DominikPeters

Mathematical writing guidelines

These guidelines explain how to present mathematical results in a way that human readers can easily understand and verify, and that respects the reader’s time and energy budget.

Reading order and forward references

A human reader is a first reader of the document. They have not read the document before starting to read it. Note the contrast to how an LLM understands a document: they first load the entire document into context, and then understand it with that context. So it is as easy for an LLM to understand a forward reference as a backward reference. This is extremely different for a human reader, who will usually stop reading if a sentence doesn’t make sense due to limited time (instead of reading the rest of the document).

Therefore, every sentence must make complete sense knowing only what has come before. As I mentioned, as an LLM it may be difficult to spot places where this is violated; if in doubt consider starting a small-model subagent (e.g. Luna or Haiku)

DominikPeters

DominikPeters

Here is what I ran, worked on 2024-05-27:

sudo apt update
sudo apt install postgresql
sudo service postgresql start
sudo visudo

add following line to end of file:

DominikPeters

import cvxpy as cp
import math

def compute_hi(rankings):
    """Compute h_i(a) for all voters and alternatives."""
    hi = []
    for ranking in rankings:
        h = {}
        for a in ranking:
            h[a] = set(ranking[:ranking.index(a)+1])

DominikPeters

// usage: node mes.js <path-to-pb-file>

const fs = require('fs');
const readline = require('readline');

function parsePBFile(filePath) {
    return new Promise((resolve, reject) => {
        const meta = {};
        const projects = {};
        const votes = {};

DominikPeters

For arXiv, run

latexpand --empty-comments --keep-includes --expand-bbl document.bbl document.tex > document-arxiv-v1.tex

Website version style

\documentclass[11pt]{scrartcl}
\usepackage[a4paper, total={16cm, 24cm}]{geometry}
\usepackage{authblk}

DominikPeters

# Adapted from https://github.com/martinlackner/abcvoting/blob/6aacadb0e3e70e4f83a82225b05730f72a6230d4/abcvoting/generate.py#L166

def mallows(reference_ranking, dispersion):
    distributions = []
    for i in range(len(reference_ranking)):
        distributions.append([dispersion ** (i - j) for j in range(i + 1)])
    while True:
        vote = []
        for i in range(len(reference_ranking)):
            pos = random.choices(range(i + 1), weights=distributions[i], k=1)[0]

DominikPeters

def nash(N, A, u, rounds=500):
    "N is set of voters, A is set of alternatives, u is a utility dictionary"
    "where u[i,x] >= 0 is the utility of i for x, usually either 0 or 1"
    p = {x : 1/len(A) for x in A}
    for _ in range(rounds):
        q = {x : 0 for x in A}
        for i in N:
            util = sum(u[i,x] * p[x] for x in A)
            for x in A:
                q[x] += (1/len(N)) * (u[i,x] * p[x]) / util

DominikPeters

# first install pdftk. For recent MacOS version, get it here: https://www.pdflabs.com/tools/pdftk-the-pdf-toolkit/pdftk_server-2.02-mac_osx-10.11-setup.pkg

import os

os.system(f"pdftk input.pdf output uncompressed.pdf uncompress")

with open("fixed.pdf", "wb") as outfile:
  for line in open("uncompressed.pdf", "rb"):
      patterns = [
          b"This content downloaded from",

DominikPeters

I often use Texpad on documents that use the microtype package which makes texpad fall back to PDFLaTeX. Instead I want Texpad to ignore the included package. Here is a way to do this, by adding a fake empty local microtype package.

Make a folder with a fake microtype package:

mkdir .fakemicrotype
echo "\ProvidesPackage{microtype}" > .fakemicrotype/microtype.sty

Add the new folder to the TexpadTex search path: (Command+Shift+. to show hidden files in the folder picker)