Download CISC 3250: Systems Neuroscience Homework 5 due April 27 or

CISC 3250: Systems Neuroscience
Homework 5
due April 27 or April 30 – your choice!
1. We are given two model neurons receiving feedforward input and memory input, as well as providing
lateral input to each other. Each neuron’s firing output rout is determined by computing the weighted
0 ℎ < 1.5
sum ℎ = ∑
and using a step function activation function
(ℎ) =
.
1 ℎ ≥ 1.5
We assume the weights on the memory and rfeedforward inputs to both neurons are 1:
wmem=1, wfwd=1
For this homework, we will explore the effects of different lateral weights.
Keep in mind wBA is the weight from A to B, and wAB is the weight from B to A.
i) Given wAB=0 and wBA=0, and given the following memory and feedforward inputs, compute the
outputs for neurons A and B over time:
Time
1
2
3
4
5
6
feedforward
r
0
1
0
0
0
0
memory 0
1
1
1
0
0
rAout
0
rBout
0
ii) Given wAB=4 and wBA=4, and given the following memory and feedforward inputs, compute the
outputs for neurons A and B over time:
Time
1
2
3
4
5
feedforward
r
1
0
0
0
0
memory 1
1
1
0
0
rAout
0
rBout
0
iii) Given wAB=4 and wBA=-4, and given the following memory and feedforward inputs, compute the
outputs for neurons A and B over time:
Time
1
2
3
4
5
6
feedforward
r
1
0
0
0
0
0
memory 1
1
1
1
0
0
rAout
0
rBout
0
iv) Which of the above weight combinations from i, ii, and iii – if any – is an example of Memory
Activity?
v) Which of the above weight combinations from i, ii, and iii – if any – is an example of Growing Activity?
2. Computing neural dynamics by hand takes a while – though our neurons are performing these
computations tens to hundreds of times per second. We can, instead, use a program I have written for
Scilab to compute behaviors of many inter-connected neurons across tens of time steps. You will not be
asked to run this code (called pfcSim) for the homework, though you are welcome to experiment with
the program. For the assignment, you will be asked to analyze some of the code’s outputs.
Consider the firing patterns over time for different sets of 10 neurons shown here.
a) Indicate whether each is a memory activity, a decaying activity, or a growing activity. For reference,
these three activities correspond to a balance of excitatory and inhibitory connections, predominant
inhibitory connections, and predominant excitatory connections, respectively.
b) Indicate at what time point the feedforward and memory input begin (they will always begin
simultaneously in these examples), at what time point the feedforward input ends (switches back from
1 to 0), and at what time point the memory inputs ends (switches back from 1 to 0). If this is not
possible for a given activity, state it is not possible to tell.
i:
ii:
iii:
The program I have written, called pfcSim.sci, is simulating neurons in a particular region of cortex.
Which region of cortex does “PFC” stand for?
3. Reflecting the binding hypothesis/binding problem, list the set of objects (e.g., “shiny red car,”
“yellow submarine”) present in the scene producing the following spiking patterns. Each row reflects the
spiking of a neuron encoding the feature named at the beginning of the row. In this assignment, spikes
are considered to be synchronous if they occur within 1 ms of one another.
a:
b:
c Let us say I redefine synchrony as spikes occurring within 20 ms of one another. Will this definition of
synchrony change the interpretation of the spiking patterns above?
d Estimate the widest spike synchrony window you can define without changing the interpretation of
the spiking patterns above.
e In class we established we can hold 7 ± 2 things in memory at a time, and it does not matter if these
things are simple (let’s say 8 letters in a list) or complicated (let’s say 8 cubist paintings). We can use the
binding-hypothesis representation to reason why we can hold just as many complicated pictures in our
memory as we can hold simple pictures. Explain why adding more objects to memory (to be encoded in
a limited time) is a problem for short term memory BUT adding more neurons encoding further features
about each object (adding more rows describing features of objects) does not pose a similar difficulty for
this representation.