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Title of the thesis: Beyond critical points: Critical manifolds in self-organizing systems

Thesis defender: Silja Sormunen 
Opponent: Professor Anna Levina, University of Tübingen, Germany
Custos: Professor Jari Saramäki, Aalto University School of Science

Many complex systems – from the brain to financial markets – have been suggested to tune themselves to the verge of a phase transition, a so-called critical state, where a qualitative change in the system’s behavior is just about to occur. Such changes arise, for example, when a non-magnetic object suddenly becomes visibly magnetic as temperature reaches a specific value, or when an infectious disease turns into an epidemic as interactions between individuals increase above a critical threshold. Although there are many types of critical states, they all share some common properties, such as extreme sensitivity to small changes in the system. Some of these properties have been thought to support efficient functioning, motivating the study of self-organized criticality, where a system naturally evolves to a critical state without any external control.

This thesis advances the theory of self-organized criticality and uncovers new phenomena within the self-organized critical state. The results demonstrate that a system can self-organize not just to one, but to several phase transitions simultaneously. These findings bring together different lines of research that have previously been viewed as competing. While prior research has suggested that the brain might operate at criticality, a lack of consensus on the phase transition in question has slowed progress in the field. This thesis shows that different transitions can smoothly connect to each other, providing a new perspective on how systems can continuously adapt to changing environments without compromising the benefits of criticality.

In addition to its theoretical contributions, this thesis addresses the methodological challenge of identifying the power-law distribution, a core hallmark of criticality, when data is heavily subsampled. The results highlight important limitations of commonly used analysis methods and call for caution in their use.

Contact information: silja.sormunen@aalto.fi 

Thesis available for public display 7 days prior to the defence at .