Related papers: On capacity computation for symmetric polygonal co…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…
The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation…
We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn-Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In…
In this paper, we describe a framework to compute expected convergence rates for residuals based on the Calder\'on identities for general second order differential operators for which fundamental solutions are known. The idea is that these…
This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…
A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix…
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…
In this paper, we introduce the so-called multiscale limit for spectral curves, associated with real finite-gap Sine-Gordon solutions. This technique allows to solve the old problem of calculating the density of topological charge for real…
We derive a computable a posteriori error estimator for the $\alpha$-harmonic extension problem, which localizes the fractional powers of elliptic operators supplemented with Dirichlet boundary conditions. Our a posteriori error estimator…
This thesis develops signal-processing algorithms and implementation schemes under constraints of minimal parallelism and memory space, with the goal of improving energy efficiency of low-power computing hardware. We propose (i) a…
We examine the application of the recently developed dual basis methods of Head-Gordon and co-workers to double hybrid density functional computations. Using the B2-PLYP, B2GP-PLYP, DSD-BLYP and DSD-PBEP86 density functionals, we assess the…
Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the…
In this paper we consider eigenfunctions of the Laplacian on a planar domain with polygonal boundary with Dirichlet, Neumann, or mixed boundary conditions. The main result is a quantitative estimate on the $L^2$ mass of eigenfunctions near…
A novel approach to parallelize the well-known Hoshen-Kopelman algorithm has been chosen, suitable for simulating huge lattices in high dimensions on massively-parallel computers with distributed memory and message passing. This method…
The capacitance of the circular parallel plate capacitor is calculated by expanding the solution to the Love integral equation into a Fourier cosine series. Previously, this kind of expansion has been carried out numerically, resulting in…
Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of…
We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the…
In this note we extend previous work on efficiency corrections for cumulant measurements [1,2]. We will discuss the limitations of the methods presented in these papers. Specifically we will consider multiplicity dependent efficiencies as…
We present a comparison of different numerical techniques for the integration of variational equations. The methods presented can be applied to any autonomous Hamiltonian system whose kinetic energy is quadratic in the generalized momenta,…