Related papers: Multifractal emergent processes: Multiplicative in…

We examine the existence of nonlinear modes and their temporal dynamics, in arrays of split-ring resonators, using a fractional extension of the Laplacian in the evolution equation. We find a closed-form expression for the dispersion…

Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent…

The task of inferring high-level causal variables from low-level observations, commonly referred to as causal representation learning, is fundamentally underconstrained. As such, recent works to address this problem focus on various…

Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear…

Various natural and engineered systems, from urban traffic flow to the human brain, can be described by large-scale networked dynamical systems. These systems are similar in being comprised of a large number of microscopic subsystems, each…

By unifying three foundational principles of modern biology, we develop a mathematical framework to analyze the growing tree of life. Contrary to the static case, where the analogy between phylogenetic trees and the tree that grows in soil…

Discontinuous piecewise differential systems exhibit dynamical behaviors with no counterpart in smooth systems, particularly in the presence of nonsmooth switching structures. In this work, we extend previous results for systems separated…

The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the last decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces…

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…

The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary…

Dynamical processes on time-varying complex networks are key to understanding and modeling a broad variety of processes in socio-technical systems. Here we focus on empirical temporal networks of human proximity and we aim at understanding…

Perceptual learning enables humans to recognize and represent stimuli invariant to various transformations and build a consistent representation of the self and physical world. Such representations preserve the invariant physical relations…

Collisionless suspensions of inertial particles (finite-size impurities) are studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of random dynamical systems are used to identify and to characterise in full generality…

To make a statement about the nature and mechanism of fragmentation, it is necessary to probe directly any competition, or lack thereof, between the emission of various particle species as a function of excitation energy. The task is then…

This research focuses on the identification and causality analysis of coherent structures that arise in turbulent flows in square and rectangular ducts. Coherent structures are first identified from direct numerical simulation data via…

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…

The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a…

In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex…

We study numerically multifractal properties of two models of one-dimensional quantum maps, a map with pseudointegrable dynamics and intermediate spectral statistics, and a map with an Anderson-like transition recently implemented with cold…

As few real systems comprise indistinguishable units, diversity is a hallmark of nature. Diversity among interacting units shapes properties of collective behavior such as synchronization and information transmission. However, the benefits…