Related papers: Turing's cascade instability supports the coordina…

We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…

Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior while others behave erratically. Predicting the emergence of these clusters and understanding the…

The effects of three-dimensional perturbations in two-dimensional turbulence are investigated, through a conformal field theory approach. We compute scaling exponents for the energy spectra of enstrophy and energy cascades, in a strong…

Based on suggested interactions of potential tipping elements in the Earth's climate and in ecological systems, tipping cascades as possible dynamics are increasingly discussed and studied as their activation would impose a considerable…

Metastability is a spurious mode of operation in digital signals, where an electrical signal fails to settle into a stable state within a specified time, leading to uncertainty and potentially failing downstream hardware. A system that…

Understanding emotional processing in the human brain requires examining the complex interactions between different brain regions. While previous studies have identified specific regions involved in emotion processing, a holistic network…

We demonstrate that final-state uncertainty is ubiquitous in multistable systems of coupled neuronal maps, meaning that predicting whether one such system will eventually be chaotic or nonchaotic is often nearly impossible. We propose a…

We derive the scale-by-scale uncertainty energy budget equation and demonstrate theoretically and computationally the presence of a self-similar equilibrium cascade of decorrelation in an inertial range of scales during the time range of…

Compressible turbulence governs energy transfer across scales in space and astrophysical systems. Capturing both the turbulence cascade and damping is therefore crucial for models of energy conversion, plasma heating, and particle transport…

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…

In real world social networks, there are multiple cascades which are rarely independent. They usually compete or cooperate with each other. Motivated by the reinforcement theory in sociology we leverage the fact that adoption of a user to…

We consolidate coherence, athermality, and nonuniformity as sub-resources within an underlying quantum resource theory: instability. We formulate instability axiomatically as the transient information within a decaying physical system.…

Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a wavenumber-localised instability superposed on stochastic forcing, in contrast to previous…

Many neural systems display cascading behavior characterized by uninterrupted sequences of neuronal firing. This gap precludes an understanding of how variations in network structure manifest in neural dynamics and either support or impinge…

Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature…

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features…

For long it has been known that specific patterns of folding are necessary for an optimally functioning brain. For instance, lissencephaly and polymicrogyria can lead to severe mental retardation, short life expectancy, epileptic seizures,…

To further advance our understanding of the brain, new concepts and theories are needed. In particular, the ability of the brain to create information flows must be reconciled with its propensity for synchronization and mass action. The…

Turing patterns in reaction-diffusion (RD) systems have classically been studied only in RD systems which do not explicitly depend on independent variables such as space. In practise, many systems for which Turing patterning is important…

We introduce a novel tool for analyzing complex network dynamics, allowing for cascades of causally-related events, which we call causal webs (c-webs), to be separated from other non-causally-related events. This tool shows that…