CAREER: Random Walk in Random Environment

职业：随机环境中的随机游走

• 批准号: 0747758
• 负责人: Firas Rassoul-Agha
• 金额: $ 47.5万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-06-01 至 2015-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0747758&HistoricalAwards=false
• 关键词: CAREER; Random; Walk; Environment

The PI will continue his work on developing techniques to address important problems in the field of random motion in random media, such as invariance principles, large deviations, etc. In addition, the PI intends to broaden the impact of his research by also applying the theory of diffusion processes to computational neuroscience. As a first step, the PI proposes to study the widely-used integrate-and-fire model with noise and adaptation. The primary questions include existence and stability of stationary solutions in response to a constant or periodically varying input. The proposal also has an educational component; see below.Traditionally, many physical systems are modeled with a diffusion process. It is often the case that the medium in which the diffusion occurs possesses certain inhomogeneities (e.g. an electron moving in an allow, waves diffusing in rocks underground, etc). The inclusion of this property makes the model far more realistic and reveals a wide variety of new effects, not present in constant or periodic media. The main goal of the PI's work is to further theunderstanding of the consequences of this disorder in the medium. Another part of the PI's research stems from his belief in the need for a stronger involvement of mathematical sciences in the explosive growth of biological research. In particular, the complexity of neuronal network models used in Neuroscience makes their modeling a computationally and analytically challenging task. A recent technique for analyzing a class of such networks allows to view the population dynamics as a certain diffusion process. The PI proposes to extend this technique to a wider class of neuronal models, including a feedback (adaptation) mechanism. The results will be applied to specific neurobiological problems, such as localization of moving sound sources and contrast adaptation in vision. The third component in the proposal is educational. The PI will develop new courses, run seminars and workshops involving local budding scientists, organize undergraduate work on research projects, and actively involve graduate students and postdoctoral fellows in his ongoing research.

PI将继续开发技术，以解决随机介质中随机运动领域的重要问题，如不变性原理，大偏差等，此外，PI还打算通过将扩散过程理论应用于计算神经科学来扩大其研究的影响。作为第一步，PI建议研究具有噪声和自适应的广泛使用的集成和火灾模型。主要的问题包括响应于恒定或周期性变化的输入的稳态解的存在性和稳定性。这个提议也有教育的成分;见下文。传统上，许多物理系统都是用扩散过程建模的。通常情况下，发生扩散的介质具有一定的不均匀性（例如，电子在土壤中运动，波在地下岩石中扩散等）。包含此属性使模型更加逼真，并揭示了各种各样的新效果，不存在于恒定或周期性介质中。 PI工作的主要目标是进一步了解这种疾病在媒介中的后果。 PI研究的另一部分源于他的信念，即需要数学科学更有力地参与生物研究的爆炸性增长。特别是，神经科学中使用的神经元网络模型的复杂性使得它们的建模在计算和分析上具有挑战性。 最近的技术分析一类这样的网络允许查看人口动态作为一个特定的扩散过程。PI建议将这种技术扩展到更广泛的神经元模型，包括反馈（适应）机制。 研究结果将应用于特定的神经生物学问题，如移动声源的定位和视觉的对比度适应。 建议的第三个组成部分是教育。PI将开发新的课程，举办研讨会和讲习班，让当地崭露头角的科学家参与，组织本科生的研究项目，并积极让研究生和博士后研究员参与他正在进行的研究。