相关论文: Orbital optimization in the perfect pairing hierar…

We present a novel method to compute unstable periodic orbits (UPOs) that optimize the infinite-time average of a given quantity for polynomial ODE systems. The UPO search procedure relies on polynomial optimization to construct nonnegative…

Perturbative approaches are methods to efficiently tackle many-body problems, offering both intuitive insights and analysis of correlation effects. However, their application to systems where light and matter are strongly coupled is…

We introduce new global and local inexact oracle concepts for a wide class of convex functions in composite convex minimization. Such inexact oracles naturally come from primal-dual framework, barrier smoothing, inexact computations of…

Quantum phase estimation (QPE) is a promising quantum algorithm for obtaining molecular ground-state energies with chemical accuracy. However, its computational cost, dominated by the Hamiltonian 1-norm $\lambda$ and the cost of the block…

This work studies optimal polynomial approximants (OPAs) in the classical Hardy spaces on the unit disk, $H^p$ ($1 < p < \infty$). For fixed $f\in H^p$ and $n\in\mathbb{N}$, the OPA of degree $n$ associated to $f$ is the polynomial which…

Optimal Bayesian design techniques provide an estimate for the best parameters of an experiment in order to maximize the value of measurements prior to the actual collection of data. In other words, these techniques explore the space of…

Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…

We present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation. The emphasis is on speed without compromising…

We define a class of "optimal" coordinate systems by requiring that the deviation from an exact Robertson-Walker metric is "as small as possible" within a given four dimensional volume. The optimization is performed by minimizing several…

Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…

The modern optical telescopes produce a huge number of asteroid observations, that are grouped into very short arcs (VSAs), each containing a few observations of the same object in one single night. To decide whether two VSAs, collected in…

This paper generalizes a previously-conceived, continuation-based optimization technique for scalar objective functions on constraint manifolds to cases of periodic and quasiperiodic solutions of delay-differential equations. A Lagrange…

The pairing symmetry of the newly proposed cobalt high temperature (high-$T_c$) superconductors formed by vertex shared cation-anion tetrahedral complexes is studied by the methods of mean field, random phase approximation (RPA) and…

Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…

Using the complete orthonormal sets of radial parts of nonrelativitistic exponential type orbitals (2,1, 0, 1, 2, ...) and spinor type tensor spherical harmonics of rank s the new formulae for the 2(2s+1)-component relativistic spinors…

Quantum chemistry is a key target for quantum computing, but benchmarking quantum algorithms for large molecular systems remains challenging due to the lack of exactly solvable yet structurally realistic models. In particular, molecular…

An accurate description of electron correlation is one of the most challenging problems in quantum chemistry. The exact electron correlation can be obtained by means of full configuration interaction (FCI). A simple strategy for…

Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…

We present an efficient implementation of the random phase approximation (RPA) for molecular systems within the domain-based local pair natural orbital (DLPNO) framework. With optimized parameters, DLPNO-RPA achieves approximately 99.9%…

If one has to attain high accuracy over long timescales during the numerical computation of the N-body problem, the method called Lie-integration is one of the most effective algorithms. In this paper we present a set of recurrence…