Related papers: LSJK - a C++ library for arbitrary-precision numer…
Traditional machine learning is generally treated as a black-box optimization problem and does not typically produce interpretable functions that connect inputs and outputs. However, the ability to discover such interpretable functions is…
Some problems related to construction of the epsilon-expansion of dimensionally regulated Feynman integrals are discussed. For certain classes of diagrams, an arbitrary term of the epsilon-expansion can be expressed in terms of log-sine…
Integer relation algorithms can convert numerical results for Feynman integrals to exact evaluations, when one has reason to suspect the existence of reductions to linear combinations of a basis, with rational or algebraic coefficients.…
We describe a C++ program that we have written and made available for calculating the evolution of interacting scalar fields in an expanding universe. The program is particularly useful for the study of reheating and thermalization after…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
We introduce Merlion, an open-source machine learning library for time series. It features a unified interface for many commonly used models and datasets for anomaly detection and forecasting on both univariate and multivariate time series,…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
We introduce FunKit, a Mathematica package for the derivation and tracing of functional equations from arbitrary master equations. FunKit provides an expression vocabulary and a set of rules that allow for derivations in any given field…
Horn functions form a subclass of Boolean functions and appear in many different areas of computer science and mathematics as a general tool to describe implications and dependencies. Finding minimum sized representations for such functions…
Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems…
An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer--Poincar\'e letters is presented. These quantities emerge in analytic single and multi--scale Feynman diagram calculations. To…
ZKCM is a C++ library developed for the purpose of multiprecision matrix computation, on the basis of the GNU MP and MPFR libraries. It provides an easy-to-use syntax and convenient functions for matrix manipulations including those often…
Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing and reasoning tasks. However, their performance in the foundational domain of arithmetic remains unsatisfactory. When…
We consider the problem of Bayesian inference in the family of probabilistic models implicitly defined by stochastic generative models of data. In scientific fields ranging from population biology to cosmology, low-level mechanistic…
In this paper, we present Q# implementations for arbitrary single-variabled fixed-point arithmetic operations for a gate-based quantum computer based on lookup tables (LUTs). In general, this is an inefficent way of implementing a function…
We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…
The Core Cosmology Library (CCL) provides routines to compute basic cosmological observables to a high degree of accuracy, which have been verified with an extensive suite of validation tests. Predictions are provided for many cosmological…
In problems involving matrix computations, the concept of leverage has found a large number of applications. In particular, leverage scores, which relate the columns of a matrix to the subspaces spanned by its leading singular vectors, are…
Generic programming is an effective methodology for developing reusable software libraries. Many programming languages provide generics and have features for describing interfaces, but none completely support the idioms used in generic…
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…