Lectures: Tues/Thur 9:00 AM - 10:30 AM Thackeray 527
by Larry Abbott and Peter Dayan.
Additional Useful Texts:
- Nature Neuroscience Computational Supplement
- Bower, J. M. & Beeman, D. (1995) The Book of GENESIS New York
- Johnston, D. & Wuu, S., (1994) Foundations of cellular neurophysiology.
Cambridge MA: MIT Press20
- Kandel, E. R., Schwartz, J. H. & Jessell, T. M. (1991) Principles of Neural
Science. New York: Elsevier.
- Koch, C & Segev, I (1998) Methods in neuronal modeling: From synapses to
networks. Cambridge MA: MIT press (new addition).
- Shephard, G. M. (1990) The synaptic organization of the brain New York:
Oxford University Press. (paper back edition)
- White, E. L. (1989) Cortical Circuits: Synaptic organization of the cerebral
cortex structure, function, and theory. Boston: Birkhauser,
Grading Grades will be based on homework (60%)
and final projects (40%). The final project can be
done individually or in small teams (preferred). This must be a
COMPUTATIONAL project in which you actually do some
computation. You should start thinking about projects early on and get
an OK from me before embarking on them. You will have to make a
written report and perhaps (time permitting) give an oral report.
Some useful links
- Goals and Math review 1-2 class periods
- Neuroelectronics - Chapt 5&6
- Phase-plane methods
- Integrate and fire models
- PHase models and references
- Neural networks - Chapt 7
- Review article on dynamics on neural nets
- Nonlinear behavior of small recurrent neural nets
- Spiking models and phase models
- Derivation of recurrent neural networks
- Feedforward networks
- Hidden layers
- Motor plans
- Recurrent networks
- Linear models and amplification
- Simple cell model - nonlinear effects
- Persistent activity and the Amari model
- Associative networks Click here
for a simulation of an associative network
- Excitatory/Inhibitory networks- the phaseplane revisited. Click here for a planar neural network that
has a limit cycle. Can you find parameters so that there
are two stable limit cycles?
- Synaptic plasticity (Chapt 8)
- Here is an ODE file illustrating
Hebbian learning with two weights -- try it! (Make sure you
read all the comments)
- Review of competition models Try
simulating some of these. For example, here is the reduced
two-dimensional model due to Harris etal. Try changing the
parameter N which is the amount of neurotrophin. For
small values (N=1) there is strong competetion and only one
weight survives; for intermediate values (N=5) there
is still competition but the binocular state is stable as
well. Finally for large (N=10) values, only the binocular state
- Here is a simulation for occular
dominance using 101 units. It is similar to models that we
looked at in class.
- Neural Coding -- Chapter 1
- Visual receptive fields
A space-time separable RF
- Decoding -- Chapter 3
- Discrimination and the receiver operator characteristic
- Population decoding
- Cricket Cercal system
- Motor cortex
- Optimal decoding
- Reverse correlation revisited: spike train decoding
- Homework, do problems 1-3 in Chapter 3 Homework
What is a neuron?
Neurons are specialized cells designed to rapidly communicate signals
over long distances in the body. Like all cells, neurons consist of a
cell membrane which separates the outside world from the cell
A schematic picture of a neuron
Cells can have very complex shapes but over all have the
The soma,axons and often, the dendrites contain
numerous ion channels which act to amplify or supress
incoming signals and help send these out to other cells.
- Soma or cell body which contains all the machinery for keeping
the cell alive
- Dendrites: long processes which act to receive signals
from other neurons and send them to the soma.
- Axons: processes which send signals to other neurons.
The signals in neuron are electrical and are measured as the
difference in potential between the inside and the outside of the
cell. This difference is called the membrane potential .
Under normal conditions it is about -70 mV .
Signals from the outside and from other neurons tend to change the
membrane potential: those that make it more negative are said
the hyperpolarize while those that make it more positive
are said to depolarize the cell.
Once a cell is sufficiently depolarized and the potential crosses a
threshold , ion flows act in a positive feedback to cause the
neuron to fire a action potential . Action potentials are
generally 100 mV above rest. Action potentials cause short term and
long term changes in the cell's ability to fire. In particular, once
a cell has fired there is a period of time, the refractory period
before which the cell cannot easily fire again. This can last up to
several tens of milliseconds.
Once a cell has fired, the action potential travels down the cell's
axon where it terminates on a specialized structure called a
synapse . Synapses release chemicals called transmitters
which depolarize or hyperpolarize the postsynaptic cell's
dendrite or soma.
An experimentalist can record electrical activity from one or more
ways. The two most common methods are
- intracellular recordings
which measure the potential of the cell relative to the
outside. These are able to measure subthreshold responses as well as
action potentials. However, they are mainly done only on the soma and
are difficult to do in an awake behaving animal.
- extracellular recordings are done near a neuron but not
inside the actual cell. They can record action potentials from one or
more nearby cells. They are easier to stably maintain and can be done
in awake animals.