Related papers: Numerical linked cluster expansions for inhomogene…
A new approximation hierarchy, called the LPSUB$m$ scheme, is described for the coupled cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-1/2…
The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as…
In this work we present a clustering technique called \textit{multi-level conformal clustering (MLCC)}. The technique is hierarchical in nature because it can be performed at multiple significance levels which yields greater insight into…
Well-spread samples are desirable in many disciplines because they improve estimation when target variables exhibit spatial structure. This paper introduces an integrated methodological framework for spreading samples over the population's…
Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially…
In the era of data-driven science, conducting computational experiments that involve analysing large datasets using heterogeneous computational clusters, is part of the everyday routine for many scientists. Moreover, to ensure the…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
We present the spectral analysis of a one-dimensional Hubbard model with a parabolic potential, using a real-space cluster perturbation theory (rCPT) designed to study spatially inhomogeneous electron systems with strong correlation. It is…
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…
The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…
In the realm of big data, discerning patterns in nonlinear systems affected by external control inputs is increasingly challenging. Our approach blends the coarse-graining strengths of centroid-based unsupervised clustering with the clarity…
Purpose: The primary goal of this study is to explore the application of evaluation metrics to different clustering algorithms using the data provided from the Canadian Longitudinal Study (CLSA), focusing on cognitive features. The…
We propose a novel method for numerical modeling of spatially inhomogeneous moment dynamics of populations with nonlocal dispersal and competition in continuous space. It is based on analytically solvable decompositions of the time…
We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from…
Several perspectives of the cluster Gutzwiller method are briefly discussed. I show that the cluster mean-field method can be used for large inhomogeneous lattices, for computing local excitations, and for the time evolution of correlated…
We often seek to estimate the impact of an exposure naturally occurring or randomly assigned at the cluster-level. For example, the literature on neighborhood determinants of health continues to grow. Likewise, community randomized trials…
We apply the microscopic coupled-cluster method (CCM) to the spin-$1\over2$ $XXZ$ models on both the one-dimensional chain and the two-dimensional square lattice. Based on a systematic approximation scheme of the CCM developed by us…
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.…
The spreading of entanglement in out-of-equilibrium quantum systems is currently at the centre of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we…
Modern data-driven and distributed learning frameworks deal with diverse massive data generated by clients spread across heterogeneous environments. Indeed, data heterogeneity is a major bottleneck in scaling up many distributed learning…