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Academy of Sciences</a>, <a class="u-tcGrayDarker" href="https://pan-pl.academia.edu/Departments/Institute_of_Fundamental_Technological_Research/Documents">Institute of Fundamental Technological Research</a>, <span class="u-tcGrayDarker">Faculty Member</span></div></div></div></div><div class="sidebar-cta-container"><button class="ds2-5-button hidden profile-cta-button grow js-profile-follow-button" data-broccoli-component="user-info.follow-button" data-click-track="profile-user-info-follow-button" data-follow-user-fname="Bogdan" data-follow-user-id="33728423" data-follow-user-source="profile_button" data-has-google="false"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">add</span>Follow</button><button class="ds2-5-button hidden profile-cta-button grow js-profile-unfollow-button" data-broccoli-component="user-info.unfollow-button" data-click-track="profile-user-info-unfollow-button" data-unfollow-user-id="33728423"><span class="material-symbols-outlined" 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href="https://unimelb.academia.edu/ElisaHillyardin">Elisa Hill-yardin</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of Melbourne</p></div></div></ul></div><div class="ri-section"><div class="ri-section-header"><span>Interests</span></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="33728423" href="https://www.academia.edu/Documents/in/Social_Studies_of_Psychological_Science_and_Technology"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://pan-pl.academia.edu/BogdanKazmierczak","location":"/BogdanKazmierczak","scheme":"https","host":"pan-pl.academia.edu","port":null,"pathname":"/BogdanKazmierczak","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" 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hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/126576316/An_averaging_principle_for_fast_diffusions_in_domains_separated_by_semi_permeable_membranes"><img alt="Research paper thumbnail of An averaging principle for fast diffusions in domains separated by semi-permeable membranes" class="work-thumbnail" src="https://attachments.academia-assets.com/120433684/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/126576316/An_averaging_principle_for_fast_diffusions_in_domains_separated_by_semi_permeable_membranes">An averaging principle for fast diffusions in domains separated by semi-permeable membranes</a></div><div class="wp-workCard_item"><span>Mathematical Models and Methods in Applied Sciences</span><span>, Mar 28, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We prove an averaging principle which asserts convergence of diffusion processes on domains separ...</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">We prove an averaging principle which asserts convergence of diffusion processes on domains separated by semi-permeable membranes, when diffusion coefficients tend to infinity while the flux through the membranes remains constant. In the limit, points in each domain are lumped into a single state of a limit Markov chain. The limit chain's intensities are proportional to the membranes' permeability and inversely proportional to the domains' sizes. Analytically, the limit is an example of a singular perturbation in which boundary and transmission conditions play a crucial role. This averaging principle is strongly motivated by recent signaling pathways models of mathematical biology, which are discussed towards the end of the paper.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="652e002d058a09a20c5c44a439b3ec2f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":120433684,"asset_id":126576316,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/120433684/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="126576316"><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="126576316"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126576316; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121827123"><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/121827123/Modeling_the_bistable_transition_between_cell_phenotypes_during_limb_precartilage_condensation"><img alt="Research paper thumbnail of Modeling the bistable transition between cell phenotypes during limb precartilage condensation" class="work-thumbnail" src="https://attachments.academia-assets.com/116617253/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/121827123/Modeling_the_bistable_transition_between_cell_phenotypes_during_limb_precartilage_condensation">Modeling the bistable transition between cell phenotypes during limb precartilage condensation</a></div><div class="wp-workCard_item"><span>bioRxiv (Cold Spring Harbor Laboratory)</span><span>, Mar 16, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Previous work showed that Gal-8 and Gal-1A, two proteins belonging to the galactoside-binding gal...</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">Previous work showed that Gal-8 and Gal-1A, two proteins belonging to the galactoside-binding galectin family, are the earliest determinants of the patterning of the skeletal elements of embryonic chicken limbs, and further, that their experimentally determined interactions in the embryonic limb bud can be interpreted through a reaction-diffusion-adhesion framework. Here, we use an ordinary differential equation-based approach to analyze the intrinsic switching modality of the galectin reaction network and characterize the states of the network independent of the diffusive and adhesive arms of the patterning mechanism. We identify two steady states: where the concentrations of both the galectins are respectively, negligible, and very high. We provide an explicit Lyapunov function, which shows that there are no periodic solutions. In an extension of the model with sigmoidal galectin production terms, we show that an analogous bistable switch-like system arises via saddle-node bifurcation from a monostable one. Our model therefore predicts that the galectin network may exist in low expression and high expression states separated in space or time without any intermediate states. We verify these predictions in experiments performed with high density micromass cultures of chick limb mesenchymal cells and observe that cells inside and outside the precartilage protocondensations exhibit distinct behaviors with respect to galectin expression, motility, and spreading behavior on their substratum. The interactional complexity of the Gal-1 and-8-based patterning network is therefore sufficient to partition the mesenchymal cell population into two discrete cell types, which can be spatially patterned when incorporated into an adhesion and diffusion-enabled system.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e9c9b21c6e77ddd71db4e73f8659b121" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116617253,"asset_id":121827123,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116617253/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="121827123"><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="121827123"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121827123; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121827122"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/121827122/A_two_galectin_network_establishes_mesenchymal_condensation_phenotype_in_limb_development"><img alt="Research paper thumbnail of A two-galectin network establishes mesenchymal condensation phenotype in limb development" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/121827122/A_two_galectin_network_establishes_mesenchymal_condensation_phenotype_in_limb_development">A two-galectin network establishes mesenchymal condensation phenotype in limb development</a></div><div class="wp-workCard_item"><span>Mathematical biosciences</span><span>, Aug 1, 2023</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="121827122"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="121827122"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121827122; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121827117"><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/121827117/Stability_of_i_n_i_dimensional_patterns_in_a_generalized_Turing_system_implications_for_biological_pattern_formation"><img alt="Research paper thumbnail of Stability of<i>n</i>-dimensional patterns in a generalized Turing system: implications for biological pattern formation" class="work-thumbnail" src="https://attachments.academia-assets.com/116617250/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/121827117/Stability_of_i_n_i_dimensional_patterns_in_a_generalized_Turing_system_implications_for_biological_pattern_formation">Stability of<i>n</i>-dimensional patterns in a generalized Turing system: implications for biological pattern formation</a></div><div class="wp-workCard_item"><span>Nonlinearity</span><span>, Oct 2, 2004</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The stability of Turing patterns in an n-dimensional cube (0, π) n is studied, where n 2. It is s...</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 stability of Turing patterns in an n-dimensional cube (0, π) n is studied, where n 2. It is shown by using a generalization of a classical result of Ermentrout concerning spots and stripes in two dimensions that under appropriate assumptions only sheet-like or nodule-like structures can be stable in an n-dimensional cube. Other patterns can also be stable in regions comprising products of lower-dimensional cubes and intervals of appropriate length. Stability results are applied to a new model of skeletal pattern formation in the vertebrate limb.