Basics in graph theory

The content here is same as the wikipedia entry at this link. I am just writing this as i can't seem to concentrate by just reading.

Complete graph - all possible pairs of vertices are adjacent or the degree of all vertices is |V|-1.
k-regular graph - every node in a graph with n nodes has the same degree k<= n-1.
Line graph - the line graph of G, denoted as L(G),  is the graph where the edges of G correspond to the nodes of L(G), and  two edges in L(G)  are adjacent if they share a node in G.

The adjacency matrix - The adjacency matrix A(X) of a directed graph X is the integer matrix with roes and columns indexed by the vertices of X,  such that the uv-entry if A(X) is equal to the number arcs FROM u TO v.
The spectrum of graph X is the set of eigen values  of A(X) along with their multiplicities.


Cycles are of two types.
1. Closed walk - sequence of vertices starting and ending at the same vertex. Its implied that the vertices are adjacent  to each other.
2. Simple cycle - closed walk with no repetition of vertices or edges allowed, other than the starting vertex.

Tree - is an undirected graph in which any two vertices are connected by a simple path.
Spanning tree - The spanning tree of a connected undirected graph G is a tree that includes all the vertices and some or all of the edges of G.

Vector spaces defined on a graph - vertex space, edge space, cycle space, cut space.

My Movie playlist

There are some movies that I keep watching over and over. some of them are,
1. Revolver(2005)
2. V for vendetta(2005)
3. MindGame(2004) (Japanese)
4. Pi(1998)
5. Waking Life(2001)
5. My fair Lady(1964)
6. Monty Python and the holy grail(1975)

Have got a new list of movies from my friends. hopefully will update this soon.

Exporting simulink model as a image

in the command window,
>> orient('myModel','portrait'); % can use landscape. based on the model
>> print -dpng -r300 -smyModel filename.png

done.

Debugging the DSO board

Our DSO board arrived. We are using two Atxmegas. One for ADC and USB communication. The other for waveform generation.
Now, for some reason the input at PA1(input to ADC) is giving us problems. The external input is scaled and shifted using opamps and then given to ADC pins. i.e., PORTA. This is so that the pins of the controller are not given voltages outside the absolute voltage specifications (-0.5V to 3.3V).

28 feb -
found out that PA0, 3.3V and ground volt were shorted.
i was "being stupid".
There was no short. Amaldev had to come all the way from his lab to verify that.
One day, he is gonna snap and throw  me in front of a running bus.

Anyways, on burning the final code we had written, the voltages at PA1 and PA2 are getting stuck at 2.1V.
On burning our earlier ADC codes, there is no problem.

Resolved. In a file included by the example project, on which our entire project stands on.

IF

I found this poem while reading inspirational comics on zenpencils.
Then searched for this awesome poem by Rudyard Kipling, titled 'If'
Posting it here.

If you can keep your head when all about you   

    Are losing theirs and blaming it on you,   

If you can trust yourself when all men doubt you,

    But make allowance for their doubting too;   

If you can wait and not be tired by waiting,

    Or being lied about, don’t deal in lies,

Or being hated, don’t give way to hating,

    And yet don’t look too good, nor talk too wise:

If you can dream—and not make dreams your master;   

    If you can think—and not make thoughts your aim;   

If you can meet with Triumph and Disaster

    And treat those two impostors just the same;   

If you can bear to hear the truth you’ve spoken

    Twisted by knaves to make a trap for fools,

Or watch the things you gave your life to, broken,

    And stoop and build ’em up with worn-out tools:

If you can make one heap of all your winnings

    And risk it on one turn of pitch-and-toss,

And lose, and start again at your beginnings

    And never breathe a word about your loss;

If you can force your heart and nerve and sinew

    To serve your turn long after they are gone,   

And so hold on when there is nothing in you

    Except the Will which says to them: ‘Hold on!’

If you can talk with crowds and keep your virtue,   

    Or walk with Kings—nor lose the common touch,

If neither foes nor loving friends can hurt you,

    If all men count with you, but none too much;

If you can fill the unforgiving minute

    With sixty seconds’ worth of distance run,   

Yours is the Earth and everything that’s in it,   

    And—which is more—you’ll be a Man, my son!

Great blog post I came across.

As I was browsing around I found this post shared on Facebook - https://medium.com/life-learning/2a1841f1335d

Really great one. Got me thinking.
I will just put up the headings. Read the entire post at that link.

7 Reasons why you will never do anything amazing with your life

1 :: Because You Have Not Failed Enough

2 :: Because You Care What Others Think About You

3 :: Because You Think You Are Smarter Than You Are

4 :: Because You Don’t Read

5 :: Because You Lack Curiosity

6 :: Because You Don’t Ask Enough Questions

7 :: Because You Can’t Handle The Truth

Read the entire article here.

The orginal article here.

 

 

 

 

 

 

Modelling of systems

Modelling of systems is the first step in doing everything with the system.
If you have modeled a system, then you know exactly how the system is going to behave or not going to behave when it receives specific inputs.
So, if you don't know how the system acts then, there is no way you can use it and make it do whatever you want it to do. Everything system that we can interact with and understand how it is going to react is modeled in our heads. What you do not understand, you cannot model, or can we?!
There are 3 different ways in which systems are modeled.
One is from the laws of nature or white box modelling.
You know the forces acting on the system and you have the laws that these forces follow. Then, you know all you need to know.
Two is, grey box modelling.
Here we know the inner workings of the system partially. Some part we do not know. Its also called Semi-deterministic model.
Three is black box modelling.
Here, we don't know what is inside the system and its inner workings. The system is like a opaque black box which cannot be opened.  You just have places where you can give your inputs and places where you can see the outputs. From this we need to find out the relation between the inputs and outputs. Plus, the systems we usually encounter are dynamic, which means the way its going to act now depends on what input it was given earlier. i.e., we have to find the relation between the current output and current input, earlier input, earlier outputs.

Its clear to me that I myself am not clear with these things, because I cannot seem to be able to write with much confidence.