LOW DIMENSIONAL CHAOS, NONLINEAR MAPS & NERVOUS SYSTEM

神经系统的行为通常有重要的组成部分， 似乎是随机的。 传统上，这种随机性被建模为 随机的，通常是线性的。 由于神经系统由高度 互联的非线性元件，然而，一个自然的选择， 解释是随机性来自复杂的非线性动力学 比如混沌。 这已经被几个神经系统的实验所证实。 系统，包括神经系统中的不规则放电模式， 腹足类软体动物，人类在深度睡眠时的脑电图， 癫痫，猫和猴视觉皮层中的单神经元记录，以及 海马的瞳孔对光反射 然而，在大多数情况下， 混乱仍然是不确定的，在很大程度上是因为数据分析是 基于众所周知的不可靠的技术，例如目前 计算分形维数的流行算法。 我们最近介绍了一种新的分析方法， 数据，这是基于识别良好的功能，通过 主成分分析的非线性推广，以及 使用非参数技术构造非线性映射，例如 局部近似 这些非线性映射可以用于多个 目的，包括预测，降噪和系统 特征化 对于时间序列数据（例如，峰间序列 它们提供了更准确和可靠的测量方法， 分形维数和确定是否存在混沌。 为了刺激- 反应实验（例如，事件相关电位和场），它们可以 用于搜索规律性和可预测性， 和概括。 我们建议进一步发展我们的方法，以应付所遇到的问题 在生物神经数据，如非平稳行为，并应用我们的 方法，从神经科学实验，包括那些上面列出的数据。 这将使我们能够比以往更精确地确定 到目前为止所取得的成就是否表明许多神经现象的明显随机性 源于复杂的非线性动力学。 如果情况确实如此，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 如果不是这样，我们可以避免毫无意义的 进一步朝着这个方向努力。 我们的最终目的是发现任何潜在的确定性结构 目前可能隐藏在看似随机的神经现象中

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.