Topics in Neural Networks, Stochastic and Dynamical Systems

神经网络、随机和动态系统主题

• 批准号: 9626575
• 负责人: Robert Burton
• 金额: $ 6万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626575&HistoricalAwards=false
• 关键词: Topics; Neural; Networks; Stochastic; Dynamical

9626575 Burton ABSTRACT Original research is pursued by the investigator and his colleagues on: (i) topics of neural networks, such as feed-forward networks and unsupervised networks, (ii) algorithms to estimate the expected extreme value of a time series given some record of the past, (iii) dynamical and metric properties of various continued fraction type expansions, and (iv) stationary processes and random fields that arise as limits of random substitutions with a view toward random tiling systems. The methods employed are taken from ergodic theory, probability, and statistical physics. This work consists of four topics: (i) mathematical properties of neural networks, (ii) extreme value estimation, (iii) continued fraction algorithms, and (iv) random substitution processes. (i) A neural network is a type of self-programming computer that learns by example, essentially adjusting itself to adapt to its environment. Neural networks--though not yet well understood, mathematically--are already in commercial use in such areas as handwriting readers, DNA classifiers, and financial forecasters. With greater understanding will come more enlightened use. (ii) The investigator and his colleagues are developing extreme value estimation algorithms to help solve an estimation problem needed in the design of structures such as off-shore oil platforms which require a high probability of withstanding storms. Typically, there is limited historical data from which to make these estimates. The algorithms are used to estimate the most powerful storm that is likely to occur in the vicinity of the structure in the next 20 years. (iii) Continued fractions have the property of being the most economical way to approximate a real number by a fraction. They consist of fractions containing fractions containing fractions, etc., etc. The investigator and his colleagues look at these as dynamical systems to study their properties. This work ties together ideas from probability theory, group theory, and flows on surfaces. (iv) The investigator is studying random substitution schemes as they are natural ways of creating strings of symbols with random properties, using a simple recipe. This idea may also be used to generate tilings of the plane or space that have properties of randomness and determinism. The construction begins with a set of tiles (or simple shapes) and decompositions of these tiles so that each piece of each decomposition is a scale replica of one of the original tiles. This procedure is continued, decomposing to finer and finer scales, zooming the scale. This may give models of materials in nature, as has been the case for non-random versions of this procedure.

9626575 Burton ABSTRACT Original research is pursued by the investigator and his colleagues on: (i) topics of neural networks, such as feed-forward networks and unsupervised networks, (ii) algorithms to estimate the expected extreme value of a time series given some record of the past, (iii) dynamical and metric properties of various continued fraction type expansions, and (iv) stationary processes and random fields that arise as随机替换的限制，以朝向随机平铺系统的视图。 所采用的方法取自Ergodic理论，概率和统计物理学。 这项工作包括四个主题：（i）神经网络的数学特性，（ii）极值估计，（iii）持续分数算法和（iv）随机替换过程。 （i）神经网络是一种自我编程的计算机，它以身作则，基本上调整自身以适应其环境。 在数学上，神经网络尚未在手写读者，DNA分类器和财务预报员等领域的商业用途中得到很好的了解。有了更大的了解，将会更加开明。 （ii）研究人员及其同事正在开发极高的价值估计算法，以帮助解决诸如越野油平台之类的建筑物设计中所需的估计问题，这些估计问题需要很高的可能性来承受风暴。 通常，有限的历史数据可以从中得出这些估计。 该算法用于估计未来20年结构附近可能发生的最强大风暴。 （iii）持续的分数具有最经济的方式，即按比例近似实际数字。 它们由包含含有分数等分数的分数组成。研究者及其同事将这些视为研究其特性的动态系统。 这项工作将概率理论，群体理论和在表面上流动的思想联系在一起。 （iv）研究人员正在研究随机替代方案，因为它们是使用简单配方创建具有随机特性的符号字符串的自然方法。 该想法也可以用于生成具有随机性和确定性特性的平面或空间的瓷砖。 构造始于一组瓷砖（或简单的形状）和这些瓷砖的分解，因此每个分解的每一部分都是原始瓷砖之一的比例复制品。 继续此过程，将其分解为更细的尺度，从而缩小量表。 这可能会提供本质上的材料模型，就像此过程的非随机版本一样。