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7e2e016c436fe403d1217b89ca0f4a7b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116617250,"asset_id":121827117,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116617250/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="121827117"><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="121827117"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121827117; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="116835301"><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/116835301/Phase_boundary_solutions_to_model_kinetic_equations_via_the_Conley_index_theory_Part_II"><img alt="Research paper thumbnail of Phase boundary solutions to model kinetic equations via the Conley index theory. Part II" class="work-thumbnail" src="https://attachments.academia-assets.com/112855308/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/116835301/Phase_boundary_solutions_to_model_kinetic_equations_via_the_Conley_index_theory_Part_II">Phase boundary solutions to model kinetic equations via the Conley index theory. Part II</a></div><div class="wp-workCard_item"><span>Mathematical and Computer Modelling</span><span>, Dec 1, 2002</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper deals with the phase state solutions to a four-velocity model of a kinetic equation Ab...</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">This paper deals with the phase state solutions to a four-velocity model of a kinetic equation Abstract-we consider phase boundary solutions to a four-velocity kinetic model of a kinetrc equation governing the motion of van der Waals fluids. These solutions connect such equrlibrrum states, which are saddle critical points of the related dynamic system. Solutrons of thrs type can be interpreted as dynamic phase transition. The mathematical apparatus is that of the Conley index theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c3a7bc5c96da21adb48fc56dba631eb1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112855308,"asset_id":116835301,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112855308/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="116835301"><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="116835301"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116835301; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=116835301]").text(description); $(".js-view-count[data-work-id=116835301]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 116835301; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='116835301']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c3a7bc5c96da21adb48fc56dba631eb1" } } $('.js-work-strip[data-work-id=116835301]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":116835301,"title":"Phase boundary solutions to model kinetic equations via the Conley index theory. Part II","internal_url":"https://www.academia.edu/116835301/Phase_boundary_solutions_to_model_kinetic_equations_via_the_Conley_index_theory_Part_II","owner_id":33728423,"coauthors_can_edit":true,"owner":{"id":33728423,"first_name":"Bogdan","middle_initials":null,"last_name":"Kazmierczak","page_name":"BogdanKazmierczak","domain_name":"pan-pl","created_at":"2015-08-08T09:01:20.824-07:00","display_name":"Bogdan Kazmierczak","url":"https://pan-pl.academia.edu/BogdanKazmierczak"},"attachments":[{"id":112855308,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112855308/thumbnails/1.jpg","file_name":"s0895-717728022900296-020240329-1-69p6uu.pdf","download_url":"https://www.academia.edu/attachments/112855308/download_file","bulk_download_file_name":"Phase_boundary_solutions_to_model_kineti.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112855308/s0895-717728022900296-020240329-1-69p6uu-libre.pdf?1711723668=\u0026response-content-disposition=attachment%3B+filename%3DPhase_boundary_solutions_to_model_kineti.pdf\u0026Expires=1739842615\u0026Signature=VTiiuxdiywsC6rJlQBQCGPqyNin5I6O7AUx9ojpiv-5pBR3WwzydWQiT0pVcK4kDSAiOi4Z7dK~8VmYoinBQYItL0rfk-a4NNAzA07a1H3zznfRUkXTgTqYi1v5edWR2Zm0kBAUvW3OHiJHCyBhjGlrCrqJUbp6SlQYYDaNL~tgTGz0OBqq-Gv9o3y9Aqj5YzySddx8Pipdft6fiLK6Cu6n8WHL45Cun2LO0q2PSnH3cQVHAOQJr8h8f~iE5nmZ6~oZIyf6lp5STlOHmxbc4YJ3LjgZzmBPV~c3xApdP0TXiy4W9BHRdQ2hV~yQQ~jBKtElAt-0ysrEgMZzZfCv9HQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="116835300"><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/116835300/Shock_waves_by_a_kinetic_model_of_van_der_Waals_fluids"><img alt="Research paper thumbnail of Shock waves by a kinetic model of van der Waals fluids" class="work-thumbnail" src="https://attachments.academia-assets.com/112855309/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/116835300/Shock_waves_by_a_kinetic_model_of_van_der_Waals_fluids">Shock waves by a kinetic model of van der Waals fluids</a></div><div class="wp-workCard_item"><span>A R I</span><span>, Jul 2, 1999</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We present a four-velocity kinetic model of van der Waals #uids. Although, from the physical poin...</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">We present a four-velocity kinetic model of van der Waals #uids. Although, from the physical point of view this model is very simple, mathematically it is quite complicated. Due to this complexity we performed various simpli"cations, which are also presented. We look for traveling wave solutions for these simpli"ed versions. A discussion of the types of the states of rest is presented. We pay some attention to the monotonicity of the density component of the traveling wave. Finally, we compare the model's kinetic and hydrodynamic shock wave structures. The new feature is that kinetic e!ects alone are unable to kill the arti"cial phenomenon of impending shock splitting.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="98e7756ad59307ed9aa11a58752f114b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112855309,"asset_id":116835300,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112855309/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="116835300"><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="116835300"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116835300; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="116835298"><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/116835298/Eigenfunction_Approach_to_Transient_Patterns_in_a_Model_of_Chemotaxis"><img alt="Research paper thumbnail of Eigenfunction Approach to Transient Patterns in a Model of Chemotaxis" class="work-thumbnail" src="https://attachments.academia-assets.com/112855278/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/116835298/Eigenfunction_Approach_to_Transient_Patterns_in_a_Model_of_Chemotaxis">Eigenfunction Approach to Transient Patterns in a Model of Chemotaxis</a></div><div class="wp-workCard_item"><span>Mathematical Modelling of Natural Phenomena</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In the paper we examine solutions to a model of cell movement governed by the chemotaxis phenomen...</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">In the paper we examine solutions to a model of cell movement governed by the chemotaxis phenomenon derived in [14] and established via macroscopic limits of corresponding microscopic cell-based models with extended cell representations. The model is given by two PDEs for the density of cells and the concentration of a chemical. To avoid singularities in cell density, the aggregating force of chemotaxis phenomenon is attenuated by a density dependent diffusion of cells, which grows to infinity with density tending to a certain critical value. In this paper we recover the quasi-periodic structures provided by this model by means of (local in time) expansion of the solution into a basis of eigenfunctions of the linearized system. Both planar and spherical geometries are considered.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="401cc9daa866520cd80ad345bd81bf5a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112855278,"asset_id":116835298,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112855278/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="116835298"><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="116835298"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116835298; 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To obtain specific form of the fluxes between the compartments, we compare it with the model proposed by Marhl et al. (2000). We examine numerically the period and shape of oscillations as a function of diffusion coefficients. We demonstrate a decay of the oscillations at the critical value of diffusion of free calcium ions.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="11c8402fdbb4dd3cdfd86b08d8e05afe" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":105302469,"asset_id":105985022,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/105302469/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="105985022"><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="105985022"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 105985022; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="101273116"><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/101273116/Effect_of_Buffers_with_Multiple_Binding_Sites_on_Calcium_Waves"><img alt="Research paper thumbnail of Effect of Buffers with Multiple Binding Sites on Calcium Waves" class="work-thumbnail" src="https://attachments.academia-assets.com/101859909/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/101273116/Effect_of_Buffers_with_Multiple_Binding_Sites_on_Calcium_Waves">Effect of Buffers with Multiple Binding Sites on Calcium Waves</a></div><div class="wp-workCard_item"><span>Bulletin of Mathematical Biology</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The existence and properties of intracellular waves of increased free cytoplasmic calcium concent...</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 existence and properties of intracellular waves of increased free cytoplasmic calcium concentration (calcium waves) are strongly affected by the binding and unbinding of calcium ions to a multitude of different buffers in the cell. These buffers can be mobile or immobile and, in general, have multiple binding sites that are not independent. Previous theoretical studies have focused on the case when each buffer molecule binds a single calcium ion. In this study, we analyze how calcium waves are affected by calcium buffers with two non-independent binding sites, and show that the interactions between the calcium binding sites can result in the emergence of new behaviors. In particular, for certain combinations of kinetic parameters, the profiles of buffer molecules with one calcium ion bound can be non-monotone.