Iago's Blog

How to install Void Linux with LVM over LUKS for full-disk encryption, boot directly from kernel EFI Stub, hibernation, and per-user encryption.

A tutorial on how to wipe, encrypt, auto mount, and decrypt an external usd drive on linux.

Quantum Computers are advancing and one should know how to fit classical problems into them.

Finite automata are awesome but inherently sequential. On the other hand, finite monoid machines solve the same problems while being amenable to parallel execution.

Did you know that Finite Automata can recognize divisibility? To find one such automaton, the procedure is simple but constructing the minimal one requires a lot of modular arithmetic.

Finite automata accept a description using linear algebra that we can translate into a system of tensors or quantum circuits. These provide examples of quantum systems only requiring a polynomial amount of information to represent and simulate classicaly.

A simple ssh workflow for interacting with Jupyter notebooks from your browser while using an HPC supercomputer’s resources.

You may be used to sampling from probabilities, but what about sampling a random finite probability? As it turns out, this is a procedure rich in geometry and symmetries.

Cutting planes are a powerful tool for solving stochastic programs. We focus on the possible ways to represent the cuts during algorithms and their consequences for parallelization.

From monads to stochastic control and from fixed points to value iteration. An exploration about using abstract concepts to construct concretes algorithms.

Approximations by cuts are common in convex optimization. How to leverage them in the presence of integer variables?

There are many kinds of finite automata. We can, however, write all of them as variations on the same definition, by making the transition monadic.

An exploration of cutting-plane approximations, a technique for representing functions via polyhedra that nicely fits into optimization problems.

A mostly visual post illustrating the graphs for many common kinds of relations.

By doing dynamic programming in an abstract Semiring, we discover that many classical algorithms are, in fact, calculating shortest paths.

By delving into the realm of abstraction, we can uncover practical applications. For example: memoizing functions with Representable Functors.

Looking at Taylor series as streams of real numbers, solving differential equations becomes as easy as writing them.

From parsing text to controling robots, dynamic programming is everywhere. Let’s explore its workings, which problems it solves, and its algorithms.

What is the difference between automatic and symbolic differentiation? With enough polymorphism, it is possible to use one to calculate the other.

Writing a symbolic calculator for derivatives may sound like a hard task. It is feasible, however, in a few dozen lines of Haskell. All this thanks to syntax trees and recursion.

The standard definition of average can be rather opaque. Nevertheless, looking at it from the perspective of minimizing a square error, sheds light on how natural the definition actually is.

Ever had to program together with someone via ssh? It can be confusing… unless you use tmux to painlessly share a terminal!

All divide-and-conquer algorithms can be separated into a construction part and a merge part. This post illustrates this in Haskell for the FFT.

Most introductions to recursion schemes are aimed at functional programmers. But what if you are a functional entusiast mathematician? Don’t worry, we have you covered in this one.