BRAIN EAGER: Analyzing and modeling power-law behaviors in neuroscience

这个急切的项目的目标是建立和应用一个计算工具箱来研究和模拟大脑中的幂定律动力学。传统上，神经科学中的任何复杂行为都被分解为多个组成部分的相互作用，每个组成部分都在自己独特的时间框架内工作。然而，越来越多的例子表明，在脑电活动记录、放电频率适应和突触重量动力学中，特征过程遵循幂定律动力学，这表明一个尺度上的机制的时间常数与系统在多个尺度上的活动高度相关。因此，系统的整体行为不能被分成在很大程度上独立的组件，并且传统的分析技术不能提供系统如何工作的适当描述。为了在多个尺度上理解神经元的信息处理，有必要建立一个框架来分析和模拟生物组织各个层次上的幂律动力学。该项目计划提供一个广泛可用的统一平台，以检测、分析、验证神经系统中的多个组织规模的幂定律行为，并对其进行建模。为了扩大影响力，该团队将为公众制作产品，解释幂定律和指数过程之间的差异，以及它们在神经科学研究中的重要性。将为学生提供研究机会，特别是在德克萨斯大学圣安东尼奥分校(UTSA)，这是一个少数族裔服务机构的代表不足的群体。这个协作团队将对大规模大脑活动和复杂行为中的幂定律关系进行分析和建模。该项目旨在建立和验证一个工具箱，以测试和表征数据流中的幂定律，并对幂定律动态系统进行建模。为此，将使用最先进的算法来表征实验数据和分数阶微分方程式，以建立幂定律动态系统的模型。这个建模平台将允许从亚细胞到行为尺度的幂规律过程的研究。该工具箱将被应用于两个截然不同的问题，涉及复杂模式的生成(鸟鸣产生)和人类语言理解。这两种应用都需要对大数据流进行分析，并对非线性序列的产生或决策进行建模。虽然最初的研究重点将集中在这两个项目上，但该框架将适用于广泛的神经科学项目，这些项目可能会影响在大脑倡议下所做的研究。互动例子将使用数学和MatLab平台实现，该团队还将更新和撰写关于这笔赠款主题的新维基百科页面。在所有项目中，研究生和本科生将同时参与研究和教育部分，不仅提供进行研究的机会，还提供提高他们的沟通能力的机会。

The objective of this EAGER project is to build and apply a computational toolbox to study and model power-law dynamics in the brain. Traditionally, any complex behavior in neuroscience is broken into the interactions of multiple components, each working in its own characteristic temporal framework. However, there is an increasing number of examples, such as in brain activity recording by electroencephalography (EEG), firing rate adaptation, and synaptic weight dynamics, in which the characteristic process follows power-law dynamics, which indicate that the time constant of a mechanism at one scale is highly correlated to the activity of the system at multiple scales. Therefore, the overall behavior of the system cannot be separated into largely independent components and traditional analysis techniques cannot provide an appropriate description of how the system works. In order to understand neuronal information processing at multiple scales it is necessary to develop a framework to analyze and model power-law dynamics at all levels of biological organization. This project plans to make widely available a unified platform to detect, analyze, validate, and model power-law behavior in the nervous system at multiple scales of organization. To broaden impact the team will generate products for the public that will explain the differences between power-law and exponential processes and their importance in neuroscience research. Research opportunities will be provided for students, especially underrepresented group at the University of Texas at San Antonio (UTSA), a minority serving institution. The collaborative team will analyze and model power-law relationships in large-scale brain activity and complex behavior. The project aims to build and validate a toolbox to test and characterize power-laws in data streams and to model power-law dynamical systems. For this purpose state-of-the art algorithms will be used to characterize experimental data and fractional differential equations to model power-law dynamical systems. This modeling platform will allow the study of power-law processes from the sub-cellular to the behavior scales. The toolbox will be applied to two very different problems dealing with complex pattern generation (birdsong production) and human language comprehension. Both applications will require the analysis of Big Data streams and model non-linear sequence production or decision-making. Although initially the focus of research will be in these two projects the framework will be built to be applicable to a wide range of neuroscience projects that can impact the research done under the BRAIN initiative. Interactive examples will be implemented using Mathematica and Matlab platforms and the team will also update and write new Wikipedia pages on the topics of this grant. In all projects, graduate and undergraduate students will be involved in both the research and educational components, providing opportunities not only to do research but to enhance their communication skills.