Public defence in Neuroscience and Biomedical Engineering, M.Sc. Merlin Dumeur

Title of the thesis: Multifractal analysis for studying criticality in neural dynamics

Thesis defender: Merlin Dumeur
Opponent: Research Director, Viktor Jirsa, Institut de Neuroscience des Systemes, Aix-Marseille University, France
Custos: Professor Matias Palva, Aalto University School of Science

This doctoral thesis investigates the relationship between multifractality—complex patterns of scale invariance—and the brain criticality hypothesis, which posits that the brain operates near a phase transition between order and disorder. The study addresses a major gap in neuroscience by providing the first systematic analysis connecting these two concepts, which until now have remained largely separate due to the complexity of multifractal methods and lack of neurophysiological grounding. The research had three primary objectives: to demonstrate multifractality in simulated models of critical brain dynamics, to resolve a key methodological issue in multifractal analysis by introducing a new algorithm capable of handling outliers in neural time series, and to apply this improved method to resting-state MEG data to uncover multifractal properties of brain oscillations. The results confirm that multifractality is present in both simulated and real neural signals and is consistent with the dynamics expected of systems operating near criticality. This establishes multifractal analysis as a valid and informative tool for studying neural activity. The findings provide new insight into how scale-invariant properties manifest in brain function and offer a robust framework for interpreting complex temporal patterns in electrophysiological recordings. These contributions are relevant across computational neuroscience, cognitive science, and clinical research, where understanding the dynamic organization of brain activity is essential. Ultimately, this thesis shows that multifractality is not merely a mathematical artifact but a fundamental characteristic of brain dynamics, particularly under the lens of criticality.

Key Words: Critical dynamics, Multifractal analysis, Scale invariance, Complex systems, Neuroimaging, Neural network modeling

Thesis available for public display 10 days prior to the defence at Aaltodoc.