LOW DIMENSIONAL CHAOS, NONLINEAR MAPS & NERVOUS SYSTEM

低维混沌、非线性地图

• 批准号: 3387003
• 负责人: J DOYNE FARMER
• 金额: $ 11.02万
• 依托单位: UNIVERSITY OF CALIF-LOS ALAMOS NAT LAB
• 依托单位国家: 美国
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-09-30 至 1991-08-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/3387003
• 关键词: computer program /software; computer simulation; electroencephalography; evoked potentials; mathematical model; neural information processing; neurobiology; single cell analysis; stimulus /response

Neural systems often have significant components of their behavior that appear to be random. Traditionally this randomness is modeled in stochastic and often linear terms. Since neural systems consist of highly interconnected nonlinear elements, however, a natural alternative explanation is that the randomness derives from complex nonlinear dynamics such as chaos. This has been suggested by experiments on several neural systems, including irregular firing patterns in the nervous systems of gastropod molluscs, the human electroencephalogram in deep sleep and epilepsy, single neuron recordings in the cat and monkey visual cortex, and hippus in the pupil-light reflex. However, inmost cases the evidence for chaos remains inconclusive, in large part because the data analysis is based on techniques that are notoriously unreliable, such as currently popular algorithms for computing fractal dimension. We have recently introduced a new approach to the analysis of experimental data, which is based on the identification of good features through nonlinear generalizations of principal component analysis, and the construction of nonlinear mappings using nonparametric techniques such as local approximation. These nonlinear mappings can be used for several purposes, including prediction, noise reduction, and system characterization. For time series data (e.g. sequences of interspike intervals) they provide more accurate and reliable methods for measuring fractal dimension and determining whether chaos is present. For stimulus- response experiments (e.g. event related potentials and fields) they can be used to search for regularity and predictability, both for classification and generalization. We propose to develop further our methods to cope with problems encountered in biological neural data, such as nonstationary behavior, and to apply our methods to data from neuroscience experiments including those listed above. This will allow us to determine with much more precision than has been achieved so far whether the apparent randomness of many neural phenomena derives from complex nonlinear dynamics. If indeed this is the case, then the result might be a significant change in the paradigm used for modeling the nervous system. If this is not the case, then we can avert pointless further work in this direction. Our ultimate purpose is to discover any underlying deterministic structure that may currently lie hidden in apparently random neural phenomena.

神经系统通常有其行为的重要组成部分， 似乎是随机的。传统上，这种随机性是在 随机项，通常是线性项。因为神经系统由高度的 然而，相互关联的非线性元素是一种自然的选择 解释是，这种随机性源于复杂的非线性动力学 比如混乱。这是通过对几个神经细胞的实验得出的结论 系统，包括神经系统中的不规则放电模式 腹足软体动物，人类睡眠中的脑电和 癫痫，猫和猴子视皮层的单个神经元记录，以及 臀部的瞳孔-光反射。然而，在大多数情况下， 混乱仍然没有定论，很大程度上是因为数据分析 基于臭名昭著的不可靠技术，例如目前 计算分维的流行算法。 我们最近引入了一种新的方法来分析实验数据 数据，其基于通过以下方式识别良好特征 主成分分析的非线性推广，以及 使用非参数技术构建非线性映射 局部近似。这些非线性映射可用于多个 目的，包括预测、降噪和系统 人物刻画。对于时间序列数据(例如，间歇波序列 间隔)，它们提供了更准确、更可靠的测量方法 分维和判断是否存在混沌。对于刺激计划- 响应实验(例如，事件相关的电位和场)它们可以 用于搜索规律性和可预测性，两者都用于分类 和泛化。 我们建议进一步发展我们的方法来处理遇到的问题。 在生物神经数据中，例如非平稳行为，并应用我们的 方法获取神经科学实验的数据，包括上面列出的数据。 这将使我们能够比以往更精确地确定 迄今为止所实现的许多神经现象是否具有明显的随机性 源自复杂的非线性动力学。如果真的是这样，那么 其结果可能是用于建模的范例发生重大变化 神经系统。如果情况并非如此，那么我们可以避免毫无意义的 在这个方向上的进一步工作。 我们的最终目的是发现任何潜在的确定性结构 目前可能隐藏在明显随机的神经现象中。