Related papers: Melnikov-Arnold integrals and optimal normal forms
The widespread adoption of the \emph{maximum mean discrepancy} (MMD) in goodness-of-fit testing has spurred extensive research on its statistical performance. However, recent studies indicate that the inherent structure of MMD may constrain…
This paper proposes a movable-antenna-based index modulation (MA-IM) framework that exploits the spatial mobility of a single reconfigurable antenna to create additional information-bearing dimensions for next-generation wireless systems.…
We introduce techniques to treat numerically Mellin-Barnes integrals in physical regions, which arise in the need of the computation of Feynman integrals for the electroweak two-loop corrections to the pseudo observables at the Z-boson…
Many photonic devices, such as photonic crystal slabs, cross gratings, and periodic metasurfaces, are biperiodic structures with two independent periodic directions, and are sandwiched between two homogeneous media. Many applications of…
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov…
An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the…
Accurately determining the underlying physical parameters of individual elements in integrated photonics is increasingly difficult as device architectures become more complex. Inferring these parameters directly from spectral measurements…
We consider the problem of Arnold's diffusion for nearly integrable isochronous Hamiltonian systems. We prove a shadowing theorem which improves the known estimates for the diffusion time. We also justify for three time scales systems that…
We consider the numerical integration of the matrix Hill's equation. Parametric resonances can appear and this property is of great interest in many different physical applications. Usually, the Hill's equations originate from a Hamiltonian…
We compute the cyclicity of open period annuli of the following generalized Rayleigh-Li\'enard equation $$\ddot{x}+ax+bx^3-(\lambda_1+\lambda_2 x^2+\lambda_3\dot{x}^2+\lambda_4 x^4+\lambda_5\dot{x}^4+\lambda_6 x^6)\dot{x}=0$$ and the…
We develop a Melnikov framework for the Kuramoto Sivashinsky (KS) equation under weak deterministic and stochastic forcing. By treating KS as an infinite dimensional dynamical system, we derive a Melnikov functional that measures splitting…
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…
Machine learning potentials (MLPs) are becoming powerful tools for performing accurate atomistic simulations and crystal structure optimizations. An approach to developing MLPs employs a systematic set of polynomial invariants including…
This article presents a comparative study of three different types of estimators used for supervised linear unmixing of two MEx/OMEGA hyperspectral cubes. The algorithms take into account the constraints of the abundance fractions, in order…
We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for…
Model averaging (MA) and ensembling play a crucial role in statistical and machine learning practice. When multiple candidate models are considered, MA techniques can be used to weight and combine them, often resulting in improved…
In the field of machine learning, model performance is usually assessed by randomly splitting data into training and test sets. Different random splits, however, can yield markedly different performance estimates, so a genuinely good model…
In recent years, "U-shaped" neural networks featuring encoder and decoder structures have gained popularity in the field of medical image segmentation. Various variants of this model have been developed. Nevertheless, the evaluation of…
Many multi-planet systems have been discovered in recent years. Some of them are in mean-motion resonances (MMR). Planet formation theory was successful in explaining the formation of 2:1, 3:1 and other low resonances as a result of…