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We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…
We explore a new method to calculate the valence light-front wave function of a system of two interacting particles, which is based on contour deformations combined with analytic continuation methods to project the Bethe-Salpeter wave…
The low-energy structure of hadrons can be described systematically using effective field theory, and the parameters of the effective theory can be determined from lattice QCD computations. Recent work, however, points to inconsistencies…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
Site diluted spin-1/2 Ising and spin-1 Blume Capel (BC) models in the presence of transverse field interactions are examined by introducing an effective-field approximation that takes into account the multi-site correlations in the cluster…
This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…
This article is concerned with tensor field tomography in a fairly general setting, that takes refraction, attenuation and time-dependence of tensor fields into account. The mathematical model is given by attenuated ray transforms of the…
The figure of merit, ZT, for a one-dimensional conductor displaying a Lorentzian resonant transmission probability is calculated. The optimum working conditions for largest ZT values are determined. It is found that, the resonance energy…
Flat beams -- beams with asymmetric transverse emittances -- have important applications in novel light-source concepts, advanced-acceleration schemes and could possibly alleviate the need for damping rings in lepton colliders. Over the…
Optimum ground states are constructed in two dimensions by using so called vertex state models. These models are graphical generalizations of the well-known matrix product ground states for spin chains. On the hexagonal lattice we obtain a…
In this work we generalise the adjoint method of inverse design to nonreciprocal media. As a test case, we use three-dimensional topology optimization via the level-set method to optimise one-way energy transfer for point-like source and…
We analyze the mixed frame equations of radiation hydrodynamics under the approximations of flux-limited diffusion and a thermal radiation field, and derive the minimal set of evolution equations that includes all terms that are of leading…
It is common to manufacture an object by decomposing it into parts that can be assembled. This decomposition is often required by size limits of the machine, the complex structure of the shape, etc. To make it possible to easily assemble…
The focus of this paper is on the analysis of the Conjugate Gradient method applied to a non-symmetric system of linear equations, arising from a Fast Fourier Transform-based homogenization method due to (Moulinec and Suquet, 1994).…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger…
Lattice calculations of hadronic observables are aggravated by short-distance fluctuations. The gradient flow, which can be viewed as a particular realisation of the coarse-graining step of momentum space RG transformations, proves a…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…
First-order optimization algorithms, often preferred for large problems, require the gradient of the differentiable terms in the objective function. These gradients often involve linear operators and their adjoints, which must be applied…