Posts

\(x \times y = k\).

Look at that again.

\(x \times y = k\).

This is the main formula behind Uniswap pricing called the Constant Product Formula. It is a formula which has allowed a fully decentralized platform to successfully trade (sometimes with high slippage due to the trade size and subsequent move along the price curve) billions of USD in daily volume in place of a traditional order book.

Sometimes, the simple answer may just be a great one. The formula itself is quite simple: \(k\) is a constant which is set to the swap rate that the pool requires and \(x\) and \(y\) are simply the amounts of each token required to meet that liquidity condition. When we look at this formula it becomes quite obvious that large orders or large quantities of orders removing a large portion of one of the tokens can affect the amount of the other token required to meet \(k\). This affects the ratio and thus the price when swapping between the two assets.

Although the introduction of Uniswap V3 has introduced new features (and complexities) surrounding this simple formula, the Constant Product Formula has remained... constant.

DNA sequence classification is a challenging problem for machine learning, and also a very relevant one for determining how DNA relates with various conditions such as diseases. This post goes through the process of setting up a pipeline to determine optimal hyperparameters in an automated fashion. This is the second part in a three part series.

DNA sequence classification is a challenging problem for machine learning, and also a very relevant one for determining how DNA relates with various conditions such as diseases. This post goes through the process of setting up the data and using kernels to extract features. This is the first part in a 3 part series.

Having a large collection of data is always a wonderful thing because it allows inferences and dependencies to be gleaned. The problem with great amounts of data is the fact that using all of this data can lead to both overfitting and being struck by the curse of dimensionality. In this post I go over a basic approach to dimension reduction and some reasons why it is so important.

Hidden Markov Models are an excellent way to predict the upcoming steps of a Markovian Process, a stochastic process in which future and past states are independent conditional upon the present state, which contains hidden states. The properties of the Hidden Markov Model make it especially useful in time based pattern recognition and reinforcement learning.

Data mining and exploratory data analysis are both key weapons in any data science toolbox. An important component of exploring data is determining dependencies and conditional independence relations so as to better be able to understand the underlying structure of data.

Missing data is a problem which plagues all manner of science and there are a number of ways which missing data can be dealt with. In this post I introduce the general ideas behind missing data, and demonstrate a few methods with which data missingness can be attacked.

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I’ve decided to let myself start with a bit of an open-ended possibility for what my page can contain.