-duid",b=""+nc++);return b}var ec=Object.create(null),dc=[""],cc=[""],Xb=Object.create(null),Vb=Object.create(null),lc=Object.create(null),kc=Object.create(null),nc=100;window.gs_evt_dsp=fc;function oc(){var a=".gs_md_li";if(typeof a==="string"){var b=a.charAt(0),c=a.slice(1);if(b=="#")a=function(d){return d.id==c&&d.offsetWidth>0};else if(b==".")a=function(d){return w(d,c)&&d.offsetWidth>0};else throw Error("bad selector: "+a);}return a}function pc(a,b){return a&&((b===void 0?0:b)?a.lastElementChild:a.firstElementChild)}function qc(a,b){return a&&((b===void 0?0:b)?a.previousElementSibling:a.nextElementSibling)}function rc(a,b,c){c=c===void 0?!1:c;return sc(a,b,oc(),c,!1)} function sc(a,b,c,d,e){for(var f;b&&a;){if(c(b)){if(e)return b}else for(f=pc(b,d);f;f=qc(f,d))if(e=sc(f,f,c,d,!0))return e;for(e=!0;;){if(b==a)return null;f=b.parentNode;if(b=qc(b,d))break;b=f}}return null};var tc=["false","true","mixed"];var U=function(){this.D=Object.create(null)};U.prototype.clear=function(){this.D=Object.create(null)};U.prototype.has=function(a){return a in this.D};U.prototype.get=function(a){return this.D[a]};U.prototype.set=function(a,b){this.has(a);this.D[a]=b};U.prototype.delete=function(a){this.has(a)&&delete this.D[a]};var uc=function(a){var b=window,c=this;this.o=new G;this.Y=0;this.W=[b,a,function(){c.Y++||Oa(d)},!1];var d=function(){c.Y=0;c.o.notify()}};uc.prototype.addListener=function(a){this.o.getSize()||H.apply(null,this.W);this.o.add(a)};uc.prototype.removeListener=function(a){this.o.remove(a);this.o.getSize()||I.apply(null,this.W)};var vc=new uc("scroll"),wc=new uc("resize");var xc=new G;function yc(){var a=document.documentElement,b=sa();b={gs_el_ph:b==1,gs_el_ta:b==2,gs_el_sm:b!=4,gs_el_tc:ta||b==1};var c;for(c in b){var d=b[c];if(w(a,c)!=d){var e=!0;x(a,c,d)}}e&&xc.notify()}x(document.documentElement,"gs_el_ios",qa);yc();wc.addListener(yc);H(window,["pageshow","load"],yc);var zc=function(a,b,c,d,e,f){this.g=a;this.B=b;this.v=c;this.A=d;this.T=e;this.s=f;this.m=null},Ac=function(a,b){a.m=b},Bc=function(){this.l=[];this.j=-1};Bc.prototype.push=function(a){++this.j;this.j==this.l.length?this.l.push(a):(this.l[this.j]=a,this.l.splice(this.j+1,this.l.length-this.j))};Bc.prototype.pop=function(){--this.j};var Ec=function(a){for(var b=W;b.j>a;)L(b.top().g)},Fc=function(a,b){for(var c=0;c<a.l.length&&!(a.l[c].s>=b);++c);return c};Bc.prototype.top=function(){return this.at(this.j)}; Bc.prototype.at=function(a){return this.l[a]||null};function Gc(a,b){var c=a==W.j;W.j=a;b&&!N&&!M(window.history.state)&&fb();c||Hc()}function Ic(a,b){b=b===void 0?"":b;var c=c===void 0?"":c;var d=d===void 0?"":d;var e=W.top();e&&a==e.g&&b==e.B&&c==e.v||(W.push(new zc(a,b,c,d,e&&e.g==a?e.T+1:1,Date.now())),b=gb(),a=hb(),a=ib(a),b=jb(b),b=kb(b)||"#",N=M(a),lb?window.history.pushState(a,"",b):window.location.assign(b),Hc())} function Jc(a){a=Kc(D(a));return!!a&&w(a,"gs_md_wmw")&&w(document.documentElement,"gs_el_ph")}function Lc(){var a=D("gs_top"),b=document.documentElement;a=a.scrollHeight>b.clientHeight;for(var c=!1,d=0;d<=W.j&&!c;++d)c=!Jc(W.at(d).g);x(D("gs_md_s"),"gs_vis",c);c=W.j;c>=1&&(c=W.at(c-1).g,d=Jc(c),x(D(c),"gs_md_ins_vis",!d));b.style.overflowY=a&&!Jc(W.top().g)?"scroll":""} function Hc(){function a(){var y=c.clientHeight,q=+B.getAttribute("data-h");q||(g.style.maxHeight="none",q=f.offsetHeight);var r=f.querySelector(".gs_md_ftr");q=Math.max((y-q)/2,10);y=Math.max(y-48-(r?r.offsetHeight:0)-2*q,10);r=Jc(e);f.style.top=r?"auto":q+"px";g.style.maxHeight=r?"none":y+"px";Mc(g)}var b=W.top(),c=document.documentElement,d=D("gs_top"),e=b.g,f=D(e),g=D(e+"-bdy"),m=1200+W.j,k=D(f.getAttribute("data-cid")||f.id+"-bdy")||f,l=b.A,p=b.v,A=b.B,C=D("gs_md_s"),V=D(e).getAttribute("data-shd")|| "",B=Kc(f),R=window.pageYOffset,Cc=A&&A[0]!="#"&&!l,Dc=W.j>0?W.at(W.j-1).g:"",ja=!!J[e];Cc?(ja?x(k,"gs_md_ldg",!0):Nc(f,k,'<div class="gs_md_prg">'+D("gs_md_ldg").innerHTML+"</div>",b),S("gs-md-ldin",k)):(l&&Nc(f,k,l,b),S("gs-md-lded",k));ja&&e==Dc||Ya(f,function(){(B||f).style.zIndex=m;Oc(V);if(!ja){B&&u(B,"gs_vis");u(f,"gs_vis");x(f,"gs_abt",sb);x(C,"gs_abt",sb);Pc(e);if(W.j==0){var y=Lc;xc.add(y);y()}else Lc();B&&g&&(a(),wc.addListener(a))}W.j==0&&(u(d,"gs_nscl"),d.style.top=-R+"px")},function(){ja|| (wc.removeListener(a),B&&v(B,"gs_vis"),v(f,"gs_vis"),v(f,"gs_abt"));for(var y=W.top()?W.top().T:0;W.top()&&W.top().g==e;){var q=W.top();Rb(q.m);q.m=null;W.pop()}if(W.top()){if(q=W.top().g,Oc(D(q).getAttribute("data-shd")||""),v(D(q),"gs_md_ins_vis"),ja){a:{q=W;for(var r=q.j;r>=0;r--)if(q.l[r].g==e){q=r;break a}q=-1}r=W.at(q);(B||f).style.zIndex=1200+q;Nc(f,k,r.A,r)}}else v(C,"gs_vis"),v(C,"gs_abt");W.j==-1?(xc.remove(Lc),c.style.overflowY="",v(d,"gs_nscl"),d.style.top="auto",window.scrollTo(0,R)): Lc();Qc||(y>0?window.history.go(-y):fb())},Rc(f),Sc(f),Dc);Cc&&(Rb(b.m),b.m=null,Ac(b,Qb(A,p,function(y,q,r){b.m=null;r=(y=y==200&&r.match(/^text\/html(;.*)?$/i))?q:Tc();Nc(f,k,r,b);if(y)for(y=e,r=0;r<W.l.length;++r){var Fa=W.at(r);y==Fa.g&&A==Fa.B&&p==Fa.v&&(Fa.A=q,r==W.j&&fb())}S("gs-md-lded",k)})))}function Kc(a){a=a.parentNode;return w(a,"gs_md_wnw")?a:null}function Rc(a){return(a=a.getAttribute("data-ifc"))?D(a):null}function Sc(a){return(a=a.getAttribute("data-cfc"))?D(a):null} function Nc(a,b,c,d){x(b,"gs_md_ldg",!1);for(var e=b.querySelectorAll("[data-duid]"),f=e.length,g={},m=0;m<f;m++){for(var k=jc(e[m]),l=kc[k],p=l?l.length:0,A=0;A<p;A++){var C=l[A],V=F(C.constructor),B=g[V];B||(B=g[V]={});B[k]=!0;C&&typeof C.dispose=="function"&&C.dispose()}delete kc[k]}for(var R in g){R=+R;e=g[R];m=(f=lc[R])?f.length:0;for(l=k=0;l<m;l++)p=f[l],p in e||(f[k++]=p);k?f.length=k:delete lc[R]}b.innerHTML=c;d.A=c;Pc(a.id);Rb(d.m);d.m=null} function Pc(a){if(a=document.querySelector("#"+a+">.gs_md_bdy"))a.scrollTop=a.scrollLeft=0,Mc(a)}function Mc(a){var b=a.style,c="padding"+(za(a)?"Left":"Right");b[c]="";var d=a.offsetWidth-a.clientWidth;d>2&&(a=parseInt(window.getComputedStyle(a,null)[c],10)||0,b[c]=Math.max(a-d,0)+"px")}function Tc(){return'<div class="gs_md_prg"><div class="gs_alrt">'+D("gs_md_err").innerHTML+"</div></div>"} function gb(){var a=W.top();return{d:a&&a.g||void 0,u:a&&a.B||void 0,p:a&&a.v?"1":void 0,t:a&&a.s||void 0}}function hb(){var a=W.top();return{n:a&&a.T||0,p:a&&a.v||"",h:a&&a.A||""}}function Oc(a){if(Uc!=a){var b=D("gs_md_s");Uc&&v(b,Uc);(Uc=a)&&u(b,a)}}var Qc=0,Uc="",W=new Bc; rb.add(function(){var a=nb(),b=a.d||"",c=b?D(b):null;++Qc;if(c){var d=a.u||"";c=+a.p>0;var e=+a.t||0,f=N||M(window.history.state)||{};a=+f.n||0;var g=""+(f.p||"");f=""+(f.h||"");d.match(Ea)||(d="");for(var m=Fc(W,e),k=m;k<W.l.length;++k){var l=W.at(k);if(e<l.s&&l.g!=b)break}for(l=m-1;l>=0;--l){var p=W.at(l);if(e>p.s&&p.g!=b)break}Ec(k-1);for(k=0;k<=l;++k)p=W.at(k).g,J[p]||Gc(l,!1);if(l=m<W.l.length)l=W.at(m),l=b==l.g&&d==l.B&&c==!!l.v&&e==l.s;l?Gc(m,!0):(a==0&&(Ec(-1),W=new Bc,e=Date.now()),c!