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I use this blog to post some interesting facts and experiences from my forays into science. They may include anything ranging from  interesting results of my homemade experiments or important (or unimportant) discoveries made in interesting ways.

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Probability and it's probability!

This post seeks to find a free meeting room in my office floor. The shores of Dirac Sea has an interesting puzzle about probabilities which also inspired the results of my findings. Let us say that someone gives you a lopsided bet. Say that with probability \(r\) one gets heads, and with probability \(1 - r\) one gets tails, and you have to pick heads or tails. You only know the outcome of the first event. Let's say after the first toss it came out heads. What is the probability that \(r > 1/2\)? The question seems redundant, the outcome of a bet is determined by another event's probability, basically what we are dealing with is - the probability, of a probability ! One day when going to one of the meeting rooms in my office floor for our daily meeting, none of the meeting rooms were vacant, since this had happened a number of times before as well I thought how would I know if any of the meeting rooms is empty or not. It immediately made me wonder how I could calcul...
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The noise inside your head

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Have you ever felt that your head was full and you couldn't think more? To my surprise, that was not just a metaphor, it was quite literally true! For an ever-growing, learning brain, and to keep in-taking information, there is a big price humans have to pay! Not delving into the biology of our brain, I'll try explaining things in a computer scientist friendly way; every-time our brain intakes new information/data, we make stronger synapses (connections) between nerve cells. The strength of these synapses determines how easily we can retrieve information from our brain, and consequently, some synapses become stronger/larger when we repeatedly intake the same information (thus when we want to memorize something, we find revision helpful for later retrieval.) In a single waking day, synapses continuously strengthen/enlarge as we absorb all kinds of experiences, but this process can't happen indefinitely as synapses reach a saturation point - hence 'our head becomes...
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Optimal server estimate with Markov chains

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I was learning about Markov chains while reading about Hidden Markov Models (HMMs), they are used in understanding and decoding the meaning behind speech. Working on system design and architecture concepts, I saw an analogy of this concept, for using them for finding an optimal number of servers for your micro-service. This post has been long overdue though, since July 16 to be precise, the day ' Amazon Prime-Day ' took place this year ; the post is inspired by that busy day for servers, where multiple customer requests hop from one server to another, sporadically sky-rocketing the read/write load on the them. For lucidity and ease of understanding, consider that there are only 5 categories and data for each category is in a separate server, and each server can serve \(100k\) customers. The most important problem for Amazon is optimizing the number of servers for each category. Let's say that through deep-learning algorithms and yada-yada we can predict the total numbe...
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