Imagine you are playing a game of Russian Roulette. This game is played, of course, with a revolver: At the start of the round, the bullets are loaded in a random order with unknown distribution, and the cylinder is cycled. The players then take turns firing the revolver. Now, a simple riddle. Assume that youContinue reading “Markovian Russian Roulette”
Category Archives: programming
Probability Theory with Linear Algebra
This post was inspired by a MathOverflow problem: Coin flipping and a recurrence relation. Let’s start by taking a look at an interesting problem from probability theory. We have 6 biased coins, each with 2 sides: heads and tails. The probability of a coin landing on heads is given as . Assume that initially, weContinue reading “Probability Theory with Linear Algebra”
Balancing Chemical Equations with Linear Algebra
This post is inspired by a Kattis problem: Stoichiometry. Let’s face it. Every one of us who has learnt chemistry would’ve come across a problem like this before: The task we’re given is to add coefficients to each chemical in order to balance the equation. This process is known as stoichiometry. It’s pretty straightforward toContinue reading “Balancing Chemical Equations with Linear Algebra”
Neural ODEs
Neural Ordinary Differential Equations (Neural ODEs) are a new and elegant type of mathematical model designed for machine learning. This model type was proposed in a 2018 paper and has caught noticeable attention ever since. The idea was mainly to unify two powerful modelling tools: Ordinary Differential Equations (ODEs) & Machine Learning. This post willContinue reading “Neural ODEs”
Hashed Potatoes 