Related papers: EKO: Evolution Kernel Operators
Using repeated Laplace transform techniques, along with newly-developed accurate numerical inverse Laplace transform algorithms, we transform the coupled, integral-differential NLO singlet DGLAP equations first into coupled differential…
We present precision Monte Carlo calculations solving the QCD evolution equations up to the next-to-leading-order (NLO) level. They employ forward Markovian Monte Carlo (FMC) algorithms, which provide the rigorous solutions of the QCD…
The differential evolution algorithm is applied to solve the optimization problem to reconstruct the production function (inverse problem) for the spatial Solow mathematical model using additional measurements of the gross domestic product…
We formulate the momentum-space Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for structure functions measurable in deeply inelastic scattering. We construct a six-dimensional basis of structure functions that…
We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization,…
Neural Operators (NOs) have emerged as powerful tools for learning mappings between function spaces. Among them, the kernel integral operator has been widely used in universally approximating architectures. Following the original…
This paper presents Automatic Algorithm Discoverer (AAD), an evolutionary framework for synthesizing programs of high complexity. To guide evolution, prior evolutionary algorithms have depended on fitness (objective) functions, which are…
We present a novel approach to compute Generalized Parton Distributions within the Lightfront Wave Function overlap framework. We show how to systematically extend Generalized Parton Distributions computed within the DGLAP region to the…
In this paper we describe Ecole (Extensible Combinatorial Optimization Learning Environments), a library to facilitate integration of machine learning in combinatorial optimization solvers. It exposes sequential decision making that must be…
We present a lattice QCD calculation of the unpolarized isovector quark parton distribution function (PDF) of the proton utilizing a perturbative matching at next-to-next-to-leading-order (NNLO). The calculations are carried out using a…
In this paper, we consider the dynamics of solutions to complex-valued evolutionary partial differential equations (PDEs) and show existence of heteroclinic orbits from nontrivial equilibria to zero via computer-assisted proofs. We also…
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…
We illustrate the implementation of a method based on the use of recursion relations in (Bjorken) $x-$space for the solution of the evolution equations of QCD for all the leading twist distributions. The algorithm has the advantage of being…
Lambert's problem has been long studied in the context of space operations; its solution enables accurate orbit determination and spacecraft guidance. This work offers an analytical solution to Lambert's problem using the Koopman Operator…
We discuss our studies of polarized parton distributions which are related to the RHIC-Spin project. First, the parametrization of unpolarized parton distributions is explained as an introduction to general audience. Second, activities of…
Evolutionary optimization is a generic population-based metaheuristic that can be adapted to solve a wide variety of optimization problems and has proven very effective for combinatorial optimization problems. However, the potential of this…
We introduce CodeEvolve, an open-source framework that couples large language models with island-based evolutionary search for end-to-end algorithmic discovery. CodeEvolve integrates inspiration-based crossover, meta-prompting, and…
The rapid development of parallel and distributed computing paradigms has brought about great revolution in computing. Thanks to the intrinsic parallelism of evolutionary computation (EC), it is natural to implement EC on parallel and…
With the end of Moore's Law, optimizing code for performance has become paramount for meeting ever-increasing compute demands, particularly in hyperscale data centers where even small efficiency gains translate to significant resource and…
Semantic diversity in Genetic Programming has proved to be highly beneficial in evolutionary search. We have witnessed a surge in the number of scientific works in the area, starting first in discrete spaces and moving then to continuous…