 
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 BYNCSA
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 HodgkinHuxley 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
Calender schedule.
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
Spiketriggered Average
WienerHopf Equations and White Noise Analysis 

4 
Visual Receptive Fields 1
Basics of the Visual System, Centersurround 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, HodgkinHuxley Model 1 

18 
HodgkinHuxley Model 2 
Assignment 5 due 
19 
Atype Potassium Channels, CalciumDependent 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 




Further Reading:

Readings
Many of the readings are from the required course text:
Dayan, Peter, and L. F. Abbott. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. Cambridge, MA: MIT Press, 2001. ISBN: 0262041995.
Course readings.
Lec # 
TOPICS 
READINGS 
1 
Introduction
Examples of Neural Coding, Simple Linear Regression 
Dayan and Abbott, section 1.1.
Wessel, R., C. Koch, and F. Gabbiani. "Coding of timevarying electric field amplitude modulations in a wavetype electric fish." J of Neurophysiology 75, no. 6 (1996): 228093.
Press, William H., Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling. "Fitting Data to a Straight Line." In Numerical Recipes in C: The Art of Scientific Computing. New York, NY: Cambridge University Press, 1992. ISBN: 0521431085. 
2 
Convolution and Correlation 1
Firing Rate 
Dayan and Abbot, section 1.21.3.
Press, William H., Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling. "Convolution and Deconvolution Using the FFT." In Numerical Recipes in C: The Art of Scientific Computing. New York, NY: Cambridge University Press, 1992. ISBN: 0521431085. 

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
Spiketriggered Average
WienerHopf Equations and White Noise Analysis 
Dayan and Abbot, sections 2.12.2.
Press, William H., Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling. "Correlation and Autocorrelation Using the FFT." In Numerical Recipes in C: The Art of Scientific Computing. New York, NY: Cambridge University Press, 1992. ISBN: 0521431085. 
4 
Visual Receptive Fields 1
Basics of the Visual System, Centersurround Receptive Fields, Simple and Complex Cortical Cells 
Palmer, Stephen E. Vision Science  Photons to Phenomenology. Cambridge, MA: MIT Press, 1999, pp. 146154. ISBN: 0262161834.
Dayan and Abbot, sections 2.32.6.
Web site: SpaceTime Receptive Fields of Visual Neurons. 

Optional Lecture 2
Probability Theory 

5 
Visual Receptive Fields 2 


Optional Lecture 3
Markov Processes 

6 
Operant Matching 1 
Gallistel, C., T. Mark, A. King, and P. Latham. "The Rat Approximates an Ideal Detector of Changes in Rates of Reward." Journal of Experimental Psychology: Animal Behavior Processes 27 (2001): 354372.
Herrnstein, R. "On the Law of Effect." Journal of the Experimental Analysis of Behavior 13, no. 2 (March 1970): 243266. 
7 
Operant Matching 2 
Seung, H. S. "Matching and maximizing are two ends of a spectrum of policy search algorithms." Manuscript (January 2, 2004.) (PDF)
Herrnstein, R., and D. Prelec. Melioration: A Theory of Distributed Choice. The Journal of Economic Perspectives 5, no. 3 (Summer, 1991): 137156. 
8 
Games 1 
Camerer, Colin F. Behavioral Game Theory. Princeton, NJ: Princeton University Press, 2003. ISBN: 0691090394. 

Optional Lecture 4
Linear Stability Analysis 

9 
Games 2 
Sanfey, A., J. Rilling, J. Aronson, L. Nystrom, and J. Cohen. "The Neural Basis of Economic DecisionMaking in the Ultimatum Game." Science 300, no. 5626 (June 13, 2003): 17558.
Camerer, C. "Strategizing in the Brain." Science 300, no. 5626 (June 13, 2003): 16735. 
10 
Project Meeting 1
Discussion of Topics, Choice of Projects, Work Begins 

11 
Project Meeting 2 

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 
Dayan and Abbott, section 5.2.
Johnston, Daniel, and Samuel MiaoSin Wu. Foundations of Cellular Neurophysiology. Cambridge, MA: MIT Press, 1995, chapter 2. ISBN: 0262100533. 
17 
The Action Potential, HodgkinHuxley Model 1 
Dayan and Abbot, sections 5.3, 5.5, and 5.6.
Koch, Christof. Biophysics of Computation, Information Processing in Single Neurons. New York, NY: Oxford University Press, 2004, chapter 6. ISBN: 0195181999. 
18 
HodgkinHuxley Model 2 

19 
Atype Potassium Channels, CalciumDependent Potassium Channels 
Dayan, and Abbott. Section 6.2. 
20 
Synapses 
Dayan, and Abbott. Section 5.8. 

Optional Lecture 5
Numerical Methods for Differential Equations 
Dayan, and Abbott. Section 5.11. (Appendices A and B)
Sherman, A. "Lecture Notes and Lab Problems on Numerical Methods." (PDF) (Courtesy of Dr. Arthur Sherman, NIDDK, National Institutes of Health. This work is in the public domain.)
Arthur Sherman's Web page on Numerical Methods in Neuronal Modeling. 
21 
Associative Memory 1 
Professor Seung's notes on the Hopfield Model (PDF)
Hopfield, J. J. "Neural networks and physical systems with emergent collective computational abilities." Proc Natl Acad Sci U.S.A. 79: 255458. 
22 
Associative Memory 2 
More of Professor Seung's notes on Associative Memory (PDF)
Miyashita, Y. "Neuronal correlate of visual associative longterm memory in the primate temporal cortex." Nature 335 (1988): 81720.
Griniasty, M., M. V. Tsodyks, and D. J. Amit. "Conversion of temporal correlations between stimuli to spatial correlations between attractors." Neural Comput 5 (1993): 117.
Amit, D. J. "The Hebbian paradigm reintegrated: local reverberations as internal representations." Behav Brain Sci 18 (1995): 61726.
Nakazawa, K., M. C. Quirk, R. A. Chitwood, et al. "Requirement for Hippocampal CA3 NMDA Receptors in Associative Memory Recall." Science 297 (2002): 211218. 
23 
Decisionmaking 

24 
Projects 

25 
Projects (cont.) 

26 
Review 


Final Exam 




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