=!!g&& (d=g="",f=Tc()),b=new zc(b,d,g,f,a,e),c=W,e=b.s,a=Fc(c,e),e=a<c.l.length&&e==c.at(a).s,c.l.splice(a,e?1:0,b),W.j=a,fb(),Hc())}else Ec(-1);--Qc});var Vc=function(a){t.call(this);this.G=a;this.R=Object.create(null);this.m=null;a=a.querySelectorAll(".gs_in_txtw>input[type=text]");for(var b=a.length;b--;){var c=a[b],d=c.parentNode.querySelector(".gs_in_txts");c=c.name;d&&c&&(this.R[c]=d.innerHTML)}};ma(Vc,t);Vc.prototype.K=function(){Rb(this.m);this.G=this.m=null;t.prototype.K.call(this)}; Vc.prototype.ja=function(a){var b=this;P(a);if((a=this.G)&&!this.m){var c="json=&"+Aa(a);Wc(this,!0);this.m=Qb(a.action,c,function(d,e){b.m=null;Wc(b,!1);var f=b.G,g=f.getAttribute("data-alrt");if(g=g?D(g):null)g.innerHTML="";try{var m=d==200&&JSON.parse(e)}catch(B){}d=!1;m&&typeof m=="object"||(Xc(g,D("gs_md_err").innerHTML),m={},d=!0);f.setAttribute("data-p",""+(m.P||""));S("gs-ajax-form-done",f);if(e=m.L){var k=""+e;k.match(Da)&&(window.location.href=k)}else{if(e=m.M)Xc(g,e),d=!0;e=1E6;g&&g.innerHTML&& (k=g,e=g.getBoundingClientRect().top);g=f.elements;m=m.E;typeof m=="object"||(m=Object.create(null));for(var l in b.R){var p=g[l],A=void 0,C=""+(m[l]||""),V=p.parentNode.querySelector(".gs_in_txts");x(p.parentNode,"gs_in_txte",!!C);V&&(V.innerHTML=C||b.R[l]||"");C&&(A=p.getBoundingClientRect().top)<e&&(k=p,e=A);d=d||!!C}(f=f.getAttribute("data-d"))&&!d&&L(f);k&&k.scrollIntoView&&(e<0||e+20>window.innerHeight)&&k.scrollIntoView()}})}}; var Wc=function(a,b){a=a.G;var c=a.getAttribute("data-bsel");a=c?document.querySelectorAll(c):a.querySelectorAll("button");for(c=a.length;c--;){var d=a[c];d.disabled=b;x(d,"gs_bsp",b)}},Xc=function(a,b){if(a)a.innerHTML=b;else{var c=c===void 0?"":c;var d=d===void 0?"":d;var e=e===void 0?[]:e;D("gs_alrt_m").innerHTML=b;Lb().action=d.match(Da)?d:"";a=D("gs_alrt_l");a.textContent=c;c=D("gs_alrt_h");c.innerHTML="";for(var f in e)b=document.createElement(xa.aa),b.type="hidden",b.name=f,b.value=e[f],c.appendChild(b); Ib();x(a,"gs_fm_s",!0);Kb()}};Ub(Vc,[new Q(".gs_ajax_frm",{submit:Vc.prototype.ja})]);var Yc=[[1,0,1],[2,0,1]];T(".gs_cb_gen","click",function(a){var b=a.currentTarget,c=(w(b,"gs_sel")?1:0)+2*(w(b,"gs_par")?1:0),d=+b.getAttribute("data-s")==2;c=Yc[+d][c];d=!0;d=d===void 0?!1:d;x(b,"gs_sel",c==1);x(b,"gs_par",c==2);b.setAttribute("aria-checked",tc[c]);d||b.setAttribute("data-s",""+c);S("gs-change",b,a.i)});T(".gs_cb_gen",["keydown","keyup"],function(a){var b=a.currentTarget,c=a.i.keyCode;b.tagName!="BUTTON"||c!=13&&c!=32||(P(a),a.type=="keydown"&&b.click())});T([".gs_cb_gen",".gs_md_li"],"keydown",function(a){var b=a.currentTarget,c=b.tagName,d=a.i.keyCode;c!="BUTTON"&&(d==32||d==13&&c!="A")&&(P(a),b.click())});var Zc=["click","contextmenu","mouseup"].concat(navigator.sendBeacon?[]:["mousedown","touchstart"]),$c="",ad=null;function bd(){ad=null}function cd(a){navigator.sendBeacon?navigator.sendBeacon(a):ad&&a==ad.src||((ad=new Image).src=a,setTimeout(bd,1E3))} function dd(){var a=document.location.href,b=a.indexOf("?")+1;a=b?a.substr(b):"";b=a.indexOf("#");a=mb(b+1?a.substr(0,b):a).hl||"";a="/scholar_bfnav?url="+encodeURIComponent(document.location.href)+"&hl="+encodeURIComponent(a)+"&ei="+GSP.eventId;cd(a)}Ma(function(){$c=Hb?"&bn=1":"";Hb&&dd()});H(window,"pageshow",function(a){a.persisted&&($c="&bn=1",dd())}); H(document,Zc,function(a){if(!(a.type=="click"&&a.button||a.type=="mouseup"&&a.button!=1)){var b,c;a:{for(a=a.target;a;){var d=a.nodeName;if(d=="A")break a;if(d=="SPAN"||d=="B"||d=="I"||d=="EM"||d=="IMG")a=a.parentNode;else break}a=null}a&&(b=a.getAttribute("href"))&&(c=a.getAttribute("data-clk"))&&(b="/scholar_url?url="+encodeURIComponent(b)+"&"+c+"&ws="+window.innerWidth+"x"+window.innerHeight+"&at=",c=encodeURIComponent,a=(a=a.getAttribute("data-clk-atid"))?D(a):null,b=b+c(a&&a.innerText||"")+ $c,cd(b))}},!1,!0);T(".gs_fm_s","click",function(a){a=a.currentTarget.getAttribute("data-fm")||"";(a=D(a))&&a.submit()});var X=function(a){this.g=E(a.querySelector(".gs_md_d"));this.J=E(a.querySelector(".gs_md_tb"))};X.prototype.N=function(a){var b=D(this.g);return a!==void 0?rc(b,b,a):null};X.prototype.open=function(a){a=this.N(a);if(w(D(this.J),"gs_sel"))try{a&&a.focus()}catch(c){}else{var b=D(this.J);Xa(this.g,function(){u(b,"gs_sel")},function(){v(b,"gs_sel")},a,b)}};X.prototype.close=function(){L(this.g)};X.prototype.ca=function(a){P(a);w(D(this.J),"gs_sel")?this.close():this.open(a.i.type=="keydown"?!1:void 0)}; X.prototype.X=function(a){var b=a.i.keyCode;if(b==38||b==40)P(a),this.open(b==38)};X.prototype.ea=function(a){a.target.id==this.g&&this.X(a)};Ub(X,[new Q(".gs_md_rmb",{}),new Q(".gs_md_tb",{"gs-press":X.prototype.ca,keydown:X.prototype.X}),new Q(".gs_md_d",{keydown:X.prototype.ea})]);var Y=function(a){X.call(this,a);this.la=E(a.querySelector(".gs_md_in"));this.ma=E(a.querySelector(".gs_md_tb .gs_lbl"))};ma(Y,X);Y.prototype.N=function(){return D(this.g).querySelector(".gs_md_li[aria-selected]")};Y.prototype.fa=function(a){ed(this,a)};Y.prototype.O=function(a){var b=a.i.keyCode;b!=13&&b!=32||ed(this,a)}; var ed=function(a,b){var c=b.currentTarget,d=D(a.la),e=a.N();c!=e&&(d.value=c.getAttribute("data-v"),D(a.ma).innerHTML=c.innerHTML,e&&fd(e,!1),fd(c,!0));P(b);a.close();S("gs-change",d,b.i)},fd=function(a,b){x(a,"gs_sel",b);b?a.setAttribute("aria-selected","true"):a.removeAttribute("aria-selected")};Ub(Y,[new Q(".gs_md_ris",{}),new Q(".gs_md_li",{click:Y.prototype.fa,keydown:Y.prototype.O})]);T("#gs_lp","click",function(a){P(a);Ic("gs_lp_d")});T("#gs_lp_cur","click",function(a){P(a);L("gs_lp_d")});var gd=function(a){this.Z=E(a)};gd.prototype.O=function(a){var b=a.currentTarget,c=a.i.keyCode;if(c==38||c==40){var d=D(this.Z);d=rc(d,b,c==38)||rc(d,d,c==38)}else if(c==37||c==39)a:{c=c==37!=za(b.parentNode);d=b.parentNode;var e=d.children,f=e.length;if(d.id!=this.Z){for(;e[--f]!=b;);d=qc(d,c)||pc(d.parentNode,c);e=d.children;if(f=Math.min(f+1,e.length))if(d=e[f-1],w(d,"gs_md_li")&&d.offsetLeft!=b.offsetLeft)break a}d=void 0}d&&(P(a),d.focus())};Ub(gd,[new Q(".gs_md_ulr",{}),new Q(".gs_md_li",{keydown:gd.prototype.O})]);T("#gs_hdr_mnu","click",function(a){P(a);Ic("gs_hdr_drw")});T("#gs_hdr_drw_mnu","click",function(a){P(a);L("gs_hdr_drw")});T("#gs_hdr_act_i","click",function(a){P(a);sa()==1?(a=document.querySelector("#gs_hdr_drw_bot>a").href,a.match(Da)&&(window.location.href=a)):Xa("gs_hdr_act_d")});T("#gs_hdr_drw","keydown",function(a){var b=a.i.keyCode;if(b==38||b==40){var c=a.currentTarget;if(b=rc(c,c,b==38))P(a),b.focus()}}); T("#gs_hdr_tsi",["focus","blur"],function(a){function b(){var g=d.getBoundingClientRect().top-10;Math.abs(g)>10&&window.scrollBy(0,g);clearTimeout(e);c()}function c(){I(window,f,b)}var d=a.target;a=a.type=="focus";x(D("gs_hdr"),"gs_hdr_ifc",a);if(a&&ta&&!