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Birthday Paradox

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We all have encountered coincidences of sort in our lives. For example, it happens that we keep on thinking about a particular person and suddenly we get a phone call or email or even a visit from that person. Similarly, we promise to meet someone at a particular time and venue but out of no where something emergency turns up and have to cancel the previously agreed meeting. A list of such coincidences can get very long. Mathematics also has a term for such coincidences and it is called Probability. There are so many things in Probability Theory that surprises us. And, one such is Birthday paradox.

In Probability Theory, ‘Birthday Paradox’ refers, that in a group containing certain randomly chosen people, there is a finite probability for some two people to have exactly the same birthday. For a group with 23 people, this probability is around 50%. This increases exponentially as the number people in the group increases. With as many as 80 people, the probability gets around 100%. This is of course, based on the idea that people are randomly chosen and each day is equally likely to become a birthday for someone.

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Birthday paradox holds an important position in computer security also. It can be used to attack the hash functions. For example, let us say f is a hash function such as f(x) = y. With hash functions, it should be impossible to guess ‘x’ given ‘y’. In other words they are one way. Another characteristic is that it should be very difficult to find two inputs that yield same output i.e. it should be hard to find x1 and x2 such that f(x1) = y and f(x2) = y. This property is called collision resistance. But using birthday paradox it becomes relatively easier to find such collisions.

Today 16 May is my birthday. And, in facebook I have around 275 friends. Interesting thing is that I do not have a single friend whose birthday coincides with mine. So either some of them have entered incorrect birth date or hidden their birth date from display or for some reason facebook is not notifying me of this. Otherwise, based on birthday paradox I should have at least one friend with birthday today. Perhaps if I include the ‘near-miss effect’ then we can get some coincidences. For example, number of people with birthday separated by certain days. Such latitude will increase the probability of coincidence. But originally birthday paradox theory does not include this near miss effect.


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May 16, 2010 at 1:13 pm

I just faced one reality of my life

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There are times when we know that we have learned everything and we have done everything. But the reality is actually something different. The truth is strikingly the opposite of what we have been thinking. It is just a matter of time that we come face to face with it and feel as if this truth has slapped us right in our face. Today, I happen to experience something similar.

Throughout my education I thought I had practical experience or say knowledge of a crucial topic of my area. I thought if I ever have to implement it professionally I would be able to do so just like that. And earlier today, completely forgetting that I was already introduced to similar methods, I was searching of ways to implement it. But now suddenly I happen to come to know about it and that I have already learned in the past. I have come to understand that I learned it theoretically but I never did it in practical. I realize that I was putting myself into an illusion of knowing everything about it. This is the result of too much theoretical learning and little practical. I think I do not want to reveal what that crucial topic is, but I will tell that it is a very important aspect of my education and my master’s degree.

Oh, I just said something that certainly sounds strange for anyone from my area and with background similar to mine. The term “too much theoretical learning and little practical” may sound awkward and hard to convince yourself. But for many people this, I believe, is true. Like I said, it is just a matter of time when you come to know this reality.

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February 17, 2009 at 9:22 pm

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Copenhegan Event

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Copenhegan is a very beautiful city and this was a nice opportunity for me to visit the city. The event was actually a conference organized by DTU (Technical University of Denmark) and was called Nordic Security Days 2008. It was 13th Nordic Workshop on Secure IT Systems held on October 8th-10th, 2008. You can go to offcial website by clicking here. Besides the conference, we manage sometime to roam around the city and visit some of the most popular tourist spots, including the lovely Mermaid.

Each day of conference was followed by expensive and lavish dinner. The best one was of course the conference dinner on October 9th, 2008.

Some of the pictures from the entire event are posted below.

