A Sparse Reformulation of the Green’s Function Formalism Allows Efficient Simulations of Morphological Neuron Models
A Sparse Reformulation of the Green’s Function Formalism Allows Efficient Simulations of Morphological Neuron Models
复制标题
格林函数形式主义的稀疏改革可以有效模拟形态神经元模型
DOI：
10.1162/neco_a_00788
复制
发表时间：
2015
影响因子：
2.9
通讯作者：
M. Gewaltig
中科院分区：
文献类型：
--
作者：
W. A. Wybo;Daniele Boccalini;B. Torben;M. Gewaltig
我们证明，当一类偏微分方程，广义电缆方程，定义在树图和输入被限制到一个空间离散的，精心挑选的一组点，绿色函数（GF）的形式主义可以重写的规模与输入位置的数量n，相反，以前报道的缩放。我们表明，线性缩放可以与扩展的剩余内核的指数的总和，以允许有效的模拟方程从上述类。我们进一步验证了这种模拟范例的神经细胞模型，并探讨其与更传统的有限差分方法的关系。预计在计算性能的增益的情况下进行了讨论。
We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green’s function (GF) formalism can be rewritten to scale as with the number n of inputs locations, contrary to the previously reported scaling. We show that the linear scaling can be combined with an expansion of the remaining kernels as sums of exponentials to allow efficient simulations of equations from the aforementioned class. We furthermore validate this simulation paradigm on models of nerve cells and explore its relation with more traditional finite difference approaches. Situations in which a gain in computational performance is expected are discussed.
DOI：
10.1016/0020-7101(84)90008-4
发表时间：
1984-01-01
期刊：
INTERNATIONAL JOURNAL OF BIO-MEDICAL COMPUTING
影响因子：
--
作者：
HINES, M
通讯作者：
HINES, M