(window.innerHeight>749)){var e=setTimeout(c,1E3),f=["scroll","resize"];H(window,f,b)}});T("#gs_hdr_tsi",["input","gs-change"],function(a){x(D("gs_hdr_frm"),"gs_hdr_tsc",!!a.currentTarget.value)}); T("#gs_hdr_tsc","mousedown",function(a){P(a);var b=D("gs_hdr_tsi");b.value="";b.focus();S("input",b,a.i)});T("#gs_hdr_sre","click",function(a){P(a);var b=D("gs_hdr");Xa("gs_hdr_frm",function(){v(b,"gs_hdr_src");u(b,"gs_hdr_srx")},function(){u(b,"gs_hdr_src");v(b,"gs_hdr_srx")},D("gs_hdr_tsi"))});T(".gs_md_x","click",function(a){(a=a.currentTarget.getAttribute("data-mdx"))&&L(a)});var Z=function(){},hd,id;Z.prototype.da=function(a){a.i.button||(P(a),jd(a))};Z.prototype.ga=function(a){kd(a)&&(P(a),jd(a))};Z.prototype.ha=function(a){kd(a)&&P(a)};Z.prototype.ia=function(a){if(!a.i.button){P(a);var b=a.i;b&&(ld=b.clientX||0,md=b.clientY||0,H(document,nd,od,!0),clearTimeout(hd),hd=setTimeout(pd,2E3));jd(a)}}; Z.prototype.ka=function(a){P(a);if(qd){var b=a.i;b=b&&b.touches||[];if(b=b.length==1?b[0]:null)rd=b.clientX,sd=b.clientY,H(document,td,ud,!0),clearTimeout(id),id=setTimeout(vd,2E3)}jd(a)}; var kd=function(a){a=a.i.keyCode;return a==32||a==13},jd=function(a){S("gs-press",a.currentTarget,a.i)},pd=function(){I(document,nd,od,!0);clearTimeout(hd);hd=void 0},od=function(a){a.type!="mousedown"&&Math.abs(a.clientX-ld)<10&&Math.abs(a.clientY-md)<10?(Pa(a),a.type=="click"&&pd()):pd()},vd=function(){I(document,td,ud,!0);clearTimeout(id);id=void 0},ud=function(a){a.type!="touchstart"&&Math.abs(a.clientX-rd)<10&&Math.abs(a.clientY-sd)<10?(Pa(a),a.type=="click"&&vd()):vd()},ld=0,md=0,nd=["mousedown", "mouseup","click"],qd=z("Android")&&!z("Chrome"),rd=0,sd=0,td=["touchstart","mousedown","mouseup","click"];Ub(Z,[new Q(".gs_press",{click:Z.prototype.da,keydown:Z.prototype.ga,keyup:Z.prototype.ha,mousedown:Z.prototype.ia,touchstart:Z.prototype.ka})]);function wd(a){xd.style.left=yd&&zd===Ad?a.left+"px":"auto";xd.style.width=yd?a.width+"px":"auto";S("gs-sth-change",D("gs_sth"))}function Bd(){var a=Cd.getBoundingClientRect(),b=a.top,c=xd.offsetHeight,d=b<0,e;if(e=d&&qa)e=document.activeElement,e=!!e&&e.tagName=="INPUT"&&e.type=="text";b=e?-b-a.height:Ad;var f=yd!=d||zd!==Ad!=e;b!==zd&&(zd=b,xd.style.transform=b===Ad?"none":"translate3d(0,"+b+"px,0)");f&&(yd=d,x(Dd,"gs_sth_vis",d),x(Dd,"gs_sth_trk",e),wd(a),Cd.style.height=yd?c+"px":"auto")} function Ed(){yd&&wd(Cd.getBoundingClientRect())}var Ad,Dd,Cd,xd,yd=!1,zd;Ma(function(){if(Dd=D("gs_sth"))Cd=Dd.querySelector(".gs_sth_g"),xd=Dd.querySelector(".gs_sth_b"),vc.addListener(Bd),wc.addListener(Ed),Bd()});(function(a){Ma(function(){return setTimeout(a,0)})})(function(){var a=document.querySelectorAll(".gs_invis");var b=typeof Symbol!="undefined"&&Symbol.iterator&&a[Symbol.iterator];if(b)a=b.call(a);else if(typeof a.length=="number")a={next:aa(a)};else throw Error(String(a)+" is not an iterable or ArrayLike");for(b=a.next();!b.done;b=a.next())v(b.value,"gs_invis")});new U;new U;var Fd=(new Date).getTimezoneOffset();T("#gs_vcpb_cita_edit","click",function(a){a.i&&Pa(a.i);a=D("gsc_vcpb").getAttribute("data-edit-link")+"&tzom="+Fd;Ic("gs_md_cita-d",a)});T("#gs_md_cita-b-save","click",function(){var a=D("gsc_ecd_form");Ba(a,"continue").value=window.location.pathname+window.location.search;S("submit",a)}); T(".gsc_ecd_form_tsel","click",function(a){var b=D("gsc_ecd_form"),c=D("gsc_ecd_table");b=Ba(b,"articletype");a=a.currentTarget;b.value=a.getAttribute("data-type")||"";c.className=a.getAttribute("data-class")||"";c=document.querySelectorAll("#gsc_ecd_citation_type button");for(b=c.length;b--;)x(c[b],"gs_sel",c[b]==a)}); }({"customAC":0,"eventId":"J4JHZ6iZCZuDy9YPs-PngA4"});</script></head><body><div id="gs_top" onclick=""><style>#gs_md_s,.gs_md_wnw{z-index:1200;position:fixed;top:0;left:0;width:100%;height:100%;visibility:hidden;}.gs_md_ds:before{content:'';position:absolute;background-color:#fff;z-index:100;opacity:0;visibility:hidden;top:0;bottom:0;right:0;left:0;}.gs_md_ds.gs_md_d:not(.gs_el_ph .gs_md_wmw):before{top:-1px;bottom:-1px;right:-1px;left:-1px;}#gs_md_s{background-color:#fff;opacity:0;}.gs_el_ta #gs_md_s,.gs_el_ph #gs_md_s,.gs_el_ta .gs_md_ds:before,.gs_el_ph .gs_md_ds:before{background-color:#666;}#gs_md_s.gs_vis,.gs_md_ds.gs_md_ins_vis:before{opacity:.5;visibility:visible;}.gs_md_wnw{transition:all 0s .218s;}.gs_md_wnw.gs_vis{visibility:visible;transition:all 0s;}.gs_el_tc .gs_md_ds:before{transition:opacity .15s,visibility 0s .15s;}.gs_el_tc .gs_md_ds.gs_md_ins_vis:before{transition:opacity .218s,visibility 0s;}.gs_md_wnw>.gs_md_d{position:relative;margin:0 auto;width:464px;box-shadow:2px 2px 8px rgba(0,0,0,.2);white-space:normal;}.gs_el_ta .gs_md_wnw>.gs_md_d,.gs_el_ph .gs_md_wnw>.gs_md_d{box-shadow:2px 2px 8px rgba(0,0,0,.65);}.gs_el_ph .gs_md_wnw>.gs_md_d{width:80%;max-width:440px;}.gs_el_ph .gs_md_wmw>.gs_md_d{display:flex;flex-direction:column;width:100%;height:100%;max-width:none;border:none;box-shadow:none;transform:translate(0,100%);transform:translate(0,100vh);transition:transform .27s cubic-bezier(.4,0,.6,1),opacity 0s .27s,visibility 0s .27s,max-height 0s .27s;}.gs_el_ph .gs_md_wmw>.gs_md_d.gs_vis{transform:translate(0,0);transition:transform .3s cubic-bezier(0,0,.2,1);}.gs_md_wmw>.gs_md_d.gs_abt,.gs_el_ph .gs_md_wmw>.gs_md_d.gs_abt{transition:none;}.gs_md_hdr{display:flex;align-items:center;height:47px;border-bottom:1px solid #e0e0e0;border-bottom-color:rgba(0,0,0,.12);background-color:#f5f5f5;}.gs_md_hdr>a,.gs_md_hdr>a.gs_btn_lrge{flex:0 0 auto;width:41px;height:47px;}.gs_el_ph .gs_md_hdr>a{margin:0 2px 0 0;}.gs_el_ph a.gs_md_hdr_c{margin:0 0 0 2px;}.gs_md_hdr_b{margin:0 41px 0 16px;}.gs_el_ph .gs_md_hdr_b{margin:0 16px;}.gs_md_hdr_t:empty~.gs_md_hdr_b{margin-left:0;}.gs_md_hdr_b:empty{width:41px;margin:0;}.gs_el_ph .gs_md_hdr_b:empty{margin-right:2px;}.gs_md_hdr_b:empty:not(:last-child){display:none;}.gs_md_hdr_b>button{min-width:51px;height:33px;}.gs_md_hdr_t{flex:1 1 auto;font-size:18px;font-weight:normal;color:#666;overflow:hidden;text-overflow:ellipsis;white-space:nowrap;text-align:center;}.gs_md_bdy{position:relative;overflow-y:auto;box-sizing:border-box;padding:24px 41px 0 41px;}.gs_md_bdy:after{display:block;content:"";clear:both;padding-bottom:24px;}.gs_el_ph .gs_md_bdy{padding:16px 16px 0 16px;}.gs_el_ph .gs_md_bdy:after{padding-bottom:16px;}.gs_el_ph .gs_md_wmw .gs_md_bdy{flex:1;}.gs_md_ftr{border-top:1px solid #e0e0e0;}.gs_md_lbl{display:block;font-size:16px;margin:0 0 16px 0;word-wrap:break-word;}.gs_md_btns{margin:24px 0 0 0;white-space:nowrap;}.gs_el_ph .gs_md_btns{margin:16px 0 0 0;}.gs_md_btns button{margin-right:16px;}.gs_md_btns button:last-child{margin-right:0;}.gs_md_prg{margin:24px 0;text-align:center;}.gs_md_prg .gs_alrt{padding:4px 16px;}.gs_md_ldg:before{content:"";position:absolute;top:0;left:0;bottom:0;right:0;background-color:#fff;opacity:.5;z-index:100;}</style><div id="gs_md_ldg" style="display:none">Loading...</div><div id="gs_md_err" style="display:none">The system can't perform the operation now. Try again later.