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We present a flexible, detailed model for the evolution of galactic discs in a cosmological context since $z\approx 4$, including a physically-motivated model for radial transport of gas and stars within galactic discs. This expansion…
This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing…
Given a polygon $P$, for two points $s$ and $t$ contained in the polygon, their \emph{geodesic distance} is the length of the shortest $st$-path within $P$. A \emph{geodesic disk} of radius $r$ centered at a point $v \in P$ is the set of…
Deep learning has shown great success in high-level image analysis problems; yet its efficacy relies on the quality and diversity of the training data. In this work, we introduce a copypaste image augmentation for ultrasound images. The…
Graph sampling set selection, where a subset of nodes are chosen to collect samples to reconstruct a smooth graph signal, is a fundamental problem in graph signal processing (GSP). Previous works employ an unbiased least-squares (LS) signal…
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to improve the upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets.…
We describe a new numerical procedure for generating dense packings of disks and spheres inside various geometric shapes. We believe that in some of the smaller cases, these packings are in fact optimal. When applied to the previously…
Optical measurements often exhibit mixed Poisson-Gaussian noise statistics, which hampers image quality, particularly under low signal-to-noise ratio (SNR) conditions. Computational imaging falls short in such situations when solely…
This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
We present a perfect simulation of the hard disks model via the partial rejection sampling method. Provided the density of disks is not too high, the method produces exact samples in $O(\log n)$ rounds, and total time $O(n)$, where $n$ is…
We generalize the classic change-point problem to a "change-set" framework: a spatial Poisson process changes its intensity on an unobservable random set. Optimal detection of the set is defined by maximizing the expected value of a gain…
The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…
We present a new algorithm for the automatic one-shot generation of scattered node sets on irregular 2D and 3D domains using Poisson disk sampling coupled to novel parameter-free, high-order parametric Spherical Radial Basis Function…
Accelerated MRI protocols routinely involve a predefined sampling pattern that undersamples the k-space. Finding an optimal pattern can enhance the reconstruction quality, however this optimization is a challenging task. To address this…
We study the problem of assigning non-overlapping geometric objects centered at a given set of points such that the sum of area covered by them is maximized. If the points are placed on a straight-line and the objects are disks, then the…
We study point processes that consist of certain centers of point tuples of an underlying Poisson process. Such processes arise in stochastic geometry in the study of exceedances of various functionals describing geometric properties of the…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
A Poisson geometry arising from maximal commutative subalgebras is studied. A spectral sequence convergent to Hochschild homology with coefficients in a bimodule is presented. It depends on the choice of a maximal commutative subalgebra…
We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic…
Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…