Related papers: A Non-Crossing Approximation for the Study of Inte…
This paper introduces a novel ansatz-based technique for solution of the Hubbard model over two length scales. Short range correlations are treated exactly using a dynamical cluster approximation QMC simulation, while longer-length-scale…
Dynamical quantum-cluster approaches, such as different cluster extensions of the dynamical mean-field theory (cluster DMFT) or the variational cluster approximation (VCA), combined with efficient cluster solvers, such as the quantum…
This study concerns the mean-clustering approach to modelling the evolution of lattice dynamics. Instead of tracking the state of individual lattice sites, this approach describes the time evolution of the concentrations of different…
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size.…
We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently…
We utilize numerical linked-cluster expansions (NLCEs) and the determinantal quantum Monte Carlo algorithm to study pairing correlations in the square lattice Hubbard model. To benchmark the NLCE, we first locate the finite-temperature…
In high-dimensional settings, Canonical Correlation Analysis (CCA) often fails, and existing sparse methods force an untenable choice between computational speed and statistical rigor. This work introduces a fast and provably consistent…
Statistical inference is central to many scientific endeavors, yet how it works remains unresolved. Answering this requires a quantitative understanding of the intrinsic interplay between statistical models, inference methods and data…
In this paper, we study the convergence rate of the DCA (Difference-of-Convex Algorithm), also known as the convex-concave procedure, with two different termination criteria that are suitable for smooth and nonsmooth decompositions…
This work introduces a reduced-order model for plate structures with periodic micro-structures by coupling self-consistent clustering analysis (SCA) with the Lippmann-Schwinger equation, enabling rapid multiscale homogenisation of…
Angular x-ray cross-correlation analysis (XCCA) is an approach to study the structure of disordered systems using the results of x-ray scattering experiments. In this paper we summarize recent theoretical developments related to the Fourier…
We explore different variants of the random phase approximation (RPA) to the correlation energy derived from closed-shell ring-diagram approximations to coupled cluster doubles theory. We implement these variants in range-separated…
The minimum sum-of-squares clustering problem (MSSC), also known as $k$-means clustering, refers to the problem of partitioning $n$ data points into $k$ clusters, with the objective of minimizing the total sum of squared Euclidean distances…
Clustering algorithms are fundamental tools across many fields, with density-based methods offering particular advantages in identifying arbitrarily shaped clusters and handling noise. However, their effectiveness is often limited by the…
The effect of disorder on lattice vibrational modes has been a topic of interest for several decades. In this work, we employ a Green's function based approach, namely the dynamical cluster approximation (DCA), to investigate phonons in…
Deep neural networks (DNNs) often produce overconfident out-of-distribution predictions, motivating Bayesian uncertainty quantification. The Linearized Laplace Approximation (LLA) achieves this by linearizing the DNN and applying Laplace…
Non-gaussian component analysis (NGCA) introduced in offered a method for high dimensional data analysis allowing for identifying a low-dimensional non-Gaussian component of the whole distribution in an iterative and structure adaptive way.…
We present a combination of local density approximation (LDA) with the dynamical cluster approximation (LDA+DCA) in the framework of the full-potential linear augmented plane-wave method, and compare our LDA+DCA results for SrVO$_3$ to LDA…
Motivation: Biomedical studies increasingly produce multi-view high-dimensional datasets (e.g., multi-omics) that demand integrative analysis. Existing canonical correlation analysis (CCA) and generalized CCA methods address at most two of…
We are commenting on the article Phys. Rev. {\bf B 65}, 155112 (2002) by G. Biroli and G. Kotliar in which they make a comparison between two cluster techniques, the {\it Cellular Dynamical Mean Field Theory} (CDMFT) and the {\it Dynamical…