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. Moreover, modifying a deep semantic part of the neural network leads to the appearance of symbolic visual representations. None of the considered networks had any access to images of human-made art.

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. We analyze incompressible as well as weakly compressible fluid flows. We quantify the complexity of the computation performed by the network via the intrinsic dimensionality of the internal feature representations and calculate the effective number of independent features which the network uses in order to distinguish between classes. In addition to providing a numerical estimate of the complexity of the computation, the measure also characterizes the neural network processing at intermediate and final stages. We construct adversarial examples and use them to identify the two point correlation spectra for the chaotic and turbulent vorticity as the feature used by the network for classification.

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.

Objective.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.Approach.The current study evaluates this approach using results from the classification and decoding of electrical brain activity associated with information retention. We designed four neural network models differing in architecture, training strategies, and input representation to classify single experimental trials of a working memory task.Main results.Our best models achieved an accuracy (ACC) of 65.29 ± 0.76 and Matthews correlation coefficient of 0.288 ± 0.018, outperforming the reference model trained on the same data. The highest correlation between classification score and behavioral performance was 0.36 (p= 0.0007). Using analysis of input perturbation, we estimated the importance of EEG channels and frequency bands in the task at hand. The set of essential features identified for each network varies. We identified a subset of features common to all models that identified brain regions and frequency bands consistent with current neurophysiological knowledge of the processes critical to attention and working memory. Finally, we proposed sanity checks to examine further the robustness of each model's set of features.Significance.Our results indicate that explainable deep learning is a powerful tool for decoding information from EEG signals. It is crucial to train and analyze a range of models to identify stable and reliable features. Our results highlight the need for explainable modeling as the model with the highest ACC appeared to use residual artifactual activity.

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. Our results provide evidence that information processing dynamics during the retrieval process vary depending on the correct or false recognition-for stimuli inducing a high level of cognitive conflict and erroneous response, information processing is prolonged. The observed phenomenon may be interpreted as the manifestation of the brain's preparation for future goal-directed action.

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. The results indicate the existence of a very rich class of inhomogeneous black hole solutions.

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. We establish that near the transition, in all cases considered, the applicability of a hydrodynamic description breaks down already at lower momenta than in the conformal case. We establish the appearance of the spinodal region in the case of the first order phase transition at temperatures for which the speed of sound squared is negative. An estimate of the preferential scale attained by the unstable modes is also given. We additionally observe a novel diffusive regime for sound modes for a range of wavelengths.

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. We formulate new evolution equations for general flows and then test them in the case of N=4 super Yang-Mills plasma by comparing their solutions alongside solutions of MIS theory with numerical computations of isotropization and boost-invariant flow based on holography. In these tests the new equations reproduce the results of MIS theory when initialized close to the hydrodynamic stage of evolution, but give a more accurate description of the dynamics when initial conditions are set in the preequilibrium regime.

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. We observe a factorial growth of gradient contributions at large orders, which indicates a zero radius of convergence of the hydrodynamic series. Furthermore, we identify the leading singularity in the Borel transform of the hydrodynamic energy density with the lowest nonhydrodynamic excitation corresponding to a 'nonhydrodynamic' quasinormal mode on the gravity side.

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. Heller, R. A. Janik, and P. Witaszczyk, arXiv:1203.0755]. Despite the very rich far-from-equilibrium evolution, we find surprising regularities in the form of clear correlations between initial entropy and total produced entropy, as well as between initial entropy and the temperature at thermalization, understood as the transition to a hydrodynamic description. For 29 different initial conditions that we consider, hydrodynamics turns out to be definitely applicable for proper times larger than 0.7 in units of inverse temperature at thermalization. We observe a sizable anisotropy in the energy-momentum tensor at thermalization, which is nevertheless entirely due to hydrodynamic effects. This suggests that effective thermalization in heavy-ion collisions may occur significantly earlier than true thermalization.

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. For the analytically known Lévy measures we explicitly construct the density of states using the method of orthogonal polynomials. We show that the Lévy tail distributions are characterized by a different novel form of microscopic universality.