论文标题
优化生物学超扩散过程的优化:用于处理观测数据的算法和动力学方程的自相似解决方案
Optimization identification of superdiffusion processes in biology: an algorithm for processing observational data and a self-similar solution of the kinetic equation
论文作者
论文摘要
这项工作是试图转移生物学的一种,在物理学中开发的方法用于制定和求解动力学方程,其中空间坐标中积分操作员的内核随着距离的增加而缓慢降低,并且属于征费分布的类别。提出了一种算法,用于重建阶梯概率密度函数(PDF),以中等数量的生物学对象轨迹(移民)(移民)和相应的integro-差异动力学方程的绿色函数的衍生,以衍生整个构造的自动时空范围,包括整个时空的构造,包括整个时空范围,包括整个时空的构造。考虑了具有模型幂律步长PDF的广泛的时间相关的超级延伸过程,这对应于移民恒定速度的给定值的“征收左右步行”,而移民之间的平均时间t则对应。 The algorithm is tested within the framework of a synthetic diagnostics, consisting in the generation of artificial experimental data for trajectories of migrants and the subsequent reconstruction of the parameters of the step-length PDF and T. For different volumes of synthetic data, to obtain a general idea of the distributions under study (non-parametric case) and to evaluate the accuracy of recovering the parameters of the PDF (in the参数表示的情况),使用平衡识别方法。证明了阶梯长度和T的参数的近似自相似解决方案,可提供移民密度的时空演化的合理精度。
This work is an attempt to transfer to biology the methods developed in physics for formulating and solving the kinetic equations in which the kernel of the integral operator in spatial coordinates is slowly decreasing with increasing distance and belongs to the class of Levy distributions. An algorithm is proposed for the reconstruction of the step-length probability density function (PDF) on a moderate number of trajectories of biological objects (migrants) and for the derivation of the Green's function of the corresponding integro-differential kinetic equation for the density of migrants in the entire space-time range, including the construction of an approximate self-similar solution. A wide class of time-dependent superdiffusion processes with a model power-law step-length PDF is considered, which corresponds to "Levy walks with rests" for given values of the migrant's constant velocity and the average time T of the migrant's stay between runs. The algorithm is tested within the framework of a synthetic diagnostics, consisting in the generation of artificial experimental data for trajectories of migrants and the subsequent reconstruction of the parameters of the step-length PDF and T. For different volumes of synthetic data, to obtain a general idea of the distributions under study (non-parametric case) and to evaluate the accuracy of recovering the parameters of the PDF (in the case of a parametric representation), the method of balanced identification is used. The approximate self-similar solution for the parameters of step-length PDF and T is shown to provide reasonable accuracy of the space-time evolution of migrant's density.