Written by prajwalan

October 28, 2008 at 3:50 pm

Writing article on programming is more tedious than programming

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I have been programming for many years now. Initially as a rookie enthusiastic, then as software engineer, and now also as a freelancer. All these days, I have found immense help from several online articles, code samples and technical forums. I had also thought for many times about writing my own articles and tutorials. But, that always remained just in the thought. However, with the launch of Developers’s Point, my technical blog, I have been writing technical articles in form of blog posts. Some of the articles/posts are just collection or abridged version of other’s work. In those cases, I have given them credit.

Well, yes, programming is a little bit difficult thing. You have to be sure of many things. It is not just writing codes. When you are programming, you are actually implementing a design, you are building a system that can and will affect many things in surrounding. So, programming is not just merely writing codes and debugging them. But, now I have understood that writing article on any particular programming topic or making a tutorial is even a harder and tedious thing. Today, I was writing an article on COM programming for Developer’s Point and it took me about 4 hours to complete my tutorial. Yesterday, I tried that code to make sure it works and it had taken around 1/2 hour for me to do that. But just see, it took 1/2 hour for programming, while nearly 4 hours to write article on it. Writing article is definitely more tedious than actual programming.

All these years, I have been only enjoying the articles written by others. I was not realizing how tedious it would have been to write article as clearly and as in depth as they were. However, now, I am also writing some of the articles and finally, I also have been able to help other programmers like myself. When I see the hits increasing day by day and the encouraging comments that I get, I find a great self satisfaction. Its even better experience than earning money by writing codes.

Knowledge is for sharing.

Written by prajwalan

July 19, 2008 at 7:52 pm

Berg… You will always remain in my memory

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August 6, around 8 PM (Norwegian Time), I entered Room no. 167, building ‘G’ in the street called Dybdahls Vei 4. The place is popularly known as Berg. Not just that moment, but that entire week was an important turning point in my life. The long flight Kathmandu-New Delhi-Amsterdam-Trondheim was not only my very first flight, but also a wish to fly in a jet plane, becoming true. Yes, I am from a very struggling family and I had never imagined I would fly in any international flights. But things changed, I managed to earn the prestigeous Erasmus Mundus scholarship.

As I write this post, I am still in Norway. But, I had to leave Berg and come to another place called Moholt. Thats where I am right now. My stay in Berg was one of the most memorable things that has happened to me. When I first entered my room, I hurriedly opened my suitcase and was eager to fill the warddrobe closet and other places like reading desk. I was tired and I went to sleep early, around 11 PM. There was still sunlight outside.

First few days, I felt like missing my home in Kathmandu. But later, that room started to become my new home. I went on a trip to Italy and France (only Paris) during the new year’s day of 2008. While the trip was amazing and a wonderful experience in itself, I started to miss my home. No no, the not the one in Kathmandu, but my room in Berg.

Not just living alone but cooking my own food was also new to me. Hence, Berg taught me many things, most importantly, independent living.

Now I have to leave this home and find a new one. I hope will be able to find a home in my new room in Moholt also. Accoding to the rules, I have to clean the place and make it look as exactly as it was when it was handed over to me. Yesterday, I brought all my stuff, but the final cleaning was yet to be done. So, today morning I went back to the room and cleaned every corners of it. Come Monday I will hand over the key back to its owners.

I have some photos for the memory. I would like to share these with you.

 Busy in my work
Busy with my work

My room
My room

A view though my window
A view though my window

My kitchen ( and also the common room )
My kitchen ( and also the common room )

Frying potatoes and brocolli
Frying potatoes and brocolli

Sunset as seen from my kitchen\'s window
Sunset as seen from my kitchen\’s window

Cleaning the window panes
Today, cleaning the window panes

A last look at my room, as bid it goodbye
After the cleaning is done, a last look at my room, as bid it goodbye

Bye bye my sweet room
Door closed and locked now. Bye bye my sweet room

Written by prajwalan

June 28, 2008 at 12:09 pm

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Lousy Sunday

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Another lousy sunday is about to be over. Again that horrifying monday will come tomorrow and life will again take a fast and tiring run. I just love morning sleep, especially when its weekend. Both, yesterday and today, I woke up very late. Someone said it right, a working man gets afraid of only one thing and that is “monday”, not ghost or evil spirits or anything else. I should however consider myself lucky to be able to get really a nice job here. The work is research oriented but I am enjoying what I am doing.