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1de2a5a42d93e982a21a863180cd6290" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101859909,"asset_id":101273116,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101859909/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="101273116"><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="101273116"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 101273116; 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It...</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">Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It is shown that progression of viral infection can be characterized by the viral replication number, time-dependent viral load, and the speed of infection spreading. These three characteristics are determined through the original model parameters including the rates of cell infection and of virus production in the infected cells. The clinical manifestations of viral infection, depending on tissue damage, correlate with the speed of infection spreading, while the infectivity of a respiratory infection depends on the viral load in the upper respiratory tract. Parameter determination from the experiments on Delta and Omicron variants allows the estimation of the infection spreading speed and viral load. Different variants of the SARS-CoV-2 infection are compared confirming that Omicron is more infectious and has less severe symptoms than Delta variant. Within the same variant, spreading speed (symptoms) correlates with viral load allowing prognosis of disease progression.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4dbc94a588ee3ff1f2175da18cdc5347" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300434,"asset_id":97767457,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300434/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="97767457"><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="97767457"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767457; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767456"><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/97767456/Mathematical_modelling_of_respiratory_viral_infection_and_applications_to_SARS_CoV_2_progression"><img alt="Research paper thumbnail of Mathematical modelling of respiratory viral infection and applications to SARS-CoV-2 progression" class="work-thumbnail" src="https://attachments.academia-assets.com/99300432/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/97767456/Mathematical_modelling_of_respiratory_viral_infection_and_applications_to_SARS_CoV_2_progression">Mathematical modelling of respiratory viral infection and applications to SARS-CoV-2 progression</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It...</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">Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It is shown that progression of viral infection can be characterized by the viral replication number, time-dependent viral load and the speed of infection spreading. These three characteristics are determined through the original model parameters including the rates of cell infection and of virus production in the infected cells. The clinical manifestations of viral infection, depending on tissue damage, correlate with the speed of infection spreading, while the infectivity of a respiratory infection depends on the viral load in the upper respiratory tract. Parameter determination from the experiments on Delta and Omicron variants allows the estimation of the infection spreading speed and viral load. Different variants of the SARS-CoV-2 infection are compared confirming that Omicron is more infectious and has less severe symptoms than Delta variant. Within the same variant, spreading speed...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="efb934c89851b02c3e544528019a9e01" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300432,"asset_id":97767456,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300432/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="97767456"><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="97767456"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767456; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767455"><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/97767455/Mathematical_Modelling_of_Natural_Phenomena"><img alt="Research paper thumbnail of Mathematical Modelling of Natural Phenomena" class="work-thumbnail" src="https://attachments.academia-assets.com/99300406/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/97767455/Mathematical_Modelling_of_Natural_Phenomena">Mathematical Modelling of Natural Phenomena</a></div><div class="wp-workCard_item"><span>Mathematical Modelling of Natural Phenomena</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We consider a class of biological models represented by a system composed of reactiondiffusion PD...</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">We consider a class of biological models represented by a system composed of reactiondiffusion PDE coupled with difference equations (renewal equations) in n-dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="07abfba1aa82291e6897f0397e91969d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300406,"asset_id":97767455,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300406/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="97767455"><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="97767455"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767455; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767454"><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/97767454/Infection_spreading_in_cell_culture_as_a_reaction_diffusion_wave"><img alt="Research paper thumbnail of Infection spreading in cell culture as a reaction-diffusion wave" class="work-thumbnail" src="https://attachments.academia-assets.com/99300404/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/97767454/Infection_spreading_in_cell_culture_as_a_reaction_diffusion_wave">Infection spreading in cell culture as a reaction-diffusion wave</a></div><div class="wp-workCard_item"><span>ESAIM: Mathematical Modelling and Numerical Analysis</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Infection spreading in cell culture occurs due to virus replication in infected cells and its ran...</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">Infection spreading in cell culture occurs due to virus replication in infected cells and its random motion in the extracellular space. Multiplicity of infection experiments in cell cultures are conventionally used for the characterization of viral infection by the number of viral plaques and the rate of their growth. We describe this process with a delay reaction-diffusion system of equations for the concentrations of uninfected cells, infected cells, virus, and interferon. Time delay corresponds to the duration of viral replication inside infected cells. We show that infection propagates in cell culture as a reaction-diffusion wave, we determine the wave speed and prove its existence. Next, we carry out numerical simulations and identify three stages of infection progression: infection decay during time delay due to virus replication, explosive growth of viral load when infected cells begin to reproduce it, and finally, wave-like infection progression in cell culture characterized...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="533c11e0434d0494492e7c8200eff7b1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300404,"asset_id":97767454,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300404/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="97767454"><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="97767454"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767454; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767452"><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/97767452/Formation_in"><img alt="Research paper thumbnail of Formation in" class="work-thumbnail" src="https://attachments.academia-assets.com/99300431/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/97767452/Formation_in">Formation in</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A recently proposed mathematical model of a "core" set of cellular and molecular interactions pre...</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">A recently proposed mathematical model of a "core" set of cellular and molecular interactions present in the developing vertebrate limb was shown to exhibit patternforming instabilities and limb skeleton-like patterns under certain restrictive conditions, suggesting that it may authentically represent the underlying embryonic process (Hentschel et al., 2004). The model, an eight-equation system of partial differential equations, incorporates the behavior of mesenchymal cells as "reactors," both participating in the generation of morphogen patterns and changing their state and position in response to them. The full system, which has smooth solutions that exist globally in time, is nonetheless highly complex and difficult to handle analytically or numerically. According to a recent classification of developmental mechanisms (Salazar-Ciudad et al., 2003), the limb model of Hentschel et al. (2004) is "morphodynamic," since differentiation of new cell types occurs simultaneously with cell rearrangement. This contrasts with "morphostatic" mechanisms, in which cell identity becomes established independently of cell rearrangement. Under the hypothesis that development of some vertebrate limbs employs the core mechanism in a morphostatic fashion, we derive in an analytically rigorous fashion a pair of equations representing the spatiotemporal evolution of the morphogen fields under the assumption that cell differentiation relaxes faster than the evolution of the overall cell density (i.e., the morphostatic limit of the full system). This simple reaction-diffusion system is unique in having been derived in an analytically rigorous fashion from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis, and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation is possible, which we refer to as its "Turing space." Obtained values of the parameters are used in numerical simulations of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection for increasingly morphostatic developmental mechanisms.