{"id":457,"date":"2021-07-05T14:14:00","date_gmt":"2021-07-05T14:14:00","guid":{"rendered":"http:\/\/grada.wp\/vara\/?p=457"},"modified":"2024-01-03T14:14:52","modified_gmt":"2024-01-03T14:14:52","slug":"expansion-of-parametric-analysis-on-william-m-penas-programming-matrix-theory-based-on-graph-theory","status":"publish","type":"post","link":"https:\/\/az-tdc.com\/index.php\/2021\/07\/05\/expansion-of-parametric-analysis-on-william-m-penas-programming-matrix-theory-based-on-graph-theory\/","title":{"rendered":"Expansion of parametric analysis on William M. Pena\u2019s programming matrix theory based on graph theory"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"457\" class=\"elementor elementor-457\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4a542246 elementor-section-boxed elementor-section-height-default elementor-section-height-default gs-locked-section-no\" data-id=\"4a542246\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5c93f7b6\" data-id=\"5c93f7b6\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7cc9f09f elementor-widget elementor-widget-text-editor\" data-id=\"7cc9f09f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 20-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<div class=\"entry-content-inner gs-cl\"><div class=\"elementor elementor-1\" data-elementor-type=\"wp-post\" data-elementor-id=\"1\" data-elementor-post-type=\"post\"><section class=\"elementor-section elementor-top-section elementor-element elementor-element-4168b281 elementor-section-boxed elementor-section-height-default elementor-section-height-default gs-locked-section-no\" data-id=\"4168b281\" data-element_type=\"section\"><div class=\"elementor-container elementor-column-gap-default\"><div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-68bb7f4a\" data-id=\"68bb7f4a\" data-element_type=\"column\"><div class=\"elementor-widget-wrap elementor-element-populated\"><div class=\"elementor-element elementor-element-7e10a5a4 elementor-widget elementor-widget-text-editor\" data-id=\"7e10a5a4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\"><div class=\"elementor-widget-container\"><h5>Extended<strong> Abstract<br \/><\/strong><strong>BACKGROUND AND OBJECTIVES:<\/strong><\/h5><p>William M. Pena described his Matrix theory, or the network information table, in 1987 in his book entitled \u201cproblem seeking\u201d. This theory presented a mechanism for architectural programming. On the other hand, the parametric paradigm has massively addressed various aspects of architecture and criticism in the past four decades. Parametric paradigm developed from formal parametric to parametric BIM in the initial dozens and ultimately to parametric automation. Parametric automation encompasses an extensive and undeniable level in the process of architectural design and criticism.<\/p><p>This research tries to expand the William M. Pena matrix based on the parametric paradigm and develop a parametric mechanism for complex data analysis on a very large scale to help designers and critics. In other words, this research is trying to expand Pena\u2019s theory in the context of the parametric paradigm by defining variables and facilities today so that it can serve as a model to guide the design process and criticism to architects and designers.<\/p><p>With the help of triple coding, Strauss\u2019 and Corbin\u2019s grounded theory hasprovided the research platform. In the following, graph theory has been used as a parametric analysis mechanism under the Gephi-version 0.9.2. The research steps are 1- Selection of the Pena Matrix and its expansion. 2- Completing content related to each cell of Matrix base and one-way communication of cells. 3- Referring the information to the team of experts for review 4- Achieving theoretical saturation measure. 5. Transfering information to Gephi software. 6-Preparation of required outputs using multiple software filters. 7- Analysis of outputs in line with the answer to the research question.<\/p><\/div><\/div><\/div><\/div><\/div><\/section><\/div><\/div>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8976990 elementor-widget elementor-widget-grada-gallery-images\" data-id=\"8976990\" data-element_type=\"widget\" data-widget_type=\"grada-gallery-images.