New class schedule for Spring 2005

This tentative schedule is likely to change once I start teaching

Any questions can be addressed to me at harel.shouval@uth.tmc.edu

or by phone to: 713-50-5708

 

Harel

 

ME 385J/GS140033: Introduction to Theoretical/Computational Neuroscience

Spring 2005 - Mondays 2:00 - 5:00 PM beginning Jan 24 2005
In Houston Room MSB G500, In Austin ETC 2.146
Course Director/Instructor: Harel Shouval, Ph.D.
For More Information: Call 713-500-5708 or via email at harel.shouval@uth.tmc.edu

Course Description

This course provides an introduction to basic mathematical and computational methods of theoretical neuroscience. Different topics including the biophysics of single neurons, population coding, synaptic plasticity and learning will be covered. The course will rely on elementary mathematical methods such as linear algebra and calculus; most assignments will be Matlab based.

Course Requirements

One semester of college level calculus and linear algebra, as well as some programming experience.

Required Textbooks

Theoretical Neuroscience by Peter Dayan and L. F. Abbott.

Spring 2005 Estimated Schedule

Date
Week No.
Topic
Jan 24
1
Introduction
a) Brief review of Neuroscience
b) The computational capabilities of formal neural networks
The Single Neuron
Jan 31
2

a) Electrical properties of Neurons
b) Voltage dependent channels, The Hodgkin-Huxley equation

Feb 7
3
a) Solutions of the Hodgkin-Huxley equation
b) Simplification of the Hodgkin-Huxley equation
Feb 14
4

a) The Cable equations

b) Stochastic Channels - the master equation.

Feb 21
5
a) Synapses, quantal release
b) AMPA and NMDA receptors
Network of Neurons
Feb 28
6
a) Firing rate models and receptive fields
b) Methods for plotting cortical receptive fields
Mar 7
7
Review and midterm exam
Mar 14
8
Spring Break- Austin
Mar 21
9
a) Recurrent networks
b) Stability analysis
Mar 28
10
a) Abstract models of associative memory
b) Mathematical methods for analyzing abstract networks
Synaptic Plasticity
April 4
11

a) The Hebb rule and PCA
b) Analysis of receptive field formation with the PCA rule

Apr 11
12
a) The BCM theory
b) Supervised learning
Apr 18
13
Biophysical models of synaptic plasticity

What is the neural code?

Apr 25
14
 
May 2
15
 
May 12
FINAL EXAM
  1. Date, time and place - To be announced.

 

Additional suggested references:

2. Gerstner and Kistler, Spiking Neuron models
3. Hertz, Krough, Plamer: Introduction to the theory of neural computation
4. Johnston, Wu: Foundations of Cellular Neurophysiology
5. Koch: Biophysics of Computation
6. Tuckwell: Introduction to theoretical neurobiology

Office hours:

When at Austin, Monday 11-1, ENS 616.

The TA is Jeff Gavornik

Email: gavornik@mail.utexas.edu

Grades:

Homework: 50%, midterm 20%, final 30%

Homework.

There will be 6 assignments; the best 5 assignments will be used for the grade. A delay of 1 day will result in -10 pt. Assignments with a delay of more than 1 day will not be accepted unless the teacher has given special premission.

Most homework problems will be based on Matlab simulations. Each assignment should be accompanied by a written report, explaining the findings and how to run the simulations.

No use of the Neural Network toolbox is allowed, and copying assignments from the web are not allowed. Students can work in groups but must submit separate and distinct codes and programs.


 

There will be some changes this year, but this can still be used

Class 1 (1/24/04)

Handout

Lecture 2

Home work due 2/6/05.

Assignment 1a (30 pt):
program in matlab a preceptron with a perceptron learning rule
and solve the OR, AND and XOR problems. (due before Feb 6).

Do not use NN toolbox

Assignment 1b (30 pt):

Implement a one layer linear and sigmoidal network, fit a 1D, a linear, a sigmoid and a quadratic function, for both networks. (Clarification – this is a network with 1 input and 1 output).

