相关论文: TaylUR 3, a multivariate arbitrary-order automatic…

In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…

We introduce the Macaulay2 package GradedLieAlgebras for doing computations in graded Lie algebras presented by generators and relations.

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…

The goal of this thesis is threefold: first, to provide a general semantic setting for reasoning about incremental computation. Second, to establish and clarify the connection between derivatives in the incremental sense and derivatives in…

We present MXtalTools, a flexible Python package for the data-driven modelling of molecular crystals, facilitating machine learning studies of the molecular solid state. MXtalTools comprises several classes of utilities: (1) synthesis,…

Incremental processing is widely-adopted in many applications, ranging from incremental view maintenance, stream computing, to recently emerging progressive data warehouse and intermittent query processing. Despite many algorithms developed…

We present NanoFlux, a novel adversarial framework for generating targeted training data to improve LLM reasoning, where adversarially-generated datasets containing fewer than 200 examples outperform conventional fine-tuning approaches. The…

We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives.

We report on the higher-order differential calculus library developed inside the Lean mathematical library mathlib. To support a broad range of applications, we depart in several ways from standard textbook definitions: we allow arbitrary…

A large amount of numerically-oriented code is written and is being written in legacy languages. Much of this code could, in principle, make good use of data-parallel throughput-oriented computer architectures. Loo.py, a…

A program dedicated to the numerical solution of the evolution equations for twist-three multiparton correlation functions is presented. The solutions are obtained by direct integration on a discretized momentum fraction grid. Both flavor…

Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…

Z3-Noodler is a fork of Z3 that replaces its string theory solver with a custom solver implementing the recently introduced stabilization-based algorithm for solving word equations with regular constraints. An extensive experimental…

Multilayer perceptron (MLP) is a class of networks composed of multiple layers of perceptrons, and it is essentially a mathematical function. Based on MLP, we develop a new numerical method to find the extrema of functionals. As…

The Functional Machine Calculus (Heijltjes 2022) is an extension of the lambda-calculus that preserves confluent reduction and typed termination, while enabling both call-by-name and call-by-value reduction behaviour and encoding the…

Automatic differentiation (AD) is a range of algorithms to compute the numeric value of a function's (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular…

Algebraic differentiators have attracted much interest in recent years. Their simple implementation as classical finite impulse response digital filters and systematic tuning guidelines may help to solve challenging problems, including, but…

For many applications, we are unable to take full advantage of the potential massive parallelisation offered by supercomputers or cloud computing because it is too hard to work out how to divide up the computation task between processors in…

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…

Language model post-training is applied to refine behaviors and unlock new skills across a wide range of recent language models, but open recipes for applying these techniques lag behind proprietary ones. The underlying training data and…