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t            <div class=\"gs-entries-wrapper gs-entries-filter\" data-entries-id=\"8976990\">\n\t            \n                <div class=\"gs-gallery-images gs-gallery-images-info-overlay\">\n\t\t            <div class=\"row isotope-container\" data-entries-source=\"41c3c506b1820a6e7a6303665d697572\">\n\t\t\t        <div class=\"iso-item col-lg-6 \" data-col-num=\"2-columns\">\n            <div class=\"gs-gallery-item wow gsFadeIn\" >\n\t            <div class=\"gallery-item-inner type-info-overlay\">\n\t\t<div class=\"gallery-item-thumbnail-holder\">\n        <div class=\"entry-image-ratio\" style=\"padding-bottom: 100.875912% !important;\"><img loading=\"lazy\" decoding=\"async\" width=\"685\" height=\"691\" src=\"https:\/\/az-tdc.com\/wp-content\/uploads\/2020\/08\/013-3-English.png\" class=\"attachment-full size-full\" alt=\"\" srcset=\"https:\/\/az-tdc.com\/wp-content\/uploads\/2020\/08\/013-3-English.png 685w, https:\/\/az-tdc.com\/wp-content\/uploads\/2020\/08\/013-3-English-297x300.png 297w, https:\/\/az-tdc.com\/wp-content\/uploads\/2020\/08\/013-3-English-150x150.png 150w, https:\/\/az-tdc.com\/wp-content\/uploads\/2020\/08\/013-3-English-600x605.png 600w, https:\/\/az-tdc.com\/wp-content\/uploads\/2020\/08\/013-3-English-100x100.png 100w\" sizes=\"auto, (max-width: 685px) 100vw, 685px\" \/><\/div>\t\t\t\t\t<\/div>\n<\/div>\n            <\/div>\n        <\/div>\n    \t\t        <div class=\"iso-item col-lg-6 \" data-col-num=\"2-columns\">\n            <div class=\"gs-gallery-item wow gsFadeIn\" data-wow-delay=0.2s>\n\t            <div class=\"gallery-item-inner type-info-overlay\">\n\t\t<div class=\"gallery-item-thumbnail-holder\">\n        <div class=\"entry-image-ratio\" style=\"padding-bottom: 76.618705% !important;\"><img loading=\"lazy\" decoding=\"async\" width=\"556\" height=\"426\" src=\"https:\/\/az-tdc.com\/wp-content\/uploads\/2020\/08\/008.png\" class=\"attachment-full size-full\" alt=\"\" srcset=\"https:\/\/az-tdc.com\/wp-content\/uploads\/2020\/08\/008.png 556w, https:\/\/az-tdc.com\/wp-content\/uploads\/2020\/08\/008-300x230.png 300w\" sizes=\"auto, (max-width: 556px) 100vw, 556px\" \/><\/div>\t\t\t\t\t<\/div>\n<\/div>\n            <\/div>\n        <\/div>\n    <\/div>\n\n\n                <\/div>\n            <\/div>\n        \t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-71f28b1 elementor-widget elementor-widget-text-editor\" data-id=\"71f28b1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h5>METHODS:<\/h5><p><strong>\u00a0<\/strong>With the help of triple coding, Strauss\u2019 and Corbin\u2019s grounded theory hasprovided the research platform. In the following, graph theory has been used as a parametric analysis mechanism under the Gephi-version 0.9.2. The research steps are 1- Selection of the Pena Matrix and its expansion. 2- Completing content related to each cell of Matrix base and one-way communication of cells. 3- Referring the information to the team of experts for review 4- Achieving theoretical saturation measure. 5. Transfering information to Gephi software. 6-Preparation of required outputs using multiple software filters. 7- Analysis of outputs in line with the answer to the research question.<\/p><h5><strong>FINDINGS:<\/strong><\/h5><p>The output facilities in the Gaffe program are the degree of nodes, the weight of the vectors, the index nodes, and the shortest path between the two specified nodes, which the filters can access in the Gaffe program. On the other hand, two basic data were obtained based on the collected questionnaires. First, the one-way communication of each matrix item and then the weight of each of these communications. In order to obtain the results, the information was transferred to the Gephi program. At first, the edge weight filter, which is one of the filters of the Gephi program, was implemented on the extractive data. (These filters are based on the mathematical theory of graphs for specific outputs and standard graph theory in the program). It is possible to display only the communications of matrix cells located in this range by specifying the desired range Using app filters. As a result, more accurate and quality categorization will be possible even in countless matrix cells altogether. This mechanism also applies to the direction of another filter called grade. The degree in the theory of graphs refers to the number of connections entered and exited to each node. In this stage, the graph can be investigated based on the number of vectors entered on the base matrix cells. Finally, by citing the order of our shortest distance between the two nodes, nodes and their communications can be achieved at this stage. The output will be obtained based on node analysis and communication between them. This is precisely\u00a0one of the most widely used practices of graph theory. Repeating this command in the program makes it possible to get the shortest route between the first cell in the first row and the fifth cell in all rows.