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The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
A major challenge in single particle reconstruction methods using cryo-electron microscopy is to attain a resolution sufficient to interpret fine details in three-dimensional (3D) macromolecular structures. Obtaining high resolution 3D…
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our…
We derive the exact longitudinal plasmon dispersion relations, $\omega(k)$ of classical one and two dimensional Wigner crystals at T=0 from the real space equations of motion, of which properly accounts for the full unscreened Coulomb…
In this paper, we solve the linearized Poisson-Boltzmann equation, used to model the electric potential of macromolecules in a solvent. We derive a corrected trapezoidal rule with improved accuracy for a boundary integral formulation of the…
An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here, we present a calculation of the electric field on the solute-solvent interface that is exact…
The evaluation of Coulomb forces is a difficult task. The summations that are involved converge only conditionally and care has to be taken in selecting the appropriate procedure to define the limits. The Ewald method is a standard method…
We gain tight rigorous bounds on the renormalisation fixed point for period doubling in families of unimodal maps with degree $4$ critical point. We use a contraction mapping argument to bound essential eigenfunctions and eigenvalues for…
This work presents a fast and scalable approach for predicting surface stability and equilibrium crystal morphology in ionic materials using electrostatic analysis. The method constructs stoichiometric slab terminations and evaluates their…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
We introduce the study of frames and equiangular lines in classical geometries over finite fields. After developing the basic theory, we give several examples and demonstrate finite field analogs of equiangular tight frames (ETFs) produced…
We present several versions of Regularized Combined Field Integral Equation (CFIER) formulations for the solution of three dimensional frequency domain electromagnetic scattering problems with Perfectly Electric Conducting (PEC) boundary…
We consider error estimates in weak parametrised norms for stabilized finite element approximations of the two-dimensional Navier-Stokes' equations. These weak norms can be related to the norms of certain filtered quantities, where the…
We bound EFT coefficients appearing in $2 \to 2$ photon scattering amplitudes in four dimensions. After reviewing unitarity and positivity conditions in this context, we use dispersion relations and crossing symmetry to compute sum rules…
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…
We calculate the electroweak and QCD corrections to W-W+ -> tt and ZZ -> tt. We also consider the interplay of these corrections with the effect of anomalous interactions that affect the massive weak bosons and the top. The results at the…
We outline a 2D algorithm for solving incompressible flow--structure interaction problems for mixed rigid/soft body representations, within a consistent framework based on the remeshed vortex method. We adopt the one--continuum formulation…
We propose an immersed boundary scheme for the numerical resolution of the Complete Electrode Model in Electrical Impedance Tomography, that we use as a main ingredient in the resolution of inverse problems in medical imaging. Such method…