Related papers: Superconcentration in surface growth
Graph convolutions have gained popularity due to their ability to efficiently operate on data with an irregular geometric structure. However, graph convolutions cause over-smoothing, which refers to representations becoming more similar…
We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete…
When measuring the roughness of rough surfaces, the limited sizes of scanned areas lead to its systematic underestimation. Levelling by polynomials and other filtering used in real-world processing of atomic force microscopy data increases…
Despite the prevalence of the attention sink phenomenon in Large Language Models (LLMs), where initial tokens disproportionately monopolize attention scores, its structural origins remain elusive. This work provides a \textit{mechanistic…
Up-directed rough sets are introduced and studied by the present author in earlier papers. This is extended by her in two different granular directions in this research, with a surprising algebraic semantics. The granules are based on ideas…
There is a growing number of tasks that work directly on point clouds. As the size of the point cloud grows, so do the computational demands of these tasks. A possible solution is to sample the point cloud first. Classic sampling…
A statistical theory of two-dimensional Laplacian growths is formulated from first-principles. First the area enclosed by the growing surface is mapped conformally to the interior of the unit circle, generating a set of dynamically evolving…
Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water…
We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson…
Disordered hyperuniformity is a description of hidden correlations in point distributions revealed by an anomalous suppression in fluctuations of local density at various coarse-graining length scales. In the absorbing phase of models…
Surface growth models may give rise to unstable growth with mound formation whose tipical linear size L increases in time. In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks.…
After decades of work, the growth of continuous thin films, i.e., two-dimensional structures, is progressively becoming a technological issue more than a field of fundamental research. Incidentally self-organization of nanostructures on…
Aiming at the problems that the convolutional neural networks neglect to capture the inherent attributes of natural images and extract features only in a single scale in the field of image super-resolution reconstruction, a network…
We propose a new supervized learning framework for oversegmenting 3D point clouds into superpoints. We cast this problem as learning deep embeddings of the local geometry and radiometry of 3D points, such that the border of objects presents…
Computer simulations and scaling theory are used to investigate the damping of oscillations during epitaxial growth on high-symmetry surfaces. The crossover from smooth to rough growth takes place after the deposition of (D/F)^\delta…
In this work, we propose a novel method for generating 3D point clouds that leverage properties of hyper networks. Contrary to the existing methods that learn only the representation of a 3D object, our approach simultaneously finds a…
Point clouds have attracted increasing attention. Significant progress has been made in methods for point cloud analysis, which often requires costly human annotation as supervision. To address this issue, we propose a novel…
We develop a global theory for complete hypersurfaces in $\mathbb{R}^{n+1}$ whose mean curvature is given as a prescribed function of its Gauss map. This theory extends the usual one of constant mean curvature hypersurfaces in…
In this paper, we present an empirical study of typical spatial augmentation techniques used in self-supervised representation learning methods (both contrastive and non-contrastive), namely random crop and cutout. Our contributions are:…
In this work, we present a variant of the multilayer random sequential adsorption (RSA) process that is inspired by orthogonal resource sharing in wireless communication networks. In the one-dimensional (1D) version of this variant, the…