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In this paper, we prove a KAM theorem in a-posteriori format, using the parameterization method to look invariant tori in non-autonomous Hamiltonian systems with $n$ degrees of freedom that depend periodically or quasi-periodically (QP) on…
We present the mathematical theory and its numerical validation of a method tailored to include eddy-current effects only in a part of the domain. This results in a heterogeneous problem combining an eddy-current model in a subset of the…
The main purpose of this paper is to develop new algorithms for computing invariant rings in a general setting. This includes invariants of nonreductive groups but also of groups acting on algebras over certain rings. In particular, we…
In this paper, we investigate the Kirkwood-Dirac nonclassicality and uncertainty diagram based on discrete Fourier transform (DFT) in a $d$ dimensional system. The uncertainty diagram of complete incompatibility bases $\mathcal {A},\mathcal…
The importance of nonlocality of mean scalar transport in 2D Rayleigh-Taylor Instability (RTI) is investigated. The Macroscopic Forcing Method (MFM) is utilized to measure spatio-temporal moments of the eddy diffusivity kernel representing…
We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…
We perform a dispersive analysis of the $\omega\pi$ electromagnetic transition form factor, using as input the discontinuity provided by unitarity below the $\omega\pi$ threshold and including for the first time experimental data on the…
In this paper, a novel decomposition method for non-stationary and nonlinear signals is proposed. This method is inspired by the adaptive wavelet filter bank of the empirical wavelet transform (EWT) and Fourier intrinsic band functions…
Environmental biotechnologies, such as drinking water biofilters, rely on complex interactions between microbial communities and their surrounding physical-chemical environments. Predicting the performance of these systems is challenging…
The identification of new rare signals in data, the detection of a sudden change in a trend, and the selection of competing models, are among the most challenging problems in statistical practice. These challenges can be tackled using a…
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
The accurate determination of non-Hermitian (NH) topological invariants plays a central role in the study of NH topological phases. In this work, we propose a general framework for directly measuring NH topological invariants in…
Biaxial anisotropy, arising from distinct optical responses along three principal directions, underlies the complex structure of many crystalline, polymeric, and biological materials. However, existing techniques such as X-ray diffraction…
Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the boundary of a conductive medium (the data) are taken according to a prescribed protocol set and inverted to map the internal…
TabPFN is a transformer that achieves state-of-the-art performance on supervised tabular tasks by amortizing Bayesian prediction into a single forward pass. However, there is currently no method for uncertainty decomposition in TabPFN.…
This work proposes an innovative approach to improve Bragg coherent diffraction imaging (BCDI) microscopy applied to time evolving crystals and/or non-homogeneous crystalline strain fields, identified as two major limitations of BCDI…
Advances in computational power and hardware efficiency have enabled tackling increasingly complex, high-dimensional problems. While artificial intelligence (AI) achieves remarkable results, the interpretability of high-dimensional…
Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity. Recently, much effort has been dedicated towards…
This article develops how to generalize the invariant subspace method for deriving the analytical solutions of the multi-component (N+1)-dimensional coupled nonlinear time-fractional PDEs (NTFPDEs) in the sense of Caputo fractional-order…
Cardiovascular waveforms contain information for clinical diagnosis. By "learning" and organizing the subtle change of waveform morphology from large amounts of raw waveform data, unsupervised manifold learning helps delineate a…