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Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…
In Lagrangian meshfree methods, the underlying spatial discretization, referred to as a point cloud or a particle cloud, moves with the flow velocity. In this paper, we consider different numerical methods of performing this movement of…
The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more…
Finding the common structural features of two molecules is a fundamental task in cheminformatics. Most drugs are small molecules, which can naturally be interpreted as graphs. Hence, the task is formalized as maximum common subgraph…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Neural networks for point clouds, which respect their natural invariance to permutation and rigid motion, have enjoyed recent success in modeling geometric phenomena, from molecular dynamics to recommender systems. Yet, to date, no model…
Point clouds are versatile representations of 3D objects and have found widespread application in science and engineering. Many successful deep-learning models have been proposed that use them as input. The domain of chemical and materials…
Point clouds, as a form of Lagrangian representation, allow for powerful and flexible applications in a large number of computational disciplines. We propose a novel deep-learning method to learn stable and temporally coherent feature…
A new type of artificial molecule is proposed, which consists of coupled defect atoms in photonic crystals, named as photonic molecule. Within the major band gap, the photonic molecule confines the resonant modes that are closely analogous…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
We analyze a method of compressing a cloud of cold atoms by dynamic control of a far off resonance optical lattice. We show that by reducing the lattice spacing either continuously or in discrete steps while cooling the atoms with optical…
A graph is called (generically) rigid in $\mathbb{R}^d$ if, for any choice of sufficiently generic edge lengths, it can be embedded in $\mathbb{R}^d$ in a finite number of distinct ways, modulo rigid transformations. Here we deal with the…
Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks utilizing symmetry invariant layers have been shown to be able to optimize…
Subtraction schemes provide a systematic way to compute fully-differential cross sections beyond the leading order in the strong coupling constant. These methods make singular real-emission corrections integrable in phase space by the…
We construct spherical, hydrostatic models of dense molecular cores and Bok globules consisting of two distinct, spatially separate gas components: a central, isothermal region surrounded by a negative-index, polytropic envelope. The clouds…
Achieving and exceeding the diversity of colloidal analogs of chemical elements and molecules as building blocks of matter has been the central goal and challenge of colloidal science ever since Einstein introduced the colloidal atom…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…