</div><div id="gs_md_s"></div><div data-h="800" class="gs_md_wnw gs_md_ds gs_md_wmw"><div id="gs_md_cita-d" class="gs_md_d gs_md_ds gs_ttzi" role="dialog" tabindex="-1" aria-labelledby="gs_md_cita-d-t" data-cid="gs_md_cita-l" data-wfc="gs_md_cita-d-x"><div class="gs_md_hdr"><a href="javascript:void(0)" id="gs_md_cita-d-x" role="button" aria-label="Cancel" data-mdx="gs_md_cita-d" class="gs_btnCLS gs_md_x gs_md_hdr_c gs_in_ib gs_btn_lrge"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl"></span></a><h2 id="gs_md_cita-d-t" class="gs_md_hdr_t"></h2><div class="gs_md_hdr_b"><button type="button" id="gs_md_cita-b-save" aria-label="Save" class="gs_btnDNW gs_in_ib gs_btn_act gs_btn_half gs_btn_lsb"><span class="gs_wr"><span class="gs_ico"></span><span class="gs_lbl"></span></span></button></div></div><div id="gs_md_cita-d-bdy" class="gs_md_bdy"><style>#gs_md_cita-d{width:90%;max-width:1000px;}.gs_el_ph #gs_md_cita-d{width:100%;max-width:none;}#gs_md_cita-d .gs_md_prg{min-height:600px;}</style><div id="gs_md_cita-l" aria-live="assertive"></div></div></div></div><div id="gs_hdr_drw" class="gs_md_ulr gs_md_ds" role="dialog" tabindex="-1" data-shd="gs_hdr_drs" data-wfc="gs_hdr_drw_mnu" data-cfc="gs_hdr_mnu"><div id="gs_hdr_drw_in"><div id="gs_hdr_drw_top"><a href="javascript:void(0)" id="gs_hdr_drw_mnu" role="button" aria-controls="gs_hdr_drw" aria-label="Options" class="gs_btnMNT gs_in_ib gs_btn_lrge"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl"></span></a><a id="gs_hdr_drw_lgo" href="/schhp?hl=en" aria-label="Homepage"></a></div><div><div class="gs_hdr_drw_sec"><a href="/citations?hl=en" role="menuitem" class="gs_btnPRO gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">My profile</span></a><a href="/scholar?scilib=1&hl=en" role="menuitem" class="gs_btnL gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">My library</span></a><a href="/citations?view_op=metrics_intro&hl=en" role="menuitem" class="gs_btnJ gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">Metrics</span></a><a href="/scholar_alerts?view_op=list_alerts&hl=en" role="menuitem" class="gs_btnM gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">Alerts</span></a></div><div class="gs_hdr_drw_sec"><a href="/scholar_settings?hl=en" role="menuitem" class="gs_btnP gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">Settings</span></a></div></div><div id="gs_hdr_drw_bot" class="gs_hdr_drw_sec"><a href="https://accounts.google.com/Login?hl=en&continue=https://scholar.google.co.in/schhp%3Fhl%3Den" class=" gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">Sign in</span></a></div></div></div><div id="gs_hdr" role="banner"><a href="/citations?view_op=list_works&hl=en&hl=en&user=mXSv_1UAAAAJ" id="gs_hdr_bck" role="button" class="gs_btnALT gs_in_ib gs_btn_lrge"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl"></span></a><div id="gs_hdr_md"><h1 dir="ltr">View article</h1></div><div id="gs_hdr_act"><a id="gs_hdr_act_s" href="https://accounts.google.com/Login?hl=en&continue=https://scholar.google.co.in/schhp%3Fhl%3Den">Sign in</a></div></div><style>#gs_alrt{position:fixed;bottom:48px;left:16px;max-width:384px;z-index:1250;display:flex;justify-content:space-between;align-items:center;font-size:13px;line-height:16px;color:#e2e2e2;background:#333;text-align:left;border-radius:3px;box-shadow:0 3px 5px -1px rgba(0,0,0,.2),0 6px 10px 0 rgba(0,0,0,.14),0 1px 18px 0 rgba(0,0,0,.12);visibility:hidden;transform-origin:center;transform:scale(0.8,0.8) translate(0,100%);}.gs_el_ph #gs_alrt{bottom:0;left:0;width:100%;max-width:none;border-radius:0;box-shadow:none;transform:scale(1,1) translate(0,100%);}#gs_alrt.gs_vis{visibility:visible;transform:scale(1,1) translate(0,0);}#gs_alrt.gs_anm{transition:transform .067s cubic-bezier(.4,0,1,1),visibility 0s .067s;}#gs_alrt.gs_vis.gs_anm{transition:transform .067s cubic-bezier(0,0,.2,1);}.gs_el_ph #gs_alrt.gs_anm{transition:transform .084s cubic-bezier(.4,0,1,1),visibility 0s .084s;}.gs_el_ph #gs_alrt.gs_vis.gs_anm{transition:transform .1s cubic-bezier(0,0,.2,1);}#gs_alrt_m{display:block;padding:16px;}#gs_alrt_l{display:block;padding:8px;margin:0 8px 0 -8px;border-radius:3px;color:#fcc934;text-transform:uppercase;text-decoration:none;}#gs_alrt_l:hover{background-color:rgba(255,255,255,.05)}#gs_alrt_l:active{background-color:rgba(255,255,255,.1)}#gs_alrt_l:empty{display:none}#gs_alrt_m a{padding:8px 0;color:#e2e2e2;text-decoration:underline;}#gs_alrt_m a:active{color:#f6aea9}</style><form action="" method="post" id="gs_alrt"><span id="gs_alrt_m"></span><span id="gs_alrt_h"></span><a id="gs_alrt_l" href="javascript:void(0)" class="gs_fm_s" data-fm="gs_alrt"></a></form><div id="gs_bdy"><div id="gs_bdy_sb" role="navigation"><div id="gs_bdy_sb_in"><div id="gsc_sb_ui" class="gs_bdy_sb_sec"><a href="/citations?user=mXSv_1UAAAAJ&hl=en" class="gs_ibl"><span class="gs_rimg gs_pp_sm"><img alt="Leo Breiman 1928-2005" sizes="56px" src="https://scholar.googleusercontent.com/citations?view_op=small_photo&user=mXSv_1UAAAAJ&citpid=2" srcset="https://scholar.googleusercontent.com/citations?view_op=small_photo&user=mXSv_1UAAAAJ&citpid=2 56w,https://scholar.googleusercontent.com/citations?view_op=view_photo&user=mXSv_1UAAAAJ&citpid=2 128w" width="56" height="39"></span></a><div><a href="/citations?user=mXSv_1UAAAAJ&hl=en">Leo Breiman 1928-2005</a></div></div></div></div><div id="gs_bdy_ccl" role="main"><div id="gsc_vcpb" data-edit-link="/citations?view_op=edit_citation&hl=en&user=mXSv_1UAAAAJ&citation_for_view=mXSv_1UAAAAJ:UeHWp8X0CEIC&citation_for_view=mXSv_1UAAAAJ:UeHWp8X0CEIC&back_view_op=view_citation"><form method="post" id="gsc_vcpb_btns" action="/citations?view_op=view_citation&hl=en"><input type="hidden" name="xsrf" value="ADIE8skAAAAAZ0jTp-fXep8K1DLoGPo_54sjxrg"><input type="hidden" name="s" value="mXSv_1UAAAAJ:UeHWp8X0CEIC"><input type="hidden" name="continue" value="/citations?view_op=list_works&hl=en&hl=en&user=mXSv_1UAAAAJ"></form><div id="gsc_oci_title_wrapper"><div id="gsc_oci_title_gg"><div class="gsc_oci_title_ggi"><a href="https://projecteuclid.org/journals/annals-of-statistics/volume-24/issue-6/Heuristics-of-instability-and-stabilization-in-model-selection/10.1214/aos/1032181158.pdf" data-clk="hl=en&sa=T&ei=J4JHZ6iZCZuDy9YPs-PngA4"><span class='gsc_vcd_title_ggt'>[PDF]</span> from projecteuclid.org</a></div></div><div id="gsc_oci_title"><a class="gsc_oci_title_link" href="https://projecteuclid.org/journals/annals-of-statistics/volume-24/issue-6/Heuristics-of-instability-and-stabilization-in-model-selection/10.1214/aos/1032181158.short" data-clk="hl=en&sa=T&ei=J4JHZ6iZCZuDy9YPs-PngA4">Heuristics of instability and stabilization in model selection</a></div></div><div id="gsc_oci_table"><div class="gs_scl"><div class="gsc_oci_field">Authors</div><div class="gsc_oci_value">Leo Breiman</div></div><div class="gs_scl"><div class="gsc_oci_field">Publication date</div><div class="gsc_oci_value">1996</div></div><div class="gs_scl"><div class="gsc_oci_field">Journal</div><div class="gsc_oci_value">The Annals of Statistics</div></div><div class="gs_scl"><div class="gsc_oci_field">Volume</div><div class="gsc_oci_value">24</div></div><div class="gs_scl"><div class="gsc_oci_field">Issue</div><div