1.4 Generalized Integrate-and-Fire Model 问题：真正的阈值在哪里？ (继续) 常电流刺激 du 1>0 91 du I>0 dt 9 不动点碰撞融合 鞍结 分岔 9=9h res ,9 不动点消失 9 du I>0 9 1.5 Quality of Integrate-and-Fire Models 问题：怎样评价一个神经元模型的好坏？ neuron I(t model optimization mathematica neuron model >注入时变电流，记录膜电位： >利用膜电位和电流关系，优化模型参数： 利用其它记录数据做测试，看是否能预测放电：
1.5 Quality of Integrate-and-Fire Models Good or not good,highly depends on your requirements egular spiking(RS) intrinsically bursting (IB chattering(CH) fast spiking(FS)】 thalamo-cortical (TC) thalamo-cortical (TC) resonator (RZ) low-threshold soikina (LTS) 20 mV 40m 63 mv 87 mV IF neurons are without adaption,bursting,and inhibitory rebound,so not biophysical But IF neurons can be mathematically analyzed,fast computation,and easy to realize Extensions and onen discussions CV 2wv J(u-Vr)/o er。-】 J(u-Vr)la Neural correlation( d =v2e-/erf dμ (,）-ea-wea()〗 Experimental data Matnemancal moael: 输入：均值+独立噪声+共同噪声 Tm dt =-Viu+avTm [V1-CEi(t)+VCEe(t)] 业=-⅓+vmva0+vc.例 Tm dt Analysis and prediction: 2 2( v放电率 p≈S(4,o)c= CV变异系数 CV2y 6 0.3 0 02 0.2 0.3 n utput rate v(splke5 Jaime de la Rocha et al.,Nature,2007
Extensions and open discussions Mean-field analysis of a single IF neuron with massive synaptic bombardment Mathematical assumption:considering a single IF neuron >receiving inputs from Cr/C excitatory /inhibitory neurons each presynaptic SP is an independent Poisson process(v or v) >each spike kicks an increment in membrane potential (Jgor-) I=+o5(t) 突触输入近似：均值+白噪声 u-Jv.+(--CJer-CJv 8(1- 。2=2u-)小+2-J,6t-) =(CeJy+CJy)δ-i)】 How to solve SDE numerically? Synaptic bombardment causes neuronal noise and drives neuron firing irregularly We can further analyze the firing dynamics of IF neuron mathematically End 以从计算神经科学到美陆智能”学术研计会 Lecture1 The Leaky Integrate-and-Fire Neuron 神经元的整合发放模型 Daqing Guo郭大肉 dqguo@uestc.edu.cn Department of Biomedical Engineering. School of Life Science and Technology, University of Electronic Science and Technology of China
Computational Neuroscience The mathematical theory of our brain Lecture 1 神经元的整合发放(IF)模型 2020年计算神经科. 号：983068756 ▣动 Daqing Guo/郭大庆 dqguo@uestc.edu.cn Department of Biomedical Engineering, School of Life Science and Technology, University of Electronic Science and Technology of China Before the course 讲授内容： Neuronal >神经元：电特性、数学模型、动力学分析方法 Dynamics >突触：数学模型、突触可塑性（与学习有关） >神经噪声：噪声源、神经元的随机动力学 >神经元网络：拓扑结构、神经计算、神经元编解码基础 http://neuronaldynamics.epfl.ch/online/index.html 考核方式： >课程设计：50% 神经网络模型的构建 >平时成绩：50%，出勤率、作业 程序语言 Matlab/Python 先行课：神经科学基础知识、数值计算、非线性动力学、微分方程
Content 0 Simple Introduction 1.1 Neurons and Synapses: 1.2 The Passive Membrane(被动膜) -Linear circuit Dirac delta-function 1.3 Leaky Integrate-and-Fire Model 1.4 Generalized Integrate-and-Fire Model 整合发放模型 1.5.Quality of Integrate-and-Fire Models Introduction 《埃德温·史密斯纸草文稿》 古埃及：人类最早关于脑的文献记录 埃及医师伊姆霍特普(Imhotep)一公元 前2600年 纸莎草纸(Papyrus)一公元前3000年 --- 盒N 脑：brain (古埃及象形文字) 于公元前1600-1700完成的纸草文稿，手稿第一位已知持有者埃德温·史密斯(1822-1906)