Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600113, India,
Cogn Neurodyn. 2007 Dec;1(4):295-303. doi: 10.1007/s11571-007-9022-0. Epub 2007 Jul 12.
Brain is an expert in producing the same output from a particular set of inputs, even from a very noisy environment. In this article a model of neural circuit in the brain has been proposed which is composed of cyclic sub-circuits. A big loop has been defined to be consisting of a feed forward path from the sensory neurons to the highest processing area of the brain and feed back paths from that region back up to close to the same sensory neurons. It has been mathematically shown how some smaller cycles can amplify signal. A big loop processes information by contrast and amplify principle. How a pair of presynaptic and postsynaptic neurons can be identified by an exact synchronization detection method has also been mentioned. It has been assumed that the spike train coming out of a firing neuron encodes all the information produced by it as output. It is possible to extract this information over a period of time by Fourier transforms. The Fourier coefficients arranged in a vector form will uniquely represent the neural spike train over a period of time. The information emanating out of all the neurons in a given neural circuit over a period of time can be represented by a collection of points in a multidimensional vector space. This cluster of points represents the functional or behavioral form of the neural circuit. It has been proposed that a particular cluster of vectors as the representation of a new behavior is chosen by the brain interactively with respect to the memory stored in that circuit and the amount of emotion involved. It has been proposed that in this situation a Coulomb force like expression governs the dynamics of functioning of the circuit and stability of the system is reached at the minimum of all the minima of a potential function derived from the force like expression. The calculations have been done with respect to a pseudometric defined in a multidimensional vector space.
大脑是从特定的输入集产生相同输出的专家，即使在非常嘈杂的环境中也是如此。本文提出了一种由循环子电路组成的大脑神经电路模型。一个大环路被定义为由感觉神经元到大脑最高处理区域的前馈路径和来自该区域的反馈路径组成，反馈路径回到接近相同的感觉神经元。已经从数学上证明了一些较小的循环如何放大信号。一个大环路通过对比和放大原理来处理信息。还提到了如何通过精确的同步检测方法识别一对突触前和突触后神经元。假设从一个放电神经元发出的尖峰序列编码了它作为输出产生的所有信息。通过傅里叶变换，可以在一段时间内提取这些信息。以向量形式排列的傅里叶系数将唯一地表示一段时间内的神经尖峰序列。在一段时间内，给定神经电路中所有神经元发出的信息可以表示为多维向量空间中的点集。这组点代表了神经电路的功能或行为形式。有人提出，大脑通过与该电路中存储的记忆和涉及的情绪量进行交互，选择特定的向量簇作为新行为的表示。有人提出，在这种情况下，类似于库仑力的表达式控制着电路的功能动力学，并且系统的稳定性在从力表达式得出的势函数的所有最小值中的最小值处达到。计算是针对多维向量空间中定义的伪度量进行的。
