Related papers: On the Atomic Cluster Expansion: interatomic poten…
A relativistic coupled-cluster (RCC) theory is implemented to study electron impact excitations of atomic species. As a test case, the electron impact excitations of the $3s ~ ^2S_{1/2} - 3p ~ ^2P_{1/2;3/2}$ resonance transitions are…
We propose a simple scheme to construct composition-dependent interatomic potentials for multicomponent systems that when superposed onto the potentials for the pure elements can reproduce not only the heat of mixing of the solid solution…
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter', and features a global symmetry. One then…
Using the multipole expansion of electromagnetic (EM) field, we present the angular magnetoelectric (AME) coupling in irreducible tensor form. We evaluate the matrix elements when the radiation source is described by electronic transitions…
We consider a scheme of equiprobable allocation of particles into cells by sets. The Edgeworth type asymptotic expansion in the local central limit theorem for a number of empty cells left after allocation of all sets of particles is…
Permutation clones generalise permutation groups and clone theory. We investigate permutation clones defined by relations, or equivalently, the automorphism groups of powers of relations. We find many structural results on the lattice of…
Clustering ensemble, or consensus clustering, has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering…
Accurately predicting crystal properties is critical for accelerating materials discovery, but it is often limited by scarce labeled data and costly theoretical calculations. To alleviate this, we propose UNATE (Unsupervised Atomic…
Continual learning (CL) refers to an agent's capability to learn from a continuous stream of data and transfer knowledge without forgetting old information. One crucial aspect of CL is forward transfer, i.e., improved and faster learning on…
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
In the context of human-in-the-loop Machine Learning applications, like Decision Support Systems, interpretability approaches should provide actionable insights without making the users wait. In this paper, we propose Accelerated…
We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy…
Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
The expansion of the universe is often viewed as a uniform stretching of space that would affect compact objects, atoms and stars, as well as the separation of galaxies. One usually hears that bound systems do not take part in the general…
A new version of the cluster expansion is proposed without breaking the translation and rotation invariance. As an application of this technique, we construct the connected Schwinger functions of the regularized $\phi^4$ theory in a…
We develop a microscopic calculation scheme for the excitation spectrum of a single-electron atom localized near a dielectric nanostructure. The atom originally has an arbitrary degenerate structure of its Zeeman sublevels on its closed…
Clustering performs an essential role in many real world applications, such as market research, pattern recognition, data analysis, and image processing. However, due to the high dimensionality of the input feature values, the data being…
Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra $E$ that is not an orthomodular lattice there…