Related papers: Atomic Cluster Expansion: Completeness, Efficiency…
We revisit the classical approach to cluster expansions, based on tree graphs, and establish a new convergence condition that improves those by Kotecky-Preiss and Dobrushin, as we show in some examples. The two ingredients of our approach…
The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of conditional…
A sequence of approximations for the determinant and its logarithm of a complex matrixis derived, along with relative error bounds. The determinant approximations are derived from expansions of det(X)=exp(trace(log(X))), and they apply to…
Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to…
We consider the effective dynamics obtained by double-passing a far-detuned laser probe through a large atomic spin system. The net result of the atom-field interaction is a type of coherent positive feedback that amplifies the values of…
We introduce a generic scheme to perform non-perturbative linked cluster expansions in long-range ordered quantum phases. Clusters are considered to be surrounded by an ordered reference state leading to effective edge-fields in the exact…
Coupled cluster theory produced arguably the most widely used high-accuracy computational quantum chemistry methods. Despite the approach's overall great computational success, its mathematical understanding is so far limited to results…
Lascoux stated that the type A Kostka-Foulkes polynomials K_{lambda,mu}(t) expand positively in terms of so-called atomic polynomials. For any semisimple Lie algebra, the former polynomial is a t-analogue of the multiplicity of the dominant…
A new approach is presented to obtain candidate structures from atomic pair distribution function (PDF) data in a highly automated way. It fetches, from web-based structural databases, all the structures meeting the experimenter's search…
Atomic-resolution imaging with scanning transmission electron microscopy is a powerful tool for characterizing the nanoscale structure of materials, in particular features such as defects, local strains, and symmetry-breaking distortions.…
A wide class of coupled-cluster methods is introduced, based on Arponen's extended coupled-cluster theory. This class of methods is formulated in terms of a coordinate transformation of the cluster operators. The mathematical framework for…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
We extend the QCD Parton Model analysis by employing a factorized nuclear structure model that explicitly accounts for both individual nucleons and correlated nucleon pairs. This novel framework establishes a paradigm that directly links…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
Polynomial expansions are important in the analysis of neural network nonlinearities. They have been applied thereto addressing well-known difficulties in verification, explainability, and security. Existing approaches span classical Taylor…
The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…
The cluster expansion formalism used in materials science is reconstructed on an axiomatic basis with the aims of clarifying underlying concepts and improving computational procedures, and without using conventional cluster functions.…