Related papers: Fast computation of analytic capacity
We introduce a fast Fourier spectral method for the spatially homogeneous Boltzmann equation with non-cutoff collision kernels. Such kernels contain non-integrable singularity in the deviation angle which arise in a wide range of…
We show how finite limits and colimits can be calculated compositionally using the algebras of spans and cospans, and give as an application a proof of the Kleene Theorem on regular languages.
Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized…
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
We give new positive and negative results (some conditional) on speeding up computational algebraic geometry over the reals: (1) A new and sharper upper bound on the number of connected components of a semialgebraic set. Our bound is novel…
We present a method to considerably improve the numerical performance for solving Eliashberg-type coupled equations on the imaginary axis. Instead of the standard practice of introducing a hard numerical cutoff for treating the infinite…
Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous…
Clustering is one of the most fundamental and important tasks in data mining. Traditional clustering algorithms, such as K-means, assign every data point to exactly one cluster. However, in real-world datasets, the clusters may overlap with…
We construct a compact set whose continuous analytic capacity does not vary continuously under a certain holomorphic motion, thereby answering a question of Paul Gauthier. Our example is inspired by holomorphic dynamics and relies on the…
The adaptive spectral Koopman (ASK) method was introduced to numerically solve autonomous dynamical systems that lay the foundation of numerous applications across different fields in science and engineering. Although ASK achieves high…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
Let $(Z,d,\mu)$ be a compact, connected, Ahlfors $Q$-regular metric space with $Q>1$. Using a hyperbolic filling of $Z$, we define the notions of the $p$-capacity between certain subsets of $Z$ and of the weak covering $p$-capacity of path…
Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated…
Graphics Processing Units (GPUs) are employed for a numerical determination of the analytic structure of two-point correlation functions of Quantum Field Theories. These functions are represented through integrals in d-dimensional Euclidean…
This paper is concerned with the cubic Szeg\H{o} equation $$ i\partial_t u=\Pi(|u|^2 u), $$ defined on the $L^2$ Hardy space on the one-dimensional torus $\mathbb T$, where $\Pi: L^2(\mathbb T)\rightarrow L^2_+(\mathbb T)$ is the Szeg\H{o}…
We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…
We prove that the Bergman kernel function associated to a finitely connected domain in the plane is given as a rational combination of only three basic functions of one complex variable: an Alhfors map, its derivative, and one other…
We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe…
Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. Existing methods to compute smooth points on semi-algebraic sets use symbolic quantifier elimination tools.…
We present an integral equation-based method for the numerical solution of two-point boundary value systems. Special care is devoted to the mathematical formulation, namely the choice of the background Green's function that leads to a…