Related papers: pySecDec: a toolbox for the numerical evaluation o…

The computation of exact barycenters for a set of discrete measures is of interest in applications where sparse solutions are desired, and to assess the quality of solutions returned by approximate algorithms and heuristics. The task is…

An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…

Intersection numbers are rational scalar products among functions that admit suitable integral representations, such as Feynman integrals. Using these scalar products, the decomposition of Feynman integrals into a basis of linearly…

Ladder Logics is a programming language standardized in IEC 61131-3 and widely used for programming industrial Programmable Logic Controllers (PLC). A PLC program consists of inputs (whose values are given at runtime by factory sensors),…

In semidefinite programming (SDP), a number of pre-processing techniques have been developed including chordal-completion procedures, which reduce the dimension of individual constraints by exploiting sparsity therein, and facial reduction,…

The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…

Deep Feynman-Kac method was first introduced to solve parabolic partial differential equations(PDE) by Beck et al. (SISC, V.43, 2021), named Deep Splitting method since they trained the Neural Networks step by step in the time direction. In…

Python is known to be a versatile language, well suited both for beginners and advanced users. Some elements of the language are easier to understand than others: some are found in any kind of code, while some others are used only by…

This paper presents an overview of the functionalities and applications of Exasim, an open-source code for generating high-order discontinuous Galerkin codes to numerically solve parametrized partial differential equations (PDEs). The…

The SPaCIFY project, which aims at bringing advances in MDE to the satellite flight software industry, advocates a top-down approach built on a domain-specific modeling language named Synoptic. In line with previous approaches to real-time…

This manual describes a set of utilities developed for Lattice QCD computations. They are collectively called QCDUtils. They comprise a set of Python programs each of them with a specific function: download gauge ensembles from the public…

We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…

partycls is a Python framework for cluster analysis of systems of interacting particles. By grouping particles that share similar structural or dynamical properties, partycls enables rapid and unsupervised exploration of the system's…

Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the…

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational…

In this paper, we present version 2.0 of cashocs. Our software automates the solution of PDE constrained optimization problems for shape optimization and optimal control. Since its inception, many new features and useful tools have been…

In this paper we present a new release of the FIESTA program (Feynman Integral Evaluation by a Sector decomposiTion Approach). FIESTA5 is performance-oriented - we implemented improvements of various kinds in order to make Feynman integral…

This note provides a lightweight tutorial on using Eigen, a C++ template library for linear algebra, to implement statistical and machine learning algorithms. The emphasis is practical rather than methodological: we show how common matrix…

We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two…

In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…