{"id":549,"date":"2019-10-03T16:33:49","date_gmt":"2019-10-03T13:33:49","guid":{"rendered":"http:\/\/modinst.lu.lv\/pakalpojums\/sistemu-optimizacija\/"},"modified":"2021-02-11T12:21:31","modified_gmt":"2021-02-11T10:21:31","slug":"sistemu-optimizacija","status":"publish","type":"portfolio","link":"https:\/\/modinst.lu.lv\/en\/pakalpojums\/sistemu-optimizacija\/","title":{"rendered":"Systems Optimization"},"content":{"rendered":"<div id='full_slider_1'  class='avia-fullwidth-slider main_color avia-shadow   avia-builder-el-0  el_before_av_one_third  avia-builder-el-first   container_wrap fullsize'  >\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-k1ap8qrb-6c5a37323ec2ab50c8cf100459ab31a8\">\n#top #wrap_all .avia-slideshow .av-slideshow-caption.av-k1ap8qrb-6c5a37323ec2ab50c8cf100459ab31a8__0 .avia-caption-title{\nfont-size:40px;\n}\n<\/style>\n<div  class='avia-slideshow av-k1ap8qrb-6c5a37323ec2ab50c8cf100459ab31a8 avia-slideshow-featured av_slideshow_full avia-slide-slider av-slideshow-ui av-control-default av-slideshow-manual av-loop-once av-loop-manual-endless av-default-height-applied   avia-slideshow-1' data-slideshow-options=\"{&quot;animation&quot;:&quot;slide&quot;,&quot;autoplay&quot;:false,&quot;loop_autoplay&quot;:&quot;once&quot;,&quot;interval&quot;:5,&quot;loop_manual&quot;:&quot;manual-endless&quot;,&quot;autoplay_stopper&quot;:false,&quot;noNavigation&quot;:false,&quot;bg_slider&quot;:false,&quot;keep_padding&quot;:false,&quot;hoverpause&quot;:false,&quot;show_slide_delay&quot;:0}\"  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><ul class='avia-slideshow-inner ' style='padding-bottom: 28.666666666667%;'><li  class='avia-slideshow-slide av-k1ap8qrb-6c5a37323ec2ab50c8cf100459ab31a8__0  av-single-slide slide-1 slide-odd'><div data-rel='slideshow-1' class='avia-slide-wrap '   ><div class='av-slideshow-caption av-k1ap8qrb-6c5a37323ec2ab50c8cf100459ab31a8__0 caption_fullwidth caption_left caption_left_framed caption_framed'><div class=\"container caption_container\"><div class=\"slideshow_caption\"><div class=\"slideshow_inner_caption\"><div class=\"slideshow_align_caption\"><h2 class='avia-caption-title '  itemprop=\"name\" >Systems Optimization<\/h2><\/div><\/div><\/div><\/div><\/div><img decoding=\"async\" fetchpriority=\"high\" class=\"wp-image-283 avia-img-lazy-loading-not-283\"  src=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/05_systems_optimization-1500x430.jpg\" width=\"1500\" height=\"430\" title='Systems Optimization' alt=''  itemprop=\"thumbnailUrl\"   \/><\/div><\/li><\/ul><\/div><\/div><div id='after_full_slider_1'  class='main_color av_default_container_wrap container_wrap fullsize'  ><div class='container av-section-cont-open' ><div class='template-page content  av-content-full alpha units'><div class='post-entry post-entry-type-page post-entry-549'><div class='entry-content-wrapper clearfix'>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-43dzw-5f07ddf63ce90020e03be11d881b717a\">\n.flex_column.av-43dzw-5f07ddf63ce90020e03be11d881b717a{\nborder-radius:0px 0px 0px 0px;\npadding:12px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-43dzw-5f07ddf63ce90020e03be11d881b717a av_one_third  avia-builder-el-1  el_after_av_slideshow_full  el_before_av_two_third  avia-builder-el-first  first flex_column_div  '     ><style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-k5r5ju3t-8ef36ac4329dccfacecaea885772b567\">\n#top .av-special-heading.av-k5r5ju3t-8ef36ac4329dccfacecaea885772b567{\npadding-bottom:10px;\n}\nbody .av-special-heading.av-k5r5ju3t-8ef36ac4329dccfacecaea885772b567 .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-k5r5ju3t-8ef36ac4329dccfacecaea885772b567 .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-k5r5ju3t-8ef36ac4329dccfacecaea885772b567 av-special-heading-h3  avia-builder-el-2  avia-builder-el-no-sibling  av-linked-heading'><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Description<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-3dc40-e854055df818c48ede0bdd9ba620687a\">\n.flex_column.av-3dc40-e854055df818c48ede0bdd9ba620687a{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-3dc40-e854055df818c48ede0bdd9ba620687a av_two_third  avia-builder-el-3  el_after_av_one_third  el_before_av_one_third  flex_column_div av-zero-column-padding  '     ><style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-k1apb7r2-20f1c323e0c138ebe244e153d2ce7d74\">\n#top .av_textblock_section.av-k1apb7r2-20f1c323e0c138ebe244e153d2ce7d74 .avia_textblock{\nfont-size:15px;\n}\n<\/style>\n<section  class='av_textblock_section av-k1apb7r2-20f1c323e0c138ebe244e153d2ce7d74 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><span style=\"font-weight: 400;\">Computer assisted systems optimization is the modern-day standard for industrial R&#038;D, reducing product time-to-market and development expense. Optimization processes can be constructed on top of virtually any physical simulation framework, provided one specifies a set of valid objectives and constraints.