class="gsc_oci_value">6</div></div><div class="gs_scl"><div class="gsc_oci_field">Pages</div><div class="gsc_oci_value">2350-2383</div></div><div class="gs_scl"><div class="gsc_oci_field">Publisher</div><div class="gsc_oci_value">Institute of Mathematical Statistics</div></div><div class="gs_scl"><div class="gsc_oci_field">Description</div><div class="gsc_oci_value" id="gsc_oci_descr"><div class="gsh_small">In model selection, usually a "best" predictor is chosen from a collection <svg class="gs_fsvg" aria-label="{\hat{\mu}(\cdot, s)}" width="36px" height="14px" style="vertical-align:-4px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 10.50000)"><g><g><g><path transform="scale(0.48828, -0.48828)" d="M 57 -385 Q 57 -373 59 -369 L 360 840 Q 369 869 392 887 T 446 905 Q 472 905 490 889 T 508 848 Q 508 842 507 838 T 506 831 L 385 352 Q 365 267 365 205 Q 365 129 401 80 T 510 31 Q 659 31 772 217 Q 773 219 773 220 T 774 223 L 922 817 Q 929 844 954 863 T 1008 883 Q 1032 883 1050 867 T 1069 825 Q 1069 813 1067 809 L 920 219 Q 905 161 905 119 Q 905 31 965 31 Q 1029 31 1061 110 T 1118 301 Q 1122 313 1135 313 H 1159 Q 1167 313 1172 306 T 1178 293 Q 1142 150 1099 63 T 961 -23 Q 893 -23 840 16 T 772 121 Q 721 57 652 17 T 508 -23 Q 380 -23 307 37 L 203 -377 Q 197 -406 173 -424 T 119 -442 Q 94 -442 75 -427 T 57 -385 Z "/></g><g transform="translate(79.05900, -11.44501)"><path transform="scale(0.48828, -0.48828)" d="M 276 1102 L 236 1145 L 512 1421 L 786 1145 L 745 1102 L 512 1307 L 276 1102 Z "/></g></g><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 602.56000, 0.00000)" d="M 635 -508 Q 521 -418 438 -302 T 303 -53 T 225 223 T 199 512 Q 199 659 225 803 T 304 1080 T 441 1329 T 635 1532 Q 635 1536 645 1536 H 664 Q 670 1536 675 1530 T 680 1518 Q 680 1509 676 1505 Q 576 1407 509 1295 T 402 1056 T 344 794 T 326 512 Q 326 -139 674 -477 Q 680 -483 680 -494 Q 680 -499 674 -506 T 664 -512 H 645 Q 635 -512 635 -508 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 991.45001, 0.00000)" d="M 172 512 Q 172 541 187 567 T 228 609 T 285 625 Q 314 625 340 609 T 382 567 T 397 512 Q 397 466 364 432 T 285 399 Q 239 399 205 432 T 172 512 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1269.22998, 0.00000)" d="M 203 -369 Q 203 -360 211 -352 Q 285 -281 326 -188 T 367 8 V 33 Q 334 0 285 0 Q 238 0 205 33 T 172 113 Q 172 161 205 193 T 285 225 Q 358 225 389 157 T 420 8 Q 420 -106 374 -209 T 246 -393 Q 238 -397 233 -397 Q 223 -397 213 -388 T 203 -369 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1713.67712, 0.00000)" d="M 178 125 Q 233 31 399 31 Q 471 31 536 55 T 643 129 T 686 248 Q 686 301 648 335 T 555 381 L 444 403 Q 368 422 319 474 T 270 600 Q 270 691 319 761 T 450 868 T 618 905 Q 711 905 784 860 T 858 729 Q 858 682 831 646 T 758 610 Q 731 610 711 627 T 692 672 Q 692 696 705 718 T 741 754 T 788 768 Q 770 812 720 832 T 614 852 Q 562 852 510 831 T 426 769 T 395 674 Q 395 637 421 609 T 485 569 L 604 545 Q 661 533 708 502 T 783 425 T 811 319 Q 811 243 768 169 T 664 51 Q 555 -23 397 -23 Q 288 -23 197 27 T 106 176 Q 106 232 138 273 T 227 315 Q 260 315 282 295 T 305 242 Q 305 195 270 160 T 188 125 H 178 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 2182.45703, 0.00000)" d="M 133 -512 Q 115 -512 115 -494 Q 115 -485 119 -481 Q 469 -139 469 512 Q 469 1163 123 1501 Q 115 1506 115 1518 Q 115 1525 120 1530 T 133 1536 H 152 Q 158 1536 162 1532 Q 309 1416 407 1250 T 550 896 T 596 512 Q 596 367 571 226 T 493 -51 T 358 -303 T 162 -508 Q 158 -512 152 -512 H 133 Z "/></g></g></svg> of predictors where <svg class="gs_fsvg" aria-label="\hat{\mu}(\cdot, s)" width="36px" height="14px" style="vertical-align:-4px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 10.50000)"><g><g><path transform="scale(0.48828, -0.48828)" d="M 57 -385 Q 57 -373 59 -369 L 360 840 Q 369 869 392 887 T 446 905 Q 472 905 490 889 T 508 848 Q 508 842 507 838 T 506 831 L 385 352 Q 365 267 365 205 Q 365 129 401 80 T 510 31 Q 659 31 772 217 Q 773 219 773 220 T 774 223 L 922 817 Q 929 844 954 863 T 1008 883 Q 1032 883 1050 867 T 1069 825 Q 1069 813 1067 809 L 920 219 Q 905 161 905 119 Q 905 31 965 31 Q 1029 31 1061 110 T 1118 301 Q 1122 313 1135 313 H 1159 Q 1167 313 1172 306 T 1178 293 Q 1142 150 1099 63 T 961 -23 Q 893 -23 840 16 T 772 121 Q 721 57 652 17 T 508 -23 Q 380 -23 307 37 L 203 -377 Q 197 -406 173 -424 T 119 -442 Q 94 -442 75 -427 T 57 -385 Z "/></g><g transform="translate(79.05900, -11.44501)"><path transform="scale(0.48828, -0.48828)" d="M 276 1102 L 236 1145 L 512 1421 L 786 1145 L 745 1102 L 512 1307 L 276 1102 Z "/></g></g><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 602.56000, 0.00000)" d="M 635 -508 Q 521 -418 438 -302 T 303 -53 T 225 223 T 199 512 Q 199 659 225 803 T 304 1080 T 441 1329 T 635 1532 Q 635 1536 645 1536 H 664 Q 670 1536 675 1530 T 680 1518 Q 680 1509 676 1505 Q 576 1407 509 1295 T 402 1056 T 344 794 T 326 512 Q 326 -139 674 -477 Q 680 -483 680 -494 Q 680 -499 674 -506 T 664 -512 H 645 Q 635 -512 635 -508 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 991.45001, 0.00000)" d="M 172 512 Q 172 541 187 567 T 228 609 T 285 625 Q 314 625 340 609 T 382 567 T 397 512 Q 397 466 364 432 T 285 399 Q 239 399 205 432 T 172 512 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1269.22998, 0.00000)" d="M 203 -369 Q 203 -360 211 -352 Q 285 -281 326 -188 T 367 8 V 33 Q 334 0 285 0 Q 238 0 205 33 T 172 113 Q 172 161 205 193 T 285 225 Q 358 225 389 157 T 420 8 Q 420 -106 374 -209 T 246 -393 Q 238 -397 233 -397 Q 223 -397 213 -388 T 203 -369 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1713.67712, 0.00000)" d="M 178 125 Q 233 31 399 31 Q 471 31 536 55 T 643 129 T 686 248 Q 686 301 648 335 T 555 381 L 444 403 Q 368 422 319 474 T 270 600 Q 270 691 319 761 T 450 868 T 618 905 Q 711 905 784 860 T 858 729 Q 858 682 831 646 T 758 610 Q 731 610 711 627 T 692 672 Q 692 696 705 718 T 741 754 T 788 768 Q 770 812 720 832 T 614 852 Q 562 852 510 831 T 426 769 T 395 674 Q 395 637 421 609 T 485 569 L 604 545 Q 661 533 708 502 T 783 425 T 811 319 Q 811 243 768 169 T 664 51 Q 555 -23 397 -23 Q 288 -23 197 27 T 106 176 Q 106 232 138 273 T 227 315 Q 260 315 282 295 T 305 242 Q 305 195 270 160 T 188 125 H 178 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 2182.45703, 0.00000)" d="M 133 -512 Q 115 -512 115 -494 Q 115 -485 119 -481 Q 469 -139 469 512 Q 469 1163 123 1501 Q 115 1506 115 1518 Q 115 1525 120 1530 T 133 1536 H 152 Q 158 1536 162 1532 Q 309 1416 407 1250 T 550 896 T 596 512 Q 596 367 571 226 T 493 -51 T 358 -303 T 162 -508 Q 158 -512 152 -512 H 133 Z "/></g></svg> is the minimum least-squares predictor in a collection <svg class="gs_fsvg" aria-label="\mathsf{U}_s" width="16px" height="12px" style="vertical-align:-2px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 9.71600)"><g><g><path transform="scale(0.48828, -0.48828)" d="M 188 473 V 1421 H 379 V 473 Q 379 370 416 279 T 528 133 T 709 78 Q 789 78 853 109 T 961 196 T 1028 323 T 1051 