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Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
In this paper a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function $f(t)$ is continuous with (known) compact support. An…
This paper develops methodology that provides a toolbox for routinely fitting complex models to realistic spatial point pattern data. We consider models that are based on log-Gaussian Cox processes and include local interaction in these by…
Discrete analogs of the classical Mehler-Fock transforms are introduced and investigated. It involves series with the associated Legendre function $P^\mu_{in-1/2}(x), x > 1,\ {\rm Re} \mu < 1/2, \ n \in \mathbb{N}, i $ is the imaginary…
Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lippmann-Schwinger style volume integral equation for…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
Laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting a potential behavior are considered. A spectral order, parallelizable method for their numerical inversion is…
Efficient inference in large language models (LLMs) has become a critical focus as their scale and complexity grow. Traditional autoregressive decoding, while effective, suffers from computational inefficiencies due to its sequential token…
In this paper, we study discrete Bessel functions which are solutions to the discretization of Bessel differential equations when the forward and the backward difference replace the time derivative. We focus on the discrete Bessel equations…
Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous…
We propose a simple and effective method to estimate the uncertainty of closed-source deep neural network image classification models. Given a base image, our method creates multiple transformed versions and uses them to query the top-1…
Our paper introduces a novel method for calculating the inverse $\mathcal{Z}$-transform of rational functions. Unlike some existing approaches that rely on partial fraction expansion and involve dividing by $z$, our method allows for the…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
This article presents a method for estimating the dynamic driving states (position, velocity, acceleration and heading) from noisy measurement data. The proposed approach is effective with both complete and partial observations, producing…
This paper addresses an optimization problem in satellite observation mission planning, focusing on the challenges of decentralized decision-making among satellites, which is crucial for optimizing strategies in dynamic observation…
Recently, it has been shown that approximations to marginal posterior distributions obtained using a low discrepancy sequence (LDS) can outperform standard grid-based methods with respect to both accuracy and computational efficiency. This…
By the end of the next decade, we hope to have detected strongly lensed gravitational waves by galaxies or clusters. Although there exist optimal methods for identifying lensed signal, it is shown that machine learning (ML) algorithms can…
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations. The main idea of the data-driven time-frequency analysis…
Accurately estimating the informativeness of individual samples in a dataset is an important objective in deep learning, as it can guide sample selection, which can improve model efficiency and accuracy by removing redundant or potentially…
The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known…