神经信息学 神经元集群编码 史忠植 shizz@ics.ict.ac.cn 中科院计算所 2018/12/3

Neural Representation of moving direction Two pieces of information are important for representing the dynamical aspects of external objects, namely, the moving speed and the moving direction of objects. A. Georgopoulos’s group carried out a series elegant experiments to explore the neural representation of moving direction. It is one of the few examples in which the coding scheme is relatively well understood. 2018/12/3

Experiment observations In the experiment, the monkey is guided to move the lever in the center of apparatus to one of eight peripheral locations. Neural activities in the motor area are recorded. A light comes on at a target position, signalling the moving direction. The monkey is trained to following the guidance in order to get food reward. Since the arm movement of monkey involves the function of motor cortex, Georgopoulos then recorded the neural activities in the motor cortex, and their observation of the activities of a particular neuron is shown in this figure. The neural activity of the same neuron for each possible moving direction is drawn at the corresponding target position. For example. Many trials results are illustrated. A dot represents one spike. Each row represents one Trial. There are two observations are notable. One is that the neuron shows different activity levels, i.e., different Firing rates, when different moving directions are presented. This implies the information of moving direction is In the activities of neurons in the motor area. Secondly, this neuron is not only to be activated by a single moving direction, but by many of them, though the strengths are different. 2018/12/3 All pictures from M. Gazzaniga et al. Cognitive Neuroscience, unless otherwise stated.

Preferred stimulus and tuning curve Preferred stimulus: for each neuron, there is a stimulus value by which the neuron has the maximum response. Tuning curve: the function mapping between the neural activity (measured by mean firing rate) and the stimulus value. Noises always exist These two observations are also true for other stimuli instead of moving direction, and motivated neuroscientists to propose two important concepts to describe neural coding. The following figure shows a typical example for the tuning curve of a neuron encoding the moving direction. The left hand figure shows that neural responses when different values of moving direction are presented. This neuron has the maximum response when the stimulus is 180 degree. This means 180 degree is the preferred Stimulus of this neuron. Here we consider the neural activity is measured the firing rate. This firing rate is of cause, fluctuated trial by Trial. Suppose we take its mean value over many trails. The right hand side figure draws the relationship between the mean firing of this neuron and the stimulus. Interestingly, we see that the tuning curve has smooth, symmetric, bell shape. This shape tells us at least two things. Symmetry implies the tuning curve must be a function of the difference between the preferred stimulus and The actual stimulus, instead of a direct function of the actual stimulus. Secondly, the bell shape, means that the Tuning curve is decay function of this difference, I.e., the neural activity decreases with the difference between the stimulus and the neuronal preferred stimulus. 2018/12/3

Why population code? How is the moving direction encoded by neural activities? By the most active neuron? This sounds reasonably if there is no noise, but it does not work in practice because of large fluctuations in neural activities. By a population of neurons? All active neurons contain a piece of information about the stimulus, why don’t we consider all of them jointly encode the moving direction. It has at least one apparent advantage of averaging out noises in individual neurons, since they are (partially) independent. Georgopoulos et al. proposed an idea to reconstruct the moving direction from the observed neural activities. In the above, we show the experimental observation. Though we note the correlation between moving directions and the neuronal firing rates, we have not figure out the coding scheme exactly. One simple suggestion, the most active neuron reports the stimulus value, since we know when The Stimulus equals to a neuron’s preferred stimulus, this neuron’s tuning function has the largest value. However, this does not work well in reality due to the noise. 2018/12/3

Mathematical Modeling of Neuronal Response The smooth bell-shape tuning curve is often modeled by the Gaussian (or cosin) function: This Gaussian function captures the main features of neural responses. It has the bell-shape. The neuron I responses most when stimulus x is equal to its preferred stimulus c_I, and decreases with the their difference. For neural activity in one trial 2018/12/3

Population Vector Georgopoulos’s idea: the neural system reads out the moving direction by the average of preferred stimuli of all active neurons weighted by their activities. This sounds reasonable since more active neurons, whose preferred stimuli are more likely close to the true stimulus, and hence should contribute more on the final vote. 2018/12/3