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1b595dbe2bdea75de63017774852e261" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300431,"asset_id":97767452,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300431/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="97767452"><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="97767452"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767452; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767451"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/97767451/Precartilage_condensation_during_limb_skeletogenesis_occurs_by_tissue_phase_separation_controlled_by_a_bistable_cell_state_switch_with_suppressed_oscillatory_dynamics"><img alt="Research paper thumbnail of Precartilage condensation during limb skeletogenesis occurs by tissue phase separation controlled by a bistable cell-state switch with suppressed oscillatory dynamics" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.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" rel="nofollow" href="https://www.academia.edu/97767451/Precartilage_condensation_during_limb_skeletogenesis_occurs_by_tissue_phase_separation_controlled_by_a_bistable_cell_state_switch_with_suppressed_oscillatory_dynamics">Precartilage condensation during limb skeletogenesis occurs by tissue phase separation controlled by a bistable cell-state switch with suppressed oscillatory dynamics</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The tetrapod limb skeleton is initiated in unpatterned limb bud mesenchyme by the formation of pr...</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 tetrapod limb skeleton is initiated in unpatterned limb bud mesenchyme by the formation of precartilage condensations. Here, based on time-lapse videographic analysis of a forming condensation in a high-density culture of chicken limb bud mesenchyme, we observe a phase transition to a more fluidized state for cells within spatial compacted foci (protocondensations that will progress to condensations), as reflected in their spatial confinement, cell-substratum interaction and speed of motion. Previous work showed that galectin-8 and galectin-1A, two proteins of the galactoside-binding galectin family, are the earliest determinants of this process in the chicken limb bud, and that their interactions in forming skeletogenic patterns of condensations can be interpreted mathematically through a reaction-diffusion-adhesion framework. Based on this framework, we use an ordinary differential equation-based approach to analyze the core switching modality of the galectin reaction network ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><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="97767451"><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="97767451"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767451; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=97767451]").text(description); $(".js-view-count[data-work-id=97767451]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 97767451; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='97767451']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=97767451]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":97767451,"title":"Precartilage condensation during limb skeletogenesis occurs by tissue phase separation controlled by a bistable cell-state switch with suppressed oscillatory dynamics","internal_url":"https://www.academia.edu/97767451/Precartilage_condensation_during_limb_skeletogenesis_occurs_by_tissue_phase_separation_controlled_by_a_bistable_cell_state_switch_with_suppressed_oscillatory_dynamics","owner_id":33728423,"coauthors_can_edit":true,"owner":{"id":33728423,"first_name":"Bogdan","middle_initials":null,"last_name":"Kazmierczak","page_name":"BogdanKazmierczak","domain_name":"pan-pl","created_at":"2015-08-08T09:01:20.824-07:00","display_name":"Bogdan Kazmierczak","url":"https://pan-pl.academia.edu/BogdanKazmierczak"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767450"><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/97767450/Some_existence_theorems_for_nonlocal_elliptic_systems_Application_to_laser_plasma"><img alt="Research paper thumbnail of Some existence theorems for nonlocal elliptic systems. Application to laser plasma" class="work-thumbnail" src="https://attachments.academia-assets.com/99300429/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/97767450/Some_existence_theorems_for_nonlocal_elliptic_systems_Application_to_laser_plasma">Some existence theorems for nonlocal elliptic systems. Application to laser plasma</a></div><div class="wp-workCard_item"><span>Applicationes Mathematicae</span><span>, 2001</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We formulate some existence theorems for systems of elliptic equations with nonlocal terms. The p...</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">We formulate some existence theorems for systems of elliptic equations with nonlocal terms. The proofs are based on the invariant region method. The results are applied to a multitemperature model of laser sustained plasma.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="efc7952dcd540c183d6ece37e54200ee" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300429,"asset_id":97767450,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300429/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="97767450"><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="97767450"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767450; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=97767450]").text(description); $(".js-view-count[data-work-id=97767450]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 97767450; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='97767450']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "efc7952dcd540c183d6ece37e54200ee" } } $('.js-work-strip[data-work-id=97767450]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":97767450,"title":"Some existence theorems for nonlocal elliptic systems. 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Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model (CPM), with a continuum reaction-diffusion (RD) model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1f946606a18599a1e3124b3a3b994b19" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300396,"asset_id":97767432,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300396/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="97767432"><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="97767432"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767432; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=97767432]").text(description); $(".js-view-count[data-work-id=97767432]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 97767432; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='97767432']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="93538293"><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/93538293/Multiscale_Models_for_Vertebrate_Limb_Development"><img alt="Research paper thumbnail of Multiscale Models for Vertebrate Limb Development" class="work-thumbnail" src="https://attachments.academia-assets.com/96249438/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/93538293/Multiscale_Models_for_Vertebrate_Limb_Development">Multiscale Models for Vertebrate Limb Development</a></div><div class="wp-workCard_item"><span>Current Topics in Developmental Biology</span><span>, 2008</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7cd29f1c8022ad52611cd3d72cacbf9d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":96249438,"asset_id":93538293,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/96249438/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="93538293"><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="93538293"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 93538293; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="87476571"><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/87476571/Viral_Infection_Spreading_and_Mutation_in_Cell_Culture"><img alt="Research paper thumbnail of Viral Infection Spreading and Mutation in Cell Culture" class="work-thumbnail" src="https://attachments.academia-assets.com/91673873/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/87476571/Viral_Infection_Spreading_and_Mutation_in_Cell_Culture">Viral Infection Spreading and Mutation in Cell Culture</a></div><div class="wp-workCard_item"><span>Mathematics</span><span>, 2022</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A new model of viral infection spreading in cell cultures is proposed taking into account virus m...</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">A new model of viral infection spreading in cell cultures is proposed taking into account virus mutation. This model represents a reaction-diffusion system of equations with time delay for the concentrations of uninfected cells, infected cells and viral load. Infection progression is characterized by the virus replication number Rv, which determines the total viral load. Analytical formulas for the speed of propagation and for the viral load are obtained and confirmed by numerical simulations. It is shown that virus mutation leads to the emergence of a new virus variant. Conditions of the coexistence of the two variants or competitive exclusion of one of them are found, and different stages of infection progression are identified.