473 V 1421 H 1219 V 473 Q 1219 336 1151 216 T 965 26 T 709 -45 Q 571 -45 450 24 T 258 213 T 188 473 Z "/></g><g transform="translate(687.50000, 150.00000)"><path transform="scale(0.34180, -0.34180)" d="M 244 123 Q 300 45 477 45 Q 544 45 615 65 T 734 131 T 782 248 Q 782 299 738 330 T 637 373 L 504 397 Q 425 413 370 468 T 315 598 Q 315 693 369 762 T 511 867 T 692 903 Q 752 903 815 885 T 919 828 T 961 727 Q 961 678 933 641 T 858 604 Q 829 604 807 623 T 786 672 Q 786 707 810 735 T 868 770 Q 822 838 688 838 Q 601 838 528 796 T 455 672 Q 455 597 561 573 L 696 549 Q 788 531 855 470 T 922 319 Q 922 242 876 168 T 762 51 Q 647 -20 475 -20 Q 350 -20 247 25 T 145 178 Q 145 235 179 277 T 270 319 Q 305 319 328 298 T 352 242 Q 352 196 321 162 T 244 123 Z "/></g></g></g></svg> of predictors. Here s is a complexity parameter; that is, the smaller s, the lower dimensional/smoother the models in <svg class="gs_fsvg" aria-label="\mathsf{U}_s" width="16px" height="12px" style="vertical-align:-2px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 9.71600)"><g><g><path transform="scale(0.48828, -0.48828)" d="M 188 473 V 1421 H 379 V 473 Q 379 370 416 279 T 528 133 T 709 78 Q 789 78 853 109 T 961 196 T 1028 323 T 1051 473 V 1421 H 1219 V 473 Q 1219 336 1151 216 T 965 26 T 709 -45 Q 571 -45 450 24 T 258 213 T 188 473 Z "/></g><g transform="translate(687.50000, 150.00000)"><path transform="scale(0.34180, -0.34180)" d="M 244 123 Q 300 45 477 45 Q 544 45 615 65 T 734 131 T 782 248 Q 782 299 738 330 T 637 373 L 504 397 Q 425 413 370 468 T 315 598 Q 315 693 369 762 T 511 867 T 692 903 Q 752 903 815 885 T 919 828 T 961 727 Q 961 678 933 641 T 858 604 Q 829 604 807 623 T 786 672 Q 786 707 810 735 T 868 770 Q 822 838 688 838 Q 601 838 528 796 T 455 672 Q 455 597 561 573 L 696 549 Q 788 531 855 470 T 922 319 Q 922 242 876 168 T 762 51 Q 647 -20 475 -20 Q 350 -20 247 25 T 145 178 Q 145 235 179 277 T 270 319 Q 305 319 328 298 T 352 242 Q 352 196 321 162 T 244 123 Z "/></g></g></g></svg>. If <svg class="gs_fsvg" aria-label="\mathsf{L}" width="8px" height="10px" style="vertical-align:0px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 9.71600)"><g><path transform="scale(0.48828, -0.48828)" d="M 188 0 V 1421 H 379 V 139 L 1022 143 V 0 H 188 Z "/></g></g></svg> is the data used to derive the sequence <svg class="gs_fsvg" aria-label="{\hat{\mu}(\cdot, s)}" width="36px" height="14px" style="vertical-align:-4px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 10.50000)"><g><g><g><path transform="scale(0.48828, -0.48828)" d="M 57 -385 Q 57 -373 59 -369 L 360 840 Q 369 869 392 887 T 446 905 Q 472 905 490 889 T 508 848 Q 508 842 507 838 T 506 831 L 385 352 Q 365 267 365 205 Q 365 129 401 80 T 510 31 Q 659 31 772 217 Q 773 219 773 220 T 774 223 L 922 817 Q 929 844 954 863 T 1008 883 Q 1032 883 1050 867 T 1069 825 Q 1069 813 1067 809 L 920 219 Q 905 161 905 119 Q 905 31 965 31 Q 1029 31 1061 110 T 1118 301 Q 1122 313 1135 313 H 1159 Q 1167 313 1172 306 T 1178 293 Q 1142 150 1099 63 T 961 -23 Q 893 -23 840 16 T 772 121 Q 721 57 652 17 T 508 -23 Q 380 -23 307 37 L 203 -377 Q 197 -406 173 -424 T 119 -442 Q 94 -442 75 -427 T 57 -385 Z "/></g><g transform="translate(79.05900, -11.44501)"><path transform="scale(0.48828, -0.48828)" d="M 276 1102 L 236 1145 L 512 1421 L 786 1145 L 745 1102 L 512 1307 L 276 1102 Z "/></g></g><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 602.56000, 0.00000)" d="M 635 -508 Q 521 -418 438 -302 T 303 -53 T 225 223 T 199 512 Q 199 659 225 803 T 304 1080 T 441 1329 T 635 1532 Q 635 1536 645 1536 H 664 Q 670 1536 675 1530 T 680 1518 Q 680 1509 676 1505 Q 576 1407 509 1295 T 402 1056 T 344 794 T 326 512 Q 326 -139 674 -477 Q 680 -483 680 -494 Q 680 -499 674 -506 T 664 -512 H 645 Q 635 -512 635 -508 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 991.45001, 0.00000)" d="M 172 512 Q 172 541 187 567 T 228 609 T 285 625 Q 314 625 340 609 T 382 567 T 397 512 Q 397 466 364 432 T 285 399 Q 239 399 205 432 T 172 512 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1269.22998, 0.00000)" d="M 203 -369 Q 203 -360 211 -352 Q 285 -281 326 -188 T 367 8 V 33 Q 334 0 285 0 Q 238 0 205 33 T 172 113 Q 172 161 205 193 T 285 225 Q 358 225 389 157 T 420 8 Q 420 -106 374 -209 T 246 -393 Q 238 -397 233 -397 Q 223 -397 213 -388 T 203 -369 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1713.67712, 0.00000)" d="M 178 125 Q 233 31 399 31 Q 471 31 536 55 T 643 129 T 686 248 Q 686 301 648 335 T 555 381 L 444 403 Q 368 422 319 474 T 270 600 Q 270 691 319 761 T 450 868 T 618 905 Q 711 905 784 860 T 858 729 Q 858 682 831 646 T 758 610 Q 731 610 711 627 T 692 672 Q 692 696 705 718 T 741 754 T 788 768 Q 770 812 720 832 T 614 852 Q 562 852 510 831 T 426 769 T 395 674 Q 395 637 421 609 T 485 569 L 604 545 Q 661 533 708 502 T 783 425 T 811 319 Q 811 243 768 169 T 664 51 Q 555 -23 397 -23 Q 288 -23 197 27 T 106 176 Q 106 232 138 273 T 227 315 Q 260 315 282 295 T 305 242 Q 305 195 270 160 T 188 125 H 178 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 2182.45703, 0.00000)" d="M 133 -512 Q 115 -512 115 -494 Q 115 -485 119 -481 Q 469 -139 469 512 Q 469 1163 123 1501 Q 115 1506 115 1518 Q 115 1525 120 1530 T 133 1536 H 152 Q 158 1536 162 1532 Q 309 1416 407 1250 T 550 896 T 596 512 Q 596 367 571 226 T 493 -51 T 358 -303 T 162 -508 Q 158 -512 152 -512 H 133 Z "/></g></g></svg>, the procedure is called unstable if a small change in <svg class="gs_fsvg" aria-label="\mathsf{L}" width="8px" height="10px" style="vertical-align:0px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 9.71600)"><g><path transform="scale(0.48828, -0.48828)" d="M 188 0 V 1421 H 379 V 139 L 1022 143 V 0 H 188 Z "/></g></g></svg> can cause large changes in <svg class="gs_fsvg" aria-label="{\hat{\mu}(\cdot, s)}" width="36px" height="14px" style="vertical-align:-4px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 10.50000)"><g><g><g><path transform="scale(0.48828, -0.48828)" d="M 57 -385 Q 57 -373 59 -369 L 360 840 Q 369 869 392 887 T 446 905 Q 472 905 490 889 T 508 848 Q 508 842 507 838 T 506 831 L 385 352 Q 365 267 365 205 Q 365 129 401 80 T 510 31 Q 659 31 772 217 Q 773 219 773 220 T 774 223 L 922 817 Q 929 844 954 863 T 1008 883 Q 1032 883 1050 867 T 1069 825 Q 1069 813 1067 809 L 920 219 Q 905 161 905 119 Q 905 31 965 31 Q 1029 31 1061 110 T 1118 301 Q 1122 313 1135 313 H 1159 Q 1167 313 1172 306 T 1178 293 Q 1142 150 1099 63 T 961 -23 Q 893 -23 840 16 T 772 121 Q 721 57 652 17 T 508 -23 Q 380 -23 307 37 L 203 -377 Q 197 -406 173 -424 T 119 -442 Q 94 -442 75 -427 T 57 -385 Z "/></g><g transform="translate(79.05900, -11.44501)"><path transform="scale(0.48828, -0.48828)" d="M 276 1102 L 236 1145 L 512 1421 L 786 1145 L 745 1102 L 512 1307 L 276 1102 Z "/></g></g><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 602.56000, 0.00000)" d="M 635 -508 Q 521 -418 438 -302 T 303 -53 T 225 223 T 199 512 Q 199 659 225 803 T 304 1080 T 441 1329 T 635 1532 Q 635 1536 645 1536 H 664 Q 670 