[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-665371-105":59,"doc-detail-665371-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","jmm2021talk-random-graph-grid-diagrams-and-knotlink-grid-diagrams","JMM2021Talk - Random Graph Grid Diagrams and Knot/Link Grid Diagrams","","Talk content explaining random spatial graphs and knot theory concepts, then focusing on grid diagrams as a computer-friendly representation of knots and links using X/O markings on square grids. It introduces questions about cycles in random spatial graphs and whether such cycles are likely to be knotted. The talk discusses students’ reproducible R coding to randomly generate grid diagrams, determine link components, and compute confidence intervals for component proportions across grid sizes, emphasizing that findings concern links represented by random grid diagrams rather than random link generation.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/jmm2021talk-random-graph-grid-diagrams-and-knotlink-grid-diagrams/665371/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/jmm2021talk-random-graph-grid-diagrams-and-knotlink-grid-diagrams/665371.png","ImageObject",300,407,{"name":92,"@type":93},"A glass of water","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is a random spatial graph and what questions does the talk raise about its cycles?","Question",{"text":112,"@type":113},"The talk defines the focus as random spatial graphs and asks what can be said about cycles, specifically whether cycles are likely to be knotted. It frames this as motivation for understanding knotting in spatial randomness.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the talk define a grid diagram for knots and links?",{"text":117,"@type":113},"A grid diagram is presented as a square grid marked with X's and O's, with exactly one X and one O in each row and column. The X/O positions determine the orientation and provide a computer-friendly way to specify a link or knot.",{"name":119,"@type":110,"acceptedAnswer":120},"What do students’ reproducible computations do with randomly generated grid diagrams?",{"text":121,"@type":113},"Students write code to randomly generate knot and link grid diagrams, determine the number of components of the link each diagram represents, and calculate confidence intervals for the proportion of links with given component counts at each grid size.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},665371,1793301552,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},962090760832,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Random Graph Grid Diagrams  \nKatherine Vance  \nSimpson College  \nJanuary 6, 2021  \nQuestions  \nI What is a random spatial graph?  \nI What can we say about the cycles in a random spatial graph?  \nAre they likely to be knotted?  \nQuestions  \nI What is a random spatial graph?  \nI What can we say about the cycles in a random spatial graph?  \nAre they likely to be knotted?  \nI Will my students care?  \nKnot Theory at Simpson College  \nI SLAC in Iowa  \nI Research serves teaching I Math, Actuarial Science,  \n& Data Science Majors I Lots of Math/Computer  \nScience Double Majors  \nKnot Theory at Simpson College  \nI SLAC in Iowa  \nI Research serves teaching I Math, Actuarial Science,  \n& Data Science Majors I Lots of Math/Computer  \nScience Double Majors I Grid diagrams are awesome! I Primary coding language: R  \nRandom Knot & Link Grid Diagrams  \nEli Marriott, Max Folkers, Miguel Sanchez (not pictured)  \nBryan Summer Research Program 2019  \nWhat is the probability that a randomly generated grid diagram of size n will represent a c component link?  \nWhat is a grid diagram?  \nI One way to represent knots and links  \nI Square grids marked with X's and O's  \nI Exactly one X and O in each row and column  \nI The position of the X's and O's determine the orientation I A computer-friendly way to specify a link or knot!  \nStudents wrote reproducible code to ...  \nI randomly generate knot & link grid diagrams  \nI determine the number of components of the link represented by each grid diagram  \nI calculate con􀀌dence intervals for the proportion of links with a given number of components represented by grid diagrams of a given size  \nNote: These are not results about random links ...  \nStudents wrote reproducible code to ...  \nI randomly generate knot & link grid diagrams  \nI determine the number of components of the link represented by each grid diagram  \nI calculate con􀀌dence intervals for the proportion of links with a given number of components represented by grid diagrams of a given size  \nNote: These are not results about random links ...  \nThey are results about links represented by random grid diagrams!","cbCaiujRoP204Zil","https://ap.wps.com/l/cbCaiujRoP204Zil","pdf",4744267,28,"English","# Questions\n## Random spatial graphs and knotting likelihood\n# Knot theory at Simpson College\n## SLAC and research-teaching connections\n# Random knot & link grid diagrams\n## Grid diagram definition (X/O encoding)\n## Probability of component links\n## Student reproducible code and confidence intervals\n## Scope note: links represented by random grid diagrams","[{\"question\":\"What is a random spatial graph and what questions does the talk raise about its cycles?\",\"answer\":\"The talk defines the focus as random spatial graphs and asks what can be said about cycles, specifically whether cycles are likely to be knotted. It frames this as motivation for understanding knotting in spatial randomness.\"},{\"question\":\"How does the talk define a grid diagram for knots and links?\",\"answer\":\"A grid diagram is presented as a square grid marked with X's and O's, with exactly one X and one O in each row and column. The X/O positions determine the orientation and provide a computer-friendly way to specify a link or knot.\"},{\"question\":\"What do students’ reproducible computations do with randomly generated grid diagrams?\",\"answer\":\"Students write code to randomly generate knot and link grid diagrams, determine the number of components of the link each diagram represents, and calculate confidence intervals for the proportion of links with given component counts at each grid size.\"}]","JMM2021Talk - Random Graph Grid Diagrams and Knot/Link Grid Diagrams | PDF",71]