Assignment 1c (30 pt):

Program a 2 layer network in matlab, solve the XOR problem. Fit the curve: x(x-1) between 0 and 1, how many hidden units did you need?

Assignment 1d (10 pt):

If the sigmoind is replaced by a linear function, what type of problems can it solve? Can it solve the XOR problem. (explain in writing).


 

Class 2 (1/31/05)

Lecture 3

HH original paper

Homework for 1/13

Assignment 2: (due Feb 13’th)
Program in matlab a Hodgkin-Huxley neuron with parameters from
DA- page 172. What happens if the Potassium conductance is set to 0?
Explore different input currents for different durations.
Is there a threshold voltage at which an AP is induced.
Program a Connor-Stevens model, DA- page 196, compare to the HH model. What is the difference between a type I and a type II response?

It is best not to use an ODE solver.
Here it will be sufficient to use a first order method such as the forward Euler method

Possible texts for numerical ODE solutions:
Appendix A of Chapter 5 in the DA book
Chapter 14 in the book Methods in Neuronal modeling by Koch and Segev, second edition. Chapter written by Mascagni and Sherman)

Remember - first homework due 1/6

 

 

Class 3 (2/7/05)

HH- dimensionality reduction and phase plane analysis

The cable equations

 

 

Class 4 (2/14/04)

Cable equations - continued (see class 3)

Stochastic ion channels

HW-3 (due Feb 28):
a. implement a 2 state voltage dependent stochastic channel, average over many and compare to the analytic solution.
Ass
ume a voltage step of 10mV, alpha=0.04*V, beta=0.2

b. Implement a stochastic and deterministic potassium channel – average over many, compare.

Note: for b use potassium channel alpha and beta, eq 5.22 on page 171 of D&A. Use 1,10 and 100 channels.


 

 

Class 5 (2/17/04)

Synaptic transmission

Receptive fields

 

 

 

 

Class 6 (2/28/05)

Receptive fields and reverse correlation

 

Class 7 -midterm

 

Spring Break

 

Class 8 - (3/21/05) - reverse correlation and simple networks

 

Homework 4 due March 28.

Download the file below. It includes a sequence of random 'white noise' inputs and the corresponding outputs (res). Using reverse correlations induce the spatio-temporal kernal. Is it seperable? If it is can you guess an exact form for the spatial and temporal kernals?

Homework 4 HW4.mat file

Extra credit: (50%) Program a complex cell using an energy model with shifted Gabor filters. Try to use reverse correlation to find the spatio-temporal kernal of this neuron. Explain in detail why you get these results. Here the writeup counts at least as much as the program.

 

 

Class 9 (3/28/05)

1) Review of networks from previous week.

2) Abstract associative memory networks - update in class next week.

 

Download Excitatory Inhibitory network

 

Class 10 (4/4/05)

Plasticity I

Download book chapter

 

Homework 5: (due 4/18)

5a) Implement a simple Hebb neuron with random 2D input, tilted at an angle, of 30 degrees, with variances 1 and 3 and mean 0. Show the synaptic weight evolution. (200 patterns at least, small learning rate)
5b) Calculate the correlation matrix of the input data. Find the eigen-values, eigen-vectors of this matrix. Compare to 5a.
5c) Repeat 5a for an Oja neuron, compare to 5b.

 


Class 11 (4/11/05)

Plasticity II

Download Book Cahapters I-III (BCM)

 

Class 12 (4/18/05)

The biophysical basis of synaptic plasticity (either this week or next).

 

Class 13 (4/25/05)

what is the neural code?

 

Below this line, last years course

---------------------------------------------------------------------------------------------------------------

Class 7 (3/2/04)

Special lecture david Eagleman

 

Class 8 (3/10/04)

Lecture 8

Class 12 (4/6/04)

Download chapter and start reading before the next class !

Download book chapter

Lecture 12

 

Class 13 (4/13/04)

Book chapters 1 and 2

Lecture 13

 

Class 14 (4/20/04)

The biophysical basis of synaptic plasticity