Computational Neuroscience

MATH/BIOL/EECS/EBME/NEUR 478
MATH/BIOL/COGS 378

Full Syllabus

Course Description

Computer simulations and mathematical analysis of neurons and neural circuits, and the computational properties of nervous systems. Students are taught a range of models for neurons and neural circuits, and are asked to implement and explore the computational and dynamic properties of these models. The course introduces students to dynamical systems theory for the analysis of neurons and neural circuits, as well as to cable theory, passive and active compartmental modeling, numerical integration methods, models of plasticity and learning, models of brain systems, and their relationship to artificial neural networks. Term project required. Recommended prerequisites: multivariate calculus (MATH 223) and a first course in differential equations (either MATH 224 or the sequence BIOL 300 and BIOL 306). Cross-listed as BIOL 378/478, MATH 378/478, COGS 378, EECS 478, EBME 478, NEUR 478. Students enrolled in MATH 478 will make arrangements with the instructor to attend additional lectures and complete additional assignments addressing mathematical topics related to the course. Consent of department required.

Instructor

Peter Thomas Asst. Prof. of Mathematics, Biology & Cognitive Science
pjthomas--at--case.edu / 216-368-3623
Office hours: MW 12:30-2:00 or by appointment.
Course meeting: MWF 10:30-11:20 a.m.
Location: White 324

Course Grader & Teaching Assistant: Catherine Kehl.

COURSE RESOURCES

Course Folder on Google Docs

Assignment Schedule
Project Instructions
Homework assignments (also available under the google docs folder):
1. First Homework Assignment.
2. Second Homework Assignment.
3. Third Homework Assignment and companion file resistor-tmp.ode.
4. Fourth Homework Assignment.
5. Fifth Homework Assignment and companion file balstk.ses.
6. Sixth Homework Assignment and companion files IzhikevichRanNet.m, mlp.m and mlp2.m.

Textbooks

Spikes, Decisions and Actions by Hugh R. Wilson.
Here is a link to the (online) chapters of Dynamical Systems in Neuroscience by Eugene Izhikevich.
Fundamentals of Computational Neuroscience by Thomas Trappenberg.
Here is Thomas Trappenberg's course page at Dalhousie University.

The NEURON simulation environment

The NEURON simulation environment.
Hands-on exercises for learning NEURON.

XPP/AUTO

Download XPP here.
Download the first set of course exercises separately or all in one tar file.

For the second set of XPP exercises (for Friday 2/12/2010) here are

the instructions and
fhn.ode.

For the third set of XPP exercises (for Monday 2/22/2010) here is a .tar file containing the following:

For the fourth set of XPP exercises (for Wednesday 4/21/2010) here are the files with

MATLAB

Matlab is available through CWRU's site license, including the Matlab Neural Network Toolbox. To see whether the version of matlab you have installed includes this toolbox, start matlab and type "ver" in the command line window.
For matlab neural network exercises you will need to download the nnet documentation and the instructions.
For the first exercise work through chapters 2 (Neuron Model and Network Architectures) and 3 (Perceptrons) and (time permitting) 5 (Backpropagation). Here is a Matlab script, or "m-file" to get you started in chapter 2 by taking you through a series of small exercises.
The second matlab neural network exercise explores Kohonen's self-organizing map. Here is an m-file with instructions and a copy of Trappenberg's code som.m.

Miscellany

Izhikevich's code for "simple models"

Download the tar file.

Statistical Neural Field Models

Download Wilson and Cowan's 1972 Biophysical Journal article.

Bursting and Dendritic Morphology

Download Mainen & Sejnowski's 1996 Nature paper and the hoc code for the associated exercise.

Contact Prof. Thomas.

Updated: January 6, 2010