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="88fe66cf96ab562d6eb59469662e3dda" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":91673873,"asset_id":87476571,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/91673873/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="87476571"><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="87476571"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 87476571; 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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="3352042" id="papers"><div class="js-work-strip profile--work_container" data-work-id="126576316"><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/126576316/An_averaging_principle_for_fast_diffusions_in_domains_separated_by_semi_permeable_membranes"><img alt="Research paper thumbnail of An averaging principle for fast diffusions in domains separated by semi-permeable membranes" class="work-thumbnail" src="https://attachments.academia-assets.com/120433684/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/126576316/An_averaging_principle_for_fast_diffusions_in_domains_separated_by_semi_permeable_membranes">An averaging principle for fast diffusions in domains separated by semi-permeable membranes</a></div><div class="wp-workCard_item"><span>Mathematical Models and Methods in Applied Sciences</span><span>, Mar 28, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We prove an averaging principle which asserts convergence of diffusion processes on domains separ...</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">We prove an averaging principle which asserts convergence of diffusion processes on domains separated by semi-permeable membranes, when diffusion coefficients tend to infinity while the flux through the membranes remains constant. In the limit, points in each domain are lumped into a single state of a limit Markov chain. The limit chain's intensities are proportional to the membranes' permeability and inversely proportional to the domains' sizes. Analytically, the limit is an example of a singular perturbation in which boundary and transmission conditions play a crucial role. This averaging principle is strongly motivated by recent signaling pathways models of mathematical biology, which are discussed towards the end of the paper.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="652e002d058a09a20c5c44a439b3ec2f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":120433684,"asset_id":126576316,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/120433684/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="126576316"><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="126576316"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126576316; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121827123"><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/121827123/Modeling_the_bistable_transition_between_cell_phenotypes_during_limb_precartilage_condensation"><img alt="Research paper thumbnail of Modeling the bistable transition between cell phenotypes during limb precartilage condensation" class="work-thumbnail" src="https://attachments.academia-assets.com/116617253/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/121827123/Modeling_the_bistable_transition_between_cell_phenotypes_during_limb_precartilage_condensation">Modeling the bistable transition between cell phenotypes during limb precartilage condensation</a></div><div class="wp-workCard_item"><span>bioRxiv (Cold Spring Harbor Laboratory)</span><span>, Mar 16, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Previous work showed that Gal-8 and Gal-1A, two proteins belonging to the galactoside-binding gal...</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">Previous work showed that Gal-8 and Gal-1A, two proteins belonging to the galactoside-binding galectin family, are the earliest determinants of the patterning of the skeletal elements of embryonic chicken limbs, and further, that their experimentally determined interactions in the embryonic limb bud can be interpreted through a reaction-diffusion-adhesion framework. Here, we use an ordinary differential equation-based approach to analyze the intrinsic switching modality of the galectin reaction network and characterize the states of the network independent of the diffusive and adhesive arms of the patterning mechanism. We identify two steady states: where the concentrations of both the galectins are respectively, negligible, and very high. We provide an explicit Lyapunov function, which shows that there are no periodic solutions. In an extension of the model with sigmoidal galectin production terms, we show that an analogous bistable switch-like system arises via saddle-node bifurcation from a monostable one. Our model therefore predicts that the galectin network may exist in low expression and high expression states separated in space or time without any intermediate states. We verify these predictions in experiments performed with high density micromass cultures of chick limb mesenchymal cells and observe that cells inside and outside the precartilage protocondensations exhibit distinct behaviors with respect to galectin expression, motility, and spreading behavior on their substratum. The interactional complexity of the Gal-1 and-8-based patterning network is therefore sufficient to partition the mesenchymal cell population into two discrete cell types, which can be spatially patterned when incorporated into an adhesion and diffusion-enabled system.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e9c9b21c6e77ddd71db4e73f8659b121" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116617253,"asset_id":121827123,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116617253/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="121827123"><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="121827123"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121827123; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121827122"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/121827122/A_two_galectin_network_establishes_mesenchymal_condensation_phenotype_in_limb_development"><img alt="Research paper thumbnail of A two-galectin network establishes mesenchymal condensation phenotype in limb development" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/121827122/A_two_galectin_network_establishes_mesenchymal_condensation_phenotype_in_limb_development">A two-galectin network establishes mesenchymal condensation phenotype in limb development</a></div><div class="wp-workCard_item"><span>Mathematical biosciences</span><span>, Aug 1, 2023</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="121827122"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="121827122"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121827122; 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=121827122]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":121827122,"title":"A two-galectin network establishes mesenchymal condensation phenotype in limb development","internal_url":"https://www.academia.edu/121827122/A_two_galectin_network_establishes_mesenchymal_condensation_phenotype_in_limb_development","owner_id":33728423,"coauthors_can_edit":true,"owner":{"id":33728423,"first_name":"Bogdan","middle_initials":null,"last_name":"Kazmierczak","page_name":"BogdanKazmierczak","domain_name":"pan-pl","created_at":"2015-08-08T09:01:20.824-07:00","display_name":"Bogdan Kazmierczak","url":"https://pan-pl.academia.edu/BogdanKazmierczak"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121827121"><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/121827121/Mathematical_modeling_of_chondrogenic_pattern_formation_during_limb_development_Recent_advances_in_continuous_models"><img alt="Research paper thumbnail of Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models" class="work-thumbnail" src="https://attachments.academia-assets.com/116617252/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/121827121/Mathematical_modeling_of_chondrogenic_pattern_formation_during_limb_development_Recent_advances_in_continuous_models">Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models</a></div><div class="wp-workCard_item"><span>Mathematical Biosciences</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad...</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">This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9b7a6e2773e8a95d897c59a2fc3abf94" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116617252,"asset_id":121827121,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116617252/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="121827121"><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="121827121"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121827121; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="121827117"><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/121827117/Stability_of_i_n_i_dimensional_patterns_in_a_generalized_Turing_system_implications_for_biological_pattern_formation"><img alt="Research paper thumbnail of Stability of<i>n</i>-dimensional patterns in a generalized Turing system: implications for biological pattern formation" class="work-thumbnail" src="https://attachments.academia-assets.com/116617250/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/121827117/Stability_of_i_n_i_dimensional_patterns_in_a_generalized_Turing_system_implications_for_biological_pattern_formation">Stability of<i>n</i>-dimensional patterns in a generalized Turing system: implications for biological pattern formation</a></div><div class="wp-workCard_item"><span>Nonlinearity</span><span>, Oct 2, 2004</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The stability of Turing patterns in an n-dimensional cube (0, π) n is studied, where n 2. It is s...