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

研究的目标是共同努力， 将缩放概念引入系统中的可处理主题 一般理论，特别是生物信号和系统。 该研究是分形系统概念的扩展， 起源于我们努力模拟两极分化的动力学， 金属-溶液界面用系统论方法增强 by concepts概念of scaling缩放. 这项研究将探索具有复杂的共振系统， 在s平面中以缩放模式排列的奇点， 揭示它们与连续但不可微函数的联系 维尔斯特拉斯那种 这种丰富的动态显示， 系统需要进一步的理论阐述和模拟。 一个自然的延伸是研究非最小相位和非最小相位的问题。 正真实的系统及其对l/F型噪声的建模 普遍存在于生理系统中。 最近的证据表明， 这种噪音的成因是由某些类别的混沌 将探讨差分方程。 新一代数据采集器的设计， 操纵和处理方案，针对一般类别的 早就应该扩展系统和信号了。 这一目标的方式是 在可行的情况下，采用现有的数字信号处理方法， 处理，使得可以在宽动态范围上缩放数据， 有效和经济地分析。 近年来，多重分形理论得到了推广， 解释复杂缩放对象中的结构异质性。 该研究将试图验证 多重分形在生物组织无损评价中的应用。

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.