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MLIR has become popular since it was open sourced in 2019. A sub-project of LLVM, the flexibility provided by MLIR to represent Intermediate Representations (IR) as dialects at different abstraction levels, to mix these, and to leverage…
We present an algorithm for the numerical solution of nonlinear parabolic partial differential equations. This algorithm extends the classical Feynman-Kac formula to fully nonlinear partial differential equations, by using random trees that…
Algorithmic Differentiation (AD) can be used to automate the generation of derivatives in arbitrary software projects. This will generate maintainable derivatives, that are always consistent with the computation of the software. If a domain…
An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials $L^{(\alpha)}_n(z)$ are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic…
In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams. Highlights of the new version…
A discrete Fourier analysis associated with translation lattices is developed recently by the authors. It permits two lattices, one determining the integral domain and the other determining the family of exponential functions. Possible…
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,…
Maclaurin Integration is a new series-based technique for solving infamously difficult integrals in terms of elementary functions. It has fairly liberal conditions for sound use, making it one of the most versatile integration techniques.…
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…
We present FeynCalc 9.3, a new stable version of a powerful and versatile Mathematica package for symbolic quantum field theory (QFT) calculations. Some interesting new features such as highly improved interoperability with other packages,…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
TauREx 3 is the next generation of the TauREx exoplanet atmospheric retrieval framework for Windows, Mac, and Linux. It is a complete rewrite with a full Python stack that makes it easy-to-use, high-performance, dynamic, and flexible. The…
We present a family of Python modules for the numerical integration of ordinary, delay, or stochastic differential equations. The key features are that the user enters the derivative symbolically and it is just-in-time-compiled, allowing…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
We introduce a continuous-order integral analog of the Maclaurin expansion that reconstructs analytic functions from fractional derivative data. The operator integrates over continuous order, replacing the discrete sum of integer…
The polylogarithm function is one of the constellation of important mathematical functions. It has a long history, and many connections to other special functions and series, and many applications, for instance in statistical physics.…
A novel model of reversible computing, the $\aleph$-calculus, is introduced. It is declarative, reversible-Turing complete, and has a local term-rewriting semantics. Unlike previously demonstrated reversible term-rewriting systems, it does…
Definition packages in theorem provers provide users with means of defining and organizing concepts of interest. This system description presents a new definition package for the hybrid systems theorem prover KeYmaera X based on…
The last improvements in programming languages, programming models, and frameworks have focused on abstracting the users from many programming issues. Among others, recent programming frameworks include simpler syntax, automatic memory…
dlordinal is a new Python library that unifies many recent deep ordinal classification methodologies available in the literature. Developed using PyTorch as underlying framework, it implements the top performing state-of-the-art deep…