Natural Sciences > Brain & Cognitive Sciences > Introduction to Computational Neuroscience

Introduction to Computational Neuroscience posted by duggu on 12/11/2007

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Abstract/Syllabus

Courseware/Lectures

Test/Tutorials

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

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 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

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 time-varying electric field amplitude modulations in a wave-type electric fish." J of Neurophysiology 75, no. 6 (1996): 2280-93. 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 1.2-1.3. 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 Spike-triggered Average Wiener-Hopf Equations and White Noise Analysis	Dayan and Abbot, sections 2.1-2.2. 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, Center-surround Receptive Fields, Simple and Complex Cortical Cells	Palmer, Stephen E. Vision Science - Photons to Phenomenology. Cambridge, MA: MIT Press, 1999, pp. 146-154. ISBN: 0262161834. Dayan and Abbot, sections 2.3-2.6. Web site: Space-Time 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): 354-372. Herrnstein, R. "On the Law of Effect." Journal of the Experimental Analysis of Behavior 13, no. 2 (March 1970): 243-266.
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): 137-156.
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 Decision-Making in the Ultimatum Game." Science 300, no. 5626 (June 13, 2003): 1755-8. Camerer, C. "Strategizing in the Brain." Science 300, no. 5626 (June 13, 2003): 1673-5.
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 Miao-Sin Wu. Foundations of Cellular Neurophysiology. Cambridge, MA: MIT Press, 1995, chapter 2. ISBN: 0262100533.
17	The Action Potential, Hodgkin-Huxley 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	Hodgkin-Huxley Model 2
19	A-type Potassium Channels, Calcium-Dependent 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: 2554-58.
22	Associative Memory 2	More of Professor Seung's notes on Associative Memory (PDF) Miyashita, Y. "Neuronal correlate of visual associative long-term memory in the primate temporal cortex." Nature 335 (1988): 817-20. Griniasty, M., M. V. Tsodyks, and D. J. Amit. "Conversion of temporal correlations between stimuli to spatial correlations between attractors." Neural Comput 5 (1993): 1-17. Amit, D. J. "The Hebbian paradigm reintegrated: local reverberations as internal representations." Behav Brain Sci 18 (1995): 617-26. Nakazawa, K., M. C. Quirk, R. A. Chitwood, et al. "Requirement for Hippocampal CA3 NMDA Receptors in Associative Memory Recall." Science 297 (2002): 211-218.
23	Decisionmaking
24	Projects
25	Projects (cont.)
26	Review
	Final Exam