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The service we provide is: for a given physical system (involving electromagnetic phenomena, heat transfer, fluid flow, solid mechanics, ray optics, particles driven by forces within the system), we can set up the mathematical model, define objectives and constraints based on the objectives of the client, and implement suitable algorithms to produce the required results.<\/span><\/p>\n<\/div><\/section><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-9y5o-4f8a7c56870639f48595133e6a463c41\">\n.flex_column.av-9y5o-4f8a7c56870639f48595133e6a463c41{\nborder-radius:0px 0px 0px 0px;\npadding:12px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-9y5o-4f8a7c56870639f48595133e6a463c41 av_one_third  avia-builder-el-5  el_after_av_two_third  el_before_av_two_third  first flex_column_div  column-top-margin'     ><style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-k5r5kv4g-7d4aceeed8183d6dcbcc9a609de744ff\">\n#top .av-special-heading.av-k5r5kv4g-7d4aceeed8183d6dcbcc9a609de744ff{\npadding-bottom:10px;\n}\nbody .av-special-heading.av-k5r5kv4g-7d4aceeed8183d6dcbcc9a609de744ff .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-k5r5kv4g-7d4aceeed8183d6dcbcc9a609de744ff .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-k5r5kv4g-7d4aceeed8183d6dcbcc9a609de744ff av-special-heading-h3  avia-builder-el-6  avia-builder-el-no-sibling  av-linked-heading'><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Methodology<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-2832w-9a10d3ed6cac4785cce6cfb11453ae57\">\n.flex_column.av-2832w-9a10d3ed6cac4785cce6cfb11453ae57{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-2832w-9a10d3ed6cac4785cce6cfb11453ae57 av_two_third  avia-builder-el-7  el_after_av_one_third  el_before_av_one_third  flex_column_div av-zero-column-padding  column-top-margin'     ><section  class='av_textblock_section av-k1apb7r2-5eee81fa3a7a1d11b35decb5f7f529bb '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><span style=\"font-weight: 400;\">We use commercial simulation packages (COMSOL) as well as our own specialized code to translate customers\u2019 goals into a mathematical model and perform physical simulations and optimize the given systems.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">We offer parametric, shape, and topological optimization, covering both geometry variations and simple parameters. Finite element method (FEM) is used for systems modelling, while for optimization we employ gradient-free algorithms, such as Nelder-Mead, COBYLA, BOBYQA, MMA, SNOPT.<\/span><\/p>\n<\/div><\/section><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-19qfg-404f02c871126d24094bc189d7491708\">\n.flex_column.av-19qfg-404f02c871126d24094bc189d7491708{\nborder-radius:0px 0px 0px 0px;\npadding:12px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-19qfg-404f02c871126d24094bc189d7491708 av_one_third  avia-builder-el-9  el_after_av_two_third  el_before_av_two_third  first flex_column_div  column-top-margin'     ><style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-k5r5lggw-6f569d21f1c4765f118fa6cb3792039d\">\n#top .av-special-heading.av-k5r5lggw-6f569d21f1c4765f118fa6cb3792039d{\npadding-bottom:10px;\n}\nbody .av-special-heading.av-k5r5lggw-6f569d21f1c4765f118fa6cb3792039d .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-k5r5lggw-6f569d21f1c4765f118fa6cb3792039d .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-k5r5lggw-6f569d21f1c4765f118fa6cb3792039d av-special-heading-h3  avia-builder-el-10  avia-builder-el-no-sibling  av-linked-heading'><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Projects<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-vqc8-0995ef62a676a626f98efab2d5647406\">\n.flex_column.av-vqc8-0995ef62a676a626f98efab2d5647406{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-vqc8-0995ef62a676a626f98efab2d5647406 av_two_third  avia-builder-el-11  el_after_av_one_third  el_before_av_one_third  flex_column_div av-zero-column-padding  column-top-margin'     ><section  class='av_textblock_section av-k1apb7r2-5eee81fa3a7a1d11b35decb5f7f529bb '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Cooperation agreement with SIA Vizulo (Latvia): development of ray tracing models for industrial luminaires and optimization of spatial illumination patterns.