Related papers: Automated Local Fourier Analysis (aLFA)
The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higher-dimensional ellipsoids to…
Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string…
Automation underpins progress across scientific and industrial disciplines. Yet, automating tasks requiring interpretation of abstract visual information remain challenging. For example, crystal alignment strongly relies on humans with the…
Local feature extraction is a standard approach in computer vision for tackling important tasks such as image matching and retrieval. The core assumption of most methods is that images undergo affine transformations, disregarding more…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex…
We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation. Using local Fourier…
In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type…
In Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion Imaging (HARDI), a tensor field or a spherical function field (e.g., an orientation distribution function field), can be estimated from measured diffusion weighted…
We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…
Multifractal Detrended Fluctuation Analysis (MFDFA) is a powerful and widely used technique for characterizing the scaling properties and long-range correlations of complex time series. However, its application often involves significant…
Multifractal detrended fluctuation analysis (MFDFA) has become a central method to characterise the variability and uncertainty in empiric time series. Extracting the fluctuations on different temporal scales allows quantifying the strength…
Mixtures of factor analysers (MFA) models represent a popular tool for finding structure in data, particularly high-dimensional data. While in most applications the number of clusters, and especially the number of latent factors within…
In this paper, we present a novel affine-invariant feature based on SIFT, leveraging the regular appearance of man-made objects. The feature achieves full affine invariance without needing to simulate over affine parameter space. Low-rank…
Faraday complexity describes whether a spectropolarimetric observation has simple or complex magnetic structure. Quickly determining the Faraday complexity of a spectropolarimetric observation is important for processing large, polarised…
Most statistical tools used to characterize the complex structures of the interstellar medium can be related to the power spectrum, and therefore to the Fourier amplitudes of the observed fields. To tap into the vast amount of information…
We propose a novel framework, termed Fourier-Activated Adapter (FAA), for parameter-efficient fine-tuning of large pre-trained language models. By incorporating random Fourier features into lightweight adapter modules, FAA decomposes…
Machine learning interatomic potentials have revolutionized complex materials design by enabling rapid exploration of material configurational spaces via crystal structure prediction with ab initio accuracy. However, critical challenges…
Fault Tree Analysis (FTA) is a well-established method in failure analysis and is widely used in safety and reliability assessments. While FTA tools enable users to manage complex analyses effectively, they can sometimes obscure the…
Fourier phases contain a vast amount of information about structure in direct space, that most statistical tools never tap into. We address ALMA's ability to detect and recover this information, using the probability distribution function…