{"id":939,"date":"2019-05-04T20:49:38","date_gmt":"2019-05-04T20:49:38","guid":{"rendered":"http:\/\/x-colony.com\/PoCo\/?page_id=939"},"modified":"2020-01-28T04:15:02","modified_gmt":"2020-01-28T04:15:02","slug":"max-module-decomposition","status":"publish","type":"page","link":"http:\/\/x-colony.com\/PoCo\/index.php\/learning\/problem-posing\/max-module-decomposition\/","title":{"rendered":"Max Module Decomposition"},"content":{"rendered":"\n<p><strong>Maximal Module Decomposition<\/strong><\/p>\n\n\n\n<p>A complex module was obtained by gluing together several cubes. You must identify a maximal module that generates a perfect decomposition of the original object (The original object can be reassembled from a number of maximal modules and nothing else).<\/p>\n\n\n\n<p>For instance, given the object shown below,<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"215\" height=\"304\" src=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/05\/image.png\" alt=\"\" class=\"wp-image-940\" srcset=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/05\/image.png 215w, http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/05\/image-212x300.png 212w\" sizes=\"(max-width: 215px) 85vw, 215px\" \/><\/figure><\/div>\n\n\n\n<p>one will find that a maximal decomposition is<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"195\" height=\"307\" src=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/05\/image-1.png\" alt=\"\" class=\"wp-image-941\" srcset=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/05\/image-1.png 195w, http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/05\/image-1-191x300.png 191w\" sizes=\"(max-width: 195px) 85vw, 195px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Proposed Problem. <\/strong>Find a Maximal Module Decomposition of the following ensembles of cubes.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"297\" height=\"309\" src=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/05\/image-2.png\" alt=\"\" class=\"wp-image-942\" srcset=\"http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/05\/image-2.png 297w, http:\/\/x-colony.com\/PoCo\/wp-content\/uploads\/2019\/05\/image-2-288x300.png 288w\" sizes=\"(max-width: 297px) 85vw, 297px\" \/><\/figure><\/div>\n\n\n\n<p>Watch the first part of the video. Pause when the message appears, find the solution and resume. One solution is presented in the second half of the video.<\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" width=\"840\" height=\"473\" src=\"https:\/\/www.youtube.com\/embed\/7KEqreGfCd8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>Note that the number of cubes in a maximal decomposition\nmodule should be a divider of the total number of cubes. In this case the\nnumber of cubes is 76. &nbsp;Therefore, the\nmaximal candidate is a 19-cube ensemble. <\/p>\n\n\n\n<p>A second idea that can be followed is to investigate\nsymmetric properties. In this case, this idea does not help.<\/p>\n\n\n\n<p>Another hint you should consider is to think how you can\nprove your solution is correct. Well, it will suffice to compose the initial\nobject using a specified number of copies of the module you proposed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Maximal Module Decomposition A complex module was obtained by gluing together several cubes. You must identify a maximal module that generates a perfect decomposition of the original object (The original object can be reassembled from a number of maximal modules and nothing else). For instance, given the object shown below, one will find that a &hellip; <a href=\"http:\/\/x-colony.com\/PoCo\/index.php\/learning\/problem-posing\/max-module-decomposition\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Max Module Decomposition&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":936,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages\/939"}],"collection":[{"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/comments?post=939"}],"version-history":[{"count":4,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages\/939\/revisions"}],"predecessor-version":[{"id":947,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages\/939\/revisions\/947"}],"up":[{"embeddable":true,"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/pages\/936"}],"wp:attachment":[{"href":"http:\/\/x-colony.com\/PoCo\/index.php\/wp-json\/wp\/v2\/media?parent=939"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}