Computing and the Brain
Biological Neural Networks Tutorial 2
Neural Coding – Answers to Questions
Question 1: Suppose we have three classes of neurons that respond to geometric
objects, colours and direction of movement, respectively. Six neurons, two from each
class, are firing action potentials at the same, regular rate to indicate the visual
perception of a green circle moving to the left and a red square moving to the right i.e.
one neuron is responding to the circle, another to the square, one to green, another to
red, one to movement to the left, another to movement to the right. With the aid of a
diagram, indicate how the precise timing of the spikes from each of the neurons can
be arranged so that the two objects can be distinguished from firing of these neurons.
Answer: The individual spikes in the spike trains of the neurons responding to the
circle, green and movement to the left should be precisely aligned in time; the spikes
of the other three neurons should also be aligned in time, but out of phase with the
first three neurons. This is an example of using synchronicity to solve the binding
problem of which features in the environment that neurons are responding to actually
come from the same physical object (this is known as temporal binding).
Question 2: Certain neurons in the hippocampus of the rat are known as place cells
because they are most active when the rat is in a certain location in the environment.
Typically, a place cell fires action potentials at its maximal rate for a particular
location, with the rate decreasing in proportion to the rat’s distance from that location.
Draw appropriate firing rate curves for place cells covering a one-dimensional line
and explain how the vector of firing rates from these cells encodes the exact location
of the rat at any time.
Answer: The diagram should show a number of bell-shaped curves that overlap to
some extent along the length of the one-dimensional line. If the rat is in a particular
place, two or three place cells should have positive firing rates, as dictated by the
curves. The vector of these rates specifies the exact position, even though one place
cell alone will fire at the same rate for two different positions of the rat ie either side
of the bell-shaped firing rate curve.
Question 3: Suppose a neuron can fire action potentials at a maximum rate of 100 per
second. The information contained in the pattern of action potentials produced by this
neuron must be assessed within 50msecs, over which time at most 5 action potentials
can be emitted. If the information is contained in the average firing rate of the neuron
over this time window, how many different states of the neuron can be distinguished?
Answer: 6 different states only, corresponding to 0, 1, 2, 3, 4 or 5 action potentials
being fired. This corresponds to firing rates of 0, 20, 40, 60, 80 and 100Hz.
How many different states can be distinguished if the timing of each action potential
can be determined to an accuracy of 10msecs, so that a 50msec period can be
described by a binary vector of length 5 (an entry of 1 corresponding to an action
potential occurring in a particular 10msec time bin)?
Answer: Now 2 to the power 5 (ie 32) states can be distinguished, corresponding to
all possible binary vectors of length 5.
Dr Bruce Graham ( b.graham@cs.stir.ac.uk )
Department of Computing Science and Mathematics
University of Stirling, Stirling FK9 4LA SCOTLAND