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Lipid vesicles appear ubiquitously in biological systems. Understanding how the mechanical and intermolecular interations deform vesicle membrane is a fundamental question in biophysics. In this article we developed a fast algorithm to…
Fracton topological phases have a large number of materialized symmetries that enforce a rigid structure on their excitations. Remarkably, we find that the symmetries of a quantum error-correcting code based on a fracton phase enable us to…
In this paper, we report on very efficient algorithms for the spherical harmonic transform (SHT). Explicitly vectorized variations of the algorithm based on the Gauss-Legendre quadrature are discussed and implemented in the SHTns library…
This short paper is concerned with the use of spherical t-designs as optimal designs for the spherical harmonic regression model in three dimensions over a range of specified criteria. The nature of the designs is explored and their…
Numerical methods in spin-foam models have significantly advanced in the last few years, yet challenges remain in efficiently extracting results for amplitudes with many quantum degrees of freedom. In this paper we sketch a proposal for a…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
Numerical integration on spheres, including the computation of the areas of spherical triangles, is a core computation in geomathematics. The commonly used techniques sometimes suffer from instabilities and significant loss of accuracy. We…
In a previous article [J. Comp. Phys. $\mathbf{357}$ (2018) 282-304], the mixed mimetic spectral element method was used to solve the rotating shallow water equations in an idealized geometry. Here the method is extended to a smoothly…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…
Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the…
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…
The problem of polycube construction or deformation is an essential problem in computer graphics. In this paper, we present a robust, simple, efficient and automatic algorithm to deform the meshes of arbitrary shapes into their polycube…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
We generalize the concept of optical scattering matrix ($S$-matrix) to characterize harmonic generation and frequency mixing in planar metasurfaces in the limit of undepleted pump approximation. We show that the symmetry properties of such…
With the surge of multi- and manycores, much research has focused on algorithms for mapping and scheduling on these complex platforms. Large classes of these algorithms face scalability problems. This is why diverse methods are commonly…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
Symmetric polynomial quadrature rules for triangles are commonly used to efficiently integrate two-dimensional domains in finite-element-type problems. While the development of such rules focuses on the maximum degree a given number of…
Combinatorial algorithms are widely used for decision-making and knowledge discovery, and it is important to ensure that their output remains stable even when subjected to small perturbations in the input. Failure to do so can lead to…