Related papers: Geometry of iteration stable tessellations: Connec…
Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer…
We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are…
In this paper, we consider a regular tessellation of the Euclidean plane and the sequence of its geometric scalings by negative powers of a fixed integer. We generate iteratively random sets as the union of adjacent tiles from these…
Processes of random tessellations of the Euclidean space $\mathbb{R}^d$, $d\geq 1$, are considered which are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until…
We study several constructions of the STIT tessellation process in a window of $\RR^\ell$ and supply an exact formula for its transition probability.
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite…
In this paper we introduce a statistic, the persistent homology transform (PHT), to model surfaces in $\mathbb{R}^3$ and shapes in $\mathbb{R}^2$. This statistic is a collection of persistence diagrams - multiscale topological summaries…
Persistent spin textures (PST) are special spin configurations in spin-orbit-coupled systems in which the spin polarization acquires a symmetry-enforced momentum-independent orientation, leading to exceptionally long spin lifetimes and…
We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not…
Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…
A branching random tessellation (BRT) is a stochastic process that transforms a coarse initial tessellation of $\mathbb{R}^d$ into a finer tessellation by means of random cell divisions in continuous time. This concept generalises the…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…
A panoptic view of architectured planar lattices based on star-polygon tilings was developed. Four star-polygon-based lattice sub-families, formed of systematically arranged triangles, squares, or hexagons, were investigated numerically and…
Kirigami tessellations, regular planar patterns formed by cutting flat, thin sheets, have attracted recent scientific interest for their rich geometries, surprising material properties and promise for technologies. Here we pose and solve…
This paper provides a practical approach to stochastic Lie systems, i.e. stochastic differential equations whose general solutions can be written as a function depending only on a generic family of particular solutions and some constants…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
We consider the problem of classifying linear systems of hypersurfaces (of a fixed degree) in some projective space up to projective equivalence via geometric invariant theory (GIT). We provide an explicit criterion that solves the problem…
In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in…
We consider the typical cell of a stationary Poisson hyperplane tessellation in d-dimensional Euclidean space. It is well known that the expected vertex number of the typical cell is independent of the directional distribution of the…
The topic of this survey are geometric functionals of a Boolean model (in Euclidean space) governed by a stationary Poisson process of convex grains. The Boolean model is a fundamental benchmark of stochastic geometry and continuum…