Conference on Waves and Continuation Methods in Biology and Related Areas

生物学及相关领域的波和延拓方法会议

• 批准号: 9801227
• 负责人: Stuart Hastings
• 金额: $ 1.5万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801227&HistoricalAwards=false
• 关键词: Conference; Waves; Continuation; Methods; Biology

Hastings 9801227 The investigator and his colleagues organize an interdisciplinary conference to bring together biologists and mathematicians to discuss wave phenomena from their varying perspectives. The conference aims to give both biologists and mathematicians insights into the types of models that can be used for wave phenomena and the parameter ranges where such behavior can be expected. To this end, the conference includes both general lectures and more technical talks where particular techniques are explored more fully. Of special interest in techniques are continuation methods in models of long range interaction, where integral equation models are involved. One-dimensional traveling waves have long been of interest to biologists, particularly in neurobiology where they describe the propopagation of electrical signals down a nerve axon or as a plane wave across a two-dimensional collection of electrically active cells. Related phenomena include spiral and other patterns, such as those thought to be responsible for some pathogenic behavior in cardiac tissue. Similar patterns in the brain are of current interest as well. Such behavior is not limited to neurobiology, and appears in a wide variety of chemical and biological systems, such as the Belousov-Zhabotinsky reaction, slime molds, and many others. On the other hand, mathematicians have studied basic questions about waves for a variety of models, including biological and chemical settings. One focus of mathematical work has been to prove the existence and stability of traveling waves. In this regard continuation methods have become particularly interesting in models of long range interaction, where integral equations are involved. The conference brings together biologists and mathematicians to discuss wave phenomena from their different perspectives. The meeting fosters interactions between the two areas that should lead to greater understanding of a variety of phenomena important in biology.

黑斯廷斯9801227 研究者和他的同事组织了一个跨学科的会议，将生物学家和数学家聚集在一起，从不同的角度讨论波现象。 会议旨在让生物学家和数学家深入了解可用于波动现象的模型类型以及可预期此类行为的参数范围。 为此，会议包括一般讲座和更多的技术讲座，其中更充分地探讨了特定的技术。 特别感兴趣的技术是连续的方法在模型中的远程相互作用，其中涉及积分方程模型。 一维行波长期以来一直是生物学家的兴趣所在，特别是在神经生物学中，它们描述了电信号沿着神经轴突的传播或作为平面波穿过二维电活性细胞的集合。 相关的现象包括螺旋和其他模式，如那些被认为是负责心脏组织中的一些致病行为。 大脑中的类似模式也是当前的兴趣所在。 这种行为不仅限于神经生物学，而且出现在各种各样的化学和生物系统中，如Belousov-Zhabotinsky反应，黏菌等。 另一方面，数学家们已经研究了各种模型的波的基本问题，包括生物和化学设置。 数学工作的一个重点是证明行波的存在性和稳定性。 在这方面，连续方法已成为特别有趣的长程相互作用的模型，其中涉及积分方程。 这次会议汇集了生物学家和数学家，从他们不同的角度讨论波现象。 会议促进了两个领域之间的互动，这应该会导致对生物学中各种重要现象的更好理解。