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The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map…
Despite the knowledge that social, economical, and ecological networks are often of a small-world nature with inter-nodal distance growing even slower than logarithmically with system size, we often assume theoretical systems to be outside…
We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable…
The protocol of quantum annealing is applied to an optimization problem with a one-dimensional continuous degree of freedom, a variant of the problem proposed by Shinomoto and Kabashima. The energy landscape has a number of local minima,…
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that…
Self-organized large-scale flow structures occur in a wide range of turbulent flows. Yet, their emergence, dynamics, and interplay with small-scale turbulence are not well understood. Here, we investigate such self-organized turbulent…
The microscopic and macroscopic dynamics of random networks is investigated in the strong-dilution limit (i.e. for sparse networks). By simulating chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show that a…
We analyze quantum-mechanical counterpart of Newtonian cosmology and show that effects of zero-point motion eliminate classical density singularity. Quantum effects are particularly significant for closed Universes where without the…
Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the…
The functional consequences of local and global dynamics can be very different in natural systems. Many such systems have a network description that exhibits strong local clustering as well as high communication efficiency, often termed as…
Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…
Deep Residual Networks present a premium in performance in comparison to conventional networks of the same depth and are trainable at extreme depths. It has recently been shown that Residual Networks behave like ensembles of relatively…
Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the…
Networks that are organized as a hierarchy of modules have been the subject of much research, mainly focusing on algorithms that can extract this community structure from data. The question of why modular hierarchical organizations are so…
Coalition forming is investigated among countries, which are coupled with short range interactions, under the influence of external fields produced by the existence of global alliances. The model rests on the natural model of coalition…
Collective stable chaos consists of the persistence of disordered patterns in dynamical spatiotemporal systems possessing a negative maximum Lyapunov exponent. We analyze the role of the topology of connectivity on the emergence and…
In this paper we analyze the effect of a non-trivial topology on the dynamics of the so-called Naming Game, a recently introduced model which addresses the issue of how shared conventions emerge spontaneously in a population of agents. We…
We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of…
The features of turbulence modulation produced by a heavy loaded suspension of small solid particles or liquid droplets are discussed by using a physically-based regularisation of particle-fluid interactions. The approach allows a robust…
We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…