Related papers: Spatial STIT Tessellations -- Distributional Resul…
Given an increasing sequence of integers a(n), it is known (due to Weyl) that for almost all reals t, the fractional parts of the dilated sequence t*a(n) are uniformly distributed in the unit interval. Some effort has been made recently to…
We study the construction of substitution tilings of the plane based on certain simplicial configurations of tangents of the deltoid with evenly distributed orientations. The random tiling ensembles are obtained as a result of tile…
Three structural populations with distinct average mobility are identified within an equilibrium two-dimensional Lennard-Jones fluid simulated via molecular dynamics at a constant temperature and varying density. Quantifying the structure…
We introduce and theoretically investigate a minimal particle-based model for a new class of active matter where particles exhibit directional, volume-conserving division in confinement while interacting sterically, mimicking cells in early…
Several systems involve spatial arrangements of elements such as molecules or cells, the characterization of which bears important implications to biological and physical investigations. Traditional approaches to quantify spatial order and…
We pursue two goals in this article. As our first goal, we construct a family $\mathcal{M}_G$ of Gibbs like measures on the set of piecewise linear convex functions $g:\mathbb{R}^2\to\mathbb{R}$. It turns out that there is a one-to-one…
Light propagation through turbulence produces speckles, whose ensemble behavior is typically characterized by snapshot intensity statistics. Here, we track the spatiotemporal evolution of individual speckles and quantify fragmentation,…
The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that…
Stencil computations represent a very common class of nested loops in scientific and engineering applications. Exploiting vector units in modern CPUs is crucial to achieving peak performance. Previous vectorization approaches often consider…
Counts in cells are used to analyse the higher order properties of the statistics of the EDSGC survey. The probability distribution is obtained from an equal area projection source catalog with infinite oversampling over the range…
We investigate image segmentation of cells under the lens of scalar fields. Our goal is to learn a continuous scalar field on image domains such that its segmentation produces robust instances for cells present in images. This field is a…
We demonstrate the existence of stable three-dimensional spatiotemporal solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental (nonspinning) STSs forming one-parameter families are stable if their propagation constant…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
In interactive medical image segmentation, anatomical structures are extracted from reconstructed volumetric images. The first iterations of user interaction traditionally consist of drawing pictorial hints as an initial estimate of the…
Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…
This paper presents a statistical explanation of filament formation in the galactic atomic hydrogen. Recently developed technique allows to determine the 3D spectrum of random HI density. We claim that even in the absence of dynamical…
In medical image segmentation tasks, diffusion models have shown significant potential. However, mainstream diffusion models suffer from drawbacks such as multiple sampling times and slow prediction results. Recently, consistency models, as…
We introduce a framework for the generation of grid-shell structures that is based on Voronoi diagrams and allows us to design tessellations that achieve excellent static performances. We start from an analysis of stress on the input…
We investigate a stochastic process where a rectangle breaks into smaller rectangles through a series of horizontal and vertical fragmentation events. We focus on the case where both the vertical size and the horizontal size of a rectangle…
We consider the joint distribution of the area and perimeter statistics on the set I_n of inversion sequences of length n represented as bargraphs. Functional equations for both the ordinary and exponential generating functions are derived…