Cognition without neurons: modelling anticipation in a basal reservoir computer

How do non-neural organisms, such as the slime mould \textit{Physarum polycephalum}, anticipate periodic events in their environment? We present a minimal, biologically inspired reservoir model that demonstrates simple temporal anticipation without neurons, spikes, or trained readouts. The model consists of a spatially embedded hexagonal network in which nodes regulate their energy through local, allostatic adaptation. Input perturbations shape energy dynamics over time, allowing the system to internalize temporal regularities into its structure. After being exposed to a periodic input signal, the model spontaneously re-enacts those dynamics even in the absence of further input -- a form of unsupervised temporal pattern completion. This behaviour emerges from internal homeodynamic regulation, without supervised learning or symbolic processing. Our results show that simple homeodynamic regulation can support unsupervised prediction, suggesting a pathway to memory and anticipation in basal organisms.

The Lost Art of Mathematical Modelling

We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities -- (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data -- inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomena can be modelled in an infinite number of different ways, through the adoption of an open/pluralistic approach. We explain the open approach using fish locomotion as a case study and illustrate some of the pitfalls -- universalism, creating models of models, etc. -- that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling. This article is dedicated to the memory of Edmund Crampin.