1536 675 1530 T 680 1518 Q 680 1509 676 1505 Q 576 1407 509 1295 T 402 1056 T 344 794 T 326 512 Q 326 -139 674 -477 Q 680 -483 680 -494 Q 680 -499 674 -506 T 664 -512 H 645 Q 635 -512 635 -508 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 991.45001, 0.00000)" d="M 172 512 Q 172 541 187 567 T 228 609 T 285 625 Q 314 625 340 609 T 382 567 T 397 512 Q 397 466 364 432 T 285 399 Q 239 399 205 432 T 172 512 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1269.22998, 0.00000)" d="M 203 -369 Q 203 -360 211 -352 Q 285 -281 326 -188 T 367 8 V 33 Q 334 0 285 0 Q 238 0 205 33 T 172 113 Q 172 161 205 193 T 285 225 Q 358 225 389 157 T 420 8 Q 420 -106 374 -209 T 246 -393 Q 238 -397 233 -397 Q 223 -397 213 -388 T 203 -369 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1713.67712, 0.00000)" d="M 178 125 Q 233 31 399 31 Q 471 31 536 55 T 643 129 T 686 248 Q 686 301 648 335 T 555 381 L 444 403 Q 368 422 319 474 T 270 600 Q 270 691 319 761 T 450 868 T 618 905 Q 711 905 784 860 T 858 729 Q 858 682 831 646 T 758 610 Q 731 610 711 627 T 692 672 Q 692 696 705 718 T 741 754 T 788 768 Q 770 812 720 832 T 614 852 Q 562 852 510 831 T 426 769 T 395 674 Q 395 637 421 609 T 485 569 L 604 545 Q 661 533 708 502 T 783 425 T 811 319 Q 811 243 768 169 T 664 51 Q 555 -23 397 -23 Q 288 -23 197 27 T 106 176 Q 106 232 138 273 T 227 315 Q 260 315 282 295 T 305 242 Q 305 195 270 160 T 188 125 H 178 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 2182.45703, 0.00000)" d="M 133 -512 Q 115 -512 115 -494 Q 115 -485 119 -481 Q 469 -139 469 512 Q 469 1163 123 1501 Q 115 1506 115 1518 Q 115 1525 120 1530 T 133 1536 H 152 Q 158 1536 162 1532 Q 309 1416 407 1250 T 550 896 T 596 512 Q 596 367 571 226 T 493 -51 T 358 -303 T 162 -508 Q 158 -512 152 -512 H 133 Z "/></g></g></svg>. With a crystal ball, one could pick the predictor in <svg class="gs_fsvg" aria-label="{\hat{\mu}(\cdot, s)}" width="36px" height="14px" style="vertical-align:-4px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 10.50000)"><g><g><g><path transform="scale(0.48828, -0.48828)" d="M 57 -385 Q 57 -373 59 -369 L 360 840 Q 369 869 392 887 T 446 905 Q 472 905 490 889 T 508 848 Q 508 842 507 838 T 506 831 L 385 352 Q 365 267 365 205 Q 365 129 401 80 T 510 31 Q 659 31 772 217 Q 773 219 773 220 T 774 223 L 922 817 Q 929 844 954 863 T 1008 883 Q 1032 883 1050 867 T 1069 825 Q 1069 813 1067 809 L 920 219 Q 905 161 905 119 Q 905 31 965 31 Q 1029 31 1061 110 T 1118 301 Q 1122 313 1135 313 H 1159 Q 1167 313 1172 306 T 1178 293 Q 1142 150 1099 63 T 961 -23 Q 893 -23 840 16 T 772 121 Q 721 57 652 17 T 508 -23 Q 380 -23 307 37 L 203 -377 Q 197 -406 173 -424 T 119 -442 Q 94 -442 75 -427 T 57 -385 Z "/></g><g transform="translate(79.05900, -11.44501)"><path transform="scale(0.48828, -0.48828)" d="M 276 1102 L 236 1145 L 512 1421 L 786 1145 L 745 1102 L 512 1307 L 276 1102 Z "/></g></g><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 602.56000, 0.00000)" d="M 635 -508 Q 521 -418 438 -302 T 303 -53 T 225 223 T 199 512 Q 199 659 225 803 T 304 1080 T 441 1329 T 635 1532 Q 635 1536 645 1536 H 664 Q 670 1536 675 1530 T 680 1518 Q 680 1509 676 1505 Q 576 1407 509 1295 T 402 1056 T 344 794 T 326 512 Q 326 -139 674 -477 Q 680 -483 680 -494 Q 680 -499 674 -506 T 664 -512 H 645 Q 635 -512 635 -508 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 991.45001, 0.00000)" d="M 172 512 Q 172 541 187 567 T 228 609 T 285 625 Q 314 625 340 609 T 382 567 T 397 512 Q 397 466 364 432 T 285 399 Q 239 399 205 432 T 172 512 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1269.22998, 0.00000)" d="M 203 -369 Q 203 -360 211 -352 Q 285 -281 326 -188 T 367 8 V 33 Q 334 0 285 0 Q 238 0 205 33 T 172 113 Q 172 161 205 193 T 285 225 Q 358 225 389 157 T 420 8 Q 420 -106 374 -209 T 246 -393 Q 238 -397 233 -397 Q 223 -397 213 -388 T 203 -369 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1713.67712, 0.00000)" d="M 178 125 Q 233 31 399 31 Q 471 31 536 55 T 643 129 T 686 248 Q 686 301 648 335 T 555 381 L 444 403 Q 368 422 319 474 T 270 600 Q 270 691 319 761 T 450 868 T 618 905 Q 711 905 784 860 T 858 729 Q 858 682 831 646 T 758 610 Q 731 610 711 627 T 692 672 Q 692 696 705 718 T 741 754 T 788 768 Q 770 812 720 832 T 614 852 Q 562 852 510 831 T 426 769 T 395 674 Q 395 637 421 609 T 485 569 L 604 545 Q 661 533 708 502 T 783 425 T 811 319 Q 811 243 768 169 T 664 51 Q 555 -23 397 -23 Q 288 -23 197 27 T 106 176 Q 106 232 138 273 T 227 315 Q 260 315 282 295 T 305 242 Q 305 195 270 160 T 188 125 H 178 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 2182.45703, 0.00000)" d="M 133 -512 Q 115 -512 115 -494 Q 115 -485 119 -481 Q 469 -139 469 512 Q 469 1163 123 1501 Q 115 1506 115 1518 Q 115 1525 120 1530 T 133 1536 H 152 Q 158 1536 162 1532 Q 309 1416 407 1250 T 550 896 T 596 512 Q 596 367 571 226 T 493 -51 T 358 -303 T 162 -508 Q 158 -512 152 -512 H 133 Z "/></g></g></svg> having minimum prediction error. Without prescience, one uses test sets, cross-validation and so forth. The difference in prediction error between the crystal ball selection and the statistician's choice we call predictive loss. For an unstable procedure the predictive loss is large. This is shown by some analytics in a simple case and by simulation results in a more complex comparison of four different linear regression methods. Unstable procedures can …</div></div></div><div class="gs_scl"><div class="gsc_oci_field">Total citations</div><div class="gsc_oci_value"><div style="margin-bottom:1em"><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5">Cited by 1773</a></div><div id="gsc_oci_graph_wrapper"><div id="gsc_oci_graph" style="width:955px;"><div id="gsc_oci_graph_x"></div><div id="gsc_oci_graph_bars"><span class="gsc_oci_g_t" style="left:0px">1996</span><span class="gsc_oci_g_t" style="left:33px">1997</span><span class="gsc_oci_g_t" style="left:66px">1998</span><span class="gsc_oci_g_t" style="left:99px">1999</span><span class="gsc_oci_g_t" style="left:132px">2000</span><span class="gsc_oci_g_t" style="left:165px">2001</span><span class="gsc_oci_g_t" style="left:198px">2002</span><span class="gsc_oci_g_t" style="left:231px">2003</span><span class="gsc_oci_g_t" style="left:264px">2004</span><span class="gsc_oci_g_t" style="left:297px">2005</span><span class="gsc_oci_g_t" style="left:330px">2006</span><span class="gsc_oci_g_t" style="left:363px">2007</span><span class="gsc_oci_g_t" style="left:396px">2008</span><span class="gsc_oci_g_t" style="left:429px">2009</span><span class="gsc_oci_g_t" style="left:462px">2010</span><span class="gsc_oci_g_t" style="left:495px">2011</span><span class="gsc_oci_g_t" style="left:528px">2012</span><span class="gsc_oci_g_t" style="left:561px">2013</span><span class="gsc_oci_g_t" style="left:594px">2014</span><span class="gsc_oci_g_t" style="left:627px">2015</span><span class="gsc_oci_g_t" style="left:660px">2016</span><span class="gsc_oci_g_t" style="left:693px">2017</span><span class="gsc_oci_g_t" style="left:726px">2018</span><span