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id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Chris Varghese</h3></div><div class="js-work-strip profile--work_container" data-work-id="86077409"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86077409/Phase_transitions_in_the_quadratic_contact_process_on_complex_networks"><img alt="Research paper thumbnail of Phase transitions in the quadratic contact process on complex networks" class="work-thumbnail" src="https://attachments.academia-assets.com/90610847/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86077409/Phase_transitions_in_the_quadratic_contact_process_on_complex_networks">Phase transitions in the quadratic contact process on complex networks</a></div><div class="wp-workCard_item"><span>Physical Review E</span><span>, 2013</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The quadratic contact process (QCP) is a natural extension of the well studied linear contact pro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where infected (1) individuals infect susceptible (0) neighbors at rate λ and infected individuals recover (1 −→ 0) at rate 1. In the QCP, a combination of two 1's is required to effect a 0 −→ 1 change. We extend the study of the QCP, which so far has been limited to lattices, to complex networks. We define two versions of the QCP-vertex centered (VQCP) and edge centered (EQCP) with birth events 1 − 0 − 1 −→ 1 − 1 − 1 and 1 − 1 − 0 −→ 1 − 1 − 1 respectively, where '−' represents an edge. We investigate the effects of network topology by considering the QCP on random regular, Erdős-Rényi and power law random graphs. We perform mean field calculations as well as simulations to find the steady state fraction of occupied vertices as a function of the birth rate. We find that on the random regular and Erdős-Rényi graphs, there is a discontinuous phase transition with a region of bistability, whereas on the heavy tailed power law graph, the transition is continuous. The critical birth rate is found to be positive in the former but zero in the latter.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="de3f41811a59fb12726a34bba279af0b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90610847,"asset_id":86077409,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90610847/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86077409"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86077409"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86077409; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="15734635" id="papers"><div class="js-work-strip profile--work_container" data-work-id="86077409"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86077409/Phase_transitions_in_the_quadratic_contact_process_on_complex_networks"><img alt="Research paper thumbnail of Phase transitions in the quadratic contact process on complex networks" class="work-thumbnail" src="https://attachments.academia-assets.com/90610847/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86077409/Phase_transitions_in_the_quadratic_contact_process_on_complex_networks">Phase transitions in the quadratic contact process on complex networks</a></div><div class="wp-workCard_item"><span>Physical Review E</span><span>, 2013</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The quadratic contact process (QCP) is a natural extension of the well studied linear contact pro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where infected (1) individuals infect susceptible (0) neighbors at rate λ and infected individuals recover (1 −→ 0) at rate 1. In the QCP, a combination of two 1's is required to effect a 0 −→ 1 change. We extend the study of the QCP, which so far has been limited to lattices, to complex networks. We define two versions of the QCP-vertex centered (VQCP) and edge centered (EQCP) with birth events 1 − 0 − 1 −→ 1 − 1 − 1 and 1 − 1 − 0 −→ 1 − 1 − 1 respectively, where '−' represents an edge. We investigate the effects of network topology by considering the QCP on random regular, Erdős-Rényi and power law random graphs. We perform mean field calculations as well as simulations to find the steady state fraction of occupied vertices as a function of the birth rate. We find that on the random regular and Erdős-Rényi graphs, there is a discontinuous phase transition with a region of bistability, whereas on the heavy tailed power law graph, the transition is continuous. The critical birth rate is found to be positive in the former but zero in the latter.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="de3f41811a59fb12726a34bba279af0b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90610847,"asset_id":86077409,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90610847/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86077409"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86077409"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86077409; 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