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Shape optimization for plastic containers for liquid foodstuff transportation and storage.<\/span><\/li>\n<\/ul>\n<\/div><\/section><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-19qfg-404f02c871126d24094bc189d7491708\">\n.flex_column.av-19qfg-404f02c871126d24094bc189d7491708{\nborder-radius:0px 0px 0px 0px;\npadding:12px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-19qfg-404f02c871126d24094bc189d7491708 av_one_third  avia-builder-el-13  el_after_av_two_third  el_before_av_two_third  first flex_column_div  column-top-margin'     ><style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-k5r5mavv-892546fc19c7b0c15d93185cb2687e87\">\n#top .av-special-heading.av-k5r5mavv-892546fc19c7b0c15d93185cb2687e87{\npadding-bottom:10px;\n}\nbody .av-special-heading.av-k5r5mavv-892546fc19c7b0c15d93185cb2687e87 .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-k5r5mavv-892546fc19c7b0c15d93185cb2687e87 .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-k5r5mavv-892546fc19c7b0c15d93185cb2687e87 av-special-heading-h3  avia-builder-el-14  avia-builder-el-no-sibling  av-linked-heading'><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Contact<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-vqc8-0995ef62a676a626f98efab2d5647406\">\n.flex_column.av-vqc8-0995ef62a676a626f98efab2d5647406{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-vqc8-0995ef62a676a626f98efab2d5647406 av_two_third  avia-builder-el-15  el_after_av_one_third  el_before_av_section  avia-builder-el-last  flex_column_div av-zero-column-padding  column-top-margin'     ><section  class='av_textblock_section av-k1apqgy8-ba0ff599884bc83483b8ac15d5f629f4 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><span lang=\"EN\"><strong>Andris Jakovi\u010ds, Dr.Phys.<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1826\" src=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2021\/02\/14231000421530272912-128-e1612427865894.png\" alt=\"\" width=\"16\" height=\"16\" \/> +371 29 155 711<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1690\" src=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2021\/01\/8817370761579252550-128.png\" alt=\"\" width=\"16\" height=\"16\" srcset=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2021\/01\/8817370761579252550-128.png 128w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2021\/01\/8817370761579252550-128-80x80.png 80w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2021\/01\/8817370761579252550-128-36x36.png 36w\" sizes=\"auto, (max-width: 16px) 100vw, 16px\" \/> <a href=\"mailto:andris.jakovics@lu.lv\">andris.jakovics@lu.lv<\/a><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1688\" src=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2021\/01\/ORCIDiD_icon128x128.png\" alt=\"\" width=\"16\" height=\"16\" srcset=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2021\/01\/ORCIDiD_icon128x128.png 128w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2021\/01\/ORCIDiD_icon128x128-80x80.png 80w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2021\/01\/ORCIDiD_icon128x128-36x36.png 36w\" sizes=\"auto, (max-width: 16px) 100vw, 16px\" \/> <a href=\"https:\/\/orcid.org\/0000-0003-3410-5081\">0000-0003-3410-5081<\/a><\/span><\/p>\n<\/div><\/section><\/div><\/div><\/div><\/div><!