Dumont Grégory, Henry Jacques, Tarniceriu Carmen Oana
École Normale Supérieure, Group for Neural Theory, Paris, France.
INRIA team Carmen, INRIA Bordeaux Sud-Ouest, 33405 Talence cedex, France.
J Theor Biol. 2016 Oct 7;406:31-41. doi: 10.1016/j.jtbi.2016.06.022. Epub 2016 Jun 19.
Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability is strikingly similar.
事实证明，确定合适的工具来表达神经活动的随机特性是计算神经科学中最大的挑战之一。即使这个问题没有确定的答案，但表达这种随机性最常用的方法是使用随机模型。根据变异性的来源，随机性的来源被分为内在的或外在的，并产生了不同的数学框架来追踪细胞的动态。虽然在诸如积分发放模型等模型中，外部变异性通常通过维纳过程来处理，但内部变异性大多通过随机发放过程来表达。在本文中，我们研究了这些不同的变异性表达如何相互关联。为此，我们研究了相应随机模型的概率密度函数，并研究它们如何通过积分变换相互映射。我们的理论发现为变异性的特定类别提供了新的见解，并证实了，尽管内在和外在变异性的性质相反，但它们的数学形式化却惊人地相似。
