论文标题
通过基于协方差的扩散参数的估计值推断在2D晶格上的各向异性随机步行速率的推断
Inference of hopping rates of anisotropic random walk on a 2D lattice via covariance-based estimators of diffusion parameters
论文作者
论文摘要
传统上，采用了均方根位移的时间开发来确定从单个颗粒的轨迹中的扩散系数。但是，这种方法对图像采集时的噪声和运动模糊敏感。最近，Vestergaard等人。已经提出了一种基于移位序列之间的协方差的新方法。这种方法给出了对一维扩散的扩散系数而没有偏差的更强大的估计器，即当平均速度为零时。在这里，我们将这种方法扩展到在二维晶格上可能有偏见的随机行走。首先，我们描述了跳跃速率与八个相邻站点的关系与随机二维位移的高阶力矩的时间发展。然后，我们为这些高阶力矩得出基于协方差的估计器。数值模拟证实，此处提供的过程允许从二维轨迹数据中推断出具有位置误差和运动模糊的随机跳率。
Traditionally, time-development of the mean square displacement has been employed to determine the diffusion coefficient from the trajectories of single particles. However, this approach is sensitive to the noise and the motion blur upon image acquisition. Recently, Vestergaard et al. has proposed a novel method based on the covariance between the shifted displacement series. This approach gives a more robust estimator of the diffusion coefficient of one-dimensional diffusion without bias, i.e., when mean velocity is zero. Here, we extend this approach to a potentially biased random walk on a two-dimensional lattice. First, we describe the relationship between the hopping rates to the eight adjacent sites and the time development of the higher-order moments of the stochastic two-dimensional displacements. Then, we derive the covariance-based estimators for these higher-order moments. Numerical simulations confirmed that the procedure presented here allows inference of the stochastic hopping rates from two-dimensional trajectory data with location error and motion blur.