-- close content main div --><\/div><\/div><div id='av_section_1'  class='avia-section av-yihs-e6df93b481533462b214a0083120c98d main_color avia-section-default avia-no-border-styling  avia-builder-el-17  el_after_av_two_third  avia-builder-el-last  avia-bg-style-scroll container_wrap fullsize'  ><div class='container av-section-cont-open' ><div class='template-page content  av-content-full alpha units'><div class='post-entry post-entry-type-page post-entry-549'><div class='entry-content-wrapper clearfix'>\n<div id='av-masonry-1' class='av-masonry av-k1apfe60-716e1976afdb3e245908ebae293fcc36 noHover av-fixed-size av-1px-gap av-hover-overlay-active av-masonry-animation-active av-masonry-col-flexible av-caption-always av-caption-style- av-masonry-gallery av-orientation-square ' data-post_id=\"549\"><div class=\"av-masonry-container isotope av-js-disabled\"><div class='av-masonry-entry isotope-item av-masonry-item-no-image '><\/div><a href=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Fotolia_63011602_Subscription_Monthly_M-1030x684.jpg\" data-srcset=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Fotolia_63011602_Subscription_Monthly_M-1030x684.jpg 1030w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Fotolia_63011602_Subscription_Monthly_M-300x199.jpg 300w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Fotolia_63011602_Subscription_Monthly_M-768x510.jpg 768w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Fotolia_63011602_Subscription_Monthly_M-1500x997.jpg 1500w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Fotolia_63011602_Subscription_Monthly_M-705x468.jpg 705w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Fotolia_63011602_Subscription_Monthly_M.jpg 1600w\" data-sizes=\"(max-width: 1030px) 100vw, 1030px\"  aria-label=\"image Example of Numerical Optimization for the Construction of a Truss Bridge\"  id='av-masonry-1-item-285' data-av-masonry-item='285' class='av-masonry-entry isotope-item post-285 attachment type-attachment status-inherit hentry  av-masonry-item-with-image' title=\"Example of Numerical Optimization for the Construction of a Truss Bridge\" alt=\"\"    itemprop=\"thumbnailUrl\" ><div class='av-inner-masonry-sizer'><\/div><figure class='av-inner-masonry main_color'><div class=\"av-masonry-outerimage-container\"><div class='av-masonry-image-container' style=\"background-image: url(https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Fotolia_63011602_Subscription_Monthly_M-705x468.jpg);\"  title=\"Example of Numerical Optimization for the Construction of a Truss Bridge\" ><\/div><\/div><\/figure><\/a><!--end av-masonry entry--><a href=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-Copy-1030x713.jpg\" data-srcset=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-Copy-1030x713.jpg 1030w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-Copy-300x208.jpg 300w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-Copy-768x531.jpg 768w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-Copy-1500x1038.jpg 1500w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-Copy-705x488.jpg 705w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-Copy.jpg 1600w\" data-sizes=\"(max-width: 1030px) 100vw, 1030px\"  aria-label=\"image Example of Numerical Optimization for the Construction of a Truss Bridge\"  id='av-masonry-1-item-286' data-av-masonry-item='286' class='av-masonry-entry isotope-item post-286 attachment type-attachment status-inherit hentry  av-masonry-item-with-image' title=\"Example of Numerical Optimization for the Construction of a Truss Bridge\" alt=\"\"    itemprop=\"thumbnailUrl\" ><div class='av-inner-masonry-sizer'><\/div><figure class='av-inner-masonry main_color'><div class=\"av-masonry-outerimage-container\"><div class='av-masonry-image-container' style=\"background-image: url(https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-Copy-705x488.jpg);\"  title=\"Example of Numerical Optimization for the Construction of a Truss Bridge\" ><\/div><\/div><\/figure><\/a><!--end av-masonry entry--><a href=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-853x1030.jpg\" data-srcset=\"https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-853x1030.jpg 853w, https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-248x300.jpg 248w, 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style=\"background-image: url(https:\/\/modinst.lu.lv\/wp-content\/uploads\/2019\/10\/Optimization-Example-584x705.jpg);\"  title=\"Example of Numerical Optimization for the Construction of a Truss Bridge\" ><\/div><\/div><\/figure><\/a><!--end av-masonry entry--><\/div><\/div>\n<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":5,"featured_media":283,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[],"portfolio_entries":[16],"class_list":["post-549","portfolio","type-portfolio","status-publish","has-post-thumbnail","hentry","portfolio_entries-research"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Systems Optimization - Institute of Numerical Modelling<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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