Related papers: Characterizing structural features of two-dimensio…
It is difficult to quantify structure-property relationships and to identify structural features of complex materials. The characterization of amorphous materials is especially challenging because their lack of long-range order makes it…
We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of…
We introduce an atomistic classifier based on a combination of spectral graph theory and a Voronoi tessellation method. This classifier allows for the discrimination between structures from different minima of a potential energy surface,…
Machine learning (ML) strategies are opening the door to faster computer simulations, allowing us to simulate more realistic colloidal systems. Since the interactions in colloidal systems are often highly many-body, stemming from e.g.…
Shape analysis and classification are popular methods for biologists, biophysicists and mathematicians investigating relationships between object function and form. Classic shape descriptors, such as sphericity, can be powerful but may be…
The Voronoi diagram-based dual-front active contour models are known as a powerful and efficient way for addressing the image segmentation and domain partitioning problems. In the basic formulation of the dual-front models, the evolving…
We consider several patchy particle models that have been proposed in literature and we investigate their candidate crystal structures in a systematic way. We compare two different algorithms for predicting crystal structures: (i) an…
Efficient, reliable and easy-to-use structure recognition of atomic environments is essential for the analysis of atomic scale computer simulations. In this work, we train two neuronal network (NN) architectures, namely PointNet and dynamic…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
Structured materials like photonic crystals require for optimal use a high precision both on position and optical characteristics of the components which they are made of. Here, we present a simple tomographic algorithm, based on a specific…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
While the microscopic structure of defected solid crystalline materials has significant impact on their physical properties, efficient and accurate determination of a given polycrystalline microstructure remains a challenge. In this paper…
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
This study proposes an innovative approach to analyze spatial patterns of behavior by integrating information in weighted Voronoi diagrams. The objective of the research is to analyze the temporal distribution of an experimental subject in…
One of the biggest challenges in characterizing 2-D topographies is succinctly communicating the dominant nature of local configurations. In a 2-D grid composed of bistate units, this could be expressed as finding the characteristic…
This paper overviews work on the use of simple chemical reactions to calculate Voronoi diagrams and undertake other related geometric calculations. This work highlights that this type of specialised chemical processor is a model example of…
This work proposes a classification algorithm based on the radical Voronoi tessellation to define the Widom delta, supercritical gas-liquid coexistence region, of polyatomic molecules. In specific, we use a weighted mean-field…
We revisit a new type of a Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, and analyze the structure and complexity of the…
Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex…