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Computational geometry for modeling neural populations: From visualization to simulation

机译:用于建模神经种群的计算几何:从可视化到仿真

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摘要

The importance of a mesoscopic description level of the brain has now been well established. Rate based models are widely used, but have limitations. Recently, several extremely efficient population-level methods have been proposed that go beyond the characterization of a population in terms of a single variable. Here, we present a method for simulating neural populations based on two dimensional (2D) point spiking neuron models that defines the state of the population in terms of a density function over the neural state space. Our method differs in that we do not make the diffusion approximation, nor do we reduce the state space to a single dimension (1D). We do not hard code the neural model, but read in a grid describing its state space in the relevant simulation region. Novel models can be studied without even recompiling the code. The method is highly modular: variations of the deterministic neural dynamics and the stochastic process can be investigated independently. Currently, there is a trend to reduce complex high dimensional neuron models to 2D ones as they offer a rich dynamical repertoire that is not available in 1D, such as limit cycles. We will demonstrate that our method is ideally suited to investigate noise in such systems, replicating results obtained in the diffusion limit and generalizing them to a regime of large jumps. The joint probability density function is much more informative than 1D marginals, and we will argue that the study of 2D systems subject to noise is important complementary to 1D systems.
机译:现在已经很好地确定了大脑的介观描述水平的重要性。基于速率的模型已被广泛使用,但有局限性。最近,已经提出了几种非常有效的人口级方法,这些方法超出了根据单个变量对人口进行表征的范围。在这里,我们介绍了一种基于二维(2D)点刺神经元模型的神经种群模拟方法,该模型根据神经状态空间上的密度函数来定义种群的状态。我们的方法的不同之处在于,我们不进行扩散近似,也不将状态空间缩小为一维(1D)。我们不对神经模型进行硬编码,而是读取网格以描述其在相关模拟区域中的状态空间。无需重新编译代码即可研究新型模型。该方法是高度模块化的:确定性神经动力学和随机过程的变化可以独立研究。当前,存在将复杂的高维神经元模型简化为2D模型的趋势,因为它们提供了1D中无法提供的丰富的动态库,例如极限环。我们将证明我们的方法非常适合研究此类系统中的噪声,复制在扩散极限中获得的结果并将其推广到大跃变状态。联合概率密度函数比一维边缘函数具有更多信息,我们将争辩说,受噪声影响的二维系统的研究是对一维系统的重要补充。

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