相关论文: Extrapolating Solution Paths of Polynomial Homotop…
The persistent homology transform (PHT) of a subset $M \subset \mathbb{R}^d$ is a map $\text{PHT}(M):\mathbb{S}^{d-1} \to \mathbf{Dgm}$ from the unit sphere to the space of persistence diagrams. This map assigns to each direction $v\in…
Understanding astrophysical and cosmological processes can be challenging due to their complexity and lack of intuitive analogies. To address this, we present \texttt{AstronomyCalc}, a Python package specifically designed to aid…
Nonlinear two-point boundary value problems arise in numerous areas of application. The existence and number of solutions for various cases has been studied from a theoretical standpoint. These results generally rely upon growth conditions…
The direct detection and characterization of planetary and substellar companions at small angular separations is a rapidly advancing field. Dedicated high-contrast imaging instruments deliver unprecedented sensitivity, enabling detailed…
This paper introduces pycvxset, a new Python package to manipulate and visualize convex sets. We support polytopes and ellipsoids, and provide user-friendly methods to perform a variety of set operations. For polytopes, pycvxset supports…
Bayesian Networks (BNs) are used in various fields for modeling, prediction, and decision making. pgmpy is a python package that provides a collection of algorithms and tools to work with BNs and related models. It implements algorithms for…
This paper presents a computationally efficient optimization algorithm for solving nonconvex optimal control problems that involve discrete logic constraints. Traditional solution methods for these constraints require binary variables and…
We introduce a new method to approximate Euclidean correlation functions by exponential sums. The Truncated Hankel Correlator (THC) method builds a Hankel matrix from the full correlator data available and truncates the eigenspectrum of…
Finding vacua for the four dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
Given a polynomial system f, a fundamental question is to determine if f has real roots. Many algorithms involving the use of infinitesimal deformations have been proposed to answer this question. In this article, we transform an approach…
The objective is to demonstrate the making of Ada software available to Python and Julia programmers using GPRbuild. GPRbuild is the project manager of the GNAT toolchain. With GPRbuild the making of shared object files is fully automated…
We consider the extension of the method of Gauss-Newton from complex floating-point arithmetic to the field of truncated power series with complex floating-point coefficients. With linearization we formulate a linear system where the…
Robust estimation provides essential tools for analyzing data that contain outliers, ensuring that statistical models remain reliable even in the presence of some anomalous data. While robust methods have long been available in R, users of…
Homotopy methods are attractive due to their capability of solving difficult optimisation and optimal control problems. The underlying idea is to construct a homotopy, which may be considered as a continuous (zero) curve between the…
Polynomial zonotopes, a non-convex set representation, have a wide range of applications from real-time motion planning and control in robotics, to reachability analysis of nonlinear systems and safety shielding in reinforcement learning.…
Algorithmic fairness has received considerable attention due to the failures of various predictive AI systems that have been found to be unfairly biased against subgroups of the population. Many approaches have been proposed to mitigate…
We describe CPMC-Lab, a Matlab program for the constrained-path and phaseless auxiliary-field Monte Carlo methods. These methods have allowed applications ranging from the study of strongly correlated models, such as the Hubbard model, to…
The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…
Quadratic eigenvalue problems (QEP) and more generally polynomial eigenvalue problems (PEP) are among the most common types of nonlinear eigenvalue problems. Both problems, especially the QEP, have extensive applications. A typical approach…