Developer’s point is also making me busy. I started this technical blog as an experiment. It seems that this experiment is going well. I have at least 30 to 40 hits everyday. But I really want to extend this idea to next level. I want to create something that is useful to many developers like me. This blog is just a starting. Let’s see how it manifests itself. But on weekdays, I am so much busy that I cannot post anything either on the technical blog or in this personal one. It is just during the weekends that I get to post anything.

Today I watched a movie called “13 game sayawng“. Its a Thai movie and is really weird kind. The character in the movie “Pusit” is having the worst day of his life. He just lost his job and is in serious debt. That is all about to change when he receives a mysterious phone call with a tempting offer. If he could complete 13 tasks, he will win 100 million Baht. Pusit agrees and the game begins. And then a very weird movie begins too. However, the movie was a nice time-pass. You may also watch it, so I have provided a hyperlink above.

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June 15, 2008 at 5:18 pm

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Living life like Mr. Bean

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Mr. Bean is a character developed by Rowan Atkinson while he was at Oxford University. He describes Mr. Bean as “a child in a grown man’s body”. While going through everyday tasks, he runs into some sort of trouble and he solves it in a very comic style. There were altogether of 14 episodes. Mr. Bean is a slow-witted, sometimes ingenious, selfish and generally likable buffoon who brings various unusual schemes and connivances to everyday tasks. He lives alone in his small flat in Highbury, North London, and is almost always seen in his trademark tweed jacket and skinny red tie. Mr. Bean rarely speaks, and when he does it is generally only a few mumbled words.
Mr. Bean

Teddy is Mr. Bean’s teddy bear, generally regarded as Mr. Bean’s best friend. The bear is a dark brown, knitted oddity with button eyes and sausage-shaped limbs, invariably ending up broken in half or in various other states of destruction and disfiguration. Although inanimate, Bean occasionally pretends Teddy is alive.
Mr. Bean and Teddy

Mr. Bean’s car, a late 1970s MK IV British Leyland Mini 1000, developed a character of sorts. The Mini was central to several antics, such as Mr. Bean getting dressed in it while driving or steering it while sitting in an armchair strapped to the roof. It also had a number of innovative security measures; Mr. Bean fitted the door with a bolt-latch and padlock, rather than use the lock fitted on the car, and he always removed the steering wheel instead of the key, which formed a running joke in several episodes, at one point deterring a car thief.

Mr. Bean's Mini

The first episode won the prestigious Golden Rose, as well as two other major prizes at the 1991 Rose d’Or Light Entertainment Festival in Montreux. In the UK, the episode “The Curse of Mr. Bean” was nominated for a number of BAFTA awards; “Best Light Entertainment Programme” in 1991, “Best Comedy” (Programme or Series) in 1992, and Rowan Atkinson was nominated three times for “Best Light Entertainment Performance” in 1991, 1992 and 1994. “Mr. Bean” also won the Norwegian comedy award “Tidleg Sædavgang”.

Almost all the episodes and clips from these episodes are available on YouTube. So, you can also enjoy the hilarious Mr. Bean. If you ask me, he is my favourite comedian. He makes me laugh with even a very simple comic behaviour, that also without speaking a single word. I have put some of the links below.

Mr. Bean goes to the swimming pool:

Mr. Bean in toilet:

Mr. Bean meets the Queen:

And there are many others, so why don’t you also just visit YouTube and enjoy Mr. Bean. And also maybe live life like Mr. Bean 😉

Source for description of Mr. Bean: Wikipedia

Written by prajwalan

June 8, 2008 at 11:01 am