<\/p><h5><strong>\u00a0<\/strong><strong>CONCLUSION:<\/strong><\/h5><p>Based on codings, cells with a greater degree and weight in the defined range and the shortest distance between the two cells and related graphs are drawn. With repetition of this stage, the ability to analyze, including a comparison of frequency and analysis of alternatives, will be possible. The graph drawn in the Gephi software will determine which content exactly defined in the Matrix cells will play a role in connecting the cells of the first columns to the cells of the fifth columns and will determine the shortest communication path between them. In other words, the mechanism designed firstly, like an initial index, will play a role in the collective concept of information, and parametric analysis of unidirectional communication between Matrix cells will be able to analyze communication on a macro scale. These analyzes are available to designers graphically and parametrically. By changing each parameter or basic communication, the ability to analyze and compare changes to the word humanity will be provided. As a result, by reference to the research question, this parametric mechanism based on William M. Pena\u2019s matrix theory with multiple accurately adjustable outputs in the Gephi program will be able to first create a parametric structure and simply observe and compare the changes in the output graphs by changing the basis information. As a guide, it will also determine the path of the required data and communication and open the path to design and criticisms.<\/p><h5><strong>HIGHLIGHTS:<\/strong><\/h5><ul><li>Expansion of William Pena\u2019s programming matrix theory based on parametric<\/li><\/ul><p>paradigm and based on the theory of graphs with Gephi software version 0.9.2<\/p><ul><li>Using the Strauss and Corbin Grounded Theory using triad coding to create a research<\/li><li>The use of output possibilities in the Gephi program such as degrees of nodes\u060c the weight of vectors\u060c specifies the shortest path between two nodes.<\/li><li>Creating a parametric structure that can be analyzed by changing the basis information of changes in output graphs.<\/li><\/ul><h5><strong>ACKNOWLEDGMENTS:<\/strong><\/h5><p>This research did not receive any specific grant from funding agencies in the public, commercial, or not-forprofit sectors.<\/p><h5><strong>CONFLICT OF INTEREST:<\/strong><\/h5><p>The authors declared no conflicts of interest.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Extended Abstract BACKGROUND AND OBJECTIVES: William M. Pena described his Matrix theory, or the network information table, in 1987 in his book entitled&#8230;<\/p>\n","protected":false},"author":1,"featured_media":4695,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[72],"tags":[78,77,76,74,75],"class_list":["post-457","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-article","tag-gephi-software","tag-graph-theory","tag-grounded-theory","tag-parametric-paradigm-2","tag-william-m-pena-matrix-theory"],"acf":[],"jetpack_featured_media_url":"https:\/\/az-tdc.com\/wp-content\/uploads\/2020\/08\/008.png","_links":{"self":[{"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/posts\/457","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/comments?post=457"}],"version-history":[{"count":156,"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/posts\/457\/revisions"}],"predecessor-version":[{"id":4701,"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/posts\/457\/revisions\/4701"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/media\/4695"}],"wp:attachment":[{"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/media?parent=457"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/categories?post=457"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/az-tdc.com\/index.php\/wp-json\/wp\/v2\/tags?post=457"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}