</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 stability of Turing patterns in an n-dimensional cube (0, π) n is studied, where n 2. It is shown by using a generalization of a classical result of Ermentrout concerning spots and stripes in two dimensions that under appropriate assumptions only sheet-like or nodule-like structures can be stable in an n-dimensional cube. Other patterns can also be stable in regions comprising products of lower-dimensional cubes and intervals of appropriate length. Stability results are applied to a new model of skeletal pattern formation in the vertebrate limb.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7e2e016c436fe403d1217b89ca0f4a7b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116617250,"asset_id":121827117,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116617250/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="121827117"><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="121827117"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 121827117; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="116835301"><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/116835301/Phase_boundary_solutions_to_model_kinetic_equations_via_the_Conley_index_theory_Part_II"><img alt="Research paper thumbnail of Phase boundary solutions to model kinetic equations via the Conley index theory. Part II" class="work-thumbnail" src="https://attachments.academia-assets.com/112855308/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/116835301/Phase_boundary_solutions_to_model_kinetic_equations_via_the_Conley_index_theory_Part_II">Phase boundary solutions to model kinetic equations via the Conley index theory. Part II</a></div><div class="wp-workCard_item"><span>Mathematical and Computer Modelling</span><span>, Dec 1, 2002</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper deals with the phase state solutions to a four-velocity model of a kinetic equation Ab...</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">This paper deals with the phase state solutions to a four-velocity model of a kinetic equation Abstract-we consider phase boundary solutions to a four-velocity kinetic model of a kinetrc equation governing the motion of van der Waals fluids. These solutions connect such equrlibrrum states, which are saddle critical points of the related dynamic system. Solutrons of thrs type can be interpreted as dynamic phase transition. The mathematical apparatus is that of the Conley index theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c3a7bc5c96da21adb48fc56dba631eb1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112855308,"asset_id":116835301,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112855308/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="116835301"><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="116835301"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116835301; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=116835301]").text(description); $(".js-view-count[data-work-id=116835301]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 116835301; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='116835301']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c3a7bc5c96da21adb48fc56dba631eb1" } } $('.js-work-strip[data-work-id=116835301]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":116835301,"title":"Phase boundary solutions to model kinetic equations via the Conley index theory. 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Although, from the physical poin...</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">We present a four-velocity kinetic model of van der Waals #uids. Although, from the physical point of view this model is very simple, mathematically it is quite complicated. Due to this complexity we performed various simpli"cations, which are also presented. We look for traveling wave solutions for these simpli"ed versions. A discussion of the types of the states of rest is presented. We pay some attention to the monotonicity of the density component of the traveling wave. Finally, we compare the model's kinetic and hydrodynamic shock wave structures. The new feature is that kinetic e!ects alone are unable to kill the arti"cial phenomenon of impending shock splitting.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="98e7756ad59307ed9aa11a58752f114b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112855309,"asset_id":116835300,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112855309/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="116835300"><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="116835300"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116835300; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="116835298"><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/116835298/Eigenfunction_Approach_to_Transient_Patterns_in_a_Model_of_Chemotaxis"><img alt="Research paper thumbnail of Eigenfunction Approach to Transient Patterns in a Model of Chemotaxis" class="work-thumbnail" src="https://attachments.academia-assets.com/112855278/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/116835298/Eigenfunction_Approach_to_Transient_Patterns_in_a_Model_of_Chemotaxis">Eigenfunction Approach to Transient Patterns in a Model of Chemotaxis</a></div><div class="wp-workCard_item"><span>Mathematical Modelling of Natural Phenomena</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In the paper we examine solutions to a model of cell movement governed by the chemotaxis phenomen...</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">In the paper we examine solutions to a model of cell movement governed by the chemotaxis phenomenon derived in [14] and established via macroscopic limits of corresponding microscopic cell-based models with extended cell representations. The model is given by two PDEs for the density of cells and the concentration of a chemical. To avoid singularities in cell density, the aggregating force of chemotaxis phenomenon is attenuated by a density dependent diffusion of cells, which grows to infinity with density tending to a certain critical value. In this paper we recover the quasi-periodic structures provided by this model by means of (local in time) expansion of the solution into a basis of eigenfunctions of the linearized system. Both planar and spherical geometries are considered.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="401cc9daa866520cd80ad345bd81bf5a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112855278,"asset_id":116835298,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112855278/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="116835298"><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="116835298"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116835298; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="105985022"><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/105985022/Calcium_Oscillations_in_a_Spatially_Extended_Three_Compartment_Cell_Model"><img alt="Research paper thumbnail of Calcium Oscillations in a Spatially Extended Three Compartment Cell Model" class="work-thumbnail" src="https://attachments.academia-assets.com/105302469/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/105985022/Calcium_Oscillations_in_a_Spatially_Extended_Three_Compartment_Cell_Model">Calcium Oscillations in a Spatially Extended Three Compartment Cell Model</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We derive a spatially extended three compartment cell model for evolution of calcium ions concetr...</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">We derive a spatially extended three compartment cell model for evolution of calcium ions concetrations. To obtain specific form of the fluxes between the compartments, we compare it with the model proposed by Marhl et al. (2000). We examine numerically the period and shape of oscillations as a function of diffusion coefficients. We demonstrate a decay of the oscillations at the critical value of diffusion of free calcium ions.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="11c8402fdbb4dd3cdfd86b08d8e05afe" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":105302469,"asset_id":105985022,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/105302469/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="105985022"><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="105985022"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 105985022; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="101273116"><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/101273116/Effect_of_Buffers_with_Multiple_Binding_Sites_on_Calcium_Waves"><img alt="Research paper thumbnail of Effect of Buffers with Multiple Binding Sites on Calcium Waves" class="work-thumbnail" src="https://attachments.academia-assets.com/101859909/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/101273116/Effect_of_Buffers_with_Multiple_Binding_Sites_on_Calcium_Waves">Effect of Buffers with Multiple Binding Sites on Calcium Waves</a></div><div class="wp-workCard_item"><span>Bulletin of Mathematical Biology</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The existence and properties of intracellular waves of increased free cytoplasmic calcium concent...</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 existence and properties of intracellular waves of increased free cytoplasmic calcium concentration (calcium waves) are strongly affected by the binding and unbinding of calcium ions to a multitude of different buffers in the cell. These buffers can be mobile or immobile and, in general, have multiple binding sites that are not independent. Previous theoretical studies have focused on the case when each buffer molecule binds a single calcium ion. In this study, we analyze how calcium waves are affected by calcium buffers with two non-independent binding sites, and show that the interactions between the calcium binding sites can result in the emergence of new behaviors. In particular, for certain combinations of kinetic parameters, the profiles of buffer molecules with one calcium ion bound can be non-monotone.