A New Approximation Technique for Maxwell's Equations

麦克斯韦方程组的一种新逼近技术

• 批准号: 0311902
• 负责人: James Bramble
• 金额: $ 32.45万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0311902&HistoricalAwards=false
• 关键词: New; Approximation; Technique; Maxwell; Equations

Bressloff0209824 The long term goal of this project is to develop a dynamicaltheory of how neurons in primary visual cortex (V1) generate atuned response to multiple (rather than single) features of avisual stimulus, and how these responses are spatially integratedacross the cortex to generate more global information about avisual scene. A primary focus of the work is to extend currentnetwork models of orientation tuning to incorporate the fact thatV1 cells are also selective for spatial frequency. This ismotivated by the considerable physiological and psychophysicalevidence suggesting that cortical circuits carry out a localizedtwo-dimensional Fourier decomposition of a stimulus rather thansimply performing local edge detection. Optical imaging of thesurface of cortex has revealed an intricate relationship betweenthe distribution of orientation and spatial frequency preferencesacross cortex. How correlations between these two featurepreference maps is manifested by the local and long-rangecircuitry of V1, and the consequences for the large-scaledynamics of V1 is also investigated. The primary visual cortex (V1) located at the back of thebrain is the first cortical area to process visual informationreceived from the eyes. One of the classical results regardingthe function of neurons (brain cells) in V1 is that they analyzevery local features of a visual image, that is, they carry outimage decomposition. (For example, V1 cells are sensitive to theorientation of an edge representing the boundary between a lightand dark region of the image. This discovery by Hubel and Wieselled to the Nobel prize in medicine). A very important questionthat follows from this is how our coherent perception of theworld is reconstructed. Until recently, it was thought that thelocal information from cells in V1 was passed through higherorder processing stages in the brain where cognition occurs.However, it is becoming clear that long-range circuitry within V1could itself contribute to the process of reconstruction. Thebasic aim of the proposal is to investigate this process bydeveloping a large-scale mathematical model of primary visualcortex that incorporates the latest anatomical data regarding itsinternal circuitry. Understanding how early stages in the visualbrain encode images has important applications to informationtechnology (such as the development of artificial vision systems)and biotechnology (such as the development of an artificialprosthesis for the visually impaired). In the latter case itmight be possible one day to artificially stimulate primaryvisual cortex to induce a visual sensation, rather like acontrolled visual hallucination.

Bressloff0209824 该项目的长期目标是开发一种动态理论，解释初级视觉皮层 (V1) 中的神经元如何对视觉刺激的多个（而不是单个）特征产生协调响应，以及这些响应如何在整个皮层上进行空间整合，以生成有关视觉场景的更多全局信息。 这项工作的主要重点是扩展当前的方向调整网络模型，以纳入 V1 细胞对空间频率也具有选择性的事实。 这是由大量的生理和心理物理证据推动的，这些证据表明皮层电路对刺激进行局部二维傅立叶分解，而不是简单地执行局部边缘检测。 皮层表面的光学成像揭示了皮层方向分布和空间频率偏好之间的复杂关系。 V1 的局部和远程电路如何体现这两个特征偏好图之间的相关性，以及 V1 的大规模动态的后果也进行了研究。 初级视觉皮层（V1）位于大脑后部，是处理从眼睛接收到的视觉信息的第一个皮质区域。 关于V1神经元（脑细胞）功能的经典结果之一是它们分析视觉图像的非常局部的特征，即它们进行图像分解。 （例如，V1 细胞对代表图像明暗区域边界的边缘方向敏感。Hubel 和 Wiesell 的这一发现获得了诺贝尔医学奖）。 由此产生的一个非常重要的问题是我们对世界的连贯感知是如何重建的。 直到最近，人们还认为来自 V1 细胞的局部信息会通过大脑中发生认知的高级处理阶段。然而，越来越清楚的是，V1 内的远程电路本身可能有助于重建过程。 该提案的基本目的是通过开发初级视觉皮层的大规模数学模型来研究这一过程，该模型结合了有关其内部电路的最新解剖数据。 了解视觉大脑的早期阶段如何编码图像对于信息技术（例如人工视觉系统的开发）和生物技术（例如针对视障人士的人工假体的开发）具有重要的应用。 在后一种情况下，有一天可能可以人为地刺激初级视觉皮层来诱发视觉感觉，就像受控的幻视一样。