Hi, I'm Ken Mendoza

Founder & Principal Investigator, MendozaLab · Independent researcher

What I actually do

I run MendozaLab, an independent research lab. My work takes information-theoretic tools — things like Minimum Description LengthA principle from information theory: the best explanation of some data is the shortest one that still reproduces it., Koopman–von Neumann operators, and a Shannon–von Neumann–Riemannian entropy hierarchy — and points them at problems that normally live in completely separate fields: pure mathematics, materials science, dynamical systems, and climate detection.

The throughline is parsimony: the simplest description that still explains the data is usually the truest one. It turns out that single idea travels remarkably well across domains. Everything I do is computational — run in-silico on public datasets or documented reference systems, with the artifacts kept so the results can be checked.

A few threads I'm proud of

• The Erdős MDL Mapper — a systematic information-theoretic re-reading of all 1,190 Erdős problemsA famous collection of hard, often decades-old open questions in mathematics, posed by Paul Erdős., with formal proofs machine-verified in Lean 4Proof-assistant software that checks a mathematical proof is airtight, step by step — no hand-waving allowed. (Mathlib).
• A Cramér bound derived from MDL parsimony — without assuming the Riemann Hypothesis.
• The Erdős–Moser problem, approached through 2-adic squeeze mechanisms.
• In materials science, information-theoretic methods for predicting how materials shift between phases, validated on large public crystal-structure datasets.
• In dynamical systems, a Koopman-operator approach to detecting channel asymmetry, with strong results on standard benchmarks.

The long way here

I didn't start in pure math. My background is in proteomics and computational biology — about twenty-five years of it, across bioinformatics, drug-target identification, and software architecture. Somewhere in there I got hooked on a single question: what is the simplest true description of a complex system? That question slowly pulled me out of biology and into the cross-domain work I do now. The pivot is basically the whole story.

Why I write here

Fibromyalgia is, underneath everything, a problem of a nervous system handling information badly — too much signal, not enough filter. That is squarely the kind of system I study. So when I write Research Notes for Fibro Hub, I'm not stepping outside my field; I'm bringing it home.

A thread from the physics side

In a recent note I argued that physical law might be fundamentally local — no master clock running the whole universe, just countless small processes each finishing on their own finite-rate schedule. That idea travels home uncomfortably well. Fibromyalgia behaves less like one broken switch and more like a system with no central conductor: lots of local signals firing, no clean global filter to settle them. The same parsimony tools I use on physics — find the simplest description that still fits — are how I try to read that noise here.

Come find me