论文标题
神经元动力学和尖峰火车统计中的热力学形式主义
Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics
论文作者
论文摘要
热力学形式主义提供了一个严格的数学框架，用于研究动态系统的定量和定性方面。从其核心上讲，具有最简单形式的各种原理与最大熵原理相应。它用作统计推理程序，以特定的概率度量（Gibbs度量）表示复杂系统的集体行为。该框架在不同的科学领域中找到了应用程序。特别是，它在神经科学中具有富有成果和影响力。在本文中，我们回顾了如何在理论神经科学领域中利用热力学形式主义作为一种概念和操作工具，以将相互作用的神经元的动力学和来自实验数据或数学模型的动作电位统计数据联系起来。我们对这种形式主义中可以解决的理论神经科学中的观点和开放问题评论。
The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle corresponding, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science. In particular, it has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.
