#
Program for mathematics 2024

**Grant to a post-doctoral position abroad**

Linnéa Gyllingberg

Uppsala University

Postdoc at University of California Los Angeles, USA,

## Models for minimal cognition

**Linnéa Gyllingberg will receive her doctoral degree in mathematics from Uppsala University in 2024. Thanks to a grant from Knut and Alice Wallenberg Foundation, she will hold a postdoctoral position with Professor Mason A. Porter at the University of California Los Angeles, USA.**

How is it that even the simplest single-celled organisms like the slime mould Physarum polycephalum appear to behave intelligently? It can make its way through labyrinths, find the best food, and avoid traps. The aim of this postdoctoral project is to create a mathematical model for the emergence of minimal cognition in slime moulds. The model will unite two different mathematical modelling paradigms – the models of oscillatory processes, from the 1970s, and current reinforcement models on graphs, which were developed almost 40 years later.

Although a slime mould lacks a central nervous system, it can build robust and cost-effective transport networks. In single-celled organisms, these networks are described by mathematical graph models inspired by electrical network equations. The slime mould is then represented by a graph with nodes and edges, around which particles are transported. The models are based on the assumption that the particle flow is constant. However, recent experimental results suggest that the flow actually varies periodically – oscillations are thus essential for endowing slime moulds and other simple organisms with cognitive abilities.

Here, oscillation theory becomes the mathematical framework for a model of the emergence of minimal cognition. The theory shows that when many regular oscillations are connected, they can self-organise and start to oscillate in a synchronised manner. This happens in our brains, for instance, where a complex network of over 100 billion neurons communicate through electrical oscillations. The slime mould lacks both a brain and a nervous system, but mathematics may be able to explain how it gets so smart.

*Foto: Adam Vesterbacka*