Related papers: Interdependent scaling exponents in the human brai…
The idea that information-processing systems operate near criticality to enhance computational performance is supported by scaling signatures in brain activity. However, external signals raise the question of whether this behavior is…
From 1/f noise to neuronal avalanches, evidence of scaling in brain activity has been increasingly linked to tuning to or near criticality. The concept of scaling is intimately related to the renormalization group (RG), in essence providing…
Brain metabolism is controlled by complex regulation mechanisms. As part of their nature many complex systems show scaling behavior in their timeseries data. Corresponding scaling exponents can sometimes be used to characterize these…
Multiple studies of neural avalanches across different data modalities led to the prominent hypothesis that the brain operates near a critical point. The observed exponents often indicate the mean-field directed-percolation universality…
Converging research suggests that the resting brain operates at the cusp of dynamic instability signified by scale-free temporal correlations. We asked if the scaling properties of these correlations differ between amplitude and phase…
Despite variations in architecture and pretraining strategies, recent studies indicate that large-scale AI models often converge toward similar internal representations that also align with neural activity. We propose that scale-invariance,…
The fluctuation properties of the human electroencephalogram (EEG) time series are studied using detrended fluctuation analysis. For all 128 channels in each of 18 subjects studied, it is found that the standard deviation of the…
Scale-free networks (SFN) arise from simple growth processes, which can encourage efficient, centralized and fault tolerant communication (1). Recently its been shown that stable network hub structure is governed by a phase transition at…
The "critical brain hypothesis" posits that neural circuitry may be tuned close to a "critical point" or "phase transition" -- a boundary between different operating regimes of the circuit. The renormalization group and theory of critical…
Scaling temporal dynamics in functional MRI (fMRI) signals have been evidenced for a decade as intrinsic characteristics of ongoing brain activity (Zarahn et al., 1997). Recently, scaling properties were shown to fluctuate across brain…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
Using a renormalization group method, we calculate 800 high-temperature coefficients of the magnetic susceptibility of the hierarchical Ising model. The conventional quantities obtained from differences of ratios of coefficients show…
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in…
The phenomenological renormalization group (PRG) has been applied to the study of scaleinvariant phenomena in neuronal data, providing evidence for critical phenomena in the brain. However, it remains unclear how reliably these observed…
In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the…
It is shown that a Hopfield recurrent neural network exhibits a scaling regime, whose specific exponents depend on the number of parcels used and the decay length of the coupling strength. This scaling regime recovers the picture introduced…
Over the past decade, studies of naturalistic language processing where participants are scanned while listening to continuous text have flourished. Using word embeddings at first, then large language models, researchers have created…
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…
The scaling properties of selfavoiding polymerized membranes are studied using renormalization group methods. The scaling exponent \nu is calculated for the first time at two loop order. \nu is found to agree with the Gaussian variational…
Graphical models have been used extensively for modeling brain connectivity networks. However, unmeasured confounders and correlations among measurements are often overlooked during model fitting, which may lead to spurious scientific…