Introduction I recently read Ed Thorpe’s Beat the Dealer, a book about how Thorpe, a mathematician, found a way to gain an edge in blackjack. In the book, Thorpe uses computer simulations to calculate the best blackjack strategy as well as card-counting strategies. Since I took a reinforcement learning class last quarter, I wanted to apply one of the most common algorithms, Q-learning, to to find the best strategy for blackjack....

Faster than a Supercomputer? In the 1980s, American physicist Richard Feynman proposed the idea of quantum computers to model complex quantum systems. In October 2019, around 40 years later, Google AI and NASA scientists unveiled a quantum computer which ran an experiment in a few minutes that would take the fastest supercomputer 10,000 years. The quantum computer sped up the computation by a factor of 1 billion! This was one of the first major successes in the nascent field of quantum computing....

Introduction In this blog post, I will implement a few simple time series models of a stock price over time. I will also see how they do if we trade using them. We will look at moving averages (MA) and exponential moving averages (EMA). Data First, we need to download the price data. For this article, we will use SPY historical open price data. We can download this from Yahoo Finance....

Introduction This blog post will discuss the delivery options for someone who is short US Treasury (UST) futures contracts. During the last month of trading, the short “delivers” the USTs specified in the futures contract to the long. The short has various options when they make delivery of the treasuries. Understanding these options is interesting and important for anyone who trades UST futures and the UST basis. UST futures are some of the most liquid financial contracts in the world....

Why Exchange Clocks Matter In high frequency trading (HFT), time is literally money. An edge of a few microseconds could translate to millions in profits. The most popular markets for cash products (equity, bonds, etc.) are in New York (NYSE, Nasdaq), while the most popular futures and options market is in Chicago (CME). Since cash and futures influence each other, getting data between New York and Chicago as fast as possible is important....

The Question I, like many others, started learning to play piano when I was around 8 years old. I took lessons, learned songs, and gained an appreciation for the instrument. I have been playing (with some breaks) until today. Although I have been playing for a while, it wasn’t until taking my first music theory class in college that I started thinking deeply about why music is constructed in the way it is....

Introduction I spent the summer of 2019 as a physics research intern at the Stanford University Solar Lab. I was very fortunate to have a wonderful advisor and had a great summer overall. I created machine learning models to characterize time series data for solar flare prediction. In this article, I will first provide some physics background about solar flares, then dive into my research. For a more in-depth analysis, check out the source code and my poster....

Recently, I wondered if I could create a random number generator using the digits of pi. Disclaimer: this article’s purpose is not to create a computationally efficient random number generator; it is just a fun proof of concept. In order to create a random number generator with pi, we must first verify that the digits of pi are randomly distributed. This can be accomplished in a few lines of python code....

Introduction This project done for my CS221 class aims to classify classical music by musical era (Baroque, Classical, Romantic, Modern) with composers as a proxy. Using audio processing techniques, such as Short-time Fourier Transform, we extracted features such as the spectrogram and chromagram of the audio data from two datasets, Free Music Archive and MAESTRO. We used two ensemble classifiers, AdaBoost and Random Forest, and found that although Adaboost performed marginally better than Random Forest, the latter made more generalizable predictions....

Introduction I recently became interested in neural networks and sought interesting applications of what they could do. Neural networks are based on how the human brain works; the networks are made up of many nodes that take inputs and predict outputs. Over time, with more data, the networks improve by correcting for error, known as backpropagation. Neural networks become especially useful when there are many “layers” between the input and output that allow for more fine-tuned fitting of data....