On the linear scaling of entropy vs. energy in human brain activity, the Hagedorn temperature and the Zipf law.

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, we introduce a machine learning based method allowing for the determination of the probabilities of all possible states at a given coarse-graining, from which all the thermodynamics can be derived.

Neural network complexity of chaos and turbulence.

Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work, we consider the relative complexity of chaos and turbulence from the perspective of deep neural networks. We analyze a set of classification problems, where the network has to distinguish images of fluid profiles in the turbulent regime from other classes of images such as fluid profiles in the chaotic regime, various constructions of noise and real-world images.

Aesthetics and neural network image representations.

We analyze the spaces of images encoded by generative neural networks of the BigGAN architecture. We find that generic multiplicative perturbations of neural network parameters away from the photo-realistic point often lead to networks generating images which appear as "artistic renditions" of the corresponding objects. This demonstrates an emergence of aesthetic properties directly from the structure of the photo-realistic visual environment as encoded in its neural network parametrization.

Perfect Fluid Hydrodynamic Picture of Domain Wall Velocities at Strong Coupling.

We show that for a range of strongly coupled theories with a first order phase transition, the domain wall or bubble velocity can be expressed in a simple way in terms of a perfect fluid hydrodynamic formula, and thus in terms of the equation of state. We test the predictions for the domain wall velocities using the gauge/gravity duality.

Decoding working memory-related information from repeated psychophysiological EEG experiments using convolutional and contrastive neural networks.

Extracting reliable information from electroencephalogram (EEG) is difficult because the low signal-to-noise ratio and significant intersubject variability seriously hinder statistical analyses. However, recent advances in explainable machine learning open a new strategy to address this problem.The current study evaluates this approach using results from the classification and decoding of electrical brain activity associated with information retention.

Neural spatio-temporal patterns of information processing related to cognitive conflict and correct or false recognitions.

Using a visual short-term memory task and employing a new methodological approach, we analyzed neural responses from the perspective of the conflict level and correctness/erroneous over a longer time window. Sixty-five participants performed the short-term memory task in the fMRI scanner. We explore neural spatio-temporal patterns of information processing in the context of correct or erroneous response and high or low level of cognitive conflict using classical fMRI analysis, surface-based cortical data, temporal analysis of interpolated mean activations, and machine learning classifiers.

Real-Time Dynamics and Phase Separation in a Holographic First-Order Phase Transition.

We study the fully nonlinear time evolution of a holographic system possessing a first order phase transition. The initial state is chosen in the spinodal region of the phase diagram, and it includes an inhomogeneous perturbation in one of the field theory directions. The final state of the time evolution shows a clear phase separation in the form of domain formation.

Nonequilibrium Dynamics and Phase Transitions in Holographic Models.

We study the poles of the retarded Green's functions of strongly coupled field theories exhibiting a variety of phase structures from a crossover up to a first order phase transition. These theories are modeled by a dual gravitational description. The poles of the holographic Green's functions appear at the frequencies of the quasinormal modes of the dual black hole background.

Coupling hydrodynamics to nonequilibrium degrees of freedom in strongly interacting quark-gluon plasma.

Relativistic hydrodynamics simulations of quark-gluon plasma play a pivotal role in our understanding of heavy ion collisions at RHIC and LHC. They are based on a phenomenological description due to Müller, Israel, Stewart (MIS) and others, which incorporates viscous effects and ensures a well-posed initial value problem. Focusing on the case of conformal plasma we propose a generalization which includes, in addition, the dynamics of the least damped far-from-equilibrium degree of freedom found in strongly coupled plasmas through the AdS/CFT correspondence.

Hydrodynamic gradient expansion in gauge theory plasmas.

We utilize the fluid-gravity duality to investigate the large order behavior of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma system. This corresponds to the inclusion of dissipative terms and transport coefficients of very high order. Using the dual gravity description, we calculate numerically the form of the stress tensor for a boost-invariant flow in a hydrodynamic expansion up to terms with 240 derivatives.

Characteristics of thermalization of boost-invariant plasma from holography.

We report on the approach toward the hydrodynamic regime of boost-invariant N=4 super Yang-Mills plasma at strong coupling starting from various far-from-equilibrium states at τ=0. The results are obtained through a numerical solution of Einstein's equations for the dual geometries, as described in detail in the companion article [M. P.

Viscous plasma evolution from gravity using anti-de sitter/conformal-field-theory correspondence.

We analyze the anti-de Sitter/conformal-field-theory dual geometry of an expanding boost-invariant plasma. We show that the requirement of nonsingularity of the dual geometry for leading and subasymptotic times predicts, without any further assumptions about gauge theory dynamics, hydrodynamic expansion of the plasma with viscosity coefficient exactly matching the one obtained earlier in the static case by Policastro, Son, and Starinets.

Free random Lévy matrices.

Using the theory of free random variables and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical one-dimensional stable Lévy distributions. We show that the resolvents for the corresponding matrices obey transcendental equations in the large size limit. We solve these equations in a number of cases, and show that the eigenvalue distributions exhibit Lévy tails.