Related papers: On Reconstructing Conservative and Primitive Varia…
When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For…
Ideal systems like MHD and Euler flow may develop singularities in vorticity (w = curl v). Viscosity and resistivity are dissipative regularizations. We propose a minimal, local, conservative, nonlinear, dispersive regularization of…
Optimization of unitary transformations in Variational Quantum Algorithms benefits highly from efficient evaluation of cost function gradients with respect to amplitudes of unitary generators. We propose several extensions of the…
Suppose that we observe $y \in \mathbb{R}^n$ and $X \in \mathbb{R}^{n \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 \beta^* +\epsilon \\ X & = & X_0 + W, \end{eqnarray*} where $X_0$ is an $n \times m$…
Electronic structure of layered van der Waals ferromagnet CrI$_{3}$ is studied with self consistent diagrammatic approaches beyond GW approximation. Considerable improvement in the calculated band gap as compared to the non-self-consistent…
We introduce a data-driven framework for approximating the convex set of $N$-representable two-electron reduced density matrices (2-RDMs). Traditional approaches characterize this set through linear matrix inequalities that define its…
We calculate the first-order (in the mass-ratio) metric perturbation produced by a small body on an eccentric, precessing bound orbit about a Kerr black hole. We reconstruct the metric perturbation from the maximal spin-weight Weyl scalars,…
Airborne LiDAR (Light Detection and Ranging) data is widely applied in building reconstruction, with studies reporting success in typical buildings. However, the reconstruction of curved buildings remains an open research problem. To this…
The aim of this paper is to establish several deep theoretical properties of principal component analysis for multiple-component spike covariance models. Our new results reveal a surprising asymptotic conical structure in critical sample…
For a nonnegative symmetric weakly irreducible tensor, its spectral radius is an eigenvalue corresponding to a unique positive eigenvector up to a scalar called the Perron vector. But including the Perron vector, there may have more than…
We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could be…
Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when: i) the feasible set is a…
We develop a unified spectral-semigroup framework that connects real-time and imaginary-time quantum dynamics through analytic continuation. Within this formulation, evolution is expressed as an exponential reweighting of spectral…
In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the…
Electron cryomicroscopy (cryo-EM) is a technique in structural biology used to reconstruct accurate volumetric maps of molecules. One step of the cryo-EM pipeline involves solving an inverse-problem. This inverse-problem, referred to as…
Despite advances in deep probabilistic models, learning discrete latent representations remains challenging. This work introduces a novel method to improve inference in discrete Variational Autoencoders by reframing the inference problem…
This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the…
Sharp comparison theorems are derived for all eigenvalues of the (weighted) Laplacian, for various classes of weighted-manifolds (i.e. Riemannian manifolds endowed with a smooth positive density). Examples include Euclidean space endowed…
There are different measures to classify a network's data set that, depending on the problem, have different success. For example, the resistance distance and eigenvector centrality measures have been successful in revealing ecological…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…