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The University of Memphis
Computer Science
COMP 4/6601 MODELS OF COMPUTATION
HOMEWORK 7
DUE: November 20, 4:00pm
1. Determine the structure Of phase-space of the two neuron net with
identity threshold activation functions and weight matrix
|-1 2 |
| 2 0 |
[You need to partition the state space into three regions F (fixed
points/memories), P (orbits of ALL initial conditions that result in a
periodic orbit of period >), and Q (all other initial conditions that
do not settle anywhere).]
2. Find the H-distance between poligos X={catagggagctg, cagctccctatg}
and Y={tattaccggcgt, acgccggtaata}.
[The H-distance |X,Y| between two poligos X={x,x'} and Y={y,y'} is the
minimum of all Hamming distances between overlaps of x and (left or
right) shifts of y, or their complements x',y'. For example,
|cgtac,gtacg|=0
because they match perfectly as complements (at shift=0). Don't forget that
WC -complemntation requires reversing and exchanging a't's and c-g's.]
3. Find a 12-mer encoding for as large an instance of HamP as you can
subject to the condition that the H-distance between any two vertices
and/or edges is at least 7.
BONUS: If you can increase 7 to a larger lower bound, you get extra credit.
4. Find the solution strands for the instance in Problem 3.
5. Find a set of 20-mer strands that folds into the following three shapes
(uniformly in number) under appropriate hybridization conditions:
```````````___``````````````````````````````````````````````````````````````
``````````/```\`````````````````````-----```````````````````````````````````
`````````/`````\```````````````````/`````\``````````````````````````````````
```------```````------```````------```````------````````-------------------`
```------```````------```````------```````------````````-------------------`
`````````\`````/```````````````````\`````/``````````````````````````````````
````````` \```/`````````````````````-----```````````````````````````````````
```````````---``````````````````````````````````````````````````````````````
[The number of strands is your choice. A multiple of 3 over 15 would be nice.]
EndOfFile
Computer Science
COMP 4/6601 MODELS OF COMPUTATION
HOMEWORK 7
DUE: November 20, 4:00pm
1. Determine the structure Of phase-space of the two neuron net with
identity threshold activation functions and weight matrix
|-1 2 |
| 2 0 |
[You need to partition the state space into three regions F (fixed
points/memories), P (orbits of ALL initial conditions that result in a
periodic orbit of period >), and Q (all other initial conditions that
do not settle anywhere).]
2. Find the H-distance between poligos X={catagggagctg, cagctccctatg}
and Y={tattaccggcgt, acgccggtaata}.
[The H-distance |X,Y| between two poligos X={x,x'} and Y={y,y'} is the
minimum of all Hamming distances between overlaps of x and (left or
right) shifts of y, or their complements x',y'. For example,
|cgtac,gtacg|=0
because they match perfectly as complements (at shift=0). Don't forget that
WC -complemntation requires reversing and exchanging a't's and c-g's.]
3. Find a 12-mer encoding for as large an instance of HamP as you can
subject to the condition that the H-distance between any two vertices
and/or edges is at least 7.
BONUS: If you can increase 7 to a larger lower bound, you get extra credit.
4. Find the solution strands for the instance in Problem 3.
5. Find a set of 20-mer strands that folds into the following three shapes
(uniformly in number) under appropriate hybridization conditions:
```````````___``````````````````````````````````````````````````````````````
``````````/```\`````````````````````-----```````````````````````````````````
`````````/`````\```````````````````/`````\``````````````````````````````````
```------```````------```````------```````------````````-------------------`
```------```````------```````------```````------````````-------------------`
`````````\`````/```````````````````\`````/``````````````````````````````````
````````` \```/`````````````````````-----```````````````````````````````````
```````````---``````````````````````````````````````````````````````````````
[The number of strands is your choice. A multiple of 3 over 15 would be nice.]
EndOfFile
