The emergent activity of biological systems can often be represented as low-dimensional, Langevin-type stochastic differential equations. In certain systems, however, large and abrupt events occur and violate the assumptions of this approach. We address this situation here by providing a novel method that reconstructs a jump-diffusion stochastic process based solely on the statistics of the original data. Our method assumes that these data are stationary, that diffusive noise is additive, and that jumps are Poisson. We use threshold-crossing of the increments to detect jumps in the time series. This is followed by an iterative scheme that compensates for the presence of diffusive fluctuations that are falsely detected as jumps. Our approach is based on probabilistic calculations associated with these fluctuations and on the use of the Fokker–Planck and the differential Chapman–Kolmogorov equations. After some validation cases, we apply this method to recordings of membrane noise in pyramidal neurons of the electrosensory lateral line lobe of weakly electric fish. These recordings display large, jump-like depolarization events that occur at random times, the biophysics of which is unknown. We find that some pyramidal cells increase their jump rate and noise intensity as the membrane potential approaches spike threshold, while their drift function and jump amplitude distribution remain unchanged. As our method is fully data-driven, it provides a valuable means to further investigate the functional role of these jump-like events without relying on unconstrained biophysical models.

中文翻译：

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数据驱动的平稳跳跃扩散过程的推断，并应用于锥体神经元的膜电压波动。

生物系统的新兴活动通常可以表示为低维Langevin型随机微分方程。但是，在某些系统中，会发生大而突然的事件，并违反了此方法的假设。我们在这里通过提供一种新颖的方法来解决这种情况，该方法仅基于原始数据的统计信息即可重建跳跃扩散随机过程。我们的方法假设这些数据是固定的，扩散噪声是可加的，并且跳跃是泊松。我们使用增量的阈值交叉来检测时间序列中的跳跃。这之后是一个迭代方案，该方案可以补偿被错误检测为跳跃的扩散波动的存在。我们的方法是基于与这些波动相关的概率计算，以及基于Fokker-Planck和微分Chapman-Kolmogorov方程的使用。经过一些验证的情况下，我们将这种方法应用于弱电鱼的电感应侧线叶的锥体神经元的膜噪声的记录。这些记录显示了随机发生的大型跳跃状去极化事件，其生物物理学是未知的。我们发现，随着膜电位接近峰值阈值，一些锥体细胞会增加其跳跃速率和噪声强度，而其漂移函数和跳跃幅度分布则保持不变。由于我们的方法完全由数据驱动，