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Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…
In an expanding universe, velocity field and gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolve in time and these can be scaled suitably so that the constant of proportionality…
Clustering categorical distributions in the finite-dimensional probability simplex is a fundamental task met in many applications dealing with normalized histograms. Traditionally, the differential-geometric structures of the probability…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
Colloidal clusters consist of small numbers of colloidal particles bound by weak, short-range attractions. The equilibrium probability of observing a cluster in a particular geometry is well-described by a statistical mechanical model…
If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a…
Recent 3D Gaussian Splatting (3DGS) representations have demonstrated remarkable performance in novel view synthesis; further, material-lighting disentanglement on 3DGS warrants relighting capabilities and its adaptability to broader…
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
Many inverse problems are ill-posed and need to be complemented by prior information that restricts the class of admissible models. Bayesian approaches encode this information as prior distributions that impose generic properties on the…
Model-independent searches in particle physics aim at completing our knowledge of the universe by looking for new possible particles not predicted by the current theories. Such particles, referred to as signal, are expected to behave as a…
A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia…
We study gravitational clustering of mass points in three dimensions with random initial positions and periodic boundary conditions (no expansion) by numerical simulations. Correlation properties are well defined in the system and a sort of…
We provide a general and malleable heuristic for the air conflict resolution problem. This heuristic is based on a new neighborhood structure for searching the solution space of trajectories and flight-levels. Using unsupervised learning,…
A general method to obtain a representation of the structural landscape of nanoparticles in terms of a limited number of variables is proposed. The method is applied to a large dataset of parallel tempering molecular dynamics simulations of…
One standard approach to describe the collective behaviour of self-propelled particles is the Vicsek model: point-like self-propelled particles tend to align their migration directions to the ones of their nearer neighbours at each…
In this paper, we propose a simple yet effective method to represent point clouds as sets of samples drawn from a cloud-specific probability distribution. This interpretation matches intrinsic characteristics of point clouds: the number of…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
The coherent process of particle deflection by aligned atomic strings and planes of oriented crystals is accompanied by incoherent scattering by atomic cores. While the coherent particle deflection, described by the axial or planar averaged…
Single-shot wide-angle diffraction imaging is a widely used method to investigate the structure of non-crystallizing objects such as nanoclusters, large proteins or even viruses. Its main advantage is that information about the…
Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…