Related papers: A Parametric Interpolation Framework for 1D Scalar…
We study Hamamoto's expanding square argument towards a 1-D minimisation problem related to the sharp solenoidal uncertainty principle. Working in the right function space, we recast the involved interpolation type inequality into an exact…
We study properties of the minimal surface in the Area Law Solution \cite{M93}, \cite{M19a}, \cite{M19b}. We find out that Area Law holds exactly for 2D turbulence as well as for arbitrary planar loop in higher dimensions. This relies on…
A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian…
Histopolation is the approximation procedure that associates a degree $ d-1 $ polynomial $ p_{d-1} \in \mathscr{P}_{d-1} (I) $ with a locally integrable function $ f $ imposing that the integral (or, equivalently, the average) of $p$…
We propose Parameter Space Analysis through Guided Visual Interpolations (ParamInter), a novel tool for high-dimensional input parameter space analysis by making interpolation towards optimal parameter sets explorable using guided…
We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
In this paper we show how ideas from spline theory can be used to construct a local basis for the space of translates of a general iterated Brownian Bridge kernel $k_{\beta,\varepsilon}$ for $\beta\in\mathbb{N}$, $\varepsilon\geq 0$. In the…
In this paper, we introduce a superconvergent approximation method that employs radial basis functions (RBFs) in the numerical solution of conservation laws. The use of RBFs for interpolation and approximation is a well developed area of…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. This best…
Given an overcomplete dictionary $A$ and a signal $b$ that is a linear combination of a few linearly independent columns of $A$, classical sparse recovery theory deals with the problem of recovering the unique sparse representation $x$ such…
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…
In this paper we derive a Gauss-Bonnet formula for the renormalized area of Graham-Witten minimal hypersurfaces of 5-dimensional Poincar\'e-Einstein spaces. The formula we derive expresses the renormalized area in terms of integrals of…
We obtain a result concerning the stability under the interpolation with functional parameter method for the approximation spaces of Lorentz-Marcinkiewicz type and also for the approximation spaces generated by symmetric norming functions…
Using very long baseline interferometry, the Event Horizon Telescope (EHT) collaboration has resolved the shadows of two supermassive black holes. Model comparison is traditionally performed in image space, where imaging algorithms…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
We consider the classical problem of finding the sparse representation of a signal in a pair of bases. When both bases are orthogonal, it is known that the sparse representation is unique when the sparsity $K$ of the signal satisfies…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…