Scaling Dynamics in Biological Signals and Systems Analysis-Faculty Awards for Women

生物信号和系统分析中的尺度动力学-女性教师奖

• 批准号: 9024077
• 负责人: Banu Onaral
• 金额: $ 26.1万
• 依托单位: Drexel University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-11-01 至 1998-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9024077&HistoricalAwards=false
• 关键词: Scaling; Dynamics; Biological; Signals; Systems

The research goal is to mount a concerted effort to facilitate the introduction of scaling concepts into amenable topics in system theory in general and biological signals and systems in particular. The research is an extension of the fractal systems concept which originated in our efforts to model the dynamics of the polarized metal-solution interfaces using methods of system theory enhanced by notions of scaling. The research will explore resonant systems with complex singularities arranged in scaling patterns in the s-plane and uncover their link to continuous but non-differentiable functions of the Weierstrass kind. The rich dynamics displayed by such systems demand further theoretical elaboration and simulations. A natural extension is the study the non-minimum phase and non- positive real systems with an eye for modelling l/F-type noises ubiquitous in physiological systems. Recent evidence concerning the genesis of such noises by certain categories of chaotic difference equations will be explored. The design of the new-generation data acquisition, manipulation, and processing schemes aimed at general classes of scaling systems and signals is long overdue. The objective will be to adapt, whenever feasible, existing methods of digital signal processing such that scaling data over broad dynamic ranges can be analyzed effectively and economically. Multifractal theories have been promoted in recent years to account for structural heterogeneities in complex scaling objects. The research will attempt to validate the suitability of multifractals in non-destructive evaluation of biological tissue.

研究的目标是作出协调一致的努力，以促进将尺度概念引入一般系统论，特别是生物信号和系统中的顺从主题。这项研究是对分形系统概念的扩展，它源于我们用标度概念增强的系统论方法对极化金属-溶液界面的动力学进行建模的努力。这项研究将探索在S平面上具有按标度模式排列的复奇点的共振系统，并揭示它们与连续但不可微的魏尔斯特拉斯类函数的联系。这类系统所表现出的丰富的动力学需要进一步的理论阐述和模拟。一个自然的扩展是研究非最小相位和非正实系统，着眼于对生理系统中普遍存在的L/F型噪声进行建模。关于某些类型的混沌差分方程类噪声的起源的最新证据将被探索。针对一般类型的定标系统和信号的新一代数据采集、处理和处理方案的设计早就应该进行了。其目标将是在可能的情况下调整现有的数字信号处理方法，以便能够有效和经济地分析广泛动态范围内的定标数据。多重分形理论近年来被用来解释复杂尺度物体中的结构异质性。这项研究将试图验证多重分形法在生物组织非破坏性评估中的适用性。