Earlier this month (July, 2019), mathematician Hao Huang posted a proof of the Sensitivity Conjecture, which has troubled mathematicians for 30 years. To people’s surprise, this proof is only 2 page’s long and involves only undergraduate level math. On the Internet, you can find some reports, written for the general public, about the background story and the interpretation of the sensitivity conjecture. Also, several experts, such as Terence Tao, are elaborating on it. Here, writing for students and non-experts, I will summarize the key steps in Hao Huang’s proof, in an attempt to help them quickly grasp the essential.
Using t-Distributed Stochastic Neighbor Embedding (t-SNE) to visualize the two-dimensional unfolding of the sophon
This guide documents one code style of static, class, and abstract methods in Python. Following this style, your code can be run in both Python 2.X and Python 3.X.
Abstract. This post introduces the concept of Nash Equilibrium into Pokémon GO meta-game, with the intention to build a minimalist PvE list. The idea is to build an all-round team for gym battles or for boss raids with few Pokémon. This approach allows the players to concentrate their resources to build a small team of strong Pokémon instead of a large group of mildly strong Pokémon. To demonstrate the usage of the Nash Equilibrium, I use Timeout as the win condition for gym battles and total damage output for boss raids. The resulting minimalist lists are for reference; I provided, at the end of the post, the dataset and the code necessary for the readers to build their own minimalist lists.
Yugioh Duel Links is a digital collectible card game (CCG), which could be played on mobile devices. Like many other CCGs, there is an in-game Ladder system, where players compete with each other to prove themselves as the best duelist in the world. However, many players complain about the mechanism of this Ladder and suggest replacing it with the Elo system. In this post, I can show you, thanks to the cutting-edge research of DeepMind, that the Elo system, or any other systems using averaging, is unavoidably inefficient for Duel links.
Many talk about data science and machine learning with enthusiasm, but few know about one of the most important building components behind them – convex optimization. Indeed, nowadays nearly every data science problem will first be transformed into an optimization problem and then solved by standard methods. Convex optimization, albeit basic, is the most important concept in optimization and the starting point of all understanding. If you are an aspiring data scientist, convex optimization is an unavoidable subject that you had better learn sooner than later.
In this post I will discuss one of the two best papers in ICML 2018 – Delayed Impact of Fair Machine Learning. Contrary to other papers constructing various innovative definitions of fairness, this paper analyzes the delayed impact of fairness policy. It shows that these policies do not necessarily improve the situation of the disadvantaged population: It may hurt them, in some cases, in the long run.
TL;DR: Evolutionary game theory, initially developed for biology, has been successfully applied to other domains such as economics, sociology, and anthropology. This post will use it to explain the various meta of Yugioh Duel Links and predict the nonexistence of the kind of meta which is simultaneously diverse, accessible, and without being Rock–paper–scissors.
Image from Gustavo Santos at DeviantArt