Related papers: Dense packing of space with various convex solids
Nearly orthogonal lattices were formally defined in [4], where their applications to image compression were also discussed. The idea of ``near orthogonality" in $2$-dimensions goes back to the work of Gauss. In this paper, we focus on…
Symmetry is an important composition feature by investigating similar sides inside an image plane. It has a crucial effect to recognize man-made or nature objects within the universe. Recent symmetry detection approaches used a smoothing…
We prove a new, efficient version of the hypergraph container theorems that is suited for hypergraphs with large uniformities. The main novelty is a refined approach to constructing containers that employs simple ideas from high-dimensional…
This article considers the relation between the spanning properties of lattice orbits of discrete series representations and the associated lattice co-volume. The focus is on the density theorem, which provides a trichotomy characterizing…
We study the optimal packing of hard spheres in an infinitely long cylinder, using simulated annealing, and compare our results with the analogous problem of packing disks on the unrolled surface of a cylinder. The densest structures are…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…
Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger…
This work puts forward a form finding problem of designing a least-volume vault that is a surface structure spanning over a plane region, which via pure compression transfers a vertically tracking load to the supporting boundary. Through a…
Consolidation of loose packages into transport units is a fundamental activity offered by logistics service-providers. Moving the transport units instead of loose packages is faster (with one movement only, multiple packages are loaded…
Static packings of perfectly rigid particles are investigated theoretically and numerically. The problem of finding the contact forces in such packings is formulated mathematically. Letting the values of the contact forces define a vector…
The Kepler conjecture asserts that the density of a packing of congruent balls in three dimensions is never greater than $\pi/\sqrt{18}$. A computer assisted verification confirmed this conjecture in 1998. This article gives a historical…
Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that…
This review paper is devoted to the problems of sphere packings in 4 dimensions. The main goal is to find reasonable approaches for solutions to problems related to densest sphere packings in 4-dimensional Euclidean space. We consider two…
The basic tool for solving problems in metric geometry and isotonic regression is the metric projection onto closed convex cones. Isotonicity of these projections with respect to a given order relation can facilitate finding the solutions…
We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain new numerical results on the Erd\H{o}s problem of finding…
This paper describes a lattice version of the Skyrme model in 2+1 and 3+1 dimensions. The discrete model is derived from a consistent discretization of the radial continuum problem. Subsequently, the existence and stability of the skyrmion…
Dense packing in pick-and-place systems is an important feature in many warehouse and logistics applications. Prior work in this space has largely focused on planning algorithms in simulation, but real-world packing performance is often…
We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…