Related papers: Solving Polynomial Systems with phcpy
We present pyroomacoustics, a software package aimed at the rapid development and testing of audio array processing algorithms. The content of the package can be divided into three main components: an intuitive Python object-oriented…
BayesPy is an open-source Python software package for performing variational Bayesian inference. It is based on the variational message passing framework and supports conjugate exponential family models. By removing the tedious task of…
This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components…
This paper introduces and evaluates a freely available cellular nonlinear network simulator optimized for the effective use of GPUs, to achieve fast modelling and simulations. Its relevance is demonstrated for several applications in…
Particle-in-cell methods couple mesh-based methods for the solution of continuum mechanics problems, with the ability to advect and evolve particles. They have a long history and many applications in scientific computing. However, they have…
Polynomial system solving has seen major progress in both theory and practice over the past decade. A landmark achievement was addressing Smale's 17th problem, establishing average-case polynomial-time algorithms for computing approximate…
Simulation is a foundational tool for the analysis and testing of cyber-physical systems (CPS), underpinning activities such as algorithm development, runtime monitoring, and system verification. As CPS grow in complexity and scale,…
With the growing complexity and capability of contemporary robotic systems, the necessity of sophisticated computing solutions to efficiently handle tasks such as real-time processing, sensor integration, decision-making, and control…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
Speedup measures how much faster we can solve the same problem using many cores. If we can afford to keep the execution time fixed, then quality up measures how much better the solution will be computed using many cores. In this paper we…
ipie is a Python-based auxiliary-field quantum Monte Carlo (AFQMC) package that has undergone substantial improvements since its initial release [J. Chem. Theory Comput., 2023, 19(1): 109-121]. This paper outlines the improved modularity…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…
Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established as the third pillar of discovery, alongside theory and experiment. Meanwhile, the performance of computing hardware grows through…
This paper introduces PolyDiM, an open-source C++ library tailored for the development and implementation of polytopal discretization methods for partial differential equations. The library provides robust and modular tools to support…
Molecular simulations are an important tool for research in physics, chemistry, and biology. The capabilities of simulations can be greatly expanded by providing access to advanced sampling methods and techniques that permit calculation of…
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…
Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems. However, current numerical methods lack parallel computation capabilities across varying conditions, severely limiting…
The open-source PyNX toolkit [Favre-Nicolin et al (2011) arXiv:1010.2641, Mandula et al (2016)] has been extended to provide tools for coherent X-ray imaging data analysis and simulation. All calculations can be executed on graphical…
Mechanistic models are important tools to describe and understand biological processes. However, they typically rely on unknown parameters, the estimation of which can be challenging for large and complex systems. We present pyPESTO, a…
Modern scientific software stacks have become extremely complex, using many programming models and libraries to exploit a growing variety of GPUs and accelerators. Package managers can mitigate this complexity using dependency solvers, but…