相关论文: hankel: A Python library for performing simple and…

Recent research in mechanistic interpretability has attempted to reverse-engineer Transformer models by carefully inspecting network weights and activations. However, these approaches require considerable manual effort and still fall short…

We present numerical methods based on the fast Fourier transform (FFT) to solve convolution integral equations on a semi-infinite interval (Wiener-Hopf equation) or on a finite interval (Fredholm equation). We extend and improve a FFT-based…

Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…

In this paper, a new method to compute a B\'ezier curve of degree n = 2m-1 is introduced, here formulated as a set of points whose coordinates are calculated from two Hankel forms in $\C^m$. From Vandermonde factorizations of the two…

Some idea, which leads to a non-trivial solution of the quantum four-simplex equation, is exposed in this paper. We call this idea "pentagonal algebra". Few examples of the realisation of this idea are given here, and thus few examples of…

PyKOALA is an innovative Python-based library designed to provide a robust and flexible framework for Integral Field Spectroscopy (IFS) data reduction. By addressing the complexities of transforming raw measurements into scientifically…

The Object Constraint Language (OCL) has been widely used in the modeling community to complement software models for precisely defining constraints and business rules for the modeled systems. There is a limited number of tools supporting…

We present a cross-language C++/Python program for simulations of quantum mechanical systems with the use of Quantum Monte Carlo (QMC) methods. We describe a system for which to apply QMC, the algorithms of variational Monte Carlo and…

OpenML is an online platform for open science collaboration in machine learning, used to share datasets and results of machine learning experiments. In this paper we introduce OpenML-Python, a client API for Python, opening up the OpenML…

Image triangulation, the practice of decomposing images into triangles, deliberately employs simplification to create an abstracted representation. While triangulating an image is a relatively simple process, difficulties arise when…

In this paper, a new python package (optipoly) is described that solves box-constrained optimization problem over multivariate polynomial cost functions. The principle of the algorithm is described before its performance is compared to…

I describe the design, implementation, and usage of galpy, a Python package for galactic-dynamics calculations. At its core, galpy consists of a general framework for representing galactic potentials both in Python and in C (for accelerated…

In this article, we give a brief overview of the current state and future potential of symbolic computation within the Python statistical modeling and machine learning community. We detail the use of miniKanren as an underlying framework…

The Fourier transforms of polyhedral cones can be used, via Brion's theorem, to compute various geometric quantities of polytopes, such as volumes, moments, and lattice-point counts. We present a novel method of computing these conic…

This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…

Integrals involving highly oscillatory Bessel functions are notoriously challenging to compute using conventional integration techniques. While several methods are available, they predominantly cater to integrals with at most a single…

A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…

In this paper, we develop a Monte Carlo method for solving PDEs involving an integral fractional Laplacian (IFL) in multiple dimensions. We first construct a new Feynman-Kac representation based on the Green function for the fractional…

Creating and maintaining computer readable geometries for use in Monte Carlo Radiation Transport (MCRT) simulations is an error-prone and time-consuming task. Simulating a system often requires geometry from different sources and modelling…

This paper discusses a Python interface for the recently published DUNE-FEM-DG module which provides highly efficient implementations of the Discontinuous Galerkin (DG) method for solving a wide range of non linear partial differential…