Related papers: A Mathematica program for numerically computing re…
We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in several variables. For fixed multi-degrees we determine the…
The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP.…
Let $S\subset R^n$ be a compact basic semi-algebraic set defined as the real solution set of multivariate polynomial inequalities with rational coefficients. We design an algorithm which takes as input a polynomial system defining $S$ and…
Let $\Omega$ be a bounded domain of $\mathbb{R}^3$ whose closure $\overline{\Omega}$ is polyhedral, and let $\mathcal{T}$ be a triangulation of $\overline{\Omega}$. Assuming that the boundary of $\Omega$ is sufficiently regular, we provide…
We describe an algorithm to count the number of rational points of an hyperelliptic curve defined over a finite field of odd characteristic which is based upon the computation of the action of the Frobenius morphism on a basis of the…
Numerical studies of the dynamics of gravitational systems, e.g., black hole-neutron star systems, require physical and constraint-satisfying initial data. In this article, we present the newly developed pseudo-spectral code Elliptica, an…
Starting from a Hamiltonian description of four dimensional general relativity in presence of a cosmological constant we perform the program of canonical quantisation. This is done using complex Ashtekar variables while keeping the…
We describe a technique to analytically compute the multipole moments of a charge distribution confined to a planar triangle, which may be useful in solving the Laplace equation using the fast multipole boundary element method (FMBEM) and…
We show how the fixed-spin asymptotics of the EPRL model can be used to perform the spin-sum for spin foam amplitudes defined on fixed two-complexes without interior faces and contracted with coherent spin-network states peaked on a…
In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…
We present a fully analytic approach for evaluating boundary integrals in two dimensions for Smoothed Particle Hydrodynamics (SPH). Conventional methods often rely on boundary particles or wall re-normalization approaches derived from…
We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with curved boundary elements. These are based on the computation of the preimage of the singularity in the…
Computing accurate splines of degree greater than three is still a challenging task in today's applications. In this type of interpolation, high-order derivatives are needed on the given mesh. As these derivatives are rarely known and are…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
The main purpose of this article is to facilitate the implementation of space-time finite element methods in four-dimensional space. In order to develop a finite element method in this setting, it is necessary to create a numerical…
Point cloud reconstruction from raw point cloud has been an important topic in computer graphics for decades, especially due to its high demand in modeling and rendering applications. An important way to solve this problem is establishing a…
We study boundary criticality at the Nishimori multicritical point of the two-dimensional (2D) random-bond Ising model. Using tensor-network methods, we construct a family of microscopic boundary conditions that incorporates both…
Critical points mark locations in the domain where the level-set topology of a scalar function undergoes fundamental changes and thus indicate potentially interesting features in the data. Established methods exist to locate and relate such…
We study higher critical points of the variational functional associated with a free boundary problem related to plasma confinement. Existence and regularity of minimizers in elliptic free boundary problems have already been studied…
Positive geometries provide a modern approach for computing scattering amplitudes in a variety of physical models. In order to facilitate the exploration of these new geometric methods, we introduce a Mathematica package called…