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1de2a5a42d93e982a21a863180cd6290" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101859909,"asset_id":101273116,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101859909/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="101273116"><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="101273116"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 101273116; 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It...</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">Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It is shown that progression of viral infection can be characterized by the viral replication number, time-dependent viral load, and the speed of infection spreading. These three characteristics are determined through the original model parameters including the rates of cell infection and of virus production in the infected cells. The clinical manifestations of viral infection, depending on tissue damage, correlate with the speed of infection spreading, while the infectivity of a respiratory infection depends on the viral load in the upper respiratory tract. Parameter determination from the experiments on Delta and Omicron variants allows the estimation of the infection spreading speed and viral load. Different variants of the SARS-CoV-2 infection are compared confirming that Omicron is more infectious and has less severe symptoms than Delta variant. Within the same variant, spreading speed (symptoms) correlates with viral load allowing prognosis of disease progression.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4dbc94a588ee3ff1f2175da18cdc5347" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300434,"asset_id":97767457,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300434/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="97767457"><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="97767457"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767457; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767456"><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/97767456/Mathematical_modelling_of_respiratory_viral_infection_and_applications_to_SARS_CoV_2_progression"><img alt="Research paper thumbnail of Mathematical modelling of respiratory viral infection and applications to SARS-CoV-2 progression" class="work-thumbnail" src="https://attachments.academia-assets.com/99300432/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/97767456/Mathematical_modelling_of_respiratory_viral_infection_and_applications_to_SARS_CoV_2_progression">Mathematical modelling of respiratory viral infection and applications to SARS-CoV-2 progression</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It...</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">Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It is shown that progression of viral infection can be characterized by the viral replication number, time-dependent viral load and the speed of infection spreading. These three characteristics are determined through the original model parameters including the rates of cell infection and of virus production in the infected cells. The clinical manifestations of viral infection, depending on tissue damage, correlate with the speed of infection spreading, while the infectivity of a respiratory infection depends on the viral load in the upper respiratory tract. Parameter determination from the experiments on Delta and Omicron variants allows the estimation of the infection spreading speed and viral load. Different variants of the SARS-CoV-2 infection are compared confirming that Omicron is more infectious and has less severe symptoms than Delta variant. Within the same variant, spreading speed...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="efb934c89851b02c3e544528019a9e01" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300432,"asset_id":97767456,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300432/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="97767456"><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="97767456"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767456; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767455"><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/97767455/Mathematical_Modelling_of_Natural_Phenomena"><img alt="Research paper thumbnail of Mathematical Modelling of Natural Phenomena" class="work-thumbnail" src="https://attachments.academia-assets.com/99300406/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/97767455/Mathematical_Modelling_of_Natural_Phenomena">Mathematical Modelling of Natural Phenomena</a></div><div class="wp-workCard_item"><span>Mathematical Modelling of Natural Phenomena</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We consider a class of biological models represented by a system composed of reactiondiffusion PD...</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">We consider a class of biological models represented by a system composed of reactiondiffusion PDE coupled with difference equations (renewal equations) in n-dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="07abfba1aa82291e6897f0397e91969d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300406,"asset_id":97767455,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300406/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="97767455"><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="97767455"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767455; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767454"><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/97767454/Infection_spreading_in_cell_culture_as_a_reaction_diffusion_wave"><img alt="Research paper thumbnail of Infection spreading in cell culture as a reaction-diffusion wave" class="work-thumbnail" src="https://attachments.academia-assets.com/99300404/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/97767454/Infection_spreading_in_cell_culture_as_a_reaction_diffusion_wave">Infection spreading in cell culture as a reaction-diffusion wave</a></div><div class="wp-workCard_item"><span>ESAIM: Mathematical Modelling and Numerical Analysis</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Infection spreading in cell culture occurs due to virus replication in infected cells and its ran...</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">Infection spreading in cell culture occurs due to virus replication in infected cells and its random motion in the extracellular space. Multiplicity of infection experiments in cell cultures are conventionally used for the characterization of viral infection by the number of viral plaques and the rate of their growth. We describe this process with a delay reaction-diffusion system of equations for the concentrations of uninfected cells, infected cells, virus, and interferon. Time delay corresponds to the duration of viral replication inside infected cells. We show that infection propagates in cell culture as a reaction-diffusion wave, we determine the wave speed and prove its existence. Next, we carry out numerical simulations and identify three stages of infection progression: infection decay during time delay due to virus replication, explosive growth of viral load when infected cells begin to reproduce it, and finally, wave-like infection progression in cell culture characterized...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="533c11e0434d0494492e7c8200eff7b1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300404,"asset_id":97767454,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300404/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="97767454"><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="97767454"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767454; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767452"><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/97767452/Formation_in"><img alt="Research paper thumbnail of Formation in" class="work-thumbnail" src="https://attachments.academia-assets.com/99300431/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/97767452/Formation_in">Formation in</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A recently proposed mathematical model of a "core" set of cellular and molecular interactions pre...</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">A recently proposed mathematical model of a "core" set of cellular and molecular interactions present in the developing vertebrate limb was shown to exhibit patternforming instabilities and limb skeleton-like patterns under certain restrictive conditions, suggesting that it may authentically represent the underlying embryonic process (Hentschel et al., 2004). The model, an eight-equation system of partial differential equations, incorporates the behavior of mesenchymal cells as "reactors," both participating in the generation of morphogen patterns and changing their state and position in response to them. The full system, which has smooth solutions that exist globally in time, is nonetheless highly complex and difficult to handle analytically or numerically. According to a recent classification of developmental mechanisms (Salazar-Ciudad et al., 2003), the limb model of Hentschel et al. (2004) is "morphodynamic," since differentiation of new cell types occurs simultaneously with cell rearrangement. This contrasts with "morphostatic" mechanisms, in which cell identity becomes established independently of cell rearrangement. Under the hypothesis that development of some vertebrate limbs employs the core mechanism in a morphostatic fashion, we derive in an analytically rigorous fashion a pair of equations representing the spatiotemporal evolution of the morphogen fields under the assumption that cell differentiation relaxes faster than the evolution of the overall cell density (i.e., the morphostatic limit of the full system). This simple reaction-diffusion system is unique in having been derived in an analytically rigorous fashion from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis, and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation is possible, which we refer to as its "Turing space." Obtained values of the parameters are used in numerical simulations of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection for increasingly morphostatic developmental mechanisms.