Department of Mathematics, University of Houston Houston, TX, USA.
Front Comput Neurosci. 2013 Jul 17;7:84. doi: 10.3389/fncom.2013.00084. eCollection 2013.
Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact the dynamics and function of neural ensembles remains an important open problem. Here we describe a new, generative model for correlated spike trains that can exhibit many of the features observed in data. Extending prior work in mathematical finance, this generalized thinning and shift (GTaS) model creates marginally Poisson spike trains with diverse temporal correlation structures. We give several examples which highlight the model's flexibility and utility. For instance, we use it to examine how a neural network responds to highly structured patterns of inputs. We then show that the GTaS model is analytically tractable, and derive cumulant densities of all orders in terms of model parameters. The GTaS framework can therefore be an important tool in the experimental and theoretical exploration of neural dynamics.
新兴技术正在揭示越来越大的神经集合中的尖峰活动。通常，这种尖峰活动远非独立的，不同细胞的尖峰时间存在相关性。了解这种相关性如何影响神经集合的动力学和功能仍然是一个重要的开放性问题。在这里，我们描述了一个新的、用于相关尖峰序列的生成模型，该模型可以表现出数据中观察到的许多特征。该广义细化和移位（GTaS）模型扩展了数学金融领域的先前工作，用具有多种时间相关结构的边际泊松尖峰序列创建了。我们给出了几个示例，突出了该模型的灵活性和实用性。例如，我们使用它来研究神经网络对高度结构化输入模式的响应。然后，我们表明 GTaS 模型是可分析的，并且可以根据模型参数推导出所有阶的累积密度。因此，GTaS 框架可以成为神经动力学实验和理论探索的重要工具。
