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We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk…
We study the sample complexity of robust binary hypothesis testing under three standard contamination models: $\varepsilon$-additive (Huber), $\varepsilon$-subtractive, and $\varepsilon$-total variation (TV), denoted by…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
After extensive quasi-static shearing, dense dry granular flows attain a steady-state condition of porosity and deviatoric stress, even as particles are continually rearranged. The paper considers two-dimensional flow and derives the…
We study the critical properties of the weakly disordered two-dimensional Ising and Baxter models in terms of the renormalization group (RG) theory generalized to take into account the replica symmetry breaking (RSB) effects. Recently it…
We calculate exactly the first cumulants of the integrated current and of the activity (which is the total number of changes of configurations) of the symmetric simple exclusion process (SSEP) on a ring with periodic boundary conditions.…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
Motivated by the phenomenologies of dynamic roughening of strings in random media and magnetohydrodynamics, we examine the universal properties of driven diffusive system with coupled fields. We demonstrate that cross-correlations between…
The pseudo-rapidity dependence of the elliptic flow at various excitation energies measured by the PHOBOS Collaboration in Au+Au collisions at RHIC is one of the surprising results that has not been explained before in terms of…
Deep neural networks (DNNs) exhibit crackling-like avalanches whose origin lacks a mechanistic explanation. Here, I derive a stochastic theory of deep information propagation (DIP) by incorporating Central Limit Theorem (CLT)-level…
Models for shallow water flow often assume that the lateral velocity is constant over the water height. The recently derived shallow water moment equations are an extension of these standard shallow water equations. The extended models…
In this paper we study the large time asymptotics of the flow of a dynamical system $X'=b(X)$ posed in the $d$-dimensional torus. Rather than using the classical unique ergodicity condition which is not fulfilled if $b$ vanishes at…
We present a computational framework for efficient learning, sampling, and distribution of general Bayesian posterior distributions. The framework leverages a machine learning approach for the construction of normalizing flows for the…
The concept of universality proposes that dynamical systems with the same power law behaviors are equivalent at large scales. We test this hypothesis on the Earth's crust and the epileptic brain, and discover that power laws also govern the…
Regionalization methods have long been used to estimate high return levels of river discharges at ungauged locations on a river network. In these methods, the recorded discharge measurements of a group of similar, gauged, stations is used…
The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i. e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of…
Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such…
The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for…
In this study, we investigate the complexity of two-phase flow (air/water) in a heterogeneous soil sample by using complex network theory, where the supposed porous media is non-deformable media, under the time-dependent gas pressure. Based…
The use of the annual maximum series for flood frequency analyses limits the considered information to one event per year and one sample that is assumed to be homogeneous. However, flood may have different generating processes, such as…