An illustration of Population Vector Let us first look at the left hand side picture. Consider two neurons with their tuning functions as shown in this figure. They have different preferred-stimuli. Cell 1 has the preferred stimulus 180 degree, cell2 has 90 degree. Suppose the real stimulus is 180 degree. So in most case, celle1 is more active than cell2. The weight summation in population vector will be looks like this. The red vector represents the weighted contribution. Its direction is the cell1’s preferred one, and the length represent the neural activity. Similarly, for the green vector which represents The contribution of cell2. Since the real stimulus is close to the cell1’s preferred stimulus, cell1 tends to be more active, and hence the red vector is longer. As a result, the summed result, will be more towards the direction of Red vector. This is we expected. Similarly for the case when the real stimulus is 90 degree is shown here. In this example, since there is only two neurons the decoding result is not good. If there are many neurons, as is the case in reality, the result will be much better. This picture shows the result of using population vector when working with experimental data. Each brown vector represent the weight contribution of each neuron. You can Individually they are very noise, but the population vector works very well. 2018/12/3

The paradigm of population coding Population vector demonstrated that information can be accurately represented by the joint activities of a population of neurons in a noise environment. This coding strategy of using a population of neurons to represent stimulus is called population coding. The idea of population coding is also found in the representation of moving direction in other parts of cortex, and the representation of other stimuli, such as the orientation of object and the spatial location. Population coding seems to be a general framework for information processing in neural systems, and worth to be analyzed in more detail theoretically. 2018/12/3

The mathematical model of population coding The encoding phase The decoding phase The first step towards answering these questions is to build up a mathematical model for population coding, clarifying what know about, what to achieve. Population vector is one of many inference strategies. 2018/12/3

功能柱 20世纪60年代末，美国科学家发现，在大脑视觉皮层中，具有相同图像特征选择性和相同感受野位置的众多神经细胞，以垂直于大脑表面的方式排列成柱状结构———功能柱。30多年来，脑研究领域一直将垂直的柱状结构看作大脑功能组织的一个基本原则。但是，传统的功能柱研究还不能阐释视觉系统究竟是如何处理大范围复杂图像信息的。 2018/12/3

功能柱 1972年: Wilson-Cowan方程来描述功能柱; 1990年: Shuster等人模拟视皮层中发现的同步振荡; 1993年: Jansen等人提出了耦合功能柱模型产生了类EEG波形和诱发电位； 1994年: Fukai设计了功能柱式的网络模型来模拟视觉图样的获取; 1997年: Hansel等人根据视皮层朝向柱的结构构建了一个超柱模型，研究其中的同步性和混沌特性，并对朝向选择性的功能柱机理做出解释; 1998年: Fransén等人把传统网络中的单细胞代换成多细胞构成的功能柱，来模拟工作记忆 2018/12/3

功能柱 功能柱结构神经网络模型中的同步振荡现象 中国科学院生物物理所 视觉信息加工重点实验室 中国科学院计算研究所 李速① 齐翔林① 胡宏② 汪云九① 功能柱结构神经网络模型中的同步振荡现象 功能柱是一个振荡子，而且表明功能柱可以成为皮层多样化 的节律活动的发生源，EEG中的各种节律均可以在结构具有 普遍性的功能柱中找到生理基础。 2018/12/3

功能柱 Rose-Hindmarsh方程来描述单神经元: x: 代表膜电位， y: 表示快速回复电流， z: 描述慢变化的调整电流， Isyn 表示突触电流， Istim表示外界输入 2018/12/3

功能柱 模型采用基于电流的突触模型，在突触前细胞的每个动作电位都将触发突触后细胞的Isyn 输入。突触电流 Isyn 表示为: gsyn 为膜电导 1,2 时间常数 Vsyn 表示突触后电位 2018/12/3

功能柱 2018/12/3

同源功能柱 2018/12/3

异源功能柱 2018/12/3

功能柱 功能柱是一个振荡子，而且表明功能柱可以成为皮层多样化的节律活动的发生源，EEG中的各种节律均可以在结构具有普遍性的功能柱中找到生理基础。 2018/12/3

功能柱 功能柱是介于单神经元和皮层脑区之间的一种中间层次的单元，理解这种中间层次的单元的活动特点，能够为脑科学中微观现象和宏观现象的研究之间建立一座桥梁   2018/12/3