Related papers: Calculating Voronoi diagrams using simple chemical…
The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on…
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…
Polygonal chains are fundamental objects in many applications like pattern recognition and protein structure alignment. A well-known measure to characterize the similarity of two polygonal chains is the famous Fr\`{e}chet distance. In this…
The Hilbert metric is a distance function defined for points lying within a convex body. It generalizes the Cayley-Klein model of hyperbolic geometry to any convex set, and it has numerous applications in the analysis and processing of…
Surprisingly, the order-$k$ Voronoi diagram of line segments had received no attention in the computational-geometry literature. It illustrates properties surprisingly different from its counterpart for points; for example, a single…
Due to the intrinsic complexity and nonlinearity of chemical reactions, direct applications of traditional machine learning algorithms may face with many difficulties. In this study, through two concrete examples with biological background,…
Holonomies are of great interest to quantum computation and simulation. The geometrical nature of these entities offers increased stability to quantum gates. Furthermore, symmetries of particle physics are naturally reflected in holonomies,…
Colloidal particles can create reconfigurable nanomaterials, with applications such as color-changing, self-repairing, and self-regulating materials and reconfigurable drug delivery systems. However, top-down methods for manipulating…
By a {\em Voronoi parallelotope} $P(a)$ we mean a parallelotope determined by a non-negative quadratic form $a$. It was studied by Voronoi in his famous memoir. For a set of vectors $\mathcal P$, we call its {\em dual} a set of vectors…
A highly adaptive load balancing algorithm for parallel simulations using particle methods, such as molecular dynamics and smoothed particle hydrodynamics (SPH), is developed. Our algorithm is based on the dynamic spatial decomposition of…
This paper presents the Voronoi diagram-based evolutionary algorithm (VorEAl). VorEAl partitions input space in abnormal/normal subsets using Voronoi diagrams. Diagrams are evolved using a multi-objective bio-inspired approach in order to…
Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to…
In this work, we introduce a new type of linear classifier that is implemented in a chemical form. We propose a novel encoding technique which simultaneously represents multiple datasets in an array of microliter-scale chemical mixtures.…
A number of geometric and topological properties of samples of crack-template based conductive films are examined to assess the degree to which Voronoi diagrams can successfully model structure and conductivity in such networks. Our…
Recently, the construction of 2D empirical wavelets based on partitioning the Fourier domain with the watershed transform has been proposed. If such approach can build partitions of completely arbitrary shapes, for some applications, it is…
Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of…
An algorithm is given in this paper for the computation of dynamically equivalent weakly reversible realizations with the maximal number of reactions, for chemical reaction networks (CRNs) with mass action kinetics.
We address the problem of replicating a Voronoi diagram $V(S)$ of a planar point set $S$ by making proximity queries, which are of three possible (in decreasing order of information content): 1. the exact location of the nearest site(s) in…
Computational techniques are required for narrowing down the vast space of possibilities to plausible prebiotic scenarios, since precise information on the molecular composition, the dominant reaction chemistry, and the conditions for that…
Stencil computations are widely used to simulate the change of state of physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping…