https://iagoleal.com Iago Leal's blog about math, programming and everything more. © Iago Leal de Freitas, 2020-2026 en-us https://iagoleal.com/static/img/me.jpg https://iagoleal.com hello@iagoleal.com hello@iagoleal.com https://validator.w3.org/feed/docs/rss2.html https://iagoleal.com/posts/usb-crypt/ https://iagoleal.com/posts/usb-crypt/ A tutorial on how to wipe, encrypt, auto mount, and decrypt an external usd drive on linux. 13 Apr 2026 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/ising-qubo-milp/ https://iagoleal.com/posts/ising-qubo-milp/ Quantum Computers are advancing and one should know how to fit classical problems into them. 29 Jan 2026 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/automata-monoids/ https://iagoleal.com/posts/automata-monoids/ Finite automata are awesome but inherently sequential. On the other hand, finite monoid machines solve the same problems while being amenable to parallel execution. 24 Sep 2025 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/automata-divisibility/ https://iagoleal.com/posts/automata-divisibility/ 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. 23 May 2025 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/automata-tensor-networks/ https://iagoleal.com/posts/automata-tensor-networks/ 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. 14 May 2025 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/jupyter-hpc/ https://iagoleal.com/posts/jupyter-hpc/ A simple ssh workflow for interacting with Jupyter notebooks from your browser while using an HPC supercomputer’s resources. 06 Apr 2025 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/sampling-probabilities/ https://iagoleal.com/posts/sampling-probabilities/ 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. 21 May 2024 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/cuts-stochastic/ https://iagoleal.com/posts/cuts-stochastic/ 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. 25 Apr 2024 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/value-iteration-haskell/ https://iagoleal.com/posts/value-iteration-haskell/ From monads to stochastic control and from fixed points to value iteration. An exploration about using abstract concepts to construct concretes algorithms. 29 Feb 2024 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/cuts-mip/ https://iagoleal.com/posts/cuts-mip/ Approximations by cuts are common in convex optimization. How to leverage them in the presence of integer variables? 15 Dec 2023 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/automata-monads/ https://iagoleal.com/posts/automata-monads/ 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. 20 Oct 2023 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/cuts/ https://iagoleal.com/posts/cuts/ An exploration of cutting-plane approximations, a technique for representing functions via polyhedra that nicely fits into optimization problems. 22 Sep 2023 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/finite-relations-graph/ https://iagoleal.com/posts/finite-relations-graph/ A mostly visual post illustrating the graphs for many common kinds of relations. 24 Aug 2023 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/algebraic-path/ https://iagoleal.com/posts/algebraic-path/ By doing dynamic programming in an abstract Semiring, we discover that many classical algorithms are, in fact, calculating shortest paths. 21 Mar 2023 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/representable-memoize/ https://iagoleal.com/posts/representable-memoize/ By delving into the realm of abstraction, we can uncover practical applications. For example: memoizing functions with Representable Functors. 18 Sep 2022 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/calculus-symbolic-ode/ https://iagoleal.com/posts/calculus-symbolic-ode/ Looking at Taylor series as streams of real numbers, solving differential equations becomes as easy as writing them. 17 Jul 2022 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/dynamic-programming/ https://iagoleal.com/posts/dynamic-programming/ From parsing text to controling robots, dynamic programming is everywhere. Let’s explore its workings, which problems it solves, and its algorithms. 25 Jun 2022 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/calculus-symbolic-ad/ https://iagoleal.com/posts/calculus-symbolic-ad/ What is the difference between automatic and symbolic differentiation? With enough polymorphism, it is possible to use one to calculate the other. 25 Apr 2022 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/calculus-symbolic/ https://iagoleal.com/posts/calculus-symbolic/ 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. 05 Apr 2022 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/shower-thoughts-averages/ https://iagoleal.com/posts/shower-thoughts-averages/ 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. 29 Dec 2021 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/tmux-pair-programming/ https://iagoleal.com/posts/tmux-pair-programming/ Ever had to program together with someone via ssh? It can be confusing… unless you use tmux to painlessly share a terminal! 03 Aug 2021 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/fft-hylo/ https://iagoleal.com/posts/fft-hylo/ 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. 20 Sep 2020 00:00:00 GMT Iago Leal de Freitas Blog https://iagoleal.com/posts/recursion-schemes/ https://iagoleal.com/posts/recursion-schemes/ 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. 10 Sep 2020 00:00:00 GMT Iago Leal de Freitas Blog