Related papers: Learning universality and scaling from simple depo…
The idea behind object-centric representation learning is that natural scenes can better be modeled as compositions of objects and their relations as opposed to distributed representations. This inductive bias can be injected into neural…
We consider an arbitrarily charged polymer driven by a weak field through a gel according to the rules of the Rubinstein-Duke model. The probability distribution in the stationary state is related to that of the model in which only the head…
The universal behavior of the continuous superconducting (glass) phase transition is studied in a YBa$_2$Cu$_3$O$_{7-\delta}$ thin film. A new analysis technique for extracting critical exponents is developed, using current-voltage…
We consider the one-dimensional Katz-Lebowitz-Spohn (KLS) model, which is a two-parameter generalization of the Totally Asymmetric Simple Exclusion Process (TASEP) with nearest neighbour interaction. Using a powerful mapping, the KLS model…
Predicting the future behaviour of complex systems exhibiting critical-like dynamics is often considered to be an intrinsically hard task. Here, we study the predictability of the depinning dynamics of elastic interfaces in random media…
What scaling limits govern neural network training dynamics when model size and training time grow in tandem? We show that despite the complex interactions between architecture, training algorithms, and data, compute-optimally trained…
The depinning of an elastic line in a random medium is studied via an extremal model. The latter gives access to the instantaneous depinning force for each successive conformation of the line. Based on conditional statistics the universal…
The equilibrium amorphous solid state -- formed, e.g., by adequately randomly crosslinking the constituents of a macromolecular fluid -- is a heterogeneous state characterized by a universal distribution of particle localization lengths.…
We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well…
Motivated by the centering of biological objects in large cells, we study the generic properties of centering forces inside a ball (or a volume of spherical topology) in $n$ dimensions. We consider two scenarios : autonomous centering (in…
In the given paper the algorithm describing original and universal principles of a triangulation of a smooth molecular surface: solvent excluding solvent (SES), received by primary and secondary rolling, and solvent accessible surface (SAS)…
We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition…
A recently introduced real space renormalization group technique, developed for the analysis of processes in the Kardar-Parisi-Zhang universality class, is generalized and tested by applying it to a different family of surface growth…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
Superdeformed nuclei in the 190 mass region exhibit a striking universality in their decay-out profiles. We show that this universality can be explained in the two-level model of superdeformed decay as related to a strong separation of…
Universality in isotropic, abelian and non-abelian, sandpile models is examined using extensive numerical simulations. To characterize the critical behavior we employ an extended set of critical exponents, geometric features of the…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
Recent years have seen a lot of progress in algorithms for learning parameters of spreading dynamics from both full and partial data. Some of the remaining challenges include model selection under the scenarios of unknown network structure,…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction…