Related papers: Interdependent scaling exponents in the human brai…
We investigate the dynamical properties of electroencephalogram (EEG) signals of human in sleep. By using a modified random walk method, We demonstrate that the scale-invariance is embedded in EEG signals after a detrending procedure.…
We study mathematical models of the collaborative solving of a two-choice discrimination task. We estimate the difference between the shared performance for a group of n observers over a single person performance. Our paper is a theoretical…
Causal relations among neuronal populations of the brain are studied through the so-called effective connectivity (EC) network. The latter is estimated from EEG or fMRI measurements, by inverting a generative model of the corresponding…
Using the density-matrix renormalization-group method we study the two-dimensional Ising model in strip geometry. This renormalization scheme enables us to consider the system up to the size 300 x infinity and study the influence of the…
A two-dimensional lattice system of non-interacting electrons in a homogeneous magnetic field with half a flux quantum per plaquette and a random potential is considered. For the large scale behavior a supersymmetric theory with collective…
We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise…
The ferromagnet-to-paramagnet transition of the four-dimensional random-field Ising model with Gaussian distribution of the random fields is studied. Exact ground states of systems with sizes up to 32^4 are obtained using graph theoretical…
We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed…
It is well established that the brain spontaneously traverses through a very large number of states. Nevertheless, despite its relevance to understanding brain function, a formal description of this phenomenon is still lacking. To this end,…
Reasoning is an integral part of many tasks performed by language models (LMs). However, the effects of scaling model sizes and data on reasoning abilities at pretraining time remain understudied. To rigorously investigate this problem, we…
The human brain is a complex network of interconnected brain regions organized into functional modules with distinct roles in cognition and behavior. An important question concerns the persistence and stability of these modules over the…
Most brain models focus on associative memory or calculation capability, experimentally inaccessible using physiological methods. Here we present a model explaining a basic feature of electroencephalograms (EEG). Our model is based on an…
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
Quantum phase transitions are usually observed in ground states of correlated systems. Remarkably, eigenstate phase transitions can also occur at finite energy density in disordered, isolated quantum systems. Such transitions fall outside…
The critical brain hypothesis posits that neural circuitry operates near criticality to reap the computational benefits of accessing a wide range of timescales. The theory of critical phenomena generally predicts heavy-tailed (power-law)…
Loss of cortical integration and changes in the dynamics of electrophysiological brain signals characterize the transition from wakefulness towards unconsciousness. The common mechanism underlying these observations remains unknown. In this…
Recently measurements on various spin-1/2 quantum magnets such as H$_3$LiIr$_2$O$_6$, LiZn$_2$Mo$_3$O$_8$, ZnCu$_3$(OH)$_6$Cl$_2$ and 1T-TaS$_2$ -- all described by magnetic frustration and quenched disorder but with no other common…
Atom interferometers can be used to study phenomena leading to irreversibility and dissipation, induced by the dynamics of fundamental objects (strings and branes) at a large mass scale. Using an effective, but physically consistent…