Related papers: Computing with B-series
Linear discriminant analysis (LDA) is a powerful tool in building classifiers with easy computation and interpretation. Recent advancements in science technology have led to the popularity of datasets with high dimensions, high orders and…
The consideration of stochastic uncertainty in optimal and predictive control is a well-explored topic. Recently Polynomial Chaos Expansions (PCE) have received considerable attention for problems involving stochastically uncertain system…
Merly.jl is a package for creating web applications in Julia. It presents features such as the creation of endpoints with function notation and with macro notation, handling of static files, use of path parameters, processing of data sent…
We present ADerrors.jl, a software for linear error propagation and analysis of Monte Carlo data. Although the focus is in data analysis in Lattice QCD, where estimates of the observables have to be computed from Monte Carlo samples, the…
The demand for high-performance computing (HPC) is ever-increasing for everyday statistical computing purposes. The downside is that we need to write specialized code for each HPC environment. CPU-level parallelization needs to be…
This paper proposes integrating Aspect-oriented Programming (AOP) into Julia, a language widely used in scientific and High-Performance Computing (HPC). AOP enhances software modularity by encapsulating cross-cutting concerns, such as…
We present Bill2d, a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. Bill2d can be used for various billiard and diffusion problems with one or more charged particles with interactions,…
We present a Julia-based interface to the precompiled HALLaR and cuHALLaR binaries for large-scale semidefinite programs (SDPs). Both solvers are established as fast and numerically stable, and accept problem data in formats compatible with…
Evaluation of relativistic molecular integrals over exponential-type spinor orbitals require using the relativistic auxiliary functions in prolate spheroidal coordinates. They have derived recently by the author [Physical Review E 91,…
This article proposes an artistic approach to increase and enrich the understanding of Julia Sets. This approach includes the mathematical, the playful, the artistic and the computational dimensions. It is argued that these four dimensions…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
AcceleratedKernels.jl is introduced as a backend-agnostic library for parallel computing in Julia, natively targeting NVIDIA, AMD, Intel, and Apple accelerators via a unique transpilation architecture. Written in a unified, compact…
We show that under the definition of computability which is natural from the point of view of applications, there exist non-computable quadratic Julia sets.
bde is a user-friendly Python package for Bayesian Deep Ensembles with a particular focus on tabular data. Built on an efficient JAX implementation of the sampling-based inference method Microcanonical Langevin Ensembles (MILE), it provides…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
BlackJAX is a library implementing sampling and variational inference algorithms commonly used in Bayesian computation. It is designed for ease of use, speed, and modularity by taking a functional approach to the algorithms' implementation.…
We show that there exist real parameters $c$ for which the Julia set $J_c$ of the quadratic map $z^2+c$ has arbitrarily high computational complexity. More precisely, we show that for any given complexity threshold $T(n)$, there exist a…
Taylor series methods show a newfound promise for the solution of non-stiff ordinary differential equations (ODEs) given the rise of new compiler-enhanced techniques for calculating high order derivatives. In this paper we detail a new…
This paper introduces \textsc{FuzzyLogic.jl}, a Julia library to perform fuzzy inference. The library is fully open-source and released under a permissive license. The core design principles of the library are: user-friendliness,…
We present a straightforward approach for distributed parallelization of stencil-based xPU applications on a regular staggered grid, which is instantiated in the package ImplicitGlobalGrid.jl. The approach allows to leverage remote direct…