Related papers: Random sampling of plane partitions
We consider a large class of random geometric graphs constructed from samples $\mathcal{X}_n = \{X_1,X_2,\ldots,X_n\}$ of independent, identically distributed observations of an underlying probability measure $\nu$ on a bounded domain…
In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and…
In current simulations of fission, the number of protons and neutrons in a given fission fragment is almost always obtained by integrating the total density of particles in the sector of space that contains the fragment. Because of the…
What particle shape will generate the highest packing fraction when randomly poured into a container? In order to explore and navigate the enormous search space efficiently, we pair molecular dynamics simulations with artificial evolution.…
Given a parametric polynomial curve $\gamma:[a,b]\rightarrow \mathbb{R}^n$, how can we sample a random point $\mathfrak{x}\in \mathrm{im}(\gamma)$ in such a way that it is distributed uniformly with respect to the arc-length? Unfortunately,…
Bayesian nonparametric space partition (BNSP) models provide a variety of strategies for partitioning a $D$-dimensional space into a set of blocks. In this way, the data points lie in the same block would share certain kinds of homogeneity.…
Spatial range joins have many applications, including geographic information systems, location-based social networking services, neuroscience, and visualization. However, joins incur not only expensive computational costs but also too large…
The paper is concerned with the asymptotic analysis of a family of Boltzmann (multiplicative) distributions over the set $\check{\varLambda}^{q}$ of strict integer partitions (i.e., with unequal parts) into perfect $q$-th powers. A…
We study the problem of sampling weighted partial triangulations of a convex polygon. We consider the distribution where each partial triangulation $\sigma$ is chosen with probability proportional to $\lambda^{|\sigma|}$, where $\lambda>0$…
Traditional Bayesian random partition models assume that the size of each cluster grows linearly with the number of data points. While this is appealing for some applications, this assumption is not appropriate for other tasks such as…
Star-shaped bodies are an important nonconvex generalization of convex bodies (e.g., linear programming with violations). Here we present an efficient algorithm for sampling a given star-shaped body. The complexity of the algorithm grows…
Projective clustering is a problem with both theoretical and practical importance and has received a great deal of attentions in recent years. Given a set of points $P$ in $\mathbb{R}^{d}$ space, projective clustering is to find a set…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…
Assuming that a plane partition of the positive integer $n$ is chosen uniformly at random from the set of all such partitions, we propose a general asymptotic scheme for the computation of expectations of various plane partition statistics…
In this paper we consider a probability distribution on plane partitions, which arises as a one-parameter generalization of the q^{volume} measure. This generalization is closely related to the classical multivariate Hall-Littlewood…
In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics…
In the paper, packings built of identical cuboids with a square base created by random sequential adsorption are studied. The result of the study show that the packing of the highest density are obtained for oblate and prolate cuboids of…
In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…
We analyse uniform random cubic rooted planar maps and obtain limiting distributions for several parameters of interest. From the enumerative point of view, we present a unified approach for the enumeration of several classes of cubic…