class="gsc_oci_g_t" style="left:759px">2019</span><span class="gsc_oci_g_t" style="left:792px">2020</span><span class="gsc_oci_g_t" style="left:825px">2021</span><span class="gsc_oci_g_t" style="left:858px">2022</span><span class="gsc_oci_g_t" style="left:891px">2023</span><span class="gsc_oci_g_t" style="left:924px">2024</span><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=1996&as_yhi=1996" class="gsc_oci_g_a" style="left:5px;height:7px;top:50px;z-index:29"><span class="gsc_oci_g_al">12</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=1997&as_yhi=1997" class="gsc_oci_g_a" style="left:38px;height:4px;top:53px;z-index:28"><span class="gsc_oci_g_al">6</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=1998&as_yhi=1998" class="gsc_oci_g_a" style="left:71px;height:9px;top:48px;z-index:27"><span class="gsc_oci_g_al">15</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=1999&as_yhi=1999" class="gsc_oci_g_a" style="left:104px;height:16px;top:41px;z-index:26"><span class="gsc_oci_g_al">27</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2000&as_yhi=2000" class="gsc_oci_g_a" style="left:137px;height:20px;top:37px;z-index:25"><span class="gsc_oci_g_al">33</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2001&as_yhi=2001" class="gsc_oci_g_a" style="left:170px;height:14px;top:43px;z-index:24"><span class="gsc_oci_g_al">23</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2002&as_yhi=2002" class="gsc_oci_g_a" style="left:203px;height:17px;top:40px;z-index:23"><span class="gsc_oci_g_al">29</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2003&as_yhi=2003" class="gsc_oci_g_a" style="left:236px;height:16px;top:41px;z-index:22"><span class="gsc_oci_g_al">27</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2004&as_yhi=2004" class="gsc_oci_g_a" style="left:269px;height:23px;top:34px;z-index:21"><span class="gsc_oci_g_al">39</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2005&as_yhi=2005" class="gsc_oci_g_a" style="left:302px;height:29px;top:28px;z-index:20"><span class="gsc_oci_g_al">49</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2006&as_yhi=2006" class="gsc_oci_g_a" style="left:335px;height:29px;top:28px;z-index:19"><span class="gsc_oci_g_al">49</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2007&as_yhi=2007" class="gsc_oci_g_a" style="left:368px;height:33px;top:24px;z-index:18"><span class="gsc_oci_g_al">55</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2008&as_yhi=2008" class="gsc_oci_g_a" style="left:401px;height:42px;top:15px;z-index:17"><span class="gsc_oci_g_al">70</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2009&as_yhi=2009" class="gsc_oci_g_a" style="left:434px;height:52px;top:5px;z-index:16"><span class="gsc_oci_g_al">86</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2010&as_yhi=2010" class="gsc_oci_g_a" style="left:467px;height:43px;top:14px;z-index:15"><span class="gsc_oci_g_al">71</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2011&as_yhi=2011" class="gsc_oci_g_a" style="left:500px;height:45px;top:12px;z-index:14"><span class="gsc_oci_g_al">75</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2012&as_yhi=2012" class="gsc_oci_g_a" style="left:533px;height:55px;top:2px;z-index:13"><span class="gsc_oci_g_al">91</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2013&as_yhi=2013" class="gsc_oci_g_a" style="left:566px;height:56px;top:1px;z-index:12"><span class="gsc_oci_g_al">93</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2014&as_yhi=2014" class="gsc_oci_g_a" style="left:599px;height:57px;top:0px;z-index:11"><span class="gsc_oci_g_al">95</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2015&as_yhi=2015" class="gsc_oci_g_a" style="left:632px;height:54px;top:3px;z-index:10"><span class="gsc_oci_g_al">90</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2016&as_yhi=2016" class="gsc_oci_g_a" style="left:665px;height:51px;top:6px;z-index:9"><span class="gsc_oci_g_al">85</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2017&as_yhi=2017" class="gsc_oci_g_a" style="left:698px;height:51px;top:6px;z-index:8"><span class="gsc_oci_g_al">85</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2018&as_yhi=2018" class="gsc_oci_g_a" style="left:731px;height:57px;top:0px;z-index:7"><span class="gsc_oci_g_al">95</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2019&as_yhi=2019" class="gsc_oci_g_a" style="left:764px;height:48px;top:9px;z-index:6"><span class="gsc_oci_g_al">80</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2020&as_yhi=2020" class="gsc_oci_g_a" style="left:797px;height:49px;top:8px;z-index:5"><span class="gsc_oci_g_al">82</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2021&as_yhi=2021" class="gsc_oci_g_a" style="left:830px;height:47px;top:10px;z-index:4"><span class="gsc_oci_g_al">79</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2022&as_yhi=2022" class="gsc_oci_g_a" style="left:863px;height:48px;top:9px;z-index:3"><span class="gsc_oci_g_al">80</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2023&as_yhi=2023" class="gsc_oci_g_a" style="left:896px;height:46px;top:11px;z-index:2"><span class="gsc_oci_g_al">76</span></a><a href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5&as_ylo=2024&as_yhi=2024" class="gsc_oci_g_a" style="left:929px;height:38px;top:19px;z-index:1"><span class="gsc_oci_g_al">63</span></a></div></div></div></div></div><div class="gs_scl"><div class="gsc_oci_field">Scholar articles</div><div class="gsc_oci_value"><div class="gsc_oci_merged_snippet"><div><a href="/scholar?oi=bibs&cluster=7867375791791795936&btnI=1&hl=en">Heuristics of instability and stabilization in model selection</a></div><div>L Breiman - The annals of statistics, 1996</div><div><a class="gsc_oms_link" href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cites=7867375791791795936&as_sdt=5">Cited by 1773</a> <a class="gsc_oms_link" href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&q=related:4O5BeJmILm0J:scholar.google.com/">Related articles</a> <a class="gsc_oms_link" href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cluster=7867375791791795936">All 14 versions</a> </div></div></div></div></div></div></div></div><div id="gs_ftr_sp" role="presentation"></div><div id="gs_ftr" class="gs_md_rmb" role="contentinfo"><div id="gs_ftr_rt"><a href="//www.google.co.in/intl/en/policies/privacy/">Privacy</a><a href="//www.google.co.in/intl/en/policies/terms/">Terms</a><a href="javascript:void(0)" ontouchstart="gs_evt_dsp(event)" role="button" aria-controls="gs_ftr_mnu" aria-haspopup="true" class="gs_press gs_md_tb">Help</a></div><div id="gs_ftr_mnu" class="gs_md_d gs_md_ds gs_ttzi gs_md_ulr" role="menu" tabindex="-1"><a role="menuitem" href="/intl/en/scholar/about.html" tabindex="-1" class="gs_md_li">About Scholar</a><a role="menuitem" href="//support.google.com/websearch?p=scholar_dsa&hl=en" tabindex="-1" class="gs_md_li">Search help</a></div></div></div></body></html>