### A Map of Mathematical Structures

In this post on the last day of the year, I thought I will share a map of mathematical structures that are useful for thinking about knowledge representation and reasoning (KRR) issues in Artificial Intelligence and Machine Learning. It is built on top of the diagram shown in Max Tegmark’s paper Is “the theory of … More A Map of Mathematical Structures

### A Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption

A few of us have been working with homomorphic encryption for a number of years now, but we never found a paper / book that covers all the foundational mathematical material in one place. So we decided to write one — well my postdoc Kelvin Yang Li decided to write one and Mike Purcell and I assisted … More A Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption

### Notes on Cyclotomic Polynomials and Their Galois Groups

Cyclotomic polynomials are widely used in the construction of lattice cryptography and homomorphic encryption schemes based on the Ring Learning With Error problem. In this short note, Kelvin Li and I attempt a self-contained introduction to the cyclotomic polynomials and the Galois groups of cyclotomic extensions.

### What Kind of a Data Scientist Are You?

Data Scientists, because of the versatility and range of their skills, can suffer from the paradox of choice when it comes to choosing a career. According to Barry Schwartz, a strategy for good decision-making when there is an abundance of choices will involve these steps, executed in a way that takes careful consideration of all … More What Kind of a Data Scientist Are You?

### Useful Technical Tutorials on Fully Homomorphic Encryption

I have gone through quite a few articles over the last 12 months in my attempt to get a proper understanding of fully homomorphic encryption (FHE) schemes. The process was somewhat frustrating because most of the articles are either too basic, giving just very high-level intuitions, or too deep, assuming too much background on the … More Useful Technical Tutorials on Fully Homomorphic Encryption

### A Note on Problem Solving for Young Researchers

Many beginning researchers find it hard to cope with the sheer amount of reading they have to do to come up to speed in a certain technical field, and the issue is often compounded by the “lacking the prerequisites to the read the prerequisites” problem due to inadequate mathematical training at the undergraduate level. Here’s … More A Note on Problem Solving for Young Researchers

### The Learn-R Algorithm

Identify a problem that would benefit from using R Read An Introduction to R by Venables, Smith, and the R Core Team Work on solving the identified problem using R Get access to resources with lots of R code templates for solving different problems (e.g. Handbook of Statistical Analysis using R by Everitt and Hothorn and Data … More The Learn-R Algorithm