Functional programming for numerical algorithms

I’ve always been attracted to the functional programming (FP) paradigm, in part because it’s how I started out writing code, in part because of my mathematical tendencies. To be sure, I’m not a FP purist. I think this is one of the benefits of learning a language like Scheme: while the language is designed to make you adopt FP ideas, it never fo... Read more 13 Mar 2023 - 11 minute read

Simulating with SimPy

Discrete event simulation is such a pain to implement from scratch. The basic premise—continuous simulations can be “discretized” by processing the moments where the state jumps—is classic and well-trodden.1 But actual implementation is a nightmare. In theory we want to have a number of features in a discrete event simulation: Versatile but ... Read more 25 May 2020 - 10 minute read

Orwell and Kohelet

Rereading Orwell’s Politics and the English language, I found myself cackling to his rendition of Kohelet: Objective considerations of contemporary phenomena compel the conclusion that success or failure in competitive activities exhibits no tendency to be commensurate with innate capacity, but that a considerable element of the unpredictabl... Read more 28 Oct 2019 - less than 1 minute read

Berge's maximum theorem is overpowered (and weak)

I’ve spent some time thinking about the Berge maximum theorem, which is a classic result in parametric optimization. It relates to some of my work with Professor Feinberg here at Stony Brook, but we are pushing in a different direction at the moment. I’m interested in the “classical” theorem, which appeared in Berge’s book Topological spaces in ... Read more 09 Jul 2019 - 14 minute read

A characterization of numerical lower semi-continuity

One can define numerical lower semi-continuity using a sequential criterion: for \(\newcommand{\RR}{\mathbb{R}} \renewcommand{\bar}{\overline} f : X \to \bar{\RR},\) we say that \(f\) is lower semi-continuous at \(x \in X\) if for any sequence \(x_n \to x\) we have \[f(x) \leq \liminf_{n \to \infty} f(x_n).\] The idea is that \(f(x_n)\) is eve... Read more 28 Jun 2018 - 2 minute read