AbstractPresNHGReyes<\/a><\/li>\n<\/ul>\n <\/p>\n
Date: Friday,\u00a0 January 27, 2012<\/strong><\/p>\n\n- Speaker: Daniele Andreucci,\u00a0 Universita di Roma “La Sapienza”, Italy<\/strong><\/span><\/li>\n
- Title:\u00a0 Modeling alternating pores in biological membranes: analytical and numerical approach<\/strong><\/span><\/li>\n
- Abstract: Channels, or pores, in cell membranes may alternate between a closed and an open state. This kind of gating has been connected to the feature of selectivity: possibly by means of sharp changes in affinity, the channel is able to select ions of preferred species for permeation.
\nWe present a preliminary analytical study of permeation through a membrane with many alternating pores, via the theory of homogenization, obtaining the explicit limiting interface condition in terms of the spatiotemporal properties of the microstructure. Introducing then selection in the model, we report on numerical Montecarlo simulations investigating the efficiency of the filter.<\/li>\n<\/ul>\n <\/p>\n
Date: Friday, February 10, 2012<\/strong><\/p>\n\n- Speaker:\u00a0 Juraj Foldes, Vanderbilt University<\/strong><\/span><\/li>\n
- Title: Qualitative properties of positive solutions of perturbed parabolic equations<\/strong><\/span><\/li>\n
- Abstract: Positive solutions of nonlinear parabolic problems can have very complex behavior. However, assuming certain symmetry\u00a0 conditions, it is possible to prove that the solutions converge to the space of symmetric functions. We show that this property is `stable’. More specifically if the symmetry conditions are replaced by asymptotically symmetric ones, the solutions still approach the space of symmetric functions. We discuss problems on bounded and unbounded domains and, by possibly suprising counterexamples, we show optimality of our\u00a0 assumptions. As an application, we formulate new results on convergence of solutions to a single equilibrium.<\/li>\n<\/ul>\n
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Date: Friday, February 17, 2012<\/strong><\/p>\n\n- Speaker:\u00a0 Georgi Kapitanov, Vanderbilt University<\/strong><\/span><\/li>\n
- Title: A mathematical model of cancer stem cell lineage population dynamics with mutation accumulation and telomere length hierarchies<\/strong><\/span><\/li>\n
- Abstract: There is evidence that cancer develops when cells acquire a sequence of mutations that alter normal cell characteristics. This sequence determines a hierarchy among the cells, based on how many more mutations they need to accumulate in order to become cancerous. When cells divide, they exhibit telomere loss and differentiate, which defines another cell hierarchy, on top of which is the stem cell. We propose a mutation-generation model, which combines the mutation-accumulation hierarchy with the differentiation hierarchy of the cells, allowing us to take a step further in examining cancer development and growth. The results of the model support the hypothesis of the cancer stem cell\u2019s role in cancer pathogenesis: a very small fraction of the cancer cell population is responsible for the cancer growth and development. Also, according to the model, the nature of mutation accumulation is sufficient to explain the faster growth of the cancer cell population. However, numerical results show that in order for a cancer to develop within a reasonable time frame, cancer cells need to exhibit a higher proliferation rate than normal cells.<\/li>\n<\/ul>\n
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Date: Friday,\u00a0 March 16, 2012<\/strong><\/p>\n\n- Speaker: Peter Hinow,\u00a0 University of Wisconsin, Milwaukee<\/strong><\/span><\/li>\n
- Title:\u00a0 Size-structured populations with distributed states at birth<\/strong><\/span><\/li>\n
- Abstract:\u00a0 Age-structured models have been employed successfully in population dynamics for a long time and are considerably well understood. In contrast to such models where every individual is born at the same age 0, size-structured models allow to take into account different, distributed birth sizes. “Size” here can be a quite general concept, for example mass, energy content or pathogen load in a disease model. This introduces a birth operator that takes values in an infinite-dimensional Banach space and complicates greatly the mathematical analysis. In this survey, we will describe some examples of models that we recently investigated in a series of joint papers with Jozsef Farkas (University of Stirling, United Kingdom). The emphasis will be on questions such as asymptotic growth for linear models and the existence and stability of steady states for nonlinear models.<\/li>\n<\/ul>\n
<\/p>\n
Vanderbilt University<\/a> | College of Arts and Science<\/a><\/strong><\/a><\/p>\n1326 Stevenson Center
\nVanderbilt University
\nNashville, TN 37240<\/p>\n
This page was last modified on 8\/16\/2013<\/p>\n","protected":false},"excerpt":{"rendered":"
Fridays 4:10pm, Stevenson Center 1307 Date: Friday, September 16, 2011 Speaker:\u00a0 Juraj Foldes, Vanderbilt University Title: On Serrin’s symmetry result in non-smooth domains and its applications Abstract:\u00a0 In this talk we discuss a famous result of Serrin on overdetermined quasilinear elliptic problems on smooth domains. Using a new approach, we show that the result can…<\/p>\n","protected":false},"author":1985,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-2","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages\/2","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/users\/1985"}],"replies":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/comments?post=2"}],"version-history":[{"count":4,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages\/2\/revisions"}],"predecessor-version":[{"id":51,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages\/2\/revisions\/51"}],"wp:attachment":[{"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/media?parent=2"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/tags?post=2"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}