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The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms. In many of these problems, convolution is performed…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
The calculation of perturbative corrections to the spectral moments observable in hadronic $\tau$ decays is reconsidered. The exact order-$\alpha_s^3$ results and the resummation procedure of Le~Diberder and Pich are compared with a partial…
The inconsistency between the fixed-order (FO) and contour-improved (CI) representation of the QCD corrections to the inclusive hadronic tau decay width limits the precision to which the strong coupling can be determined from this process.…
We present an extended range of stable flux reconstruction (FR) methods on triangles through the development and application of the summation-by-parts framework in two-dimensions. This extended range of stable schemes is then shown to…
Let f be a polynomial of degree n in ZZ[x_1,..,x_n], typically reducible but squarefree. From the hypersurface {f=0} one may construct a number of other subschemes {Y} by extracting prime components, taking intersections, taking unions, and…
We study the long-time behaviour of the growth-fragmentation equation, a nonlocal linear evolution equation describing a wide range of phenomena in structured population dynamics. We show the existence of a spectral gap under conditions…
Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier…
The determination of alpha_s from hadronic tau decays is impeded by the fact that two choices for the renormalisation group resummation, namely fixed-order (FOPT) and contour-improved perturbation theory (CIPT), yield systematically…
Motivated by the construction of tractable robust estimators via convex relaxations, we present conditions on the sample size which guarantee an augmented notion of Restricted Eigenvalue-type condition for Gaussian designs. Such a notion is…
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…
Hypergraphs are a generalized data structure of graphs to model higher-order correlations among entities, which have been successfully adopted into various research domains. Meanwhile, HyperGraph Neural Network (HGNN) is currently the…
Focused ion beam (FIB) tomography provides high resolution volumetric images on a micro scale. However, due to the physical acquisition process the resulting images are often corrupted by a so-called curtaining or waterfall effect. In this…
The gluon recombination functions in the twist-4 QCD evolution equations are studied at the leading logarithmic approximation using both the covariant and non-covariant methods. We justify that the infrared singularities in the twist-4…
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of…
Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely…
Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we…
In this paper, we study the phenomenon of Hopf or more specifically quantum double symmetry breaking. We devise a criterion for this type of symmetry breaking which is more general than the one existing in the literature, and therefore…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…