A mathematical model for resolution enhancement in layered sensory systems.
A mathematical model for resolution enhancement in layered sensory systems.
复制标题
分层感觉系统中分辨率增强的数学模型。
DOI：
10.1007/bf00224702
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发表时间：
1991
影响因子：
1.9
通讯作者：
Miller,JP
中科院分区：
文献类型：
--
作者：
Zhang,J;Miller,JP
海利根贝格(1987)最近提出了一个模型来解释如何通过宽调谐的感受器的有序阵列来表示刺激变量，使得刺激的分辨率可以大大超过组成阵列的单个感受器的分辨率。在他的模型中，这种“超敏度”是通过根据线性突触加权函数将受体连接到更高水平的池中间神经元来实现的。我们将该模型推广到任意多项式突触加权函数的一般情况，并证明了这种高级中间神经元的响应函数是与加权函数同阶的多项式。证明了Hermite多项式是系统的本征函数。此外，通过允许更高水平池中的多个中间神经元，每个中间神经元根据不同的正交权函数连接到感受器，我们证明了扩展刺激函数可以更精确地表示，而不仅仅是单个点刺激的值。最后，我们提出了一种解决有限接收器阵列端部附近产生的“边缘效应”误差问题的方法。
Heiligenberg (1987) recently proposed a model to explain how the representation of a stimulus variable through an ordered array of broadly tuned receptors could allow a degree of stimulus resolution greatly exceeding the resolution of the individual receptors which make up the array. In his model, this “hyperacuity” is achieved by connecting the receptors to a higher level pool interneuron according to a linear synaptic weighting function. We have extended this model to the general case of arbitrary polynomial synaptic weighting functions, and showed that the response function of this higher level interneuron is a polynomial of the same order as the weighting function. We also proved that Hermite polynomials are eigen-functions of the system. Further, by allowing multiple interneurons in the higher level pool, each of which is connected to the receptors according to a different orthogonal weighting function, we demonstrated that extended stimulus functions can be represented with enhanced precision, rather than just the value of individual point stimuli. Finally, we suggest a solution to the problem of “edge effect” errors arising near the ends of finite receptor arrays.