Related papers: Circle packing in arbitrary domains

Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…

In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…

Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…

AI-enabled precision medicine promises a transformational improvement in healthcare outcomes by enabling data-driven personalized diagnosis, prognosis, and treatment. However, the well-known "curse of dimensionality" and the clustered…

To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME)…

The goal of cross-domain object matching (CDOM) is to find correspondence between two sets of objects in different domains in an unsupervised way. Photo album summarization is a typical application of CDOM, where photos are automatically…

We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…

We consider the problem of finding all enclosing rectangles of minimum area that can contain a given set of rectangles without overlap. Our rectangle packer chooses the x-coordinates of all the rectangles before any of the y-coordinates. We…

A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…

We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…

Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…

In an Euclidean $d$-space, the container problem asks to pack $n$ equally sized spheres into a minimal dilate of a fixed container. If the container is a smooth convex body and $d\geq 2$ we show that solutions to the container problem can…

Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. In the abstract form of the problem, where no noise or other corruptions are present, the data are assumed to lie in general position…

In this paper, we present a cluster algorithm for the simulation of hard spheres and related systems. In this algorithm, a copy of the configuration is rotated with respect to a randomly chosen pivot point. The two systems are then…

We develop an algorithm to construct new self-similar space-filling packings of spheres. Each topologically different configuration is characterized by its own fractal dimension. We also find the first bi-cromatic packing known up to now.

Following the work of arXiv:2101.09512, we are interested in clustering a given multi-variate series in an unsupervised manner. We would like to segment and cluster the series such that the resulting blocks present in each cluster are…

The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…

Many approaches to 3D image segmentation are based on hierarchical clustering of supervoxels into image regions. Here we describe a distributed algorithm capable of handling a tremendous number of supervoxels. The algorithm works…

We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex…

Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…