Solve your IGNOU Doubts

Question:

b) Describe the Function Approximation in MLP. Also, explain Generalization of MLP.

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Question:

a) Define Kohonen networks with examples.

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Question:

Consider the set of pattern vectors P. Obtain the connectivity matrix (CM) for the patterns in P (four patterns).

$P=\begin{bmatrix} 1 &1 &1 &0 &0 &0 &0 &0 &0 &0 \\0 &0 &0 &0 &0 &0 &0 &1 &1 &1 \\1 &1 &1 &0 &0 &0 &0 &0 &0 &1 \\1 &0 &1 &0 &1 &0 &1 &0 &1 &0 \end{bmatrix}$

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Question:

b) Write the types of Neural Memory Models. Also, give one example of each.

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Question:

a) Define Error Correction Learning with examples.

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Question:

Consider a dataset of six points given in the following table, each of which has two features $f_{1}$ and $f_{2}.$ Assuming the values of the parameters c and m as 2 and the initial cluster centers $V_{1}=(,5,5)$ and $V_{2}=(10,10),$ apply FCm algorithm to find the new cluster center after one iteration.

	$F_{1}$	$F_{2}$
$X_{1}$	3	11
$X_{2}$	3	10

$X_{3}$	8	12
$X_{4}$	10	6
$X_{5}$	13	6
$X_{6}$	13	5

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Question:

Let A and B are two fuzzy sets and $x\epsilon U,if\mu _{A}(x)=0.4$ and $\mu _{B}(x)=0.8$ then find out the following membership values:

i) $\mu _{A\cup B}(X),$ ii) $\mu _{A\cap B}(X),$ iii) $\mu _{\bar{A}\cup \bar{B}}(x),$

iv) $\mu _{\bar{A}\\\cap \bar{B}}(x),$ v) $\mu __{\bar{A}\bar\cup \bar{B}}(X),$ vi) $\mu __{\bar{A}\bar\cap \bar{B}}(X),$

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Question:

b) Apply the “very” hedge on the fuzzy sets defined in Q. 1(b) to get the new modified fuzzy sets. Show the modified fuzzy sets through numeration.

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Question:

a) Construct the α − cut at α = 4.0 for the fuzzy sets defined in Q. 1(b)

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Question:

b) Consider a subset of natural numbers from 1 to 30, as the universe of discourse, U. Define the fuzzy sets “small” and “medium” by enumeration.

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Question:

a) Two sensors based upon their detection levels and gain settings are compared. The following of gain setting and sensor detection levels with a standard item being monitored provides typical membership values to represent the detection levels for each of the sensors.

Gain Setting	Sensor detection levels	Sensor 2 detection levels
0	0	0
20	0.5	0.35
40	0.65	0.5
60	0.85	0.75
80	1	0.90
100	1	1

The universe of discourse is $x= [0,20,40,60,80,100].$ Find the membership function for the two sensors. Also, verify De-morgon’s laws for these membership functions.

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Question:

Use Miller-Rabin test to check whether 75521 is a strong pseuodprime to the base 2.

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Question:

Find the inverse of 13 (mod 51) using extended euclidean algorithm

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Question:

Another version of the columnar transposition cipher is the cipher using a key word. In this cipher, we encrypt as follows: Given a key word, we remove all the duplicate characters in the key word. For example, if the key word is ‘SECRET’, we remove the second ‘E’ and use ‘SECRT’ as the key word. To encrypt, we form a table as follows: In the first row, we write down the key word. In the following rows, we write the plaintext. Suppose we want to encrypt the text ‘ATTACKATDAWN’. We make a table as follows:

S	E	C	R	T
A	T	T	A	C
K	A	T	D	A
W	N	X	X	X

Then we read off the columns in alphabetical order. We first read the column under ‘C’, followed by the columns under ‘E’, ‘R’, ‘S’ and ‘T’. We get the cipher text TTX TAN ADX AKW CAX. To decrypt, we reverse the process. Note that, since we know the length of the keyword, we can find the length of the columns by dividing the length of the message by the length of the keyword. Given the ciphertext ‘HNDWUEOESSRORUTXLARFASUXTINOOGFNEGASTORX’ and the key word ‘LANCE’, find the plaintext.

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Question:

b) Draw the Tanner graph of the code L with parity check matrix $\begin{bmatrix} 1 &0 &0 &0 &1 &0 &0 &1 & 0 &1 \\0 &1 &0 &0 &1 &1 &0 &0 &1 &0 \\0 &0 &1 &0 &0 &1 &1 &0 &0 &1 \\0 &0 &0 &1 &0 &0 &1 &1 & 1 &0 \end{bmatrix}.$

c) Find the convolutional code for the message 11011. The convolutional encoder is given in Fig. 1.

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Question:

Text:"KSTYZKESLNZUV", encrypted with Vigenère cipher with key "RESULT"

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Question:

Text: "CBBGYAEBBFZCFEPXYAEBB", encrypted with affine cipher with key (7,2)

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Question:

Let $f(x)=x^{2}-x-1\in$ $Z_5[x].$ We represent the field $F_2$ by $F_2[x]/(f(x)).$ LEt us write $y=x=(f(x)).$ the table of values is given below:

i	$y^{i}$	Vector	i	$y^{i}$	Vector
0	1	(0,0,0,1)	8	$y^{2}+1$	(0,1,0,1)
1	$y$	(0,0,1,0)	9	$y^{3}+y$	(1,0,1,0
2	$y^{2}$	(0,0,1,0)	10	$y^{3}+y+1$	(0,1,1,1)
3	$y^{3}$	(1,0,0,0)	11	$y^{3}+y^{2}+y$	(1,1,1,0)
4	$y+1$	(1,0,0,0)	12	$y^{3}+y^{2}+y+1$	(1,1,1,1)
5	$y^{2}+y$	(0,1,1,0)	13	$y^{3}+y^{2}+1$	(1,1,0,1)
6	$y^{3}+y^{2}$	(1,1,0,0)	14	$y^{3}+1$	(1,0,0,1)
7	$y^{3}+y+1$	(1,0,1,1)

i) Prepare logarithm and antilogarithm tables as given in page 23 of block 1.

ii) Compute $\frac{(y^{4}+y^{2})+(y^{3}+y+1)}{(1+y^{2}+y^{4})(1+y^{3})}\: and\: \frac{y^{2}(y^{2}+y+1)}{(y^{3}+y^{2})(1+y^{5})}$ using the logarithm and antilogarithm tables.