Blog chronicle for all time

On experimental mathematics Tobias Sat, 17 Jul 2021

Experimental mathematics uses computers to inspire research in terms of finding examples and counterexamples, suggesting conjectures or informing proof strategies. I present a strange phenomenon in this practice at two examples: it happens that mathematical software confirms conjectured properties of very large objects very quickly. Much, much more quickly than one might expect a general problem of that type to be solved. In these cases, the software apparently knows a “proof” of the conjecture and the human can either look it up in the source code or at least be more confident in the conjecture.

In his article “Gaussian Representation of Independence Models over Four Random Variables” Petr Šimeček gives realizations of all conditional independence models arising from (not necessarily regular) Gaussian distributions in dimension 4. Only one of these models, M85, is given with irrational correlations. Here I give a rational representation of this model. The question whether all Gaussian CI models are realizable by rational correlation matrices is still open and M85 was the only concrete undecided example I am aware of.

tappp.hpp v0.2.0 released Tobias Thu, 27 Feb 2020

tappp.hpp is a header-only TAP producer for C++17.

The symmetry reduction of LUBF-gaussoids in dimension 8 was a tough nut. I learned that precomputing invariants of the symmetry classes first allows more intelligent distribution of tasks in a parallel symmetry reduction algorithm. In this case, I achieved a 160-fold speedup.

bah! Another static site generator Tobias Wed, 30 Jan 2019

Yet another static site generator – with blackjack and hookers.