Related papers: Two Dimensional Random Patterns
This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear subspaces generated by the best…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point correlated undirected random networks without self- or…
In order to better model complex real-world data such as multiphase flow, one approach is to develop pattern recognition techniques and robust features that capture the relevant information. In this paper, we use deep learning methods, and…
Despite the astonishing progress in generative AI, 4D dynamic object generation remains an open challenge. With limited high-quality training data and heavy computing requirements, the combination of hallucinating unseen geometry together…
The application of Voronoi and Delaunay tessellation based methods for reconstructing continuous fields from discretely sampled data sets is discussed. The succesfull operation as ``multidimensional interpolation'' method is corroborated…
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…
Generating high-fidelity 3D indoor scenes remains a significant challenge due to data scarcity and the complexity of modeling intricate spatial relations. Current methods often struggle to scale beyond training distribution to dense scenes…
We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
Random recursive hypergraphs grow by adding, at each step, a vertex and an edge formed by joining the new vertex to a randomly chosen existing edge. The model is parameter-free, and several characteristics of emerging hypergraphs admit neat…
We present an algorithm for effectively generating binary sequences which would be rated by people as highly likely to have been generated by a random process, such as flipping a fair coin.
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define…
Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is…
Neural networks with random hidden nodes have gained increasing interest from researchers and practical applications. This is due to their unique features such as very fast training and universal approximation property. In these networks…
A new interactive approach to navigate on approximations of in general non-convex but connected Pareto fronts is introduced. Given a finite number of precalculated representative Pareto-efficient solutions, an adapted Delaunay triangulation…
We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…
While the standard unweighted Voronoi diagram in the plane has linear worst-case complexity, many of its natural generalizations do not. This paper considers two such previously studied generalizations, namely multiplicative and semi…
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to…
Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions using a large number of samples. When trained successfully, we can use the DGMs to…