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 Introduction to Computational Neuroscience  posted by  duggu   on 12/11/2007  Add Courseware to favorites Add To Favorites  
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Abstract/Syllabus:

Seung, Sebastian, 9.29J Introduction to Computational Neuroscience, Spring 2004. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 08 Jul, 2010). License: Creative Commons BY-NC-SA

Voltage modulation versus time in milliseconds.

Data from an experiment on the weakly electric fish Eigenmannia. The frequency of action potential firing increases when the stimulus increases. (Image by Prof. Sebastian Seung from his notes on neural coding: Linear models.)

Course Highlights

This course features a selection of downloadable lecture notes, and problem sets in the assignments section.

Course Description

This course gives a mathematical introduction to neural coding and dynamics. Topics include convolution, correlation, linear systems, game theory, signal detection theory, probability theory, information theory, and reinforcement learning. Applications to neural coding, focusing on the visual system are covered, as well as Hodgkin-Huxley and other related models of neural excitability, stochastic models of ion channels, cable theory, and models of synaptic transmission.

Visit the Seung Lab Web site.

Technical Requirements

Special software is required to use some of the files in this course: .mat, and .m.

Syllabus

 
 

Course Philosophy

The central assumption of computational neuroscience is that the brain computes. What does that mean? Generally speaking, a computer is a dynamical system whose state variables encode information about the external world. In short, computation equals coding plus dynamics. Some neuroscientists study the way that information is encoded in neural activity and other dynamical variables of the brain. Others try to characterize how these dynamical variables evolve with time. The study of neural dynamics can be further subdivided into two separate strands. One tradition, exemplified by the work of Hodgkin and Huxley, focuses on the biophysics of single neurons. The other focuses on the dynamics of networks, concerning itself with phenomena that emerge from the interactions between neurons. Therefore computational neuroscience can be divided into three subspecialties: neural coding, biophysics of neurons, and neural networks.

Prerequisites

  • Basic biology, chemistry, and physics.
  • Differential equations or permission of instructor. Linear algebra is also desirable.
  • Knowledge of MATLAB® or willingness to learn.

Course Requirements

  • Weekly problem sets
  • Midterm project
  • Final project

Textbook

We will follow the first six chapters of the book very closely, and the later chapters more sketchily.

Dayan, Peter, and L. F. Abbott. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. Cambridge, MA: MIT Press, 2001. ISBN: 0262041995.

 

 

Calendar

 
 
Lec # TOPICS KEY DATES
1 Introduction

Examples of Neural Coding, Simple Linear Regression
 
2 Convolution and Correlation 1

Firing Rate
 
  Optional Lecture 1

Initializing and Using Vectors and Matrices in MATLAB®, Matrix Shortcuts, Plots in MATLAB®, Useful Commands

Simple Statistics and Linear Regression
 
3 Convolution and Correlation 2

Spike-triggered Average

Wiener-Hopf Equations and White Noise Analysis
 
4 Visual Receptive Fields 1

Basics of the Visual System, Center-surround Receptive Fields, Simple and Complex Cortical Cells
Assignment 1 due
  Optional Lecture 2

Probability Theory
 
5 Visual Receptive Fields 2 Assignment 2 due
  Optional Lecture 3

Markov Processes
 
6 Operant Matching 1  
7 Operant Matching 2 Assignment 3 due
8 Games 1  
  Optional Lecture 4

Linear Stability Analysis
 
9 Games 2  
10 Project Meeting 1

Discussion of Topics, Choice of Projects, Work Begins
 
11 Project Meeting 2 Assignment 4 due
12 Project Meeting 3  
13 Project Meeting 4  
14 Project Presentations 1  
15 Project Presentations 2  
16 Ion Channels, Nernst Equation, Passive Electrical Properties of Neurons  
17 The Action Potential, Hodgkin-Huxley Model 1  
18 Hodgkin-Huxley Model 2 Assignment 5 due
19 A-type Potassium Channels, Calcium-Dependent Potassium Channels  
20 Synapses Assignment 6 due
  Optional Lecture 5

Numerical Methods for Differential Equations
 
21 Associative Memory 1  
22 Associative Memory 2 Assignment 7 due
23 Decisionmaking  
24 Projects  
25 Projects (cont.)  
26 Review  
  Final Exam  
 

 




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