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1b595dbe2bdea75de63017774852e261" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300431,"asset_id":97767452,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300431/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="97767452"><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="97767452"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767452; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767451"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/97767451/Precartilage_condensation_during_limb_skeletogenesis_occurs_by_tissue_phase_separation_controlled_by_a_bistable_cell_state_switch_with_suppressed_oscillatory_dynamics"><img alt="Research paper thumbnail of Precartilage condensation during limb skeletogenesis occurs by tissue phase separation controlled by a bistable cell-state switch with suppressed oscillatory dynamics" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.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" rel="nofollow" href="https://www.academia.edu/97767451/Precartilage_condensation_during_limb_skeletogenesis_occurs_by_tissue_phase_separation_controlled_by_a_bistable_cell_state_switch_with_suppressed_oscillatory_dynamics">Precartilage condensation during limb skeletogenesis occurs by tissue phase separation controlled by a bistable cell-state switch with suppressed oscillatory dynamics</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The tetrapod limb skeleton is initiated in unpatterned limb bud mesenchyme by the formation of pr...</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 tetrapod limb skeleton is initiated in unpatterned limb bud mesenchyme by the formation of precartilage condensations. Here, based on time-lapse videographic analysis of a forming condensation in a high-density culture of chicken limb bud mesenchyme, we observe a phase transition to a more fluidized state for cells within spatial compacted foci (protocondensations that will progress to condensations), as reflected in their spatial confinement, cell-substratum interaction and speed of motion. Previous work showed that galectin-8 and galectin-1A, two proteins of the galactoside-binding galectin family, are the earliest determinants of this process in the chicken limb bud, and that their interactions in forming skeletogenic patterns of condensations can be interpreted mathematically through a reaction-diffusion-adhesion framework. Based on this framework, we use an ordinary differential equation-based approach to analyze the core switching modality of the galectin reaction network ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><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="97767451"><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="97767451"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767451; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=97767451]").text(description); $(".js-view-count[data-work-id=97767451]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 97767451; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='97767451']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=97767451]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":97767451,"title":"Precartilage condensation during limb skeletogenesis occurs by tissue phase separation controlled by a bistable cell-state switch with suppressed oscillatory dynamics","internal_url":"https://www.academia.edu/97767451/Precartilage_condensation_during_limb_skeletogenesis_occurs_by_tissue_phase_separation_controlled_by_a_bistable_cell_state_switch_with_suppressed_oscillatory_dynamics","owner_id":33728423,"coauthors_can_edit":true,"owner":{"id":33728423,"first_name":"Bogdan","middle_initials":null,"last_name":"Kazmierczak","page_name":"BogdanKazmierczak","domain_name":"pan-pl","created_at":"2015-08-08T09:01:20.824-07:00","display_name":"Bogdan Kazmierczak","url":"https://pan-pl.academia.edu/BogdanKazmierczak"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="97767450"><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/97767450/Some_existence_theorems_for_nonlocal_elliptic_systems_Application_to_laser_plasma"><img alt="Research paper thumbnail of Some existence theorems for nonlocal elliptic systems. Application to laser plasma" class="work-thumbnail" src="https://attachments.academia-assets.com/99300429/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/97767450/Some_existence_theorems_for_nonlocal_elliptic_systems_Application_to_laser_plasma">Some existence theorems for nonlocal elliptic systems. Application to laser plasma</a></div><div class="wp-workCard_item"><span>Applicationes Mathematicae</span><span>, 2001</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We formulate some existence theorems for systems of elliptic equations with nonlocal terms. The p...</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">We formulate some existence theorems for systems of elliptic equations with nonlocal terms. The proofs are based on the invariant region method. The results are applied to a multitemperature model of laser sustained plasma.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="efc7952dcd540c183d6ece37e54200ee" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300429,"asset_id":97767450,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300429/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="97767450"><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="97767450"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767450; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=97767450]").text(description); $(".js-view-count[data-work-id=97767450]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 97767450; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='97767450']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "efc7952dcd540c183d6ece37e54200ee" } } $('.js-work-strip[data-work-id=97767450]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":97767450,"title":"Some existence theorems for nonlocal elliptic systems. 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Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model (CPM), with a continuum reaction-diffusion (RD) model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1f946606a18599a1e3124b3a3b994b19" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":99300396,"asset_id":97767432,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/99300396/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="97767432"><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="97767432"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 97767432; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=97767432]").text(description); $(".js-view-count[data-work-id=97767432]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 97767432; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='97767432']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="93538293"><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/93538293/Multiscale_Models_for_Vertebrate_Limb_Development"><img alt="Research paper thumbnail of Multiscale Models for Vertebrate Limb Development" class="work-thumbnail" src="https://attachments.academia-assets.com/96249438/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/93538293/Multiscale_Models_for_Vertebrate_Limb_Development">Multiscale Models for Vertebrate Limb Development</a></div><div class="wp-workCard_item"><span>Current Topics in Developmental Biology</span><span>, 2008</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7cd29f1c8022ad52611cd3d72cacbf9d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":96249438,"asset_id":93538293,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/96249438/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="93538293"><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="93538293"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 93538293; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="87476571"><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/87476571/Viral_Infection_Spreading_and_Mutation_in_Cell_Culture"><img alt="Research paper thumbnail of Viral Infection Spreading and Mutation in Cell Culture" class="work-thumbnail" src="https://attachments.academia-assets.com/91673873/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/87476571/Viral_Infection_Spreading_and_Mutation_in_Cell_Culture">Viral Infection Spreading and Mutation in Cell Culture</a></div><div class="wp-workCard_item"><span>Mathematics</span><span>, 2022</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A new model of viral infection spreading in cell cultures is proposed taking into account virus m...</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">A new model of viral infection spreading in cell cultures is proposed taking into account virus mutation. This model represents a reaction-diffusion system of equations with time delay for the concentrations of uninfected cells, infected cells and viral load. Infection progression is characterized by the virus replication number Rv, which determines the total viral load. Analytical formulas for the speed of propagation and for the viral load are obtained and confirmed by numerical simulations. It is shown that virus mutation leads to the emergence of a new virus variant. 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