Conference on Waves and Continuation Methods in Biology and Related Areas

研究人员黑斯廷斯9801227和他的同事们组织了一次跨学科会议，将生物学家和数学家聚集在一起，从不同的角度讨论波浪现象。这次会议的目的是让生物学家和数学家深入了解可以用于波浪现象的模型类型，以及可以预期这种行为的参数范围。为此，会议包括一般性讲座和更多的技术讲座，在这些讲座中，特定的技术得到了更充分的探索。在技术上特别感兴趣的是长程相互作用模型中的延拓方法，其中涉及积分方程模型。长期以来，生物学家一直对一维行波感兴趣，特别是在神经生物学领域，他们将电信号沿着神经轴突传播，或将其描述为平面波穿过二维电活动细胞集合。相关现象包括螺旋和其他模式，例如那些被认为与心脏组织中的一些致病行为有关的模式。大脑中类似的模式目前也引起了人们的兴趣。这种行为不仅限于神经生物学，还出现在各种各样的化学和生物系统中，如别洛索夫-扎博廷斯基反应、黏液霉菌和许多其他系统。另一方面，数学家们研究了各种模型中有关波的基本问题，包括生物和化学环境。数学工作的一个焦点一直是证明行波的存在和稳定性。在这一点上，延拓方法在涉及积分方程组的长程相互作用模型中变得特别有趣。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了波浪现象。这次会议促进了这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。

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.