Related papers: Scaling invariance: a bridge between geometry, dyn…
Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For…
Cognition is not passive data accumulation but the active resolution of uncertainty through symmetry breaking. This paper argues that both cognitive evolution and development unfold via sequential symmetry-breaking transitions that disrupt…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
Universality is a common quality in different physical parameters that is rooted in the deep nature of physical systems. Scaling relation is a typical universality for critical phenomena around a quantum phase transition, while topological…
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…
Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. While notable progress has been made, the capabilities of differentiable physics solvers remain limited. We…
We present the theoretical underpinnings of scale without conformal invariance in quantum field theory. In light of our results the gradient-flow interpretation of renormalization-group (RG) flow is challenged, due to deep connections…
We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for…
Models of faults incorporating slip rate- and state-dependent friction have reproduced phenomena from spontaneous slow, aseismic slip to earthquake-generating dynamic rupture. Numerical explorations of model parameter space regularly show…
We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
Intermittency is one of central obstacles for understanding small-scale dynamics in the fully developed hydrodynamic turbulence. The modern approach is largely based on the multifractal theory of Parisi and Frisch which is, however,…
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…
Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour…
Fundamental constants are a cornerstone of the physical laws. Any constant varying in space and/or time would signal a violation of local position invariance and be associated with a violation of the universality of free fall, and hence of…
The success of machine learning has resulted from its structured representation of data. Similar data have close internal representations as compressed codes for classification or emerged labels for clustering. We observe that the frequency…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $\epsilon$…
As in an earlier paper we start from the hypothesis that physics on the Planck scale should be described by means of concepts taken from ``discrete mathematics''. This goal is realized by developing a scheme being based on the dynamical…