Related papers: Coupled cluster theory: Towards an algebraic geome…
We discuss computational aspects of the spherical coupled-cluster method specific to the nuclear many-body problem. Using chiral nucleon-nucleon interaction at next-to-next-to-next-to leading order (N3LO) with cutoff Lambda = 500MeV, we…
The distinguishable cluster approximation applied to coupled cluster doubles equations greatly improves absolute and relative energies. We apply the same approximation to the triples equations and demonstrate that it can also improve…
Cluster states are an essential component in one-way quantum computation protocols. We present two schemes to generate addressable continuous-variable cluster states from quadrature squeezed cylindrically polarized modes. By including…
In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…
We present the first formulation and application of relativistic unitary coupled cluster theory to atomic properties. The remarkable features of this theory are highlighted, and it is used to calculate the lifetimes of $5^{2}D_{3/2}$ and…
We present a diagrammatic notation to derive the quantum-electrodynamic coupled cluster (QED-CC) equations needed for the description for polaritonic ground and excited states. Our presented notation is a generalization of the existing…
Let $Q$ be a Dynkin quiver and $\Pi$ the corresponding set of positive roots. For the preprojective algebra $\Lambda$ associated to $Q$ we produce a rigid $\Lambda$-module $I_Q$ with $r=|\Pi|$ pairwise non-isomorphic indecomposable direct…
This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…
Convex clustering is an attractive clustering algorithm with favorable properties such as efficiency and optimality owing to its convex formulation. It is thought to generalize both k-means clustering and agglomerative clustering. However,…
We report an ongoing work on clustering algorithms for complex roots of a univariate polynomial $p$ of degree $d$ with real or complex coefficients. As in their previous best subdivision algorithms our root-finders are robust even for…
The author introduces the notion of a quantum form of an algebraic torus. In the case of diagonal algebraic torus we get the algebra of Laurent twisted polynomials. Quantum algebraic torus can be characterized in terms of exact sequences.…
We construct two bases for each cluster algebra coming from a triangulated surface without punctures. We work in the context of a coefficient system coming from a full-rank exchange matrix, for example, principal coefficients.
Clustering is one of the main tasks in exploratory data analysis and descriptive statistics where the main objective is partitioning observations in groups. Clustering has a broad range of application in varied domains like climate,…
The past several years have seen renewed interest in the use of symmetry-projected Hartree-Fock for the description of strong correlations. Unfortunately, these symmetry-projected mean-field methods do not adequately account for dynamic…
We introduce a novel class of coupled cluster (CC) methods that leverage the seniority concept to enhance efficiency and accuracy in electronic structure calculations. While existing approaches, such as the pair coupled cluster doubles…
We consider a new formulation of the stochastic coupled cluster method in terms of the similarity transformed Hamiltonian. We show that improvement in the granularity with which the wavefunction is represented results in a reduction in the…
Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges…
We give a geometric interpretation of cluster varieties in terms of blowups of toric varieties. This enables us to provide, among other results, an elementary geometric proof of the Laurent phenomenon for cluster algebras (of geometric…
We study Newton polytopes for cluster variables in cluster algebras $\mathcal{A}(\Sigma)$ of types A and D. A famous property of cluster algebras is the Laurent phenomenon: each cluster variable can be written as a Laurent polynomial in the…