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摘要翻译：
高斯白噪声经常被用来模拟物理系统中的涨落。在Fokker-Planck理论中，这导致在阈值模型吸收边界附近的概率密度消失。本文导出了一阶随机微分方程的平稳密度的边界条件，并证明了阈值单元的响应性质是定性改变的。应用于集成-激发神经元模型，反应是瞬时的，而不是低通特性，高度非线性，兴奋和抑制不对称。这种新的机制在网络层次上表现出来，是门限单元脉冲耦合系统的一般特性。
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英文标题：
《A Fokker-Planck formalism for diffusion with finite increments and
absorbing boundaries》
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作者：
M. Helias, M. Deger, S. Rotter, M. Diesmann
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最新提交年份：
2009
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分类信息：
一级分类：Quantitative Biology 数量生物学
二级分类：Quantitative Methods 定量方法
分类描述：All experimental, numerical, statistical and mathematical contributions of value to biology
对生物学价值的所有实验、数值、统计和数学贡献
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一级分类：Quantitative Biology 数量生物学
二级分类：Other Quantitative Biology 其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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一级分类：Quantitative Biology 数量生物学
二级分类：Populations and Evolution 种群与进化
分类描述：Population dynamics, spatio-temporal and epidemiological models, dynamic speciation, co-evolution, biodiversity, foodwebs, aging; molecular evolution and phylogeny; directed evolution; origin of life
种群动力学；时空和流行病学模型；动态物种形成；协同进化；生物多样性；食物网；老龄化；分子进化和系统发育；定向进化；生命起源
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英文摘要：
Gaussian white noise is frequently used to model fluctuations in physical systems. In Fokker-Planck theory, this leads to a vanishing probability density near the absorbing boundary of threshold models. Here we derive the boundary condition for the stationary density of a first-order stochastic differential equation for additive finite-grained Poisson noise and show that the response properties of threshold units are qualitatively altered. Applied to the integrate-and-fire neuron model, the response turns out to be instantaneous rather than exhibiting low-pass characteristics, highly non-linear, and asymmetric for excitation and inhibition. The novel mechanism is exhibited on the network level and is a generic property of pulse-coupled systems of threshold units.
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PDF链接：
https://arxiv.org/pdf/0908.1960
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