Related papers: Interdependent scaling exponents in the human brai…
An important side effect of the evolution of the human brain is an increased capacity to form opinions in a very large domain of issues, which become points of aggressive interpersonal disputes. Remarkably, such disputes are often no less…
In this viewpoint article, we discuss the electric properties of the medium around neurons, which are important to correctly interpret extracellular potentials or electric field effects in neural tissue. We focus on how these electric…
Background: Information processing in the brain requires large amounts of metabolic energy, the spatial distribution of which is highly heterogeneous reflecting complex activity patterns in the mammalian brain. Results: Here, it is found…
The critical behavior of the chiral quark-meson model is studied within the Functional Renormalization Group (FRG). We derive the flow equation for the scale dependent thermodynamic potential at finite temperature and density in the…
We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent kernels, and focus on the role of the scale. These estimators interpolate the…
In this paper, we introduce new reference observables to establish a scaling formula in the renormalization group equation. Using the transfer matrix method, we calculate the two point observables of the one dimensional Ising model without…
Mental and cognitive representations are believed to reside on low-dimensional, non-linear manifolds embedded within high-dimensional brain activity. Uncovering these manifolds is key to understanding individual differences in brain…
{}From a finite-size scaling (FSS) theory of cumulants of the order parameter at phase coexistence points, we reconstruct the scaling of the moments. Assuming that the cumulants allow a reconstruction of the free energy density no better…
The scale dependent intermittency exponents in developed hydrodynamic turbulence are calculated assuming a natural hierarchy of correlations in the turbulence. The major correlations are taken into account explicitly, while the remaining…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…
An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made…
We extend existing renormalization group calculations for the exponents describing scaling of star polymers and polymer networks constituted by chains of different species (the so-called copolymer star exponents). Our four loop results find…
Fluctuation scaling has been observed universally in a wide variety of phenomena. In time series that describe sequences of events, fluctuation scaling is expressed as power function relationships between the mean and variance of either…
The scaling behaviors of the human electroencephalogram (EEG) time series are studied using detrended fluctuation analysis. Two scaling regions are found in nearly every channel for all subjects examined. The scatter plot of the scaling…
Scale free dynamics are observed in a variety of physical and biological systems. These include neural activity in which evidence for scale freeness has been reported using a range of imaging modalities. Here, we derive the ways in which…
Analytic phenomenological scaling is carried out for the random field Ising model in general dimensions using a bar geometry. Domain wall configurations and their decorated profiles and associated wandering and other exponents…
Many complex systems display self-organized critical states characterized by 1/f frequency scaling of power spectra. Global variables such as the electroencephalogram, scale as 1/f, which could be the sign of self-organized critical states…
With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
The critical brain hypothesis posits that neural systems operate near a phase transition, optimizing the processing of information. While scale invariance and non-Gaussian dynamics--hallmarks of criticality--have been observed in brain…