Related papers: Cubic-scaling algorithm and self-consistent field …
Recently, Czumaj et.al. (arXiv 2017) presented a parallel (almost) $2$-approximation algorithm for the maximum matching problem in only $O({(\log\log{n})^2})$ rounds of the massive parallel computation (MPC) framework, when the memory per…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially…
In this work, a scalable algorithm for the approximate quantum state preparation problem is proposed, facing a challenge of fundamental importance in many topic areas of quantum computing. The algorithm uses a variational quantum circuit…
We explore unsolved nuclear structure problems related with the spin and isospin degree of freedom by using microscopic models which accommodate realistic isoscalar and isovector pairing interactions, and also tensor correlations. For the…
Electron collisions, described by stochastic differential equations (SDEs), were simulated using a second-order weak convergence algorithm. Using stochastic analysis, we constructed an SDE for energetic electrons in Lorentz plasma to…
A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the…
In Constrained Correlation Clustering, the goal is to cluster a complete signed graph in a way that minimizes the number of negative edges inside clusters plus the number of positive edges between clusters, while respecting hard constraints…
Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for \textit{ab initio} calculations of electronic correlation energies in solids and molecules. The method is an extension of the…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
We give new sublinear and parallel algorithms for the extensively studied problem of approximating n-variable r-CSPs (constraint satisfaction problems with constraints of arity r up to an additive error. The running time of our algorithms…
The Bundle Adjustment (BA) model is commonly optimized using a nonlinear least squares method, with the Levenberg-Marquardt (L-M) algorithm being a typical choice. However, despite the L-M algorithm's effectiveness, its sensitivity to…
Sparse Subspace Clustering (SSC) is a state-of-the-art method for clustering high-dimensional data points lying in a union of low-dimensional subspaces. However, while $\ell_1$ optimization-based SSC algorithms suffer from high…
We check the accuracy of the constrained random phase approximation (cRPA) downfolding scheme by considering one-dimensional two- and three-orbital Hubbard models with a target band at the Fermi level and one or two screening bands away…
A new formalism for calculation of the partition function of single stranded nucleic acids is presented. Secondary structures and the topology of structure elements are the level of resolution that is used. The folding model deals with…
This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…
We present a constrained Random Phase Approximation (cRPA) method, termed spectral cRPA (s-cRPA), and compare it to established cRPA approaches for Scandium and Copper by varying the 3d shell filling. The s-cRPA method generally produces…
Finding an approximate second-order stationary point (SOSP) is a well-studied and fundamental problem in stochastic nonconvex optimization with many applications in machine learning. However, this problem is poorly understood in the…
Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear…