通过施罗丁格桥在概率测量的空间中作为早期预警指标的行动功能
Peng Zhang1,2,3, Ting Gao1,2,3, Jin Guo1,2,3
1School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan China.
Quantitative biology (Beijing, China)
|February 12, 2026
概括
这项研究引入了早期预警信号 (EWS) 的新框架,用于预测复杂系统中的关键过渡. 该方法使用概率测量和产量来识别临界点,显示疾病进展预测的前景.
科学领域:
- 动态系统和复杂性科学 动态系统和复杂性科学
- 计算神经科学是一种神经科学.
- 生物医学数据分析
背景情况:
- 在随机动态系统中,关键过渡和倾斜现象是重要的科学挑战.
- 早期预警指标 (EWI) 的现有方法依赖于统计分析,分叉理论,信息理论,统计物理,拓学和图形理论.
- 在分析不变集合上的概率测量之间的过渡动态的方法中存在一个差距.
研究的目的:
- 扩展用于识别使用Onsager-Machlup动作函数和施罗丁格桥的元稳定状态之间的最可能的过渡路径的方法.
- 引入一个新的早期预警信号 (EWS) 框架,基于概率测量和生产率.
- 通过Morris-Lecar模型和真实阿尔茨海默病数据验证EWS框架.
主要方法:
- 利用Onsager-Machlup动作函数和施罗丁格桥来研究元稳定不变集合之间的过渡动态.
- 开发了一个新的早期预警信号 (EWS) 框架,在与生产率一致的概率测量领域.
- 将框架应用于莫里斯-莱卡尔模型,并分析了阿尔茨海默病神经成像计划 (ADNI) 数据库数据.
主要成果:
- 成功地应用了新的EWS框架来识别Morris-Lecar模型中的过渡动态.
- 通过使用ADNI数据,证明了该框架能够检测从健康状态过渡到阿尔茨海默病前状态的早期预警信号.
- 验证了过渡路径分析扩展到对不变集合的指定密度之间的测量.
结论:
- 拟议的EWS框架为理解和预测动态系统中的关键过渡提供了一种新的方法.
- 该框架显示了复杂疾病的应用潜力,为疾病进展提供了早期指标.
- 这项工作将过渡路径分析扩展到概率测量,为系统动态提供了新的见解.
相关概念视频
Probability Laws
44.5K
Overview
44.5K
Transfer Function to State Space
818
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
In an RLC...
818
State Space to Transfer Function
595
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
595
Indicators
61.1K
Certain organic substances change color in dilute solution when the hydronium ion concentration reaches a particular value. For example, phenolphthalein is a colorless substance in any aqueous solution with a hydronium ion concentration greater than 5.0 × 10−9 M (pH < 8.3). In more basic solutions where the hydronium ion concentration is less than 5.0 × 10−9 M (pH > 8.3), it is red or pink. Substances such as phenolphthalein, which can be used to determine the pH of a solution, are...
61.1K
Applications of Integration to Probability Density Functions
73
Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF),...
73
Probability Distributions
12.2K
The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
12.2K


