author: Indrek Klanberg
title: A discrete model for neuronal network dynamics
keywords: Graph Transformation, Neuronal Networks
topics: Algorithms and Data Structures , Case studies and Applications , Graphs
committee: Arend Rensink ,
Hajo Broersma
started: November 2018
end: August 2019


One of the more speculative branches of computer science is the search for alternative models of computation, not based on man-made electrical circuits. In particular, a lot of attention is paid to principles from biology: it is hard to see why our body manages to achieve a level of functionality that cannot be mimicked even by the most powerful of nowadays' computers.

An obvious source of inspiration of this kind is the neuronal network (or "biological neural network" to distinguish them from the well-known machine learning technique) in the brain. How this small clump of matter manages to give us thought and (the illusion of) self is still a mystery, but that it does so is a fact, and scientists would dearly like to understand such networks better.

This project is about applying graph transformation to create a model for neuronal interaction. The fact that a neuronal network can be thought of as a graph is rather obvious, but the rule-based modelling principle of graph transformation gives an easy and transparant way to model the dynamics of such a graph; this is an approach that has not yet been tried out so far, and offers advantages over existing, physics-based models in offering discrete abstractions that may make the analysis of neuronal networks more tractable.

Part of the project is to design a good graph representation of the networks in question, where the criteria for what is "good" themselves have to be worked out at the same time. Given such a graph representation, either simulation or analysis become possible avenues of exploration, either of which carry their own further questions. To name just one, the graphs in question are truly large, and to carry out their transformation efficiently will require distributed algorithms that yet have to be established. Alternatively, heuristics may be applied to search for interesting patterns within such a network.