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Computing the Normal Distribution Function

Every once in a while, I need to evaluate the normal distribution function $\Phi(x)$:

$$ \Phi(x) = \frac{1}{2 \pi} \int_{-\infty}^x \! e^{-t^2} \, dt $$

Unfortunately, it is not always available in the standard math libraries, and hence I have to implement a “good-enough” version myself. Here are some options.

Better Highlighting for the Emacs Region

The default highlighting of the Emacs “region” (the part of a buffer between “point” and “mark” — selected text, if any, in other words) is, out of the box, barely visible, at least against a light background. An attempt to customize it runs into an interesting problem when used in a text- or terminal-based environment, rather than a GUI.

Compiling Emacs 29 for Debian/Ubuntu/Mint

I wanted to explore some of the new features in Emacs 29 (in particular Eglot). The version of Emacs that ships with my version of Linux Mint is Emacs 27, so I decided to build Emacs 29 from scratch.

This turned out to be absolutely painless; but installing the new version seamlessly into the existing environment did cause some hang-ups.

Queueing and Occupancy: The Linear Case

Imagine a parking lot, consisting of a long, linear strip of slots. Cars enter at one end and leave by the other. Let’s also stipulate that each arriving car takes the first available slot that it encounters, that is, it will park in the first empty slot that is nearest to the parking lot entrance. Cars arrive randomly, with a given, average interarrival time $\tau_A$. Furthermore, cars occupy each slot for a random amount of time, but all with a common average dwell time $\tau_D$.

If we number the slots, starting at the entrance, we may now ask the question: what is the probability that the slot with index $n$ is occupied?

Terrain Generation: River Networks

Terrain Generation: River Networks

A while back, I looked at the Diamond-Square Algorithm for terrain generation. That is a purely procedural algorithm that only attempts to generate realistic looking landscapes, without trying to model any physical or geological processes. By contrast, we will now look at an algorithm to generate realistic river networks, which is based on a (simplified) model of geological erosion.

Book Review: Learning eBPF

The extended Berkeley Packet Filter, or eBPF for short, is a plugin architecture for the Linux kernel. Using eBPF, it is possible to load (short) programs into the kernel at runtime, and have them be executed by the kernel. As the name suggests, the technology started out as a method to build custom filters for network packets, but it has since been extended and become much more general.

Ants and Chips

Imagine a bunch of wood chips randomly distributed on a surface. Now add an ant, randomly walking around amongst the chips. Whenever it bumps into a chip, the ant picks up the chip; if it bumps into another chip, it drops the one it is carrying and keeps walking.

How will such a system evolve over time?