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Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…
We study the heterogeneous nucleation of Ising model on complex networks under a non-equilibrium situation where the impurities perform degree-biased motion controlled by a parameter \alpha. Through the forward flux sampling and detailed…
The brain may be thought of as a many-body architecture with a spatio-temporal dynamics described by neuronal structures. The oscillatory nature of brain activity allows these structures (nodes) to be described as a set of coupled…
Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure…
Persistent homology applied to the activity of grid cells in the Medial Entorhinal Cortex suggests that this activity lies on a toroidal manifold. By analyzing real data and a simple model, we show that neural oscillations play a key role…
Quantum networks are an integral component in performing efficient computation and communication tasks that are not accessible using classical systems. A key aspect in designing an effective and scalable quantum network is generating…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of…
Many biological neuronal networks exhibit highly variable spiking activity. Balanced networks offer a parsimonious model of this variability. In balanced networks, strong excitatory synaptic inputs are canceled by strong inhibitory inputs…
Networks of fast-spiking interneurons are crucial for the generation of neural oscillations in the brain. Here we study the synchronous behavior of interneuronal networks that are coupled by delayed inhibitory and fast electrical synapses.…
We report experimental studies of synchronization phenomena in a pair of biological neurons that interact through naturally occurring, electrical coupling. When these neurons generate irregular bursts of spikes, the natural coupling…
In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.
Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…
Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…
Synchronization is an important collective phenomenon in interacting oscillatory agents. Many functional features of the brain are related to synchronization of neurons. The type of synchronization transition that may occur (explosive vs.…
For infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in…
The stability of a flexible fluid membrane containing a distribution of mobile, active proteins (e.g. proton pumps) is shown to depend on the structure and functional asymmetry of the proteins. A stable active membrane is in a…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…