论文标题
神经系统中固定作用的原则
The principle of stationary action in neural systems
论文作者
论文摘要
固定作用的原理是现代物理学的基石，为调查经典力学中发现的动态系统提供了一个强大的框架，直到量子场理论。但是，尽管计算神经科学非常依赖物理学的概念，但在这方面却是异常的，因为其主要运动方程与拉格朗日的表述不兼容，因此与固定作用的原则。以动态因果建模神经元状态方程，Hodgkin-Huxley模型和泄漏的集成和射击模型为示例，我们表明可以根据单个Lagrangian来编写这些方程的复杂振荡形式。因此，我们将计算神经科学中的数学描述放在固定行动原则的范围下，并使用该重新制定来表达在神经系统中产生的对称性和相关的保护法。
The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in classical mechanics through to quantum field theory. However, computational neuroscience, despite its heavy reliance on concepts in physics, is anomalous in this regard as its main equations of motion are not compatible with a Lagrangian formulation and hence with the principle of stationary action. Taking the Dynamic Causal Modelling neuronal state equation, Hodgkin-Huxley model, and the Leaky Integrate-and-Fire model as examples, we show that it is possible to write complex oscillatory forms of these equations in terms of a single Lagrangian. We therefore bring mathematical descriptions in computational neuroscience under the remit of the principle of stationary action and use this reformulation to express symmetries and associated conservation laws arising in neural systems.
