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Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics…

It has long been suggested that the biological brain operates at some critical point between two different phases, possibly order and chaos. Despite many indirect empirical evidence from the brain and analytical indication on simple neural…

Experiments suggest that cerebral cortex gains several functional advantages by operating in a dynamical regime near the critical point of a phase transition. However, a long-standing criticism of this hypothesis is that critical dynamics…

The brain is in a state of perpetual reverberant neural activity, even in the absence of specific tasks or stimuli. Shedding light on the origin and functional significance of such a dynamical state is essential to understanding how the…

The brain forms and stores distributed representations from sparse external input that compete for neuronal resources with already stored memory traces. It is unclear what dynamical properties of neural systems allow formation and…

Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…

A recurrent idea in the study of complex systems is that optimal information processing is to be found near bifurcation points or phase transitions. However, this heuristic hypothesis has few (if any) concrete realizations where a standard…

Backpropagation-optimized artificial neural networks, while precise, lack robustness, leading to unforeseen behaviors that affect their safety. Biological neural systems do solve some of these issues already. Unlike artificial models,…

Advancing our knowledge of how the brain processes information remains a key challenge in neuroscience. This thesis combines three different approaches to the study of the dynamics of neural networks and their encoding representations: a…

The "edge of chaos" phase transition in artificial neural networks is of renewed interest in light of recent evidence for criticality in brain dynamics. Statistical mechanics traditionally studied this transition with connectivity $k$ as…

The success of deep neural networks in real-world problems has prompted many attempts to explain their training dynamics and generalization performance, but more guiding principles for the training of neural networks are still needed.…

While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular…

Transient or partial synchronization can be used to do computations, although a fully synchronized network is frequently related to epileptic seizures. Here, we propose a homeostatic mechanism that is capable of maintaining a neuronal…

Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point…

As a promising computational paradigm, occurrence of critical states in artificial and biological neural networks has attracted wide-spread attention. An often-made explicit or implicit assumption is that one single critical state is…

Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline…

Echo state networks represent a special type of recurrent neural networks. Recent papers stated that the echo state networks maximize their computational performance on the transition between order and chaos, the so-called edge of chaos.…

The critical brain hypothesis states that there are information processing advantages for neuronal networks working close to the critical region of a phase transition. If this is true, we must ask how the networks achieve and maintain this…

Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information…

Complex systems are typically characterized as an intermediate situation between a complete regular structure and a random system. Brain signals can be studied as a striking example of such systems: cortical states can range from highly…