MH 8300 Tutorial Activity 10
PageRank
Question 1. Consider the following webgraph with four websites.
(a) Write down the adjacency matrix A for the webgraph.
0 1
1 0
A=
0 1
0 0
(b) Write down the Markov matrix M for the webgraph.
0 12
1 0
M =
0 1
2
0
Reliable communication over
unreliable channel
Shannons Noisy Channel Coding Theorem
Coding Theory
Channel
Channel
Sender
Channel
Receiver
Cheryl
Mobile Network
Albert
Phone
WiFi Network
Router
You
Disk Drive
You
Noisy Channel
NOISY
Channel
Channel is un
How many points
determine a line?
Coding Theory
A Game
I draw a straight line on the paper
(which I do not tell you).
You are to guess as many points as
possible on the line.
Before guessing, you may request for
some points on the line.
How many points
Can we
communicate reliably over an
unreliable channel?
Coding Theory
You have 1TB of data
You have 1TB of data
replicate
You have 1TB of data
You have 600TB of data
1
2
3
100
101
102
103
200
501
502
503
600
You have 600TB of data
1
1
2
2
3
3
100
100
200
The War of Codemakers & Codebreakers
etin Kaya Ko
[email protected]
Since the time of Caesar or even earlier, people are interested
in secret communications
Communication Line
Caesar
Generals
Enemy
To hide the content of his messages from the enemy, Caesar
MH 8300 Tutorial Activity 1
Modular Arithmetic
Group Members
Name
Marks :
NTU Email ID
/10
Question 0. For the following values of M , fill up the diagrams with numbers and determine
5
(mod M ) and 31
(mod M ).
M =2
M =3
M =6
M = 10
M = 11
M = 13
Question
MH 8300 Tutorial Activity 1
Modular Arithmetic
Group Members
Name
Marks :
NTU Email ID
/10
Question 0. For the following values of M , fill up the diagrams with numbers and determine
5
(mod M ) and 31
(mod M ).
M =2
M =3
M =6
M = 10
M = 11
M = 13
Question
MH 8300 Tutorial Activity 4
Caesar Cipher, Affine Cipher
Group Members
Name
Marks :
NTU Email ID
/10
Question A. Consider a Caesar cipher with the following plaintexts.
jan
feb
mar
apr
may
jun
jul
aug
sep
oct
nov
dec
(i) Randomly pick a key k and a plaint
MH 8300 Tutorial Activity 2
Single Parity Check Code
Hamming Code
Group Members
Name
Marks :
NTU Email ID
/10
Question A1. Consider the following code C.
C = cfw_(x1 , x2 , x3 , x4 , x5 , x6 , x1 + x2 + x3 + x4 + x5 + x6 ) : xi cfw_0, 1.
(i) Determine the
MH 8300 Tutorial Activity 3
Reed-Solomon Codes
Group Members
Name
Marks :
NTU Email ID
/10
Question A. Consider a Reed-Solomon code of length n = 6 and dimension k = 3, defined over the
integers modulo p = 7. We choose the evaluation points : 1 = 1, 2 = 2
MH 8300 Tutorial Activity 3
Reed-Solomon Codes
Group Members
Name
Marks :
NTU Email ID
/10
Question A. Consider a Reed-Solomon code of length n = 6 and dimension k = 3, defined over the
integers modulo p = 7. We choose the evaluation points : 1 = 1, 2 = 2
MH 8300 Tutorial Activity 5
Diffie Hellman Key Exchange
Group Members
Name
Marks :
NTU Email ID
/10
Question 0. Use the square-multiply method to compute
826
(mod 107).
t
A
Question 1. In this tutorial, the following pairs of groups will communicate each
2016S1 PH1012: Physics A
Work, Energy and Power
Dr Ho Shen Yong
Lecturer, School of Physical and Mathematical Sciences
Nanyang Technological University
Weeks 6 and 7
Giancoli 7.1-7.4, 8.1-8.4
"Long-range goals keep you from being frustrated by short-term
2016S1 PH1012: Physics A
Basics and Fluids
Dr Ho Shen Yong
Lecturer, School of Physical and Mathematical Sciences
Nanyang Technological University
Week 1
Giancoli Chap 13.1 13.7
"The true sign of intelligence is not knowledge but imagination."
- Albert Ei
2016S1 PH1012: Physics A
Vectors, Projectile and Circular Motion
Dr Ho Shen Yong
Lecturer, School of Physical and Mathematical Sciences
Nanyang Technological University
Week 4
Giancoli Chap 5.2, 10.1-10.3
"We are what we repeatedly do; excellence, then, i
MH 8300 Tutorial Activity 3
Caesar Cipher, Affine Cipher and Frequency Analysis
Set A
Question 1. (Frequency Analysis of the Caesar Cipher)
Consider the following ciphertext that has been encrypted by a Caesar cipher using the key k.
PDA A KDG DQ HAWUD VP
MH 8300 Tutorial Activity 4
RSA
Set A
The following describes the communication between Alice and Bob via RSA public key encryption. Eve is
eavesdropping on their communication and trying to decrypt the message sent.
Question 1. Bob prepares the RSA proto
MH 8300 Tutorial Activity 6
Mutilated Chessboard Problem
Question 1. Consider the following mutilated chessboard with 5 white squares and 5 black squares.
Figure 1: Mutilated Chessboard
(a) Construct the chessboard graph based on the mutilated chessboard
MH 8300 Tutorial Activity 5
De Bruijn Graphs and Sequence Assembly
Set A
Question 1. Suppose we have a circular sequence of length 14 over the alphabet cfw_A, T, C, G. We obtain
the following 14 fragments of length three,
X = cfw_AAT, ATA, ATT, ATC, ATG,
MH 8300 Tutorial Activity 8
Minimum Spanning Tree
Consider the following undirected edge-weighted graph G on the vertex set V = cfw_A, B, C, D, E, F, G, H, I,
J.
Question 1. Answer the following questions.
(a) Apply Kruskals algorithm to find T , the mini
MH 8300 Tutorial Activity 7
Assignment Problem
Your company is now doing very well and your business clients have increased. Your sales representatives,
Albert (A), Bernard (B) and Cheryl (C) are now joined by Denise (D) to cater to the high demand of you
MH 8300 Tutorial Activity 1
Principles of Error Correction
Set A
Question 1. Let the code C1 = cfw_00000, 11011, 11100, 00111.
Sender sends the codeword 11011 across a channel and the receiver received 11001. The receiver decodes
11001 using Minimum Dista
Algebra: Matrices II - Determinants
Tang Wee Kee
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
(Division of Mathematical Sciences School of Physical and Mathematical
DeterminantsSciences Na
2016S1 PH1012: Physics A
More about forces
Dr Ho Shen Yong
Lecturer, School of Physical and Mathematical Sciences
Nanyang Technological University
Week 5
Giancoli Chap 5.1, 5.6, 14.1
"Sometimes it is not enough that we do our best; we must do what is requ
MH1810 Math 1 Part 1 Algebra
Tang Wee Kee
Nanyang Technological University
(Nanyang Technological University)
Complex Numbers
1 / 66
Imaginary number
Does the quadratic equation x 2 + 1 = 0 have a real root? That is, are
there real numbers x at which x 2
2016S1 PH1012: Physics A
Static Equilibrium
Dr Ho Shen Yong
Lecturer, School of Physical and Mathematical Sciences
Nanyang Technological University
Week 5
Giancoli Chap 12.1-12.3, 12.6
"We are what we repeatedly do; excellence, then, is not an act but a h