Related papers: LSJK - a C++ library for arbitrary-precision numer…
Next-to-leading logarithmic final-state resummed predictions have traditionally been calculated, manually, separately for each observable. In this article we derive NLL resummed results for generic observables. We highlight and discuss the…
This paper studies the approximation of generalized ridge functions, namely of functions which are constant along some submanifolds of $\mathbb{R}^N$. We introduce the notion of linear-sleeve functions, whose function values only depend on…
We propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the normalized B-basis of a user-specified extended Chebyshev (EC) space that…
The article deals with a kind of recursive function templates in C++, where the recursion is realized corresponding template parameters to achieve better computational performance. Some specialization of these template functions ends the…
Solving linear systems of polynomial equations is a ubiquitous problem in both mathematics and physics. The standard approach, Gaussian elimination, scales cubically with system size and often constitutes a computational bottleneck. The…
This work proposes a methodology to develop new numerical integration algorithms for ordinary differential equations based on state quantization, generalizing the notions of Linearly Implicit Quantized State Systems (LIQSS) methods. Using…
Program termination is a hot research topic in program analysis. The last few years have witnessed the development of termination analyzers for programming languages such as C and Java with remarkable precision and performance. These…
A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar $\phi ^{3}\oplus \phi ^{4}$ theory, is presented. The representation…
In the very near future the first data from LHC will be available. The searches for the Higgs boson and for new physics will require precise predictions both for the signal and the background processes. Tree level calculations typically…
We study functional clones, which are sets of non-negative pseudo-Boolean functions (functions $\{0,1\}^k\to\mathbb{R}_{\geq 0}$) closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice…
We present FUEL (Fractional Universal Evaluation Library), a C++ library for performing rational function arithmetic with a flexible choice of third-party computer algebra systems as simplifiers. FUEL is an outgrowth of a C++ interface to…
Lagrange coded computation (LCC) is essential to solving problems about matrix polynomials in a coded distributed fashion; nevertheless, it can only solve the problems that are representable as matrix polynomials. In this paper, we propose…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
The development of the mlpack C++ machine learning library (http://www.mlpack.org/) has required the design and implementation of a flexible, robust optimization system that is able to solve the types of arbitrary optimization problems that…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
In this paper, we obtain various series and asymptotic expansions involving the modified Bessel function of the second kind for the normal inverse Gaussian cumulative distribution function. The new expansions accelerate computations,…
In real world, large language models (LLMs) can serve as the assistant to help users accomplish their jobs, and also support the development of advanced applications. For the wide application of LLMs, the inference efficiency is an…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…