{"id":1299,"date":"2024-12-29T20:25:45","date_gmt":"2024-12-29T20:25:45","guid":{"rendered":"https:\/\/www2.isep.ipp.pt\/coupled80\/?page_id=1299"},"modified":"2024-12-29T20:25:45","modified_gmt":"2024-12-29T20:25:45","slug":"jiaxin-jin","status":"publish","type":"page","link":"https:\/\/www2.isep.ipp.pt\/coupled80\/?page_id=1299","title":{"rendered":"Jiaxin Jin"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"782\" height=\"829\" src=\"https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/jiaxin-1.jpeg\" alt=\"\" class=\"wp-image-1301\" style=\"width:219px;height:auto\" srcset=\"https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/jiaxin-1.jpeg 782w, https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/jiaxin-1-283x300.jpeg 283w, https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/jiaxin-1-768x814.jpeg 768w\" sizes=\"auto, (max-width: 782px) 100vw, 782px\" \/><figcaption class=\"wp-element-caption\">University of Louisiana at <br>Lafayette, USA<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Title:<\/strong> Homeostasis Patterns\u00a0\u00a0\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract:<\/strong> Homeostasis is a regulatory mechanism that keeps a specific variable close to a set value as other variables fluctuate. The notion of homeostasis can be rigorously formulated when the model of interest is represented as an input-output network, with distinguished\u00a0<em>input<\/em>\u00a0and\u00a0<em>output<\/em>\u00a0nodes, and the dynamics of the network determines the corresponding\u00a0<em>input-output function<\/em>\u00a0of the system. In this context, homeostasis can be defined as an \u201cinfinitesimal\u201d notion, namely, the derivative of the input-output function is zero at an isolated point. We introduce the notion of a\u00a0<em>homeostasis pattern,<\/em>\u00a0defined as a set of nodes, in addition to the output node, that are simultaneously infinitesimally homeostatic. We prove that each homeostasis type leads to a distinct homeostasis pattern. Moreover, we describe all homeostasis patterns supported by a given input-output network in terms of a combinatorial structure associated to the input-output network. We call this structure the homeostasis pattern network.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Bio:<\/strong> I joined the Department of Mathematics as an assistant professor in August 2024. I received my B.S. in Mathematics from Shanghai Jiao Tong University in 2014, my M.S. in Mathematics from the University of Wisconsin-Madison in 2015, and my Ph.D. in Mathematics from the University of Wisconsin-Madison in 2021. Prior to joining UL Lafayette, I served as a Zassenhaus Assistant Professor in the Department of Mathematics at The Ohio State University.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">My research focuses on applying dynamical systems to mathematical biology or biochemistry and applied partial differential equations in mathematical physics, with three distinct areas of emphasis: (i) investigation of the dynamical equivalence between reaction models and the relationship between reaction rates and graph structures with complex-balanced realizations, (ii) analysis of the network structure in input-output networks to characterize homeostasis points in the input-output function, (iii) exploration of the existence and regularity of solutions for the kinetic equations and the stability of the equilibrium of some kinetic models.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title: Homeostasis Patterns\u00a0\u00a0\u00a0 Abstract: Homeostasis is a regulatory mechanism that keeps a specific variable close to a set value as other variables fluctuate. The notion of homeostasis can be rigorously formulated when the model of interest is represented as an input-output network, with distinguished\u00a0input\u00a0and\u00a0output\u00a0nodes, and the dynamics of the network determines the corresponding\u00a0input-output function\u00a0of the &hellip; <\/p>\n","protected":false},"author":2,"featured_media":0,"parent":239,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1299","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/1299","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1299"}],"version-history":[{"count":3,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/1299\/revisions"}],"predecessor-version":[{"id":1303,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/1299\/revisions\/1303"}],"up":[{"embeddable":true,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/239"}],"wp:attachment":[{"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}