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The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have…
In this paper we develop an evolution of the $C^1$ virtual elements of minimal degree for the approximation of the Cahn-Hilliard equation. The proposed method has the advantage of being conforming in $H^2$ and making use of a very simple…
We show how to extract a monotonic learning algorithm from a classical proof of a geometric statement by interpreting the proof by means of interactive realizability, a realizability sematics for classical logic. The statement is about the…
Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic…
A real symmetric matrix (resp., tensor) is said to be copositive if the associated quadratic (resp., homogeneous) form is greater than or equal to zero over the nonnegative orthant. The problem of detecting their copositivity is NP-hard.…
While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this paper we present and study the logic rLTL which provides a means to formally reason about both correctness and…
This work explores the potential of spatial model checking of polyhedral models on a number of selected examples. In computer graphics polyhedral models can be found in the form of triangular surface meshes of tetrahedral volume meshes…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
Hybrid density functional calculation is indispensable to accurate description of electronic structure, whereas the formidable computational cost restricts its broad application. Here we develop a deep equivariant neural network method…
This paper reviews the standard algorithm for converting spacecraft state vectors to Keplerian orbital elements with a focus on its computer implementation. It analyzes the shortcomings of the scheme as described in the literature, and…
A set $S \subset \mathbb{Z}^d$ is digital convex if $conv(S) \cap \mathbb{Z}^d = S$, where $conv(S)$ denotes the convex hull of $S$. In this paper, we consider the algorithmic problem of testing whether a given set $S$ of $n$ lattice points…
This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element approximation. The stopping criterion consists of the evaluations…
Edge (or N\'ed\'elec) finite elements are theoretically sound and widely used by the computational electromagnetics community. However, its implementation, specially for high order methods, is not trivial, since it involves many…
Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
We present a new set of basis functions for H(curl)-conforming, H(div)-conforming, and L2 -conforming finite elements of arbitrary order on a tetrahedron. The basis functions are expressed in terms of Bernstein polynomials and augment the…
A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack…
In 2011, Aaronson gave a striking proof, based on quantum linear optics, showing that the problem of computing the permanent of a matrix is #P-hard. Aaronson's proof led naturally to hardness of approximation results for the permanent, and…
Exact scientific discovery requires more than heuristic search: candidate constructions must be turned into exact objects and checked independently. We address this gap by extending TeXRA with an independent Lean 4 verification layer,…
A key question in evaluation of computer models is Does the computer model adequately represent reality? A six-step process for computer model validation is set out in Bayarri et al. [Technometrics 49 (2007) 138--154] (and briefly…