相关论文: Unfolding the Hierarchy of Voids

Hierarchical clustering is one of the standard methods taught for identifying and exploring the underlying structures that may be present within a data set. Students are shown examples in which the dendrogram, a visual representation of the…

Using two-dimensional numerical simulations of gravitational clustering, with initial power spectra of a power-law form with index n, we compare the properties of voids in real space to their properties in redshift space. Both the void…

The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…

Object Cluster Hierarchies is a new variant of Hierarchical Cluster Analysis that gains interest in the field of Machine Learning. Being still at an early stage of development, the lack of tools for systematic analysis of Object Cluster…

Width-based search methods have demonstrated state-of-the-art performance in a wide range of testbeds, from classical planning problems to image-based simulators such as Atari games. These methods scale independently of the size of the…

We introduce a new approach for identifying and characterizing voids within two-dimensional (2D) point distributions through the integration of Delaunay triangulation and Voronoi diagrams, combined with a Minimal Distance Scoring algorithm.…

Deep neural network algorithms are difficult to analyze because they lack structure allowing to understand the properties of underlying transforms and invariants. Multiscale hierarchical convolutional networks are structured deep…

We introduce and systematically study \emph{hierarchical filtrations} of vector bundles on smooth projective varieties. These are filtrations by saturated subsheaves of equal rank whose successive quotients are torsion sheaves supported in…

Using cosmological $N$-body simulations and the void probability function (VPF), we investigate the statistical properties of voids within a wide range of initially Gaussian models for the origin of large-scale structure. We pay particular…

A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a…

In this paper we explore the mathematical structure of hierarchical organization in smooth dynamical systems. We start by making precise what we mean by a level in a hierarchy, and how the higher le vels need to respect the dynamics on the…

Network-theoretic tools contribute to understanding real-world system dynamics, e.g., in wildlife conservation, epidemics, and power outages. Network visualization helps illustrate structural heterogeneity; however, details about…

We present a novel method for simulation of the interior of large cosmic voids, suitable for study of the formation and evolution of objects lying within such regions. Following Birkhoff's theorem, void regions dynamically evolve as…

We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes…

Uncovering structural patterns in collaboration networks is key for understanding how knowledge flows and innovation emerges. These networks often exhibit a rich interplay of meso-scale structures, such as communities, core-periphery…

A new numerical technique to identify the cosmic web is proposed. It is based on locating multi-stream flows, i.e. the places where the velocity field is multi-valued. The method is local in Eulerian space, simple and computaionally…

A new watermarking algorithm is given, it is based on the so-called chaotic iterations and on the choice of some coefficients which are deduced from the description of the carrier medium. After defining these coefficients, chaotic discrete…

Functional 3D scene graphs offer a versatile and flexible representation for 3D scene understanding and robotic manipulation, defined by object nodes, interactive elements, and functional relationship edges. However, their potential remains…

Open-vocabulary 3D segmentation enables exploration of 3D spaces using free-form text descriptions. Existing methods for open-vocabulary 3D instance segmentation primarily focus on identifying object-level instances but struggle with…

Time domain surveys such as the Vera C. Rubin Observatory are projected to annually discover millions of astronomical transients. This and complementary programs demand fast, automated methods to constrain the physical properties of the…