{"id":192766,"date":"2015-09-18T00:00:00","date_gmt":"2015-09-18T06:08:23","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/local-views-and-global-conclusions\/"},"modified":"2016-07-15T15:26:36","modified_gmt":"2016-07-15T22:26:36","slug":"local-views-and-global-conclusions","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/local-views-and-global-conclusions\/","title":{"rendered":"Local Views and Global Conclusions"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Graph-structured data has become a universal phenomenon in the sciences, and novel mathematics is required to tackle the problems stemming from analyzing this data. The following challenge in bioinformatics exemplifies this general class of problems: the protein Interaction graph G of an organism has one vertex for each of its proteins and an edge for each pair of interacting proteins; several competing theories attempt to describe how such graphs emerge in evolution and we wish to tell which theory provides a better explanation.<\/p>\n<p>A major difficulty in resolving such problems is that G is huge so it is unrealistic to calculate most of its nontrivial graph parameters. But even a huge graph G can be efficiently sampled. Given a small integer k (say k=10), the k-profile of G is a distribution on k-vertex graphs. It is derived by randomly sampling k vertices in G and observing the subgraph that they induce. A theory largely developed in MSR (&#8220;Theory of graph limits&#8221; &#8211; Lovasz, Szegedy, Chayes, Borgs, Cohn, Friedman&#8230;) offers a clue. It says essentially that to decide whether a series of large graphs is derived from a given statistical model it is enough to check that the graphs&#8217; profiles behave as they should.<\/p>\n<p>I will give you some sense of the theory of graph limits and then move to discuss profiles. The two main questions are: (i) Which profiles are possible? (ii) What global properties of G can you derive, based on its profiles?<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Graph-structured data has become a universal phenomenon in the sciences, and novel mathematics is required to tackle the problems stemming from analyzing this data. The following challenge in bioinformatics exemplifies this general class of problems: the protein Interaction graph G of an organism has one vertex for each of its proteins and an edge for [&hellip;]<\/p>\n","protected":false},"featured_media":199271,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-192766","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/Vhhba3Vz-tc","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192766"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192766\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/199271"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=192766"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=192766"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=192766"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=192766"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=192766"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=192766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}